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Izumi Lab. 15

Απ’ τα ξημερώματα της Δευτέρας ήταν στην Αθήνα κι αφότου πέρασε τις ιατρικές εξετάσεις και υπέγραψε το νέο του συμβόλαιο, ήταν η ώρα να ανακοινωθεί η απόκτηση του Μπούι απ’ τον Παναθηναϊκό. Όπως κι έγινε, με τον Ολλανδό άσο να αποτελεί και τυπικά το νέο μεταγραφικό απόκτημα των πράσινων, που θα παίξει στην χώρα μας μέχρι το επόμενο καλοκαίρι ως δανεικός απ’ τη Γιουβέντους. Η ανακοίνωση της ΠΑΕ: «Η ΠΑΕ Παναθηναϊκός ανακοινώνει τη συμφωνία της με τον Ουασίμ Μπούι. Ο Ολλανδός μέσος θα αγωνιστεί στην ομάδα μας τη νέα σεζόν, όντας δανεικός από την Γιουβέντους». «Είμαι πολύ χαρούμενος που θα παίξω για ένα τόσο σημαντικό Σύλλογο όπως ο Παναθηναϊκός, έχω λοιπόν μεγάλο κίνητρο και θα δώσω τα πάντα για να βοηθήσω την ομάδα να πετύχει τους στόχους της στο τέλος της σεζόν αλλά και να βελτιωθώ κι εγώ ακόμα περισσότερο σε προσωπικό επίπεδο», ήταν τα πρώτα λόγια του Μπούι, μετά την υπογραφή του συμβολαίου του.

Tulsi Gabbard, 2020 presidential candidate, is closing in on the number of donations that she needs in order to qualify to participate in the Democratic debates. As of March 20, 2019, she has 40,456 donations, which leaves her needing just a little less than 25,000 more donations to participate in the DNC debates. In total, as of March 20, she needs 24,544 more donations in order to qualify for the debates. In a phone call with volunteers on March 18, Gabbard shared that they had 38,000 donors so far, Daniel Clark shared. Clark is a volunteer for Tulsi Gabbard and was also a delegate for Bernie Sanders in 2016. He ran for Congress in 2020. Just two days after Gabbard’s campaign shared the news, that number of donations that she had received had already increased by more than 2,000. The updated donation number has also been confirmed by Status Coup. Clark also noted in his video that Gabbard needs 65,000 unique donors, not donations, and she’s already met (or is close to meeting) the 20 state threshold that the DNC also requires. People interested in donating to Gabbard’s campaign can donate directly on her website here. Contribution amounts start at $5, but you can change the amount if you wish to donate more or less than the suggested amounts. The donations made at that link are through ActBlue and will be directed to Gabbard’s campaign. However, personal checks can also be mailed to Gabbard at: Tulsi Now, PO Box 75255, Kapolei, HI, 96707. Here’s a graphic being shared that shows just how many donations Gabbard’s campaign still needs. The DNC has changed the debate rules this year and is going to limit its presidential debates to 20 candidates, Politico reported. In order to qualify for the first debate, candidates must receive donations from 65,000 people in at least 20 states, FiveThirtyEight reported. This includes a minimum of 200 different donors in at least 20 states, NBC News clarified. Candidates can also qualify by polling with at least 1 percent in three “qualifying” polls. Previously the DNC relied solely on polling, but is changing the rules due to the large number of candidates this time around. If more than 20 candidates meet this requirement, then the DNC will give preference to candidates who meet both polling and fundraising requirements. Then the field will be further limited to those who are polling the highest, followed by those with the most unique donors, NBC noted. The first debate will be in June. As a result of these new rules, Gabbard has asked for donations as small as $1 in order for her to meet the debate requirements. The first debate in June will be hosted by NBC, MSNBC, and Telemundo. The second debate in July will be hosted by CNN. The debates may feature back-to-back nights with candidates separated into two groups, but only a total of 20 will be able to participate, The Hill noted. You can stay updated on Tulsi Gabbard news written by this article’s author by joining the email list here and choosing the Bernie Sanders and Tulsi category.

Q: Where is the Registry running I can create a container running a registry: docker run -d -p 5000:5000 --restart=always --name registry registry:2 But docker has a default registry, I can see that the registry is at Registry: https://index.docker.io/v1/ and it must be local, but where is it - do you know? It is correct that if using a browser and go to: https://index.docker.io/v1/ it will take you to docker hub: https://index.docker.io/v1/ But all my local images is local on my machine, so there must be some where the registry is running. You can see the registry if you do: docker system info Containers: 32 Running: 29 Paused: 0 Stopped: 3 Images: 205 Server Version: 18.06.0-ce Storage Driver: overlay2 Backing Filesystem: extfs Supports d_type: true Native Overlay Diff: true Logging Driver: json-file Cgroup Driver: cgroupfs Plugins: Volume: local Network: bridge host ipvlan macvlan null overlay Log: awslogs fluentd gcplogs gelf journald json-file logentries splunk syslog Swarm: inactive Runtimes: runc Default Runtime: runc Init Binary: docker-init containerd version: d64c661f1d51c48782c9cec8fda7604785f93587 runc version: 69663f0bd4b60df09991c08812a60108003fa340 init version: fec3683 Security Options: seccomp Profile: default Kernel Version: 4.9.93-linuxkit-aufs Operating System: Docker for Mac OSType: linux Architecture: x86_64 CPUs: 2 Total Memory: 2.934GiB Name: linuxkit-025000000001 ID: Q6IO:V5CP:OHJL:4KJP:ZG2X:GV5W:YHMM:2WCK:4V4O:O6T3:A4E4:BJHM Docker Root Dir: /var/lib/docker Debug Mode (client): false Debug Mode (server): true File Descriptors: 206 Goroutines: 223 System Time: 2018-08-29T11:56:34.8224409Z EventsListeners: 2 HTTP Proxy: gateway.docker.internal:3128 HTTPS Proxy: gateway.docker.internal:3129 Registry: https://index.docker.io/v1/ Labels: Experimental: true Insecure Registries: 127.0.0.0/8 Live Restore Enabled: false A: That is the default registry which is dockerhub: https://hub.docker.com/ Also see: https://github.com/moby/moby/issues/7203 You cannot change the default registry (which is dockerhub). What you can do is push and pull using your registry as a prefix. For example: docker push localhost:5000/yourimage docker pull localhost:5000/yourimage As per my comment below - this registry runs locally and with docker ps | grep registry:2 you can see it running. You can then use it's id to get the logs where you will see the activity. You can also make use of the api by doing a call to: curl -X GET http://localhost:5000/v2/_catalog This will list all the images you have pushed to your local registry.

Milestones to recovery: preliminary validation of a framework to promote recovery and map progress through the medium secure inpatient pathway. Forensic mental health care in the UK has undergone a rapid expansion since the late 1990s. In medium secure units (MSUs), there is growing emphasis on developing care pathways without much theoretical underpinning. We developed a concept of 'Milestones to Recovery' (MTR) to measure progress through the MSU pathway. Our aim was to validate the MTR framework. Our hypotheses were that patients scoring higher on the MTR Scale would be more likely to be aggressive to others in the following 6 months and resident in the acute areas of the unit and that those scoring lower would be more likely to be discharged within 6 months of the assessment. An MTR scale was developed to enable the investigation of the validity of the MTR framework and evaluated with staff evaluations of 80 resident patients using a prospective, longitudinal and naturalistic design. The results suggest that the MTR framework is valid in discriminating between different stages on the MSU pathway. Therapeutic engagement was particularly important in terms of progress through the MSU, whereas current behaviour was important in predicting future aggression. Further research is required to test the MTR framework across different levels of security, with larger samples and within different populations. Provides a framework to map progress through the service. Identifies key factors that influence recovery and rehabilitation. Potential to promote dialogue between patients and staff, and enhance motivation.

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Q: Bootstrap tree-view: Tree doesn't show up I'm new to tree-view, I'm trying to show a basic tree but it doesn't work and I don't know where I made the mistake. I made test.html that follow the same structure of my basic.html (I'm sparing you code of the navbar, alerts, etc). I have other js functions in functions.js that work fine. test.html: {% csrf_token %} {% load groupfilter %} {% load staticfiles %} <!DOCTYPE html> <html lang="en"> <head> <meta name="viewport" content="width=device-width, initial-scale=1" charset="utf-8"> <link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/css/bootstrap.min.css" integrity="sha384-ggOyR0iXCbMQv3Xipma34MD+dH/1fQ784/j6cY/iJTQUOhcWr7x9JvoRxT2MZw1T" crossorigin="anonymous"> <link rel="stylesheet" href="{% static 'bootstrap-treeview.min.css' %}"> <script src="{% static 'bootstrap-treeview.min.js' %}"></script> <script src="https://code.jquery.com/jquery-3.3.1.slim.min.js" integrity="sha384-q8i/X+965DzO0rT7abK41JStQIAqVgRVzpbzo5smXKp4YfRvH+8abtTE1Pi6jizo" crossorigin="anonymous"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.14.7/umd/popper.min.js" integrity="sha384-UO2eT0CpHqdSJQ6hJty5KVphtPhzWj9WO1clHTMGa3JDZwrnQq4sF86dIHNDz0W1" crossorigin="anonymous"></script> <script src="https://stackpath.bootstrapcdn.com/bootstrap/4.3.1/js/bootstrap.min.js" integrity="sha384-JjSmVgyd0p3pXB1rRibZUAYoIIy6OrQ6VrjIEaFf/nJGzIxFDsf4x0xIM+B07jRM" crossorigin="anonymous"></script> <title>Test</title> </head> <body> <div class="container"> <div id="tree"></div> </div> <!-- JavaScript functions --> <script src="{% static 'functions.js' %}"></script> </body> </html> extract of functions.js: $(function(){ var mytree = [ { text: "Parent 1", nodes: [ { text: "Child 1", nodes: [ { text: "Grandchild 1" }, { text: "Grandchild 2" } ] }, { text: "Child 2" } ] }, { text: "Parent 2" } ]; $('#tree').treeview({data: mytree}); }); A: Can you share sample link that you are following? It seems like you are importing Twitter Bootstrap 4.3.1 But as I know, Offical Bootstrap still not provide TreeView on their document.

In the Community Nearby Schools 3208 Perdot Avenue, Rosamond, CA 93560 (MLS# SR16727560) is a Single Family property with 4 bedrooms, 2 full bathrooms and 1 partial bathroom. 3208 Perdot Avenue is currently listed for $294,990 and was received on October 17, 2016. Want to learn more about 3208 Perdot Avenue? Do you have questions about finding other Single Family real estate for sale in Rosamond? You can browse all Rosamond real estate or contact a Coldwell Banker agent to request more information.

Exclusive Collection Of Rear View Cameras From TVC-Mall.com A car rear view camera is a special type of video camera that is produced specifically for the purpose of being attached to the rear of a vehicle to aid in backing up, and to alleviate the rear blind spot. TVC-Mall.com’s rear view cameras are well-known for the powerful functions and premium quality materials. Recently, TVC-Mall.com has released its new models, and launched a rear view cameras promotion. Anyone who want to buy wholesale rear view cameras can visit TVC-Mall.com for more details. TVC-Mall.com is a leader in cell phone accessories and other electronic accessories. Its rear view cameras are well-known for the powerful functions and premium quality materials. The new collection consists of many different designs. From IR night vision rear view cameras, to 2.4G wireless car rear view camera systems, TVC-Mall.com has everything to ensure customer satisfaction. “We are excited to launch this promotion, and we encourage wholesalers and retailers to keep coming back to our store to see what new products are available. Those who want to buy wireless car rear view camera systems should visit our online store as soon as possible, because the promotion is for a limited time only,” says a sales manager of the company. “We have the global reach, expertise and infrastructure necessary to guarantee our customers that their data is secure.” In addition, TVC-Mall.com’s online store features attractive low prices on its a hundred thousand of different styles ofelectronics and related accessories. Superior customer service, high-quality, speedy delivery, and affordable prices, are the reasons to choose TVC-Mall.com About The TVC Mall (TVC-Mall.com) Launched in 2008, TVC Mall has a sensitive marketing sense and it has established strong relationships with many original manufacturers of Apple products (iPhone, iPad, iWatch, etc.). Some Apple accessories used to have been sold at TVC-Mall.com before their official launch. The business used to be widely reported by some top media (like BusinessInsider.com, AppleInsider.com, CNET.com, etc.). Please visit http://www.tvc-mall.com or subscribe its newsletter for the best deals, special prices, rebate savings, exclusive bundles and more.

Q: XML Schema for analysis in C# Is it possible to use a XML Schema to check against the contents of a XML file? For instance, in ASP.NET web.config, can I create a schema to check that <customErrors mode = "On">? This will ultimately be used in a C# app, the C# app should take in the XML document and the XML Schema and check if the XML Document violates any of the "rules" listed in the XML schema, i.e. <customErrors mode = "Off"> Is it possible to do the checking without any boundary to the structure of the XML file? i.e. the attribute <customErrors> can be within any part of the XML document and the schema will still work. A: Possible: Yes, in XML Schema 1.1 using assertions. Practical or recommended: No. XML Schema is intended to be used to validate the "structure of the XML file," as you anticipate in your question. You can skip much of that via xsd:any and then use assertions to express the sort of spot-checks that you describe via XPath expressions. However, it'd be more natural to just apply XPath expressions directly to your XML from within C#, or using Schematron, which is a standard for applying XPath expressions to do validation.

View Transcript Transcript Wally The Economist. Dilbert: I wonder if you'll win the Nobel Prize for Economics. Man: There is no "Nobel Prize for Economics," you idiot! You mean The Sveriges Riksbank Prize In Memory of Alfred Nobel. Dilbert; Do we know you? Man: I'm Dick, from the Internet. Everyone knows me.

Eochrysis, a new replacement name for the fossil Protochrysis Bischoff, 1916 (Insecta: Hymenoptera: Chrysididae) nec Pascher, 1911 (Protista: Cryptomonada). The genus Protochrysis (type species P. succinalis Bischoff, 1916, by monotypy) was established by Bischoff (1916: 139) for distinctive fossil insect remains of Eocene (Lutetian) age from the former Königsberg outskirts of East Prussia (now Kalinigrad, Russian Federation), referred at present to the Chrysididae (Hymenoptera) (Brues 1933; Carpenter 1985, 1992). However, an identical generic name Protochrysis had previously been proposed by Pascher (1911: 191) for a living protist (Cryptomonada). Bischoff's (1916) name is therefore an invalid junior homonym. Carpenter (1985: 577) proposed a new replacement name for the fossil genus, but overlooked the fact that his newly proposed generic name Protochrysidis was also preoccupied, again by the name of another protist genus, Protochrysidis [Protista: Chrysomonada] described by Skvortzov (1969: 346) from Harbin (China). In fact, the protistan genus Protochrysidis had initially been published as chrysophyte algae following the International Code of Nomenclature for Algae, Fungi, and Plants (McNeill et al. 2012) by Skvortzov (1961: 4) who had failed to designate holotype of the species, but later fulfilled all conditions for valid publication in 1969 by providing necessary typification and reference to formerly published description and illustrations. At present chrysophyte algae are still maintained as Chrysomonada in protozoology due to a continued somewhat archaic tradition (Preisig & Anderson 2002). Protochrysidis Skvortzov, 1969 remained little studied since the time of its first description and is currently treated as an incertae sedis protistan taxon.

# frozen_string_literal: true require File.expand_path('lib/jekyll-last-modified-at/version.rb', __dir__) Gem::Specification.new do |s| s.name = 'jekyll-last-modified-at' s.version = Jekyll::LastModifiedAt::VERSION s.summary = 'A liquid tag for Jekyll to indicate the last time a file was modified.' s.authors = 'Garen J. Torikian' s.homepage = 'https://github.com/gjtorikian/jekyll-last-modified-at' s.license = 'MIT' s.files = Dir['lib/**/*.rb'] s.add_dependency 'jekyll', '>= 3.7', ' < 5.0' s.add_dependency 'posix-spawn', '~> 0.3.9' s.add_development_dependency 'rake' s.add_development_dependency 'rspec', '~> 3.4' s.add_development_dependency 'rubocop' s.add_development_dependency 'rubocop-performance' s.add_development_dependency 'rubocop-standard' s.add_development_dependency 'spork' end

Florida National Cemetery Florida National Cemetery is a United States National Cemetery located near the city of Bushnell in Sumter County, Florida. Administered by the United States Department of Veterans Affairs it encompasses and began interments in 1988. It is now one of the busiest cemeteries in the United States. History Florida National Cemetery is located in the Withlacoochee State Forest, approximately north of Tampa. The forest was acquired by the federal government from private landowners between 1936 and 1939 under the provisions of the U.S. Land Resettlement Administration. The United States Forest Service managed the property until a lease-purchase agreement transferred it to the Florida Board of Forestry in 1958. Currently, Withlacoochee State Forest is the second-largest state forest in Florida, divided into eight distinct tracts of land. In 1842, Congress encouraged settlement here by establishing the Armed Occupation Act. The law granted a patent for to any man who kept a gun and ammunition, built a house, cultivated of the land and remained there for at least five years. Settlers moved in to take advantage of the generous offer. The area contained abundant timber and suitable farmland, appealing attributes to frontiersmen. In 1845 Florida was granted statehood. During the Civil War, a sugar mill on the Homosassa River supplied sugar to the Confederacy. A robust citrus-growing industry developed in the eastern part of the area and became a focus of intense economic expansion soon after the war. In 1980, the Department of Veterans Affairs (VA) announced that it would establish a new national cemetery in Florida, its fourth. Two major locations for the cemetery were studied: property near the Cross Florida Barge Canal and the Withlacoochee State Forest. The Withlacoochee site, though more environmentally sensitive, was supported by government officials. In February 1983, the state transferred land to the VA for the development of a Florida National Cemetery. The first burial was in 1988 and a columbarium was opened in November 2001. In 1999, federal officials asked the Florida Cabinet to grant land for the expansion of the Florida National Cemetery, providing 65,000 to 100,000 grave sites for veterans in the state. Environmentalists argued that Florida Department of Agriculture and Consumer Services Forestry Division officials did not state whether the 179 acres of land within the Withlacoochee State Forest was surplus in accordance to a Florida constitutional amendment concerning the acquisition of land for conservation. Before the Florida Cabinet meeting on October 26, the Department Veterans Affairs and the Florida Cabinet agreed that 42 acres would be removed as they served as the habitat for several endangered species. Florida governor Jeb Bush and the Florida Cabinet voted 7-0 in favor of selling 137 acres of land to the Department of Veterans Affairs for the cemetery's expansion. Notable interments Medal of Honor recipients Master Chief Hospital Corpsman William R. Charette, U.S. Navy, for action with the Marine Corps in the Korean War. Master Sergeant James R. Hendrix, U.S. Army, for action with the 4th Armored Division at the Battle of the Bulge in World War II. Sergeant Major Franklin D. Miller, U.S. Army Special Forces, for action in the Vietnam War. Others Frank Baker, professional baseball player Philip J. Corso, U.S. Army lieutenant colonel Raymond Fernandez, aka "Hercules Hernandez", professional wrestler. Scott Helvenston, film trainer-stuntman and former Navy SEAL. Lieutenant Commander Mike Holovak, A U.S. Navy, skipper of PT boat in the South Pacific credited with sinking nine Japanese ships in World War II. Hal Jeffcoat, Major League Baseball pitcher and outfielder Major David Moniac, veteran of the Second Seminole War, first Native American graduate of United States Military Academy. Blackjack Mulligan, professional wrestler, author and football player Ernie Oravetz, Major League Baseball outfielder Colonel Leonard T. Schroeder Jr., the first soldier ashore in the Normandy Landings on D-Day, June 6, 1944, during World War II. Frank Stanley, cinematographer for Clint Eastwood films such as Breezy (1973), Magnum Force (1973), Thunderbolt and Lightfoot (1974) and The Eiger Sanction (1975) Champ Summers, Major League Baseball outfielder Notable monuments A carillon was constructed by the World War II AMVETS organization in an open area adjacent to the first administration building. It was dedicated on October 9, 1993. The cemetery contains a Memorial Pathway that in 2003 featured 47 plaques, statues, monuments, etc., honoring America's soldiers from 20th-century conflicts. References External links National Cemetery Administration Florida National Cemetery Category:Cemeteries in Florida Category:Protected areas of Sumter County, Florida Category:United States national cemeteries Category:1988 establishments in Florida

Debbie Gregory DNP, RN Dr. Debbie Gregory is a national leader in healthcare design, innovation, and transformation. As a nurse executive and interior designer, Dr. Gregory is passionate about “Intentional Design” that aligns People, Place, and Process. She creates and transforms environments into functional ecosystems using complex systems science and strategic thinking. Dr. Gregory has Doctorate of Nursing Practice in Health Innovation and Leadership from the University of Minnesota and a bachelors in nursing from Vanderbilt University. Currently, she serves as Senior Clinical Consultant for the Technology Planning Group at Smith, Seckman, Reid, Inc., a national engineering firm. In today’s healthcare environment, clinical transformation and innovation are essential in navigating and reengineering the care delivery model of the future. She serves as a liaison and visionary between the clinical community, the design and construction community, and the IT/engineering community to interpret and enhance the clinical operations and functionality of the healthcare environment. She develops strategies for operational and financial improvements designed to advance clinical excellence, improve quality of care, patient experience, and overall patient outcomes. She is a frequent presenter at national conferences and has authored many articles in national publications. Dr. Gregory provides educational summits that bring healthcare leaders, technology experts, and visionaries together to discuss the future of the healthcare delivery model and the integration of technology. She is the co-founder and past president of the Nursing Institute for Healthcare Design (NIHD) and current President of the Nursing Institute for Healthcare Design Foundation. NIHD is an international not for profit organization created from a need, an idea, and a passion to engage and include clinicians at the design table to improve the healthcare environment.

Teen angel Keisha Grey cant hide her large natural mangos under her tiny t-shirt counting up as Johnny Sins cant hide his large cock in his pants. That babe gets apropos on her knees to take his pistol in her hawt mouth

Medical Designers Save Time, Parts With Software HIGH STRESS: The sensor in Tensys’ new blood-pressure monitor floats within a rigid frame attached to a serpentine arm designed to flex. Engineers used SolidWorks and COSMOSWORKS to design the arm and see how it would perform under real-world flexing, saving prototypes. “Faster, cheaper, better” is a phrase that may have its genesis in the aerospace industry, but it has launched breakthrough designs in other industries as well. Case in point: the medical industry, where device manufacturers have used CAD and FEA to give flight to new design ideas while slashing product-development time. Two recent examples, one in the U.S. and one in the U.K., show the improvements and time/cost savings engineers have realized from their use of engineering software. In Camberly, U.K., the design team at reseller Williams Medical Supplies set up a new technical development department to design medical products and settled on Solid Edge (UGS) as its core design tool. “Our aim is to take a routine surgical instrument and bring something new to the design that will provide significant benefit,” says Robert Steele, technical development director. Among their projects: the Opmaster Series 4 surgery operating table. The enhanced design allows a patient to be examined, operated on, and recover on the same table. Using Solid Edge, the team modeled parts and ran collision and interference analyses and motion simulation. “We were able to sit with sales and marketing during the initial design stage and get feedback,” says Steele. “Engineers don’t always get it right, but with the software we could rehearse the design and minimize the risk of getting it wrong.” The result was a major time savings, largely the result of not doing many prototypes. “In fact, we were almost able to dispense with the prototyping phase and go straight to manufacturing,” Steele asserts. Working with different software and on a vastly different product line, engineers at San Diego-based Tensys Medical, Inc. had similar results. Using SolidWorks for CAD and COSMOSWorks for FEA (both from Dassault Systemes, Inc.) the engineering team developed the T-Line[R] Tensymeter, a non-invasive arterial blood-pressure management system for use in surgery. Their goal was to replace the traditional cuff-based monitors that provide only intermittent measurements every few minutes. That kind of irregular monitoring can delay recognition of rapid changes in blood pressure. The design concept uses an actuator to move a sensor over the patient’s wrist to find the best position for producing a continuous waveform. “The sensor has to float within a rigid frame attached to a serpentine arm that’s designed to flex. The team used COSMOSWORKS to identify areas of high stress for the olefin-based serpentine arm and used the analysis results to make design modifications. Among those modifications, says Senior Engineer Russ Hempstead: “We removed the stress risers, added radii, and added thickening sections.” He and the engineering team didn’t expect to see the stress risers, but when they did they put static flexing on part of the serpentine arm so they could move it the way it would move in the real world. The software enabled the team to shorten the design cycle by 60 percent. They cut manufacturing time by four percent, material costs by three percent, and labor costs by three-four percent. In all, engineers did seven or eight analysis studies in just a couple of days. Hempstead says the team cut the number of parts by putting as much functionality in a part as possible. It’s a strategy he recommends to others. “It may complicate tooling, but it still eases manufacturing,” he says. “We got rid of four components.” Industrial workplaces are governed by OSHA rules, but this isn’t to say that rules are always followed. While injuries happen on production floors for a variety of reasons, of the top 10 OSHA rules that are most often ignored in industrial settings, two directly involve machine design: lockout/tagout procedures (LO/TO) and machine guarding. Focus on Fundamentals consists of 45-minute on-line classes that cover a host of technologies. You learn without leaving the comfort of your desk. All classes are taught by subject-matter experts and all are archived. So if you can't attend live, attend at your convenience.

I listened to this one, narrated by Justine Eyre. It was about 12 hours long, but it passed by quickly with this fun read. It's not particularly deep or magical and it doesn't call life as we know it into question. It's a nice read/listen, light and intriguing for anyone in the mood for a little escape from the disappointments that have been abounding. Funny enough, the only problems with the book are also reasons why I liked it. Lily Kaiser's journey is a little too convenient throughout the book but that can be just perfect sometimes. It can be exactly what I need to read or listen in order to balance out the pressure of the world. So, yes, the book is a little too neat. The story a little too beautiful and coincidental and works a little too well, but I didn't mind it at all. Mostly because it was also written incredibly well. It moves between times, giving insight into Rose Gallway's life that Lily doesn't readily have and let's the reader piece some of it together on our own. I do enjoy that. And then the author lays it all out and it's just perfect. A little too perfect, like in one of those rom-coms that we watch to feel good but that we all know aren't the way the world works. I really loved that about it. It's going to be one of my comfort books, to peruse when I'm down, maybe listen to when I wanna revel in new beginnings, like the mood I re-watch Stardust in. If you've read a few too many mysteries lately, or too many books that ripped your heart out (like I have recently), than this is the perfect book to recover with. It's comforting and sweet and romantic and doesn't take itself too seriously. But it's not the book for that serious deep read. Don't expect it to be.

My new global trends book is out now: The Future of Almost Everything. But it takes at least 20 years to evaluate how good a trends analyst was / is – so what about forecasts made by me in previous books, about what to expect over the following decade or two or three? How did those forecasts measure up? I had to answer that question for myself by re-reading what I wrote in the past about the future, before writing my latest book. Read FREE SAMPLE of The Truth about Almost Everything. So you can judge for yourself, here are loads of predictions I made in the past - and the book in which they were made plus date. Every one of these is already a reality or looks like it soon could be, as of August 2015....And yes I got some things wrong - not many fortunately. I am going to publish the entire text of Futurewise 1998 edition on this website for a complete picture - but of course on this site already are hundreds of posts and videos going back in some cases over 20 years. Here's one I got wrong: I thought video streaming would take off - but with more use of live video using smartphones that we have actually seen. Most personal video streaming is of course things like YouTube clips. Most forecasting errors in my experience are not over WHAT is going to happen as the trend is usually fairly obvious, but by WHEN with questions about real impact. So here goes: how did I see the future of banking, global economy, mobile, smartphones, Internet of Things, Big Data and so on...? Banking Banking as it is in 1998 will never survive and will fall in profitability. 1998 - Futurewise Internet of Things and Smart Homes All new homes in developed nations will be intelligent by 2010, Smart homes will boast 15-20% energy savings. 1998 - Futurewise Every device with a power socket will be online. Washing machine will call engineer. Garage doors will open automatically, alarm will be turned off, lights will go on, coffee machine will begin to pour a coffee and so on. 1998 - Futurewise Power generation in many homes from solar cells and wind in rural areas 1998 – Futurewise Retail and e-commerce Basic shopping will be done online and the rest will become a recreational activity – so shopping centres will have to learn from theme parks to reinvent themselves as a leisure experience. 1998 - Futurewise Loss of millions of small retailers by 2005 as huge chains expand market share, These global chains will increase own brand sales from 15% to 30% by 2010. However many corner shops will survive because of convenience, parking restrictions and so on. We will see a big reversal of the trend to build more out of town superstores, with rapid growth of smaller outlets of the same chains. 1998 - Futurewise Millions of people will buy and sell from each other directly at cut throat prices for new and second-hand goods, by posting information online, with instant matching of buyers and sellers, creating virtual “street markets”. 1998 – Futurewise Europe and global economy Major economic disruptions will occur affecting many nations from a series of very low probability but very high impact events, with combined impact. 1998 - Futurewise Expect increasingly complicated financial instruments to be developed, which will add to risks of economic instability. 1998 – Futurewise The next global economic shock is likely to be triggered by events relating to complex financial products (derivatives) and hedge funds, overwhelming markets and governments - 2003 Futurewise Speed of change will be a fundamental and rapidly growing global risk, with sudden collapse of economies in different nations, related to loss of market confidence. 1998 – Futurewise Massive future economic tensions in Eurozone in next two decades, which may threaten the Euro project. 1998 – Futurewise Expect more rioting on the streets as workers untie to vent their anger and frustration at leaders, global institutions and wealthy ethnic minorities. 1998 – Futurewise Interest rate targeting set at 2% will turn out to be too low because no room to manage the deflationary economic shocks that we are going to see, without risk of tipping over into deflation. Expect central banks to begin relaxing such low targets – 2003 Futurewise 2nd edition Expect a growing backlash against globalization, blamed by workers in many nations for lack of jobs and economic decline. 1998 – Futurewise Expect growing anger and resentment against market speculators, blamed for price instabilities of commodities and currencies, and for destabilizing entire nations by over-trading complex financial products, which very few people fully understand. 1998 – Futurewise More governments will take refuge in larger trading blocs, with more grouped, linked of fused economies by 2020, particularly in Asia, but it will not be entirely effective as speculators also grow rapidly in global power. ASEAN will become stronger as part of this process. 1998 – Futurewise Outsourcing of manufacturing and service jobs to China and India will go into reverse, as inflation in Asia wipes out the economic argument for doing so, and as companies look to become more agile and reduce risk. 2003 - Futurewise Many people will be surprised at how rapidly China overtakes the US as the world’s largest economy. Futurewise 1998 Health AIDS will become a global pandemic which will require massive community mobilization over more than 20 years. Prevention programmes will prove effective, but a vaccine will be almost impossible to make, and certainly will not be developed before 2003. 1987 – Truth about AIDS Life expectancy will go on increasing rapidly with official forecasts revised every 12 months, over the next two decades and beyond, each of which will create added pressures on pension fund solvency. 1998 - Futurewise Viruses will be used to treat or prevent diseases such as cancer or cystic fibrosis. Viruses will be used to infect cancer cells and teach them to manufacture chemotherapy agents to poison cancer cells directly – 1993 Genetic Revolution We will repair damaged tissue using a person’s own cells, grown in the laboratory. – 1993 Genetic Revolution GM foods – new crops and improved animals - will be important and widely grown. – 1993 Genetic Revolution Genetically engineered animal and human cells will be used to manufacture next-generation pharma products including new types of vaccines. – 1993 Genetic Revolution Huge numbers of human genes will be linked to patterns of disease, enabling very accurate predictions to be made about future medical problems in an individual. – 1993 Genetic Revolution Monoclonal antibodies will become a very important treatment in future for cancer and other conditions. – 1993 Genetic Revolution Technology to create human cloned embryos in the laboratory for research purposes will become routine. 1993 – Genetic Revolution We will see many new virus threats emerge around the world by 2020, of which several will trigger global containment efforts. 1998 – Futurewise= Pensions crisis Pensions crisis will hit Germany and Italy, while France will be shaken by riots and demonstrations on the streets when governments try to increase retirement age. 1998 – Futurewise In 20 years time, many older people will carry on working to 75, or 85, or until they drop, with virtually no pension. 1998 – Futurewise Calls to legalise euthanasis will grow far stronger, with many high profile cases where doctors or family have taken the law into their own hands. 1998 – Futurewise Personal pension plans and investment funds will be growth markets for those approaching retirement, with increasing questions about charges and performance of actively managed funds. 1998 – Futurewise Future of Europe Eurozone will not be sustainable without huge pain. Economic conditions that enable some countries to swim will cause other economies to drown. 1998 - Futurewise Tribalism will be the downfall of Europe and will feed terrorism. 1998 - Futurewise Many former Eastern Bloc nations will not stabilize economically until beyond 2008, and even then there will still be a huge gap compared to Western Europe. 1998 - Futurewise It will take until beyond 2018 for new democratic traditions to take root in former Soviet bloc nations. Economic crisis in these nations may lead to riots, civil disobedience, internal military action or worse. Expect the EU to try to reduce these risks by early inclusion into an enlarged community. 1998 - Futurewise Enlarging the EU from15 to 25 nations will change it forever, adding to paralysis in decision-making. 1998 - Futurewise People tribes will sometimes be very hostile to the emerging mega-state. 1998 - Futurewise One of the final destructions of the United States of Europe will be high unemployment caused by rapidly changing economic conditions and labour force immobility. 1998 - Futurewise However Europe will benefit in the short term from instability elsewhere. 1998 – Futurewise Future of the UK UK will continue to disintegrate in the final death pangs of the English imperialistic dream. Scots will look to Europe as a way of staying together in a broader alliance, rather than close rule from London. 1998 - Futurewise The English will become increasingly resentful of rulings imposed by the EU. 1998 - Futurewise As Scotland asserts its own right to govern itself, the English will become more strident about being English. 1998 - Futurewise UK home ownership will prove a good long term investment, despite market collapse and many pundits claiming the end of the sector as a sound investment. Web posts 2007-2008 on globalchange.com and YouTube. London will remain very popular and powerful London will continue to be one of the most popular cities in the world for the next 30 years, and will continue to be dominated by financial service despite aggressive global competition. 1998 - Futurewise The City will keep top position or near top in cross-border lending, and will fight to remain the largest global centre for Forex. 1998 - Futurewise Cities will be popular places to live Hundreds of millions will migrate to large cities: city life will be increasingly popular, despite forecasts by some that cities will decay and die as wealthy people move out to escape crime, congestion, pollution and chaos. 1998 - Futurewise Politics, tribalism, new patterns of war and rapid rise of new terrorist groups Political whirlwinds will affect whole continents. 1998 – Futurewise Rise of new, sinister radical people movements, which are totally convinced of their moral cause and use tribalism, social networking and terrorism – these groups will seize great powers. 1998 – Futurewise Terrorist groups will multiply rapidly in the third millennium, taking advantage of new technologies to frighten, sabotage and attack for the sake of a cause. 1998 – Futurewise Security forces will use ever more sophisticated tools for surveillance, violating privacy of hundreds of millions. 1998 – Futurewise Traditional left-right political divides will be swept away in many nations by polarized debates over things like sustainability, or the application of Islamic laws, or whether a nation should be in or out of the Eurozone. 1998 - Futurewise Ever present video cameras will make large-scale traditional wars harder to fight, because horrors will be seen very clearly. 1998 – Futurewise World military spending will fall and then rise – with investment in drones, cruise missiles etc but experience show that wars are won by house to house fighting not by remote control smart weapons. 1998 – Futurewise Sustainability and single issues Left-right politics will give way to single issue politics eg should we be in or out of the Eurozone, or become independent from the UK, or spend more on carbon taxes. 1998 - Futurewise The environment will be the number 1 dominant single issue for decades to come. 1998 - Futurewise Marriage and children Marriage will become less fashionable but the dominant household pattern for middle aged people will still be having children and bringing them up together. 1998 - Futurewise A new generation of teenagers will emerge in the early Third Millennium, the M Generation: more conservative than in the past – less sex, less drunkenness, less drugs, more study, more concerned about issues like environment. They will still follow traditional romantic dreams… of one day finding a wonderful partner for a very long term relationship. 1998 - Futurewise Drugs and smoking We will see widespread drug testing – at work and in prisons, greater investment in drug rehab. 1998 - Futurewise We will see progressive criminalisation of smoking with ever stricter regulations on tobacco, and a bitter fight in some nations over decriminalization of cannabis. 1998 - Futurewise We will see hundreds of new designer drugs that fall outside government legal powers, of which some will enhance memory and intelligence, becoming widely abused by students. 1998 - Futurewise Feminisation Feminisation of workplace and wider society with men in retreat, labeled as testosterone addicts, dangerous, ill-behaved variants of human species prone to violence and sexual predatory acts. 1998 – Futurewise

Sandusky Sent Down River After a Commonwealth of Pennsylvania Corrections Department review, convicted child molester and former Penn State assistant coach Jerry Sandusky has been sent to the Greene State Prison, where he will serve out his sentence (and probably, his life) in protective custody. He’s still pursuing appeals, which no one expects to go anywhere. Greene is a maximum security prison, classified as a “Supermax“, which contains a Death Row. Lifers there include Philadelphia serial killer Juan Covington, and three convicts await execution. This is one tough place. “We make individual decisions based on facts,” Corrections Secretary John Wetzel said in a written statement. “Given the high-profile nature of this individual, coupled with the nature of his crimes, this makes him very vulnerable in a prison setting.” Noooo kidding, John! (We all know from watching TV crime dramas what happens to guys like Jer in da Big House.) Just how effective will the security measures be? Better be Biohazard Level 5 containment for Ol’ Jer. He will not have a cellmate and will be subjected to heightened supervision and an escort when not in his cell. He will get an hour of individual exercise five days a week and three showers a week — alone, save for the escort. He will eat meals in his cell. All other services, including religion, medications, and treatment programming will be conducted in his cell. All visits will be non-contact. No touching of or by the Tickle Monster. Sandusky’s legal representations did not return phone calls. This is close to home for “Jer”. His home town of “Little Washington” is a half-hour north on I-79. A further half-hour north lies the thriving, post-ferrous metropolis of Pittsburgh. The State Correctional Institution at Greene, as it is formally known, is a maximum-security prison that houses a total of 1,800 inmates and employs 700 people. Friends' Blogs Whodat Turkey? The Nittany Turkey is a retired techno-geek who thinks he knows something about Penn State football and everything else in the world. If there's a topic, we have an opinion on it, and you know what "they" say about opinions! Most of what is posted here involves a heavy dose of hip-shooting conjecture, but unlike some other blogs, we don't represent it as fact. Read More…

French luxury group Kering and Alibaba Group have established a joint task force to fight against counterfeiting on Alibaba’s online marketplaces. The deal, which was agreed last week, will see Kering drop its lawsuit against Alibaba and Alipay, the Ant Financial subsidiary that is part of Alibaba Group. Kering, which owns the luxury fashion brands Gucci and Saint Laurent, launched the legal action in 2015 accusing Alibaba of being complicit in the sale of counterfeit goods on its websites. This partnership will see the two companies work together to protect intellectual property in a bid to “provide the best consumer experience and a trusted environment”. According to a statement, “the companies have established a joint task force with the purpose of collaborating fully, exchanging useful information, and working closely with law enforcement bodies to take appropriate action against infringers of Kering’s brands identified with Alibaba’s advanced technology capabilities". Kering said it will continue to “vigorously enforce” the intellectual property rights of its brands “against individuals and third parties responsible for the production, distribution and sale of unauthorized materials in China and throughout the world”. The move comes in the same week that Kering’s Saint Laurent brand announced it would sell its products on Farfetch’s Greater China platform, which has launched in partnership with Alibaba rival JD.com. Farfetch has made clear that the ecommerce platform’s commitment to protecting brand’s intellectual property was a key factor behind its decision to partner with JD.com. The task force is the latest in a string of anti-counterfeiting initiatives launched by Alibaba, which includes the Alibaba Anti-Counterfeiting Alliance (AACA) which was established in partnership with brands such as Louis Vuitton, Swarovski, Samsung and Mars. Alibaba recently claimed it seized more than three billion yuan of counterfeit goods in 2016, a figure more than double that of the previous year.

Life at depth: Photobacterium profundum genome sequence and expression analysis. Deep-sea life requires adaptation to high pressure, an extreme yet common condition given that oceans cover 70% of Earth's surface and have an average depth of 3800 meters. Survival at such depths requires specific adaptation but, compared with other extreme conditions, high pressure has received little attention. Recently, Photobacterium profundum strain SS9 has been adopted as a model for piezophily. Here we report its genome sequence (6.4 megabase pairs) and transcriptome analysis. The results provide a first glimpse into the molecular basis for life in the largest portion of the biosphere, revealing high metabolic versatility.

Araucaria clonal forestry: types of cuttings and mother tree sex in field survival and growth Resumo: Araucaria angustifolia (Bert.) O Kuntze (Paraná pine or Araucaria) is a potential forestry native species for Brazilian silviculture. However, a number of challenges and technical restraints persist, hindering its silvicultural expansion, among which are the lack of cloning technologies of superior genetic materials and their assessment under field conditions. Thus, we evaluated the potential use of araucaria plants derived from cuttings and seeds for timber production, by assessing field survival, growth and strobilus production using cuttings from male and female plants, collected from different positions, compared with those produced by sexual reproduction. Clones of male and female trees from different types of cuttings and seedlings were planted in 3 x 3 m spacing. The experiment was conducted in a completely randomized design of one tree plot with three treatments. Female clones and apical cuttings showed higher growth in diameter at breast height (6.4 cm) and total height (3.6 m) 74 months after planting, followed by seedlings and other clones, with similar results. We conclude that cuttings technique is potential for araucaria propagation for wood production purposes, and it is favored by the use of apical cuttings from female mother trees.

Historical conceptualizations of depression =========================================== There is a long tradition in phenomenologlcal psychopathology that stresses basic bodily alterations as core features of depressive states. Thus, Wernicke used the term "vital feelings" to describe certain somatic symptoms occurring in affective psychoses.^[@ref1]^ Vital feelings refer to the close relationship of the body to the awareness of self. They determine the way we experience our body and the impression we assume our physical presence makes on other people. Vital feelings are somatic affects localized In different parts of the body. Whereas vital feelings constitute the bodily background of our normal experiences, they may move to the fore In a depressive mood. For example, depressed patients very often complain of a headache which is described not exactly as an ordinary pain, but more as an unbearable pressure "like a band around the head." Other disturbed vital feelings affect the chest or the abdomen, and mediate unpleasant sensations of weight, tension, heaviness, or Inhibition, totally absorbing the focus of attention. In quite a similar way Dupré speaks of "coenestopathic states" which mean a distressing, qualitative change of normal physical feeling In certain areas of the body during an episode of depressive mood. It Is a global loss of vitality In which all bodily parts and functions may be altered, and all their performances depressed.^[@ref2]^ Kurt Schneider considered these disturbances of vital feelings to be the core of cyclothymic depression. In his psychopathologlcal assessment they were of paramount diagnostic significance In depressive Illness, more or less equivalent to the first-rank symptoms In schizophrenia.^[@ref3]^ Huber discriminated between vital disturbances on the one hand and vegetative symptoms In depression on the other.^[@ref4]^ Vital disturbances refer to the vital feelings just mentioned. They comprise a loss of general vital tone of the body, a prevailing fatigue or exhaustibility, and various forms of somatic dysesthesia, typically of a static, more localized character affecting head, chest, heart region, or abdomen. All-pervasive sensations of anesthesia, stiffness, and alienation of the total body may characterize a somatopsychic depersonalization in depression which may appear as a Cotard\'s syndrome in its extreme form. If the vital disturbances take on a peculiar form that is difficult to describe in ordinary everyday words, Huber speaks of a "coenesthetic" depression which must be typologically differentiated from the bizarre states of coenesthetic schizophrenia. Vegetative symptoms are closely associated with these vital disturbances and coenesthesias in depression. Disturbances of sleep, appetite, and digestion are most frequent. However, there may be many other vegetative symptoms in depression such as disordered salivation, transpiration and lacrimation, cardiac arrhythmias and dyspnea, loss of libido and various sexual dysfunctions, dys- or amen? orrhea, loss of or increase in body weight, decreased turgor of the skin, loss of hair, decrease in body temperature, nausea, vomiting, meteorism, dizziness, sweating, or sensations of coldness. Both vital disturbances, coenesthesias and vegetative symptoms, are typically coexistent with the well-known affective, behavioral, and cognitive symptoms of depression. With respect to the different settings of medical care, however, these psychological symptoms of depression may be masked by a dominant reporting of somatic symptoms. M. Bleuler addressed the point in his book *Depressions in Primary Care,* in 1943: *"It is a common and frequent observation that depressive patients with single somatic complaints come to the consulting room of the general practitioner, internal specialist, and even the surgeon, gynecologist, ophthalmologist, urologist and other medical specialists, and spontaneously, they only speak of somatic phenomena while concealing their state of depressive mood. They report palpitations, tightness of the chest, loss of appetite, obstipation, pollakiuria, amenorrhea and many others. Only when one looks at their psychic state does one discover that they report numerous hypochondriac ideas also in other areas, that in addition they produce depressive ideas of impoverishment and sin, that beyond that their whole stream of thoughts is inhibited, that the depression manifests itself not only in the somatic complaints reported, but in various other bodily expressions."^[@ref5]^* In spite of this long-standing psychopathological view on the somatic foundation of depressive mood, at least in moderate and severe clinical states, it is bewildering that the official psychiatric classification systems of the *Diagnostic and Statistical Manual of Mental Disorders,* 4th edition *(DSM-IV)* and the *ICD-10* *Classification of Mental and Behavioral Disorders. Clinical Descriptions and Diagnostic guidelines (ICD-10)* only marginally appreciate somatic symptoms as diagnostic criteria for depressive disorders while focussing on the psychological symptoms of affect and cognition. So, *DSM-IV* lists only three criteria of somatic symptoms for major depressive disorder: sleep disturbance, appetite disturbance, and fatigue or loss of energy. And correspondingly, in *ICD-10,* disturbances of sleep and appetite, loss of libido, and amenorrhea are the only somatic symptoms considered to be of diagnostic significance for major depression. Beyond this short list of predominantly vegetative symptoms, no painful physical symptoms are mentioned in either the *DSM-IV* or *ICD-10.* There seems to be a major shift In diagnostic practice, however; the second version of the *Diagnostic and Statistical Manual of Mental Disorders,* 4th edition, Text Revision *(DSM-IV TR)* now Includes new criteria referring to "excessive worry over physical health and complaints of pain (eg, headaches or joint, abdominal, or other pains)."^[@ref6]^ This supplement of diagnostic criteria Is Indicative of an againIncreasing awareness of the importance of somatic symptoms in depression. What is meant by "somatic" in somatic symptoms of depression? ============================================================= In the literature there are many terms used to describe somatic symptoms in depression: somatic, somatlzed, physical, bodily, somatoform, painful, psychosomatic, vegetative, medically unexplained, masked, etc.^[@ref7]^ These diverse terms refer to different theoretical or diagnostic concepts. For states of depressive mood the neutral term "somatic" is preferred, comprising various bodily sensations that a depressed individual perceives as unpleasant or worrisome. These dysesthesias are very often localized In certain body parts or organs, or may affect the whole body In Its vital condition, as In the case of fatigue or loss of energy. Several basic physical dysfunctions, such as those of sleep, appetite, or digestion, are also to be included in the term "somatic." In addition, It may be clinically relevant to differentiate between painful and nonpalnful somatic symptoms of depression. From a diagnostic perspective one has to keep in mind that somatic symptoms play a significant role both in primary psychiatric disorders, first and foremost depressive and anxiety disorders, and in somatoform disorders. And In differential diagnosis, somatic symptoms must be considered as possibly even Indicative of underlying somatic diseases. A diagnostic challenge may be seen In the well-known fact that depressive, anxiety, somatoform disorders, and medical conditions are frequently coexistent, or Interact In the Individual patient.^[@ref8]-[@ref10]^ Regarding the assessment of somatic symptoms, Kroenke correctly points out that diagnosis very often is more approximative than precise. Presented somatic symptoms may be either clearly attributed to a distinct medical disorder or be placed into one of the following heuristic categories: somatoform disorder, another primary psychiatric disorder (often depression and/or anxiety), functional somatic syndrome (eg, irritable bowel syndrome, fibromyalgia, chronic fatigue syndrome), "symptom-only" diagnosis (eg, low back pain, idiopathic dizziness) or only partially explained by a defined medical disorder (eg, many states of chronic pain).^[@ref11]^ Epidemiological studies may provide an illuminating survey of the prevalence of somatic symptoms in depressive disorders, especially those encountered in primary care, and the prognostic value of somatic symptoms regarding their development in the further course of illness. Somatic symptoms of depressive disorders in inpatient care and primary care =========================================================================== In a clinical study, Hamilton reported that somatic symptoms prevailed in a great majority of depressed patients.^[@ref12]^ Somatic symptoms, particularly somatic anxiety and fatigue, were documented in up to 80% of a sample of 260 women and 239 men suffering from major depression. These somatic symptoms very frequently had an underlying psychopathologically relevant hypochondriasis, both in women and men. This study confirmed earlier studies showing that depressive disorders with predominantly somatic presentation were likely to be the most common form of depression, both in inpatient and outpatient care.^[@ref13],[@ref14]^ Hagnell and Rorsman stressed the Indicative significance of somatic symptoms in depressed primary care patients regarding their risk of suicide.^[@ref15]^ Epidemiological studies designed to establish prevalence figures for depressive disorders In primary care during recent years have uniformly demonstrated that depressive disorders are highly prevalent at this level of medical care.^[@ref16]-[@ref19]^ For the great majority of depressed patients seeking professional help in the official health care system, general practitioners and internists are the decisive interface for diagnosis and treatment of depression.^[@ref20]^ Primary-care patients with depression very often present with somatic complaints. This seems to be more the rule than the exception worldwide.^[@ref21],[@ref22]^ Two of the three most common symptoms reported during a current depressive episode were somatic (tlred/no energy/listless: 73%, broken sleep/decreased sleep: 63%) as shown by the European Study Society study (DEPRES II).^[@ref23]^ This study, however, also underlined that 65% of the depressed primary care patients suffered from a concomitant medical condition pointing to some likely difficulties In differential diagnosis. The multlcenter International study (n =1146) conducted by the World Health Organization (WHO) confirmed that two thirds of the patients presented their depressive mood with somatic symptoms exclusively, and more than half complained of multiple medically unexplained somatic symptoms.^[@ref24]^ In another primary care study, Kirmayer et al arrived at a similar finding of patients presenting their depressive or anxiety disorders exclusively with somatic symptoms in an overwhelming majority (73%). The identified somatic symptoms were the main reason for the initial visit to the primary care physician.^[@ref25]^ In a US study in 573 patients with the diagnosis of major depression, two thirds (69%) complained of general aches and pains, hinting at a close relationship between pain symptoms and depression.^[@ref26]^ The diagnostic situation In primary care frequently manifests Itself, however, as somewhat more complicated. Many patients present only with a single or a few somatic symptoms which remain medically unexplained and do not fulfill the affective and cognitive criteria for a discrete depressive or anxiety disorder at the end of the clinical interview. Single somatic symptoms are the primary reason for more than 50% of patients visiting a general practitioner or an outpatient clinic. In some 20% to 25%, these somatic symptoms are recurrent or chronic. Somatic symptoms that remain unexplained after a careful medical assessment generally bear a high risk for psychiatric morbidity, regardless of the type of symptoms.^[@ref27]-[@ref29]^ Up to two thirds of these patients develop a depressive disorder in the medium term, and between 40% to 50% fulfill the criteria for an anxiety disorder.^[@ref30]-[@ref33]^ In a cross-sectional study in 1042 primary care patients, Gerber et al investigated the differential relationship between specific somatic complaints and underlying depressive symptoms. Some somatic symptoms showed a high positive predictive value (PPV) for depression: Sleep disturbances (PPV: 61%), fatigue (PPV: 60%), three or more complaints (PPV: 56%), nonspecific musculoskeletal complaints (PPV: 43%), back pain (PPV: 39%), amplified complaints (PPV: 39%), vaguely stated complaints (PPV: 37 %).^[@ref34]^ Some somatic symptoms are typically covarlant In the patients\' complaints without having received the nosological status of a discrete medical condition. These clusters of symptoms are instead considered as functional somatic syndromes and termed according to the diagnostic standards of the various medical disciplines, eg, fibromyalgia, chronic fatigue syndrome, and irritable bowel syndrome, etc. For some authors in psychiatry these functional somatic syndromes represent typical variants of somatoform disorders. There is still a controversial dispute in the medical literature, however, as to whether to assemble all these functional somatic syndromes within one general category of somatization,^[@ref35],[@ref36]^ or to split them up into separate clinical entities.^[@ref37]^ From an empirical standpoint, it is remarkable that among these syndromes there is a significant overlap on the level of symptoms and a strong association with depressive and anxiety disorders.^[@ref38]-[@ref41]^ A close relationship between states of depressive mood and symptoms of pain, especially of chronic pain, has been impressively established in many empirical studies.^[@ref26],[@ref42]-[@ref44]^ Depression and painful symptoms commonly occur together. As both conditions are highly prevalent in the general population, their frequent co-occurrence might be due to mere statistical coincidence.^[@ref45],[@ref46]^ From an empirical standpoint, however, the prevalence figures of coexistence are far beyond statistical expectation. In a meta-analytical survey, Bair et al demonstrated that around two thirds of all depressed patients treated in primary, secondary, and tertiary centers, both in outpatient and inpatient settings, report distressing painful somatic symptoms.^[@ref26]^ Conversely, the prevalence rate of major depression in patients with various pain syndromes is about 50%. There seem to be higher rates in clinical states characterized by multiple diffuse pain symptoms than by more defined types of pain. The risk of major depression is considered to be dependent on the severity, frequency, persistence, and number of pain symptoms.^[@ref47],[@ref48]^ From the perspective of primary care an epidemiological study assessing the predictive power of chronic pain for depressive morbidity showed that the prevalence rate of at least one chronic painful physical condition (CPPC) in the general population was 17.1%. At least one depressive symptom was present in 16.5% of subjects; 27.6% of these subjects had at least one CPPC. Major depression was diagnosed in 4% of subjects, and 43.4% of these subjects had at least one CPPC, which was 4 times more often than in subjects without depressive disorder.^[@ref49]^ This significant Interrelationship of CPPC and depression confirmed the earlier clinical advice of Katon, suggesting that if all patients with painful physical conditions were systematically assessed regarding a possible underlying depression, some 60% of all states of depression could be detected in primary care.^[@ref50]^ Generally, one has to keep in mind that, both from a cross-sectional and a longitudinal perspective, there is a relevant overlap of depressive, anxiety, and somatoform disorders, especially chronic painful physical conditions, among primary care patients presenting with medically unexplained symptoms.^[@ref51]-[@ref58]^ It is an important clinical finding that, with an increasing number of medically unexplained symptoms, the risk of an underlying depressive disorder increases in an impressive dose-response relationship. In a study which included 1000 adults and another study comprising 500 patients with a chief complaint of somatic symptoms, the presence of any somatic symptom increased the likelihood of a mood or anxiety disorder by two- or threefold. Only 2% of patients with no or only one somatic symptom had a mood disorder, but 60% of those patients presented nine or more somatic symptoms.^[@ref31],[@ref59]^ Patients with multiple medically unexplained somatic symptoms also show a greater amount of associated other psychiatric comorbidity.^[@ref60],[@ref61]^ Somatic symptoms in depression and rates of diagnostic recognition within primary care ====================================================================================== The typical form of presenting a depression In primary care Is via somatization. This form of somatic presentation, however, is considered to be one of the main reasons for low rates of recognition of depression In this sector of the medical care system.^[@ref20],[@ref62]^ It must be acknowledged that the alarmingly low figures of diagnosed and consecutively treated depressive disorders in only 25% to 33% of affected patients found in epidemiological studies during the early 1990s have increased up to some 60%. ^[@ref17],[@ref19]^ From a perspective of primary care, general practitioners are consulted by two groups of depressed patients who may pose a diagnostic challenge. Patients suffering from a medical condition have a frequent depressive comorbidity^[@ref23],[@ref63]^ These associated depressions often remain undetected, as the diagnostic focus of the primary care physicians is led by a dominant model of somatic disease.^[@ref64]^ Indeed, certain somatic symptoms such as sleep disturbances, diffuse bodily pains and aches, fatigue, changes of appetite, etc, may characterize both the pathophysiological process of a discrete medical condition and a depressive disorder as well. The differential diagnosis may be difficult. The role and significance of somatic symptoms for the diagnosis of depression in medically ill patients have been a controversial issue in the scientific literature. Meanwhile, a clinically reasonable consensus has been arrived at that the *DSM-IV* criteria for major depression do not require significant modification for patients with medical comorbidities.^[@ref65]-[@ref67]^ Somatic symptoms can positively contribute to a diagnosis if they are assessed in line with typical concomitant affective, behavioral, and cognitive symptoms of depression.^[@ref9]^ For a primary care physician It Is Important to know that at least 20% to 30% of patients with chronic medical conditions suffer from a coexisting depression.^[@ref68]^ It must be assumed that, even In those patients being diagnosed with an acute somatic disease for the first time, depression coexists In a significant percentage.^[@ref69]^ All In all, patients with medical conditions are to be considered as a risk group for nonrecognitlon of concomitant depression.^[@ref70]^ This especially applies to elderly medically ill patients.^[@ref71]^ In the other major group of depressed primary care patients, the somatic symptoms complained of very often remain medically unexplained. If one focuses on the mode of presentation, about 50% of the patients report somatic symptoms exclusively, and a minor percentage of some 20% present their depressive disorder with prevailing psychological, ie, affective and cognitive symptoms.^[@ref7],[@ref21],[@ref72],[@ref73]^ There is not, however, a categorical split between a somatic mode of presentation on the one hand and a psychological mode on the other. Rather, a broad spectrum of transition must be assumed, and the grading of somatization has an impact on the probability of recognition of an underlying depression.^[@ref25]^ As a rule, primary care physicians do not recognize a depression with an individual patient better when he or she is complaining of many actual medically unexplained somatic symptoms (here they rather prefer a diagnostic standpoint of wait and see), but when the patient returns again and again to consult because of these symptoms.^[@ref74]^ In addition, the extent of hypochondriacal worries and health anxieties facilitate, a correct diagnosis of depression.^[@ref75],[@ref76]^ Patients with somatic complaints that are not explained medically in an adequate way, however, do not represent a uniform group regarding diagnostic categorization. Besides depressive disorders, which in primary care manifest themselves according to the traditional concept of an endogenous type only in minority but instead show many atypical features,^[@ref77]-[@ref79]^ one must consider various anxiety and somatoform disorders in differential diagnosis.^[@ref60],[@ref61],[@ref80]-[@ref82]^ Again as a rule, there exists an Impressive overlap on the level of symptoms among all these diagnostic categories.^[@ref10]^ Aspects facilitating somatic symptoms in depression =================================================== Many factors may contribute to the form and extent to which a depression is presented in somatic symptoms. Female gender has been confirmed to be closely associated with somatization in many studies covering differential aspects on various theoretical levels.^[@ref83]^ In a gender differential analysis, Sllversteln draws some Interesting conclusions from the epidemiological data of the National Comorblty Survey.^[@ref84],[@ref85]^ By dividing respondents Into those who met overall criteria for major depression and exhibited fatigue, appetite, and sleep disturbances ("somatic depression") and those who met overall criteria without these somatic symptoms ("pure depression") she demonstrated gender differences only for "somatic depression" but not for "pure depression." The higher prevalence of "somatic depression" In females was strongly associated with a high frequency of anxiety disorders. Interestingly, this type of "somatic depression" among female patients already had Its onset during early adolescent years with predominantly bodily pains and aches. Wenzel et al attributed the higher prevalence of "somatic depression" in women largely to changes in appetite.^[@ref86]^ Gender differences can also be found in primary care. Women consistently reported most typical somatic symptoms at least 50% more often than men. Although mental disorders, above all depressive and anxiety disorders, were found to be correlated with this mode of somatic presentation, there was also an independent female gender effect on somatic symptom reporting.^[@ref87]^ In a later study Jackson et al found that among primary care patients with somatic symptoms, on the whole, women were younger, more likely to report stress, endorsed more "other, currently bothersome" symptoms, were more likely to have a mental disorder, and were less likely to be satisfied with the care.^[@ref88]^ A greater susceptibility of women, both to psychosocial stress and somatic illness stress, was held responsible for this higher prevalence of depressive and anxiety disorders in female patients.^[@ref89]^ A greater vulnerability to depressive and anxiety disorders on the one hand, and a strong neurobiological association to defined functional somatic syndromes (eg, fibromyalgia, irritable bowel syndrome, chronic fatigue syndrome) on the other may further increase the extent of this gender difference.^[@ref40],[@ref90]^ The disposition both to somatization and to depressive and anxiety disorder may be intermingled in various ways. Thus, a depressive mood may trigger the immediate illness behavior to enter the medical care system and to report somatized problems caused otherwise.^[@ref91]^ The very high frequency of somatic anxiety symptoms in patients with major depression may be interpreted by the idea that anxiety appears to be a major source of bodily distress and consecutive hypochondriasis, thus fostering somatization behavior.^[@ref12]^ Indeed, specific effects of depression, panic, and somatic symptoms on illness behavior must be considered.^[@ref92]^ Various causal illness interpretations, a tendency to amplify somatic distress, and difficulties In Identifying and communicating emotional distress, all have an impact on the form and extent of a somatic mode of presentation.^[@ref93]-[@ref95]^ Again, regarding the course of Illness, depressive and anxiety disorders following somatoform disorders may significantly contribute to the chronlflcatlon and complication of the latter.^[@ref39],[@ref96]^ From a perspective of etiologically relevant risk factors It Is a well-established epidemiological finding that the extent and severity of early adverse events, especially manifold traumatic experiences, are tightly connected with the mental and somatic state of adults. This general disposition may be detected In a series of psychiatric disorders, as In conversion and somatization syndromes,^[@ref97]-[@ref103]^ several chronic pain conditions,^[@ref104]-[@ref106]^ hypochondriacal attitudes,^[@ref107]^ factitious disorders,^[@ref98]^ and depressive, anxiety, and substance disorders.^[@ref108]-[@ref110]^ One can draw a basic conclusion from many epldemiologlcally designed longitudinal studies that the more a person has been exposed to severe and early trauma, the higher the risk will be that she/he will suffering from recurrent or chronic depression with pronounced suicidality, multiple medically unexplained somatic symptoms, especially chronic physical pain conditions with an onset already during adolescence or young adulthood, the more her/his psychic and somatic state as a whole will be negatively affected, and the more she/he will demonstrate abnormal illness behavior.^[@ref61],[@ref111]^ Culture and society are other factors that may have an important impact on the way a depressive mood is presented in a predominantly somatic way.^[@ref25]^ Interestingly, the comprehensive international WHO study on depression in primary care, conducted in 12 countries on different continents, was not able to identify clear cultural influences on the somatic mode of presenting a depression. A somatic presentation was much more common at centers where patients lacked an ongoing relationship with a primary care physician than at centers where most patients had a personal physician. This variable had a robustly differentiating effect beyond the various cultural settings.^[@ref24]^ Besides gender, culture, and type of patient-physician relationship, there may be many other factors influencing a more somatic mode of presentation, such as different ages in life cycle, association with medical conditions, earning a lower income, and imprisonment.^[@ref7],[@ref112]^ Burden of somatic symptoms in depression ======================================== Most patients who are psychopharmacologically treated for depression fail to reach full remission.^[@ref113]-[@ref114]^ A majority of patients may respond to antidepressants (by definition a reduction of symptoms by some 50% or more), but still suffer from residual symptoms. These residual symptoms are often somatic in nature. Symptoms of somatic anxiety and various painful conditions seem be especially common in states of incomplete remission.^[@ref115]^ Residual symptoms which are not treated must effectively be considered as a negative risk factor with respect to earlier relapse, and a more severe and chronic future course of illness.^[@ref116]-[@ref119]^ The clinical significance of somatic symptoms in depression may best be illustrated with the relationship between depression and painful physical conditions. In general, the worse the painful somatic symptoms, the more severe and the longer a depressive episode persists. In their general population-based study, Ohayon and Schatzberg found that depressed patients with chronic pain symptoms reported a longer duration of depressive mood (19.0 months) than those without chronic pain (13.3 months). In addition, a chronic physical pain condition in persons with at least one key symptom of depression was associated with an elevated rate of suicidal thoughts.^[@ref49]^ Fishbain considered chronic pain as a major suicide risk factor in depression.^[@ref120]^ Von Korff and Simon demonstrated a significant correlation between the intensity of pain symptoms and a worse outcome of depressive disorders. This worse outcome included more pain-related functional impairments, a worse state of general health, higher rates of unemployment, use of more opiates, more frequent polypharmacy, and more intensive utilization of medical services due to pain complaints. ^[@ref121]^ Although both painful and nonpainful somatic symptoms improve with antidepressant treatment, It Is the Intensity and extent of pain symptoms at baseline that significantly contribute to a less favorable response to medication, and to a longer duration of treatment necessary for a satisfying result, if at all.^[@ref122]-[@ref124]^ If one asssembles painful and nonpainful somatic symptoms of depression into a single dimension of somatization, It is this factor that must be correlated with an impressively increased overall use of health care services,^[@ref125]-[@ref127]^ to significant treatment nonadherence and a resulting higher risk of relapse and more chronic course of illness.^[@ref128]^ Again, a recurrent or chronic depression includes a higher risk of suicide^[@ref129]^ and an increased morbidity and mortality due to Illness-inherent factors or associated natural causes.^[@ref130]-[@ref132]^ All in all, it must be concluded that: when somatic symptoms, above all painful physical conditions, accompany the already debilitating psychiatric and behavioral symptoms of depression, the economic burden that ensues for patients and their employers increases considerably,^[@ref133]-[@ref134]^ the functional status may be hampered signifiacantly,^[@ref135]^ and the health-related quality of life is lowered dramatically^[@ref136]^ Neurobiological underpinnings of somatic symptoms in depression =============================================================== Various psychosocial and biological stressors may trigger a depression. Neurobiological processes underlying any depressive illness are manifold; this applies to the different somatic symptoms in particular. A strong heritable disposition, polygenetic in nature, seems to be established, but maladaptive neurobiological stress response systems already acquired by stressful and traumatic experiences during early development may play a major role in the pathophysiology of depression as well.^[@ref137]^ Dysfunctions in the serotonergic, noradrenergic, and dopaminergic neurotransmitter systems have been considered as relevant for quite a long time. Drawing from the neuroanatomical serotonergic tracts, starting in the midbrain raphe cell bodies and projecting to the frontal cortex, basal ganglia, limbic system, and hypothalamus on the one hand, of noradrenergic pathways originating in the locus ceruleus of the brain stem and projecting again to the same regions of the frontal cortex, limbic areas, and hypothalamus, but also uniquely to other parts of the frontal cortex and to the cerebellum on the other, Stahl stressed that deficiencies in the activity of specific pathways of serotonin and norepinephrine might account for the differential clinical phenomenology in depression. This seems to be true both for the typical psychological and somatic symptoms. Regarding somatic symptoms, especially vegetative symptoms such as changes in appetite or weight, lack of pleasure and sexual appetence, and sleep abnormalities, dysfunctional hypothalamic and sleep centers may be of paramount importance, all influenced by both serotonin and norepinephrine.^[@ref138]^ Fatigue, exhaustibility, or loss of energy, common distressing symptoms during a depressive episode, but also obstinate residual symptoms, may be mediated by different malfunctioning neuronal circuits that are regulated by multiple neurotransmitters.^[@ref139]^ Fatigue can be experienced as reduction in either mental or more physical vital feeling. Likely candidates for the neuronal structures that may mediate physical fatigue refer to brain areas regulating motor functions, such as striatum or cerebellum, but also to certain spinal pathways transferring sensory input from the body and thus modulating the perception of physical tiredness. In addition to serotonin and norepinephrine, dopamine may be involved in this process. Mental tiredness, on the other hand, may be mediated by diffuse cortical circuits and be influenced by cholinergic, histaminergic, noradrenergic, and dopaminergic neurotransmitters. The various painful somatic symptoms in depression may essentially be associated with serotonergic and noradrenergic pathways descending from brain stem centers to the spinal cord. An imbalance in these neurotransmitters, normally serving to inhibit the sensory input from the intestines, musculoskeletal system, and other body regions, may accentuate pain sensitivity.^[@ref26],[@ref140]^ As a matter of course, neither psychological nor somatic symptoms in depression can be explained by dysfunctional neurotransmitters exclusively. Many other neurobiological processes are involved in the pathophysiology of depression, such as an abnormal HPA axis with a disordered feedback mechanism of the corticotropin-releasing factor (CRF) -adrenocorticotropic hormone (ACTH) - Cortisol stress response, a reduced secretion of the neuropeptide hypocretin thus contributing to a desynchronization of the sleep-wake cycle, various abnormalities in the inflammatory system with an increased production of certain proinflammatory cytokines, a resulting depletion of the serotonin system, sickness behavior and depressive mood, reduced concentrations of various neurotrophlns such as brain-derived neurotropic factor (BDNF) causing Impaired neuroplastlcity, cell resistance, and neurogenesis.^[@ref137],[@ref141]-[@ref147]^ The intricate pathophysiological interplay of neuroendocrine stress response, inflammation, and neurotransmitter systems, both centrally and peripherally, may perhaps best be illustrated by the relationship between chronic pain conditions and depressive mood states (succinctly summarized in refs 148-150). In short, chronic stress evoked by chronic pain leads to a loss of negative glucocorticoid feedback in the (hypothalamic-pituitary-adrenocortical (HPA) axis and downregulation of the glucocorticoid receptors within the brain and the body periphery. Inflammation and nerve injury stimulate nociresponsive neurons within the dorsal horn of the spinal cord, and the relay of the nociceptive information ascends to the brain stem to be gated within the thalamus, prior to its cognitive appraisal within the somatosensory cortex. Monoamlnergic neurons In the brain stem normally descend to the spinal cord to act as a "brake" on nociceptive transmission. During chronic pain, loss of serotonergic and noradrenergic tone In response to glucocortlcold-lnduced monoamlnergic depletion may lead to descending Inhibitory Impulses to the spinal cord to effect an enhancement of pain sensation. Loss of glucocorticoid Inhibition of proinflammatory cytokines leads to proliferation of peripheral inflammatory events, contributing to pain sensitization. Although acute stress may be analgesic, implying an inhibitory circuitry between the limbic and somatosensory cortices, chronic stress evoked by chronic pain, leads to downregulation of glucocorticoid-mediated activity of this inhibitory connection, causing enhanced pain perception. Similarly, although acute pain may be mood-enhancing via both sympathetic and glucocorticoid routes (implying an excitatory reciprocal link between the somatosensory and limbic cortices), chronic pain-Induced downregulation of glucocorticoid modulation of this link may lead to depressed mood. Psychopharmacological implications for the treatment of somatic symptoms in depression ====================================================================================== Numerous trials with antidepressants have demonstrated that full remission of the psychological, and especially of the somatic, symptoms in depression can be achieved only by a minority group of depressed patients within a usual 6- to 8-week treatment period.^[@ref62],[@ref151],[@ref152]^ These sobering facts are reflected by a higher risk of relapse, a worse course of illness with many associated psychosocial disabilities, and a hampered health-related quality of life. Therefore, achieving a state of symptomatic remission must be a treatment goal of utmost clinical importance. Targeting both serotonin and norepinephrine in those neuronal circuits that mediate somatic symptoms is the most widely employed strategy to reduce painful and nonpainful somatic symptoms in depression.^[@ref90]^ In comparison with selective serotonin reuptake inhibitors, antidepressants with a dual action on both the serotonin and norepinephrine system were significantly superior in alleviating these somatic symptoms and achieving full symptomatic remission of depression. This may be a promising approach, even to treating chronic pain conditions, eg, fibromyalgia, without prevailing depressive symptoms.^[@ref153],[@ref154]^ This seems to have been well established In clinical trials with venlafaxlne,^[@ref155]-[@ref159]^ duloxetlne,^[@ref160]-[@ref163]^ mllnaclpran,^[@ref164]^ or mlrtazaplne.^[@ref165]^ In order to Improve distressing symptoms of fatigue, the use of psychostimulants, modafinil, bupropion, or selective norepinephrine reuptake inhibitors such as reboxetine or atomoxetine may be recommended.^[@ref166]^ As a rule, psychopharmacological efforts to treat severe states of depression or states of depression with prominent somatic symptoms effectively must be guided by a perspective of a longer duration than usual. Higher dosages of a selected antidepressant have to be used very often. Sometimes shifts within or between pharmacological classes of antidepressants or an augmentation with, eg, lithium or tri-iodthyronine, are necessary to arrive at the desired aim. From a pragmatic standpoint, clinically rational algorithms may favorably guide this endeavor.^[@ref167]^ Finally, it must be stressed that a reasonable combination of pharmacological and psychotherapeutic approaches can improve the treatment results in many depressed patients.^[@ref168],[@ref169]^

A yellow police tape marks the crime scene at a poultry processing plant in Jalan Batu Maung, Penang, where a family of four were shot dead at 2.45am today. ― Picture courtesy of the Penang police GEORGE TOWN, July 13 ― A family of four, including a two-year-old boy, was shot dead in an early morning incident at a poultry processing factory on Jalan Batu Maung here today. Penang police Criminal Investigation Department (CID) chief Datuk Razaruddin Husain identified the victims as factory owner Toh Hock Choon, 50; his wife Tan Saw Sim, 55; and Tan’s son Chung Wah Thong. The toddler was Chung’s son. Razaruddin told reporters at the crime scene that the incident is believed to have happened about 2.45am, following an altercation between the factory owner and another stepson aged 32. The senior policeman believed the suspect shot the three adults first and turned on the child later when he came to check the commotion. “We believe when he shot the three victims, the two-year-old heard the commotion and came down the stairs where he too was shot,” he said. Malay Mail Online was able to obtain a recording of the news conference at the crime scene. Razaruddin said the police only knows the toddler by his nickname, Ah Bee, at the moment, and are looking to find his mother who lives in George Town. Initial investigations revealed that the suspected killer may be a drug addict and often argued with the victims. “A CCTV recording showed the suspect rummaging through things in the factory premises before he got into an argument with his stepfather,” Razaruddin said. “We believe he wanted to get money to get more drugs,” he added. A total of 11 bullet casings were found at the scene, and police believe 11 shots were fired at close range. The police have mounted a massive search for the suspect who is believed to be armed with a 9mm semi-automatic weapon. “He is believed to have shot the victims with the semi-automatic weapon and escaped in a Toyota Hilux with the plate number PLJ 7392,” Razaruddin said. He said patrol cars have been deployed in a massive hunt for the armed suspect and the borders have also been alerted. He appealed to the public to come forward if they have any information on the incident or the suspect. Editor’s note: An earlier report stated the child’s gender as female instead of male and has since been corrected. Malay Mail Online apologises for the mistake.

Q: Cell should contain example input value for user to see I want to create automated cells in Excel which will show the type of data to be entered in that cells. I want to create cells which will show "Enter Username here", " Enter DOB here" same as that which shows in fb and Gmail login page. I don't want to save any credentials. I had created multiple dropdown lists and people are not understanding that there is a dropdown until they click on that cell. So I want to create automated cells which will show the type of data to be entered into it. It should disappear when I click on that cell and should appear if I erase the contents from that cell which I anyone had entered. A: Look into the change selection event: Private Sub Worksheet_SelectionChange(ByVal Target As Range) if target.address = "$A$1" then target.value = "" else Dim value as string value = range("$A$1").value if value="" then 'Note: It'd be better to check here if the user input is correct! range("$A$1").value = "Enter DOB here" end if end if End Sub Edit to user's comments: Private Sub Worksheet_SelectionChange(ByVal Target As Range) if target.address = "$A$1" then if target.value = "Enter DOB here" target.value = "" end if else Dim value as string value = range("$A$1").value if value="" then 'Note: It'd be better to check here if the user input is correct! range("$A$1").value = "Enter DOB here" end if end if End Sub

#if !defined(BOOST_PP_IS_ITERATING) ///// header body #ifndef BOOST_MPL_AUX778076_ADVANCE_BACKWARD_HPP_INCLUDED #define BOOST_MPL_AUX778076_ADVANCE_BACKWARD_HPP_INCLUDED // Copyright Aleksey Gurtovoy 2000-2004 // // Distributed under the Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // // See http://www.boost.org/libs/mpl for documentation. // $Id$ // $Date$ // $Revision$ #if !defined(BOOST_MPL_PREPROCESSING_MODE) # include <boost/mpl/prior.hpp> # include <boost/mpl/apply_wrap.hpp> #endif #include <boost/mpl/aux_/config/use_preprocessed.hpp> #if !defined(BOOST_MPL_CFG_NO_PREPROCESSED_HEADERS) \ && !defined(BOOST_MPL_PREPROCESSING_MODE) # define BOOST_MPL_PREPROCESSED_HEADER advance_backward.hpp # include <boost/mpl/aux_/include_preprocessed.hpp> #else # include <boost/mpl/limits/unrolling.hpp> # include <boost/mpl/aux_/nttp_decl.hpp> # include <boost/mpl/aux_/config/eti.hpp> # include <boost/preprocessor/iterate.hpp> # include <boost/preprocessor/cat.hpp> # include <boost/preprocessor/inc.hpp> namespace boost { namespace mpl { namespace aux { // forward declaration template< BOOST_MPL_AUX_NTTP_DECL(long, N) > struct advance_backward; # define BOOST_PP_ITERATION_PARAMS_1 \ (3,(0, BOOST_MPL_LIMIT_UNROLLING, <boost/mpl/aux_/advance_backward.hpp>)) # include BOOST_PP_ITERATE() // implementation for N that exceeds BOOST_MPL_LIMIT_UNROLLING template< BOOST_MPL_AUX_NTTP_DECL(long, N) > struct advance_backward { template< typename Iterator > struct apply { typedef typename apply_wrap1< advance_backward<BOOST_MPL_LIMIT_UNROLLING> , Iterator >::type chunk_result_; typedef typename apply_wrap1< advance_backward<( (N - BOOST_MPL_LIMIT_UNROLLING) < 0 ? 0 : N - BOOST_MPL_LIMIT_UNROLLING )> , chunk_result_ >::type type; }; }; }}} #endif // BOOST_MPL_CFG_NO_PREPROCESSED_HEADERS #endif // BOOST_MPL_AUX778076_ADVANCE_BACKWARD_HPP_INCLUDED ///// iteration, depth == 1 // For gcc 4.4 compatability, we must include the // BOOST_PP_ITERATION_DEPTH test inside an #else clause. #else // BOOST_PP_IS_ITERATING #if BOOST_PP_ITERATION_DEPTH() == 1 #define i_ BOOST_PP_FRAME_ITERATION(1) template<> struct advance_backward< BOOST_PP_FRAME_ITERATION(1) > { template< typename Iterator > struct apply { typedef Iterator iter0; #if i_ > 0 # define BOOST_PP_ITERATION_PARAMS_2 \ (3,(1, BOOST_PP_FRAME_ITERATION(1), <boost/mpl/aux_/advance_backward.hpp>)) # include BOOST_PP_ITERATE() #endif typedef BOOST_PP_CAT(iter,BOOST_PP_FRAME_ITERATION(1)) type; }; #if defined(BOOST_MPL_CFG_MSVC_60_ETI_BUG) /// ETI workaround template<> struct apply<int> { typedef int type; }; #endif }; #undef i_ ///// iteration, depth == 2 #elif BOOST_PP_ITERATION_DEPTH() == 2 # define AUX778076_ITER_0 BOOST_PP_CAT(iter,BOOST_PP_DEC(BOOST_PP_FRAME_ITERATION(2))) # define AUX778076_ITER_1 BOOST_PP_CAT(iter,BOOST_PP_FRAME_ITERATION(2)) typedef typename prior<AUX778076_ITER_0>::type AUX778076_ITER_1; # undef AUX778076_ITER_1 # undef AUX778076_ITER_0 #endif // BOOST_PP_ITERATION_DEPTH() #endif // BOOST_PP_IS_ITERATING

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Please note, if you have non BNPL purchases on your account you will still need to make at least your minimum payment as detailed on your statement. Buy Now Pay Later (BNPL) allows you to delay payment for 12 months. The payment free period starts when you place your order (including items which are purchased on pre-order and/or are not ready for immediate dispatch). Select BNPL at checkout and the repayment period of either 104 or 156 weeks. This is the repayment period you will pay over, once the payment free period (12 months) has ended. The interest rate typically used to calculate BNPL interest is 44.9% per annum. Your interest rate will be detailed in checkout. The interest is calculated on the payment free period and the repayment period. You can avoid interest by paying the cash price in full within the payment free period. Delivery charges and other Financial Services products are not available on Buy Now Pay Later and will appear on your next statement. Please note, if you have non BNPL purchases on your account you will still need to make at least your minimum payment as detailed on your statement. Buy Now Pay Later (BNPL) allows you to delay payment for 12 months. The payment free period starts when you place your order (including items which are purchased on pre-order and/or are not ready for immediate dispatch). Select BNPL at checkout and the repayment period of either 104 or 156 weeks. This is the repayment period you will pay over, once the payment free period (12 months) has ended. Your interest rate will be detailed in checkout. The interest is calculated on the payment free period and the repayment period. You can avoid interest by paying the cash price in full within the payment free period. Delivery charges and other Financial Services products are not available on Buy Now Pay Later and will appear on your next statement. Please note, if you have non BNPL purchases on your account you will still need to make at least your minimum payment as detailed on your statement.

Julia Kogan Julia Kogan is an American-French operatic coloratura soprano, writer, and presenter of Ukrainian ancestry. Biography Kogan's opera roles have included Queen of the Night in Die Zauberflöte, Zerbinetta in Ariadne auf Naxos, Blonde in Die Entführung, Madame Herz in Der Schauspieldirektor, Greta Fiorentino in Street Scene, and Fiordiligi Cosi fan tutte at the opera houses of Avignon, Indianapolis, Limoges, Manitoba, Toulon, Toulouse and in Oxford. She has been described as "a lively actress" with "a warm voice, round, elegant and expressive phrasing, and a remarkable knack for coloratura passages", "up to the challenge of a stratospheric soprano line". Kogan has concertized with repertoire ranging from Baroque to contemporary in Europe, North and South America, and Africa, including such venues as Carnegie Hall, Alice Tully Hall at the Lincoln Center, St. Petersburg's Glinka Hall, the Hôtel de Ville in Paris, the Alcazar Palace in Seville, the Library of Congress in Washington D.C., and collaborated with Chamber Orchestra Kremlin, Ensemble Calliopée, Figueiredo Consort, Junge Philharmonie Wien, Les Passions, The Little Orchestra Society, the Oxford Philharmonic, the Newcastle Baroque Orchestra, Saint Petersburg Chamber Philharmonic, Toulon Opera Orchestra, and Ukrainian National Symphony, among others. Julia Kogan wrote and presented the BBC Radio 4 documentary "The Lost Songs of Hollywood", which aired on 12 November 2015. It was chosen "Pick of the Week" on BBC radio. Releases Kogan's first solo album, "Vivaldi Fioritura" (2010), was recorded with Chamber Orchestra Kremlin under Misha Rachlevsky. Her second solo album, Troika (2011), was recorded with the St. Petersburg Chamber Philharmonic under Jeffery Meyer. Both albums were released on Rideau Rouge Records with distribution by Harmonia Mundi. References External links Official website http://www.bbc.co.uk/programmes/b06nrqvk Category:American operatic sopranos Category:Living people Category:Ukrainian emigrants to the United States Category:Year of birth missing (living people)

Perirhinal and hippocampal contributions to visual recognition memory can be distinguished from those of occipito-temporal structures based on conscious awareness of prior occurrence. The ability of humans to distinguish consciously between new and previously encountered objects can be probed with visual recognition memory tasks that require explicit old-new discriminations. Medial temporal-lobe (MTL) lesions impair performance on such tasks. Within the MTL, both perirhinal cortex and the hippocampus have been implicated. Cognitive processes can also be affected by past object encounters in the absence of conscious recognition, as in repetition priming tasks. Past functional neuroimaging findings in healthy individuals suggest that even in tasks that require conscious recognition decisions for visual stimuli, posterior cortical structures in the ventral visual pathway distinguish between old and new objects at a nonconscious level. Conclusive evidence that differentiates the neural underpinnings of conscious from nonconscious processes in recognition memory, however, is still missing. In particular, functional magnetic resonance imaging (fMRI) findings for the MTL have been inconsistent towards this end. In the present fMRI study, we tested whether perirhinal and hippocampal contributions to recognition memory can be distinguished from those of occipito-temporal structures in the ventral visual pathway based on the participants' reported conscious awareness of prior occurrence. Images of objects with a large degree of feature overlap served as stimuli; they were selected to ensure an involvement of perirhinal cortex in the present recognition task, based on evidence from past lesion-based research. We found that both perirhinal cortex and occipito-temporal cortex showed a differential old-new response that reflected a repetition-related decrease in activity (i.e., new > old). Whereas in perirhinal cortex this decrease was observed with respect to whether subjects reported objects to be old or new, irrespective of the true item status, in occipito-temporal cortex it occurred in relation to whether objects were truly old or new, irrespective of the participants' conscious reports. Hippocampal responses differed in their exact pattern from those of perirhinal cortex, but were also related to the conscious recognition reports. These results indicate that both perirhinal and hippocampal contributions can be distinguished from those of occipito-temporal structures in the ventral visual pathway based on the participants' reported conscious awareness of prior occurrence.

Hey Everyone, This is my first post on the board, and I'm glad to see there is a section specifically on Spanish wines as they've always been a favorite of mine! I recently drank the wine mentioned in the tile and absoultely loved it. The only problem is that I bought it in Sevilla, and haven't been able to find the exact wine at the local wine superstores. Any advice on how to find if this wine is imported and how to get it. Welcome to the board, MrB. A Website we commonly use when looking for an elusive bottle is wine-searcher.com, but unfortunately it turned up a no-find. Also checked my regional benchmark, Spec's in Houston, with the same result. You may need to settle for a reasonable sub. Despite all you see in the stores, both Spain and Italy (the largest wine producers in the world) only export a relatively small number of wines to the U.S. or anyone else. Find something you like in Chi-town and enjoy.

Breech position, delivery route and congenital hip dislocation. The purpose of this study was to investigate whether the mode of delivery for fetuses in breech presentation in any way influenced the frequency of congenital hip dislocation. In 13,559 singleton births 583 fetuses were in breech position, and the cesarean section rate was 39.1%. Eighty-three infants were born with congenital hip dislocation, 11 of whom had been in breech position. Of these 11, cesarean section was required in 5 cases. There was no difference in frequency of congenital hip dislocation between fetuses in breech presentation delivered by cesarean section vs. by the vaginal route. The frequency of breech presentation in congenital hip dislocation was 13.3%. Including 7 external versions, the rate was 21.7%. Female to male ratio was 4:1. The frequency of congenital hip dislocations in infants born in vertex presentation was 5.5 per mille and for infants born in breech presentation it was 18.9 per mille.

"Ryan got six months probation and five public work days," a source told Radar. "He has random drug tests in between." Edwards, 30, showed up to Red Bank City Court in a pink button-down shirt without his supportive wife Mackenzie by his side. The legal trouble started when Maci Bookout 's baby daddy was hit with a citation on March 12, 2017. Police pulled him over during a traffic stop for expired registration. During the stop, an officer saw a hypodermic needle in an open backpack on the passenger seat "I asked Edwards if he had any medical conditions and he replied, 'No,'" the citation obtained from Red Bank City Court read. "I then asked why he had a hypodermic needle in his backpack and he replied, 'I don't know.' I told them that the vehicle will be searched and he should inform me if there are more and Edwards replied, 'Yes, probably." Cops confiscated 14 hypodermic needles, one of which was loaded with heroin, and a bag with a dark substance inside. "I asked Edwards what it was and he replied, 'It's heroin and I have a problem.'" Authorities also recovered two silver spoons with residue on them and a scale. The heroin was weighed and found to be 1.8 grams. He was issued a misdemeanor citation for simple possession of heroin, possession of paraphernalia and expired registration. He pled guilty to the simple possession of heroin charge. He was sentenced to 11 months and 29 days in jail. The sentence was suspended upon payment of a $750 fine and good behavior. He was ordered to take drug screenings for six months. The possession of drug paraphernalia and expired registration offenses were dismissed. He entered rehab for heroin use after he was caught on camera slurring his words and falling asleep at the wheel while driving to his May wedding to wife Mackenzie. Edwards and wife have claimed he has remained sober since the stint But then on March 27, 2018, he was arrested for petition to revoke, which means breaking probation. Radar exclusively revealed he failed a court-ordered drug test on January 17, 2018. He tested positive for opiates and morphine in a urine sample. Edwards' drug of choice heroin is classified as an opiate "He failed the scheduled drug test," a source told Radar. "That is why they charged him with Petition to Revoke."

Q: Is a low number of members in a class considered a code smell? I am currently making a simple to-do list program using the MVC pattern, and thus have a model class for the Notebook. However, something feels "off" as it has a very low number of members. The Notebook is composed of categories, which are composed of To-do lists, which are composed of Items. What I cannot place is whether this is a case poor analysis (e.g. there are more members and responsibilities I am just missing them..) or perhaps a code smell that the class is not needed (in that case I'm not sure what to do as I could just have a list of categories in that controller, but then I don't have a notebook entity modelled which seems wrong as well). Below is the very simple class I have: class Notebook { private String title; private List<Category> categories; public Notebook(String title, List<Category> categories) { } public void setCategories(List<Category> categories) { } public List<Category> getCategories() { } } I often have this issue where it feels like I am making classes for the sake of it and they have a very number of members/responsibilities, so it would be nice to know whether I am stressing for no reason or not. A: Not necessarily, there is the concept in Domain Driven Design of what is called a "Standard Type". Which is really a basic primitive wrapped in an object class. The idea is that the primitive contains no information about what information it contains, it's just a string/int/whatever. So by having say an object that surrounds the primitive and ensures that it is always valid ensures that the object has a meaning far beyond just the primitive it contains e.g. a Name is not just a string, it's a Name. Here's an example taken from the comments of Velocity public class Velocity { private readonly decimal _velocityInKPH; public static Velocity VelocityFromMPH(decimal mph) { return new Velocity(toKph(mph)); } private Velocity(decimal kph) { this._velocityInKPH = kph; } public decimal Kph { get{ return this._velocityInKPH; } } public decimal Mph { get{ return toMph(this._velocityInKPH); } } // equals addition subtraction operators etc. private static decimal ToMph(decimal kph){ // conversion code } private static decimal ToKph(decimal mph){ // conversion code } }

<UIView; frame = (0 0; 1112 834); autoresize = W+H; layer = <CALayer>> | <UILabel; frame = (528.333 20; 55.6667 20.3333); text = 'What's'; userInteractionEnabled = NO; layer = <_UILabelLayer>> | <UILabel; frame = (0 417; 25 20.3333); text = 'the'; userInteractionEnabled = NO; layer = <_UILabelLayer>> | <UILabel; frame = (1073 417; 39 20.3333); text = 'point'; userInteractionEnabled = NO; layer = <_UILabelLayer>> | <UILabel; frame = (552.333 816; 7.66667 18); text = '?'; userInteractionEnabled = NO; layer = <_UILabelLayer>>

Q: Is it focus or depth of field? I was trying to shoot a group of people standing clumped but at different distances, quite close to me, think disorganized portrait. I have a Nikon d750, and was not able to get everyone into focus. If I brought the people closer to me in focus, then the background were blurred and vice versa. I pushed the aperture all the way to f18 or so and it didn't bring the whole scene into focus. Was I shooting from too close .... Or this makes me wonder is this about AF-S vs AF-A instead of aperture and the camera choosing one point to focus upon instead of the area? How would you compose a group shot like this to all be in focus? Thanks! A: It sounds like depth of field. If (with an APS crop sensor, 30 mm lens, f/4), if you focus at say 6 feet you might have about 2 feet of DOF span, like from 5 feet to 7 feet (coarse approximations). If your subject is distributed at say 6 to 8 feet, this 5-7 DOF zone does not include the far ones. If you focus far, you miss the near ones. Which is your description. If you focus on the near ones, or on the far ones, you have wasted half of your DOF range in empty space where there is no one. There are DOF calculators which compute these numbers. Normal procedure would be to focus more near the middle depth of the group (or slightly in front of the middle), to put the zone more centered on your group. So yes, you do chose your point of focus too. And of course, stopping down the f/stop, like from f/4 to f/8 or f/11, could greatly increase the span of DOF, so that the zone size is double or more. DOF is rather vague, and is NOT a critically precise number. If the calculator say DOF is 5 to 7 feet, then 7.02 feet is no different than 6.98 feet, both are at the limit of acceptability. These 5 to 7 feet numbers are considered the extremes of acceptability, and the actual focused distance will of course always be the sharpest point.

I admit I never thought I’d do any analytical work on Resident Evil 4. Don’t get me wrong; it’s one of my favorite games. Being extremely fun to play, and a having a wonderfully creepy aesthetic are just a few of the game’s strengths. But it’s a silly game in a lot of ways. There aren’t larger messages and meanings to glean from it. And at some moments, the game mechanics and the overall story don’t match up very well. I’d like to discuss one of those moments: Luis’s famous death in castle. I’ll use this example to discuss the elements of motivation and capacity in video games. You may recall from my previous article a discussion of a player’s motivation and capacity while playing a video game. Although I mentioned these terms, I never adequately defined them, so I’ll do so now. A player’s motivation is the reason he or she cares about playing the game and effecting some kind of difference in the world and story in which he or she is immersed. This element is present in other mediums—it’s the reason we continue to read/watch the story. A player’s capacity, unlike motivation, is intrinsically tied to game mechanics; it consists of the things that the player is able to do in the game world. The analogue of capacity in other media is simply the reader’s ability to continue to watch or read the story. There are further complexities in games, however, including that a player’s degree of capacity can effect his or her motivation, but that is a discussion for another time (probably focusing on Deus Ex). For now, recall my claim that in order for a game to be truly impactful, both of these elements must exist (or noticeably not exist, as I’ll discuss in my next article). Note also that the capacity element is harder and more important to make present, since it’s the element that video games have introduced to storytelling. So let’s see whether both motivation and capacity exist in the case of Luis’s death. For those who haven’t played the game, you can watch a video of the moment below. [youtube https://www.youtube.com/watch?v=NsfebZKsp94&w=420&h=315] I’ll summarize the scene: Luis was attempting to help you get a “sample” of great value from the game’s primary villain, Saddler. But Saddler kills Luis, taking back the sample (classic). As Luis lies dying before you, he gives you a temporary antidote to the parasite that you are infected with, and tells you to stop Saddler. When he finally passes away, Leon yells out him name in anguish. So this moment most certainly provides the player with motivation. And there are multiple reasons for this. In his final moments, Luis literally gives the player the primary plot incentive for the remainder of the game: stop Saddler and get the sample back. On top of that, finding out that Leon isn’t doomed to die at the hands of his parasite energies the player with a new sense of hope. But, most importantly, the player’s motivation is an extension of Leon’s grief. If the player empathizes with Leon (hopefully they do if they’ve gotten this far in the game), when Leon cries out in agony over the death of his friend, the player, too, is motivated seek justice for a lost friend. This is the opposite of Link’s silence that I discussed in my last article. Unlike Link, who leaves you to form your experience for yourself, Leon hands you his grief, and in this way motivates you to action. This is good storytelling. Clearly Resident Evil 4 has nailed the motivational aspect of making a powerful narrative in a game. But at this point there’s no particular reason story-wise to play the game instead of just watching it. So let’s think about capacity. Capacity is the additional element that makes a video game unique as opposed to movies or books. And the extent of what video games can do with capacity hasn’t been fully explored. So, even though it’s not necessary for a game to use dynamics of capacity in order to tell a good story, ignoring this element is missing an opportunity for better storytelling. Since capacity is unique to games, if there’s no interesting storytelling or fun mechanics, there’s no reason to play the game instead of just watch it. Now, in order to discuss capacity in the case of death, capacity takes on a slight nuance. When a character dies in a game, the key aspect of capacity is actually the change in capacity. It doesn’t matter so much what the capacity level is in general, it just matters if there is a difference before and after a character’s death. This provides meaning for the death within the structure of the game mechanics. For example, if a character dies in a game but is immediately replaced by an almost identical analogue, their death has little visceral impact for the player, who can’t feel the impact of the character’s death on the gameplay. This actually does happen: in Legend of The Dragoon, when one of your party members, Lavitz, dies, Albert, who literally takes on the stats of Lavitz, almost immediately replaces him. Even more notably, Cait Sith dies in Final Fantasy VII, but is quite literally replaced by an entirely identical avatar called “Cait Sith 2”. In these situations the player’s capacity has not changed, and thus the deaths have lost some of their potential narrative impact. That’s kind of what it feels like when Luis dies in Resident Evil 4. Although he helps you out as a non-player character (NPC) at various points in the game, it’s not as though he’s the only character who does this. And there’s nothing to distinguish him mechanics-wise from the other characters you meet and team up with. What’s more, you continue to have access to other NPCs you can get help from after he dies. So, in terms of how it feels to play the game, you don’t even notice he’s gone. As far as the player’s capacity to team up with others in order to stay alive, very little changes after Luis’s death. The player’s capacity thus changes very little when he dies, and though the player grieves with Leon, it’s difficult to feel a real sense of loss. To sum up, although the story of Luis’s death in Resident Evil is well told in terms of movies and books, the developers missed the opportunity to tell this story through the game mechanics in terms of a change in player capacity. Luis was not a unique character mechanically, and other characters that Leon meets effectively replace his avatar. The death is meaningful to watch, but far less meaningful to play. Nathan Randall - Video Game Analyst Nathan Randall is a Master’s candidate in game design at FIEA. He analyzes how gameplay mechanics and design impact the storytelling of video games. Learn more here. With a Terrible Fate is dedicated to developing the best video game analysis anywhere, without any ads or sponsored content. If you liked what you just read, please consider supporting us by leaving a one-time tip or becoming a contributor on Patreon.

Confederación Revolucionaria de Obreros y Campesinos The Confederación Revolucionaria de Obreros y Campesinos (CROC) is a Mexican trade union confederation. It is one of the most important and influential trade unions in the History of Mexico. It was founded in April 1952. during a congress made by four workers centrals. Until 1980 the CROC had 750 000 workers inside the union, in only 17 of the 31 states and the Federal District (Mexico City); in this year the statements change in order to change the organization of the union by changing the presidency of the union, that was rotative and with only one year of duration to a presidency headed by a National Secretary General (Secretario General del Comité Ejecutivo Nacional). It currently has 4.5 million worker members throughout the 32 states in the country having also 17 National Industrial Confederacies; also 3.600 unions with 15 000 collective contracts. External links History of the Confederación Revolucionaria de Obreros y Campesinos (Campesinos an Workers Revolutionary Confederacy) Category:National trade union centers of Mexico Category:World Federation of Trade Unions Category:1952 establishments in Mexico Category:Trade unions established in 1952

Q: ¿Cuál es el valor primitivo de [] con base en ECMAScript 2016 (versión 7)? Para escribir una respuesta a ¿Cómo funciona el condicional if (!+[]+!+[] == 2) en JavaScript? me aventuré a utilizar https://www.ecma-international.org/ecma-262/7.0/index.html para las referencias. En ToPrimitive se explica el procedimiento para convertir una valor en un valor primitivo pero no he logrado asimilarlo para el caso de []. Sé que [] es un objeto y que es equivalente a new Array() También sé que un array es un objeto exótico, así que uno o más de sus métodos internos esenciales no tiene comportamiento predeterminado. Notas: Comentario de Paul Vargas (chat) Revisar Array objects (sección de ECMAScript 2016) Otras pregunta relacionadas: ¿Por qué _=$=+[],++_+''+$ es igual a 10? A: Respuesta corta El valor primitivo de [] es '' (cadena de texto vacía). Explicación Finalmente me decidí a googlear y encontré esta respuesta a Why does ++[[]][+[]]+[+[]] return the string “10”?1, la cual es similar a mi respuesta a ¿Cómo funciona el condicional if (!+[]+!+[] == 2) en JavaScript? en cuando a que hace referencia a una especificación ECMASCript sólo que aquella no especifica a cual versión se refieren las citas, sin embargo, me ha sido útil para llenar el "hueco" que derivó en esta pregunta. Mas abajo incluyo un par de extractos los cuales se pueden resumir como document.write([].join() === '') // Resultado true Extractos de la ECMAScript 2016 (versión 7) 12.2.5Array Initializer NOTE An ArrayLiteral is an expression describing the initialization of an Array > object, using a list, of zero or more expressions each of which represents an array element, enclosed in square brackets. The elements need not be literals; they are evaluated each time the array initializer is evaluated. Array elements may be elided at the beginning, middle or end of the element list. Whenever a comma in the element list is not preceded by an AssignmentExpression (i.e., a comma at the beginning or after another comma), the missing array element contributes to the length of the Array and increases the index of subsequent elements. Elided array elements are not defined. If an element is elided at the end of an array, that element does not contribute to the length of the Array. 7.1.1 ToPrimitive ( input [ , PreferredType ] ) The abstract operation ToPrimitive takes an input argument and an optional argument PreferredType. The abstract operation ToPrimitive converts its input argument to a non-Object type. If an object is capable of converting to more than one primitive type, it may use the optional hint PreferredType to favour that type. Conversion occurs according to Table 9: Table 9: ToPrimitive Conversions Input Type Result Undefined Return input. Null Return input. Boolean Return input. Number Return input. String Return input. Symbol Return input. Object Perform the steps following this table. When Type(input) is Object, the following steps are taken: If PreferredType was not passed, let hint be "default". Else if PreferredType is hint String, let hint be "string". Else PreferredType is hint Number, let hint be "number". Let exoticToPrim be ? GetMethod(input, @@toPrimitive). If exoticToPrim is not undefined, then Let result be ? Call(exoticToPrim, input, « hint »). If Type(result) is not Object, return result. Throw a TypeError exception. If hint is "default", let hint be "number". Return ? OrdinaryToPrimitive(input, hint). When the abstract operation OrdinaryToPrimitive is called with arguments O and hint, the following steps are taken: Assert: Type(O) is Object. Assert: Type(hint) is String and its value is either "string" or "number". If hint is "string", then Let methodNames be « "toString", "valueOf" ». Else, Let methodNames be « "valueOf", "toString" ». For each name in methodNames in List order, do Let method be ? Get(O, name). If IsCallable(method) is true, then Let result be ? Call(method, O). If Type(result) is not Object, return result. Throw a TypeError exception. NOTE When ToPrimitive is called with no hint, then it generally behaves as if the hint were Number. However, objects may over-ride this behaviour by defining a @@toPrimitive method. Of the objects defined in this specification only Date objects (see 20.3.4.45) and Symbol objects (see 19.4.3.4) over-ride the default ToPrimitive behaviour. Date objects treat no hint as if the hint were String. En el caso de un objeto de tipo Array, el método para determinar el valor primitivo es join() de acuerdo a lo siguiente: 22.1.3.28 Array.prototype.toString ( ) When the toString method is called, the following steps are taken: Let array be ? ToObject(this value). Let func be ? Get(array, "join"). If IsCallable(func) is false, let func be the intrinsic function %ObjProto_toString%. Return ? Call(func, array). NOTE The toString function is intentionally generic; it does not require that its this value be an Array object. Therefore it can be transferred to other kinds of objects for use as a method.

Q: Modoboa 1.1.1 Deployment Errors I tried to install modoboa follow this steps: http://modoboa.readthedocs.org/en/latest/getting_started/install.html I installed modoboa with pip install modoboa: Traceback (most recent call last): File "manage.py", line 10, in <module> execute_from_command_line(sys.argv) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 453, in execute_from_command_line utility.execute() File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 392, in execute self.fetch_command(subcommand).run_from_argv(self.argv) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 272, in fetch_command klass = load_command_class(app_name, subcommand) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 77, in load_command_class module = import_module('%s.management.commands.%s' % (app_name, name)) File "/usr/local/lib/python2.7/dist-packages/django/utils/importlib.py", line 35, in import_module __import__(name) File "/usr/local/lib/python2.7/dist-packages/django/core/management/commands/syncdb.py", line 8, in <module> from django.core.management.sql import custom_sql_for_model, emit_post_sync_signal File "/usr/local/lib/python2.7/dist-packages/django/core/management/sql.py", line 9, in <module> from django.db import models File "/usr/local/lib/python2.7/dist-packages/django/db/__init__.py", line 40, in <module> backend = load_backend(connection.settings_dict['ENGINE']) File "/usr/local/lib/python2.7/dist-packages/django/db/__init__.py", line 34, in __getattr__ return getattr(connections[DEFAULT_DB_ALIAS], item) File "/usr/local/lib/python2.7/dist-packages/django/db/utils.py", line 93, in __getitem__ backend = load_backend(db['ENGINE']) File "/usr/local/lib/python2.7/dist-packages/django/db/utils.py", line 27, in load_backend return import_module('.base', backend_name) File "/usr/local/lib/python2.7/dist-packages/django/utils/importlib.py", line 35, in import_module __import__(name) File "/usr/local/lib/python2.7/dist-packages/django/db/backends/mysql/base.py", line 17, in <module> raise ImproperlyConfigured("Error loading MySQLdb module: %s" % e) django.core.exceptions.ImproperlyConfigured: Error loading MySQLdb module: No module named MySQLdb python manage.py syncdb --noinput failed, check your configuration Traceback (most recent call last): File "manage.py", line 10, in <module> execute_from_command_line(sys.argv) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 453, in execute_from_command_line utility.execute() File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 392, in execute self.fetch_command(subcommand).run_from_argv(self.argv) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 272, in fetch_command klass = load_command_class(app_name, subcommand) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 77, in load_command_class module = import_module('%s.management.commands.%s' % (app_name, name)) File "/usr/local/lib/python2.7/dist-packages/django/utils/importlib.py", line 35, in import_module __import__(name) File "/usr/local/lib/python2.7/dist-packages/django/core/management/commands/syncdb.py", line 8, in <module> from django.core.management.sql import custom_sql_for_model, emit_post_sync_signal File "/usr/local/lib/python2.7/dist-packages/django/core/management/sql.py", line 9, in <module> from django.db import models File "/usr/local/lib/python2.7/dist-packages/django/db/__init__.py", line 40, in <module> backend = load_backend(connection.settings_dict['ENGINE']) File "/usr/local/lib/python2.7/dist-packages/django/db/__init__.py", line 34, in __getattr__ return getattr(connections[DEFAULT_DB_ALIAS], item) File "/usr/local/lib/python2.7/dist-packages/django/db/utils.py", line 93, in __getitem__ backend = load_backend(db['ENGINE']) File "/usr/local/lib/python2.7/dist-packages/django/db/utils.py", line 27, in load_backend return import_module('.base', backend_name) File "/usr/local/lib/python2.7/dist-packages/django/utils/importlib.py", line 35, in import_module __import__(name) File "/usr/local/lib/python2.7/dist-packages/django/db/backends/mysql/base.py", line 17, in <module> raise ImproperlyConfigured("Error loading MySQLdb module: %s" % e) django.core.exceptions.ImproperlyConfigured: Error loading MySQLdb module: No module named MySQLdb python manage.py syncdb failed, check your configuration Unknown command: 'migrate' Type 'manage.py help' for usage. python manage.py migrate --fake failed, check your configuration Traceback (most recent call last): File "manage.py", line 10, in <module> execute_from_command_line(sys.argv) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 453, in execute_from_command_line utility.execute() File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 392, in execute self.fetch_command(subcommand).run_from_argv(self.argv) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 272, in fetch_command klass = load_command_class(app_name, subcommand) File "/usr/local/lib/python2.7/dist-packages/django/core/management/__init__.py", line 77, in load_command_class module = import_module('%s.management.commands.%s' % (app_name, name)) File "/usr/local/lib/python2.7/dist-packages/django/utils/importlib.py", line 35, in import_module __import__(name) File "/usr/local/lib/python2.7/dist-packages/django/core/management/commands/loaddata.py", line 11, in <module> from django.core import serializers File "/usr/local/lib/python2.7/dist-packages/django/core/serializers/__init__.py", line 22, in <module> from django.core.serializers.base import SerializerDoesNotExist File "/usr/local/lib/python2.7/dist-packages/django/core/serializers/base.py", line 5, in <module> from django.db import models File "/usr/local/lib/python2.7/dist-packages/django/db/__init__.py", line 40, in <module> backend = load_backend(connection.settings_dict['ENGINE']) File "/usr/local/lib/python2.7/dist-packages/django/db/__init__.py", line 34, in __getattr__ return getattr(connections[DEFAULT_DB_ALIAS], item) File "/usr/local/lib/python2.7/dist-packages/django/db/utils.py", line 93, in __getitem__ backend = load_backend(db['ENGINE']) File "/usr/local/lib/python2.7/dist-packages/django/db/utils.py", line 27, in load_backend return import_module('.base', backend_name) File "/usr/local/lib/python2.7/dist-packages/django/utils/importlib.py", line 35, in import_module __import__(name) File "/usr/local/lib/python2.7/dist-packages/django/db/backends/mysql/base.py", line 17, in <module> raise ImproperlyConfigured("Error loading MySQLdb module: %s" % e) django.core.exceptions.ImproperlyConfigured: Error loading MySQLdb module: No module named MySQLdb python manage.py loaddata initial_users.json failed, check your configuration Unknown command: 'collectstatic' Type 'manage.py help' for usage. python manage.py collectstatic --noinput failed, check your configuration I tried to install pip install MySQL-python but I received this error: Downloading/unpacking MySQL-python Downloading MySQL-python-1.2.5.zip (108kB): 108kB downloaded Running setup.py egg_info for package MySQL-python sh: mysql_config: orden no encontrada Traceback (most recent call last): File "<string>", line 16, in <module> File "/tmp/pip_build_root/MySQL-python/setup.py", line 17, in <module> metadata, options = get_config() File "setup_posix.py", line 43, in get_config libs = mysql_config("libs_r") File "setup_posix.py", line 25, in mysql_config raise EnvironmentError("%s not found" % (mysql_config.path,)) EnvironmentError: mysql_config not found Complete output from command python setup.py egg_info: sh: mysql_config: orden no encontrada Traceback (most recent call last): File "<string>", line 16, in <module> File "/tmp/pip_build_root/MySQL-python/setup.py", line 17, in <module> metadata, options = get_config() File "setup_posix.py", line 43, in get_config libs = mysql_config("libs_r") File "setup_posix.py", line 25, in mysql_config raise EnvironmentError("%s not found" % (mysql_config.path,)) EnvironmentError: mysql_config not found ---------------------------------------- Cleaning up... Command python setup.py egg_info failed with error code 1 in /tmp/pip_build_root/MySQL-python Storing complete log in /root/.pip/pip.log Seems that error is caused by MySQL module but I don't know how to resolve it. A: You should install the python mysqldb package provided with your distribution. On a debian/ubuntu one: $ apt-get install python-mysqldb

A small city in Iowa has taken an action to save the bees from extinction. Acres of land were donated to increase the local habitats of the bees. Over the past decade, bees are steadily disappearing. Worker bees disappear and leaving behind the queen. With a few nursing bees to take care of the immature bees, a colo… Read More To stay updated with the latest in the apiculture industry to can visit our beekeeping latest news. On the other hand if you are starting beekeeping and would like to begin professional beekeeping today download a copy of our beekeeping for beginners ebook. Beekeeping can be a full-time profession or a hobby that is simple. Nonetheless, more often than not, what started as a hobby would turn into a profession. But you cannot simply tell and decide yourself you will start to do beekeeping. Before starting on any avocation or profession, you need to have understanding and satisfactory knowledge on the subject that you are going to enter. If you’ve been putting off your interest in beekeeping for quite a while, then it’s about time to indulge yourself in your line of interest. Bee farming may seem simple; learning the basic beekeeping lessons can enable you to get away to a good start. What does a beekeeper need to understand? On beekeeping to start at the right foot you should have interest that is complete. You need to spend time taking care of your colonies of bees. You should have also agreed to share your home space with the bees. There are potential risks in beekeeping that can harm not only you but your family also. Your focus is not only to make money by selling honey; a good beekeeper should have passion and a keen interest in rearing bees. An apiarist should know the right place for the beehives. You have to make sure beekeeping is allowed in your area, if you decide to place your beehives at your backyard. There are several places restricted to beekeeping; you have to get permission concerning this. Beekeepers must know whether beekeeping supplies are available in the area where the beehives are situated. When you must go to a neighborhood beekeeping shop you may never understand; it is best that a nearby beekeeping store is reachable. Equipment and protective tools are also very important to beekeepers to know. Know the right kind of suit to choose to keep you from any possible danger in beekeeping. If you’re incapable to harvest honey from your bees all the efforts that are beekeeping would be futile. A beekeeper should know the methods in gathering the honey from the comb; beeswax is also part of the returns in beekeeping.

Defending champion Reilly Opelka and 2018 champ Kevin Anderson headline a stacked field of singles players committed to compete in this year’s New York Open men’s tennis tournament, which takes place Feb. 9-16 on the unique black courts at NYCB LIVE’s Nassau Veterans Memorial Coliseum. more The Kumon Method was founded in Japan in 1954. Toru Kumon, a high school math teacher, was trying to help his own child. Convinced that his second-grade son could be taught the necessary skills to understand advanced mathematics, he created . . . more After a number of residents urged the city to install mats on the barrier island’s beaches so that those with mobility issues can easily access Long Beach’s iconic shoreline, the city last week released a plan to do just that. more

Comparison of pulpal sensitivity between a conventional and two resin-modified glass ionomer luting cements. This clinical study compared handling and any short-term tooth sensitivity associated with using one conventional and two resin-modified glass ionomer cements marketed for luting gold and ceramometal crowns. The patient's response to a 10-second blast of air applied to the vital tooth was scored pre-operatively and again within a one-to-four week post-cementation recall period. A score was also recorded for any sensitivity present at the time of cementation of the crown on the unanesthetized tooth. All three cements were easy to mix and place. Most of the teeth had no response to pulpal stimulation pre-operatively, associated with the cementation procedure or post-cementation, and there were no instances of severe sensitivity recorded. For all cements, the level of post-cementation tooth sensitivity was similar, and less than that found pre-operatively.

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--- abstract: 'Dark Matter detectors with directional sensitivity have the potential of yielding an unambiguous positive observation of WIMPs as well as discriminating between galactic Dark Matter halo models. In this article, we introduce the motivation for directional detectors, discuss the experimental techniques that make directional detection possible, and review the status of the experimental effort in this field.' address: - 'Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA' - 'Temple University, 1900 N. 13-th Street, Philadelphia, PA 19122, USA' author: - G Sciolla - C J Martoff bibliography: - 'all\_DM.bib' title: Gaseous Dark Matter Detectors --- Introduction ============ Astronomical and cosmological observations have recently shown that Dark Matter (DM) is responsible for 23% of the energy budget of the Universe and 83% of its mass [@Hinshaw2008]. The most promising candidate for Dark Matter is the so-called Weakly Interacting Massive Particle (WIMP). The existence of WIMPs is independently suggested by considerations of Big Bang cosmology and theoretical supersymmetric particle phenomenology [@LeeWeinberg; @Weinberg82; @Jungman1996]. Over the years, many direct detection experiments have been performed to search for nuclear recoils due to elastic scattering of WIMPs off the nuclei in the active volume of the detector. The main challenge for these experiments is to suppress the backgrounds that mimic WIMP-induced nuclear recoils. Today’s leading experiments have achieved excellent rejection of electromagnetic backgrounds, i.e., photons, electrons and alpha particles, that have a distinct signature in the detector. However, there are sources of background for which the detector response is nearly identical to that of a WIMP-induced recoil, such as the coherent scattering of neutrinos from the sun [@Monroe2007], or the elastic scattering of neutrons produced either by natural radioactivity or by high-energy cosmic rays. While neutron and neutrino interactions do not limit today’s experiments, they are expected to become dangerous sources of background when the scale of DM experiments grows to fiducial masses of several tons. In traditional counting experiments, the presence of such backgrounds could undermine the unambiguous identification of a Dark Matter signal because neutrinos are impossible to suppress by shielding and underground neutron backgrounds are notoriously difficult to predict [@Mei2006]. An unambiguous positive identification of a Dark Matter signal even in presence of unknown amounts of irreducible backgrounds could still be achieved if one could correlate the observation of a nuclear recoil in the detector with some unique astrophysical signature which no background could mimic. This is the idea that motivates directional detection of Dark Matter. The Dark Matter Wind --------------------- The observed rotation curve of our Galaxy suggests that at the galactic radius of the sun the galactic potential has a significant contribution from Dark Matter. The Dark Matter distribution in our Galaxy, however, is poorly constrained. A commonly used DM distribution, the standard dark halo model [@SmithLewin1990], assumes a non-rotating, isothermal sphere extending out to 50 kpc from the galactic center. The DM velocity is described by a Maxwell-Boltzmann distribution with dispersion $\sigma_v=155$ km/s. Concentric with the DM halo is the galactic disk of luminous ordinary matter, rotating with respect to the halo, with an average orbital velocity of about 220 km/s at the radius of the solar system. Therefore in this model, an observer on Earth would see a wind of DM particles with average velocity of 220 km/s. The Dark Matter wind creates two observable effects. The first was pointed out in 1986 by Drukier, Freese, and Spergel [@Drukier1986] who predicted that the Earth’s motion relative to the galactic halo leads to an annual modulation of the rates of interactions observed above a certain threshold in direct detection experiments. In its annual rotation around the sun, the Earth’s orbital velocity has a component that is anti-parallel to the DM wind during the summer, and parallel to it during the winter. As a result, the apparent velocity of the DM wind will increase (decrease) by about 10% in summer (winter), leading to a corresponding increase (decrease) of the observed rates in DM detectors. Unfortunately, this effect is difficult to detect because the seasonal modulation is expected to be small (a few %) and very hard to disentangle from other systematic effects, such as the seasonal dependence of background rates. These experimental difficulties cast a shadow on the recent claimed observation of the yearly asymmetry by the DAMA/LIBRA collaboration [@Bernabei2008]. A larger modulation of the WIMP signal was pointed out by Spergel [@Spergel] in 1988. The Earth spins around its axis with a period of 24 sidereal hours. Because its rotation axis is oriented at 48$^\circ$ with respect to the direction of the DM wind, an observer on Earth sees the average direction of the WIMPs change by 96$^\circ$ every 12 sidereal hours. This modulation in arrival direction should be resolvable by a Dark Matter directional detector, e.g., a detector able to determine the direction of the DM particles. Most importantly, no known background is correlated with the direction of the DM wind. Therefore, a directional detector could hold the key to the unambiguous observation of Dark Matter. In addition to background rejection, the determination of the direction of the arrival of Dark Matter particles can discriminate [@Copi1999; @Vergados2003; @Morgan2004; @Freese2005; @Alenazi2008] between various DM halo distributions including the standard dark halo model, models with streams of WIMPs, the Sikivie late-infall halo model [@Sikivie1999; @Tkachev1997; @Sikivie1995], and other anisotropic models. The discrimination power is further enhanced if a determination of the sense as well as the direction of WIMPs is possible [@Green2007]. This capability makes directional detectors unique observatories for underground WIMP astronomy. Directional Dark Matter Detection ----------------------------------- When Dark Matter particles interact with regular matter, they scatter elastically off the atoms and generate nuclear recoils with typical energies $E_R$ of a few tens of keV, as explained in more detail in section \[NuclearRecoils\]. The direction of the recoiling nucleus encodes the direction of the incoming DM particle. To observe the daily modulation in the direction of the DM wind, an angular resolution of 20–30 degrees in the reconstruction of the recoil nucleus is sufficient, because the intrinsic spread in direction of the DM wind is $\approx$ 45 degrees. Assuming that sub-millimeter tracking resolution can be achieved, the length of a recoil track has to be of at least 1–2 mm, which can be obtained by using a very dilute gas as a target material. An ideal directional detector should provide a 3-D vector reconstruction of the recoil track with a spatial resolution of a few hundred microns in each coordinate, and combine a very low energy threshold with an excellent background rejection capability. Such a detector would be able to reject isotropy of the recoil direction, and hence identify the signature of a WIMP wind, with just a handful of events [@Morgan2004]. More recently, Green and Morgan [@Green2007] studied how the number of events necessary to detect the WIMP wind depends on the detector performance in terms of energy threshold, background rates, 2-D versus 3-D reconstruction of the nuclear recoil, and ability to determine the sense of the direction by discriminating between the “head” and “tail” of the recoil track. The default configuration used for this study assumes a CS$_2$ gaseous TPC running at 0.05 bar using 200 $\mu$m pixel readout providing 3-D reconstruction of the nuclear recoil and “head-tail” discrimination. The energy threshold is assumed to be 20 keV, with perfect background rejection. In such a configuration, 7 events would be sufficient to establish observation of the WIMP wind at 90% C.L.. In presence of background with S/N=1, the number of events necessary to reject isotropy would increase by a factor 2. If only 2D reconstruction is available, the required number of events doubles compared to the default configuration. “Head-tail” discrimination turns out to be the most important capability: if the sense cannot be measured, the number of events necessary to observe the effects of the WIMP wind increases by one order of magnitude. Nuclear Recoils in Gaseous Detectors {#NuclearRecoils} ==================================== To optimize the design of gaseous detectors for directional detection of Dark Matter one must be able to calculate the recoil atom energy spectrum expected for a range of WIMP parameters and halo models. The detector response in the relevant energy range must also be predictable. The response will be governed first and foremost by the track length and characteristics (multiple scattering) as a function of recoil atom type and energy. Since gas detectors require ionization for detection, design also requires knowledge of the ionization yield in gas and its distribution along the track as a function of recoil atom type and energy, and possibly electric field. The large momentum transfer necessary to produce a detectable recoil in gas implies that the scattering atom can be treated as a free particle, making calculations of the recoil spectrum essentially independent of whether the target is a solid, liquid, or gas. An estimate of the maximum Dark Matter recoil energy for simple halo models is given by the kinematically allowed energy transfer from an infinitely heavy halo WIMP with velocity equal to the galactic escape speed. This speed is locally about 500-600 km/sec [@rave]; WIMPS with higher velocities than this would not be gravitationally bound in the halo and would presumably be rare. The corresponding maximum energy transfer amounts to $<$ 10 keV/nucleon. The integrated rate will be concentrated at lower energies than this, at least in halo models such as the isothermal sphere. For that model, the recoil energy ($E_R$) distribution [@SmithLewin1990] is proportional to $\exp(-E_R/E_I)$, with $E_I$ a constant that depends on the target and WIMP masses and the halo model. For a 100 GeV WIMP and the isothermal halo model parameters of Ref. [@SmithLewin1990], $E_I / A$ varies from 1.05 to 0.2 keV/nucleon for target mass numbers from 1 to 131. These are very low energy particles, well below the Bragg Peak at $\sim$200–800 keV/A. In this regime dE/dx [*decreases*]{} with decreasing energy, and the efficiency of ionization is significantly reduced. Lindhard Model for Low-Energy Stopping -------------------------------------- The stopping process for such low energy particles in homoatomic[^1] substances was treated by Lindhard, Scharff, and Schiott [@Lindhard1963; @Lindhard-int] (LSS). This treatment has stood the test of time and experiment, making it worthwhile to summarize the results here. As is now well-known, the primary energy loss mechanisms for low energy particles in matter can be divided into “nuclear stopping”, due to atom-atom scattering, and “electronic stopping”, due to atom-electron scattering. These mechanisms refer only to the initial interaction causing the incident particle to lose energy. Nuclear stopping eventually contributes to electronic excitations and ionization, and electronic stopping eventually contributes to thermal excitations [@Lindhard-int]. In Ref. [@Lindhard1963] the stopping is described using a Thomas-Fermi atom model to obtain numerical results for universal stopping-power curves in terms of two variables, the scaled energy $\epsilon=E_R/E_{TF}$, and the scaled range $\rho=R/R_{TF}$, where $E_R$ and $R$ are respectively the energy and the stopping distance of the recoil, and $E_{TF}$ and $R_{TF}$ are scale factors[^2]. In Ref. [@Lindhard1963] it was shown that nuclear stopping dominates in the energy range where most of the rate for Dark Matter detection lies. This can be seen as follows. The scaled variables $\epsilon$ and $\rho$ depend algebraically on the atomic numbers and mass numbers of the incident and target particles. The scale factor $E_{TF}$ corresponds to 0.45 keV/nucleon for homoatomic recoils in Carbon, 1.7 keV/nucleon for Ar in Ar and 6.9 keV/nucleon for Xe in Xe. Nuclear stopping $\frac{d\epsilon_n}{d\rho}$ was found to be larger than the electronic stopping $\frac{d\epsilon_e}{d\rho}$ for $\epsilon < 1.6$, which covers the energy range $0 < E_R < E_I$ where most of the Dark Matter recoil rate can be expected. Because of the dominance of nuclear stopping, detectors can be expected to respond differently to Dark Matter recoils than to radiations such as x-rays or even $\alpha$ particles, for which electronic stopping dominates. Nuclear stopping yields less ionization and electronic excitation per unit energy loss than does electronic stopping, implying that the W factor, defined as the energy loss required to create one ionization electron, will be larger for nuclear recoils. Reference [@Lindhard-int] presents calculations of the ultimate energy loss partitioning between electronic and atomic motion. Experimenters use empirical “quenching factors" to describe the variation of energy per unit of ionization (the “W" parameter) compared to that from x-rays. The different microscopic distribution of ionization in tracks dominated by nuclear stopping can also lead to unexpected changes in the interactions of ionized and electronically excited target atoms (e.g., dimer formation, recombination). Such interactions are important for particle identification signatures such as the quantity and pulse shape of scintillation light output, the variation of scintillation pulse shape with applied electric field, and the field variation of ionization charge collection efficiency. Such effects are observed in gases [@White2007; @Martin2009], and even more strongly in liquid and solid targets [@Aprile2006]. Electronic stopping [@Lindhard1963] was found to vary as $\frac{d\epsilon_e}{d\rho} = k \sqrt{\epsilon}$ with the parameter $k$ varying only from 0.13 to 0.17 for homonuclear recoils in A=1 to 131[^3]. Let us define the total stopping as $\frac{d\epsilon}{d\rho}= \frac{d\epsilon_n}{d\rho} + \frac{d\epsilon_e}{d\rho}$ and the total scaled range as $\rho_o = \int _0 ^\epsilon \frac{d\epsilon}{(\frac{d\epsilon}{d\rho})}$. The relatively small contribution of electronic stopping and the small variation in $k$ for homoatomic recoils, makes the total scaled range for this case depend on the target and projectile almost entirely through $E_{TF}$. Predictions for the actual range of homoatomic recoils can be obtained from the nearly-universal scaled range curve as follows. Numerically integrating the stopping curves of Ref. [@Lindhard1963] with $k$ set to 0.15 gives a scaled range curve that fits the surprisingly simple expression $$\rho_o \stackrel{.}{=} 2.04 \epsilon + 0.04 \label{eq:range}$$ with accuracy better than 10% for $0.12 < \epsilon < 10 $. According to the formula given earlier, the scale factor $R_{TF}$ lies between 1 and 4 $\times$ 10$^{17}$ atoms/cm$^2$ for homoatomic recoils in targets with $12 \leq A \leq 131$. Thus the model predicts ranges of several times 10$^{17}$ atoms/cm$^2$ at $E_R = E_I$. This is of the order of a few mm for a monoatomic gas at 0.05 bar. As a consequence, tracking devices for Dark Matter detection must provide accurate reconstruction of tracks with typical lengths between 1 and a few mm while operating at pressures of a small fraction of an atmosphere. When comparing LSS predictions with experimental results, two correction factors must be considered. First, the widely-used program SRIM [@SRIM] produces range-energy tables which contain the “projected range", while LSS calculate the path length along the track. On the other hand, many older experiments report “extrapolated ranges", which are closer in magnitude to the path length than to the “projected range". To compare the SRIM tables with LSS, the projected range should be multiplied by a factor [@Lindhard1963] $(1+\frac{M_T}{3M_P})$ where $M_T$ and $M_P$ are the target and projectile masses. This correction has generally been applied in the next section, where experimental data are discussed. In addition, it must be noted that the LSS calculations described above were obtained for solids. Therefore, one should consider a gas-solid correction in ranges and stopping powers, as discussed by Bohr, Lindhard and Dan [@BLD]. In condensed phases, the higher collision frequency results in a higher probability for stripping of excited electrons before they can relax, which leads to a higher energy loss rate than for gases. This correction is rather uncertain and has generally not been applied in the following section of this paper. Finally, numerical calculations to extend the LSS model to the case of targets of mixed atomic number are given in Ref. [@Hitachi2008]. Experimental Data on Low Energy Stopping in Gases ------------------------------------------------- The literature of energy loss and stopping of fast particles in matter is vast and still growing [@Ziegler1985; @Sigmund1998]. However, there is not a lot of experimental data available for particle ranges and ionization yields in gas at the very low energies typical of Dark Matter recoils, where E/A $\sim$ 1 keV per nucleon. Comprehensive collections of citations for all energies are available [@SRIM; @MSTAR], upon which the widely-used theory-guided-fitting computer programs SRIM and MSTAR [@MSTAR] are based. Several older references [@Evans1953; @Lassen1964; @Cano1968] still appear representative of the available direct measurements at very low energy. More recent studies [@SnowdenIfft2003] provide indirect information based on large detector simulations. Both references [@Evans1953] and [@Lassen1964] used accelerated beams of He, N, Ne, Ar and $^{24}$Na, $^{66}$Ga, and $^{198}$Au in differentially pumped gas target chambers filled with pure-element gases. In [@Evans1953] the particles were detected with an ionization chamber, while in [@Lassen1964] radioactive beams were used. The stopped particles were collected on segmented walls of the target chamber and later counted. Typical results were ranges of 2(3.2) $\times$ 10$^{17}$ atoms/cm$^2$ for 26(40) keV Ar$^+$ in Argon. The fit to LSS theory given above predicts ranges that are shorter than the experimental results by 10-40%, which is consistent with experimental comparisons given by LSS. Accuracy of agreement with the prediction from the SRIM code is about the same. As in all other cases discussed below, the direction of the deviation from LSS is as expected from the gas-solid effect mentioned in the previous section. In Ref. [@SnowdenIfft2003] nuclear recoils from $^{252}$Cf neutrons were recorded by a Negative Ion Time Projection Chamber (NITPC) filled with 40 Torr CS$_2$. The device was simulated fitting the observed pulse height and event size distributions. The best fit range curves given for C and S recoils in the gas are 10-20% higher at 25-100 keV than LSS predictions computed by the present authors by assuming simple additivity of stopping powers for the constituent atoms of the polyatomic gas target. Ionization Yields ----------------- Tracking readouts in gas TPC detectors are sensitive only to ionization of the gas. As noted above, both nuclear and electronic stopping eventually contribute to both electronic excitations (including ionization) and to kinetic energy of target atoms, as primary and subsequent generations of collision products interact further with the medium. Some guidance useful for design purposes is available from Ref. [@Lindhard-int], where the energy cascade was treated numerically using integral equations. In terms of the scaled energy $\epsilon$ and the electronic stopping coefficient $k$ introduced above, the (scaled) energy $\eta$ ultimately transferred to electrons was found to be well approximated [@SmithLewin1996] by $\eta = \frac{\epsilon}{1+\frac{1}{k\dot g(\epsilon)}}$ with $g(\epsilon)= \epsilon + 3 \epsilon^{0.15} + 0.7 \epsilon^{0.6}$. This function interpolates smoothly from $\eta = 0$ at $\epsilon = 0$ to $\eta = \epsilon$ for $\epsilon \rightarrow \infty$, giving $\eta = 0.4$ at $\epsilon = 1$. In other words, this theory predicts only about 40% as much ionization per unit of energy deposited by Dark Matter recoils as by low LET radiation such as electrons ejected by x-rays. Several direct measurements of total ionization by very low energy particles are available in literature. Many of these results are for recoil nuclei from alpha decays [@Cano1965; @Cano1968; @Stone1957]. These $\sim$ 100 keV, A $\sim$ 200 recoils are of interest as backgrounds in Dark Matter experiments, but their scaled energy $\epsilon \cong 0.07$ is below the range of interest for most WIMP recoils. Measured ionization yield parameters W were typically 100-120 eV/ion pair, in good agreement with the approximate formula for $\eta$ given above. Data more applicable to Dark Matter recoils are given in Refs. [@Phipps1964; @Boring1965; @McDonald1969; @Price1993]. Some representative results from these works include [@Boring1965] W = 91 (65) eV/IP for 25 (100) keV Ar in Ar, both values about 20% higher than would be predicted by the preceding approximate LSS expression. Higher W for gases than for condensed media is expected [@BLD] as mentioned above. Ref. [@McDonald1969] measured total ionization from particles with 1 $<$ Z $<22$ in methane. While in principle the LSS treatment does not apply to heteroatomic gases, using the LSS prescription to predict the W factor for a carbon target (rather than methane) yields a value that is 15% lower than the experimental results. The authors of Ref. [@SnowdenIfft2003] also fit their data to derive W-values for C and S recoils. Their best-fit values are again 10-25% higher than an LSS-based estimate by the present author using additivity. To summarize, most of the Dark Matter recoils expected from an isothermal galactic halo have very low energies, and therefore nuclear stopping plays an important role. The sparse available experimental data on track lengths and ionization yields agrees at the $\sim$20% level with simple approximate formulas based on the Lindhard model. Without applying any gas-phase correction, LSS-based estimates for range tend to be slightly longer than those experimentally measured in gases. The predicted ionization parameter W also tends to be slightly lower than the experimental data. This situation is adequate for initial design of detectors, but with the present literature base, each individual experiment will require its own dedicated calibration measurements. Considerations for Directional Detector Design ============================================== Detector Architecture --------------------- From the range-energy discussion in the previous section, we infer that track lengths of typical Dark Matter recoils will be only of the order of 0.1 $\mu$m in condensed matter, while track lengths of up to a few millimeters are expected in gas at a tenth of the atmospheric pressure. Several techniques relevant to direction-sensitive detection using condensed matter targets have been reported, including track-etch analysis of ancient mica [@Bander1995], bolometric detection of surface sputtered atoms [@Martoff1996], and use of nuclear emulsions [@Natsume2007]. The ancient mica etch pit technique was actually used to obtain Dark Matter limits. However, recently the focus of directional Dark Matter detection has shifted to low-pressure gas targets, and that is the topic of the present review. The TPC [@NygrenTPC; @Fancher1979] is the natural detector architecture for gaseous direction-sensitive Dark Matter detectors, and essentially all experiments use this configuration. The active target volume contains only the active gas, free of background-producing material. Only one wall of the active volume requires a readout system, leading to favorable cost-volume scaling. TPCs with nearly 100 m$^3$ of active volume have been built for high energy physics, showing the possibility of large active masses. Background Rejection Capabilities ---------------------------------- Gaseous DM detectors have excellent background rejection capability for different kinds of backgrounds. First and foremost, direction sensitivity gives gas detectors the capability of statistically rejecting neutron and neutrino backgrounds. In addition, tracking also leads to extremely effective discrimination against x-ray and $\gamma$-ray backgrounds [@Snowden-Ifft:PRD2000; @Sciolla:2009fb]. The energy loss rates for recoils discussed in the previous section are hundreds of times larger than those of electrons with comparable total energy. The resulting much longer electron tracks are easily identified and rejected in any direction-sensitive detector. Finally, the measured rejection factors for gamma rays vs. nuclear recoils varies between 10$^4$ and 10$^6$ depending on the experiment [@Miuchi2007-58; @SnowdenIfft2003; @Dujmic2008-58]. Choice of Pressure ------------------ It can be shown that there is an optimum pressure for operation of any given direction sensitive WIMP recoil detector. This optimum pressure depends on the fill gas, the halo parameter set and WIMP mass, and the expected track length threshold for direction measurement. The total sensitive mass, and hence the total number of expected events, increases proportionally to the product of the pressure $P$ and the active volume $V$. Equation \[eq:range\] above shows that the range in atoms/cm$^2$ for WIMP recoils is approximately proportional to their energy. Since the corresponding range in cm is inversely proportional to the pressure ($R \propto E_r/P$), the energy threshold imposed by a particular minimum track length $E_{r,min}$ will scale down linearly with decreasing pressure, $E_{r,min} \propto R_{min} P$, where $R_{min}$ is the shortest detectable track length. For the exponentially falling recoil energy spectrum of the isothermal halo [@SmithLewin1996] the fraction of recoils above a given energy threshold is proportional to $\exp(-E_{min}/E_0 r)$. Hence the rate of tracks longer than the tracking threshold R$_{min}$ will scale as $N \propto PV \exp(-\xi R_{min}P)$, with $\xi$ a track length factor depending on the target gas, WIMP mass, halo model, etc., and the track length threshold $R_{min}$ depending on the readout technology and the drift distance. This expression has a maximum at $P_{opt} = 1/[\xi R_{min}]$, which shows that the highest event rate is obtained by taking advantage of improvement in tracking threshold to run at higher target pressure. Operating at this optimum pressure, the track-able event rate still scales as $P_{opt}V$, which increases linearly as the tracking threshold decreases. Achieving the shortest possible tracking threshold $R_{min}$ is seen to be the key to sensitive experiments of this type. Tracking Limit due to Diffusion ------------------------------- Diffusion of track charge during its drift to the readout plane sets the ultimate limit on how short a track can be measured in a TPC. Diffusion in gases has a rich phenomenology for which only a simplified discussion is given here. More complete discussion with references to the literature is given by Rolandi and Blum [@RnB]. For low values of electric fields, elementary kinetic theory arguments predict equal transverse and longitudinal diffusion to the drift field $E_d$, with the rms diffusion spread $\delta$ given by $$\label{eq:diff} \delta = \sqrt{\frac{2kTL}{eE_d}} = 0.7 mm \sqrt{\frac{[L/1m]}{[E_d/1 kV/cm]}}.$$ Here $k$ is the Boltzmann constant, $T$ the gas temperature, and $L$ the drift distance. No pressure or gas dependence appears in this equation. The diffusion decreases inversely as the square root of the applied drift field. Increasing the drift field would appear to allow diffusion to be reduced as much as desired, allowing large detectors to be built while preserving good tracking resolution. However, in reality diffusion is not so easily controlled. The low-field approximation given by Equation \[eq:diff\] holds only below a certain maximum drift field value $E_d^{max}$, which depends on the pressure and target gas. The drift field must not violate the condition $eE_d^{max} \lambda << kT$, where the effective mean free path $\lambda = 1/f n \sigma$ decreases inversely as the pressure. Here $\sigma$ is the average total cross section for scattering of the drifting species on the fill gas molecules, $n$ is the number density of molecules, and $f$ is an energy-exchange-efficiency factor for the scattering of charge carriers from gas molecules. This condition amounts to requiring that the work done by the drift field on a charge carrier between collisions and not lost to collisions, must be much smaller than the carrier’s thermal energy. If this condition is fulfilled it will ensure that the drifting carriers’ random (thermal) velocity remains consistent with the bulk gas temperature. A larger scattering cross section $\sigma$ or a more effective energy exchange due to strong inelastic scattering processes will lead to a shorter effective mean free path and a larger value of $E_d^{max}$. Importantly, $E_d^{max}$ for electrons in a given gas generally scales inversely as the pressure, as would be expected from the presence of the mean free path in the “low field" condition. If the drift field exceeds $E_d^{max}$, the energy gained from the drift field becomes non-negligible. The average energy of drifting charge carriers begins to increase appreciably, giving them an effective temperature $T_{eff}$ which can be orders of magnitude larger than that of the bulk gas. Under these conditions, the kinetic theory arguments underlying equation \[eq:diff\] remain approximately valid if the gas temperature $T$ is replaced by $T_{eff}$. Diffusion stops dropping with increasing drift field and may rapidly [ *increase*]{} in this regime, with longitudinal diffusion increasing more rapidly than transverse. Values of $E_d^{max}/P$ for electrons drifting in various gases and gas mixtures vary from $\sim$0.1–1 V/cm/Torr at 300 K [@SauliBible; @Caldwell]. With drift fields limited to this range and a gas pressure of $\sim$ 50 Torr, the rms diffusion for a 1 meter drift distance would be several mm, severely degrading the tracking resolution. Effects of diffusion can be significantly reduced by drifting negative ions instead of electrons [@Martoff2000; @Martoff2009; @Ohnuki:NIMA2001]. Electronegative vapors have been found which, when mixed into detector gases, reversibly capture primary ionization electrons within $\sim$ 100 $\mu$m of their creation. The resulting negative ions drift to the gain region of the chamber, where collisional processes free the electrons and initiate normal Townsend avalanches [@Dion2009]. Ions have E$_d^{max}$ values corresponding to E/P = 20 V/cm Torr and higher. This is because the ions’ masses are comparable to the gas molecules, so the energy-exchange-efficiency factor $f$ which determines $E_d^{max}$ is much larger than for electrons. Ion-molecule scattering cross sections also tend to be larger than electron-molecule cross sections. The use of negative ion drift in TPCs would allow sub-millimeter rms diffusion for drift distances of 1 meter or larger, although total drift voltage differences in the neighborhood of 100 kV would be required. The above outline shows that diffusion places serious constraints on the design of detectors with large sensitive mass and millimeter track resolution, particularly when using a conventional electron drift TPC. Challenges of Directional Detection ------------------------------------ The current limits on spin-independent interactions of WIMPs in the 60 GeV/c$^2$ mass range have been set using 300-400 kg-day exposures, for example by the XENON10 [@XENON2008] and CDMS [@CDMS2009] experiments. Next generation non-directional experiments are being planned to achieve zero background with hundreds or thousands of times larger exposures [@Arisaka2009]. To be competitive, directional detectors should be able to use comparable exposures. However, integrating large exposures is particularly difficult for low-pressure gaseous detectors. A fiducial mass of a few tons will be necessary to observe DM-induced nuclear recoils for much of the theoretically-favored range of parameter space [@Jungman1996]. This mass of low-pressure gas would occupy thousands of cubic meters. It is, therefore, key to the success of the directional DM program to develop detectors with a low cost per unit volume. Since for standard gaseous detectors the largest expense is represented by the cost of the readout electronics, it follows that a low-cost read-out is essential to make DM directional detectors financially viable. Dark Matter TPC Experiments =========================== Early History of Direction-Sensitive WIMP Detectors --------------------------------------------------- As early as 1990, Gerbier [*et al.*]{} [@Gerbier1990] discussed using a hydrogen-filled TPC at 0.02 bar, drifting electrons in a 0.1 T magnetic field to detect proton recoils from Dark Matter collisions. This proposal was made in the context of the “cosmion", a then-current WIMP candidate with very large (10$^{-36}$ cm$^2$) cross section for scattering on protons. These authors explicitly considered the directional signature, but they did not publish any experimental findings. A few years later, the UCSD group led by Masek [@Buckland1994] published results of early trials of the first detector system specifically designed for a direction-sensitive Dark Matter search. This pioneering work used optical readout of light produced in a parallel plate avalanche counter (PPAC) located at the readout plane of a low-pressure TPC. The minimum discernible track length was about 5 mm. Electron diffusion at low pressures and its importance for the performance of gas detectors was also studied [@MattDiff]. This early work presaged some of the most recent developments in the field, described in section \[DMTPC\]. DRIFT ----- The DRIFT-I collaboration [@Snowden-Ifft:PRD2000] mounted the first underground experiment designed for direction sensitive WIMP recoil detection [@Alner2004]. Re-designed detectors were built and further characterization measurements were performed by the DRIFT-II [@Lawson2005] collaboration. Both DRIFT detectors were cubical 1 m$^3$ negative-ion-drifting TPCs with two back-to-back 0.5 m drift spaces. To minimize material possibly contributing radioactive backgrounds, the central drift cathode was designed as a plane of 20 micron wires on 2 mm pitch. The endcap MWPCs used 20 $\mu$m anode wires on 2 mm-pitch, read out with transient digitizers. In DRIFT-II the induced signals on grid wires between the MWPC anode and the drift space were also digitized. DRIFT-I had an amplifier- and digitizer-per-wire readout, while DRIFT-II signals were cyclically grouped onto a small number of amplifiers and digitizers. Both detectors used the negative ion drift gas CS$_2$ at nominally 40 Torr, about one eighth of the atmospheric pressure. The 1 m$^3$ volume gave approximately 170 grams of target mass per TPC. The CS$_2$ gas fill allowed diffusion suppression by running with very high drift fields despite the low pressure. DRIFT-II used drift fields up to 624 V/cm (16 V/cm/Torr). The detectors were calibrated with alpha particles, $^{55}$Fe x-rays and $^{252}$Cf neutrons. Alpha particle Bragg peaks and neutron recoil events from sources were quickly seen after turn-on of DRIFT-I underground in 2001. Neutron exposures gave energy spectra in agreement with simulations when the energy per ion pair W was adjusted in accordance with the discussion of ionization yields given above. Simulations of DRIFT-II showed that the detector and software analysis chain had about 94% efficiency for detection of those $^{252}$Cf neutron recoils producing between 1000 and 6000 primary ion pairs, and a $^{60}$Co gamma-ray rejection ratio better than a few times 10$^{-6} $ [@drift_II_n]. A study of the direction sensitivity of DRIFT-II for neutron recoils [@driftIIfb] showed that a statistical signal distinguishing the beginning and end of Sulfur recoil tracks (“head-tail discrimination") was available, though its energy range and statistical power was limited by the 2 mm readout pitch. At present two 1 m$^3$ DRIFT-II modules are operating underground. Backgrounds due to radon daughters implanted in the internal surfaces of the detector [@drift_II_n] are under study and methods for their mitigation are being developed. The absence of nonzero spin nuclides in the CS$_2$ will require a very large increase in target mass or a change of gas fill in order to detect WIMPs with this device. Dark Matter Searches Using Micropattern Gas-Gain Devices -------------------------------------------------------- It was shown above that the event rate and therefore the sensitivity of an optimized tracking detector improves linearly as the track length threshold gets smaller. In recent years there has been widespread development of gas detectors achieving very high spatial resolution by using micropatterned gain elements in place of wires. For a recent overview of micropattern detector activity, see Ref. [@pos-sens]. These devices typically have 2-D arrays of individual gain elements on a pitch of $\sim$ 0.1 mm. Rows of elements [@Black2007] or individual gain elements can be read out by suitable arrangements of pickup electrodes separate from the gain structures, or by amplifier-per-pixel electronics integrated with the gain structure [@medipix]. Gain-producing structures known as GEM (Gas Electron Multiplier [@gem]) and MicroMegas (MICRO-MEsh GAseous Structure [@Giomataris1996]) have found particularly wide application. The gas CF$_4$ also figures prominently in recent micropattern Dark Matter search proposals. This gas was used for low background work in the MUNU experiment [@munu] and has the advantage of high $E_d^{max}$, allowing relatively low diffusion for electron drift at high drift field and reduced pressure [@Dujmic2008-327; @Christo1996; @Caldwell], though it does not approach negative ions in this regard. Containing the odd-proton nuclide $^{19}$F is also an advantage since it confers sensitivity to purely spin-coupled WIMPs [@Ellis1991], allowing smaller active mass experiments to be competitive. Another attractive feature of CF$_4$ is that its Townsend avalanches copiously emit visible and near infrared light [@Pansky1995; @Kaboth2008; @Fraga2003], allowing optical readout as in the DMTPC detector discussed in section \[DMTPC\]. The ultraviolet part of the spectrum may also be seen by making use of a wavelength shifter. Finally, CF$_4$ is non-flammable and non-toxic, and, therefore, safe to operate underground. The NEWAGE project is a current Dark Matter search program led by a Kyoto University group. This group has recently published the first limit on Dark Matter interactions derived from the absence of a directional modulation during a 0.15 kg-day exposure [@Miuchi2007-58]. NEWAGE uses CF$_4$-filled TPCs with a microwell gain structure [@Miuchi2003; @Tanimori2004; @Miuchi2007-43]. The detector had an active volume of 23 x 28 x 30 cm$^3$ and contained CF$_4$ at 150 Torr. Operation at higher-than-optimal gas pressure was chosen to enhance the HV stability of the gain structure. The chamber was read out by a single detector board referred to as a “$\mu$-PIC", preceded by a GEM for extra gas gain. The $\mu$-PIC has a micro-well gain structure produced using multi-layer printed circuit board technology. It is read out on two orthogonal, 400 micron-pitch arrays of strips. One array is connected to the central anode dots of the micro-well gain structure, and the other array to the surrounding cathodes. The strip amplifiers and position decoding electronics are on-board with the gain structures themselves, using an 8 layer PCB structure. The detector was calibrated with a $^{252}$Cf neutron source. Nuclear recoils were detected and compared to a simulation, giving a detection efficiency rising from zero at 50 keV to 90% near 250 keV. For comparison, the maximum energy of a $^{19}$F recoil from an infinitely heavy WIMP with the galactic escape speed is about 180 keV. The measured rejection factor for $^{137}$Cs gamma rays was about 10$^{-4}$. The angular resolution was reported as 25$^{\circ}$ HWHM. Measurement of the forward/backward sense of the tracks (“head-tail" discrimination) was not reported. Another gaseous Dark Matter search collaboration known as MIMAC [@santos2006] is led by a group at IPN Grenoble, and has reported work toward an electronically read-out direction sensitive detector. They proposed the use of $^3$He mixtures with isobutane near 1 bar, and also CF$_4$ gas fills to check the dependence on the atomic number A of any candidate Dark Matter signal. The advantages claimed for $^3$He as a Dark Matter search target include nonzero nuclear spin, low mass and hence sensitivity to low WIMP masses, and a very low Compton cross section which suppresses backgrounds from gamma rays. The characteristic (n,p) capture interaction with slow neutrons gives a strong signature for the presence of slow neutrons. The ionization efficiency of $\sim$ 1 keV $^3$He recoils is also expected to be very high, allowing efficient detection of the small energy releases expected for this target and for light WIMPs. A micropattern TPC with $\sim$ 350 $\mu$m anode pitch was proposed to obtain the desired electron rejection factor at a few keV. The MIMAC collaboration uses an ion source to generate monoenergetic $^3$He and F ions for measuring the ionization yield in their gas mixtures [@Guillaudin:2009fp]. DMTPC {#DMTPC} ----- The Dark Matter Time Projection Chamber (DMTPC) collaboration has developed a new detector concept [@Sciolla:2009fb] that addresses the issue of scalability of directional Dark Matter detectors by using optical readout, a potentially very inexpensive readout solution. The DMTPC detector [@Sciolla:2008ak; @Sciolla:2008mpla] is a low-pressure TPC filled with CF$_4$ at a nominal pressure of 50 torr. The detector is read out by an array of CCD cameras and photomultipliers (PMTs) mounted outside the vessel to reduce the amount of radioactive material in the active volume. The CCD cameras image the visible and near infrared photons that are produced by the avalanche process in the amplification region, providing a projection of the 3-D nuclear recoil on the 2-D amplification plane. The 3-D track length and direction of the recoiling nucleus is reconstructed by combining the measurement of the projection along the amplification plane (from pattern recognition in the CCD) with the projection along the direction of drift, determined from the waveform of the signal from the PMTs. The sense of the recoil track is determined by measuring dE/dx along the length of the track. The correlation between the energy of the recoil, proportional to the number of photons collected in the CCD, and the length of the recoil track provides an excellent rejection of all electromagnetic backgrounds. Several alternative implementations of the amplification region [@Dujmic2008-58] were developed. In a first design, the amplification was obtained by applying a large potential difference ($\Delta$V = 0.6–1.1 kV) between a copper plate and a conductive woven mesh kept at a uniform distance of 0.5 mm. The copper or stainless steel mesh was made of 28 $\mu$m wire with a pitch of 256 $\mu$m. In a second design the copper plate was replaced with two additional woven meshes. This design has the advantage of creating a transparent amplification region, which allows a substantial cost reduction since a single CCD camera can image tracks originating in two drift regions located on either side of a single amplification region. The current DMTPC prototype [@dujmicICHEP] consists of two optically independent regions contained in one stainless steel vessel. Each region is a cylinder with 30 cm diameter and 20 cm height contained inside a field cage. Gas gain is obtained using the mesh-plate design described above. The detector is read out by two CCD cameras, each imaging one drift region. Two f/1.2 55 mm Nikon photographic lenses focus light onto two commercial Apogee U6 CCD cameras equipped with Kodak 1001E CCD chips. Because the total area imaged is $16\times16$ cm$^2$, the detector has an active volume of about 10 liters. For WIMP-induced nuclear recoils of 50 keV, the energy and angular resolutions obtained with the CCD readout were estimated to be $\approx$ 15% and 25$^{\circ}$, respectively. This apparatus is currently being operated above ground with the goal of characterizing the detector response and understanding its backgrounds. A second 10-liter module is being constructed for underground operations at the Waste Isolation Pilot Plant (WIPP) in New Mexico. A 5.5 MeV alpha source from $^{241}$Am is used to study the gain of the detector as a function of the voltage and gas pressure, as well as to measure the resolution as a function of the drift distance of the primary electrons to quantify the effect of the transverse diffusion. These studies [@Dujmic2008-327; @Caldwell] show that the transverse diffusion allows for a sub-millimeter spatial resolution in the reconstruction of the recoil track for drift distances up to 20–25 cm. The gamma ray rejection factor, measured using a $^{137}$Cs source, is better than 2 parts per million [@Dujmic2008-327]. The performance of the DMTPC detector in determining the sense and direction of nuclear recoils has been evaluated by studying the recoil of fluorine nuclei in interaction with low-energy neutrons. The initial measurements were obtained running the chamber at 280 Torr and using 14 MeV neutrons from a deuteron-triton generator and a $^{252}$Cf source. The “head-tail” effect was clearly observed [@Dujmic2008-327; @Dujmic:2008iq] for nuclear recoils with energy between 200 and 800 keV. Better sensitivity to lower energy thresholds was achieved by using higher gains and lowering the CF$_4$ pressure to 75 torr. These measurements demonstrated [@Dujmic2008-58] “head-tail” discrimination for recoils above 100 keV, and reported a good agreement with the predictions of the SRIM [@SRIM] simulation. “Head-tail” discrimination is expected to extend to recoils above 50 keV when the detector is operated at a pressure of 50 torr. To evaluate the event-by-event “head-tail” capability of the detector as a function of the energy of the recoil, the DMTPC collaboration introduced a quality factor $Q(E_R) = \epsilon(E_R) \times (1 - 2 w(E_R))^2$, where $\epsilon$ is the recoil reconstruction efficiency and $w$ is the fraction of wrong “head-tail” assignments. The $Q$ factor represents the effective fraction of reconstructed recoils with “head-tail” information, and the error on the “head-tail” asymmetry scales as $1/\sqrt(Q)$. Early measurements demonstrated a $Q$ factor of 20% at 100 keV and 80% at 200 keV [@Dujmic2008-58]. The DMTPC collaboration is currently designing a 1-m$^3$ detector. The apparatus consists of a stainless steel vessel of 1.3 m diameter and 1.2 m height. Nine CCD cameras and nine PMTs are mounted on each of the top and bottom plates of the vessel, separated from the active volume of the detector by an acrylic window. The detector consists of two optically separated regions. Each of these regions is equipped with a triple-mesh amplification device, located between two symmetric drift regions. Each drift region has a diameter of 1.2 m and a height of 25 cm, for a total active volume of 1 m$^3$. A field cage made of stainless steel rings keeps the uniformity of the electric field within 1% in the fiducial volume. A gas system recirculates and purifies the CF$_4$. When operating the detector at a pressure of 50 torr, a 1 m$^3$ module will contain 250 g of CF$_4$. Assuming a detector threshold of 30 keVee (electron-equivalent energy, corresponding to nuclear recoil energy threshold $\sim$ 50 keV), and an overall data-taking efficiency of 50%, a one-year underground run will yield an exposure of 45 kg-days. Assuming negligible backgrounds, such an exposure will allow the DMTPC collaboration to improve the current limits on spin-dependent interactions on protons by about a factor of 50 [@Dujmic2008-58]. Conclusion ============ Directional detectors can provide an unambiguous positive observation of Dark Matter particles even in presence of insidious backgrounds, such as neutrons or neutrinos. Moreover, the dynamics of the galactic Dark Matter halo will be revealed by measuring the direction of the incoming WIMPs, opening the path to WIMP astronomy. In the past decade, several groups have investigated new ideas to develop directional Dark Matter detectors. Low-pressure TPCs are best suited for this purpose if an accurate (sub-millimeter) 3-D reconstruction of the nuclear recoil can be achieved. A good tracking resolution also allows for an effective rejection of all electromagnetic backgrounds, in addition to statistical discrimination against neutrinos and neutrons based on the directional signature. The choice of different gaseous targets makes these detectors well suited for the study of both spin-dependent (CS$_2$) or spin-independent (CF$_4$ and $^3$He) interactions. A vigorous R&D program has explored both electronic and optical readout solutions, demonstrating that both technologies can effectively and efficiently reconstruct the energy and vector direction of the nuclear recoils expected from Dark Matter interactions. The challenge for the field of directional Dark Matter detection is now to develop and deploy very sensitive and yet inexpensive readout solutions, which will make large directional detectors financially viable. Acknowledgments {#acknowledgments .unnumbered} =============== The authors are grateful to D. Dujmic and M. Morii for useful discussions and for proofreading the manuscript. G. S. is supported by the M.I.T. Physics Department and the U.S. Department of Energy (contract number DE-FG02-05ER41360). C. J. M. is supported by Fermilab and Temple University. References {#references .unnumbered} ========== [^1]: A homoatomic molecular entity is a molecular entity consisting of one or more atoms of the same element. [^2]: The scale factors are (in cgs-Gaussian units): $E_{TF} = \frac{e^2}{a} Z_i Z_T \frac{M_i +M_T}{M_T}$, $R_{TF} = \frac{1}{4 \pi a^2 N} \frac{(M_i + M_T)^2}{M_i M_T}$. Here, $N$= number density of target atoms, subscripts i and T refer to the incident particle and the target substance, and $a = a_0 \frac{.8853}{\sqrt{Z_i ^{2/3} + Z_T ^{2/3}}} $, with $a_0$ the Bohr radius. [^3]: The parameter $k \stackrel{.}{=} \frac{0.0793Z_1^{1/6}}{(Z_1^{2/3} + Z_2^{2/3})^{3/4}} \left[\frac{Z_1Z_2(A_1+A_2)^3}{A_1^3A_2}\right] ^{1/2}$ becomes substantially larger only for light recoils in heavy targets.

GREATER ....a study of the book of Hebrews A sermon series by Jay Lovelace....beginning February 18, 2018 ANNOUNCEMENTS AND HAPPENINGS... This week and next... AWANA...February 21 - Regular Night! Begins at 6:30 p.m.Small Groups…The Friday Small Groups will meet on February 23 at 6:30 p.m.; the Lovelace group at the Wilson’s home and the Barker group at the church. AWANA Grand Prix Garage...Kids, if you want advice on your race car for the Grand Prix or time to test the ride, come to the church at 9:00 a.m. on Saturday, February 24. Volunteers will be there to help you with any finishing touches. (Note: the Grand Prix will be held on Saturday, March 3, beginning at 10:00 a.m.). Prayer Meeting...February 25 at 4:30 p.m. at the church Defending Your Faith...Join Marty Engel on Monday, February 26 for discussion time about everyday questions that Christians are asked of nonbelievers. Mark your calendars!

The present invention relates generally to digital copy protection, digital rights management, and conditional access, and more particularly but not exclusively to enabling transferable entitlements using Entitlement Management Messages (EMMs) for providing content to different network devices. Today a consumer can readily purchase an entitlement to content such as a ticket to the opera, a sports event, movie, or the like. Often, the purchased ticket can be redeemed at some later stage and location. Similarly a consumer may purchase an airline ticket and redeem it for an airplane flight. However, there is a difference of transferability between these two ticket transactions. For various reasons, of both pricing and security, airline tickets represent non-transferable entitlements, where only the named recipient of the entitlement may redeem it, whereas movie tickets, or the like, are typically transferable. Transferability is an attribute of the entitlement granted by an original owner to the recipient. It means that the recipient may be free to resell or transfer title to the entitlement prior to its redemption. It also typically means that the owner or its distributors agree to honor the redemption of the entitlement from whoever presents the entitlement. Thus, in some situations, a transferable entitlement may become an object of trade. However, in today's realm of content, such as in the Internet Protocol Television (IPTV) domain, or the like, entitlements do not readily support transferability. If a recipient were to purchase an entitlement on one set top box (STB) there presently is no mechanism to enable the transfer of that entitlement to another set top box or other network device for redemption. Transfer of entitlements between devices on the same or different networks may open a wealth of opportunity for consumers and for content providers. Moreover, IPTV, and the like, may be currently served in discrete networks—so-called ‘walled-garden’ networks. These networks typically ensure a level of quality of service and security. However the walls often impose a barrier to a market of consumers inside the wall. The broader commercial motivation of this invention therefore includes allowing third-party content providers outside the walls to gain access to this market. Thus, it is with respect to these considerations and others that the present invention has been made

ニュース 2016年01月01日 2016年に年女となる、1992年の申年生まれのグラビアアイドルたち。サルといえば、動物園のショーなどで愛嬌とひょうきんさで人々を楽しませてくれるが、それと同じようにグラビア界の申年女子たちも、持ち前のサービス精神で今年もファンを盛り上げてくれそうだ。 今年24歳となるグラドルの代表格的な存在といえば、篠崎愛だろう。昨年デビュー10周年を迎えた彼女は、愛くるしい顔立ちと似つかわしくない迫力満点のバストで「最強のロリ巨乳」とも呼ばれて高い人気を誇る。昨年は、もともと定評のあった歌唱力を生かして歌手活動も本格化させ、ソロ歌手としてアルバムをリリースした。テレビCMで伸びやかな歌声を披露した巨乳ナース姿が目に焼きついている人も多いことだろう。 篠崎はSNSへの投稿もマメで、プライベート感あふれるセクシーな自画撮り画像のほか、深夜にラーメンやカツ丼を食べる様子をアップした「飯テロ写真」も好評。豊満なスタイルが絶賛される彼女らしいファンサービスには今年も期待したいところだ。 そんな篠崎とはタイプが違い、175センチという高身長で大人びた魅力を放つのが、染谷有香だ。スレンダーなスタイルながらGカップという迫力のある胸を持つ彼女は「エロデカいグラドル」と言われ、グラビア界でもこれまでになかなかいなかった逸材として人気と知名度を高めている。 2015年は、多数のバラエティ番組にゲスト出演したほか、深夜のグラドル育成番組『ドラマ！7人のアイドルゴーゴー！』（テレビ朝日系）でドSキャラを発揮した染谷。ドスのきいた低い声で共演したグラドルたちを罵倒する姿にM心をくすぐられた男子も多かったようで、「染谷ちゃんに怒られたい」などの声が相次いだ。しかし、そんな個性とは裏腹に、雑誌のインタビューなどでは「男性との経験が1度もないんです」とバージンを公言しており、処女厨と呼ばれる人々からも注目を集める存在だ。

Mind The Gap America’s British population has taken to the web to voice its displeasure at news that U.S. candy giant Hershey has successfully blocked our much loved U.K.-produced chocolate from being exported to the land of the free. So the Oscar nominations were announced this morning, and, as expected, the great British hope, Atonement, was nominated for Best Picture. However, its two stars, James McAvoy and Keira Knightley, were omitted for the top acting … The British dominance of Hollywood has been a big story throughout award season. But one could be forgiven for mistaking last night’s Oscars for a World Cup match, and, predictably, Britain got beaten by Mexico. Latest Interviews The Latest from Mind The Gap America’s British population has taken to the web to voice its displeasure at news that U.S. candy giant Hershey has successfully blocked our much loved U.K.-produced chocolate from being exported to the land of the free.

This invention relates to a method for applying normally dry relatively large particle size (granular) fertilizers to crops, such as lawns. Lawn fertilizers are available in various forms including solutions of nutrients in water, dispersions (suspensions) of fine powders (70-80 mesh and smaller) in an aqueous medium, dry powders and dry granules. In some cases, the nutrient materials are supported on an inert carrier, e.g. sand or clay. Both liquid fertilizers and dispersions of fine powders in aqueous mediums are usually spray applied using conventional types of liquid solution fertilizer spraying equipment. A typical example of a spray applied dispersion of a powdered fertilizer material is illustrated by the U.S. Pat. No. to Funk 4,036,627. This patent discloses a high analysis fertilizer formulaton of low bulk density powdered ureaformaldehyde having soluble and insoluble portions combined with soluble monopotassium phosphate in which the resultant mixture is a dry homogeneous blend, free of fillers and binding agents, and which may be carried in a liquid medium for application to surface or subsurface areas by conventional liquid solution fertilizer applying equipment. The suspension generally has a fairly high concentration of the fine powder particles in the liquid medium. Dry fertilizers in the powder form or the granular form are conventionally applied by dry spreaders. Numerous examples of dry powdered and granular fertilizer compositions are well known to those skilled in the art. Recently, these have begun to be formulated with provisions for timed (slow) release of the nutrients to avoid "burning" the crop and to reduce the number of applications in a growing season. Each of the various physical forms of fertilizer compositions has its advantages and disadvantages. Spray applied liquid fertilizer solutions and dispersions of powdered nutrient materials are characterized by the ability to be applied evenly and from a tank truck, for example. These fertilizer forms usually provide nutrients which are immediately available to the lawn, and therefore enable quick response of the lawn to the application, i.e. quick "greening" of the lawn. However, such liquid solutions are often too rich in immediately available nutrients, particularly nitrogen. A solution which is too rich in nutrients can cause "burning" of the lawn. Additionally, insect and fungus growth may be accelerated. Still further, liquid solution type fertilizers do not often possess long life on or in the ground and their effect is quickly lost. Frequent application is required to maintain a desired nutrient level in the soil during a growing season. With the finely divided powder or dispersion, a principal problem is retention on the leaves or blades of grass. This can also cause burning. Additionally, ambient conditions and normal lawn care procedures may result in loss of a significant value of the fertilizer. For example, application of dry powder is usually accompanied by considerable dusting and wind loss. Moreover, when the lawn is cut, and the clippings collected, a substantial portion of a powdered fertilizer, whether dry or dispersion applied, is carried away and lost. With a rotary lawn mower, dusting of a powdered fertilizer can also be a problem. Granular fertilizers which are spread on the lawn in a dry condition, do not generally have the foregoing types of application problems encountered with powdered fertilizers. Because of the larger particle size, dusting is not a problem. Further, retention on the blades of grass or on leaves is not generally a problem with granular fertilizers. Thus, loss on removal of grass clippings is negligible. However, like any spreader applied fertilizer, application is usually uneven because of turns at the end of a row, skips, overlaps, etc. Without care, overfertilizing can occur in certain areas and under fertilizing in others. A blotchy appearance results. Furthermore, the immediate nutrient availability of granular fertilizers may be lost due to leaching. Thus, with granular fertilizers obtaining quick "greening" can be a problem. Thus, as can be seen from the foregoing discussion the problems which are often encountered in the application of liquid, liquid dispersion or dry spread granular fertilizers are also manifested in the quality of performance of the fertilizer.

Recently, I sat down to talk with a group of eight students from a large prominent church in Southern California. They were raised in the church. They were regulars at youth group. They claimed to be in relationship with Christ. Yet, they were dead. As I tried to engage them, most seemed unmoved and uninterested. And I was not surprised. As I work with churches around the country, I encounter countless Christian students who are apathetic toward spiritual things. Their relationship with Christ is passionless. Talk of God is ho-hum. But why? Shouldn’t our relationship with Christ be life’s most exciting adventure? I’m not suggesting the Christian life is one, big, emotional high, but why are students more willing to plug into their iPods than their Bibles? Why are they more excited about the latest celebrity gossip than the Gospel? Why aren’t their lives filled with the drama of God’s Kingdom? I think a big part of the problem is that Christian students rarely engage their world for the cause of Christ. Here’s what I’ve observed in my training over the years. The most exciting events I do, the events where students seem to come to life, are those where there is some component of engagement. Let me illustrate. For almost ten years now, I’ve been taking students on mission trips to Berkeley and Utah. Each trip requires hours of training, typically in the form of classroom instruction and the reading of required books. This training is important and necessary, but it’s not what generates the most buzz among the students. Students get fired up on the trip when we give them opportunities to engage non-believers. On these trips we invite Mormon leaders, Unitarians, gay activists, Hare Krishna priests, skeptics, and atheists to dialogue with students. We give our non-Christian guests time to share their views, followed by a time of questions from our students. It’s during Q&A when students really come to life. They ask question after question, graciously yet firmly force our skeptical guests to give a reason for their views. At the conclusion of each encounter, we thank our guests and then spend time debriefing. At this point, students are always abuzz, asking me question after question. Before I know it, an hour of discussing apologetics and theology with youth will have flown by. In addition, we send our groups onto college campuses, like BYU or Berkeley, to conduct surveys. The surveys are designed to get our students into conversation with non-Christians students about spiritual issues. At first, students are fearful and anxious. They’re skeptical about people’s willingness to engage with them. But after an hour or two of surveys, students return and they are always pumped. During our debrief time, students can’t wait to share about their encounters. They’re filled with excitement about their conversations on campus with non-Christians. When we create opportunities for students to engage, there is a vibrancy that infuses the events. But this shouldn’t come as a surprise. Christianity is not a spectator sport. Our teaching should not remain in a classroom or behind the four walls of the church. If we want to train students who can defend the faith not just intelligently but passionately, we need to get them in the game. Think about any sports teams. It’s the starters who are the most passionate about the game, right? The benchwarmers, not so much. I think that’s one reason why our mission trips to Berkeley and Utah are exciting and successful. They get students in the game. They get students engaging a lost world with the truth of Jesus Christ. In 2014, students will get a taste of being in the game as I take them to Berkeley and Utah. I’ve already maxed out the number of mission trips I’m capable of taking through July. Indeed, we’ve had to turn groups away or ask them to start scheduling for 2015. So this year, we’ll be getting students off the sidelines and igniting their fire for Christ. I can’t wait. As a parent of 5 kids, summer gets expensive. I have to pay for swim lessons, soccer camps, VBS, youth group trips, family vacations, and more. And these costs don't even include feeding my kids all … > Read full article

Gerda Gilboe Gerda Gilboe (5 July 1914 – 11 April 2009) was a Danish actress and singer. She appeared in 18 films between 1943 and 2003. Life Gilboe was born in 1914. She was the daughter of a blacksmith, Gilboe started her career in musical theatre and operas in Aarhus before she moved to Copenhagen to work at different theatres. Her national breakthrough came, when she accepted the role as Eliza in My Fair Lady at Falkoner Teatret at short notice in 1960. Although she was then in her mid-40s and had only five days to learn the part, the production was a huge success. In the following years she took on more and more non-singing roles, and besides her theatre career she took a degree in rhetoric. Later in her life she started teaching rhetoric and drama. She appeared in several films, receiving particular acclaim for her appearance as Esther in Carlo & Esther, a 1994 film. She plays a woman in her 70s who catches the attention of Carlo who has a wife with Alzheimer's disease. Rides on his motorbike lead to an affair. Death Gilboe died on 11 April 2009 at an actors' home in Copenhagen, aged 94. Filmography A Time for Anna (2003) Kærlighed ved første hik (1999) Dybt vand (1999) Besat (1999) Antenneforeningen (1999) Kun en pige (1995) Elsker elsker ikke... (1995) Carlo & Ester (1994) Lad isbjørnene danse (1990) Isolde (1989) Sidste akt (1987) Walter og Carlo – yes, det er far (1986) Pas på ryggen, professor (1977) Kun sandheden (1975) Den kyske levemand (1974) Lise kommer til Byen (1947) En ny dag gryer (1945) Moster fra Mols (1943) References External links Category:1914 births Category:2009 deaths Category:Danish female singers Category:Danish film actresses Category:Danish musical theatre actresses Category:People from Aarhus Category:Place of birth missing Category:Place of death missing Category:20th-century Danish actresses Category:20th-century singers Category:20th-century women singers

Abstract The entorhinal cortex receives a large projection from the piriform cortex, and synaptic plasticity in this pathway may affect olfactory processing. In vitro whole cell recordings have been used here to investigate postsynaptic signalling mechanisms that mediate the induction of long-term synaptic depression (LTD) in layer II entorhinal cortex cells. To induce LTD, pairs of pulses, using a 30-millisecond interval, were delivered at 1 Hz for 15 minutes. Induction of LTD was blocked by the NMDA receptor antagonist APV and by the calcium chelator BAPTA, consistent with a requirement for calcium influx via NMDA receptors. Induction of LTD was blocked when the FK506 was included in the intracellular solution to block the phosphatase calcineurin. Okadaic acid, which blocks activation of protein phosphatases 1 and 2a, also prevented LTD. Activation of protein phosphatases following calcium influx therefore contributes to induction of LTD in layer II of the entorhinal cortex. 1. Introduction The mechanisms that mediate the induction of long-term synaptic potentiation (LTP) [1, 2] and depression (LTD) [3–5] have been studied intensively within the hippocampus, but less is known about the signalling mechanisms for LTP and LTD in the entorhinal cortex. Because the entorhinal cortex receives highly processed inputs from sensory and association cortices and also provides the hippocampal region with much of its sensory input [6, 7], lasting changes in the strength of synaptic inputs to the entorhinal cortex could alter the manner in which multimodal cortical inputs are integrated, modulate the strength of transmission of specific patterns of sensory input within the hippocampal formation, and contribute to mnemonic function [8–11]. Determining the effective stimulation parameters and the intracellular signals that mediate synaptic plasticity in the entorhinal cortex should allow insight into basic mechanisms that contribute to the cognitive functions of the parahippocampal region. Long-term potentiation of cortical inputs to the superficial layers of the entorhinal cortex has been described in vivo [11–14] and in vitro [15, 16]. Stimulation patterns required to induce LTP tend to be more intense in the entorhinal cortex than in the hippocampus [12, 14], and we have also found that induction of LTD in the entorhinal cortex requires intense low-frequency stimulation [17, 18]. In the hippocampus, conventional 1 Hz stimulation trains have been most effective in slices taken from juvenile animals [19, 20] but are generally ineffective in adult slices [21–23] and in intact animals ([31, 32], see also [33]). Similarly, 1 Hz stimulation induces entorhinal LTD in slices from young animals [28, 29] but is not effective in vivo [17] or in slices from older animals [18]. Repeated stimulation using pairs of pulses separated by a short 25- to 50-millisecond interval can induce LTD more effectively in both the CA1 ([24–26], but see [27]) and entorhinal cortex [17, 18, 33, 34]. In the CA1, the LTD induced by this stimulation pattern is NMDA receptor-dependent, but it also depends upon activation of local inhibitory mechanisms by the pulse-pairs [30, 31]. In the entorhinal cortex, however, repeated paired-pulse stimulation using a 10-millisecond interval that evokes maximal paired-pulse inhibition does not induce LTD, and LTD is induced when a 30-millisecond interval is used that evokes maximal paired-pulse facilitation [17]. The LTD can also be enhanced when GABAA transmission is reduced with bicuculline [18]. This further suggests that LTD in the entorhinal cortex does not require activation of local inhibitory mechanisms but rather requires prolonged stimulation patterns that are strong enough to overcome local inhibition and lead to NMDA receptor activation. Strong local inhibition in the entorhinal cortex [8, 35] may thus place a restraint on activity-dependent synaptic modification. Consistent with this idea is the finding that the same pairing stimulation protocol that induces LTP in hippocampus leads to LTD in entorhinal cortex [28]. Signalling mechanisms that mediate LTD in the superficial layers of the entorhinal cortex share some similarities with NMDA receptor-dependent LTD in the hippocampus. Long-term depression of superficial layer inputs to layer II is dependent on NMDA receptor activation both in vivo and in vitro [17, 18, 28, 33] but does not require activation of group I/II metabotropic glutamate receptors ([18, 28], see [36, 37]). In the hippocampus, moderate and prolonged influx of calcium via NMDA receptors activates calmodulin which leads to LTD via activation of the protein phosphatase calcineurin (PP2b). Calcineurin increases the activity of protein phosphatase 1 by reducing the activity of inhibitor 1, and this can cause rapid reductions in AMPA-mediated responses [2, 38, 39]. Hippocampal LTD is expressed partly through the reduced conductance of AMPA receptors caused by dephosphorylation of the GluR1 subunit by PP1 [2, 4], but careful study has shown that calcineurin-dependent LTD in deep layer inputs to layer II neurons in the young entorhinal cortex is not associated with a reduced AMPA conductance, but rather involves internalization of AMPA receptors and their proteosome-mediated degradation [28]. In the present study, the early postsynaptic signalling mechanisms that mediate LTD in layer I inputs to layer II neurons of the medial entorhinal cortex have been investigated using recordings of whole cell excitatory postsynaptic potentials. Long-term depression was induced using a prolonged paired-pulse stimulation pattern that was previously found to be effective for induction of NMDA-receptor-dependent LTD [18]. Pharmacological agents applied to the bathing medium or intracellular solution were used to assess the dependence of LTD on calcium-dependent signalling mechanisms including the phosphatases calcineurin and PP1/PP2a. 2. Experimental Procedures 2.1. Slices and Whole Cell Recordings Experiments were performed on slices from male Long-Evans rats (4 to 8 weeks old). Animals were anesthetized with halothane and brains were rapidly removed and cooled (4°C) in oxygenated artificial cerebrospinal fluid (ACSF). ACSF consisted of (in mM) 124 NaCl, 5 KCl, 1.25 NaH2PO4, 2 MgSO4, 2 CaCl2, 26 NaHCO3, and 10 dextrose and was saturated with 95% O2–5% CO2. All chemicals were obtained from Sigma (St. Louis, Mo, USA) unless otherwise indicated. Horizontal slices (300𝜇m) were cut with a vibratome (WPI, Vibroslice NVSL, Sarasota, Fla, USA) and were allowed to recover for at least one hour before recordings. Slices were maintained in a recording chamber with oxygenated ACSF at a rate of 2.0 mL/min, and a temperature from 22 to 24°C was used to minimize metabolic demands on slices [18, 28]. Neurons were viewed with an upright microscope (Leica DML-FS, Wetzlar, Germany) equipped with a 40x objective, differential interference contrast optics, and an infrared video camera (Cohu, 4990 series, San Diego, Calif, USA). 2.2. LTD Induction and Pharmacology Whole-cell current clamp recordings of EPSPs were monitored 10 minutes before and 30 minutes after LTD induction by delivering test-pulses every 20 seconds. Intensity was adjusted to evoke EPSPs that were approximately 3 to 4 mV in amplitude, and cells were held 5 mV below threshold when necessary to prevent the occurrence of spikes in response to EPSPs. Stimulus parameters for LTD induction were based on those used previously in vivo and in vitro [17, 18]. The induction of LTD was tested using pairs of stimulation pulses (30-millisecond interpulse interval) delivered at a frequency of 1 Hz for either 7.5 or 15 minutes [18]. Control cells received test-pulses throughout the recording period and did not receive conditioning stimulation. Signalling mechanisms mediating the induction of LTD were tested using stock solutions of pharmacological agents that were stored frozen and diluted on the day of use. NMDA glutamate receptors were blocked by constant bath application of 50𝜇M DL-2-amino-5-phosphonovalerate (APV). The calcium chelator 1,2-bis(2-aminophenoxy)-ethane-N,N,N′N′-tetraacetic acid (BAPTA, 10 mM) was included in the recording electrode solution to block increases in intracellular calcium. To block activation of the calmodulin-dependent protein phosphatase calcineurin (PP2b) slices were pre-exposed to 250𝜇M cyclosporin A (Toronto Research Chemicals Inc., North York, Ontario, Canada) for 1.5 to 3 hours [39]. In other experiments, FK506 (50𝜇M) was included in the recording electrode solution to block calcineurin [39, 40]. In other experiments, okadaic acid (0.1 or 1.0𝜇M) was included in the recording solution to block activation of protein phosphatases 1 and 2a [40, 41]. Control recordings without paired-pulse stimulation were used to verify the stability of recordings in cells filled with FK506 and 1.0𝜇M okadaic acid. 2.3. Data Analysis Synaptic responses and electrophysiological properties of layer II neurons were analyzed using the program Clampfit 8.2 (Axon Instr.). Data were standardized to the mean of baseline responses for plotting and were expressed as the mean ±SEM. Changes in EPSP amplitude were assessed using mixed-design ANOVAs and Neuman-Keuls tests that compared the average responses during the baseline period, 5 minutes after conditioning stimulation, and during the last 5 minutes of the recording period. Layer II neurons were classified as putative stellate or nonstellate neurons based on electrophysiological characteristics described by Alonso and Klink [42]. Stellate neurons were characterized by the presence of low-frequency subthreshold membrane potential oscillations, a depolarizing afterpotential following spikes, and prominent inward rectification in response to hyperpolarizing current pulses. Both pyramidal and stellate neurons in layer II can show inward rectifying sag responses [43]. Here, neurons recorded were clearly in layer II, usually near the border with layer I, and a proportion of these neurons did not show clear sag and were classified as pyramidal neurons. Input resistance was determined from the peak voltage response to −100 pA current pulses (500-millisecond duration), and rectification ratio was quantified by expressing peak input resistance as a proportion of the steady-state resistance at the end of the current pulse. 3. Results Stable recordings were obtained from 57 putative stellate neurons and 21 putative nonstellate cells. Peak input resistance was similar in stellate and pyramidal neurons (stellate, 95 ± 6 MΩ; pyramidal, 96 ± 10 MΩ) but there was a much larger sag in voltage responses to hyperpolarizing current injection in stellate cells (rectification ratio 1.37±0.04 in stellate cells versus 1.06±0.01 in pyramidal cells). The amplitude of baseline synaptic responses evoked by layer I stimulation was similar in stellate (3.9±0.2 mV) and pyramidal cells (3.7±0.4 mV), and the amount of depression induced was also similar for recording conditions in which significant LTD was obtained (71.2±5.6% in 14 stellate and 76.8±7.6% in 6 pyramidal cells). 3.1. LTD Induction To determine if a relatively brief LTD induction protocol could be used to induce LTD in whole-cell recordings, the first tests attempted to induce LTD using paired-pulse delivery at 1 Hz for 7.5 minutes (𝑛=10) which can induce moderate LTD of field potentials in a gas-fluid interface recording chamber [18]. Paired-pulse stimulation for 7.5 minutes did not induce depression of EPSPs relative to control cells (93.0±10.0% of baseline after 30 minutes; F2,28=0.09,𝑃=.92). We previously observed stronger LTD of field potentials in the interface recording chamber after 15 minutes versus 7.5 minutes of paired-pulse stimulation [18], and prolonged paired-pulse stimulation for 15 minutes also reliably induced LTD of whole-cell EPSPs (𝑛=7, Figure 1). EPSP amplitude was reduced to 56.3±9.5% of baseline levels 5 minutes after the conditioning stimulation, and remained at 58.6±6.1% of baseline levels at the end of the 30 minutes follow-up period (F2,22=14.2,𝑃<.001). Responses in control cells were stable (𝑛=6), and remained at 99.6±2.6% of baseline levels at the end of the recording period (Figures 1(b2), 1(c)). Figure 1: Prolonged, low-frequency stimulation induces long-term depression of EPSPs in neurons in layer II of the entorhinal cortex. (a) The location of stimulating and recording electrodes in acute slices containing the entorhinal cortex. (b) and (c) Long-term depression was induced by repetitive delivery of pairs of stimulation pulses at a rate of 1 Hz for 15 minutes (PP-LFS). The amplitude of synaptic responses remained stable in control cells that did not receive conditioning stimulation. Traces in (b) compare responses recorded during the baseline period (1) and during the follow-up period (2) in a neuron that received low-frequency stimulation (b1) and in a control cell (b2). Responses were obtained at the times indicated in (c). Averaged points in (b) indicate the mean ±1 SEM in this and subsequent figures. (d) Long-term depression was not reliably induced when low-frequency stimulation was delivered for only 7.5 minutes rather than 15 minutes, indicating that induction of LTD requires prolonged stimulation. 3.2. NMDA Receptors and Postsynaptic Calcium The NMDA receptor antagonist MK-801 blocks induction of LTD in the entorhinal cortex in vivo [17] and the NMDA receptor blocker APV has been shown to prevent LTD of field potentials and EPSPs in entorhinal cortex slices [18, 28, 33]. We therefore tested for the NMDA receptor-dependence of LTD of EPSPs in the current preparation using constant bath application of APV (50𝜇M). Induction of LTD by 15 minutes of paired-pulse stimulation was blocked by APV (𝑛=6, Figure 2(a)). There was a tendency for responses to be potentiated immediately following conditioning stimulation, but this variable effect was not statistically significant, and responses were close to baseline levels at the end of the recording period (96.7±13.2% of baseline; F2,10=2.99,𝑃=.09). Figure 2: The induction of long-term depression is dependent on activation of NMDA glutamate receptors and on increases in postsynaptic calcium. (a) Constant bath application of the NMDA receptor antagonist APV (50𝜇M) blocked the induction of long-term depression by 15 minutes of paired-pulse low-frequency stimulation (PP LFS). (b) Blocking increases in postsynaptic calcium by including the calcium chelator BAPTA (10 mM) in the recording electrode solution also blocked the induction of LTD. The transient facilitation of EPSPs immediately following stimulation was significant for the BAPTA condition but not the APV condition, and responses were at baseline levels at the end of the recording periods. The block of lasting depression suggests that calcium influx via NMDA receptors is required for induction of LTD. The role of postsynaptic calcium in LTD induction was tested by recording from cells in which the calcium chelator BAPTA (10 mM) was included in the recording electrode solution (10 mM, 𝑛=6, Figure 2(b)). Cells filled with BAPTA had longer-duration action potentials than control cells (6.1±0.7 versus 3.3±0.1 milliseconds measured at the base; 𝑡1,9=3,57,𝑃<.01) consistent with a reduction in calcium-dependent potassium conductances. The induction of LTD was blocked in cells loaded with BAPTA. There was a significant increase in the amplitude of EPSPs immediately following paired-pulse stimulation (to 122.3±6.0% of baseline; F2,10=5.46,𝑃<.05; N–K, 𝑃<.05), but responses returned to baseline levels within 10 minutes and were at 94.8±7.1% of baseline levels after 30 minutes (N–K, 𝑃=0.50, Figure 2(b)). An increase in postsynaptic calcium is therefore required for induction of LTD in layer II neurons of the entorhinal cortex. 3.3. Protein Phosphatases The role of the calmodulin-dependent protein phosphatase calcineurin (PP2b) in LTD in layer II neurons was tested using either pre-exposure to 250𝜇M cyclosporin A in the bathing medium [39], or by including 50𝜇M FK506 postsynaptically in the recording electrode solution. In cells pre-exposed to cyclosporin A, paired-pulse stimulation was followed by a depression in EPSP amplitude that reached 82.4±7.5% of baseline levels after 30 minutes (Figure 3(a)). Although the depression in the cyclosporin group was not statistically significant (F2,10=3.51,𝑃=0.07,𝑛=6), the depression obtained was also not significantly less than that observed in control ACSF (F1,11=3.79,𝑃=.08). The result was therefore ambiguous with respect to the role of calcineurin in LTD. To test the involvement of calcineurin more definitively and to avoid potential presynaptic effects, the calcineurin blocker FK506 was included in the recording electrode solution for additional groups of cells [40]. Responses in cells filled with FK506 showed a significant potentiation immediately following paired-pulse stimulation (𝑛=8), but there was no lasting change in response amplitudes in comparison to control cells filled with FK506 that did not receive conditioning stimulation (𝑛=7). Responses were increased to 134.9±10.5% of baseline levels immediately following paired-pulse stimulation, (F2,26=7.71,𝑃<.01; N–K, 𝑃<.001;𝑛=8) but returned to 102.2±6.1% of baseline levels after 30 minutes (Figure 3(b)). Figure 3: Long-term depression is dependent on activation of the calmodulin-dependent protein phosphatase calcineurin. Although LTD was only partially inhibited by pre-exposure to cyclosporin A, it was completely blocked when FK506 was included in the recording electrode solution. (a) Pre-exposure of slices to the calcineurin inhibitor cyclosporin A (250𝜇M) for 1.5 to 3 hours resulted in a partial block of LTD by repeated paired-pulse stimulation. The amount of LTD induced was smaller than in control ACSF and was close to statistical significance (𝑛=6,𝑃=.07). (b) Including the FK506 in the recording electrode solution to directly block postsynaptic calcineurin prevented the induction of LTD. Analysis of group responses showed a significant increase in responses during the baseline period, but responses in control cells indicate that this increase is transient and unlikely to have affected measurement of LTD. Inhibition of postsynaptic calcineurin therefore prevents induction of LTD in layer II cells of the entorhinal cortex. Inspection of averaged responses suggested that there was an initial increase in responses during the baseline period among cells filled with FK506, and comparison of responses recorded during the first and last minutes of the baseline period showed that the increase was significant (𝑡14=3.09,𝑃<.01). Interestingly, then, interfering with calcineurin function can lead to enhanced basal synaptic transmission in entorhinal neurons. This increase is not likely to have affected measures of LTD in conditioned cells, however, because control responses showed only a transient increase after which responses remained stable. Protein phosphatase 1 is thought to contribute directly to suppression of hippocampal EPSPs during LTD by dephosphorylation of the GluR1 AMPA receptor subunit. The involvement of PP1 to LTD in the entorhinal cortex was therefore tested by including okadaic acid in the recording electrode solution. In early experiments, a low concentration of 0.1𝜇M okadaic acid [41] did not block LTD induction, and responses were depressed to 72.7±8.7% of baseline levels at the end of the recording period (F2,24=4.65,𝑃<.05; N–K, 𝑃<.001;𝑛=8). However, increasing the concentration of okadaic acid to 1.0𝜇M [40] blocked the induction of LTD. There was a variable and nonsignificant reduction in responses immediately following conditioning stimulation (to 89.0±14.9% of baseline) and responses were also near baseline levels after 30 minutes (96.0±6.6% of baseline 30; F2,22=0.18,𝑃=.84;𝑛=7; Figure 4). Activation of PP1 is therefore likely to contribute to mechanisms of LTD in the entorhinal cortex. Figure 4: The induction of LTD was blocked in a dose-dependent manner by including okadaic acid in the recording electrode solution to block activation of protein phosphatase 1 (PP1). (a) and (b) A low concentration of 0.1𝜇M okadaic acid failed to block LTD induction, but raising the concentration to 1.0𝜇M resulted in a block of LTD induction (compare traces in A1 versus A2). Responses in control cells filled with 1.0𝜇M okadaic acid that did not receive conditioning stimulation remained stable. The block of LTD by okadaic acid suggests that activation of PP1 mediates LTD in the entorhinal cortex. 4. Discussion The current paper has used prolonged repetitive paired-pulse stimulation to induce LTD in layer I inputs to layer II neurons of the medial entorhinal cortex and has determined the early postsynaptic signals that mediate LTD in these cells. Consistent with previous observations, the LTD observed here was obtained in both putatively identified stellate [28] and pyramidal [44] cells. The induction of LTD was blocked by the NMDA glutamate receptor antagonist APV, and by the calcium chelator BAPTA, indicating that calcium influx via NMDA receptors is required for LTD. The induction of LTD was also blocked by the calcineurin inhibitor FK506, and by okadaic acid which blocks activation of protein phosphatases 1 and 2a. Calcineurin is required for LTD of deep layer inputs to layer II stellate cells [28], and calcineurin-dependent activation of PP1 contributes to NMDA receptor-dependent LTD of AMPA responses in the hippocampus [2, 4]. The dependence of LTD in the entorhinal cortex on activation of NMDA receptors has been a consistent finding in vivo and in slices. It has been observed following stimulation protocols including 1 Hz trains, pairing of presynaptic stimulation at 0.33 Hz with postsynaptic depolarization [28], repeated paired-pulse stimulation [18, 33], and spike-timing-dependent induction of LTD [44]. Long-term depression was blocked by including the calcium chelator BAPTA in the recording electrode solution (Figure 2) [28], and this is consistent with calcium influx via NMDA receptors as a critical trigger for entorhinal LTD. Metabotropic glutamate receptor activation and release of calcium from intracellular stores can contribute to LTD in the hippocampus [2, 36, 37, 45], but activation of metabotropic glutamate receptors is not required for entorhinal LTD [18, 28]. Calcium influx through voltage-gated calcium channels can contribute to spike-timing-dependent LTD in the entorhinal cortex, however. Cells with broadened action potentials that result in larger calcium transients show greater NMDA receptor-dependent spike-timing-dependent LTD in layer II-III cells [44]. Calcium influx through voltage-gated channels also mediates bidirectional spike-timing-dependent plasticity of inhibitory synapses in entorhinal cortex [46]. A form of long-term depression on layer V-VI neurons, expressed presynaptically through reduced transmitter release, is also dependent on activation of voltage-dependent calcium channels [33]. Calcium signalling mediated by voltage-gated channels therefore plays a number of roles in modulating synaptic plasticity in the entorhinal cortex. The contribution of the calmodulin-dependent protein phosphatase calcineurin to LTD was tested by incubating slices in cyclosporin A or by including FK506 in the recording electrode solution. Cyclosporin A appeared to cause a partial block of LTD, and responses were reduced to 82.4% of baseline as compared to 58.6% in untreated cells (compare Figures 1(c) and 3(a)), but the sizes of these LTD effects were not statistically different. We obtained a more conclusive result with FK506, however, and LTD was completely blocked by including FK506 in the recording electrode solution. Including FK506 in the bathing medium has been used to block calcineurin-dependent depression effects in entorhinal cortex [28], and in excitatory [47] and inhibitory [48] synapses of the CA1 region. Here, we have loaded FK506 into the recording electrode solution to avoid possible presynaptic effects of the drug and to ensure that FK506 could act on calcineurin [39, 40, 49, 50]. The block of LTD by FK506 indicates that LTD is dependent on calcineurin, and this suggests that cyclosporin A resulted in only a partial block of calcineurin activity. Calcineurin is thought to mediate expression of LTD in part by dephosphorylating inhibitor 1 and thereby increasing the activity of PP1 [2, 4, 39]. The PP1/PP2a inhibitor okadaic acid blocks LTD in the CA1 region [38, 40], and we have shown here that the induction of LTD in the entorhinal cortex was blocked by including okadaic acid in the recording electrode solution. This is the first report of LTD in the entorhinal cortex dependent on PP1/PP2a. Protein phosphatases can regulate synaptic function through a variety of mechanisms [51] that include dephosphorylation of the ser-845 residue on the AMPA GluR1 subunit, and LTD in the entorhinal cortex may be expressed partly through this mechanism. In addition, the work of Deng and Lei [28] has found entorhinal LTD to be associated with a reduction in the number of postsynaptic AMPA receptors, with no change in AMPA receptor conductance, and has shown that this effect is dependent on proteosomes that degrade AMPA receptors internalized through ubiquitinization. As in the hippocampus, therefore, entorhinal LTD can be expressed through mechanisms involving trafficking of AMPA receptors [52]. Long-term depression was induced here using strong repetitive paired-pulse stimulation which we have used previously to induce LTD in the entorhinal cortex in vivo and in slices ([17, 18], see also [33, 34]). LTD was induced following 15 minutes, but not 7.5 minutes of paired-pulse stimulation; this is consistent with a requirement for prolonged activation of calcium-dependent signalling mechanisms, and is also consistent with the possibility that NMDA receptor-dependent metaplastic changes early in the train may promote LTD induced by stimuli that occurred later in the 15-minute duration trains [53]. We previously found 1 Hz stimulation to be ineffective in vivo and in slices from Long-Evans rats [17, 18], but deep layer inputs to stellate neurons in slices from 2 to 3 week-old Sprague-Dawley rats express NMDA receptor-dependent LTD following 15 minutes of 1 Hz stimulation, or following low-frequency stimulation paired with postsynaptic depolarization [28]. Thus, there may be developmental, strain-related, or pathway-specific factors that affect the ability of 1 Hz stimulation to activate these signalling mechanisms. The entorhinal cortex is embedded within the temporal lobe through an extensive array of anatomical connections [7] and has been linked behaviorally to a variety of sensory and cognitive functions (e.g., [9, 10]). Lasting synaptic plasticity in the entorhinal cortex is therefore likely to serve a variety of functions depending on the synaptic pathways involved. Synaptic depression effects are generally thought to complement synaptic potentiation during the formation of memory [45, 54–56], and it is possible that depression effects contribute to short and/or long-term memory processing. However, the laminar architecture of the entorhinal cortex, with superficial layers mediating much of the cortical input to the hippocampal formation, suggests that long-term depression of synaptic transmission in layer II may lead to long-term reductions in the salience of particular elements or patterns of cortical input and may thus lead to lasting changes in the multimodal inputs processed by the hippocampal formation. Similarly, the general resistance of the entorhinal cortex to induction of LTD could serve to maintain relatively stable information processing and integration of multimodal sensory inputs within the medial entorhinal cortex. Acknowledgments This research was funded by grants to C. A. Chapman from the Natural Sciences and Engineering Research Council of Canada and the Canada Foundation for Innovation, and by a postdoctoral fellowship to S.K. from Fondation Fyssen (France). C.A. Chapman is a member of the Center for Studies in Behavioral Neurobiology funded by the Fonds pour la Recherche en Santé du Québec. A. Alonso, M. de Curtis, and R. Llinás, “Postsynaptic Hebbian and non-Hebbian long-term potentiation of synaptic efficacy in the entorhinal cortex in slices and in the isolated adult guinea pig brain,” Proceedings of the National Academy of Sciences of the United States of America, vol. 87, no. 23, pp. 9280–9284, 1990.View at Publisher · View at Google Scholar S. M. Dudek and M. F. Bear, “Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-D-aspartate receptor blockade,” Proceedings of the National Academy of Sciences of the United States of America, vol. 89, no. 10, pp. 4363–4367, 1992.View at Publisher · View at Google Scholar M. F. Bear, “A synaptic basis for memory storage in the cerebral cortex,” Proceedings of the National Academy of Sciences of the United States of America, vol. 93, no. 24, pp. 13453–13459, 1996.View at Publisher · View at Google Scholar

Divesting Of Kruger’s Cash (Updated) Freshman Sen. David Carlucci, one of 17 Senate Democrats who received campaign contributions from Sen. Carl Kruger during the 2010 election cycle, is getting rid of that money after learning of the federal corruption charges lodged against his colleague earlier today. “It is unfortunate that these types of allegations have clouded the legislature, tainting the hard working men and women who work diligently and honorably to serve their constituents,” Carlucci said in a statement. “I ran on a platform of ethics reform and these unsavory allegations are just another example of why ethics reform in Albany needs to be addressed immediately. The people of New York deserve better. In light of these allegations, I will be donating the $5,000 given to me during my campaign from Senator Kruger to a charitable organization in my district.” All told, Kruger, a prodigious fundraiser who had close to $1.9 million in his campaign committee, “Friends of Carl,” as of Jan. 15, doled out $49,000 to fellow senators this cycle, according to campaign finance records on file at the state Board of Elections. He also gave $450,000 to the DSCC. Sen. Gustavo Rivera, who received $2,500 from Kruger, was the first lawmaker to announce he would divest himself of the scandal-scarred Brooklyn lawmaker’s contributions. Now, apparently, all four of the Independent Democratic Conference members – Carlucci, Diane Savino, Jeff Klein, and Dave Valesky – are following suit. UPDATE: DSCC spokesman Josh Cherwin says: “We will not be returning these funds, which were contributed during a previous election cycle and already spent.” “This is yet another sad day for New York residents who rightfully expect integrity and accountability from their elected officials.” “During the last election cycle, Senator Kruger’s campaign committee contributed a combined total of $8,000 to Independent Democratic Conference members. We decided to donate that amount to charitable organizations in our communities. We believe this to be the best use for this money.”

Local graft-versus-host-reaction in mice specifically inhibited by anti-receptor antibodies. The local graft-versus-host (GVH) reaction provoked by parental spleen cells in F1 mice was shown to be T-cell-dependent. GVH reactions were suppressed in F1 hybrid mice immunized with parental T lymphocytes of the same genotype, but not in F1 mice immunized with parental B cells. In some cases this immunity could be passively transferred by serum into normal F1 mice. The specific activity of such sera could be removed by absorption with either parental T or B cells. Some of the F1 antisera were specificlly cytotoxic for parental GVH-reactive lymphocytes.

Die ursprünglich aus Südamerika stammenden Tiere verursachen erhebliche Schäden auf Raps und Getreideflächen. Vergrämungsversuche zeigten bisher keine Erfolge. Deshalb hatte das Biosphärenreservatsamt Schaalsee-Elbe wiederholt einen Antrag des Kreisbauernverbandes auf eine Manipulation der Gelege genehmigt. Dazu wurden die frisch gelegten noch gelben Eier teilweise mit Paraffin überzogen oder angebohrt. „Die aktuelle Entwicklung ist für mich Anlass prüfen zu lassen, ob weitere Möglichkeiten bestehen, mit denen wir dem Populationsanstieg entgegenwirken können“, so der Minister für Landwirtschaft und Umwelt Dr. Till Backhaus.

Holiday Punch — Plus a Cozy Fire Charles Dickens gave us so much. Including this. In A Christmas Carol,when Ebenezer Scrooge is presented with the Ghost of Christmas Present, he finds the "jolly Giant" sitting in state on an enormous heap of roast meats and other traditional English Christmas delicacies and flanked by "seething bowls of punch that made the chamber dim with their delicious steam." Charles Dickens knew all about delicious steam. He was a committed English traditionalist in his drinking. He didn't drink the international celebrity's customary champagne, champagne, and more champagne or the trendy drinks of his day — gin cocktails, claret cups, brandy smashes, or the like. Rather, his greatest affinity was for a drink that was fading faster and faster into the past by the time he came into fame. From 1700 to 1830, give or take a couple years on each end, the preeminent English social drink was the bowl of punch, a large-bore mixture of spirits (usually rum and cognac), citrus juice, sugar, water, and spice that was guaranteed to unite any gathering in jollity and boozy good cheer. But with the industrialization, commercialization, and urbanization of day-to-day life that the Victorian years brought, the convivial ritual of clustering around the flowing bowl became as quaint and outmoded as the tricorn hat. Dickens, however, not only bucked the trend but made a whole performance out of bucking it. When he was among friends, it was his custom to brew up a bowl of punch, complete with a running disquisition on the techniques he was using and the ingredients he was deploying, thus adding instruction to delight (as one of his characters might say). Fortunately, in 1847, he wrote the whole procedure out for a friend's wife. It's not hard to follow, and there's no better way to get a holiday party started than by getting everybody involved in draining a bowl of punch. All it takes is a little preparation in advance, a willingness to hold forth a bit in front of your guests, and a high enough ceiling that you won't burn your house down. Dickens was never afraid to employ cheap sensationalism if it would help him get over, and there's nothing more sensational for selling a drink than setting it on fire. Here's our interpretation. Advertisement - Continue Reading Below Charles Dickens's Punch Ritual For 12 to 16 people Step 1: Three hours before your party, peel 3 lemons with a swivel-bladed vegetable peeler, trying to end up with three long spirals of peel. Put them in a 3- or 4-quart fireproof bowl with 3/4 cup demerara sugar or other raw sugar. Muddle the peels and the sugar together and let sit. Talking Points: One of the secrets of punch making is to use the fragrant, sweet oil that resides in lemon peels as the sugar extract. The resulting sugar-oil mix ("oleo-saccharum") adds body to the punch. Talking Points: The cognac is for body and smoothness, the strong rum for bouquet and (frankly) flammability, and the other rum for taming the strong one. Step 3: Set 1 quart water to boil and put the bowl containing the lemon peels and sugar on a wooden cutting board or other heat-resistant surface in a spot where everyone can gather around. When the water boils, turn it off, gather your guests around the bowl, and pour in the cognac and rum, noting what you're adding and why. Step 4: With a long-handled barspoon, remove a spoonful of the rum-cognac mixture and set it on fire. Return it to the bowl, using it to ignite the rest. Stir with a ladle or long-handled spoon, attempting to dissolve the sugar. Let burn for 2 or 3 minutes, occasionally lifting one of the lemon peels up so people can admire the flames running down it. Talking Points: You're setting the punch alight not because it looks cool but to burn off some of the more volatile elements of the alcohol. That's the story, anyway. Step 5: Extinguish the flames by covering the bowl with a tray, and add the reserved lemon juice and the boiling water. (For cold punch, add 3 cups cold water, stir, and slide in a 1-quart block of ice, easily made by freezing a quart bowl of water for 24 hours.) Step 6: Grate fresh nutmeg over the top and ladle out in 3-oz servings. A Part of Hearst Digital Media Esquire participates in various affiliate marketing programs, which means we may get paid commissions on editorially chosen products purchased through our links to retailer sites.

Go back to /usr/src/vdr-1.2.5 and run runvdr.remote. If you use Red Hat, set the environment variable LD_ASSUME_KERNEL=2.4.1, because VDR doesn't yet work with the native posix layer that Red Hat introduced in the latest version. The modules for the DVB card then are loaded, and the VDR is started. Hook up your TV, and you should see a black screen prompting you to define the keys on your remote. After finishing the wizard, you're ready to watch TV, record shows and remove commercials. You can listen to your MP3s and watch videos. There's a manual in VDR's root that explains how to record and edit TV events, using the time-shift feature. Back It Up In case you're disappointed that the end of the article is within reach, don't worry; there still are some optional things you can do. The automatic backup feature has some limitations. Although the (S)VCD backup works flawlessly, the DivX encoding does not crop the picture to remove black bands, should they exist. This has quite a negative impact on bit rate, size and overall picture quality. If you really want a high-quality, small-size MPEG-4, you should back it up manually. The improved picture quality is well worth the trouble. Figure 3. The information bar shows the program name, running TV show and what's on next. VDR splits its recordings into 2GB files, which is a bit inconvenient for transcoding the videos. If you go for manual conversion, which gives you finer control over the quality/size aspect, mencoder or transcode are good options. Use the speedy mencoder, which I found to be perfect for backups to MPEG-4, or transcode, which comes with a lot of tools. If you favor the I-don't-want-to-care approach, get a hold of VDRCONVERT. The README file offers a pretty simple approach to installing it, and at least you can watch some TV while downloading and compiling. With VDRCONVERT you have to change some scripts and configuration files to adapt the DVD/(S)VCD resolutions to NTSC, in case PAL is not used where you live. It's too bad that a Linux PVR doesn't make the TV programs themselves any better, but I guess you can't have everything, can you? Christian A. Herzog is a programmer focused on Web development using open-source technologies. He's still on his never-ending quest to bring a Linux-based device to every home and company he comes across. Write him at noeffred@gmx.net. Comment viewing options I was wonder if you could also include a connection diagram . I was looking at the nexus-s card and didn't see a TV out, just a loop connection is this the connection used for the TV. Or are using additional card to get the TV output?

package x509util import ( "crypto/rand" "crypto/rsa" "crypto/x509" "crypto/x509/pkix" "testing" ) func TestCreateCertificateRequest(t *testing.T) { r := rand.Reader priv, err := rsa.GenerateKey(r, 1024) if err != nil { t.Fatal(err) } template := CertificateRequest{ CertificateRequest: x509.CertificateRequest{ Subject: pkix.Name{ CommonName: "test.acme.co", Country: []string{"US"}, }, }, ChallengePassword: "foobar", } derBytes, err := CreateCertificateRequest(r, &template, priv) if err != nil { t.Fatal(err) } out, err := x509.ParseCertificateRequest(derBytes) if err != nil { t.Fatalf("failed to create certificate request: %s", err) } if err := out.CheckSignature(); err != nil { t.Errorf("failed to check certificate request signature: %s", err) } challenge, err := ParseChallengePassword(derBytes) if err != nil { t.Fatalf("failed to parse challengePassword attribute: %s", err) } if have, want := challenge, template.ChallengePassword; have != want { t.Errorf("have %s, want %s", have, want) } }

Dymas In Greek mythology, Dymas (Ancient Greek: Δύμας) is the name attributed to the following individuals: Dymas, a Mariandynian who warned the Argonauts about the cruelty of Amycus, king of the Bebrycians. Both Mariandynians and Bebrycians lived in northwestern Asia Minor. Dymas, a soldier who fought on the side of the Seven Against Thebes. He took part in the foot-race at Opheltes' funeral games in Nemea. Dymas was wounded in battle and killed himself when the enemy started questioning him. Dymas, a Dorian and the ancestor of the Dymanes. His father, Aegimius, adopted Heracles' son, Hyllas. Dymas and his brother, Pamphylus, submitted to Hyllas. Dymas, king of Phrygia and father of Hecuba. Dymas, perhaps the same as the first. According to Quintus Smyrnaeus this Dymas was the father of Meges, a Trojan whose sons fought at Troy. Dymas, an Aulian warrior, who came to fight at Troy under the leadership of Archesilaus. He died at the hands of Aeneas. Dymas, a Trojan soldier who fought with Aeneas and was killed at Troy. Dymas, was mentioned in Homer's Odyssey as a Phaeacian captain, whose daughter was a friend to the princess Nausicaa. References Category:Kings of Phrygia Category:Characters in Greek mythology Category:Dorian mythology

MacEwan International MacEwan International promotes an internationally informed and cross-culturally sensitive learning environment. Our vision is to be a leader in internationalization, preparing all students, as well as faculty and staff, to succeed in and contribute to a global society and economy as members of an interconnected world community.

Robinsons ready to roll Twins Tyrell and Tyree Robinson making their marks in football, basketball A quick look at twin brothers Tyree and Tyrell Robinson (San Diego/Lincoln) reveals one big misconception: They're not identical. Tyree, older by two minutes, is taller by a full inch and likes to distinguish himself by wearing headbands. Tyrell is bulkier and less flashy with his wardrobe choices. And when the dual-sport athletes take the football field, their differences continue to stack up.

// Copyright 2000-2020 JetBrains s.r.o. Use of this source code is governed by the Apache 2.0 license that can be found in the LICENSE file. package com.intellij.openapi.vcs.impl import com.intellij.ProjectTopics import com.intellij.openapi.application.ApplicationManager import com.intellij.openapi.components.service import com.intellij.openapi.extensions.ExtensionNotApplicableException import com.intellij.openapi.module.Module import com.intellij.openapi.module.ModuleManager import com.intellij.openapi.project.ModuleListener import com.intellij.openapi.project.Project import com.intellij.openapi.project.rootManager import com.intellij.openapi.roots.ModuleRootEvent import com.intellij.openapi.roots.ModuleRootListener import com.intellij.openapi.startup.StartupActivity import com.intellij.openapi.vcs.AbstractVcs import com.intellij.openapi.vcs.ProjectLevelVcsManager import com.intellij.openapi.vcs.VcsDirectoryMapping import com.intellij.openapi.vfs.VirtualFile internal class ModuleVcsDetector(private val project: Project) { private val vcsManager by lazy(LazyThreadSafetyMode.NONE) { (ProjectLevelVcsManager.getInstance(project) as ProjectLevelVcsManagerImpl) } internal class MyPostStartUpActivity : StartupActivity.DumbAware { init { if (ApplicationManager.getApplication().isUnitTestMode) { throw ExtensionNotApplicableException.INSTANCE } } override fun runActivity(project: Project) { val vcsDetector = project.service<ModuleVcsDetector>() val listener = vcsDetector.MyModulesListener() val busConnection = project.messageBus.connect() busConnection.subscribe(ProjectTopics.MODULES, listener) busConnection.subscribe(ProjectTopics.PROJECT_ROOTS, listener) if (vcsDetector.vcsManager.needAutodetectMappings()) { vcsDetector.autoDetectVcsMappings(true) } } } private inner class MyModulesListener : ModuleRootListener, ModuleListener { private val myMappingsForRemovedModules: MutableList<VcsDirectoryMapping> = mutableListOf() override fun beforeRootsChange(event: ModuleRootEvent) { myMappingsForRemovedModules.clear() } override fun rootsChanged(event: ModuleRootEvent) { myMappingsForRemovedModules.forEach { mapping -> vcsManager.removeDirectoryMapping(mapping) } // the check calculates to true only before user has done any change to mappings, i.e. in case modules are detected/added automatically // on start etc (look inside) if (vcsManager.needAutodetectMappings()) { autoDetectVcsMappings(false) } } override fun moduleAdded(project: Project, module: Module) { myMappingsForRemovedModules.removeAll(getMappings(module)) autoDetectModuleVcsMapping(module) } override fun beforeModuleRemoved(project: Project, module: Module) { myMappingsForRemovedModules.addAll(getMappings(module)) } } private fun autoDetectVcsMappings(tryMapPieces: Boolean) { if (vcsManager.haveDefaultMapping() != null) return val usedVcses = mutableSetOf<AbstractVcs?>() val detectedRoots = mutableSetOf<Pair<VirtualFile, AbstractVcs>>() val roots = ModuleManager.getInstance(project).modules.flatMap { it.rootManager.contentRoots.asIterable() }.distinct() for (root in roots) { val moduleVcs = vcsManager.findVersioningVcs(root) if (moduleVcs != null) { detectedRoots.add(Pair(root, moduleVcs)) } usedVcses.add(moduleVcs) // put 'null' for unmapped module } val commonVcs = usedVcses.singleOrNull() if (commonVcs != null) { // Remove existing mappings that will duplicate added <Project> mapping. val rootPaths = roots.map { it.path }.toSet() val additionalMappings = vcsManager.directoryMappings.filter { it.directory !in rootPaths } vcsManager.setAutoDirectoryMappings(additionalMappings + VcsDirectoryMapping.createDefault(commonVcs.name)) } else if (tryMapPieces) { val newMappings = detectedRoots.map { (root, vcs) -> VcsDirectoryMapping(root.path, vcs.name) } vcsManager.setAutoDirectoryMappings(vcsManager.directoryMappings + newMappings) } } private fun autoDetectModuleVcsMapping(module: Module) { if (vcsManager.haveDefaultMapping() != null) return val newMappings = mutableListOf<VcsDirectoryMapping>() for (file in module.rootManager.contentRoots) { val vcs = vcsManager.findVersioningVcs(file) if (vcs != null && vcs !== vcsManager.getVcsFor(file)) { newMappings.add(VcsDirectoryMapping(file.path, vcs.name)) } } if (newMappings.isNotEmpty()) { vcsManager.setAutoDirectoryMappings(vcsManager.directoryMappings + newMappings) } } private fun getMappings(module: Module): List<VcsDirectoryMapping> { return module.rootManager.contentRoots .mapNotNull { root -> vcsManager.directoryMappings.firstOrNull { it.directory == root.path } } } }

Enhanced absorption and inhibited metabolism of emodin by 2, 3, 5, 4'-tetrahydroxystilbene-2-O-β-D-glucopyranoside: Possible mechanisms for Polygoni Multiflori Radix-induced liver injury. Polygoni Multiflori Radix (PMR) has been commonly used as a tonic in China for centuries. However, PMR-associated hepatotoxicity is becoming a safety issue. In our previous in vivo study, an interaction between stilbenes and anthraquinones has been discovered and a hypothesis is proposed that the interaction between stilbene glucoside-enriching fraction and emodin may contribute to the side effects of PMR. To further support our previous in vivo results in rats, the present in vitro study was designed to evaluate the effects of 2, 3, 5, 4'-tetrahydroxystilbene-2-O-β-D-glucopyranoside (TSG) on the cellular absorption and human liver microsome metabolism of emodin. The obtained results indicated that the absorption of emodin in Caco-2 cells was enhanced and the metabolism of emodin in human liver microsomes was inhibited after TSG treatment. The effects of the transport inhibitors on the cellular emodin accumulation were also examined. Western blot assay suggested that the depressed metabolism of emodin could be attributed to the down-regulation of UDP-glucuronosyltransferases (UGTs) 1A8, 1A10, and 2B7. These findings definitively demonstrated the existence of interaction between TSG and emodin, which provide a basis for a better understanding of the underlying mechanism for PMR-induced liver injury.

ES News email The latest headlines in your inbox twice a day Monday - Friday plus breaking news updates Enter your email address Continue Please enter an email address Email address is invalid Fill out this field Email address is invalid You already have an account. Please log in Register with your social account or click here to log in I would like to receive lunchtime headlines Monday - Friday plus breaking news alerts, by email Update newsletter preferences Travellers lost nearly 1,000 items on the Tube — including golf clubs, shoes and underwear — during the busiest weekend of Christmas celebrations last year, data shows. Analysis showed 949 items were lost on the London Underground in two days, ranging from credit cards and wallets to hats and mobile phones. Partygoers are being urged to be careful of their belongings this weekend, as people finish work for the festive break. Today is widely known as Mad Friday — traditionally the last working Friday before Christmas when thousands of revellers go to pubs and bars. Data obtained from Transport for London by the home insurance company Policy Expert shows people lost 200 debit and credit cards, 62 hats, 54 mobile phones, 47 purses and wallets and three passports. Other lost items included footwear, which was found at Bond Street, earrings, which were lost at Cockfosters, and ear muffs at Rayners Lane. Underwear was left behind in Wood Green, while two golf clubs, 32 scarves and four suitcases also went missing. The stations where most items were lost last year were Hammersmith, Oxford Circus and King’s Cross. In total, just 120 items were claimed back. Adam Powell, Policy Expert’s operations director, said: “Thousands of people will celebrate the start of the Christmas break in the capital this weekend and whilst there is no need to dampen the festive spirit, Mad Friday revellers should keep a close eye on their personal belongings. “We carry hundreds of pounds of belongings on us when we go out and it could be an expensive ordeal should they disappear down the gap. Making sure you have away-from-home cover included in your home insurance policy can give you peace of mind that if something does go missing, you won’t be out of pocket.” Mad Friday, also known as Frantic Friday, is one of the busiest nights for the emergency services. On the equivalent Friday last year paramedics received 300 calls per hour. The emergency services usually station extra staff on the streets in anticipation.

Friends of the Crow Collection: Adults/ Children ($10/ $3) || General Public: Adults/ Children ($18/ $5) Otsukimi Celebration, 2012 The Japan America Society celebrates the full autumn moon each year with an outdoor picnic, Japanese music, and haiku poetry. Although not commonly observed in modern-day Japan, the moon viewing tradition dates back to the Heian Period (794–A.D. 1185), when the evening was marked with poetry and music by court aristocrats. The celebration later spread to warriors, townspeople, and farmers, and became a harvest festival. Bring a picnic supper, beverage, and something to sit on as no food or drink will be sold at the event or pre-order an Obento from Mr. Sushi for $18 when purchasing your celebration tickets. Alcohol is not allowed at Winfrey Point, a City of Dallas park facility. For more information, visit jasdfw.org.

Probing molecules in integrated silicon-molecule-metal junctions by inelastic tunneling spectroscopy. Molecular electronics has drawn significant attention for nanoelectronic and sensing applications. A hybrid technology where molecular devices are integrated with traditional semiconductor microelectronics is a particularly promising approach for these applications. Key challenges in this area include developing devices in which the molecular integrity is preserved, developing in situ characterization techniques to probe the molecules within the completed devices, and determining the physical processes that influence carrier transport. In this study, we present the first experimental report of inelastic electron tunneling spectroscopy of integrated metal-molecule-silicon devices with molecules assembled directly to silicon contacts. The results provide direct experimental confirmation that the chemical integrity of the monolayer is preserved and that the molecules play a direct role in electronic conduction through the devices. Spectra obtained under varying measurement conditions show differences related to the silicon electrode, which can provide valuable information about the physics influencing carrier transport in these molecule/Si hybrid devices.

Promethium: uses The following uses for promethium are gathered from a number of sources as well as from anecdotal comments. I'd be delighted to receive corrections as well as additional referenced uses (please use the feedback mechanism to add uses). shows promise as a portable X-ray unit possibly useful as a heat source to provide auxilliary power for space probes and satellites

Prevalence of varicocoele and its association with body mass index among 39,559 rural men in eastern China: a population-based cross-sectional study. Varicocoele is a common cause of male infertility. We undertook a population-based cross-sectional study to evaluate the prevalence of varicocoele among rural men in eastern China and its association with body mass index. A total of 39,559 rural men in six counties in Beijing, Guangdong and Shandong provinces were recruited from 2011 to 2012. The presence and severity of varicocoele were measured by physical examinations. Univariate and multivariate logistic regression models were constructed to assess the association between varicocoele and body mass index after adjusting for possible confounders. Varicocoele was diagnosed in 1911 of 39,559 participants with an overall prevalence of 4.83%. The prevalence of varicocoele was highest in underweight (6.29%) and lowest in obese patients (3.71%, p < 0.05). The prevalence also decreased as body mass index increased in all three varicocoele grades. In multivariate logistic regression analysis after adjusting for region, age, height, occupation, cigarette smoking and alcohol consumption, body mass index was still inversely and independently associated with varicocoele (p < 0.001). Compared with normal weight men, underweight men (OR = 1.34; 95% CI, 1.10-1.63) were more likely to have varicocoele, whereas overweight men (OR = 0.88; 95% CI, 0.79-0.99) and obese men (OR = 0.75; 95% CI, 0.58-0.97) were less likely to have varicocoele. This study revealed that the prevalence of varicocoele was 4.83% among rural men in eastern China; body mass index was inversely and independently associated with the presence of varicocoele. Future efforts should be made to validate the risk factors for varicocoele and strengthen the prevention and treatment of varicocoele, especially in underweight men.

We use cookies to give you the best experience possible. By using this website you consent to our use of these cookies to find out more about how we use cookies and how to manage them, please see our Privacy Policy and our Terms & Conditions. Accept The Huffington Post: Top Design Destinations for 2017 2017-02-23 By Janette Ewen Ever since Frank Gehry’s spectacular Guggenheim Bilbao put its sleepy namesake city on the radar of architecture buffs two decades ago, design has became an integral aspect of travel and tourism, joining food, culture and climate when it comes to visitor draws. This year, the list of destinations sure to entice design fans includes spots from the West Indies to North Africa. They offer a wide range of aesthetic attractions, from cutting-edge urban design to exquisite historical gems. OLD HAVANA, NEW URGENCY Whether the recent detente between the United States and Cuba will result in an onslaught of American visitors to the island or not, Canadians aren’t waiting to find out: According to KAYAK, a world-leading travel search engine, Havana is one of the year’s top 10 trending destinations among travellers from the Great White North, whose online inquiries about the city skyrocketed by 230 percent compared to last year. In anticipation of more visitors, hotels in Havana are being modernized and restaurants given new polish, but it’s the bustling metropolis’ status as a living design museum that no doubt appeals to most foreigners. For architecture fans, hotels like the Nacional offer glimpses into long-gone eras, while automobile buffs would be hard-pressed to find a greater parade of vintage cars. Speaking of moveable feasts, bars like La Floridita, where Ernest Hemingway indulged his fondness for daiquiris, are modern-day links to literary and artistic legends. Clearly, the time to visit Havana is now, whatever your aesthetic bent. CARIBBEAN COOL Over the past several years, restaurant-rich Grand Cayman, the largest of the Cayman Islands, has been nurturing a reputation as the culinary capital of the Caribbean. Now, its growing foodie cred is being matched by its design cachet. In November, the ultra-sleek Kimpton Seafire Resort + Spa, designed by U.S. firm SB Architects, opened on Seven Mile Beach, bringing a welcome shot of global chic (plus four more dining options) to that pristine stretch of coastline. Not far away, Camana Bay, an ambitious mixed-use development, has been heralded as a rare example of new urbanism in the region, its 500 acres encompassing high-end shops, office and residential space, interactive fountains and a pedestrianized main street called the Paseo. Situated between the Kimpton and Camana Bay is the Caribbean Club, a luxury apartment hotel and ideal base for exploring the area; it also houses one of Grand Cayman’s foremost eateries, the trattoria Luca. ROAD TO MOROCCO Another top trender among Canadian travellers according to KAYAK is Casablanca, the romantic Moroccan city that has long offered a beguiling mix of French and Arabic cultures. Nowhere is this hybrid allure more visible than in its architecture, which ranges from the art deco elegance of Place Mohammed V to contemporary showstoppers like the Four Seasons Casablanca on the oceanfront Corniche. At bustling Marche Centrale, the Moorish-style setting is as enticing as the fried fish and grilled vegetables, while L’Atelier 21, the city’s leading modern art gallery, showcases emerging and established artists in an au courant space. New air links to Casablanca from Canada this year make visiting even easier. LONDON CALLING The British capital has always been a magnet for design aficionados, but 2017 offers an extra-special reason to visit: the recently transplanted Design Museum, which has been moved from its previous home on the south bank of the Thames to much larger digs in Kensington. Ten years in the making, the $140-million wood-and-concrete marvel, reimagined by minimalist architect John Pawson on the site of the former Commonwealth Institute, is the Brit superstar’s first public building in London. Visitors must pay to see special exhibitions, but the museum’s extensive permanent collection, which includes everything from a 2012 Olympic torch to a full-size Tube car, is free to view. Another area museum completing a major update this year is the venerable Victoria and Albert, which will unveil a new underground gallery and a new entrance on Exhibition Road in July. Even the city’s best watering holes are offering new eye candy: Check out the restored blue walls in The Berkeley’s expanded Blue Bar.

Mai-Mai The term Mayi-Mayi or Mai-Mai refers to any kind of community-based militia group active in the Democratic Republic of the Congo (DRC), formed to defend their local territory against other armed groups. Most were formed to resist the invasion of Rwandan forces and Rwanda-affiliated Congolese rebel groups, but some may have formed to exploit the war for their own advantage by looting, cattle rustling or banditry. Groups that fall under the umbrella term "Mai-Mai" include armed forces led by warlords, traditional tribal elders, village heads, and politically motivated resistance fighters. Because Mai Mai have had only the most tenuous internal cohesion, different Mai-Mai groups allied themselves with a variety of domestic and foreign government and guerrilla groups at different times. The term Mai-Mai does not refer to any particular movement, affiliation or political objective but to a broad variety of groups. Mai-Mai were particularly active in the eastern Congolese provinces bordering Rwanda, North Kivu and South Kivu (the "Kivus"), which were under the control of the Rwanda-allied Banyamulenge-dominated rebel faction, the Rally for Congolese Democracy–Goma (RCD-Goma) during the Second Congo War. While militias have long been common in the Kivus, particularly among the minority Batembo and Babembe ethnic groups, the recent wars and conflicts caused large numbers of town dwellers to form Mai-Mai. Although the Mai-Mai, either as a group or as individual groups, were not party to the 1999 Lusaka Accord meant to end the Second Congo War, they remained one of the most powerful forces in the conflict and the lack of cooperation from some groups has been problematic for the peace process. Mai-Mai in North and South Kivu According to a 2001 UN report, 20,000 to 30,000 Mai-Mai were active in the two Kivu provinces. The two most powerful and well-organized Mai-Mai groups in the Kivus were led by Generals Padiri and Dunia. Currently most active is a group which is called Mai-Mai Yakutumba, was organized in 2007 by General Yakutumba. They were reported to have received aid from the government of the Democratic Republic of Congo and are widely viewed by other Mai Mai groups as the leaders, though not the commanders, of the Kivu Mai-Mai. A number of smaller Mai-Mai groups, such as the Mudundu 40/Front de Résistance et de Défense du Kivu (FRDKI) and Mouvement de Lutte contre l'Agression au Zaïre/Forces Unies de Résistance Nationale contre l'Agression de la Républíque Démocratique du Congo (MLAZ/FURNAC), were reported to cooperate with the Rwandan military and Rally for Congolese Democracy–Goma (RCD-Goma). Walikale and Masisi north of Goma were the centres of Mai-Mai activity in North Kivu. In South Kivu, there have historically been concentrations around Walungu and Bunyakiri south of Lake Kivu, around Uvira and Mwenaga at the northern end of Lake Tanganyika, further south around Fizi, and around Shabunda, between the Rwandan border and Kindu. A Mai-Mai leader, Colonel Mayele, was arrested by UN forces in October 2010, allegedly being the leader behind mass rapes in the Walikale region of North Kivu province. Mai-Mai in Katanga A former leader of the Mai-Mai, Gédéon Kyungu Mutanga, turned himself over to MONUC troops in May 2006. He was found guilty of numerous war crimes between October 2003 and May 2006 and was sentenced to death by the Kipushi Military Tribunal in Katanga Province on 6 March 2009. He escaped from prison in September 2011 and formed the Mai-Mai Kata Katanga ("Secede Katanga"). Other Mai-Mai groups There was a large Mai-Mai presence in Maniema, in particular around Kindu and Kalemie. Province Orientale also hosts a number of Mai-Mai, but these groups were apparently involved in long-standing ethnic disputes. Mai-Mai Gedeon is also commanded by Gedeon Kyungu Mutanga and loosely tied to his Mai-Mai Kata Katanga. The Corak Kata Katanga also known as the Co-ordination for a Referendum on Self-determination for Katanga, composed mainly of former Katanga Tigers, a separatist group active in the 1960s. They claim to be behind the attack on the Katanga airport in February 2011. It is unclear to what extent all these groups are co-ordinated. The Nduma Defense of Congo (or Mai-Mai Sheka) was formed in 2009 by former minerals trader Ntabo Ntaberi Sheka, an ethnic Nyanga. Sheka claims the group was formed to liberate the mines of Walikale Territory in North Kivu. The NDC are accused of a mass rape of at least 387 women, men, and children over a three day span in Walikale in 2010. Mai-Mai and the mountain gorillas In May 2007, Mai-Mai killed two wildlife officers in Virunga National Park and threatened to kill mountain gorillas if the government retaliated. The Mai-Mai are also suspected of the killings of nine mountain gorillas, with the use of machetes, and automatic weapons. In an October 2012 incident, Mai-Mai killed two park staff and a soldier, while three soldiers were injured. From 1990 to 2018 some 170 Virunga Rangers have died in such attacks, according to the World Wildlife Foundation. Six Virunga Park Rangers were reported to have been killed in Virunga National Park. Five rangers and a driver were killed in an ambush and a sixth ranger was injured in the Central section of the vast reserve on April 9, 2018. Officials suspected the attacks were by the Mai-Mai. See also Resistance Patriots Maï-Maï Mai-Mai Kata Katanga Gédéon Kyungu Mutanga References External links Global Security description UN Assessment of armed groups in Congo, 1 April 2002 National Geographic Mai-mai atrocities included canibalism Category:Factions of the Second Congo War Category:History of the Democratic Republic of the Congo Category:History of Rwanda Category:Rebel groups in the Democratic Republic of the Congo Category:Rebel groups that actively control territory Category:Vigilantism

Methylglyoxal activates NF-κB nuclear translocation and induces COX-2 expression via a p38-dependent pathway in synovial cells. There is growing evidence of an increased prevalence of osteoarthritis (OA) among people with diabetes. Synovial inflammation and increased expression of cyclooxygenase-2 (COX-2) are two key features of patients with OA. Methylglyoxal (MGO) is a common intermediate in the formation of advanced glycation end-products, and its concentration is also typically higher in diabetes. In this study, we investigated the effects of the treatment of different MGO concentrations to rabbit HIG-82 synovial cells on COX-2 expression. The MGO induced COX-2 mRNA expression was detected by quantitative polymerase chain reaction. The MGO induced COX-2 protein production and its signaling pathways were detected by western blotting. The nuclear factor-kappa B (NF-κB) nuclear translocation by MGO was examined by immunofluorescence. In the present study, we find that MGO has no toxic effects on rabbit synovial cells under the experimental conditions. Our analysis demonstrates that MGO induced COX-2 mRNA and protein production. Moreover, MGO induces p38-dependent COX-2 protein expression as well as the phosphorylations of extracellular signal-regulated kinase, c-Jun N-terminal kinase (JNK), and Akt/mammalian target of rapamycin (mTOR)/p70S6K; however, inhibition of JNK and Akt/mTOR/p70S6K phosphorylations further activates COX-2 protein expression. Furthermore, MGO is shown to activate of nuclear factor-kappa B (NF-κB) nuclear translocation. Our results suggest that MGO can induce COX-2 expression via a p38-dependent pathway and activate NF-κB nuclear translocation in synovial cells. These results provide insight into the pathogenesis of the synovial inflammation under the diabetic condition associated with higher MGO levels.

Q: Do we want an xkcd tag? xkcd is referred to often on PPCG, with at least 47 questions which are based on concepts or directly related to the xkcd webcomic. Therefore, is it worthwhile introducing an xkcd tag to group all of these challenges together? A: No Tags are meant to classify questions according to some distinctive quality that they share. Simply referencing an xkcd comic is not a distinctive quality that would create a meaningful classification.

[A meningioma in the posterior fossa without dural attachment: case report]. An extremely rare case of a meningioma in the posterior fossa without dural attachment has been reported. The patient was a 56-year-old male whose chief manifestation was the abnormality of his CT scan. His past history included gastric and colonic polyp when he was 54, 55 years old, and non-Hodgkin's lymphoma before hospitalization in our department. CT scan showed a small round non-enhancing lesion located at the lateral site of the right cerebellar cortex. T1 weighted image of MRI showed a homogeneous low intensity lesion with partial enhancing with Gd-DTPA. Proton image showed a remarkable low intensity lesion which showed an extramedullary mass. Right retromastoid craniectomy was performed. The mass was an extramedullary tumor which had no relation with the cerebellar cortex and dura matter. The arachnoid membrane around the tumor was intact. The tumor was totally resected and the patient had no neurological deficits. Histopathologically, the tumor was delineated into laminar structures by collagen fiber. Tumor cells were spindle in shape and made a whorling formation. There was no psammoma body and it had a hyperchromatic nuclei without mitotic features. Electron microscopic studies revealed no typical interdigitation but irregularity of the cell membrane. Abundant collagen fibers were in contact with basement membrane of the tumor. According to these findings, we diagnosed fibroblastic meningioma with atypical forms. Meningiomas without dural attachment are rare in adults, especially extremely rare of the posterior fossa. There are only 23 previous reports of "meningioma of the posterior fossa without dural attachment". Cantore divided these meningiomas into three groups (IV ventricle, inferior tela choroidea and cisterna magna).(ABSTRACT TRUNCATED AT 250 WORDS)

Genetic diversity studies of Brazilian garlic cultivars and quality control of garlic-clover production. The garlic cultivars grown in Brazil evolved from somatic mutations and clone selection by breeding programs and by the introduction of germplasm from other countries. Morphological characters have been used to differentiate these cultivars. Two hundred and six random amplified polymorphic DNA markers were utilized for a diversity analysis of the 17 most planted garlic cultivars in Brazil. Bootstrap analysis showed that the number of markers was efficient and sufficient to obtain a coefficient of variation of 10%. Similarity varied between 16 and 98% and cluster analysis showed that, in general, genetic similarities correlate with morphological characters of the cultivars and production cycle variation. High bootstrap values at most of the nodes supported the dendrogram stability. The grouping of most varieties agreed well with previous reports based on morphological characters. As a vegetative-propagated species, viral diseases are a key problem regarding production and quality of the bulbs, causing gradual loss of yield and decrease in storage capacity. To improve the health quality of garlic seed, a virus-free stock of garlic cloves of the Amarante cultivar was obtained. The ability to distinguish garlic cultivars to detect varietal mixing after in vitro multiplication is extremely important, since correct identification is not possible until bulbs are produced. Random amplified polymorphic DNA markers were also used to differentiate cultivars while they are in vitro and not amenable to morphological discrimination. No difference was identified between the fingerprints of the virus-free or of the infected bulks of Amarante, showing that there was no clove mixing in the handling of material in the clonal multiplication phase.

Conventional methods for producing metal powder include a water atomizing method, which provides metal powder by injecting a high pressure water jet to a flow of a molten material; a gas atomizing method, which employs spraying of N2 gas or Ar gas in place of the water jet used in the atomizing method; and a centrifugation method, in which a molten material jet is injected into cooling water present in a rotary drum rotating at high speed. Fine particles are also produced through a breakdown method such as mechanical formation employing a mill or the like and also through a buildup method such as a precipitation method or a sol-gel method. However, in the water atomizing method and the gas atomizing method, the nozzle structure is complicated and an excessive load is imposed on nozzles, resulting in lowered durability of the nozzle, since the molten material is formed into powder form by a flow of high pressure cooling water or cooling gas. Meanwhile, in the centrifugation method, the structure of the apparatus is complicated, in order to enable high-speed rotation of the rotary drum. Furthermore, in these methods, the molten metal is pulverized on the basis of collision energy. Thus, the resulting particle size is varied, and the yield of fine particles is poor. The breakdown method employing mechanical formation or the like can produce only large particles having a minimum size of, for example, approximately 100 μm. The buildup method such as a precipitation method can produce fine particles having a maximum size of approximately 1 μm, and particles which are larger than approximately 1 μm cannot be obtained. Therefore, when conventional methods and apparatuses for producing fine particles are employed, fine particles having a size ranging from several micrometers to the order of 10 μm, particularly fine particles having a size of about 3 μm, are difficult to obtain. Also, in the breakdown method, a large portion of the molten metal cannot be converted into fine particles and remains as a lump, thereby deteriorating the yield thereof. In addition, the particle size distribution assumes a broaden profile, causing the problem that fine particles having a desired particle diameter cannot be obtained in a large amount. Conventionally, a liquid quenching method has been known for producing amorphous metal. According to the liquid quenching method, a molten material is cooled and solidified by, for example, causing a molten metal liquid to spout into a coolant, whereby amorphous metal is produced. Even when a centrifugation method, which can attain a relatively large cooling rate, is employed in combination with the liquid quenching method, the heat flux between two liquids (i.e., molten material and coolant) is limited to the critical heat flux in the case where heat conduction is induced by cooling based on convection or a conventional boiling method. Thus, the cooling rate is limited to 104 to 105 K/s, which problematically imposes limitation on the type of metal which can be converted into an amorphous material. Previously, the present applicant filed a patent application for a method for producing fine particles and amorphous material of molten material which includes supplying into a liquid coolant a molten material which has been formed by melting a raw material to be converted into fine particles or amorphous material, with a small difference in flow speed of the two liquids, to thereby cause boiling by spontaneous bubble nucleation and employing the resultant pressure wave for producing fine particles and amorphous material thereof (see Patent Documents: WO 01/81033 and WO 01/81032). However, according to the method for which the present applicant previously filed a patent application, when a high-melting material having a melting point of, for example, 800° C. or higher is used, vapor film cannot be broken satisfactorily through condensation. Thus, formation of fine particles or amorphous material of molten material cannot be fully achieved. Thus, an object of the present invention is to provide, on the basis of improvement of the previously developed technique, a method for producing fine particles, the method being capable of producing fine particles from a high-melting-point raw material and readily producing submicron fine particles which have not been readily produced through the previously developed technique. Another object of the invention is to provide an apparatus therefor.

package io.gitlab.arturbosch.detekt.generator.collection import io.gitlab.arturbosch.detekt.api.DetektVisitor import io.gitlab.arturbosch.detekt.generator.collection.exception.InvalidDocumentationException import io.gitlab.arturbosch.detekt.rules.isOverride import org.jetbrains.kotlin.psi.KtCallExpression import org.jetbrains.kotlin.psi.KtClassOrObject import org.jetbrains.kotlin.psi.KtFile import org.jetbrains.kotlin.psi.KtProperty import org.jetbrains.kotlin.psi.KtReferenceExpression import org.jetbrains.kotlin.psi.KtSuperTypeList import org.jetbrains.kotlin.psi.KtValueArgumentList import org.jetbrains.kotlin.psi.psiUtil.containingClass import org.jetbrains.kotlin.psi.psiUtil.referenceExpression data class MultiRule( val name: String, val rules: List<String> = listOf() ) { operator fun contains(ruleName: String) = ruleName in this.rules } private val multiRule = io.gitlab.arturbosch.detekt.api.MultiRule::class.simpleName ?: "" class MultiRuleCollector : Collector<MultiRule> { override val items = mutableListOf<MultiRule>() override fun visit(file: KtFile) { val visitor = MultiRuleVisitor() file.accept(visitor) if (visitor.containsMultiRule) { items.add(visitor.getMultiRule()) } } } class MultiRuleVisitor : DetektVisitor() { val containsMultiRule get() = classesMap.any { it.value } private var classesMap = mutableMapOf<String, Boolean>() private var name = "" private val rulesVisitor = RuleListVisitor() private val properties: MutableMap<String, String> = mutableMapOf() fun getMultiRule(): MultiRule { val rules = mutableListOf<String>() val ruleProperties = rulesVisitor.ruleProperties .mapNotNull { properties[it] } rules.addAll(ruleProperties) rules.addAll(rulesVisitor.ruleNames) if (name.isEmpty()) { throw InvalidDocumentationException("MultiRule without name found.") } if (rules.isEmpty()) { throw InvalidDocumentationException("MultiRule $name contains no rules.") } return MultiRule(name, rules) } override fun visitSuperTypeList(list: KtSuperTypeList) { val isMultiRule = list.entries ?.mapNotNull { it.typeAsUserType?.referencedName } ?.any { it == multiRule } ?: false val containingClass = list.containingClass() val className = containingClass?.name if (containingClass != null && className != null && !classesMap.containsKey(className)) { classesMap[className] = isMultiRule } super.visitSuperTypeList(list) } override fun visitClassOrObject(classOrObject: KtClassOrObject) { super.visitClassOrObject(classOrObject) if (classesMap[classOrObject.name] != true) { return } name = classOrObject.name?.trim() ?: "" } override fun visitProperty(property: KtProperty) { super.visitProperty(property) if (classesMap[property.containingClass()?.name] != true) { return } if (property.isOverride() && property.name != null && property.name == "rules") { property.accept(rulesVisitor) } else { val name = property.name val initializer = property.initializer?.referenceExpression()?.text if (name != null && initializer != null) { properties[name] = initializer } } } } class RuleListVisitor : DetektVisitor() { var ruleNames: MutableSet<String> = mutableSetOf() private set var ruleProperties: MutableSet<String> = mutableSetOf() private set override fun visitValueArgumentList(list: KtValueArgumentList) { super.visitValueArgumentList(list) val argumentExpressions = list.arguments.map { it.getArgumentExpression() } // Call Expression = Constructor of rule ruleNames.addAll(argumentExpressions .filterIsInstance<KtCallExpression>() .map { it.calleeExpression?.text ?: "" }) // Reference Expression = variable we need to search for ruleProperties.addAll(argumentExpressions .filterIsInstance<KtReferenceExpression>() .map { it.text ?: "" }) } }

Failure of covalently cross-linked human IgG myeloma subclass protein to release histamine from human leukocytes. We have examined the ability of IgG subclass antibodies to release histamine from human leukocytes using covalently cross-linked oligomers of human myeloma proteins. Purified IgG1, G2, G3, G4, (or IgE) was incubated with dimethyl suberimidate to induce cross-linking. The resulting dimers, trimers, and higher molecular weight oligomers were isolated using gel filtration columns (Sephadex G200 and Ultrogel AcA 22) connected in tandem. None of the oligomers of IgG1, G2, G3, or G4 released histamine from leukocytes of donors whose basophils released histamine when challenged with IgE dimer. Furthermore, preincubation with subclass specific oligomers did not desensitize cells to challenge with IgE dimer or to anti-IgE. We conclude that, under our experimental conditions, oligomers of human IgG myeloma subclass antibodies do not trigger histamine release nor modulate IgE-mediated reactions.

Because of the extreme temperatures of exhaust systems, we do not recommend J-B Weld for use on exhaust manifolds and catalytic converters. Nor do we recommend the product for repairs within the combustion chamber. However, in areas where the continuous temperature is less than 450º F, we do recommend our HighHeat epoxy putty stick.

Those words (choice profanity included) woke me with a start the other night. What was I thinking, organizing this trip to Vietnam to connect sons and daughters who lost fathers on both sides of the Vietnam War? I have a lot of fears about this journey. There’s the mundane ones about getting sick, or bitten by something slimy. Maybe I'll become separated from the group because something in a shop caught my eye (this, given my nature, is the most likely scenario). But the deeper fears are right under the surface. What’s going to happen when we come face to face with the Vietnamese sons and daughters? Will they be angry? Worse, will I? It was easy to push past these bigger fears earlier this year when I first formed the 2 Sides Project. Now the trip is getting closer—we leave four weeks from today—and they’re keeping me up at night. I’m going to have to remember what I know in the daylight: there have been moments in my life when I’ve found people who shared my experience, who spoke the same language as me, who felt the same way I did about things. These moments are profound. They make me feel connected, anchored in the world. They are often turning points that lead me to a better place. That was the case when I met other sons and daughters in the U.S. who lost fathers in the war. So, I’ll keep my focus on them. And on the amazing experience we have in store. Six of us will be meeting Vietnamese sons and daughters and visiting the sites where our fathers died. I’ll profile them all -- Mike, Ron, Margaret, Susan and Patty -- here in the coming weeks as we get ready. Come with us virtually. It’s going to be quite a journey, and we’re looking forward to sharing it with you.

Cognitive and behavioral effects of carbamazepine in children: data from benign rolandic epilepsy. The effects of antiepileptic drugs on cognition are difficult to delineate, yet of critical importance for children with epilepsy. We investigated the cognitive and behavioral effects of carbamazepine in children with benign rolandic epilepsy. Ten subjects with benign rolandic epilepsy were evaluated with and without carbamazepine treatment. Fourteen unmedicated subjects with migraine headache evaluated twice served as a control group. Subjects were 6 to 12 years of age, fluent in English, and not mentally retarded. We found that children with benign rolandic epilepsy were quicker on a visual-search task and recalled stories better when not treated than when treated with carbamazepine. After correction for multiple comparisons only the memory finding remained significant. Higher carbamazepine serum level was associated with slower performance on the same visual-search task. This latter finding did not meet multiple comparison criteria. Numerous significant practice effects were found within the control group. Comparisons with reliable change indices identified two subjects with benign rolandic epilepsy with particularly poor scores while receiving carbamazepine. These findings suggest some effects on memory from carbamazepine; however, they do not support meaningful dosage-related effects, within the recommended range. Significant practice effects confirmed the need to control for such effects when evaluating treatments. Finally, identification of two subjects who performed more poorly while on carbamazepine suggests that some children might experience particular difficulties while receiving this medication and highlights the need to investigate individual subject responses to treatment.

Got this cute little sewing chair from Sara and Stacy at SugarSCOUT–they have “super sweet finds of all kinds”…just check out their Etsy Shop. (lots of great ideas on their blog @ www.sugarSCOUT.com, too!) I do love spending time in my studio that has become a haven for creating my upcycled bags. I’m adding new bags as quick as I get them done to my Etsy shop. Take a look…it’s called itzaChicThing. I love to layer color, pattern and texture. I created this bag using a fusing process. After making many bags, all shapes and sizes (you can see some of them at bohochicbag.com), I decided to use the same concept to create pieces for hanging.

This invention relates generally to enzymes that convert sucrose to isomaltulose. More particularly, the present invention relates to novel sucrose isomerases, to polynucleotides encoding these enzymes, to methods for isolating such polynucleotides and to nucleic acid constructs that express these polynucleotides. The invention also relates to cells, particularly transformed bacterial or plant cells, and to differentiated plants comprising cells, which express these polynucleotides. The invention further relates to the use of the polypeptides, polynucleotides, cells and plants of the invention for producing isomaltulose. Isomaltulose α-D-glucopyranosyl-1,6-D-fructofuranose (also called palatinose) is a naturally occurring structural isomer of sucrose (α-D-glucosyl-1,2-D-fructose). Isomaltulose is a nutritive disaccharide, with sweetness and bulk similar to sucrose. Several characteristics make isomaltulose advantageous over sucrose for some applications in the food industry: 1) noncariogenic (not causing dental decay); 2) low glycemic index (useful for diabetics); 3) selective promotion of growth of beneficial bifidobacteria among human intestinal microflora; 4) greater stability of isomaltulose-containing foods and beverages; 5) less hygroscopic; 6) simple conversion into sugar alcohols with other useful properties as foods. The safety of isomaltulose has been comprehensively verified, resulting in unqualified approval as human food, and it is widely used commercially as a sucrose substitute in foods, soft drinks and medicines (Takazoe, 1989, Palatinose—an isomeric alternative to sucrose. In: Progress in Sweeteners (T H Grengy, ed.) pp 143-167. Elsevier, Barking, UK). Furthermore, because isomaltulose has an accessible carbonyl group, it has attracted attention as a renewable starting material for the manufacture of bioproducts such as polymers and surfactants with potential advantages over substances manufactured from petroleum (Cartarius et al., 2001, Chemical Engineering and Technology 24: 55A-59A; Kunz, 1993, From sucrose to semisynthetical polymers. In: Carbohydrates as Organic Raw Materials II (G Descotes, ed.) pp 135-161. VCH, Weinheim; Lichtenthaler et al., 2001, Green Chemistry 3: 201-209; Schiweck et al., 1991, New developments in the use of sucrose as an industrial bulk chemical. In: Carbohydrates as Organic Raw Materials (F W Lichtenthaler, ed.) pp 57-94. VCH, Weinheim). Commercial isomaltulose is produced from food-grade sucrose by enzymatic rearrangement from a (1,2)-fructoside to a (1,6)-fructoside followed by crystallization. Sucrose isomerase (SI) enzymes (also known as isomaltulose synthases), which are able to convert sucrose to isomaltulose, have been demonstrated in Protaminobacter rubrum, Erwinia rhapontici, E. carotovora var atroseptica, Serratia plymuthica, S. marcesens, Pseudomonas mesoacidophila, Leuconostoc mesenteroides, Klebsiella spp., Agrobacterium sp., haploid yeast and Enterobacter sp. (Avigad 1959, Biochemical Journal 73: 587-593; Bornke et al., 2001, Journal of Bacteriology 183: 2425-2430; Cheetham et al., 1982 Nature 299: 628-631; Huang et al., 1998, Journal of Industrial Microbiology & Biotechnology 21: 22-27; Lund and Waytt, 1973, Journal of General Microbiology 78: 331-3; Mattes et al., 1998, U.S. Pat. No. 5,786,140; McAllister et al., 1990, Biotechnology Letters 12: 667-672; Miyata et al., 1992, Bioscience Biotechnology and Biochemistry 56: 1680-1681; Munir et al., 1987, Carbohydrate Research 164: 477-485; Nagai et al., 1994, Bioscience Biotechnology and Biochemistry 58: 1789-1793; Nagai-Miyata et al., 1993, Bioscience Biotechnology and Biochemistry 57: 2049-2053; Park et al., 1996, Revista De Microbiology 27: 131-136; Schmidt-Berg-Lorenz and Maunch, 1964, Zeitung fur die Zuckerindustrie 14: 625-627; Stotola et al., 1956, Journal of the American Chemical Society 78: 2514-2518; Tsuyuki et al., 1992, Journal of General and Applied Microbiology 38: 483-490; Zhang et al., 2002, Applied and Environmental Microbiology 68: 2676-2682). Isomaltulose is currently produced in industrial scale column reactors containing immobilized bacterial cells. Initially, natural isolates have been used for this purpose but it is anticipated that higher yields of isomaltulose may be achieved using recombinant techniques. Mattes et al. (1998, supra) disclose isolated polynucleotides from Protaminobacter rubrum (CBS 547,77), Erwinia rhapontici (NCPPB 1578), the microorganism SZ 62 (Enterobacter species) and the microorganism MX-45 (Pseudomonas mesoacidophila FERM 11808 or FERM BP 3619) for producing recombinant partial or full-length sucrose isomerase enzymes in host cells such as Escherichia coli. Mattes et al. also disclose conserved amino acid sequences for designing degenerate oligonucleotides for cloning sucrose isomerase-encoding polynucleotides by the polymerase chain reaction (PCR). In addition to isomaltulose, reported SIs produce varying proportions of the isomer trehalulose (1-O-α-D-glucopyranosyl-D-fructose) along with glucose and fructose as by-products. Some purified SIs produce predominantly isomaltulose (75-85%), others predominantly trehalulose (90%). The ratio of these products varies with reaction conditions, particularly temperature and pH, and under some conditions small quantities of other products such as isomaltose and isomelezitose may be formed (Véronèse and Perlot, 1999, Enzyme and Microbial Technology 24: 263-269). The formation of multiple products lowers the yield and complicates the recovery of the desired isomer. Slow conversion of sucrose into isomaltulose, and a narrow range of optimal reaction conditions also limit the industrial efficiency of isomaltulose production (Cheetham, 1984, Biochemical Journal 220: 213-220; Schiweck et al., 1990, Zuckerindustrie 115: 555-565.). An ideal SI would show high speed, complete conversion, high specificity and a wide window of reaction conditions for isomaltulose production.

Twist relates to tubular epithelial-mesenchymal transition and interstitial fibrogenesis in the obstructed kidney. Epithelial-mesenchymal transition (EMT) is a critical step in renal fibrosis. It has been recently reported that a transcription factor, Twist, plays a pivotal role in metastasis of breast tumors by inducing EMT. In this study, we examined whether Twist relates to renal fibrogenesis including EMT of tubular epithelia, evaluating Twist expression level in the unilateral ureteral obstruction (UUO) model. Kidneys of mice subjected to UUO were harvested 1, 3, 7, and 10 days after obstruction. Compared with control kidneys, Twist mRNA-level significantly increased 3 days after UUO (UUO day 3 kidney) and further augmented until 10 days after UUO. Twist expression increased in tubular epithelia of the dilated tubules and the expanded interstitial areas of UUO kidneys, where cell-proliferating appearances were frequently found in a time-dependent manner. Although a part of tubular cells in whole nephron segment were immunopositive for Twist in UUO day 7 kidneys, tubular epithelia downstream of nephron more frequently expressed Twist than upstream of nephron. In UUO day 7 kidneys, some tubular epithelia were confirmed to coexpress Twist and fibroblast-specific protein-1, a marker for EMT, indicating that Twist is involved in tubular EMT under pathological state. Twist was expressed also in a number of alpha-smooth muscle actin-positive myofibroblasts located in the expanded interstitial area of UUO kidneys. From these findings, the present investigation suggests that Twist is associated with tubular EMT, proliferation of myofibroblasts, and subsequent renal fibrosis in obstructed kidneys.

[Justin Timberlake & Chris Stapleton:] Sometimes the greatest way to say something is to say nothing at all Sometimes the greatest way to say something is to say nothing at all Sometimes the greatest way to say something is to say nothing But I can't help myself, no I can't help myself, no, no Caught up in the middle of it No I can't help myself, no I can't help myself, no, no, no Caught up in the rhythm of it [Justin Timberlake & Chris Stapleton:] Sometimes the greatest way to say something is to say nothing at all Sometimes the greatest way to say something is to say nothing at all Sometimes the greatest way to say something is to say nothing

It’s a crime so horrible that it’s hard to imagine. On Thursday, a man in Canggu cut off his wife’s left foot and attempted to cleave off her right foot as well. The attack occurred in front of the couple’s young children, who have now been sent to their grandmother in Singaraja for care. The woman, Putu (33), was attacked by her husband, identified as KAP (36) with a machete at their home. At some point, KAP started feeling remorse for his actions and took her to the local clinic for treatment. He has been detained by police and will undergo psychiatric testing. Putu, meanwhile, is in the hospital and her left leg has been operated on. Too little, too late. 由 Coconuts Bali 发布于 2017年9月6日 The Tribun Bali reports a family member saying that Putu was often physically abused by her husband; screenshots of WhatsApp conversations allege that he even put out cigarettes on her skin. Unfortunately, for people familiar with cases of domestic violence, this sort of incremental increase in violence is not uncommon. Domestic violence can begin mildly, through controlling behavior, but often escalates to physical trauma or even death. Family friends have said that Putu had long wanted to divorce her husband, and would often show up with bruises covering her body. Jenny Jusuf, a writer who knows a relative of Putu’s, said that “Putu’s family constantly talked her out of [getting a divorce]. They asked her to stay. The last time she asked them permission to get a divorce was just last week, and again, they advised her not to,” says Jenny. “Now, they regret it. Her mother cried, saying that if only they had let her get a divorce, she wouldn’t have become handicapped.” Worst of all, Jenny adds, “this is a very common issue here [in Bali]. Even if a woman wants to get a divorce, her family will talk her out of it. They tell her that ‘maybe he will change’.” In 2016, according to data collected by the Menghitung Pembunuhan Perempuan (Counting Dead Women – Indonesia) project, there were media reports of 193 women being murdered across Indonesia. Only four women were killed by other women. Overall, 50% of women were killed by their husbands, boyfriends, former partners, or men who were attracted to them. This is in line with regional statistics; the United Nations Office on Drugs and Crime claims that 55% of female homicide victims in Asia are killed by family members or intimate partners. For men, the same statistic is just 6%. Statistics gathered by Komnas Perempuan (the National Commission on Violence against Women) showed there were 13,602 reported cases throughout all of 2016, which averages to around 37 each day. Of course, we can’t begin to know how many cases go unreported. Jealousy is often a major motive for men who kill or hurt their wives. Putu’s husband, for example, apparently claimed that his wife was having an affair. And Putu is lucky in the terrible sense that she survived her horrific attack; many other women have seen their lives snuffed out by jealous husbands. In February, a man cut his girlfriend’s throat when she refused to have sex with him. He had seen her a few days before on the back of another man’s motorbike; he decided he was cheating on her, and killed her. In April, a 16-year-old girl was strangled to death by her 19-year-old boyfriend in a forest in Cilacap, Central Java; she received an SMS and he wanted to know who it was from. When she did not tell him, he jumped up, strangled her, then stamped on her head. Twice. Her body was found a week later. In June, a man in Gresik, East Java, burnt his wife to death after he found messages on her mobile phone from another man and “kiss marks” on her body. If found guilty, the suspect could be given the death penalty. 由 Coconuts Jakarta 发布于 2017年6月14日 Unfortunately, what happened to Putu in Canggu is reflective of a wider patriarchal culture — one that, unfortunately, exists in many other countries besides Indonesia as well. It’s a culture that leads men to become so infuriated by the idea that their wife or girlfriend might be interested in someone else, that they become willing to do anything they can to stop her from leaving. It’s the same primitive ‘If I can’t have her, no-one can’ attitude that leads jealous men in countries ranging from Bangladesh to Cambodia to South Africa to throw acid in the faces of the women who spurned them. “Jealousy is often used as an excuse by abusive husbands or intimate partners to justify their violent act,” explains Yenni Kwok, a freelance journalist who often writes about violence against women in Asia. “It is a weapon to control women, and it reflects a man’s sense of entitlement, that nobody but him can possess ‘his’ woman.” Mariana Amiruddin, the chairperson of Komnas Perempuan, agrees. “Jealousy can make someone kill someone else because they feel as though their partner is their possession, their property,” says Mariana. “Women who cheat are especially thought of as deserving revenge, in comparison with men who cheat, because women are considered to be the property of their husbands. Men whose partners cheat on them feel that it reduces their value as men, because they are not needed any more.” “This means that the problem isn’t jealousy, as such, but psychological and social,” Mariana concludes. A 2012-2013 masculinity study carried out in Jakarta, Purworejo and Jayapura asked 2,577 about men questions about sexual violence. In Jakarta, 24.1% respondents said they had, in their lifetime, raped their spouse; in Purworejo the figure was 17.9%, while in Papua it was 43.8%. Relatively few of the men surveyed cited inebriation as a primary motivator. But 75.7% of men in Jakarta said they had done so because they felt entitled and 29.7% because they had wanted to “have fun”. In total, 46.9% of the respondents in the three cities who had admitted to sexual violence said they had suffered no consequences for their actions. Only 21.5% said the consequences had been of a legal nature. Women’s rights activists have long argued that Indonesia needs to amend its laws to take into account different forms of domestic abuse and sexual violence to end this culture of impunity for victimizers. A piece of legislation that would do just that, RUU Penghapusan Kekerasan Seksual (Bill on the Eradication of Sexual Violence) has been under considerations since 2014 but there has not yet been any major movement on it. "A culture of sexual violence is pervasive across Indonesia and its institutions. Virginity testing for female recruits… 由 Coconuts Jakarta 发布于 2016年11月8日 But that might change soon, as Minister of Women and Children of the Republic of Indonesia Yohanna Yembise said the bill will be discussed in the House of Representatives in mid-September. So if you think the government needs to pass the bill to prevent more from suffering a fate like Putu’s, now is the time to make your voices heard. *** Putu needs your help. You can donate to help her recovery by credit card on Go Fund Me, or via bank transfer from an Indonesian bank account on KitaBisa.com. Grove: Coconuts Brand Studio Fast. Funny. Digital. We produce creativity that delights and influences customers. Join forces with us to slay buzzwords, rise above the noise, and sow the seeds of something great.

Q: Binding value to select in angular js across 2 controllers Working with angularJS I am trying to figure out a way to bind the value of a select element under the scope of controller A to use it as an argument for an ng-click call [getQuizByCampID() Function] under the scope of controller B. My first idea was to use jquery, but I have read in the link below that using jquery is not recommended when starting with angularJS. "Thinking in AngularJS" if I have a jQuery background? I also read in the link below that this is performed using ng-model, the only problem is that that the example provided is all under the same controller. and Binding value to input in Angular JS What is the angularJS way to get the value of the select element under controller A into the function call in the select under controller B? Price.html view <div class="col-sm-3" ng-controller="campCtrl"> **Controller A** <select id="selCampID" class="form-control" ng-model="campInput" > <option ng-repeat="camp in campaigns" value="{{camp.camp_id}}">{{camp.camp_name}}</option> </select> </div> <div class="col-sm-3" ng-controller="quizCtrl"> **Controller B** <select ng-click="getQuizByCampID($('#selCampID').val())" class="form-control" ng-model="quizInput"> <option ng-controller="quizCtrl" ng-repeat="quiz in quizzesById" value="{{quiz.quiz_id}}">{{quiz.quiz_name}}</option> </select> </div> App.js var app= angular.module('myApp', ['ngRoute']); app.config(['$routeProvider', function($routeProvider) { $routeProvider.when('/price', {templateUrl: 'partials/price.html', controller: 'priceCtrl'}); }]); $routeProvider.when('/price', {templateUrl: 'partials/price.html', controller: 'priceCtrl'}); Quiz Controller 'use strict'; app.controller('quizCtrl', ['$scope','$http','loginService', function($scope,$http,loginService){ $scope.txt='Quiz'; $scope.logout=function(){ loginService.logout(); } getQuiz(); // Load all available campaigns function getQuiz(campID){ $http.post("js/ajax/getQuiz.php").success(function(data){ $scope.quizzes = data; //console.log(data); }); }; $scope.getQuizByCampID = function (campid) { alert(campid); $http.post("js/ajax/getQuiz.php?campid="+campid).success(function(data){ $scope.quizzesById = data; $scope.QuizInput = ""; }); }; $scope.addQuiz = function (quizid, quizname, campid) { console.log(quizid + quizname + campid); $http.post("js/ajax/addQuiz.php?quizid="+quizid+"&quizname="+quizname+"&campid="+campid).success(function(data){ getQuiz(); $scope.QuizInput = ""; }); }; }]) A: You should store the value in a service. example: app.factory('SharedService', function() { this.inputValue = null; this.setInputValue = function(value) { this.inputValue = value; } this.getInputValue = function() { return this.inputValue; } return this; }); Example on Plunkr Read: AngularJS Docs on services or check this Egghead.io video

Retroactive effects of irrelevant speech on serial recall from short-term memory. The authors report 5 serial-recall experiments. In 4 of the 5 experiments, they show that irrelevant sound (IS) has a retroactive effect on material already in memory. In Experiment 1, IS presented during a filled retention interval had a reliable effect on list recall. Four further experiments, 3 of which used retroactive IS, showed that IS continued to-have an effect on recall following a long, filled retention interval. Articulatory suppression during visual input was found to abolish the long-lasting, retroactive effect of IS, supporting the idea that IS affects the phonological-loop component of short-term memory. IS also, therefore, seems to affect a longer term memory system with which the loop interacts.

One hundred years of chronic obstructive pulmonary disease (COPD). Chronic obstructive pulmonary disease (COPD) is an increasing health problem and one of the leading causes of morbidity and mortality worldwide, but knowledge about its pathogenesis has increased substantially in recent years. The disease results from interaction between individual risk factors (like enzymatic deficiencies) and environmental exposures to noxious agents, like cigarette smoking, occupational dusts, air pollution and infections in childhood. The main mechanisms that may contribute to airflow limitation in COPD are fixed narrowing of small airways, emphysema and luminal obstruction with mucus secretions. COPD is characterised by a chronic inflammatory process in the pulmonary tissue, with a pattern different from bronchial asthma, associated with extrapulmonary effects and is considered now a complex, systemic disease. Optimal therapeutic targeting of COPD depends on a clear understanding of the precise mechanisms of these complex processes and on early and correct evaluation of disease severity. A combination of pharmacological and non-pharmacological approaches is used to treat COPD. Bronchodilators are the mainstay of COPD treatment and can be combined with inhaled corticosteroids for greater efficacy and fewer side effects. The use of LTOT for hypoxemic patients has resulted in increased survival, and expanded drug therapy options have effectively improved dyspnoea and quality of life. Recent studies have documented the benefits of pulmonary rehabilitation. In addition, non-invasive mechanical ventilation offers new alternatives for patients with acute or chronic failure.

The case of the vanished sword By washingtonpost.com editors By John Lockwood Washington One of our memorials is missing a sword. The General Sherman memorial just south of the Treasury Building shows General William Tecumseh Sherman on horseback atop a 32-foot pedestal guarded at each ground-level corner by a soldier. The memorial was designed by a Danish sculptor named Carl Rohl-Smith. It was dedicated on Oct. 15, 1903. The northwest soldier is an infantryman, holding his rifle by the barrel, with the butt resting on the ground. The southwest soldier is an engineer, holding his rifle in the same position. He also carries a cylinder or tube, about 3 feet long. Perhaps it contains surveying instruments. The southeast soldier is a cavalryman, with sword pointed upward across his left shoulder. At the northeast is an artilleryman — whose hands close upon empty air. When I saw the northeast soldier, the question arose: Is he missing a rifle or a sword? Well, what would one of my heroes, Sherlock Holmes, do? Look for a cartridge box, or a scabbard. There was a scabbard there, an empty one. So it was indeed a missing sword — a fact later verified in The Post’s Oct. 16, 1903, edition, which included a drawing showing the soldier with a sword, its point touching the ground. The lost sword is probably rusting in somebody’s attic or slowly corroding in a landfill. I doubt even Holmes could find it now.

Q: Pass values to IN operator in a Worklight SQL adapter I have started to work with SQL adapters in Worklight, but I do not understand how can I pass values to an IN condition when invoking my adapter procedure. A: You will need to edit your question with your adapter's XML as well as implementation JavaScript... Also, make sure to read the SQL adapters training module. What you need to do is have your function get the values: function myFunction (value1, value2) { ... } And your SQL query will use them, like so (just as an example how to pass variables to any SQL query, doesn't matter if it contains an IN condition or not): SELECT * FROM person where name='$[value1]' or id=$[value2]; Note the quotation marks for value1 (for text) and lack of for value2 (for numbers).

Bob Alcivar Bob Alcivar (born July 8, 1938, in Chicago, Illinois) is an American music producer, composer, conductor and keyboard player. He is the father of rock keyboard player Jim Alcivar (Montrose, Gamma). Discography The Signatures - Their Voices and Instruments (1957) bass, arranger, vocals The Signatures - Sing In (1958) The Signatures - Prepare to Flip! (1959) Julie London - Around Midnight (1960) - composer The New Christy Minstrels - The Wandering Minstrels (1965) - vocal arrangement The New Christy Minstrels - New Kick! (1966) arranger, director The 5th Dimension - The Age of Aquarius (1969) - arranger The Association - The Association (1969) - arranger The Carnival - The Carnival (1969) - arranger Seals & Crofts - Seals & Crofts (1970) - producer The Sandpipers - Come Saturday Morning (1970) - producer & arranger The 5th Dimension - Portrait (1970) - arranger Sérgio Mendes & Brasil '77 - Love Music (1973) - arranger, keyboards, vocals Tim Weisberg - Dreamspeaker - (1974) - arranger Tom Waits - The Heart of Saturday Night (1974) - arranger The 5th Dimension - Soul & Inspiration - (1974) - arranger Sérgio Mendes & Brasil '77 - Vintage 74 - (1974) - vocal arrangement, rhythm arrangement Sérgio Mendes & Brasil '77 - Sérgio Mendes - (1975) vocal arrangement Montrose - Jump On It (1976) - string arrangement Bette Midler - Broken Blossom - (1977) - arranger on "I Never Talk To Strangers" (duet with Tom Waits) Bruce Johnston - Going Public (1977) - horn arrangement, string arrangement Tim Weisberg - Live at Last (1977) - producer Marilyn McCoo & Billy Davis, Jr. - The Two of Us (1977) - keyboards Ronnie Montrose - Open Fire (1978) - orchestra arrangement, conductor Tom Waits - Blue Valentine (1978) - orchestra The Beach Boys - Keepin' the Summer Alive (1980) - horn arrangements Tom Waits - Heartattack and Vine (1980) - string arrangement, orchestral arrangement, conductor Seals & Crofts - Longest Road (1980) - string arrangement Tom Waits - One from the Heart (1982) - piano, orchestral arrangement, conductor Ceremony - Hang Out Your Poetry (1993) - arranger, string arrangement Jazz at the Movies Band - One from the Heart: Sax at the Movies II (1994) - arranger, conductor Royal Philharmonic Orchestra - Symphonic Sounds: The Music of Beach Boys (1998) - conductor, orchestral arrangement Jazz at the Movies - The Bedroom Mixes (2000) - arranger Bob Alcivar - Bahai Prayers - (2000) Film Butterflies Are Free (1972) The Crazy World of Julius Vrooder (1974) Olly Olly Oxen Free (1978) One From the Heart (1982) The Best Little Whorehouse in Texas (arranger, 1982) Hysterical (1983) That Secret Sunday (TV) (1986) Blind Witness (TV) (1999) Naked Lie [TV] (1989) Roxanne: The Prize Pulitzer [TV] (1989) Sparks: The Price of Passion [TV] (1990) Deadly Medicine [TV] (1991) External links [ allmusic Biography] Film Reference Biography Category:1938 births Category:Living people Category:Musicians from Chicago Category:20th-century American keyboardists Category:Record producers from Illinois

[Significance of serum CD62p and CD63 levels in patients with head injury]. To determine the serum levels of CD62p (alpha-granular membrane protein) and CD63 (lysosome intact membrane protein) in patients with head injury and to observe its relation to injury severity. Fifty-three patients with head injury were divided into 3 groups; Group A patients with mild head injury; Group B with moderate head injury; and Group C with severe head injury. The serum levels of CD62p, CD63 were measured on 12 h, d 1, 3, 5 and 7 after injury. The serum levels of CD62p and CD63 in Group B and Group C were higher than those in Group A and control (P<0.05). The serum level of CD62p in Group C was higher than that in Group B (P<0.05). The serum levels of CD62p in Group C on d 1, 3, 5 after injury were higher than those on 12 h (P<0.05). The serum level of CD63 in Group B on d 3 after injury were higher than that on 12 h (P<0.05). The serum levels of CD63 in Group C on d 1, 3, 5 after injury were higher than those on 12 h (P<0.05). The serum levels of CD62p and CD63 in patients with head injury may be helpful for identifying the severity of injury, and CD62p seems to be more sensitive.

Peter Cooley Peter Cooley (born November 19, 1940) is an American poet and Professor of English in the Department of English at Tulane University. He also directs Tulane's Creative Writing Program. Born in Detroit, Michigan, he holds degrees from Shimer College, the University of Chicago and the University of Iowa. He is the father of poet Nicole Cooley. Career Prior to joining Tulane, Cooley taught at the University of Wisconsin, Green Bay. He was the Robert Frost Fellow at the Bread Loaf Writers’ Conference in 1981. Poetry and awards Cooley has published several books of poetry with the Carnegie Mellon University Press. He received the Inspirational Professor Award in 2001 and the Newcomb Professor of the Year Award in 2003. On August 14, 2015 he was named Louisiana's poet laureate. Bibliography Poetry Collections The Room Where Summer Ends (Pittsburgh: Carnegie Mellon University Press, 1979) Nightseasons (Pittsburgh: Carnegie Mellon University Press, 1983) The Van Gogh Notebook (Pittsburgh: Carnegie Mellon University Press, 1987) The Astonished Hours (Pittsburgh: Carnegie Mellon University Press, 1992) Sacred Conversations (Pittsburgh: Carnegie Mellon University Press, 1998) A Place Made of Starlight (Pittsburgh: Carnegie Mellon University Press, 2003) Divine Margins (Pittsburgh: Carnegie Mellon University Press, 2009) Night Bus to the Afterlife (Pittsburgh: Carnegie Mellon University Press, 2014) World Without Finishing (Pittsburgh: Carnegie Mellon University Press, 2018) List of poems References External links Peter Cooley listing in The Literary Encyclopedia Peter Cooley’s faculty page, Tulane University Peter Cooley author page at Virginia Quarterly Review, with links to poems Category:1940 births Category:Living people Category:American male poets Category:Poets Laureate of Louisiana Category:Shimer College alumni Category:The New Yorker people Category:Tulane University faculty

/** * ScriptDev2 is an extension for mangos providing enhanced features for * area triggers, creatures, game objects, instances, items, and spells beyond * the default database scripting in mangos. * * Copyright (C) 2006-2013 ScriptDev2 <http://www.scriptdev2.com/> * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA * * World of Warcraft, and all World of Warcraft or Warcraft art, images, * and lore are copyrighted by Blizzard Entertainment, Inc. */ /** * ScriptData * SDName: bug_trio * SD%Complete: 75 * SDComment: Summon Player spell NYI; Poison Cloud damage spell NYI; Timers need adjustments * SDCategory: Temple of Ahn'Qiraj * EndScriptData */ #include "precompiled.h" #include "temple_of_ahnqiraj.h" enum { // kri SPELL_CLEAVE = 26350, SPELL_TOXIC_VOLLEY = 25812, SPELL_SUMMON_CLOUD = 26590, // summons 15933 // vem SPELL_CHARGE = 26561, SPELL_VENGEANCE = 25790, SPELL_KNOCKBACK = 26027, // yauj SPELL_HEAL = 25807, SPELL_FEAR = 26580, NPC_YAUJ_BROOD = 15621 }; struct MANGOS_DLL_DECL boss_kriAI : public ScriptedAI { boss_kriAI(Creature* pCreature) : ScriptedAI(pCreature) { m_pInstance = (ScriptedInstance*)pCreature->GetInstanceData(); Reset(); } ScriptedInstance* m_pInstance; uint32 m_uiCleaveTimer; uint32 m_uiToxicVolleyTimer; void Reset() override { m_uiCleaveTimer = urand(4000, 8000); m_uiToxicVolleyTimer = urand(6000, 12000); } void JustDied(Unit* /*pKiller*/) override { // poison cloud on death DoCastSpellIfCan(m_creature, SPELL_SUMMON_CLOUD, CAST_TRIGGERED); if (!m_pInstance) { return; } // If the other 2 bugs are still alive, make unlootable if (m_pInstance->GetData(TYPE_BUG_TRIO) != DONE) { m_creature->RemoveFlag(UNIT_DYNAMIC_FLAGS, UNIT_DYNFLAG_LOOTABLE); m_pInstance->SetData(TYPE_BUG_TRIO, SPECIAL); } } void JustReachedHome() override { if (m_pInstance) { m_pInstance->SetData(TYPE_BUG_TRIO, FAIL); } } void UpdateAI(const uint32 uiDiff) override { // Return since we have no target if (!m_creature->SelectHostileTarget() || !m_creature->getVictim()) { return; } // Cleave_Timer if (m_uiCleaveTimer < uiDiff) { if (DoCastSpellIfCan(m_creature->getVictim(), SPELL_CLEAVE) == CAST_OK) { m_uiCleaveTimer = urand(5000, 12000); } } else { m_uiCleaveTimer -= uiDiff; } // ToxicVolley_Timer if (m_uiToxicVolleyTimer < uiDiff) { if (DoCastSpellIfCan(m_creature, SPELL_TOXIC_VOLLEY) == CAST_OK) { m_uiToxicVolleyTimer = urand(10000, 15000); } } else { m_uiToxicVolleyTimer -= uiDiff; } DoMeleeAttackIfReady(); } }; struct MANGOS_DLL_DECL boss_vemAI : public ScriptedAI { boss_vemAI(Creature* pCreature) : ScriptedAI(pCreature) { m_pInstance = (ScriptedInstance*)pCreature->GetInstanceData(); Reset(); } ScriptedInstance* m_pInstance; uint32 m_uiChargeTimer; uint32 m_uiKnockBackTimer; void Reset() override { m_uiChargeTimer = urand(15000, 27000); m_uiKnockBackTimer = urand(8000, 20000); } void JustDied(Unit* /*pKiller*/) override { // Enrage the other bugs DoCastSpellIfCan(m_creature, SPELL_VENGEANCE, CAST_TRIGGERED); if (!m_pInstance) { return; } // If the other 2 bugs are still alive, make unlootable if (m_pInstance->GetData(TYPE_BUG_TRIO) != DONE) { m_creature->RemoveFlag(UNIT_DYNAMIC_FLAGS, UNIT_DYNFLAG_LOOTABLE); m_pInstance->SetData(TYPE_BUG_TRIO, SPECIAL); } } void JustReachedHome() override { if (m_pInstance) { m_pInstance->SetData(TYPE_BUG_TRIO, FAIL); } } void UpdateAI(const uint32 uiDiff) override { // Return since we have no target if (!m_creature->SelectHostileTarget() || !m_creature->getVictim()) { return; } // Charge_Timer if (m_uiChargeTimer < uiDiff) { if (Unit* pTarget = m_creature->SelectAttackingTarget(ATTACKING_TARGET_RANDOM, 0)) { if (DoCastSpellIfCan(pTarget, SPELL_CHARGE) == CAST_OK) { m_uiChargeTimer = urand(8000, 16000); } } } else { m_uiChargeTimer -= uiDiff; } // KnockBack_Timer if (m_uiKnockBackTimer < uiDiff) { if (DoCastSpellIfCan(m_creature, SPELL_KNOCKBACK) == CAST_OK) { if (m_creature->GetThreatManager().getThreat(m_creature->getVictim())) { m_creature->GetThreatManager().modifyThreatPercent(m_creature->getVictim(), -80); } m_uiKnockBackTimer = urand(15000, 25000); } } else { m_uiKnockBackTimer -= uiDiff; } DoMeleeAttackIfReady(); } }; struct MANGOS_DLL_DECL boss_yaujAI : public ScriptedAI { boss_yaujAI(Creature* pCreature) : ScriptedAI(pCreature) { m_pInstance = (ScriptedInstance*)pCreature->GetInstanceData(); Reset(); } ScriptedInstance* m_pInstance; uint32 m_uiHealTimer; uint32 m_uiFearTimer; void Reset() override { m_uiHealTimer = urand(25000, 40000); m_uiFearTimer = urand(12000, 24000); } void JustDied(Unit* /*Killer*/) override { // Spawn 10 yauj brood on death float fX, fY, fZ; for (int i = 0; i < 10; ++i) { m_creature->GetRandomPoint(m_creature->GetPositionX(), m_creature->GetPositionY(), m_creature->GetPositionZ(), 10.0f, fX, fY, fZ); m_creature->SummonCreature(NPC_YAUJ_BROOD, fX, fY, fZ, 0.0f, TEMPSUMMON_TIMED_OOC_DESPAWN, 30000); } if (!m_pInstance) { return; } // If the other 2 bugs are still alive, make unlootable if (m_pInstance->GetData(TYPE_BUG_TRIO) != DONE) { m_creature->RemoveFlag(UNIT_DYNAMIC_FLAGS, UNIT_DYNFLAG_LOOTABLE); m_pInstance->SetData(TYPE_BUG_TRIO, SPECIAL); } } void JustReachedHome() override { if (m_pInstance) { m_pInstance->SetData(TYPE_BUG_TRIO, FAIL); } } void UpdateAI(const uint32 uiDiff) override { // Return since we have no target if (!m_creature->SelectHostileTarget() || !m_creature->getVictim()) { return; } // Fear_Timer if (m_uiFearTimer < uiDiff) { if (DoCastSpellIfCan(m_creature, SPELL_FEAR) == CAST_OK) { DoResetThreat(); m_uiFearTimer = 20000; } } else { m_uiFearTimer -= uiDiff; } // Heal if (m_uiHealTimer < uiDiff) { if (Unit* pTarget = DoSelectLowestHpFriendly(100.0f)) { if (DoCastSpellIfCan(pTarget, SPELL_HEAL) == CAST_OK) { m_uiHealTimer = urand(15000, 30000); } } } else { m_uiHealTimer -= uiDiff; } DoMeleeAttackIfReady(); } }; CreatureAI* GetAI_boss_yauj(Creature* pCreature) { return new boss_yaujAI(pCreature); } CreatureAI* GetAI_boss_vem(Creature* pCreature) { return new boss_vemAI(pCreature); } CreatureAI* GetAI_boss_kri(Creature* pCreature) { return new boss_kriAI(pCreature); } void AddSC_bug_trio() { Script* pNewScript; pNewScript = new Script; pNewScript->Name = "boss_kri"; pNewScript->GetAI = &GetAI_boss_kri; pNewScript->RegisterSelf(); pNewScript = new Script; pNewScript->Name = "boss_vem"; pNewScript->GetAI = &GetAI_boss_vem; pNewScript->RegisterSelf(); pNewScript = new Script; pNewScript->Name = "boss_yauj"; pNewScript->GetAI = &GetAI_boss_yauj; pNewScript->RegisterSelf(); }

--- abstract: 'The aim of this paper is to establish a global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Lévy process and a Gaussian white noise experiment observed up to a time $T$, with $T$ tending to $\infty$. These approximations are given in the sense of the Le Cam distance, under some smoothness conditions on the unknown Lévy density. All the asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.' address: - '*Laboratoire LJK, Université Joseph Fourier UMR 5224 51, Rue des Mathématiques, Saint Martin d’Hères BP 53 38041 Grenoble Cedex 09*' - 'Corresponding Author, Ester.Mariucci@imag.fr' author: - Ester Mariucci bibliography: - 'refs.bib' title: Asymptotic equivalence for pure jump Lévy processes with unknown Lévy density and Gaussian white noise --- Nonparametric experiments,Le Cam distance,asymptotic equivalence,Lévy processes. 62B15,(62G20,60G51). Introduction ============ Lévy processes are a fundamental tool in modelling situations, like the dynamics of asset prices and weather measurements, where sudden changes in values may happen. For that reason they are widely employed, among many other fields, in mathematical finance. To name a simple example, the price of a commodity at time $t$ is commonly given as an exponential function of a Lévy process. In general, exponential Lévy models are proposed for their ability to take into account several empirical features observed in the returns of assets such as heavy tails, high-kurtosis and asymmetry (see [@tankov] for an introduction to financial applications). From a mathematical point of view, Lévy processes are a natural extension of the Brownian motion which preserves the tractable statistical properties of its increments, while relaxing the continuity of paths. The jump dynamics of a Lévy process is dictated by its Lévy density, say $f$. If $f$ is continuous, its value at a point $x_0$ determines how frequent jumps of size close to $x_0$ are to occur per unit time. Concretely, if $X$ is a pure jump Lévy process with Lévy density $f$, then the function $f$ is such that $$\int_Af(x)dx=\frac{1}{t}{\ensuremath {\mathbb{E}}}\bigg[\sum_{s\leq t}{\ensuremath {\mathbb{I}}}_A(\Delta X_s)\bigg],$$ for any Borel set $A$ and $t>0$. Here, $\Delta X_s\equiv X_s-X_{s^-}$ denotes the magnitude of the jump of $X$ at time $s$ and ${\ensuremath {\mathbb{I}}}_A$ is the characteristic function. Thus, the Lévy measure $$\nu(A):=\int_A f(x)dx,$$ is the average number of jumps (per unit time) whose magnitudes fall in the set $A$. Understanding the jumps behavior, therefore requires to estimate the Lévy measure. Several recent works have treated this problem, see e.g. [@bel15] for an overview. When the available data consists of the whole trajectory of the process during a time interval $[0,T]$, the problem of estimating $f$ may be reduced to estimating the intensity function of an inhomogeneous Poisson process (see, e.g. [@fig06; @rey03]). However, a continuous-time sampling is never available in practice and thus the relevant problem is that of estimating $f$ based on discrete sample data $X_{t_0},\dots,X_{t_n}$ during a time interval $[0,T_n]$. In that case, the jumps are latent (unobservable) variables and that clearly adds to the difficulty of the problem. From now on we will place ourselves in a high-frequency setting, that is we assume that the sampling interval $\Delta_n=t_i-t_{i-1}$ tends to zero as $n$ goes to infinity. Such a high-frequency based statistical approach has played a central role in the recent literature on nonparametric estimation for Lévy processes (see e.g. [@fig09; @comte10; @comte11; @bec12; @duval12]). Moreover, in order to make consistent estimation possible, we will also ask the observation time $T_n$ to tend to infinity in order to allow the identification of the jump part in the limit. Our aim is to prove that, under suitable hypotheses, estimating the Lévy density $f$ is equivalent to estimating the drift of an adequate Gaussian white noise model. In general, asymptotic equivalence results for statistical experiments provide a deeper understanding of statistical problems and allow to single out their main features. The idea is to pass via asymptotic equivalence to another experiment which is easier to analyze. By definition, two sequences of experiments ${\ensuremath {\mathscr{P}}}_{1,n}$ and ${\ensuremath {\mathscr{P}}}_{2,n}$, defined on possibly different sample spaces, but with the same parameter set, are asymptotically equivalent if the Le Cam distance $\Delta({\ensuremath {\mathscr{P}}}_{1,n},{\ensuremath {\mathscr{P}}}_{2,n})$ tends to zero. For ${\ensuremath {\mathscr{P}}}_{i}=({\ensuremath {\mathscr{X}}}_i,{\ensuremath {\mathscr{A}}}_i, \big(P_{i,\theta}:\theta\in\Theta)\big)$, $i=1,2$, $\Delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)$ is the symmetrization of the deficiency $\delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)$ where $$\delta({\ensuremath {\mathscr{P}}}_{1},{\ensuremath {\mathscr{P}}}_{2})=\inf_K\sup_{\theta\in\Theta}\big\|KP_{1,\theta}-P_{2,\theta}\big\|_{TV}.$$ Here the infimum is taken over all randomizations from $({\ensuremath {\mathscr{X}}}_1,{\ensuremath {\mathscr{A}}}_1)$ to $({\ensuremath {\mathscr{X}}}_2,{\ensuremath {\mathscr{A}}}_2)$ and $\| \cdot \|_{TV}$ denotes the total variation distance. Roughly speaking, the Le Cam distance quantifies how much one fails to reconstruct (with the help of a randomization) a model from the other one and vice versa. Therefore, we say that $\Delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)=0$ can be interpreted as “the models ${\ensuremath {\mathscr{P}}}_1$ and ${\ensuremath {\mathscr{P}}}_2$ contain the same amount of information about the parameter $\theta$.” The general definition of randomization is quite involved but, in the most frequent examples (namely when the sample spaces are Polish and the experiments dominated), it reduces to that of a Markov kernel. One of the most important feature of the Le Cam distance is that it can be also interpreted in terms of statistical decision theory (see [@lecam; @LC2000]; a short review is presented in the Appendix). As a consequence, saying that two statistical models are equivalent means that any statistical inference procedure can be transferred from one model to the other in such a way that the asymptotic risk remains the same, at least for bounded loss functions. Also, as soon as two models, ${\ensuremath {\mathscr{P}}}_{1,n}$ and ${\ensuremath {\mathscr{P}}}_{2,n}$, that share the same parameter space $\Theta$ are proved to be asymptotically equivalent, the same result automatically holds for the restrictions of both ${\ensuremath {\mathscr{P}}}_{1,n}$ and ${\ensuremath {\mathscr{P}}}_{2,n}$ to a smaller subclass of $\Theta$. Historically, the first results of asymptotic equivalence in a nonparametric context date from 1996 and are due to [@BL] and [@N96]. The first two authors have shown the asymptotic equivalence of nonparametric regression and a Gaussian white noise model while the third one those of density estimation and white noise. Over the years many generalizations of these results have been proposed such as [@regression02; @GN2002; @ro04; @C2007; @cregression; @R2008; @C2009; @R2013; @schmidt14] for nonparametric regression or [@cmultinomial; @j03; @BC04] for nonparametric density estimation models. Another very active field of study is that of diffusion experiments. The first result of equivalence between diffusion models and Euler scheme was established in 1998, see [@NM]. In later papers generalizations of this result have been considered (see [@C14; @esterdiffusion]). Among others we can also cite equivalence results for generalized linear models [@GN], time series [@GN2006; @NM], diffusion models [@D; @CLN; @R2006; @rmultidimensionale], GARCH model [@B], functional linear regression [@M2011], spectral density estimation [@GN2010] and volatility estimation [@R11]. Negative results are somewhat harder to come by; the most notable among them are [@sam96; @B98; @wang02]. There is however a lack of equivalence results concerning processes with jumps. A first result in this sense is [@esterESAIM] in which global asymptotic equivalences between the experiments generated by the discrete or continuous observation of a path of a Lévy process and a Gaussian white noise experiment are established. More precisely, in that paper, we have shown that estimating the drift function $h$ from a continuously or discretely (high frequency) time inhomogeneous jump-diffusion process: $$\label{ch4X} X_t=\int_0^th(s)ds+\int_0^t\sigma(s)dW_s +\sum_{i=1}^{N_t}Y_i,\quad t\in[0,T_n],$$ is asymptotically equivalent to estimate $h$ in the Gaussian model: $$ dy_t=h(t)dt+\sigma(t)dW_t, \quad t\in[0,T_n].$$ Here we try to push the analysis further and we focus on the case in which the considered parameter is the Lévy density and $X=(X_t)$ is a pure jump Lévy process (see [@carr02] for the interest of such a class of processes when modelling asset returns). More in details, we consider the problem of estimating the Lévy density (with respect to a fixed, possibly infinite, Lévy measure $\nu_0$ concentrated on $I\subseteq {\ensuremath {\mathbb{R}}}$) $f:=\frac{d\nu}{d\nu_0}:I\to {\ensuremath {\mathbb{R}}}$ from a continuously or discretely observed pure jump Lévy process $X$ with possibly infinite Lévy measure. Here $I\subseteq {\ensuremath {\mathbb{R}}}$ denotes a possibly infinite interval and $\nu_0$ is supposed to be absolutely continuous with respect to Lebesgue with a strictly positive density $g:=\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}}$. In the case where $\nu$ is of finite variation one may write: $$\label{eqn:ch4Levy} X_t=\sum_{0<s\leq t}\Delta X_s$$ or, equivalently, $X$ has a characteristic function given by: $${\ensuremath {\mathbb{E}}}\big[e^{iuX_t}\big]=\exp\bigg(-t\bigg(\int_{I}(1-e^{iuy})\nu(dy)\bigg)\bigg).$$ We suppose that the function $f$ belongs to some a priori set ${\ensuremath {\mathscr{F}}}$, nonparametric in general. The discrete observations are of the form $X_{t_i}$, where $t_i=T_n\frac{i}{n}$, $i=0,\dots,n$ with $T_n=n\Delta_n\to \infty$ and $\Delta_n\to 0$ as $n$ goes to infinity. We will denote by ${\ensuremath {\mathscr{P}}}_n^{\nu_0}$ the statistical model associated with the continuous observation of a trajectory of $X$ until time $T_n$ (which is supposed to go to infinity as $n$ goes to infinity) and by ${\ensuremath {\mathscr{Q}}}_n^{\nu_0}$ the one associated with the observation of the discrete data $(X_{t_i})_{i=0}^n$. The aim of this paper is to prove that, under adequate hypotheses on ${\ensuremath {\mathscr{F}}}$ (for example, $f$ must be bounded away from zero and infinity; see Section \[subsec:ch4parameter\] for a complete definition), the models ${\ensuremath {\mathscr{P}}}_n^{\nu_0}$ and ${\ensuremath {\mathscr{Q}}}_n^{\nu_0}$ are both asymptotically equivalent to a sequence of Gaussian white noise models of the form: $$dy_t=\sqrt{f(t)}dt+\frac{1}{2\sqrt{T_n}}\frac{dW_t}{\sqrt{g(t)}},\quad t\in I.$$ As a corollary, we then get the asymptotic equivalence between ${\ensuremath {\mathscr{P}}}_n^{\nu_0}$ and ${\ensuremath {\mathscr{Q}}}_n^{\nu_0}$. The main results are precisely stated as Theorems \[ch4teo1\] and \[ch4teo2\]. A particular case of special interest arises when $X$ is a compound Poisson process, $\nu_0\equiv {\ensuremath{\textnormal{Leb}}}([0,1])$ and ${\ensuremath {\mathscr{F}}}\subseteq {\ensuremath {\mathscr{F}}}_{(\gamma,K,\kappa,M)}^I$ where, for fixed $\gamma\in (0,1]$ and $K,\kappa, M$ strictly positive constants, ${\ensuremath {\mathscr{F}}}_{(\gamma,K,\kappa,M)}^I$ is a class of continuously differentiable functions on $I$ defined as follows: $$\label{ch4:fholder} {\ensuremath {\mathscr{F}}}_{(\gamma,K,\kappa,M)}^I=\Big\{f: \kappa\leq f(x)\leq M, \ |f'(x)-f'(y)|\leq K|x-y|^{\gamma},\ \forall x,y\in I\Big\}.$$ In this case, the statistical models ${\ensuremath {\mathscr{P}}}_n^{\nu_0}$ and ${\ensuremath {\mathscr{Q}}}_n^{\nu_0}$ are both equivalent to the Gaussian white noise model: $$dy_t=\sqrt{f(t)}dt+\frac{1}{2\sqrt{T_n}}dW_t,\quad t\in [0,1].$$ See Example \[ex:ch4CPP\] for more details. By a theorem of Brown and Low in [@BL], we obtain, a posteriori, an asymptotic equivalence with the regression model $$Y_i=\sqrt{f\Big(\frac{i}{T_n}\Big)}+\frac{1}{2\sqrt{T_n}}\xi_i, \quad \xi_i\sim{\ensuremath {\mathscr{Nn}}}(0,1), \quad i=1,\dots, [T_n].$$ Note that a similar form of a Gaussian shift was found to be asymptotically equivalent to a nonparametric density estimation experiment, see [@N96]. Let us mention that we also treat some explicit examples where $\nu_0$ is neither finite nor compactly-supported (see Examples \[ch4ex2\] and \[ex3\]). Without entering into any detail, we remark here that the methods are very different from those in [@esterESAIM]. In particular, since $f$ belongs to the discontinuous part of a Lévy process, rather then its continuous part, the Girsanov-type changes of measure are irrelevant here. We thus need new instruments, like the Esscher changes of measure. Our proof is based on the construction, for any given Lévy measure $\nu$, of two adequate approximations $\hat \nu_m$ and $\bar \nu_m$ of $\nu$: the idea of discretizing the Lévy density already appeared in an earlier work with P. Étoré and S. Louhichi, [@etore13]. The present work is also inspired by the papers [@cmultinomial] (for a multinomial approximation), [@BC04] (for passing from independent Poisson variables to independent normal random variables) and [@esterESAIM] (for a Bernoulli approximation). This method allows us to construct explicit Markov kernels that lead from one model to the other; these may be applied in practice to transfer minimax estimators. The paper is organized as follows: Sections \[subsec:ch4parameter\] and \[subsec:ch4experiments\] are devoted to make the parameter space and the considered statistical experiments precise. The main results are given in Section \[subsec:ch4mainresults\], followed by Section \[sec:ch4experiments\] in which some examples can be found. The proofs are postponed to Section \[sec:ch4proofs\]. The paper includes an Appendix recalling the definition and some useful properties of the Le Cam distance as well as of Lévy processes. Assumptions and main results ============================ The parameter space {#subsec:ch4parameter} ------------------- Consider a (possibly infinite) Lévy measure $\nu_0$ concentrated on a possibly infinite interval $I\subseteq{\ensuremath {\mathbb{R}}}$, admitting a density $g>0$ with respect to Lebesgue. The parameter space of the experiments we are concerned with is a class of functions ${\ensuremath {\mathscr{F}}}={\ensuremath {\mathscr{F}}}^{\nu_0,I}$ defined on $I$ that form a class of Lévy densities with respect to $\nu_0$: For each $f\in{\ensuremath {\mathscr{F}}}$, let $\nu$ (resp. $\hat \nu_m$) be the Lévy measure having $f$ (resp. $\hat f_m$) as a density with respect to $\nu_0$ where, for every $f\in{\ensuremath {\mathscr{F}}}$, $\hat f_m(x)$ is defined as follows. Suppose first $x>0$. Given a positive integer depending on $n$, $m=m_n$, let $J_j:=(v_{j-1},v_j]$ where $v_1=\varepsilon_m\geq 0$ and $v_j$ are chosen in such a way that $$\label{eq:ch4Jj} \mu_m:=\nu_0(J_j)=\frac{\nu_0\big((I\setminus[0,\varepsilon_m])\cap {\ensuremath {\mathbb{R}}}_+\big)}{m-1},\quad \forall j=2,\dots,m.$$ In the sequel, for the sake of brevity, we will only write $m$ without making explicit the dependence on $n$. Define $x_j^*:=\frac{\int_{J_j}x\nu_0(dx)}{\mu_m}$ and introduce a sequence of functions $0\leq V_j\leq \frac{1}{\mu_m}$, $j=2,\dots,m$ supported on $[x_{j-1}^*, x_{j+1}^*]$ if $j=3,\dots,m-1$, on $[\varepsilon_m, x_3^*]$ if $j=2$ and on $(I\setminus [0,x_{m-1}^*])\cap {\ensuremath {\mathbb{R}}}_+$ if $j=m$. The $V_j$’s are defined recursively in the following way. - $V_2$ is equal to $\frac{1}{\mu_m}$ on the interval $(\varepsilon_m, x_2^*]$ and on the interval $(x_2^*,x_3^*]$ it is chosen so that it is continuous (in particular, $V_2(x_2^*)=\frac{1}{\mu_m}$), $\int_{x_2^*}^{x_3^*}V_2(y)\nu_0(dy)=\frac{\nu_0((x_2^*, v_2])}{\mu_m}$ and $V_2(x_3^*)=0$. - For $j=3,\dots,m-1$ define $V_j$ as the function $\frac{1}{\mu_m}-V_{j-1}$ on the interval $[x_{j-1}^*,x_j^*]$. On $[x_j^*,x_{j+1}^*]$ choose $V_j$ continuous and such that $\int_{x_j^*}^{x_{j+1}^*}V_j(y)\nu_0(dy)=\frac{\nu_0((x_j^*,v_j])}{\mu_m}$ and $V_j(x_{j+1}^*)=0$. - Finally, let $V_m$ be the function supported on $(I\setminus [0,x_{m-1}^*]) \cap {\ensuremath {\mathbb{R}}}_+$ such that $$\begin{aligned} V_m(x)&=\frac{1}{\mu_m}-V_{m-1}(x), \quad\text{for } x \in [x_{m-1}^*,x_m^*],\\ V_m(x)&=\frac{1}{\mu_m}, \quad\text{for } x \in (I\setminus [0,x_m^*])\cap {\ensuremath {\mathbb{R}}}_+.\end{aligned}$$ (It is immediate to check that such a choice is always possible). Observe that, by construction, $$\sum_{j=2}^m V_j(x)\mu_m=1, \quad \forall x\in (I\setminus[0,\varepsilon_m])\cap {\ensuremath {\mathbb{R}}}_+ \quad \textnormal{and} \quad \int_{(I\setminus[0,\varepsilon_m])\cap {\ensuremath {\mathbb{R}}}_+}V_j(y)\nu_0(dy)=1.$$ Analogously, define $\mu_m^-=\frac{\nu_0\big((I\setminus[-\varepsilon_m,0])\cap {\ensuremath {\mathbb{R}}}_-\big)}{m-1}$ and $J_{-m},\dots,J_{-2}$ such that $\nu_0(J_{-j})=\mu_m^-$ for all $j$. Then, for $x<0$, $x_{-j}^*$ is defined as $x_j^*$ by using $J_{-j}$ and $\mu_m^-$ instead of $J_j$ and $\mu_m$ and the $V_{-j}$’s are defined with the same procedure as the $V_j$’s, starting from $V_{-2}$ and proceeding by induction. Define $$\label{eq:ch4hatf} \hat f_m(x)={\ensuremath {\mathbb{I}}}_{[-\varepsilon_m,\varepsilon_m]}(x)+\sum_{j=2}^m \bigg(V_j(x)\int_{J_j} f(y)\nu_0(dy)+V_{-j}(x)\int_{J_{-j}} f(y)\nu_0(dy)\bigg).$$ The definitions of the $V_j$’s above are modeled on the following example: \[ex:Vj\] Let $\nu_0$ be the Lebesgue measure on $[0,1]$ and $\varepsilon_m=0$. Then $v_j=\frac{j-1}{m-1}$ and $x_j^*=\frac{2j-3}{2m-2}$, $j=2,\dots,m$. The standard choice for $V_j$ (based on the construction by [@cmultinomial]) is given by the piecewise linear functions interpolating the values in the points $x_j^*$ specified above: The function $\hat f_m$ has been defined in such a way that the rate of convergence of the $L_2$ norm between the restriction of $f$ and $\hat f_m$ on $I\setminus[-\varepsilon_m,\varepsilon_m]$ is compatible with the rate of convergence of the other quantities appearing in the statements of Theorems \[ch4teo1\] and \[ch4teo2\]. For that reason, as in [@cmultinomial], we have not chosen a piecewise constant approximation of $f$ but an approximation that is, at least in the simplest cases, a piecewise linear approximation of $f$. Such a choice allows us to gain an order of magnitude on the convergence rate of $\|f-\hat f_m\|_{L_2(\nu_0|{I\setminus{[-\varepsilon_m,\varepsilon_m]}})}$ at least when ${\ensuremath {\mathscr{F}}}$ is a class of sufficiently smooth functions. We now explain the assumptions we will need to make on the parameter $f \in {\ensuremath {\mathscr{F}}}= {\ensuremath {\mathscr{F}}}^{\nu_0, I}$. The superscripts $\nu_0$ and $I$ will be suppressed whenever this can lead to no confusion. We require that: 1. There exist constants $\kappa, M >0$ such that $\kappa\leq f(y)\leq M$, for all $y\in I$ and $f\in {\ensuremath {\mathscr{F}}}$. For every integer $m=m_n$, we can consider $\widehat{\sqrt{f}}_m$, the approximation of $\sqrt{f}$ constructed as $\hat f_m$ above, i.e. $\widehat{\sqrt{f}}_m(x)=\displaystyle{{\ensuremath {\mathbb{I}}}_{[-\varepsilon_m,\varepsilon_m]}(x)+\sum_{\substack{j=-m\dots,m\\ j\neq -1,0,1.}}V_j(x)\int_{J_j} \sqrt{f(y)}\nu_0(dy)}$, and introduce the quantities: $$\begin{aligned} A_m^2(f)&:= \int_{I\setminus \big[-\varepsilon_m,\varepsilon_m\big]}\Big(\widehat{\sqrt {f}}_m(y)-\sqrt{f(y)}\Big)^2\nu_0(dy),\\ B_m^2(f)&:= \sum_{\substack{j=-m\dots,m\\ j\neq -1,0,1.}}\bigg(\int_{J_j}\frac{\sqrt{f(y)}}{\sqrt{\nu_0(J_j)}}\nu_0(dy)-\sqrt{\nu(J_j)}\bigg)^2,\\ C_m^2(f)&:= \int_{-\varepsilon_m}^{\varepsilon_m}\big(\sqrt{f(t)}-1\big)^2\nu_0(dt). \end{aligned}$$ The conditions defining the parameter space ${\ensuremath {\mathscr{F}}}$ are expressed by asking that the quantities introduced above converge quickly enough to zero. To state the assumptions of Theorem \[ch4teo1\] precisely, we will assume the existence of sequences of discretizations $m = m_n\to\infty$, of positive numbers $\varepsilon_m=\varepsilon_{m_n}\to 0$ and of functions $V_j$, $j = \pm 2, \dots, \pm m$, such that: 1. \[cond:ch4hellinger\] $\lim\limits_{n \to \infty}n\Delta_n\sup\limits_{f \in{\ensuremath {\mathscr{F}}}}\displaystyle{\int_{I\setminus(-\varepsilon_m,\varepsilon_m)}}\Big(f(x)-\hat f_m(x)\Big)^2 \nu_0(dx) = 0$. 2. \[cond:ch4ABC\]$\lim\limits_{n \to \infty}n\Delta_n\sup\limits_{f \in{\ensuremath {\mathscr{F}}}} \big(A_m^2(f)+B_m^2(f)+C_m^2(f)\big)=0$. Remark in particular that Condition (C\[cond:ch4ABC\]) implies the following: 1. $\displaystyle \sup_{f\in{\ensuremath {\mathscr{F}}}}\int_I (\sqrt{f(y)}-1)^2 \nu_0(dy) \leq L,$ where $L = \sup_{f \in {\ensuremath {\mathscr{F}}}} \int_{-\varepsilon_m}^{\varepsilon_m} (\sqrt{f(x)}-1)^2\nu_0(dx) + (\sqrt{M}+1)^2\nu_0\big(I\setminus (-\varepsilon_m, \varepsilon_m)\big)$, for any choice of $m$ such that the quantity in the limit appearing in Condition (C\[cond:ch4ABC\]) is finite. Theorem \[ch4teo2\] has slightly stronger hypotheses, defining possibly smaller parameter spaces: We will assume the existence of sequences $m_n$, $\varepsilon_m$ and $V_j$, $j = \pm 2, \dots, \pm m$ (possibly different from the ones above) such that Condition (C1) is verified and the following stronger version of Condition (C2) holds: 1. $\lim\limits_{n \to \infty}n\Delta_n\sup\limits_{f \in{\ensuremath {\mathscr{F}}}} \big(A_m^2(f)+B_m^2(f)+nC_m^2(f)\big)=0$. Finally, some of our results have a more explicit statement under the hypothesis of finite variation which we state as: - $\int_I (|x|\wedge 1)\nu_0(dx)<\infty$. The Condition (C1) and those involving the quantities $A_m(f)$ and $B_m(f)$ all concern similar but slightly different approximations of $f$. In concrete examples, they may all be expected to have the same rate of convergence but to keep the greatest generality we preferred to state them separately. On the other hand, conditions on the quantity $C_m(f)$ are purely local around zero, requiring the parameters $f$ to converge quickly enough to 1. \[ex:ch4esempi\] To get a grasp on Conditions (C1), (C2) we analyze here three different examples according to the different behavior of $\nu_0$ near $0\in I$. In all of these cases the parameter space ${\ensuremath {\mathscr{F}}}^{\nu_0, I}$ will be a subclass of ${\ensuremath {\mathscr{F}}}_{(\gamma,K,\kappa,M)}^I$ defined as in . Recall that the conditions (C1), (C2) and (C2’) depend on the choice of sequences $m_n$, $\varepsilon_m$ and functions $V_j$. For the first two of the three examples, where $I = [0,1]$, we will make the standard choice for $V_j$ of triangular and trapezoidal functions, similarly to those in Example \[ex:Vj\]. Namely, for $j = 3, \dots, m-1$ we have $$\label{eq:ch4vj} V_j(x) = {\ensuremath {\mathbb{I}}}_{(x_{j-1}^*, x_j^*]}(x) \frac{x-x_{j-1}^*}{x_j^*-x_{j-1}^*} \frac{1}{\mu_m} + {\ensuremath {\mathbb{I}}}_{(x_{j}^*, x_{j+1}^*]}(x) \frac{x_{j+1}^*-x}{x_{j+1}^*-x_{j}^*} \frac{1}{\mu_m};$$ the two extremal functions $V_2$ and $V_m$ are chosen so that $V_2 \equiv \frac{1}{\mu_m}$ on $(\varepsilon_m, x_2^*]$ and $V_m \equiv \frac{1}{\mu_m}$ on $(x_m^*, 1]$. In the second example, where $\nu_0$ is infinite, one is forced to take $\varepsilon_m > 0$ and to keep in mind that the $x_j^*$ are not uniformly distributed on $[\varepsilon_m,1]$. Proofs of all the statements here can be found in Section \[subsec:esempi\]. **1. The finite case:** $\nu_0\equiv {\ensuremath{\textnormal{Leb}}}([0,1])$. In this case we are free to choose ${\ensuremath {\mathscr{F}}}^{{\ensuremath{\textnormal{Leb}}}, [0,1]} = {\ensuremath {\mathscr{F}}}_{(\gamma, K, \kappa, M)}^{[0,1]}$. Indeed, as $\nu_0$ is finite, there is no need to single out the first interval $J_1=[0,\varepsilon_m]$, so that $C_m(f)$ does not enter in the proofs and the definitions of $A_m(f)$ and $B_m(f)$ involve integrals on the whole of $[0,1]$. Also, the choice of the $V_j$’s as in guarantees that $\int_0^1 V_j(x) dx = 1$. Then, the quantities $\|f-\hat f_m\|_{L_2([0,1])}$, $A_m(f)$ and $B_m(f)$ all have the same rate of convergence, which is given by: $$\sqrt{\int_0^1\Big(f(x)-\hat f_m(x)\Big)^2 \nu_0(dx)}+A_m(f)+B_m(f)=O\Big(m^{-\gamma-1}+m^{-\frac{3}{2}}\Big),$$ uniformly on $f$. See Section \[subsec:esempi\] for a proof. **2. The finite variation case:** $\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}}(x)=x^{-1}{\ensuremath {\mathbb{I}}}_{[0,1]}(x)$. In this case, the parameter space ${\ensuremath {\mathscr{F}}}^{\nu_0, [0,1]}$ is a proper subset of ${\ensuremath {\mathscr{F}}}_{(\gamma, K, \kappa, M)}^{[0,1]}$. Indeed, as we are obliged to choose $\varepsilon_m > 0$, we also need to impose that $C_m(f) = o\big(\frac{1}{n\sqrt{\Delta_n}}\big)$, with uniform constants with respect to $f$, that is, that all $f \in {\ensuremath {\mathscr{F}}}$ converge to 1 quickly enough as $x \to 0$. Choosing $\varepsilon_m = m^{-1-\alpha}$, $\alpha> 0$ we have that $\mu_m=\frac{\ln (\varepsilon_m^{-1})}{m-1}$, $v_j =\varepsilon_m^{\frac{m-j}{m-1}}$ and $x_j^* =\frac{(v_{j}-v_{j-1})}{\mu_m}$. In particular, $\max_j|v_{j-1}-v_j|=|v_m-v_{m-1}|=O\Big(\frac{\ln m}{m}\Big)$. Also in this case one can prove that the standard choice of $V_j$ described above leads to $\int_{\varepsilon_m}^1 V_j(x) \frac{dx}{x} = 1$. Again, the quantities $\|f-\hat f_m\|_{L_2(\nu_0|{I\setminus{[0,\varepsilon_m]}})}$, $A_m(f)$ and $B_m(f)$ have the same rate of convergence given by: $$\label{eq:ch4ex2} \sqrt{\int_{\varepsilon_m}^1\Big(f(x)-\hat f_m(x)\Big)^2 \nu_0(dx)} +A_m(f)+B_m(f)=O\bigg(\bigg(\frac{\ln m}{m}\bigg)^{\gamma+1} \sqrt{\ln (\varepsilon_m^{-1})}\bigg),$$ uniformly on $f$. The condition on $C_m(f)$ depends on the behavior of $f$ near $0$. For example, it is ensured if one considers a parametric family of the form $f(x)=e^{-\lambda x}$ with a bounded $\lambda > 0$. See Section \[subsec:esempi\] for a proof. **3. The infinite variation, non-compactly supported case:** $\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}}(x)=x^{-2}{\ensuremath {\mathbb{I}}}_{{\ensuremath {\mathbb{R}}}_+}(x)$. This example involves significantly more computations than the preceding ones, since the classical triangular choice for the functions $V_j$ would not have integral equal to 1 (with respect to $\nu_0$), and the support is not compact. The parameter space ${\ensuremath {\mathscr{F}}}^{\nu_0, [0, \infty)}$ can still be chosen as a proper subclass of ${\ensuremath {\mathscr{F}}}_{(\gamma, K, \kappa, M)}^{[0,\infty)}$, again by imposing that $C_m(f)$ converges to zero quickly enough (more details about this condition are discussed in Example \[ex3\]). We divide the interval $[0, \infty)$ in $m$ intervals $J_j = [v_{j-1}, v_j)$ with: $$v_0 = 0; \quad v_1 = \varepsilon_m; \quad v_j = \frac{\varepsilon_m(m-1)}{m-j};\quad v_m = \infty; \quad \mu_m = \frac{1}{\varepsilon_m(m-1)}.$$ To deal with the non-compactness problem, we choose some “horizon” $H(m)$ that goes to infinity slowly enough as $m$ goes to infinity and we bound the $L_2$ distance between $f$ and $\hat f_m$ for $x > H(m)$ by $2\sup\limits_{x\geq H(m)}\frac{f(x)^2}{H(m)}$. We have: $$\|f-\hat f_m\|_{L_2(\nu_0|{I\setminus{[0,\varepsilon_m]}})}^2+A_m^2(f)+B_m^2(f)=O\bigg(\frac{H(m)^{3+4\gamma}}{(\varepsilon_m m)^{2+2\gamma}}+\sup_{x\geq H(m)}\frac{f(x)^2}{H(m)}\bigg).$$ In the general case where the best estimate for $\displaystyle{\sup_{x\geq H(m)}f(x)^2}$ is simply given by $M^2$, an optimal choice for $H(m)$ is $\sqrt{\varepsilon_m m}$, that gives a rate of convergence: $$\|f-\hat f_m\|_{L_2(\nu_0|{I\setminus{[0,\varepsilon_m]}})}^2+A_m^2(f)+B_m^2(f) =O\bigg( \frac{1}{\sqrt{\varepsilon_m m}}\bigg),$$ independently of $\gamma$. See Section \[subsec:esempi\] for a proof. Definition of the experiments {#subsec:ch4experiments} ----------------------------- Let $(x_t)_{t\geq 0}$ be the canonical process on the Skorokhod space $(D,{\ensuremath {\mathscr{D}}})$ and denote by $P^{(b,0,\nu)}$ the law induced on $(D,{\ensuremath {\mathscr{D}}})$ by a Lévy process with characteristic triplet $(b,0,\nu)$. We will write $P_t^{(b,0,\nu)}$ for the restriction of $P^{(b,0,\nu)}$ to the $\sigma$-algebra ${\ensuremath {\mathscr{D}}}_t$ generated by $\{x_s:0\leq s\leq t\}$ (see \[sec:ch4levy\] for the precise definitions). Let $Q_t^{(b,0,\nu)}$ be the marginal law at time $t$ of a Lévy process with characteristic triplet ${(b,0,\nu)}$. In the case where $\int_{|y|\leq 1}|y|\nu(dy)<\infty$ we introduce the notation $\gamma^{\nu}:=\int_{|y|\leq 1}y\nu(dy)$; then, Condition (H2) guarantees the finiteness of $\gamma^{\nu-\nu_0}$ (see Remark 33.3 in [@sato] for more details). Recall that we introduced the discretization $t_i=T_n\frac{i}{n}$ of $[0,T_n]$ and denote by $\textbf Q_n^{(\gamma^{\nu-\nu_0},0,\nu)}$ the laws of the $n+1$ marginals of $(x_t)_{t\geq 0}$ at times $t_i$, $i=0,\dots,n$. We will consider the following statistical models, depending on a fixed, possibly infinite, Lévy measure $\nu_0$ concentrated on $I$ (clearly, the models with the subscript $FV$ are meaningful only under the assumption (FV)): $$\begin{aligned} {\ensuremath {\mathscr{P}}}_{n,FV}^{\nu_0}&=\bigg(D,{\ensuremath {\mathscr{D}}}_{T_n},\Big\{P_{T_n}^{(\gamma^{\nu},0,\nu)}:f:=\frac{d\nu}{d\nu_0}\in{\ensuremath {\mathscr{F}}}^{\nu_0,I}\Big\}\bigg),\\ {\ensuremath {\mathscr{Q}}}_{n,FV}^{\nu_0}&=\bigg({\ensuremath {\mathbb{R}}}^{n+1},{\ensuremath {\mathscr{B}}}({\ensuremath {\mathbb{R}}}^{n+1}),\Big\{ \textbf Q_{n}^{(\gamma^{\nu},0,\nu)}:f:=\frac{d\nu}{d\nu_0}\in{\ensuremath {\mathscr{F}}}^{\nu_0,I}\Big\}\bigg),\\ {\ensuremath {\mathscr{P}}}_{n}^{\nu_0}&=\bigg(D,{\ensuremath {\mathscr{D}}}_{T_n},\Big\{P_{T_n}^{(\gamma^{\nu-\nu_0},0,\nu)}:f:=\frac{d\nu}{d\nu_0}\in{\ensuremath {\mathscr{F}}}^{\nu_0,I}\Big\}\bigg),\\ {\ensuremath {\mathscr{Q}}}_{n}^{\nu_0}&=\bigg({\ensuremath {\mathbb{R}}}^{n+1},{\ensuremath {\mathscr{B}}}({\ensuremath {\mathbb{R}}}^{n+1}),\Big\{\textbf Q_{n}^{(\gamma^{\nu-\nu_0},0,\nu)}:f:=\frac{d\nu}{d\nu_0}\in{\ensuremath {\mathscr{F}}}^{\nu_0,I}\Big\}\bigg). \end{aligned}$$ Finally, let us introduce the Gaussian white noise model that will appear in the statement of our main results. For that, let us denote by $(C(I),{\ensuremath {\mathscr{C}}})$ the space of continuous mappings from $I$ into ${\ensuremath {\mathbb{R}}}$ endowed with its standard filtration, by $g$ the density of $\nu_0$ with respect to the Lebesgue measure. We will require $g>0$ and let $\mathbb W_n^f$ be the law induced on $(C(I),{\ensuremath {\mathscr{C}}})$ by the stochastic process satisfying: $$\begin{aligned} \label{eqn:ch4Wf} dy_t=\sqrt{f(t)}dt+\frac{dW_t}{2\sqrt{T_n}\sqrt{g(t)}}, \quad t\in I,\end{aligned}$$ where $(W_t)_{t\in{\ensuremath {\mathbb{R}}}}$ denotes a Brownian motion on ${\ensuremath {\mathbb{R}}}$ with $W_0=0$. Then we set: $${\ensuremath {\mathscr{W}}}_n^{\nu_0}=\Big(C(I),{\ensuremath {\mathscr{C}}},\{\mathbb W_n^{f}:f\in{\ensuremath {\mathscr{F}}}^{\nu_0,I}\}\Big).$$ Observe that when $\nu_0$ is a finite Lévy measure, then ${\ensuremath {\mathscr{W}}}_n^{\nu_0}$ is equivalent to the statistical model associated with the continuous observation of a process $(\tilde y_t)_{t\in I}$ defined by: $$\begin{aligned} d\tilde y_t=\sqrt{f(t)g(t)}dt+\frac{d W_t}{2\sqrt{T_n}}, \quad t\in I.\end{aligned}$$ Main results {#subsec:ch4mainresults} ------------ Using the notation introduced in Section \[subsec:ch4parameter\], we now state our main results. For brevity of notation, we will denote by $H(f,\hat f_m)$ (resp. $L_2(f,\hat f_m)$) the Hellinger distance (resp. the $L_2$ distance) between the Lévy measures $\nu$ and $\hat\nu_m$ restricted to $I\setminus{[-\varepsilon_m,\varepsilon_m]}$, i.e.: $$\begin{aligned} H^2(f,\hat f_m)&:=\int_{I\setminus{[-\varepsilon_m,\varepsilon_m]}}\Big(\sqrt{f(x)}-\sqrt{\hat f_m(x)}\Big)^2 \nu_0(dx),\\ L_2(f,\hat f_m)^2&:=\int_{I\setminus{[-\varepsilon_m,\varepsilon_m]}}\big(f(y)-\hat f_m(y)\big)^2\nu_0(dy).\end{aligned}$$ Observe that Condition (H1) implies (see Lemma \[lemma:ch4hellinger\]) $$\frac{1}{4M}L_2(f,\hat f_m)^2\leq H^2(f,\hat f_m)\leq \frac{1}{4\kappa}L_2(f,\hat f_m)^2.$$ \[ch4teo1\] Let $\nu_0$ be a known Lévy measure concentrated on a (possibly infinite) interval $I\subseteq {\ensuremath {\mathbb{R}}}$ and having strictly positive density with respect to the Lebesgue measure. Let us choose a parameter space ${\ensuremath {\mathscr{F}}}^{\nu_0, I}$ such that there exist a sequence $m = m_n$ of integers, functions $V_j$, $j = \pm 2, \dots, \pm m$ and a sequence $\varepsilon_m \to 0$ as $m \to \infty$ such that Conditions [(H1), (C1), (C2)]{.nodecor} are satisfied for ${\ensuremath {\mathscr{F}}}= {\ensuremath {\mathscr{F}}}^{\nu_0, I}$. Then, for $n$ big enough we have: $$\begin{aligned} \Delta({\ensuremath {\mathscr{P}}}_n^{\nu_0}, {\ensuremath {\mathscr{W}}}_n^{\nu_0}) &= O\bigg(\sqrt{n\Delta_n}\sup_{f\in {\ensuremath {\mathscr{F}}}}\Big(A_m(f)+B_m(f)+C_m(f)\Big)\bigg) \nonumber \\ & +O\bigg(\sqrt{n\Delta_n}\sup_{f\in{\ensuremath {\mathscr{F}}}}L_2(f, \hat f_m)+\sqrt{\frac{m}{n\Delta_n}\Big(\frac{1}{\mu_m}+\frac{1}{\mu_m^-}\Big)}\bigg). \label{eq:teo1}\end{aligned}$$ \[ch4teo2\] Let $\nu_0$ be a known Lévy measure concentrated on a (possibly infinite) interval $I\subseteq {\ensuremath {\mathbb{R}}}$ and having strictly positive density with respect to the Lebesgue measure. Let us choose a parameter space ${\ensuremath {\mathscr{F}}}^{\nu_0, I}$ such that there exist a sequence $m = m_n$ of integers, functions $V_j$, $j = \pm 2, \dots, \pm m$ and a sequence $\varepsilon_m \to 0$ as $m \to \infty$ such that Conditions [(H1), (C1), (C2’)]{.nodecor} are satisfied for ${\ensuremath {\mathscr{F}}}= {\ensuremath {\mathscr{F}}}^{\nu_0, I}$. Then, for $n$ big enough we have: $$\begin{aligned} \Delta({\ensuremath {\mathscr{Q}}}_n^{\nu_0}, {\ensuremath {\mathscr{W}}}_n^{\nu_0})& = O\bigg( \nu_0\Big(I\setminus[-\varepsilon_m,\varepsilon_m]\Big)\sqrt{n\Delta_n^2}+\frac{m\ln m}{\sqrt{n}}+\sqrt{n\sqrt{\Delta_n}\sup_{f\in{\ensuremath {\mathscr{F}}}}C_m(f)}\bigg) \nonumber \\ &+O\bigg(\sqrt{n\Delta_n}\sup_{f\in{\ensuremath {\mathscr{F}}}}\Big(A_m(f)+B_m(f)+H(f,\hat f_m)\Big)\bigg).\label{eq:teo2}\end{aligned}$$ \[cor:ch4generale\] Let $\nu_0$ be as above and let us choose a parameter space ${\ensuremath {\mathscr{F}}}^{\nu_0, I}$ so that there exist sequences $m_n'$, $\varepsilon_m'$, $V_j'$ and $m_n''$, $\varepsilon_m''$, $V_j''$ such that: - Conditions (H1), (C1) and (C2) hold for $m_n'$, $\varepsilon_m'$, $V_j'$, and $\frac{m'}{n\Delta_n}\Big(\frac{1}{\mu_{m'}}+\frac{1}{\mu_{m'}^-}\Big)$ tends to zero. - Conditions (H1), (C1) and (C2’) hold for $m_n''$, $\varepsilon_m''$, $V_j''$, and $\nu_0\Big(I\setminus[-\varepsilon_{m''},\varepsilon_{m''}]\Big)\sqrt{n\Delta_n^2}+\frac{m''\ln m''}{\sqrt{n}}$ tends to zero. Then the statistical models ${\ensuremath {\mathscr{P}}}_{n}^{\nu_0}$ and ${\ensuremath {\mathscr{Q}}}_{n}^{\nu_0}$ are asymptotically equivalent: $$\lim_{n\to\infty}\Delta({\ensuremath {\mathscr{P}}}_{n}^{\nu_0},{\ensuremath {\mathscr{Q}}}_{n}^{\nu_0})=0,$$ If, in addition, the Lévy measures have finite variation, i.e. if we assume (FV), then the same results hold replacing ${\ensuremath {\mathscr{P}}}_{n}^{\nu_0}$ and ${\ensuremath {\mathscr{Q}}}_{n}^{\nu_0}$ by ${\ensuremath {\mathscr{P}}}_{n,FV}^{\nu_0}$ and ${\ensuremath {\mathscr{Q}}}_{n,FV}^{\nu_0}$, respectively (see Lemma \[ch4LC\]). Examples {#sec:ch4experiments} ======== We will now analyze three different examples, underlining the different behaviors of the Lévy measure $\nu_0$ (respectively, finite, infinite with finite variation and infinite with infinite variation). The three chosen Lévy measures are ${\ensuremath {\mathbb{I}}}_{[0,1]}(x) dx$, ${\ensuremath {\mathbb{I}}}_{[0,1]}(x) \frac{dx}{x}$ and ${\ensuremath {\mathbb{I}}}_{{\ensuremath {\mathbb{R}}}_+}(x)\frac{dx}{x^2}$. In all three cases we assume the parameter $f$ to be uniformly bounded and with uniformly $\gamma$-Hölder derivatives: We will describe adequate subclasses ${\ensuremath {\mathscr{F}}}^{\nu_0, I} \subseteq {\ensuremath {\mathscr{F}}}_{(\gamma, K, \kappa, M)}^I$ defined as in . It seems very likely that the same results that are highlighted in these examples hold true for more general Lévy measures; however, we limit ourselves to these examples in order to be able to explicitly compute the quantities involved ($v_j$, $x_j^*$, etc.) and hence estimate the distance between $f$ and $\hat f_m$ as in Examples \[ex:ch4esempi\]. In the first of the three examples, where $\nu_0$ is the Lebesgue measure on $I=[0,1]$, we are considering the statistical models associated with the discrete and continuous observation of a compound Poisson process with Lévy density $f$. Observe that ${\ensuremath {\mathscr{W}}}_n^{{\ensuremath{\textnormal{Leb}}}}$ reduces to the statistical model associated with the continuous observation of a trajectory from: $$dy_t=\sqrt{f(t)}dt+\frac{1}{2\sqrt{T_n}}dW_t,\quad t\in [0,1].$$ In this case we have: \[ex:ch4CPP\](Finite Lévy measure). Let $\nu_0$ be the Lebesgue measure on $I=[0,1]$ and let ${\ensuremath {\mathscr{F}}}= {\ensuremath {\mathscr{F}}}^{{\ensuremath{\textnormal{Leb}}}, [0,1]}$ be any subclass of ${\ensuremath {\mathscr{F}}}_{(\gamma, K, \kappa, M)}^{[0,1]}$ for some strictly positive constants $K$, $\kappa$, $M$ and $\gamma\in(0,1]$. Then: $$\lim_{n\to\infty}\Delta({\ensuremath {\mathscr{P}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}},{\ensuremath {\mathscr{W}}}_n^{{\ensuremath{\textnormal{Leb}}}})=0 \ \textnormal{ and } \ \lim_{n\to\infty}\Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}},{\ensuremath {\mathscr{W}}}_n^{{\ensuremath{\textnormal{Leb}}}})=0.$$ More precisely, $$\Delta({\ensuremath {\mathscr{P}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}},{\ensuremath {\mathscr{W}}}_n^{{\ensuremath{\textnormal{Leb}}}})=\begin{cases}O\Big((n\Delta_n)^{-\frac{\gamma}{4+2\gamma}}\Big)\quad \textnormal{if } \ \gamma\in\big(0,\frac{1}{2}\big],\\ O\Big((n \Delta_n)^{-\frac{1}{10}}\Big)\quad \textnormal{if } \ \gamma\in\big(\frac{1}{2},1\big]. \end{cases}$$ In the case where $\Delta_n = n^{-\beta}$, $\frac{1}{2} < \beta < 1$, an upper bound for the rate of convergence of $\Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}}, {\ensuremath {\mathscr{W}}}_n^{{\ensuremath{\textnormal{Leb}}}})$ is $$\Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}}, {\ensuremath {\mathscr{W}}}_n^{{\ensuremath{\textnormal{Leb}}}})=\begin{cases} O\Big(n^{-\frac{\gamma+\beta}{4+2\gamma}}\ln n\Big)\quad \textnormal{if } \ \gamma\in\big(0,\frac{1}{2}\big) \text{ and }\frac{2+2\gamma}{3+2\gamma} \leq \beta < 1,\\ O\Big(n^{\frac{1}{2}-\beta}\ln n\Big)\quad \textnormal{if } \ \gamma\in\big(0,\frac{1}{2}\big) \text{ and } \frac{1}{2} < \beta < \frac{2+2\gamma}{3+2\gamma},\\ O\Big(n^{-\frac{2\beta+1}{10}}\ln n\Big)\quad \textnormal{if } \ \gamma\in\big[\frac{1}{2},1\big] \text{ and } \frac{3}{4} \leq \beta < 1,\\ O\Big(n^{\frac{1}{2}-\beta}\ln n\Big)\quad \textnormal{if } \ \gamma\in\big[\frac{1}{2},1\big] \text{ and } \frac{1}{2} < \beta < \frac{3}{4}. \end{cases}$$ See Section \[subsec:ch4ex1\] for a proof. \[ch4ex2\](Infinite Lévy measure with finite variation). Let $X$ be a truncated Gamma process with (infinite) Lévy measure of the form: $$\nu(A)=\int_A \frac{e^{-\lambda x}}{x}dx,\quad A\in{\ensuremath {\mathscr{B}}}([0,1]).$$ Here ${\ensuremath {\mathscr{F}}}^{\nu_0, I}$ is a 1-dimensional parametric family in $\lambda$, assuming that there exists a known constant $\lambda_0$ such that $0<\lambda\leq \lambda_0<\infty$, $f(t) = e^{-\lambda t}$ and $d\nu_0(x)=\frac{1}{x}dx$. In particular, the $f$ are Lipschitz, i.e. ${\ensuremath {\mathscr{F}}}^{\nu_0, [0,1]} \subset {\ensuremath {\mathscr{F}}}_{(\gamma = 1, K, \kappa, M)}^{[0,1]}$. The discrete or continuous observation (up to time $T_n$) of $X$ are asymptotically equivalent to ${\ensuremath {\mathscr{W}}}_n^{\nu_0}$, the statistical model associated with the observation of a trajectory of the process $(y_t)$: $$dy_t=\sqrt{f(t)}dt+\frac{\sqrt tdW_t}{2\sqrt{T_n}},\quad t\in[0,1].$$ More precisely, in the case where $\Delta_n = n^{-\beta}$, $\frac{1}{2} < \beta < 1$, an upper bound for the rate of convergence of $\Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{\nu_0}, {\ensuremath {\mathscr{W}}}_n^{\nu_0})$ is $$\Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0}) = \begin{cases} O\big(n^{\frac{1}{2}-\beta} \ln n\big) & \text{if } \frac{1}{2} < \beta \leq \frac{9}{10}\\ O\big(n^{-\frac{1+2\beta}{7}} \ln n\big) & \text{if } \frac{9}{10} < \beta < 1. \end{cases}$$ Concerning the continuous setting we have: $$\Delta({\ensuremath {\mathscr{P}}}_{n,FV}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})=O\Big(n^{\frac{\beta-1}{6}} \big(\ln n\big)^{\frac{5}{2}}\Big) = O\Big(T_n^{-\frac{1}{6}} \big(\ln T_n\big)^\frac{5}{2}\Big).$$ See Section \[subsec:ch4ex2\] for a proof. \[ex3\](Infinite Lévy measure, infinite variation). Let $X$ be a pure jump Lévy process with infinite Lévy measure of the form: $$\nu(A)=\int_A \frac{2-e^{-\lambda x^3}}{x^2}dx,\quad A\in{\ensuremath {\mathscr{B}}}({\ensuremath {\mathbb{R}}}^+).$$ Again, we are considering a parametric family in $\lambda > 0$, assuming that the parameter stays bounded below a known constant $\lambda_0$. Here, $f(t) =2- e^{-\lambda t^3}$, hence $1\leq f(t)\leq 2$, for all $t\geq 0$, and $f$ is Lipschitz, i.e. ${\ensuremath {\mathscr{F}}}^{\nu_0, {\ensuremath {\mathbb{R}}}_+} \subset {\ensuremath {\mathscr{F}}}_{(\gamma = 1, K, \kappa, M)}^{{\ensuremath {\mathbb{R}}}_+}$. The discrete or continuous observations (up to time $T_n$) of $X$ are asymptotically equivalent to the statistical model associated with the observation of a trajectory of the process $(y_t)$: $$dy_t=\sqrt{f(t)}dt+\frac{tdW_t}{2\sqrt{T_n}},\quad t\geq 0.$$ More precisely, in the case where $\Delta_n = n^{-\beta}$, $0 < \beta < 1$, an upper bound for the rate of convergence of $\Delta({\ensuremath {\mathscr{Q}}}_{n}^{\nu_0}, {\ensuremath {\mathscr{W}}}_n^{\nu_0})$ is $$\Delta({\ensuremath {\mathscr{Q}}}_{n}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0}) = \begin{cases} O\big(n^{\frac{1}{2} - \frac{2}{3}\beta}\big)& \text{if } \frac{3}{4} < \beta < \frac{12}{13}\\ O\big(n^{-\frac{1}{6}+\frac{\beta}{18}} (\ln n)^{\frac{7}{6}}\big) &\text{if } \frac{12}{13}\leq \beta<1. \end{cases}$$ In the continuous setting, we have $$\Delta({\ensuremath {\mathscr{P}}}_{n}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})=O\big(n^{\frac{3\beta-3}{34}}(\ln n)^{\frac{7}{6}}\big) = O\big(T_n^{-\frac{3}{34}} (\ln T_n)^{\frac{7}{6}}\big).$$ See Section \[subsec:ch4ex3\] for a proof. Proofs of the main results {#sec:ch4proofs} ========================== In order to simplify notations, the proofs will be presented in the case $I\subseteq {\ensuremath {\mathbb{R}}}^+$. Nevertheless, this allows us to present all the main difficulties, since they can only appear near 0. To prove Theorems \[ch4teo1\] and \[ch4teo2\] we need to introduce several intermediate statistical models. In that regard, let us denote by $Q_j^f$ the law of a Poisson random variable with mean $T_n\nu(J_j)$ (see for the definition of $J_{j}$). We will denote by $\mathscr{L}_m$ the statistical model associated with the family of probabilities $\big\{\bigotimes_{j=2}^m Q_j^f:f\in{\ensuremath {\mathscr{F}}}\big\}$: $$\label{eq:ch4l} \mathscr{L}_m=\bigg(\bar{{\ensuremath {\mathbb{N}}}}^{m-1},\mathcal P(\bar{{\ensuremath {\mathbb{N}}}}^{m-1}), \bigg\{\bigotimes_{j=2}^m Q_j^f:f\in{\ensuremath {\mathscr{F}}}\bigg\}\bigg).$$ By $N_{j}^f$ we mean the law of a Gaussian random variable ${\ensuremath {\mathscr{Nn}}}(2\sqrt{T_n\nu(J_j)},1)$ and by $\mathscr{N}_m$ the statistical model associated with the family of probabilities $\big\{\bigotimes_{j=2}^m N_j^f:f\in{\ensuremath {\mathscr{F}}}\big\}$: $$\label{eq:ch4n} \mathscr{N}_m=\bigg({\ensuremath {\mathbb{R}}}^{m-1},\mathscr B({\ensuremath {\mathbb{R}}}^{m-1}), \bigg\{\bigotimes_{j=2}^m N_j^f:f\in{\ensuremath {\mathscr{F}}}\bigg\}\bigg).$$ For each $f\in{\ensuremath {\mathscr{F}}}$, let $\bar \nu_m$ be the measure having $\bar f_m$ as a density with respect to $\nu_0$ where, for every $f\in{\ensuremath {\mathscr{F}}}$, $\bar f_m$ is defined as follows. $$\label{eq:ch4barf} \bar f_m(x):= \begin{cases} \quad 1 & \textnormal{if } x\in J_1,\\ \frac{\nu(J_j)}{{\nu_0}(J_{j})} & \textnormal{if } x\in J_{j}, \quad j = 2,\dots,m. \end{cases}$$ Furthermore, define $$\label{eq:ch4modellobar} \bar{\ensuremath {\mathscr{P}}}_{n}^{\nu_0}=\bigg(D,{\ensuremath {\mathscr{D}}}_{T_n},\Big\{P_{T_n}^{(\gamma^{\bar \nu_m-\nu_0},0,\bar\nu_m)}:\frac{d\bar\nu_m}{d\nu_0}\in{\ensuremath {\mathscr{F}}}\Big\}\bigg).$$ Proof of Theorem \[ch4teo1\] ---------------------------- We begin by a series of lemmas that will be needed in the proof. Before doing so, let us underline the scheme of the proof. We recall that the goal is to prove that estimating $f=\frac{d\nu}{d\nu_0}$ from the continuous observation of a Lévy process $(X_t)_{t\in[0,T_n]}$ without Gaussian part and having Lévy measure $\nu$ is asymptotically equivalent to estimating $f$ from the Gaussian white noise model: $$dy_t=\sqrt{f(t)}dt+\frac{1}{2\sqrt{T_n g(t)}}dW_t,\quad g=\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}},\quad t\in I.$$ Also, recall the definition of $\hat \nu_m$ given in and read ${\ensuremath {\mathscr{P}}}_1 \overset{\Delta} \Longleftrightarrow {\ensuremath {\mathscr{P}}}_2$ as ${\ensuremath {\mathscr{P}}}_1$ is asymptotically equivalent to ${\ensuremath {\mathscr{P}}}_2$. Then, we can outline the proof in the following way. - Step 1: $P_{T_n}^{(\gamma^{\nu-\nu_0},0,\nu)} \overset{\Delta} \Longleftrightarrow P_{T_n}^{(\gamma^{\hat\nu_m-\nu_0},0,\hat\nu_m)}$; - Step 2: $P_{T_n}^{(\gamma^{\hat\nu_m-\nu_0},0,\hat\nu_m)} \overset{\Delta} \Longleftrightarrow \bigotimes_{j=2}^m {\ensuremath {\mathscr{P}}}(T_n\nu(J_j))$ (Poisson approximation). Here $\bigotimes_{j=2}^m {\ensuremath {\mathscr{P}}}(T_n\nu(J_j))$ represents a statistical model associated with the observation of $m-1$ independent Poisson r.v. of parameters $T_n\nu(J_j)$; - Step 3: $\bigotimes_{j=2}^m {\ensuremath {\mathscr{P}}}(T_n \nu(J_j)) \overset{\Delta} \Longleftrightarrow \bigotimes_{j=2}^m {\ensuremath {\mathscr{Nn}}}(2\sqrt{T_n\nu(J_j)},1)$ (Gaussian approximation); - Step 4: $\bigotimes_{j=2}^m {\ensuremath {\mathscr{Nn}}}(2\sqrt{T_n\nu(J_j)},1)\overset{\Delta} \Longleftrightarrow (y_t)_{t\in I}$. Lemmas \[lemma:ch4poisson\]–\[lemma:ch4kernel\], below, are the key ingredients of Step 2. \[lemma:ch4poisson\] Let $\bar{\ensuremath {\mathscr{P}}}_{n}^{\nu_0}$ and $\mathscr{L}_m$ be the statistical models defined in and , respectively. Under the Assumption (H2) we have: $$\Delta(\bar{\ensuremath {\mathscr{P}}}_{n}^{\nu_0}, \mathscr{L}_m)=0, \textnormal{ for all } m.$$ Denote by $\bar {\ensuremath {\mathbb{N}}}={\ensuremath {\mathbb{N}}}\cup \{\infty\}$ and consider the statistics $S:(D,{\ensuremath {\mathscr{D}}}_{T_n})\to \big(\bar{\ensuremath {\mathbb{N}}}^{m-1},\mathcal{P}(\bar{\ensuremath {\mathbb{N}}}^{m-1})\big)$ defined by $$\label{eq:ch4S} S(x)=\Big(N_{T_n}^{x;\,2},\dots,N_{T_n}^{x;\,m}\bigg)\quad \textnormal{with} \quad N_{T_n}^{x;\,j}=\sum_{r\leq T_n}{\ensuremath {\mathbb{I}}}_{J_{j}}(\Delta x_r).$$ An application of Theorem \[ch4teosato\] to $P_{T_n}^{(\gamma^{\bar \nu_m-\nu_0},0,\bar \nu_m)}$ and $P_{T_n}^{(0,0,\nu_0)}$, yields $$\frac{d P_{T_n}^{(\gamma^{\bar \nu_m-\nu_0},0,\bar \nu_m)}}{dP_{T_n}^{(0,0,\nu_0)}}(x)=\exp\bigg(\sum_{j=2}^m \bigg(\ln\Big(\frac{\nu(J_j)}{\nu_0(J_j)}\Big)\bigg) N_{T_n}^{x;j}-T_n\int_I(\bar f_m(y)-1)\nu_0(dy)\bigg).$$ Hence, by means of the Fisher factorization theorem, we conclude that $S$ is a sufficient statistics for $\bar{\ensuremath {\mathscr{P}}}_{n}^{\nu_0}$. Furthermore, under $P_{T_n}^{(\gamma^{\bar \nu_m-\nu_0},0,\bar \nu_m)}$, the random variables $N_{T_n}^{x;j}$ have Poisson distributions $Q_{j}^f$ with means $T_n\nu(J_j)$. Then, by means of Property \[ch4fatto3\], we get $\Delta(\bar{\ensuremath {\mathscr{P}}}_{n}^{\nu_0}, \mathscr{L}_m)=0, \textnormal{ for all } m.$ Let us denote by $\hat Q_j^f$ the law of a Poisson random variable with mean $T_n\int_{J_j}\hat f_m(y)\nu_0(dy)$ and let $\hat{\mathscr{L}}_m$ be the statistical model associated with the family of probabilities $\{\bigotimes_{j=2}^m \hat Q_j^f:f\in {\ensuremath {\mathscr{F}}}\}$. \[lemma:ch4poissonhatf\] $$\Delta(\mathscr L_m,\hat{\mathscr{L}}_m)\leq \sup_{f\in {\ensuremath {\mathscr{F}}}}\sqrt{\frac{T_n}{\kappa}\int_{I\setminus[0,\varepsilon_m]}\big(f(y)-\hat f_m(y)\big)^2\nu_0(dy)}.$$ By means of Facts \[ch4h\]–\[fact:ch4hellingerpoisson\], we get: $$\begin{aligned} \Delta(\mathscr L_m,\hat{\mathscr{L}}_m)&\leq \sup_{f\in{\ensuremath {\mathscr{F}}}}H\bigg(\bigotimes_{j=2}^m Q_j^f,\bigotimes_{j=2}^m \hat Q_j^f\bigg)\\ &\leq \sup_{f\in{\ensuremath {\mathscr{F}}}}\sqrt{\sum_{j=2}^m 2 H^2(Q_j^f,\hat Q_j^f)}\\ & =\sup_{f\in{\ensuremath {\mathscr{F}}}}\sqrt 2\sqrt{\sum_{j=2}^m\bigg(1-\exp\bigg(-\frac{T_n}{2}\bigg[\sqrt{\int_{J_j}\hat f(y)\nu_0(dy)}-\sqrt{\int_{J_j} f(y)\nu_0(dy)}\bigg]^2\bigg)\bigg)}.\end{aligned}$$ By making use of the fact that $1-e^{-x}\leq x$ for all $x\geq 0$ and the equality $\sqrt a-\sqrt b= \frac{a-b}{\sqrt a+\sqrt b}$ combined with the lower bound $f\geq \kappa$ (that also implies $\hat f_m\geq \kappa$) and finally the Cauchy-Schwarz inequality, we obtain: $$\begin{aligned} &1-\exp\bigg(-\frac{T_n}{2}\bigg[\sqrt{\int_{J_j}\hat f(y)\nu_0(dy)}-\sqrt{\int_{J_j} f(y)\nu_0(dy)}\bigg]^2\bigg)\\ &\leq \frac{T_n}{2}\bigg[\sqrt{\int_{J_j}\hat f(y)\nu_0(dy)}-\sqrt{\int_{J_j} f(y)\nu_0(dy)}\bigg]^2\\ & \leq \frac{T_n}{2} \frac{\bigg(\int_{J_j}(f(y)-\hat f_m(y))\nu_0(dy)\bigg)^2}{\kappa \nu_0(J_j)}\\ &\leq \frac{T_n}{2\kappa} \int_{J_j}\big(f(y)-\hat f_m(y)\big)^2\nu_0(dy). \end{aligned}$$ Hence, $$H\bigg(\bigotimes_{j=2}^m Q_j^f,\bigotimes_{j=2}^m \hat Q_j^f\bigg)\leq \sqrt{\frac{T_n}{\kappa}\int_{I\setminus[0,\varepsilon_m]}\big(f(y)-\hat f_m(y)\big)^2\nu_0(dy)}.$$ \[lemma:ch4kernel\] Let $\hat\nu_m$ and $\bar \nu_m$ the Lévy measures defined as in and , respectively. For every $f\in {\ensuremath {\mathscr{F}}}$, there exists a Markov kernel $K$ such that $$KP_{T_n}^{(\gamma^{\bar\nu_m-\nu_0},0,\bar\nu_m)}=P_{T_n}^{(\gamma^{\hat \nu_m-\nu_0},0,\hat \nu_m)}.$$ By construction, $\bar\nu_m$ and $\hat\nu_m$ coincide on $[0,\varepsilon_m]$. Let us denote by $\bar \nu_m^{\textnormal{res}}$ and $\hat\nu_m^{\textnormal{res}}$ the restriction on $I\setminus[0,\varepsilon_m]$ of $\bar\nu_m$ and $\hat\nu_m$ respectively, then it is enough to prove: $KP_{T_n}^{(\gamma^{\bar\nu_m^{\textnormal{res}}-\nu_0},0,\bar\nu_m^{\textnormal{res}})}=P_{T_n}^{(\gamma^{\hat \nu_m^{\textnormal{res}}-\nu_0},0,\hat \nu_m^{\textnormal{res}})}.$ First of all, let us observe that the kernel $M$: $$M(x,A)=\sum_{j=2}^m{\ensuremath {\mathbb{I}}}_{J_j}(x)\int_A V_j(y)\nu_0(dy),\quad x\in I\setminus[0,\varepsilon_m],\quad A\in{\ensuremath {\mathscr{B}}}(I\setminus[0,\varepsilon_m])$$ is defined in such a way that $M \bar\nu_m^{\textnormal{res}} = \hat \nu_m^{\textnormal{res}}$. Indeed, for all $A\in{\ensuremath {\mathscr{B}}}(I\setminus[0,\varepsilon_m])$, $$\begin{aligned} M\bar\nu_m^{\textnormal{res}}(A)&=\sum_{j=2}^m\int_{J_j}M(x,A)\bar\nu_m^{\textnormal{res}}(dx)=\sum_{j=2}^m \int_{J_j}\bigg(\int_A V_j(y)\nu_0(dy)\bigg)\bar\nu_m^{\textnormal{res}}(dx)\nonumber\\ &=\sum_{j=2}^m \bigg(\int_A V_j(y)\nu_0(dy)\bigg)\nu(J_j)=\int_A \hat f_m(y)\nu_0(dy)=\hat \nu_m^{\textnormal{res}}(A). \label{eqn:M} \end{aligned}$$ Observe that $(\gamma^{\bar\nu_m^{\textnormal{res}}-\nu_0},0,\bar\nu_m^{\textnormal{res}})$ and $(\gamma^{\hat \nu_m^{\textnormal{res}}-\nu_0},0,\hat \nu_m^{\textnormal{res}})$ are Lévy triplets associated with compound Poisson processes since $\bar\nu_m^{\textnormal{res}}$ and $\hat \nu_m^{\textnormal{res}}$ are finite Lévy measures. The Markov kernel $K$ interchanging the laws of the Lévy processes is constructed explicitly in the case of compound Poisson processes. Indeed if $\bar X$ is the compound Poisson process having Lévy measure $\bar\nu_m^{\textnormal{res}}$, then $\bar X_{t} = \sum_{i=1}^{N_t} \bar Y_{i}$, where $N_t$ is a Poisson process of intensity $\iota_m:=\bar\nu_m^{\textnormal{res}}(I\setminus [0,\varepsilon_m])$ and the $\bar Y_{i}$ are i.i.d. random variables with probability law $\frac{1}{\iota_m}\bar\nu_m^{\textnormal{res}}$. Moreover, given a trajectory of $\bar X$, both the trajectory $(n_t)_{t\in[0,T_n]}$ of the Poisson process $(N_t)_{t\in[0,T_n]}$ and the realizations $\bar y_i$ of $\bar Y_i$, $i=1,\dots,n_{T_n}$ are uniquely determined. This allows us to construct $n_{T_n}$ i.i.d. random variables $\hat Y_i$ as follows: For every realization $\bar y_i$ of $\bar Y_i$, we define the realization $\hat y_i$ of $\hat Y_i$ by throwing it according to the probability law $M(\bar y_i,\cdot)$. Hence, thanks to , $(\hat Y_i)_i$ are i.i.d. random variables with probability law $\frac{1}{\iota_m} \hat \nu_m^{\text{res}}$. The desired Markov kernel $K$ (defined on the Skorokhod space) is then given by: $$K : (\bar X_{t})_{t\in[0,T_n]} \longmapsto \bigg(\hat X_{t} := \sum_{i=1}^{N_t} \hat Y_{i}\bigg)_{t\in[0,T_n]}.$$ Finally, observe that, since $$\begin{aligned} \iota_m=\int_{I\setminus[0,\varepsilon_m]}\bar f_m(y)\nu_0(dy)&=\int_{I\setminus[0,\varepsilon_m]} f(y)\nu_0(dy)=\int_{I\setminus[0,\varepsilon_m]}\hat f_m(y)\nu_0(dy), \end{aligned}$$ $(\hat X_t)_{t\in[0,T_n]}$ is a compound Poisson process with Lévy measure $\hat\nu_m^{\textnormal{res}}.$ Let us now state two lemmas needed to understand Step 4. \[lemma:ch4wn\] Denote by ${\ensuremath {\mathscr{W}}}_m^\#$ the statistical model associated with the continuous observation of a trajectory from the Gaussian white noise: $$dy_t=\sqrt{f(t)}dt+\frac{1}{2\sqrt{T_n}\sqrt{g(t)}}dW_t,\quad t\in I\setminus [0,\varepsilon_m].$$ Then, according with the notation introduced in Section \[subsec:ch4parameter\] and at the beginning of Section \[sec:ch4proofs\], we have $$\Delta(\mathscr{N}_m,{\ensuremath {\mathscr{W}}}_m^\#)\leq 2\sqrt{T_n}\sup_{f\in {\ensuremath {\mathscr{F}}}} \big(A_m(f)+B_m(f)\big).$$ As a preliminary remark observe that ${\ensuremath {\mathscr{W}}}_m^\#$ is equivalent to the model that observes a trajectory from: $$d\bar y_t=\sqrt{f(t)}g(t)dt+\frac{\sqrt{g(t)}}{2\sqrt{T_n}}dW_t,\quad t\in I\setminus [0,\varepsilon_m].$$ Let us denote by $\bar Y_j$ the increments of the process $(\bar y_t)$ over the intervals $J_j$, $j=2,\dots,m$, i.e. $$\bar Y_j:=\bar y_{v_j}-\bar y_{v_{j-1}}\sim{\ensuremath {\mathscr{Nn}}}\bigg(\int_{J_j}\sqrt{f(y)}\nu_0(dy),\frac{\nu_0(J_j)}{4T_n}\bigg)$$ and denote by $\bar{\mathscr{N}}_m$ the statistical model associated with the distributions of these increments. As an intermediate result, we will prove that $$\label{eq:ch4normali} \Delta(\mathscr{N}_m,\bar{\mathscr{N}}_m)\leq 2\sqrt{T_n} \sup_{f\in {\ensuremath {\mathscr{F}}}} B_m(f), \ \textnormal{ for all m}.$$ To that aim, remark that the experiment $\bar{\mathscr{N}}_m$ is equivalent to observing $m-1$ independent Gaussian random variables of means $\frac{2\sqrt{T_n}}{\sqrt{\nu_0(J_j)}}\int_{J_j}\sqrt{f(y)}\nu_0(dy)$, $j=2,\dots,m$ and variances identically $1$, name this last experiment $\mathscr{N}^{\#}_m$. Hence, using also Property \[ch4delta0\], Facts \[ch4h\] and \[fact:ch4gaussiane\] we get: $$\begin{aligned} \Delta(\mathscr{N}_m, \bar{\mathscr{N}}_m)\leq\Delta(\mathscr{N}_m, \mathscr{N}^{\#}_m)&\leq \sqrt{\sum_{j=2}^m\bigg(\frac{2\sqrt{T_n}}{\sqrt{\nu_0(J_j)}}\int_{J_j}\sqrt{f(y)}\nu_0(dy)-2\sqrt{T_n\nu(J_j)}\bigg)^2}.\end{aligned}$$ Since it is clear that $\delta({\ensuremath {\mathscr{W}}}_m^\#,\bar{\mathscr{N}}_m)=0$, in order to bound $\Delta(\mathscr{N}_m,{\ensuremath {\mathscr{W}}}_m^\#)$ it is enough to bound $\delta(\bar{\mathscr{N}}_m,{\ensuremath {\mathscr{W}}}_m^\#)$. Using similar ideas as in [@cmultinomial] Section 8.2, we define a new stochastic process as: $$Y_t^*=\sum_{j=2}^m\bar Y_j\int_{\varepsilon_m}^t V_j(y)\nu_0(dy)+\frac{1}{2\sqrt{T_n}}\sum_{j=2}^m\sqrt{\nu_0(J_j)}B_j(t),\quad t\in I\setminus [0,\varepsilon_m],$$ where the $(B_j(t))$ are independent centered Gaussian processes independent of $(W_t)$ and with variances $$\textnormal{Var}(B_j(t))=\int_{\varepsilon_m}^tV_j(y)\nu_0(dy)-\bigg(\int_{\varepsilon_m}^tV_j(y)\nu_0(dy)\bigg)^2.$$ These processes can be constructed from a standard Brownian bridge $\{B(s), s\in[0,1]\}$, independent of $(W_t)$, via $$B_i(t)=B\bigg(\int_{\varepsilon_m}^t V_i(y)\nu_0(dy)\bigg).$$ By construction, $(Y_t^*)$ is a Gaussian process with mean and variance given by, respectively: $$\begin{aligned} {\ensuremath {\mathbb{E}}}[Y_t^*]&=\sum_{j=2}^m{\ensuremath {\mathbb{E}}}[\bar Y_j]\int_{\varepsilon_m}^t V_j(y)\nu_0(dy)=\sum_{j=2}^m\bigg(\int_{J_j}\sqrt{f(y)}\nu_0(dy)\bigg)\int_{\varepsilon_m}^t V_j(y)\nu_0(dy),\\ \textnormal{Var}[Y_t^*]&=\sum_{j=2}^m\textnormal{Var}[\bar Y_j]\bigg(\int_{\varepsilon_m}^t V_j(y)\nu_0(dy)\bigg)^2+\frac{1}{4T_n}\sum_{j=2}^m \nu_0(J_j)\textnormal{Var}(B_j(t))\\ &= \frac{1}{4T_n}\int_{\varepsilon_m}^t \sum_{j=2}^m \nu_0(J_j) V_j(y)\nu_0(dy)= \frac{1}{4T_n}\int_{\varepsilon_m}^t \nu_0(dy)=\frac{\nu_0([\varepsilon_m,t])}{4T_n}.\end{aligned}$$ One can compute in the same way the covariance of $(Y_t^*)$ finding that $$\textnormal{Cov}(Y_s^*,Y_t^*)=\frac{\nu_0([\varepsilon_m,s])}{4 T_n}, \ \forall s\leq t.$$ We can then deduce that $$Y^*_t=\int_{\varepsilon_m}^t \widehat{\sqrt {f}}_m(y)\nu_0(dy)+\int_{\varepsilon_m}^t\frac{\sqrt{g(s)}}{2\sqrt{T_n}}dW^*_s,\quad t\in I\setminus [0,\varepsilon_m],$$ where $(W_t^*)$ is a standard Brownian motion and $$\widehat{\sqrt {f}}_m(x):=\sum_{j=2}^m\bigg(\int_{J_j}\sqrt{f(y)}\nu_0(dy)\bigg)V_j(x).$$ Applying Fact \[fact:ch4processigaussiani\], we get that the total variation distance between the process $(Y_t^*)_{t\in I\setminus [0,\varepsilon_m]}$ constructed from the random variables $\bar Y_j$, $j=2,\dots,m$ and the Gaussian process $(\bar y_t)_{t\in I\setminus [0,\varepsilon_m]}$ is bounded by $$\sqrt{4 T_n\int_{I\setminus [0,\varepsilon_m]}\big(\widehat{\sqrt {f}}_m-\sqrt{f(y)}\big)^2\nu_0(dy)},$$ which gives the term in $A_m(f)$. \[lemma:ch4limitewn\] In accordance with the notation of Lemma \[lemma:ch4wn\], we have: $$\label{eq:ch4wn} \Delta({\ensuremath {\mathscr{W}}}_m^\#,{\ensuremath {\mathscr{W}}}_n^{\nu_0})=O\bigg(\sup_{f\in{\ensuremath {\mathscr{F}}}}\sqrt{T_n\int_0^{\varepsilon_m}\big(\sqrt{f(t)}-1\big)^2\nu_0(dt)}\bigg).$$ Clearly $\delta({\ensuremath {\mathscr{W}}}_n^{\nu_0},{\ensuremath {\mathscr{W}}}_m^\#)=0$. To show that $\delta({\ensuremath {\mathscr{W}}}_m^\#,{\ensuremath {\mathscr{W}}}_n^{\nu_0})\to 0$, let us consider a Markov kernel $K^\#$ from $C(I\setminus [0,\varepsilon_m])$ to $C(I)$ defined as follows: Introduce a Gaussian process, $(B_t^m)_{t\in[0,\varepsilon_m]}$ with mean equal to $t$ and covariance $$\textnormal{Cov}(B_s^m,B_t^m)=\int_0^{\varepsilon_m}\frac{1}{4 T_n g(s)}{\ensuremath {\mathbb{I}}}_{[0,s]\cap [0,t]}(z)dz.$$ In particular, $$\textnormal{Var}(B_t^m)=\int_0^t\frac{1}{4 T_n g(s)}ds.$$ Consider it as a process on the whole of $I$ by defining $B_t^m=B_{\varepsilon_m}^m$ $\forall t>\varepsilon_m$. Let $\omega_t$ be a trajectory in $C(I\setminus [0,\varepsilon_m])$, which again we constantly extend to a trajectory on the whole of $I$. Then, we define $K^\#$ by sending the trajectory $\omega_t$ to the trajectory $\omega_t + B_t^m$. If we define $\mathbb{\tilde W}_n$ as the law induced on $C(I)$ by $$d\tilde{y}_t = h(t) dt + \frac{dW_t}{2\sqrt{T_n g(t)}}, \quad t \in I,\quad h(t) = \begin{cases} 1 & t \in [0, \varepsilon_m]\\ \sqrt{f(t)} & t \in I\setminus [0,\varepsilon_m], \end{cases}$$ then $K^\# \mathbb{W}_n^f|_{I\setminus [0,\varepsilon_m]} = \mathbb{\tilde W}_n$, where $\mathbb{W}_n^f$ is defined as in . By means of Fact \[fact:ch4processigaussiani\] we deduce . The proof of the theorem follows by combining the previous lemmas together: - Step 1: Let us denote by $\hat{\ensuremath {\mathscr{P}}}_{n,m}^{\nu_0}$ the statistical model associated with the family of probabilities $(P_{T_n}^{(\gamma^{\hat\nu_m-\nu_0},0,\hat\nu_m)}:\frac{d\nu}{d\nu_0}\in{\ensuremath {\mathscr{F}}})$. Thanks to Property \[ch4delta0\], Fact \[ch4h\] and Theorem \[teo:ch4bound\] we have that $$\Delta({\ensuremath {\mathscr{P}}}_n^{\nu_0},\hat{\ensuremath {\mathscr{P}}}_{n,m}^{\nu_0})\leq \sqrt{\frac{T_n}{2}}\sup_{f\in {\ensuremath {\mathscr{F}}}}H(f,\hat f_m).$$ - Step 2: On the one hand, thanks to Lemma \[lemma:ch4poisson\], one has that the statistical model associated with the family of probability $(P_{T_n}^{(\gamma^{\bar \nu_m-\nu_0},0,\bar\nu_m)}:\frac{d\nu}{d\nu_0}\in{\ensuremath {\mathscr{F}}})$ is equivalent to $\mathscr{L}_m$. By means of Lemma \[lemma:ch4poissonhatf\] we can bound $\Delta(\mathscr{L}_m,\hat{\mathscr{L}}_m)$. On the other hand it is easy to see that $\delta(\hat{\ensuremath {\mathscr{P}}}_{n,m}^{\nu_0}, \hat{\mathscr{L}}_m)=0$. Indeed, it is enough to consider the statistics $$S: x \mapsto \bigg(\sum_{r\leq T_n}{\ensuremath {\mathbb{I}}}_{J_2}(\Delta x_r),\dots,\sum_{r\leq T_n}{\ensuremath {\mathbb{I}}}_{J_m}(\Delta x_r)\bigg)$$ since the law of the random variable $\sum_{r\leq T_n}{\ensuremath {\mathbb{I}}}_{J_j}(\Delta x_r)$ under $P_{T_n}^{(\gamma^{\hat\nu_m-\nu_0},0,\hat\nu_m)}$ is Poisson of parameter $T_n\int_{J_j}\hat f_m(y)\nu_0(dy)$ for all $j=2,\dots,m$. Finally, Lemmas \[lemma:ch4poisson\] and \[lemma:ch4kernel\] allows us to conclude that $\delta(\mathscr{L}_m,\hat{\ensuremath {\mathscr{P}}}_{n,m}^{\nu_0})=0$. Collecting all the pieces together, we get $$\Delta(\hat{\ensuremath {\mathscr{P}}}_{n,m}^{\nu_0},\mathscr{L}_m)\leq \sup_{f\in {\ensuremath {\mathscr{F}}}}\sqrt{\frac{T_n}{\kappa}\int_{I\setminus[0,\varepsilon_m]}\big(f(y)-\hat f_m(y)\big)^2\nu_0(dy)}.$$ - Step 3: Applying Theorem \[ch4teomisto\] and Fact \[ch4hp\] we can pass from the Poisson approximation given by $\mathscr{L}_m$ to a Gaussian one obtaining $$\Delta(\mathscr{L}_m,\mathscr{N}_m)=C\sup_{f\in {\ensuremath {\mathscr{F}}}}\sqrt{\sum_{j=2}^m\frac{2}{T_n\nu(J_j)}}\leq C\sqrt{\sum_{j=2}^m\frac{2\kappa}{T_n\nu_0(J_j)}}=C\sqrt{\frac{(m-1)2\kappa}{T_n\mu_m}}.$$ - Step 4: Finally, Lemmas \[lemma:ch4wn\] and \[lemma:ch4limitewn\] allow us to conclude that: $$\begin{aligned} \Delta({\ensuremath {\mathscr{P}}}_n^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})&=O\bigg(\sqrt{T_n}\sup_{f\in {\ensuremath {\mathscr{F}}}}\big(A_m(f)+B_m(f)+C_m\big)\bigg)\\ & \quad + O\bigg(\sqrt{T_n}\sup_{f\in {\ensuremath {\mathscr{F}}}}\sqrt{\int_{I\setminus{[0,\varepsilon_m]}}\big(f(y)-\hat f_m(y)\big)^2\nu_0(dy)}+\sqrt{\frac{m}{T_n\mu_m}}\bigg).\end{aligned}$$ Proof of Theorem \[ch4teo2\] ---------------------------- Again, before stating some technical lemmas, let us highlight the main ideas of the proof. We recall that the goal is to prove that estimating $f=\frac{d\nu}{d\nu_0}$ from the discrete observations $(X_{t_i})_{i=0}^n$ of a Lévy process without Gaussian component and having Lévy measure $\nu$ is asymptotically equivalent to estimating $f$ from the Gaussian white noise model $$dy_t=\sqrt{f(t)}dt+\frac{1}{2\sqrt{T_n g(t)}}dW_t,\quad g=\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}},\quad t\in I.$$ Reading ${\ensuremath {\mathscr{P}}}_1 \overset{\Delta} \Longleftrightarrow {\ensuremath {\mathscr{P}}}_2$ as ${\ensuremath {\mathscr{P}}}_1$ is asymptotically equivalent to ${\ensuremath {\mathscr{P}}}_2$, we have: - Step 1. Clearly $(X_{t_i})_{i=0}^n \overset{\Delta} \Longleftrightarrow (X_{t_i}-X_{t_{i-1}})_{i=1}^n$. Moreover, $(X_{t_i}-X_{t_{i-1}})_i\overset{\Delta} \Longleftrightarrow (\epsilon_iY_i)$ where $(\epsilon_i)$ are i.i.d Bernoulli r.v. with parameter $\alpha=\iota_m \Delta_n e^{-\iota_m\Delta_n}$, $\iota_m:=\int_{I\setminus [0,\varepsilon_m]} f(y)\nu_0(dy)$ and $(Y_i)_i$ are i.i.d. r.v. independent of $(\epsilon_i)_{i=1}^n$ and of density $\frac{ f}{\iota_m}$ with respect to ${\nu_0}_{|_{I\setminus [0,\varepsilon_m]}}$; - Step 2. $(\epsilon_iY_i)_i \overset{\Delta} \Longleftrightarrow \mathcal M(n;(\gamma_j)_{j=1}^m)$, where $\mathcal M(n;(\gamma_j)_{j=1}^m)$ is a multinomial distribution with $\gamma_1=1-\alpha$ and $\gamma_i:=\alpha\nu(J_i)$ $i=2,\dots,m$; - Step 3. Gaussian approximation: $\mathcal M(n;(\gamma_1,\dots\gamma_m)) \overset{\Delta} \Longleftrightarrow \bigotimes_{j=2}^m {\ensuremath {\mathscr{Nn}}}(2\sqrt{T_n\nu(J_j)},1)$; - Step 4. $\bigotimes_{j=2}^m {\ensuremath {\mathscr{Nn}}}(2\sqrt{T_n\nu(J_j)},1)\overset{\Delta} \Longleftrightarrow (y_t)_{t\in I}$. \[lemma:ch4discreto\] Let $\nu_i$, $i=1,2$, be Lévy measures such that $\nu_1\ll\nu_2$ and $b_1-b_2=\int_{|y|\leq 1}y(\nu_1-\nu_2)(dy)<\infty$. Then, for all $0<t<\infty$, we have: $$\Big\|Q_t^{(b_1,0,\mu_1)}-Q_t^{(b_2,0,\mu_2)}\Big\|_{TV}\leq \sqrt \frac{t}{2} H(\nu_1,\nu_2).$$ For all given $t$, let $K_t$ be the Markov kernel defined as $K_t(\omega,A):={\ensuremath {\mathbb{I}}}_A(\omega_t)$, $\forall \ A\in{\ensuremath {\mathscr{B}}}({\ensuremath {\mathbb{R}}})$, $\forall \ \omega\in D$. Then we have: $$\begin{aligned} \big\|Q_t^{(b_1,0,\nu_1)}-Q_t^{(b_2,0,\nu_2)}\big\|_{TV}&=\big\|K_tP_t^{(b_1,0,\nu_1)}-K_tP_t^{(b_2,0,\nu_2)}\big\|_{TV}\\ &\leq \big\|P_t^{(b_1,0,\nu_1)}-P_t^{(b_2,0,\nu_2)}\big\|_{TV}\\ &\leq \sqrt \frac{t}{2} H(\nu_1,\nu_2), \end{aligned}$$ where we have used that Markov kernels reduce the total variation distance and Theorem \[teo:ch4bound\]. \[lemma:ch4bernoulli\] Let $(P_i)_{i=1}^n$, $(Y_i)_{i=1}^n$ and $(\epsilon_i)_{i=1}^n$ be samples of, respectively, Poisson random variables ${\ensuremath {\mathscr{P}}}(\lambda_i)$, random variables with common distribution and Bernoulli random variables of parameters $\lambda_i e^{-\lambda_i}$, which are all independent. Let us denote by $Q_{(Y_i,P_i)}$ (resp. $Q_{(Y_i,\epsilon_i)}$) the law of $\sum_{j=1}^{P_i} Y_j$ (resp., $\epsilon_i Y_i$). Then: $$\label{eq:ch4lambda} \Big\|\bigotimes_{i=1}^n Q_{(Y_i,P_i)}-\bigotimes_{i=1}^n Q_{(Y_i,\epsilon_i)}\Big\|_{TV}\leq 2\sqrt{\sum_{i=1}^n\lambda_i^2}.$$ The proof of this Lemma can be found in [@esterESAIM], Section 2.1. \[lemma:ch4troncatura\] Let $f_m^{\textnormal{tr}}$ be the truncated function defined as follows: $$f_m^{\textnormal{tr}}(x)=\begin{cases} 1 &\mbox{ if } x\in[0,\varepsilon_m]\\ f(x) &\mbox{ otherwise} \end{cases}$$ and let $\nu_m^{\textnormal{tr}}$ (resp. $\nu_m^{\textnormal{res}}$) be the Lévy measure having $f_m^{\textnormal{tr}}$ (resp. ${f|_{I\setminus [0,\varepsilon_m]}}$) as a density with respect to $\nu_0$. Denote by ${\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{tr},\nu_0}$ the statistical model associated with the family of probabilities $\Big(\bigotimes_{i=1}^nQ_{t_i-t_{i-1}}^{(\gamma^{\nu_m^{\textnormal{tr}}-\nu_0},0,\nu_m^{\textnormal{tr}})}:\frac{d\nu_m^{\textnormal{tr}}}{d\nu_0}\in{\ensuremath {\mathscr{F}}}\Big)$ and by ${\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{res},\nu_0}$ the model associated with the family of probabilities $\Big(\bigotimes_{i=1}^nQ_{t_i-t_{i-1}}^{(\gamma^{\nu_m^{\textnormal{res}}-\nu_0},0,\nu_m^{\textnormal{res}})}:\frac{d\nu_m^{\textnormal{res}}}{d\nu_0}\in{\ensuremath {\mathscr{F}}}\Big)$. Then: $$\Delta({\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{tr},\nu_0},{\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{res},\nu_0})=0.$$ Let us start by proving that $\delta({\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{tr},\nu_0},{\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{res},\nu_0})=0.$ For that, let us consider two independent Lévy processes, $X^{\textnormal{tr}}$ and $X^0$, of Lévy triplets given by $\big(\gamma^{\nu_m^{\textnormal{tr}}-\nu_0},0,\nu_m^{\textnormal{tr}-\nu_0}\big)$ and $\big(0,0,\nu_0|_{[0,\varepsilon_m]}\big)$, respectively. Then it is clear (using the *Lévy-Khintchine formula*) that the random variable $X_t^{\textnormal{tr}}- X_t^0$ is a randomization of $X_t^{\textnormal{tr}}$ (since the law of $X_t^0$ does not depend on $\nu$) having law $Q_t^{(\gamma^{\nu_m^{\textnormal{res}}-\nu_0},0,\nu_m^{\textnormal{res}})}$, for all $t\geq 0$. Similarly, one can prove that $\delta({\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{res},\nu_0},{\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{tr},\nu_0})=0.$ As a preliminary remark, observe that the model ${\ensuremath {\mathscr{Q}}}_n^{\nu_0}$ is equivalent to the one that observes the increments of $\big((x_t),P_{T_n}^{(\gamma^{\nu-\nu_0},0,\nu)}\big)$, that is, the model $\tilde{\ensuremath {\mathscr{Q}}}_n^{\nu_0}$ associated with the family of probabilities $\Big(\bigotimes_{i=1}^nQ_{t_i-t_{i-1}}^{(\gamma^{\nu-\nu_0},0,\nu)}:\frac{d\nu}{d\nu_0}\in{\ensuremath {\mathscr{F}}}\Big)$. - Step 1: Facts \[ch4h\]–\[ch4hp\] and Lemma \[lemma:ch4discreto\] allow us to write $$\begin{aligned} &\Big\|\bigotimes_{i=1}^nQ_{\Delta_n}^{(\gamma^{\nu-\nu_0},0,\nu)}-\bigotimes_{i=1}^nQ_{\Delta_n}^{(\gamma^{\nu_m^{\textnormal{tr}}-\nu_0},0, \nu_m^{\textnormal{tr}})}\Big\|_{TV}\leq \sqrt{n\sqrt\frac{\Delta_n}{2}H(\nu,\nu_m^{\textnormal{tr}})}\\&=\sqrt{n\sqrt\frac{\Delta_n}{2}\sqrt{\int_0^{\varepsilon_m}\big(\sqrt{f(y)}-1\big)^2\nu_0(dy)}}.\end{aligned}$$ Using this bound together with Lemma \[lemma:ch4troncatura\] and the notation therein, we get $\Delta({\ensuremath {\mathscr{Q}}}_n^{\nu_0}, {\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{res},\nu_0})\leq \sqrt{n\sqrt\frac{\Delta_n}{2}\sup_{f\in {\ensuremath {\mathscr{F}}}}H(f, f_m^{\textnormal{tr}})}$. Observe that $\nu_m^{\textnormal{res}}$ is a finite Lévy measure, hence $\Big((x_t),P_{T_n}^{(\gamma^{\nu_m^{\textnormal{res}}},0,\nu_m^{\textnormal{res}})}\Big)$ is a compound Poisson process with intensity equal to $\iota_m:=\int_{I\setminus [0,\varepsilon_m]} f(y)\nu_0(dy)$ and jumps size density $\frac{ f(x)g(x)}{\iota_m}$, for all $x\in I\setminus [0,\varepsilon_m]$ (recall that we are assuming that $\nu_0$ has a density $g$ with respect to Lebesgue). In particular, this means that $Q_{\Delta_n}^{(\gamma^{\nu_m^{\textnormal{res}}},0,\nu_m^{\textnormal{res}})}$ can be seen as the law of the random variable $\sum_{j=1}^{P_i}Y_j$ where $P_i$ is a Poisson variable of mean $\iota_m \Delta_n$, independent from $(Y_i)_{i\geq 0}$, a sequence of i.i.d. random variables with density $\frac{ fg}{\iota_m}{\ensuremath {\mathbb{I}}}_{I\setminus[0,\varepsilon_m]}$ with respect to Lebesgue. Remark also that $\iota_m$ is confined between $\kappa \nu_0\big(I\setminus [0,\varepsilon_m]\big)$ and $M\nu_0\big(I\setminus [0,\varepsilon_m] \big)$. Let $(\epsilon_i)_{i\geq 0}$ be a sequence of i.i.d. Bernoulli variables, independent of $(Y_i)_{i\geq 0}$, with mean $\iota_m \Delta_n e^{-\iota_m\Delta_n}$. For $i=1,\dots,n$, denote by $Q_i^{\epsilon,f}$ the law of the variable $\epsilon_iY_i$ and by ${\ensuremath {\mathscr{Q}}}_n^{\epsilon}$ the statistical model associated with the observations of the vector $(\epsilon_1Y_1,\dots,\epsilon_nY_n)$, i.e. $${\ensuremath {\mathscr{Q}}}_n^{\epsilon}=\bigg(I^n,{\ensuremath {\mathscr{B}}}(I^n),\bigg\{\bigotimes_{i=1}^n Q_i^{\epsilon,f}:f\in{\ensuremath {\mathscr{F}}}\bigg\}\bigg).$$ Furthermore, denote by $\tilde Q_i^f$ the law of $\sum_{j=1}^{P_i}Y_j$. Then an application of Lemma \[lemma:ch4bernoulli\] yields: $$\begin{aligned} \Big\|\bigotimes_{i=1}^n\tilde Q_i^f&-\bigotimes_{i=1}^nQ_i^{\epsilon,f}\Big\|_{TV} \leq 2\iota_m\sqrt{n\Delta_n^2}\leq 2M\nu_0\big(I\setminus [0,\varepsilon_m]\big)\sqrt{n\Delta_n^2}.\end{aligned}$$ Hence, we get: $$\label{eq:ch4bernoulli} \Delta({\ensuremath {\mathscr{Q}}}_{n}^{\textnormal{res},\nu_0},{\ensuremath {\mathscr{Q}}}_n^{\epsilon})=O\bigg(\nu_0\big(I\setminus [0,\varepsilon_m]\big)\sqrt{n\Delta_n^2}\bigg).$$ Here the O depends only on $M$. - Step 2: Let us introduce the following random variables: $$Z_1=\sum_{j=1}^n{\ensuremath {\mathbb{I}}}_{\{0\}}(\epsilon_jY_j); \quad Z_i=\sum_{j=1}^n{\ensuremath {\mathbb{I}}}_{J_i}(\epsilon_jY_j),\ i=2,\dots,m.$$ Observe that the law of the vector $(Z_1,\dots,Z_m)$ is multinomial $\mathcal M(n;\gamma_1,\dots,\gamma_m)$ where $$\gamma_1=1-\iota_m \Delta_n e^{-\iota_m \Delta_n},\quad \gamma_i=\Delta_n e^{-\iota_m \Delta_n}\nu(J_i),\quad i=2,\dots,m.$$ Let us denote by $\mathcal M_n$ the statistical model associated with the observation of $(Z_1,\dots,Z_m)$. Clearly $\delta({\ensuremath {\mathscr{Q}}}_n^{\epsilon},\mathcal M_n)=0$. Indeed, $\mathcal M_n$ is the image experiment by the random variable $S:I^n\to\{1,\dots,n\}^{m}$ defined as $$S(x_1,\dots,x_n)=\Big(\#\{j: x_j=0\}; \#\big\{j: x_j\in J_2\big\};\dots;\#\big\{j: x_j\in J_m\big\}\Big),$$ where $\# A$ denotes the cardinal of the set $A$. We shall now prove that $\delta(\mathcal M_n,{\ensuremath {\mathscr{Q}}}_n^{\epsilon}) \leq \sup_{f\in{\ensuremath {\mathscr{F}}}}\sqrt{n\Delta_n H^2(f,\hat f_m)}$. We start by defining a discrete random variable $X^*$ concentrated at the points $0$, $x_i^*$, $i=2,\dots,m$: $${\ensuremath {\mathbb{P}}}(X^*=y)=\begin{cases} \gamma_i &\mbox{ if } y=x_i^*,\quad i=1,\dots,m,\\ 0 &\mbox{ otherwise}, \end{cases}$$ with the convention $x_1^*=0$. It is easy to see that $\mathcal M_n$ is equivalent to the statistical model associated with $n$ independent copies of $X^*$. Let us introduce the Markov kernel $$K(x_i^*, A) = \begin{cases} {\ensuremath {\mathbb{I}}}_A(0) & \text{if } i = 1,\\ \int_A V_i(x) \nu_0(dx) & \text{otherwise.} \end{cases}$$ Denote by $P^*$ the law of the random variable $X^*$ and by $Q_i^{\epsilon,\hat f}$ the law of a random variable $\epsilon_i \hat Y_i$ where $\epsilon_i$ is Bernoulli independent of $\hat Y_i$, with mean $\iota_m\Delta_n e^{-\iota_m\Delta_n}$ and $\hat Y_i$ has a density $\frac{\hat f_m g}{\iota_m}{\ensuremath {\mathbb{I}}}_{I\setminus[0,\varepsilon_m]}$ with respect to Lebesgue. The same computations as in Lemma \[lemma:ch4kernel\] prove that $KP^*=Q_i^{\epsilon,\hat f}$. Hence, thanks to Remark \[ch4independentkernels\], we get the equivalence between $\mathcal M_n$ and the statistical model associated with the observations of $n$ independent copies of $\epsilon_i \hat Y_i$. In order to bound $\delta(\mathcal M_n,{\ensuremath {\mathscr{Q}}}_n^{\epsilon})$ it is enough to bound the total variation distance between the probabilities $\bigotimes_{i=1}^n Q_i^{\epsilon,f}$ and $\bigotimes_{i=1}^n Q_i^{\epsilon,\hat f}$. Alternatively, we can bound the Hellinger distance between each of the $Q_i^{\epsilon,f}$ and $Q_i^{\epsilon,\hat f}$, thanks to Facts \[ch4h\] and \[ch4hp\], which is: $$\begin{aligned} \bigg\|\bigotimes_{i=1}^nQ_i^{\epsilon,f} -\bigotimes_{i=1}^nQ_i^{\epsilon,\hat f}\bigg\|_{TV} &\leq \sqrt{\sum_{i=1}^n H^2\big(Q_i^{\epsilon,f}, Q_i^{\epsilon,\hat f}\big)}\\ &= \sqrt{\sum_{i=1}^n \frac{1-\gamma_1}{\iota} H^2(f, \hat f_m)} \leq \sqrt{n\Delta_n H^2(f, \hat f_m)}.\end{aligned}$$ It follows that $$\delta(\mathcal M_n,{\ensuremath {\mathscr{Q}}}_n^{\epsilon})\leq \sqrt{n\Delta_n} \sup_{f \in {\ensuremath {\mathscr{F}}}}H(f,\hat f_m).$$ - Step 3: Let us denote by $\mathcal N_m^*$ the statistical model associated with the observation of $m$ independent Gaussian variables ${\ensuremath {\mathscr{Nn}}}(n\gamma_i,n\gamma_i)$, $i=1,\dots,m$. Very similar computations to those in [@cmultinomial] yield $$\Delta(\mathcal M_n,\mathcal N_m^*)=O\Big(\frac{m \ln m}{\sqrt{n}}\Big).$$ In order to prove the asymptotic equivalence between $\mathcal M_n$ and $\mathcal N_m$ defined as in we need to introduce some auxiliary statistical models. Let us denote by $\mathcal A_m$ the experiment obtained from $\mathcal{N}_m^*$ by disregarding the first component and by $\mathcal V_m$ the statistical model associated with the multivariate normal distribution with the same means and covariances as a multinomial distribution $\mathcal M(n,\gamma_1,\dots,\gamma_m)$. Furthermore, let us denote by $\mathcal N_m^{\#}$ the experiment associated with the observation of $m-1$ independent Gaussian variables ${\ensuremath {\mathscr{Nn}}}(\sqrt{n\gamma_i},\frac{1}{4})$, $i=2,\dots,m$. Clearly $\Delta(\mathcal V_m,\mathcal A_m)=0$ for all $m$: In one direction one only has to consider the projection disregarding the first component; in the other direction, it is enough to remark that $\mathcal V_m$ is the image experiment of $\mathcal A_m$ by the random variable $S:(x_2,\dots,x_m)\to (n(1-\frac{\sum_{i=2}^m x_i}{n}),x_2,\dots,x_m)$. Moreover, using two results contained in [@cmultinomial], see Sections 7.1 and 7.2, one has that $$\Delta(\mathcal A_m,\mathcal N_m^*)=O\bigg(\sqrt{\frac{m}{n}}\bigg),\quad \Delta(\mathcal A_m,\mathcal N_m^{\#})=O\bigg(\frac{m}{\sqrt n}\bigg).$$ Finally, using Facts \[ch4h\] and \[fact:ch4gaussiane\] we can write $$\begin{aligned} \Delta(\mathcal N_m^{\#},\mathcal N_m)&\leq \sqrt{2\sum_{i=2}^m \Big(\sqrt{T_n\nu(J_i)}-\sqrt{T_n\nu(J_i)\exp(-\iota_m\Delta_n)}\Big)^2}\\ &\leq\sqrt{2T_n\Delta_n^2\iota_m^3}\leq \sqrt{2n\Delta_n^3M^3\big(\nu_0\big(I\setminus [0,\varepsilon_m]\big)\big)^3}. \end{aligned}$$ To sum up, $\Delta(\mathcal M_n,\mathcal N_m)=O\Big(\frac{m \ln m}{\sqrt{n}}+\sqrt{n\Delta_n^3\big(\nu_0\big(I\setminus [0,\varepsilon_m]\big)\big)^3}\Big)$, with the $O$ depending only on $\kappa$ and $M$. - Step 4: An application of Lemmas \[lemma:ch4wn\] and \[lemma:ch4limitewn\] yield $$\Delta(\mathcal N_m,{\ensuremath {\mathscr{W}}}_n^{\nu_0}) \leq 2\sqrt T_n \sup_{f\in{\ensuremath {\mathscr{F}}}} \big(A_m(f)+B_m(f)+C_m(f)\big).$$ Proofs of the examples ====================== The purpose of this section is to give detailed proofs of Examples \[ex:ch4esempi\] and Examples \[ex:ch4CPP\]–\[ex3\]. As in Section \[sec:ch4proofs\] we suppose $I\subseteq {\ensuremath {\mathbb{R}}}_+$. We start by giving some bounds for the quantities $A_m(f)$, $B_m(f)$ and $L_2(f, \hat f_m)$, the $L_2$-distance between the restriction of $f$ and $\hat f_m$ on $I\setminus[0,\varepsilon_m].$ Bounds for $A_m(f)$, $B_m(f)$, $L_2(f, \hat{f}_m)$ when $\hat f_m$ is piecewise linear. --------------------------------------------------------------------------------------- In this section we suppose $f$ to be in ${\ensuremath {\mathscr{F}}}_{(\gamma, K, \kappa, M)}^I$ defined as in . We are going to assume that the $V_j$ are given by triangular/trapezoidal functions as in . In particular, in this case $\hat f_m$ is piecewise linear. \[lemma:ch4hellinger\] Let $0<\kappa < M$ be two constants and let $f_i$, $i=1,2$ be functions defined on an interval $J$ and such that $\kappa \leq f_i\leq M$, $i=1,2$. Then, for any measure $\nu_0$, we have: $$\begin{aligned} \frac{1}{4 M} \int_J \big(f_1(x)-f_2(x)\big)^2 \nu_0(dx)&\leq\int_J \big(\sqrt{f_1(x)} - \sqrt{f_2(x)}\big)^2\nu_0(dx)\\ &\leq \frac{1}{4 \kappa} \int_J \big(f_1(x)-f_2(x)\big)^2\nu_0(dx). \end{aligned}$$ This simply comes from the following inequalities: $$\begin{aligned} \frac{1}{2\sqrt M} (f_1(x)-f_2(x)) &\leq \frac{f_1(x)-f_2(x)}{\sqrt{f_1(x)}+\sqrt{f_2(x)}} = \sqrt{f_1(x)} - \sqrt{f_2(x)}\\ &\leq \frac{1}{2 \sqrt{\kappa}} (f_1(x)-f_2(x)). \end{aligned}$$ Recall that $x_i^*$ is chosen so that $\int_{J_i} (x-x_i^*) \nu_0(dx) = 0$. Consider the following Taylor expansions for $x \in J_i$: $$f(x) = f(x_i^*) + f'(x_i^*) (x-x_i^*) + R_i(x); \quad \hat{f}_m(x) = \hat{f}_m(x_i^*) + \hat{f}_m'(x_i^*) (x-x_i^*),$$ where $\hat{f}_m(x_i^*) = \frac{\nu(J_i)}{\nu_0(J_i)}$ and $\hat{f}_m'(x_i^*)$ is the left or right derivative in $x_i^*$ depending whether $x < x_i^*$ or $x > x_i^*$ (as $\hat f_m$ is piecewise linear, no rest is involved in its Taylor expansion). \[lemma:ch4bounds\] The following estimates hold: $$\begin{aligned} |R_i(x)| &\leq K |\xi_i - x_i^*|^\gamma |x-x_i^*|; \\ \big|f(x_i^*) - \hat{f}_m(x_i^*)\big| &\leq \|R_i\|_{L_\infty(\nu_0)} \text{ for } i = 2, \dots, m-1; \label{eqn:bounds}\\ \big|f(x)-\hat{f}_m(x)\big| &\leq \begin{cases} 2 \|R_i\|_{L_\infty(\nu_0)} + K |x_i^*-\eta_i|^\gamma |x-x_i^*| & \text{ if } x \in J_i, \ i = 3, \dots, m-1;\\ C |x-\tau_i| & \text { if } x \in J_i, \ i \in \{2, m\}. \end{cases} \end{aligned}$$ for some constant $C$ and points $\xi_i \in J_i$, $\eta_i\in J_{i-1} \cup J_i\cup J_{i+1}$, $\tau_2 \in J_2 \cup J_3$ and $\tau_m \in J_{m-1} \cup J_m$. By definition of $R_i$, we have $$|R_i(x)| = \Big| \big(f'(\xi_i) - f'(x_i^*)\big)(x-x_i^*) \Big| \leq K |\xi_i - x_i^*|^\gamma |x-x_i^*|,$$ for some point $\xi_i \in J_i$. For the second inequality, $$\begin{aligned} |f(x_i^*)-\hat{f}_m(x_i^*)| &= \frac{1}{\nu_0(J_i)} \Big| \int_{J_i} (f(x_i^*)-f(x)) \nu_0(dx)\Big|\\ &= \frac{1}{\nu_0(J_i)} \bigg|\int_{J_i} R_i(x) \nu_0(dx)\bigg| \leq \|R_i\|_{L_\infty(\nu_0)}, \end{aligned}$$ where in the first inequality we have used the defining property of $x_i^*$. For the third inequality, let us start by proving that for all $2 < i < m-1$, $\hat{f}_m'(x_i^*) = f'(\chi_i)$ for some $\chi_i \in J_i\cup J_{i+1}$ (here, we are considering right derivatives; for left ones, this would be $J_{i-1} \cup J_i$). To see that, take $x\in J_i\cap [x_i^*,x_{i+1}^*]$ and introduce the function $h(x):=f(x)-l(x)$ where $$l(x)=\frac{x-x_i^*}{x_{i+1}^*-x_i^*}\big(\hat f_m(x_{i+1}^*)-\hat f_m(x_i^*)\big)+\hat f_m(x_i^*).$$ Then, using the fact that $\int_{J_i}(x-x_i^*)\nu_0(dx)=0$ joint with $\int_{J_{i+1}}(x-x_{i+1}^*)\nu_0(dx)=(x_{j+1}^*-x_j^*)\mu_m$, we get $$\int_{J_i}h(x)\nu_0(dx)=0=\int_{J_{i+1}}h(x)\nu_0(dx).$$ In particular, by means of the mean theorem, one can conclude that there exist two points $p_i\in J_i$ and $p_{i+1}\in J_{i+1}$ such that $$h(p_i)=\frac{\int_{J_i}h(x)\nu_0(dx)}{\nu_0(J_i)}=\frac{\int_{J_{i+1}}h(x)\nu_0(dx)}{\nu_0(J_{i+1})}=h(p_{i+1}).$$ As a consequence, we can deduce that there exists $\chi_i\in[p_i,p_{i+1}]\subseteq J_i\cup J_{i+1}$ such that $h'(\chi_i)=0$, hence $f'(\chi_i)=l'(\chi_i)=\hat f_m'(x_i^*)$. When $2 < i < m-1$, the two Taylor expansions joint with the fact that $\hat{f}_m'(x_i^*) = f'(\chi_i)$ for some $\chi_i \in J_i\cup J_{i+1}$, give $$\begin{aligned} |f(x) - \hat{f}_m (x)| &\leq |f(x_i^*) - \hat{f}_m(x_i^*)| + |R_i(x)| + K |x_i^* - \chi_i|^\gamma |x-x_i^*|\\ & \leq 2 \|R_i\|_{L_\infty(\nu_0)} + K |x_i^* - \chi_i|^\gamma |x-x_i^*| \end{aligned}$$ whenever $x \in J_i$ and $x > x_i^*$ (the case $x < x_i^*$ is handled similarly using the left derivative of $\hat f_m$ and $\xi_i \in J_{i-1} \cup J_i$). For the remaining cases, consider for example $i = 2$. Then $\hat{f}_m(x)$ is bounded by the minimum and the maximum of $f$ on $J_2 \cup J_3$, hence $\hat{f}_m(x) = f(\tau)$ for some $\tau \in J_2 \cup J_3$. Since $f'$ is bounded by $C = 2M +K$, one has $|f(x) - \hat{f}_m(x)| \leq C|x-\tau|$. \[lemma:ch4abc\] With the same notations as in Lemma \[lemma:ch4bounds\], the estimates for $A_m^2(f)$, $B_m^2(f)$ and $L_2(f, \hat{f}_m)^2$ are as follows: $$\begin{aligned} L_2(f, \hat{f}_m)^2&\leq \frac{1}{4\kappa} \bigg( \sum_{i=3}^m \int_{J_i} \Big(2 \|R_i\|_{L_\infty(\nu_0)} + K |x_i^*-\eta_i|^\gamma|x-x_i^*|\Big)^2 \nu_0(dx) \\ &\phantom{=}\ + C^2 \Big(\int_{J_2}|x-\tau_2|^2\nu_0(dx) + \int_{J_m}|x-\tau_m|^2\nu_0(dx)\Big).\\ A_m^2(f) &= L_2\big(\sqrt{f}, \widehat{\sqrt{f}}_m\big)^2 = O\Big(L_2(f, \hat{f}_m)^2\Big)\\ B_m^2(f) &= O\bigg( \sum_{i=2}^{m} \frac{1}{\sqrt{\kappa}} \nu_0(J_i) (2 \sqrt{M} + 1)^2 \|R_i\|_{L_\infty(\nu_0)}^2\bigg). \end{aligned}$$ The $L_2$-bound is now a straightforward application of Lemmas \[lemma:ch4hellinger\] and \[lemma:ch4bounds\]. The one on $A_m(f)$ follows, since if $f \in {\ensuremath {\mathscr{F}}}_{(\gamma, K, \kappa, M)}^I$ then $\sqrt{f} \in {\ensuremath {\mathscr{F}}}_{(\gamma, \frac{K}{\sqrt{\kappa}}, \sqrt{\kappa}, \sqrt{M})}^I$. In order to bound $B_m^2(f)$ write it as: $$B_m^2(f)=\sum_{j=1}^m \nu_0(J_j)\bigg(\frac{\int_{J_j}\sqrt{f(y)}\nu_0(dy)}{\nu_0(J_j)}-\sqrt{\frac{\nu(J_j)}{\nu_0(J_j)}}\bigg)^2=:\sum_{j=1}^m \nu_0(J_j)E_j^2.$$ By the triangular inequality, let us bound $E_j$ by $F_j+G_j$ where: $$F_j=\bigg|\sqrt{\frac{\nu(J_j)}{\nu_0(J_j)}}-\sqrt{f(x_j^*)}\bigg| \quad \textnormal{ and }\quad G_j=\bigg|\sqrt{f(x_j^*)}-\frac{\int_{J_j}\sqrt{f(y)}\nu_0(dy)}{\nu_0(J_j)}\bigg|.$$ Using the same trick as in the proof of Lemma \[lemma:ch4hellinger\], we can bound: $$\begin{aligned} F_j \leq 2 \sqrt{M} \bigg|\frac{\int_{J_j} \big(f(x)-f(x_i^*)\big)\nu_0(dx)}{\nu_0(J_j)}\bigg| \leq 2 \sqrt{M} \|R_j\|_{L_\infty(\nu_0)}. \end{aligned}$$ On the other hand, $$\begin{aligned} G_j&=\frac{1}{\nu_0(J_j)}\bigg|\int_{J_j}\big(\sqrt{f(x_j^*)}-\sqrt{f(y)}\big)\nu_0(dy)\bigg|\\ &=\frac{1}{\nu_0(J_j)}\bigg|\int_{J_j}\bigg(\frac{f'(x_j^*)}{2\sqrt{f(x_j^*)}}(x-x_j^*)+\tilde R_j(y)\bigg)\nu_0(dy)\bigg| \leq \|\tilde R_j\|_{L_\infty(\nu_0)}, \end{aligned}$$ which has the same magnitude as $\frac{1}{\kappa}\|R_j\|_{L_\infty(\nu_0)}$. Observe that when $\nu_0$ is finite, there is no need for a special definition of $\hat{f}_m$ near $0$, and all the estimates in Lemma \[lemma:ch4bounds\] hold true replacing every occurrence of $i = 2$ by $i = 1$. \[rmk:nonlinear\] The same computations as in Lemmas \[lemma:ch4bounds\] and \[lemma:ch4abc\] can be adapted to the general case where the $V_j$’s (and hence $\hat f_m$) are not piecewise linear. In the general case, the Taylor expansion of $\hat f_m$ in $x_i^*$ involves a rest as well, say $\hat R_i$, and one needs to bound this, as well. Proofs of Examples \[ex:ch4esempi\] {#subsec:esempi} ----------------------------------- In the following, we collect the details of the proofs of Examples \[ex:ch4esempi\]. **1. The finite case:** $\nu_0\equiv {\ensuremath{\textnormal{Leb}}}([0,1])$. Remark that in the case where $\nu_0$ if finite there are no convergence problems near zero and so we can consider the easier approximation of $f$: $$\hat f_m(x):= \begin{cases} m\theta_1 & \textnormal{if } x\in \big[0,x_1^*\big],\\ m^2\big[\theta_{j+1}(x-x_j^*)+\theta_j(x_{j+1}^*-x)\big] & \textnormal{if } x\in (x_j^*,x_{j+1}^*] \quad j = 1,\dots,m-1,\\ m\theta_m & \textnormal{if } x\in (x_m^*,1] \end{cases}$$ where $$x_j^*=\frac{2j-1}{2m},\quad J_j=\Big(\frac{j-1}{m},\frac{j}{m}\Big],\quad \theta_j=\int_{J_j}f(x)dx, \quad j=1,\dots,m.$$ In this case we take $\varepsilon_m = 0$ and Conditions $(C2)$ and $(C2')$ coincide: $$\lim_{n\to\infty}n\Delta_n\sup_{f\in {\ensuremath {\mathscr{F}}}}\Big(A_m^2(f)+B_m^2(f)\Big) = 0.$$ Applying Lemma \[lemma:ch4abc\], we get $$\sup_{f\in {\ensuremath {\mathscr{F}}}} \Big(L_2(f,\hat f_m)+ A_m(f)+ B_m(f)\Big)= O\big(m^{-\frac{3}{2}}+m^{-1-\gamma}\big);$$ (actually, each of the three terms on the left hand side has the same rate of convergence). **2. The finite variation case:** $\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}}(x)=x^{-1}{\ensuremath {\mathbb{I}}}_{[0,1]}(x).$ To prove that the standard choice of $V_j$ described at the beginning of Examples \[ex:ch4esempi\] leads to $\displaystyle{\int_{\varepsilon_m}^1 V_j(x)\frac{dx}{x}=1}$, it is enough to prove that this integral is independent of $j$, since in general $\displaystyle{\int_{\varepsilon_m}^1 \sum_{j=2}^m V_j(x)\frac{dx}{x}=m-1}.$ To that aim observe that, for $j=3,\dots,m-1$, $$\mu_m\int_{\varepsilon_m}^1 V_j(x)\nu_0(dx)=\int_{x_{j-1}^*}^{x_j^*}\frac{x-x_{j-1}^*}{x_j^*-x_{j-1}^*}\frac{dx}{x}+\int_{x_j^*}^{x_{j+1}^*}\frac{x_{j+1}^*-x}{x_{j+1}^*-x_j^*}\frac{dx}{x}.$$ Let us show that the first addendum does not depend on $j$. We have $$\int_{x_{j-1}^*}^{x_j^*}\frac{dx}{x_j^*-x_{j-1}^*}=1\quad \textnormal{and}\quad -\frac{x_{j-1}^*}{x_j^*-x_{j-1}^*}\int_{x_{j-1}^*}^{x_j^*}\frac{dx}{x}=\frac{x_{j-1}^*}{x_j^*-x_{j-1}^*}\ln\Big(\frac{x_{j-1}^*}{x_j^*}\Big).$$ Since $x_j^*=\frac{v_j-v_{j-1}}{\mu_m}$ and $v_j=\varepsilon_m^{\frac{m-j}{m-1}}$, the quantities $\frac{x_j^*}{x_{j-1}^*}$ and, hence, $\frac{x_{j-1}^*}{x_j^*-x_{j-1}^*}$ do not depend on $j$. The second addendum and the trapezoidal functions $V_2$ and $V_m$ are handled similarly. Thus, $\hat f_m$ can be chosen of the form $$\hat f_m(x):= \begin{cases} \quad 1 & \textnormal{if } x\in \big[0,\varepsilon_m\big],\\ \frac{\nu(J_2)}{\mu_m} & \textnormal{if } x\in \big(\varepsilon_m, x_2^*\big],\\ \frac{1}{x_{j+1}^*-x_j^*}\bigg[\frac{\nu(J_{j+1})}{\mu_m}(x-x_j^*)+\frac{\nu(J_{j})}{\mu_m}(x_{j+1}^*-x)\bigg] & \textnormal{if } x\in (x_j^*,x_{j+1}^*] \quad j = 2,\dots,m-1,\\ \frac{\nu(J_m)}{\mu_m} & \textnormal{if } x\in (x_m^*,1]. \end{cases}$$ A straightforward application of Lemmas \[lemma:ch4bounds\] and \[lemma:ch4abc\] gives $$\sqrt{\int_{\varepsilon_m}^1\Big(f(x)-\hat f_m(x)\Big)^2 \nu_0(dx)} +A_m(f)+B_m(f)=O\bigg(\bigg(\frac{\ln m}{m}\bigg)^{\gamma+1} \sqrt{\ln (\varepsilon_m^{-1})}\bigg),$$ as announced. **3. The infinite variation, non-compactly supported case:** $\frac{d\nu_0}{d{\ensuremath{\textnormal{Leb}}}}(x)=x^{-2}{\ensuremath {\mathbb{I}}}_{{\ensuremath {\mathbb{R}}}_+}(x)$. Recall that we want to prove that $$L_2(f,\hat f_m)^2+A_m^2(f)+B_m^2(f)=O\bigg(\frac{H(m)^{3+4\gamma}}{(\varepsilon_m m)^{2\gamma}}+\sup_{x\geq H(m)}\frac{f(x)^2}{H(m)}\bigg),$$ for any given sequence $H(m)$ going to infinity as $m\to\infty$. Let us start by addressing the problem that the triangular/trapezoidal choice for $V_j$ is not doable. Introduce the following notation: $V_j = {\ensuremath {\accentset{\triangle}{V}}}_j + A_j$, $j = 2, \dots, m$, where the ${\ensuremath {\accentset{\triangle}{V}}}_j$’s are triangular/trapezoidal function similar to those in . The difference is that here, since $x_m^*$ is not defined, ${\ensuremath {\accentset{\triangle}{V}}}_{m-1}$ is a trapezoid, linear between $x_{m-2}^*$ and $x_{m-1}^*$ and constantly equal to $\frac{1}{\mu_m}$ on $[x_{m-1}^*,v_{m-1}]$ and ${\ensuremath {\accentset{\triangle}{V}}}_m$ is supported on $[v_{m-1},\infty)$, where it is constantly equal to $\frac{1}{\mu_m}$. Each $A_j$ is chosen so that: 1. It is supported on $[x_{j-1}^*, x_{j+1}^*]$ (unless $j = 2$, $j = m-1$ or $j = m$; in the first case the support is $[x_2^*, x_3^*]$, in the second one it is $[x_{m-2}^*, x_{m-1}^*]$, and $A_m \equiv 0$); 2. ${A_j}$ coincides with $-A_{j-1}$ on $[x_{j-1}^*, x_j^*]$, $j = 3, \dots, m-1$ (so that $\sum V_j \equiv \frac{1}{\mu_n}$) and its first derivative is bounded (in absolute value) by $\frac{1}{\mu_m(x_j^* - x_{j-1}^*)}$ (so that $V_j$ is non-negative and bounded by $\frac{1}{\mu_n}$); 3. $A_j$ vanishes, along with its first derivatives, on $x_{j-1}^*$, $x_j^*$ and $x_{j+1}^*$. We claim that these conditions are sufficient to assure that $\hat f_m$ converges to $f$ quickly enough. First of all, by Remark \[rmk:nonlinear\], we observe that, to have a good bound on $L_2(f, \hat f_m)$, the crucial property of $\hat f_m$ is that its first right (resp. left) derivative has to be equal to $\frac{1}{\mu_m(x_{j+1}^*-x_j^*)}$ (resp. $\frac{1}{\mu_m(x_{j}^*-x_{j-1}^*)}$) and its second derivative has to be small enough (for example, so that the rest $\hat R_j$ is as small as the rest $R_j$ of $f$ already appearing in Lemma \[lemma:ch4bounds\]). The (say) left derivatives in $x_j^*$ of $\hat f_m$ are given by $$\hat f_m'(x_j^*) = \big({\ensuremath {\accentset{\triangle}{V}}}_j'(x_j^*) + A_j'(x_j^*)\big) \big(\nu(J_j)-\nu(J_{j-1})\big); \quad \hat f_m''(x_j^*) = A_j''(x_j^*)\big(\nu(J_j)-\nu(J_{j-1})\big).$$ Then, in order to bound $|\hat f_m''(x_j^*)|$ it is enough to bound $|A_j''(x_j^*)|$ because: $$\big|\hat f_m''(x_j^*)\big| \leq |A_j''(x_j^*)| \Big|\int_{J_j} f(x) \frac{dx}{x^2} - \int_{J_{j-1}} f(x) \frac{dx}{x^2}\Big| \leq |A_j''(x_j^*)| \displaystyle{\sup_{x\in I}}|f'(x)|(\ell_{j}+\ell_{j-1}) \mu_m,$$ where $\ell_{j}$ is the Lebesgue measure of $J_{j}$. We are thus left to show that we can choose the $A_j$’s satisfying points 1-3, with a small enough second derivative, and such that $\int_I V_j(x) \frac{dx}{x^2} = 1$. To make computations easier, we will make the following explicit choice: $$A_j(x) = b_j (x-x_j^*)^2 (x-x_{j-1}^*)^2 \quad \forall x \in [x_{j-1}^*, x_j^*),$$ for some $b_j$ depending only on $j$ and $m$ (the definitions on $[x_j^*, x_{j+1}^*)$ are uniquely determined by the condition $A_j + A_{j+1} \equiv 0$ there). Define $j_{\max}$ as the index such that $H(m) \in J_{j_{\max}}$; it is straightforward to check that $$j_{\max} \sim m- \frac{\varepsilon_m(m-1)}{H(m)}; \quad x_{m-k}^* = \varepsilon_m(m-1) \log \Big(1+\frac{1}{k}\Big), \quad k = 1, \dots, m-2.$$ One may compute the following Taylor expansions: $$\begin{aligned} \int_{x_{m-k-1}^*}^{x_{m-k}^*} {\ensuremath {\accentset{\triangle}{V}}}_{m-k}(x) \nu_0(dx) &= \frac{1}{2} - \frac{1}{6k} + \frac{5}{24k^2} + O\Big(\frac{1}{k^3}\Big);\\ \int_{x_{m-k}^*}^{x_{m-k+1}^*} {\ensuremath {\accentset{\triangle}{V}}}_{m-k}(x) \nu_0(dx) &= \frac{1}{2} + \frac{1}{6k} + \frac{1}{24k^2} + O\Big(\frac{1}{k^3}\Big). \end{aligned}$$ In particular, for $m \gg 0$ and $m-k \leq j_{\max}$, so that also $k \gg 0$, all the integrals $\int_{x_{j-1}^*}^{x_{j+1}^*} {\ensuremath {\accentset{\triangle}{V}}}_j(x) \nu_0(dx)$ are bigger than 1 (it is immediate to see that the same is true for ${\ensuremath {\accentset{\triangle}{V}}}_2$, as well). From now on we will fix a $k \geq \frac{\varepsilon_m m}{H(m)}$ and let $j = m-k$. Summing together the conditions $\int_I V_i(x)\nu_0(dx)=1$ $\forall i>j$ and noticing that the function $\sum_{i = j}^m V_i$ is constantly equal to $\frac{1}{\mu_m}$ on $[x_j^*,\infty)$ we have: $$\begin{aligned} \int_{x_{j-1}^*}^{x_j^*} A_j(x) \nu_0(dx) &= m-j+1 - \frac{1}{\mu_m} \nu_0([x_j^*, \infty)) - \int_{x_{j-1}^*}^{x_j^*} {\ensuremath {\accentset{\triangle}{V}}}_j(x) \nu_0(dx)\\ &= k+1- \frac{1}{\log(1+\frac{1}{k})} - \frac{1}{2} + \frac{1}{6k} + O\Big(\frac{1}{k^2}\Big) = \frac{1}{4k} + O\Big(\frac{1}{k^2}\Big) \end{aligned}$$ Our choice of $A_j$ allows us to compute this integral explicitly: $$\int_{x_{j-1}^*}^{x_j^*} b_j (x-x_{j-1}^*)^2(x-x_j^*)^2 \frac{dx}{x^2} = b_j \big(\varepsilon_m (m-1)\big)^3 \Big(\frac{2}{3} \frac{1}{k^4} + O\Big(\frac{1}{k^5}\Big)\Big).$$ In particular one gets that asymptotically $$b_j \sim \frac{1}{(\varepsilon_m(m-1))^3} \frac{3}{2} k^4 \frac{1}{4k} \sim \bigg(\frac{k}{\varepsilon_m m}\bigg)^3.$$ This immediately allows us to bound the first order derivative of $A_j$ as asked in point 2: Indeed, it is bounded above by $2 b_j \ell_{j-1}^3$ where $\ell_{j-1}$ is again the length of $J_{j-1}$, namely $\ell_j = \frac{\varepsilon_m(m-1)}{k(k+1)} \sim \frac{\varepsilon_m m}{k^2}$. It follows that for $m$ big enough: $$\displaystyle{\sup_{x\in I}|A_j'(x)|} \leq \frac{1}{k^3} \ll \frac{1}{\mu_m(x_j^*-x_{j-1}^*)} \sim \bigg(\frac{k}{\varepsilon_m m}\bigg)^2.$$ The second order derivative of $A_j(x)$ can be easily computed to be bounded by $4 b_j \ell_j^2$. Also remark that the conditions that $|f|$ is bounded by $M$ and that $f'$ is Hölder, say $|f'(x) - f'(y)| \leq K |x-y|^\gamma$, together give a uniform $L_\infty$ bound of $|f'|$ by $2M + K$. Summing up, we obtain: $$|\hat f_m''(x_j^*)| \lesssim b_j \ell_m^3 \mu_m \sim \frac{1}{k^3\varepsilon_m m}$$ (here and in the following we use the symbol $\lesssim$ to stress that we work up to constants and to higher order terms). The leading term of the rest $\hat R_j$ of the Taylor expansion of $\hat f_m$ near $x_j^*$ is $$\hat f_m''(x_j^*) |x-x_j^*|^2 \sim |f_m''(x_j^*)| \ell_j^2 \sim \frac{\varepsilon_m m}{k^7}.$$ Using Lemmas \[lemma:ch4bounds\] and \[lemma:ch4abc\] (taking into consideration Remark \[rmk:nonlinear\]) we obtain $$\begin{aligned} \int_{\varepsilon_m}^{\infty} |f(x) - \hat f_m(x)|^2 \nu_0(dx) &\lesssim \sum_{j=2}^{j_{\max}} \int_{J_j} |f(x) - \hat f_m(x)|^2 \nu_0(dx) + \int_{H(m)}^\infty |f(x)-\hat f_m(x)|^2 \nu_0(dx) \nonumber \\ &\lesssim \sum_{k=\frac{\varepsilon_m m}{H(m)}}^{m}\mu_m \bigg( \frac{(\varepsilon_m m)^{2+2\gamma}}{k^{4+4\gamma}} + \frac{(\varepsilon_m m)^2}{k^{14}}\bigg) + \frac{1}{H(m)}\sup_{x\geq H(m)}f(x)^2 \label{eq:xquadro} \\ &\lesssim \bigg(\frac{H(m)^{3+4\gamma}}{(\varepsilon_m m)^{2+2\gamma}} + \frac{H(m)^{13}}{(\varepsilon_m m)^{10}}\bigg) + \frac{1}{H(m)}. \nonumber \end{aligned}$$ It is easy to see that, since $0 < \gamma \leq 1$, as soon as the first term converges, it does so more slowly than the second one. Thus, an optimal choice for $H(m)$ is given by $\sqrt{\varepsilon_m m}$, that gives a rate of convergence: $$L_2(f,\hat f_m)^2 \lesssim \frac{1}{\sqrt{\varepsilon_m m}}.$$ This directly gives a bound on $H(f, \hat f_m)$. Also, the bound on the term $A_m(f)$, which is $L_2(\sqrt f,\widehat{\sqrt{f}}_m)^2$, follows as well, since $f \in {\ensuremath {\mathscr{F}}}_{(\gamma,K,\kappa,M)}^I$ implies $\sqrt{f} \in {\ensuremath {\mathscr{F}}}_{(\gamma, \frac{K}{\sqrt\kappa}, \sqrt \kappa, \sqrt M)}^I$. Finally, the term $B_m^2(f)$ contributes with the same rates as those in : Using Lemma \[lemma:ch4abc\], $$\begin{aligned} B_m^2(f) &\lesssim \sum_{j=2}^{\lceil m-\frac{\varepsilon_m(m-1)}{H(m)} \rceil} \nu_0(J_j) \|R_j\|_{L_\infty}^2 + \nu_0([H(m), \infty))\\ &\lesssim \mu_m \sum_{k=\frac{\varepsilon_m (m-1)}{H(m)}}^m \Big(\frac{\varepsilon_m m}{k^2}\Big)^{2+2\gamma} + \frac{1}{H(m)}\\ &\lesssim \frac{H(m)^{3+4\gamma}}{(\varepsilon_m m)^{2+2\gamma}} + \frac{1}{H(m)}. \end{aligned}$$ Proof of Example \[ex:ch4CPP\] {#subsec:ch4ex1} ------------------------------ In this case, since $\varepsilon_m = 0$, the proofs of Theorems \[ch4teo1\] and \[ch4teo2\] simplify and give better estimates near zero, namely: $$\begin{aligned} \Delta({\ensuremath {\mathscr{P}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}}, {\ensuremath {\mathscr{W}}}_n^{\nu_0}) &\leq C_1 \bigg(\sqrt{T_n}\sup_{f\in {\ensuremath {\mathscr{F}}}}\Big(A_m(f)+ B_m(f)+L_2(f,\hat f_m)\Big)+\sqrt{\frac{m^2}{T_n}}\bigg)\nonumber \\ \Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}}, {\ensuremath {\mathscr{W}}}_n^{\nu_0}) &\leq C_2\bigg(\sqrt{n\Delta_n^2}+\frac{m\ln m}{\sqrt{n}}+\sqrt{T_n}\sup_{f\in{\ensuremath {\mathscr{F}}}}\Big( A_m(f)+ B_m(f)+H\big(f,\hat f_m\big)\Big) \bigg) \label{eq:CPP},\end{aligned}$$ where $C_1$, $C_2$ depend only on $\kappa,M$ and $$\begin{aligned} &A_m(f)=\sqrt{\int_0^1\Big(\widehat{\sqrt f}_m(y)-\sqrt{f(y)}\Big)^2dy},\quad B_m(f)=\sum_{j=1}^m\bigg(\sqrt m\int_{J_j}\sqrt{f(y)}dy-\sqrt{\theta_j}\bigg)^2.\end{aligned}$$ As a consequence we get: $$\begin{aligned} \Delta({\ensuremath {\mathscr{P}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}},{\ensuremath {\mathscr{W}}}_n^{\nu_0})&\leq O\bigg(\sqrt{T_n}(m^{-\frac{3}{2}}+m^{-1-\gamma})+\sqrt{m^2T_n^{-1}}\bigg).\end{aligned}$$ To get the bounds in the statement of Example \[ex:ch4CPP\] the optimal choices are $m_n = T_n^{\frac{1}{2+\gamma}}$ when $\gamma \leq \frac{1}{2}$ and $m_n = T_n^{\frac{2}{5}}$ otherwise. Concerning the discrete model, we have: $$\begin{aligned} \Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{{\ensuremath{\textnormal{Leb}}}},{\ensuremath {\mathscr{W}}}_n^{\nu_0})&\leq O\bigg(\sqrt{n\Delta_n^2}+\frac{m\ln m}{\sqrt{n}}+ \sqrt{n\Delta_n}\big(m^{-\frac{3}{2}}+m^{-1-\gamma}\big)\bigg).\end{aligned}$$ There are four possible scenarios: If $\gamma>\frac{1}{2}$ and $\Delta_n=n^{-\beta}$ with $\frac{1}{2}<\beta<\frac{3}{4}$ (resp. $\beta\geq \frac{3}{4}$) then the optimal choice is $m_n=n^{1-\beta}$ (resp. $m_n=n^{\frac{2-\beta}{5}}$). If $\gamma\geq\frac{1}{2}$ and $\Delta_n=n^{-\beta}$ with $\frac{1}{2}<\beta<\frac{2+2\gamma}{3+2\gamma}$ (resp. $\beta\geq \frac{2+2\gamma}{3+2\gamma}$) then the optimal choice is $m_n=n^{\frac{2-\beta}{4+2\gamma}}$ (resp. $m_n=n^{1-\beta}$). Proof of Example \[ch4ex2\] {#subsec:ch4ex2} --------------------------- As in Examples \[ex:ch4esempi\], we let $\varepsilon_m=m^{-1-\alpha}$ and consider the standard triangular/trapezoidal $V_j$’s. In particular, $\hat f_m$ will be piecewise linear. Condition (C2’) is satisfied and we have $C_m(f)=O(\varepsilon_m)$. This bound, combined with the one obtained in , allows us to conclude that an upper bound for the rate of convergence of $\Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})$ is given by: $$\Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})\leq C \bigg(\sqrt{\sqrt{n^2\Delta_n}\varepsilon_m}+\sqrt{n\Delta_n}\Big(\frac{\ln (\varepsilon_m^{-1})}{m}\Big)^{2}+\frac{m\ln m}{\sqrt n}+\sqrt{n\Delta_n^2}\ln (\varepsilon_m^{-1}) \bigg),$$ where $C$ is a constant only depending on the bound on $\lambda > 0$. The sequences $\varepsilon_m$ and $m$ can be chosen arbitrarily to optimize the rate of convergence. It is clear from the expression above that, if we take $\varepsilon_m = m^{-1-\alpha}$ with $\alpha > 0$, bigger values of $\alpha$ reduce the first term $\sqrt{\sqrt{n^2\Delta_n}\varepsilon_m}$, while changing the other terms only by constants. It can be seen that taking $\alpha \geq 15$ is enough to make the first term negligeable with respect to the others. In that case, and under the assumption $\Delta_n = n^{-\beta}$, the optimal choice for $m$ is $m = n^\delta$ with $\delta = \frac{5-4\beta}{14}$. In that case, the global rate of convergence is $$\Delta({\ensuremath {\mathscr{Q}}}_{n,FV}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0}) = \begin{cases} O\big(n^{\frac{1}{2}-\beta} \ln n\big) & \text{if } \frac{1}{2} < \beta \leq \frac{9}{10}\\ O\big(n^{-\frac{1+2\beta}{7}} \ln n\big) & \text{if } \frac{9}{10} < \beta < 1. \end{cases}$$ In the same way one can find $$\Delta({\ensuremath {\mathscr{P}}}_{n,FV}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})=O\bigg( \sqrt{n\Delta_n} \Big(\frac{\ln m}{m}\Big)^2 \sqrt{\ln(\varepsilon_m^{-1})} + \sqrt{\frac{m^2}{n\Delta_n \ln(\varepsilon_m)}} + \sqrt{n \Delta_n} \varepsilon_m \bigg).$$ As above, we can freely choose $\varepsilon_m$ and $m$ (in a possibly different way from above). Again, as soon as $\varepsilon_m = m^{-1-\alpha}$ with $\alpha \geq 1$ the third term plays no role, so that we can choose $\varepsilon_m = m^{-2}$. Letting $\Delta_n = n^{-\beta}$, $0 < \beta < 1$, and $m = n^\delta$, an optimal choice is $\delta = \frac{1-\beta}{3}$, giving $$\Delta({\ensuremath {\mathscr{P}}}_{n,FV}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})=O\Big(n^{\frac{\beta-1}{6}} \big(\ln n\big)^{\frac{5}{2}}\Big) = O\Big(T_n^{-\frac{1}{6}} \big(\ln T_n\big)^\frac{5}{2}\Big).$$ Proof of Example \[ex3\] {#subsec:ch4ex3} ------------------------ Using the computations in , combined with $\big(f(y)-\hat f_m(y)\big)^2\leq 4 \exp(-2\lambda_0 y^3) \leq 4 \exp(-2\lambda_0 H(m)^3)$ for all $y \geq H(m)$, we obtain: $$\begin{aligned} \int_{\varepsilon_m}^\infty \big|f(x) - \hat f_m(x)\big|^2 \nu_0(dx) &\lesssim \frac{H(m)^{7}}{(\varepsilon_m m)^{4}} + \int_{H(m)}^\infty \big|f(x) - \hat f_m(x)\big|^2 \nu_0(dx)\\ &\lesssim \frac{H(m)^{7}}{(\varepsilon_m m)^{4}} + \frac{e^{-2\lambda_0 H(m)^3}}{H(m)}. \end{aligned}$$ As in Example \[ex:ch4esempi\], this bounds directly $H^2(f, \hat f_m)$ and $A_m^2(f)$. Again, the first part of the integral appearing in $B_m^2(f)$ is asymptotically smaller than the one appearing above: $$\begin{aligned} B_m^2(f) &= \sum_{j=1}^m \bigg(\frac{1}{\sqrt{\mu_m}} \int_{J_j} \sqrt{f} \nu_0 - \sqrt{\int_{J_j} f(x) \nu_0(dx)}\bigg)^2\\ &\lesssim \frac{H(m)^{7}}{(\varepsilon_m m)^{4}} + \sum_{k=1}^{\frac{\varepsilon_m m}{H(m)}} \bigg( \frac{1}{\sqrt{\mu_m}} \int_{J_{m-k}} \sqrt{f} \nu_0 - \sqrt{\int_{J_{m-k}} f(x) \nu_0(dx)}\bigg)^2\\ &\lesssim \frac{H(m)^{7}}{(\varepsilon_m m)^{4}} + \frac{e^{-\lambda_0 H(m)^3}}{H(m)}. \end{aligned}$$ As above, for the last inequality we have bounded $f$ in each $J_{m-k}$, $k \leq \frac{\varepsilon_m m}{H(m)}$, with $\exp(-\lambda_0 H(m)^3)$. Thus the global rate of convergence of $L_2(f,\hat f_m)^2 + A_m^2(f) + B_m^2(f)$ is $\frac{H(m)^{7}}{(\varepsilon_m m)^{4}} + \frac{e^{-\lambda_0 H(m)^3}}{H(m)}$. Concerning $C_m(f)$, we have $C_m^2(f) = \int_0^{\varepsilon_m} \frac{(\sqrt{f(x)} - 1)^2}{x^2} dx \lesssim \varepsilon_m^5$. To write the global rate of convergence of the Le Cam distance in the discrete setting we make the choice $H(m) = \sqrt[3]{\frac{\eta}{\lambda_0}\ln m}$, for some constant $\eta$, and obtain: $$\begin{aligned} \Delta({\ensuremath {\mathscr{Q}}}_{n}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0}) &= O \bigg( \frac{\sqrt{n} \Delta_n}{\varepsilon_m} + \frac{m \ln m}{\sqrt{n}} + \sqrt{n \Delta_n} \Big( \frac{(\ln m)^{\frac{7}{6}}}{(\varepsilon_m m)^2} + \frac{m^{-\frac{\eta}{2}}}{\sqrt[3]{\ln m}} \Big) + \sqrt[4]{n^2 \Delta_n \varepsilon_m^5}\bigg). \end{aligned}$$ Letting $\Delta_n = n^{-\beta}$, $\varepsilon_m = n^{-\alpha}$ and $m = n^\delta$, optimal choices give $\alpha = \frac{\beta}{3}$ and $\delta = \frac{1}{3}+\frac{\beta}{18}$. We can also take $\eta = 2$ to get a final rate of convergence: $$\Delta({\ensuremath {\mathscr{Q}}}_{n}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0}) = \begin{cases} O\big(n^{\frac{1}{2} - \frac{2}{3}\beta}\big)& \text{if } \frac{3}{4} < \beta < \frac{12}{13}\\ O\big(n^{-\frac{1}{6}+\frac{\beta}{18}} (\ln n)^{\frac{7}{6}}\big) &\text{if } \frac{12}{13} \leq \beta < 1. \end{cases}$$ In the continuous setting, we have $$\Delta({\ensuremath {\mathscr{P}}}_{n}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})=O\bigg(\sqrt{n\Delta_n} \Big( \frac{(\ln m)^\frac{7}{6}}{(\varepsilon_m m)^2} + \frac{m^{-\frac{\eta}{2}}}{\sqrt[3]{\ln m}} + \varepsilon_m^{\frac{5}{2}}\Big) + \sqrt{\frac{\varepsilon_m m^2}{n\Delta_n}} \bigg).$$ Using $T_n = n\Delta_n$, $\varepsilon_m = T_n^{-\alpha}$ and $m = T_n^\delta$, optimal choices are given by $\alpha = \frac{4}{17}$, $\delta = \frac{9}{17}$; choosing any $\eta \geq 3$ we get the rate of convergence $$\Delta({\ensuremath {\mathscr{P}}}_{n}^{\nu_0},{\ensuremath {\mathscr{W}}}_n^{\nu_0})=O\big(T_n^{-\frac{3}{34}} (\ln T_n)^{\frac{7}{6}}\big).$$ Background ========== Le Cam theory of statistical experiments {#sec:ch4lecam} ---------------------------------------- A *statistical model* or *experiment* is a triplet ${\ensuremath {\mathscr{P}}}_j=({\ensuremath {\mathscr{X}}}_j,{\ensuremath {\mathscr{A}}}_j,\{P_{j,\theta}; \theta\in\Theta\})$ where $\{P_{j,\theta}; \theta\in\Theta\}$ is a family of probability distributions all defined on the same $\sigma$-field ${\ensuremath {\mathscr{A}}}_j$ over the *sample space* ${\ensuremath {\mathscr{X}}}_j$ and $\Theta$ is the *parameter space*. The *deficiency* $\delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)$ of ${\ensuremath {\mathscr{P}}}_1$ with respect to ${\ensuremath {\mathscr{P}}}_2$ quantifies “how much information we lose” by using ${\ensuremath {\mathscr{P}}}_1$ instead of ${\ensuremath {\mathscr{P}}}_2$ and it is defined as $\delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)=\inf_K\sup_{\theta\in \Theta}||KP_{1,\theta}-P_{2,\theta}||_{TV},$ where TV stands for “total variation” and the infimum is taken over all “transitions” $K$ (see [@lecam], page 18). The general definition of transition is quite involved but, for our purposes, it is enough to know that Markov kernels are special cases of transitions. By $KP_{1,\theta}$ we mean the image measure of $P_{1,\theta}$ via the Markov kernel $K$, that is $$KP_{1,\theta}(A)=\int_{{\ensuremath {\mathscr{X}}}_1}K(x,A)P_{1,\theta}(dx),\quad\forall A\in {\ensuremath {\mathscr{A}}}_2.$$ The experiment $K{\ensuremath {\mathscr{P}}}_1=({\ensuremath {\mathscr{X}}}_2,{\ensuremath {\mathscr{A}}}_2,\{KP_{1,\theta}; \theta\in\Theta\})$ is called a *randomization* of ${\ensuremath {\mathscr{P}}}_1$ by the Markov kernel $K$. When the kernel $K$ is deterministic, that is $K(x,A)={\ensuremath {\mathbb{I}}}_{A}S(x)$ for some random variable $S:({\ensuremath {\mathscr{X}}}_1,{\ensuremath {\mathscr{A}}}_1)\to({\ensuremath {\mathscr{X}}}_2,{\ensuremath {\mathscr{A}}}_2)$, the experiment $K{\ensuremath {\mathscr{P}}}_1$ is called the *image experiment by the random variable* $S$. The Le Cam distance is defined as the symmetrization of $\delta$ and it defines a pseudometric. When $\Delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)=0$ the two statistical models are said to be *equivalent*. Two sequences of statistical models $({\ensuremath {\mathscr{P}}}_{1}^n)_{n\in{\ensuremath {\mathbb{N}}}}$ and $({\ensuremath {\mathscr{P}}}_{2}^n)_{n\in{\ensuremath {\mathbb{N}}}}$ are called *asymptotically equivalent* if $\Delta({\ensuremath {\mathscr{P}}}_{1}^n,{\ensuremath {\mathscr{P}}}_{2}^n)$ tends to zero as $n$ goes to infinity. A very interesting feature of the Le Cam distance is that it can be also translated in terms of statistical decision theory. Let ${\ensuremath {\mathscr{D}}}$ be any (measurable) decision space and let $L:\Theta\times {\ensuremath {\mathscr{D}}}\mapsto[0,\infty)$ denote a loss function. Let $\|L\|=\sup_{(\theta,z)\in\Theta\times{\ensuremath {\mathscr{D}}}}L(\theta,z)$. Let $\pi_i$ denote a (randomized) decision procedure in the $i$-th experiment. Denote by $R_i(\pi_i,L,\theta)$ the risk from using procedure $\pi_i$ when $L$ is the loss function and $\theta$ is the true value of the parameter. Then, an equivalent definition of the deficiency is: $$\begin{aligned} \delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)=\inf_{\pi_1}\sup_{\pi_2}\sup_{\theta\in\Theta}\sup_{L:\|L\|=1}\big|R_1(\pi_1,L,\theta)-R_2(\pi_2,L,\theta)\big|.\end{aligned}$$ Thus $\Delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)<\varepsilon$ means that for every procedure $\pi_i$ in problem $i$ there is a procedure $\pi_j$ in problem $j$, $\{i,j\}=\{1,2\}$, with risks differing by at most $\varepsilon$, uniformly over all bounded $L$ and $\theta\in\Theta$. In particular, when minimax rates of convergence in a nonparametric estimation problem are obtained in one experiment, the same rates automatically hold in any asymptotically equivalent experiment. There is more: When explicit transformations from one experiment to another are obtained, statistical procedures can be carried over from one experiment to the other one. There are various techniques to bound the Le Cam distance. We report below only the properties that are useful for our purposes. For the proofs see, e.g., [@lecam; @strasser]. \[ch4delta0\] Let ${\ensuremath {\mathscr{P}}}_j=({\ensuremath {\mathscr{X}}},{\ensuremath {\mathscr{A}}},\{P_{j,\theta}; \theta\in\Theta\})$, $j=1,2$, be two statistical models having the same sample space and define $\Delta_0({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2):=\sup_{\theta\in\Theta}\|P_{1,\theta}-P_{2,\theta}\|_{TV}.$ Then, $\Delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)\leq \Delta_0({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)$. In particular, Property \[ch4delta0\] allows us to bound the Le Cam distance between statistical models sharing the same sample space by means of classical bounds for the total variation distance. To that aim, we collect below some useful results. \[ch4h\] Let $P_1$ and $P_2$ be two probability measures on ${\ensuremath {\mathscr{X}}}$, dominated by a common measure $\xi$, with densities $g_{i}=\frac{dP_{i}}{d\xi}$, $i=1,2$. Define $$\begin{aligned} L_1(P_1,P_2)&=\int_{{\ensuremath {\mathscr{X}}}} |g_{1}(x)-g_{2}(x)|\xi(dx), \\ H(P_1,P_2)&=\bigg(\int_{{\ensuremath {\mathscr{X}}}} \Big(\sqrt{g_{1}(x)}-\sqrt{g_{2}(x)}\Big)^2\xi(dx)\bigg)^{1/2}. \end{aligned}$$ Then, $$\|P_1-P_2\|_{TV}=\frac{1}{2}L_1(P_1,P_2)\leq H(P_1,P_2).$$ \[ch4hp\] Let $P$ and $Q$ be two product measures defined on the same sample space: $P=\otimes_{i=1}^n P_i$, $Q=\otimes_{i=1}^n Q_i$. Then $$H ^2(P,Q)\leq \sum_{i=1}^nH^2(P_i,Q_i).$$ \[fact:ch4hellingerpoisson\] Let $P_i$, $i=1,2$, be the law of a Poisson random variable with mean $\lambda_i$. Then $$H^2(P_1,P_2)=1-\exp\bigg(-\frac{1}{2}\Big(\sqrt{\lambda_1}-\sqrt{\lambda_2}\Big)^2\bigg).$$ \[fact:ch4gaussiane\] Let $Q_1\sim{\ensuremath {\mathscr{Nn}}}(\mu_1,\sigma_1^2)$ and $Q_2\sim{\ensuremath {\mathscr{Nn}}}(\mu_2,\sigma_2^2)$. Then $$\|Q_1-Q_2\|_{TV}\leq \sqrt{2\bigg(1-\frac{\sigma_1^2}{\sigma_2^2}\bigg)^2+\frac{(\mu_1-\mu_2)^2}{2\sigma_2^2}}.$$ \[fact:ch4processigaussiani\] For $i=1,2$, let $Q_i$, $i=1,2$, be the law on $(C,{\ensuremath {\mathscr{C}}})$ of two Gaussian processes of the form $$X^i_t=\int_{0}^t h_i(s)ds+ \int_0^t \sigma(s)dW_s,\ t\in[0,T]$$ where $h_i\in L_2({\ensuremath {\mathbb{R}}})$ and $\sigma\in{\ensuremath {\mathbb{R}}}_{>0}$. Then: $$L_1\big(Q_1,Q_2\big)\leq \sqrt{\int_{0}^T\frac{\big(h_1(y)-h_2(y)\big)^2}{\sigma^2(s)}ds}.$$ \[ch4fatto3\] Let ${\ensuremath {\mathscr{P}}}_i=({\ensuremath {\mathscr{X}}}_i,{\ensuremath {\mathscr{A}}}_i,\{P_{i,\theta}, \theta\in\Theta\})$, $i=1,2$, be two statistical models. Let $S:{\ensuremath {\mathscr{X}}}_1\to{\ensuremath {\mathscr{X}}}_2$ be a sufficient statistics such that the distribution of $S$ under $P_{1,\theta}$ is equal to $P_{2,\theta}$. Then $\Delta({\ensuremath {\mathscr{P}}}_1,{\ensuremath {\mathscr{P}}}_2)=0$. \[ch4independentkernels\] Let $P_i$ be a probability measure on $(E_i,\mathcal{E}_i)$ and $K_i$ a Markov kernel on $(G_i,\mathcal G_i)$. One can then define a Markov kernel $K$ on $(\prod_{i=1}^n E_i,\otimes_{i=1}^n \mathcal{G}_i)$ in the following way: $$K(x_1,\dots,x_n; A_1\times\dots\times A_n):=\prod_{i=1}^nK_i(x_i,A_i),\quad \forall x_i\in E_i,\ \forall A_i\in \mathcal{G}_i.$$ Clearly $K\otimes_{i=1}^nP_i=\otimes_{i=1}^nK_iP_i$. Finally, we recall the following result that allows us to bound the Le Cam distance between Poisson and Gaussian variables. \[ch4teomisto\](See [@BC04], Theorem 4) Let $\tilde P_{\lambda}$ be the law of a Poisson random variable $\tilde X_{\lambda}$ with mean $\lambda$. Furthermore, let $P_{\lambda}^*$ be the law of a random variable $Z^*_{\lambda}$ with Gaussian distribution ${\ensuremath {\mathscr{Nn}}}(2\sqrt{\lambda},1)$, and let $\tilde U$ be a uniform variable on $\big[-\frac{1}{2},\frac{1}{2}\big)$ independent of $\tilde X_{\lambda}$. Define $$\tilde Z_{\lambda}=2\textnormal{sgn}\big(\tilde X_{\lambda}+\tilde U\big)\sqrt{\big|\tilde X_{\lambda}+\tilde U\big|}.$$ Then, denoting by $P_{\lambda}$ the law of $\tilde Z_{\lambda}$, $$H ^2\big(P_{\lambda}, P_{\lambda}^*\big)=O(\lambda^{-1}).$$ Thanks to Theorem \[ch4teomisto\], denoting by $\Lambda$ a subset of ${\ensuremath {\mathbb{R}}}_{>0}$, by $\tilde {\ensuremath {\mathscr{P}}}$ (resp. ${\ensuremath {\mathscr{P}}}^*$) the statistical model associated with the family of probabilities $\{\tilde P_\lambda: \lambda \in \Lambda\}$ (resp. $\{P_\lambda^* : \lambda \in \Lambda\}$), we have $$\Delta\big(\tilde {\ensuremath {\mathscr{P}}}, {\ensuremath {\mathscr{P}}}^*\big) \leq \sup_{\lambda \in \Lambda} \frac{C}{\lambda},$$ for some constant $C$. Indeed, the correspondence associating $\tilde Z_\lambda$ to $\tilde X_\lambda$ defines a Markov kernel; conversely, associating to $\tilde Z_\lambda$ the closest integer to its square, defines a Markov kernel going in the other direction. Lévy processes {#sec:ch4levy} -------------- A stochastic process $\{X_t:t\geq 0\}$ on ${\ensuremath {\mathbb{R}}}$ defined on a probability space $(\Omega,{\ensuremath {\mathscr{A}}},{\ensuremath {\mathbb{P}}})$ is called a *Lévy process* if the following conditions are satisfied. 1. $X_0=0$ ${\ensuremath {\mathbb{P}}}$-a.s. 2. For any choice of $n\geq 1$ and $0\leq t_0<t_1<\ldots<t_n$, random variables $X_{t_0}$, $X_{t_1}-X_{t_0},\dots ,X_{t_n}-X_{t_{n-1}}$are independent. 3. The distribution of $X_{s+t}-X_s$ does not depend on $s$. 4. There is $\Omega_0\in {\ensuremath {\mathscr{A}}}$ with ${\ensuremath {\mathbb{P}}}(\Omega_0)=1$ such that, for every $\omega\in \Omega_0$, $X_t(\omega)$ is right-continuous in $t\geq 0$ and has left limits in $t>0$. 5. It is stochastically continuous. Thanks to the *Lévy-Khintchine formula*, the characteristic function of any Lévy process $\{X_t\}$ can be expressed, for all $u$ in ${\ensuremath {\mathbb{R}}}$, as: $$\label{caratteristica} {\ensuremath {\mathbb{E}}}\big[e^{iuX_t}\big]=\exp\bigg(-t\Big(iub-\frac{u^2\sigma^2}{2}-\int_{{\ensuremath {\mathbb{R}}}}(1-e^{iuy}+iuy{\ensuremath {\mathbb{I}}}_{\vert y\vert \leq 1})\nu(dy)\Big)\bigg),$$ where $b,\sigma\in {\ensuremath {\mathbb{R}}}$ and $\nu$ is a measure on ${\ensuremath {\mathbb{R}}}$ satisfying $$\nu(\{0\})=0 \textnormal{ and } \int_{{\ensuremath {\mathbb{R}}}}(|y|^2\wedge 1)\nu(dy)<\infty.$$ In the sequel we shall refer to $(b,\sigma^2,\nu)$ as the characteristic triplet of the process $\{X_t\}$ and $\nu$ will be called the *Lévy measure*. This data characterizes uniquely the law of the process $\{X_t\}$. Let $D=D([0,\infty),{\ensuremath {\mathbb{R}}})$ be the space of mappings $\omega$ from $[0,\infty)$ into ${\ensuremath {\mathbb{R}}}$ that are right-continuous with left limits. Define the *canonical process* $x:D\to D$ by $$\forall \omega\in D,\quad x_t(\omega)=\omega_t,\;\;\forall t\geq 0.$$ Let ${\ensuremath {\mathscr{D}}}_t$ and ${\ensuremath {\mathscr{D}}}$ be the $\sigma$-algebras generated by $\{x_s:0\leq s\leq t\}$ and $\{x_s:0\leq s<\infty\}$, respectively (here, we use the same notations as in [@sato]). By the condition (4) above, any Lévy process on ${\ensuremath {\mathbb{R}}}$ induces a probability measure $P$ on $(D,{\ensuremath {\mathscr{D}}})$. Thus $\{X_t\}$ on the probability space $(D,{\ensuremath {\mathscr{D}}},P)$ is identical in law with the original Lévy process. By saying that $(\{x_t\},P)$ is a Lévy process, we mean that $\{x_t:t\geq 0\}$ is a Lévy process under the probability measure $P$ on $(D,{\ensuremath {\mathscr{D}}})$. For all $t>0$ we will denote $P_t$ for the restriction of $P$ to ${\ensuremath {\mathscr{D}}}_t$. In the case where $\int_{|y|\leq 1}|y|\nu(dy)<\infty$, we set $\gamma^{\nu}:=\int_{|y|\leq 1}y\nu(dy)$. Note that, if $\nu$ is a finite Lévy measure, then the process having characteristic triplet $(\gamma^{\nu},0,\nu)$ is a compound Poisson process. Here and in the sequel we will denote by $\Delta x_r$ the jump of process $\{x_t\}$ at the time $r$: $$\Delta x_r = x_r - \lim_{s \uparrow r} x_s.$$ For the proof of Theorems \[ch4teo1\], \[ch4teo2\] we also need some results on the equivalence of measures for Lévy processes. By the notation $\ll$ we will mean “is absolutely continuous with respect to”. \[ch4teosato\] Let $P^1$ (resp. $P^2$) be the law induced on $(D,{\ensuremath {\mathscr{D}}})$ by a Lévy process of characteristic triplet $(\eta,0,\nu_1)$ (resp. $(0,0,\nu_2)$), where $$\label{ch4gamma*} \eta=\int_{\vert y \vert \leq 1}y(\nu_1-\nu_2)(dy)$$ is supposed to be finite. Then $P_t^1\ll P_t^2$ for all $t\geq 0$ if and only if $\nu_1\ll\nu_2$ and the density $\frac{d\nu_1}{d\nu_2}$ satisfies $$\label{ch4Sato} \int\bigg(\sqrt{\frac{d\nu_1}{d\nu_2}(y)}-1\bigg)^2\nu_2(dy)<\infty.$$ Remark that the finiteness in implies that in . When $P_t^1\ll P_t^2$, the density is $$\frac{dP_t^1}{dP_t^2}(x)=\exp(U_t(x)),$$ with $$\label{ch4U} U_t(x)=\lim_{\varepsilon\to 0} \bigg(\sum_{r\leq t}\ln \frac{d\nu_1}{d\nu_2}(\Delta x_r){\ensuremath {\mathbb{I}}}_{\vert\Delta x_r\vert>\varepsilon}- \int_{\vert y\vert > \varepsilon} t\bigg(\frac{d\nu_1}{d\nu_2}(y)-1\bigg)\nu_2(dy)\bigg),\\ P^{(0,0,\nu_2)}\textnormal{-a.s.}$$ The convergence in is uniform in $t$ on any bounded interval, $P^{(0,0,\nu_2)}$-a.s. Besides, $\{U_t(x)\}$ defined by is a Lévy process satisfying ${\ensuremath {\mathbb{E}}}_{P^{(0,0,\nu_2)}}[e^{U_t(x)}]=1$, $\forall t\geq 0$. Finally, let us consider the following result giving an explicit bound for the $L_1$ and the Hellinger distances between two Lévy processes of characteristic triplets of the form $(b_i,0,\nu_i)$, $i=1,2$ with $b_1-b_2=\int_{\vert y \vert \leq 1}y(\nu_1-\nu_2)(dy)$. \[teo:ch4bound\] For any $0<T<\infty$, let $P_T^i$ be the probability measure induced on $(D,{\ensuremath {\mathscr{D}}}_T)$ by a Lévy process of characteristic triplet $(b_i,0,\nu_i)$, $i=1,2$ and suppose that $\nu_1\ll\nu_2$. If $H^2(\nu_1,\nu_2):=\int\big(\sqrt{\frac{d\nu_1}{d\nu_2}(y)}-1\big)^2\nu_2(dy)<\infty,$ then $$H^2(P_T^1,P_T^2)\leq \frac{T}{2}H^2(\nu_1,\nu_2).$$ We conclude the Appendix with a technical statement about the Le Cam distance for finite variation models. \[ch4LC\] $$\Delta({\ensuremath {\mathscr{P}}}_n^{\nu_0},{\ensuremath {\mathscr{P}}}_{n,FV}^{\nu_0})=0.$$ Consider the Markov kernels $\pi_1$, $\pi_2$ defined as follows $$\pi_1(x,A)={\ensuremath {\mathbb{I}}}_{A}(x^d), \quad \pi_2(x,A)={\ensuremath {\mathbb{I}}}_{A}(x-\cdot \gamma^{\nu_0}), \quad \forall x\in D, A \in {\ensuremath {\mathscr{D}}},$$ where we have denoted by $x^d$ the discontinuous part of the trajectory $x$, i.e. $\Delta x_r = x_r - \lim_{s \uparrow r} x_s,\ x_t^d=\sum_{r \leq t}\Delta x_r$ and by $x-\cdot \gamma^{\nu_0}$ the trajectory $x_t-t\gamma{\nu_0}$, $t\in[0,T_n]$. On the one hand we have: $$\begin{aligned} \pi_1 P^{(\gamma^{\nu-\nu_0},0,\nu)}(A)&=\int_D \pi_1(x,A)P^{(\gamma^{\nu-\nu_0},0,\nu)}(dx)=\int_D {\ensuremath {\mathbb{I}}}_A(x^d)P^{(\gamma^{\nu-\nu_0},0,\nu)}(dx)\\ &=P^{(\gamma^{\nu},0,\nu)}(A),\end{aligned}$$ where in the last equality we have used the fact that, under $P^{(\gamma^{\nu-\nu_0},0,\nu)}$, $\{x_t^d\}$ is a Lévy process with characteristic triplet $(\gamma^{\nu},0,\nu)$ (see [@sato], Theorem 19.3). On the other hand: $$\begin{aligned} \pi_2 P^{(\gamma^{\nu},0,\nu)}(A)&=\int_D \pi_2(x,A)P^{(\gamma^{\nu_0},0,\nu)}(dx)=\int_D {\ensuremath {\mathbb{I}}}_A(x-\cdot \gamma^{\nu_0})P^{(\gamma^{\nu},0,\nu)}(dx)\\ &=P^{(\gamma^{\nu-\nu_0},0,\nu)}(A),\end{aligned}$$ since, by definition, $\gamma^{\nu}-\gamma^{\nu_0}$ is equal to $\gamma^{\nu-\nu_0}$. The conclusion follows by the definition of the Le Cam distance. Acknowledgements {#acknowledgements .unnumbered} ---------------- I am very grateful to Markus Reiss for several interesting discussions and many insights; this paper would never have existed in the present form without his advice and encouragement. My deepest thanks go to the anonymous referee, whose insightful comments have greatly improved the exposition of the paper; some gaps in the proofs have been corrected thanks to his/her remarks.

Moss (Physcomitrella patens) GH3 proteins act in auxin homeostasis. Auxins are hormones involved in many cellular, physiological and developmental processes in seed plants and in mosses such as Physcomitrella patens. Control of auxin levels is achieved in higher plants via synthesis of auxin conjugates by members of the GH3 family. The role of the two GH3-like proteins from P. patens for growth and auxin homeostasis was therefore analysed. The in vivo-function of the two P. patens GH3 genes was investigated using single and double knockout mutants. The two P. patens GH3 proteins were also heterologously expressed to determine their enzymatic activity. Both P. patens GH3 enzymes accepted the auxin indole acetic acid (IAA) as substrate, but with different preferences for the amino acid to which it is attached. Cytoplasmic localization was shown for PpGH3-1 tagged with green fluorescent protein (GFP). Targeted knock-out of either gene exhibited an increased sensitivity to auxin, resulting in growth inhibition. On plain mineral media mutants had higher levels of free IAA and less conjugated IAA than the wild type, and this effect was enhanced when auxin was supplied. The DeltaPpGH3-1/DeltaPpGH3-2 double knockout had almost no IAA amide conjugates but still synthesized ester conjugates. Taken together, these data suggest a developmentally controlled involvement of P. patens GH3 proteins in auxin homeostasis by conjugating excess of physiologically active free auxin to inactive IAA-amide conjugates.

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Summer Flowers at Danckerts Summer is now well and truly on its way now as we come upon another Bank Holiday this weekend. We have some lovely gardens plants and pots at the shop, as well as a new range of "Vivid Arts" garden animals on display, which are a fantastically realistic range of life size animals and birds to enhance the garden...from frogs to foxes, and rabbits to robins, pop in and take a look! The gardens in Wednesbury are going to be coming alive with plants, animals, and barbies! The summer flower collection is now in full swing, with some delightful bouquets and vases full of Snaps, Sweet Williams, and other summer favourites. Keep in touch via Facebook, and we'll keep you notified of any Special Offers that are coming up! We recently had St Georges day, and the St Georges Day March was hugely popular, starting at Stone Cross, just past the Wednesbury/ West Bromwich border, and finishing up at Dartmouth Park in the Sandwell Valley.

From 1 July 2018, the Tax Office is advising Australians that if they find an error in their tax return or activity statement they will not incur a penalty but will advise of the error and how to get it right next time. Penalty relief will only apply to eligible taxpayers or entities (i.e., turnover of less than $10 million) every three years. Eligible individuals will only be given penalty relief on their tax return or activity statement if they make an inadvertent error because they either: – took a position on income tax that is not reasonably arguable, or – failed to take reasonable care The ATO will not provide penalty relief when individuals have (in the past three years): Received penalty relief – Avoided tax payment or committed fraud – Accrued taxation debts with no intention of being able to pay (i.e., phoenix activity) – Previously penalised for reckless or intentional disregard of the law – Participated in the management or control of another entity which has evaded tax. Individuals can not apply for penalty relief. The ATO is reminding individuals that they will provide relief during an audit should it apply. Penalty relief will not be applied to: – Wealthy individuals and their businesses – Associates of wealthy individuals (that may be deemed a small business entity in their own right) – Public groups, significant global entities and associates Penalty relief will also not be applied to certain taxes, i.e., fringe benefits tax (FBT) or super guarantee (SG).

Q: How to change XML from dataset into HTML UL I'm working on a C# webforms application and have a datalayer which gathers information about the menu a customer can see, based on their customer number and order type. I was using the ASP.NET menu control for this until the qa department asked to change the menu to expand on click instead of hover. At that point, I decided to try and do the menu with a simpler css/html/jquery approach but I've hit a jam. I have the following method in my datalayer that gets information for the menu and returns it as XML. What I'm stuck on is how to take the XML that was being gathered, when I was using the menu control and hopefully reformat it into a UL for using in the html/css approach I'd like to do. public static string BuildMenu(string cprcstnm, string docType) { DataSet ds = new DataSet(); string connStr = ConfigurationManager.ConnectionStrings["DynamicsConnectionString"].ConnectionString; using (SqlConnection conn = new SqlConnection(connStr)) { string sql = "usp_SelectItemMenuByCustomer"; SqlDataAdapter da = new SqlDataAdapter(sql, conn); da.SelectCommand.CommandType = CommandType.StoredProcedure; da.SelectCommand.Parameters.Add("@CPRCSTNM", SqlDbType.VarChar).Value = cprcstnm; da.SelectCommand.Parameters.Add("@DOCID", SqlDbType.VarChar).Value = docType; da.Fill(ds); da.Dispose(); } ds.DataSetName = "Menus"; ds.Tables[0].TableName = "Menu"; DataRelation relation = new DataRelation("ParentChild", ds.Tables["Menu"].Columns["MenuID"], ds.Tables["Menu"].Columns["ParentID"], false); relation.Nested = true; ds.Relations.Add(relation); return ds.GetXml(); } A sample of XMl that is output is as follows: <Menus> - <Menu> <MenuID>23</MenuID> <ITEMNMBR>0</ITEMNMBR> <Text>ACC</Text> <Description>ACC</Description> <ParentID>0</ParentID> - <Menu> <MenuID>34</MenuID> <ITEMNMBR>1</ITEMNMBR> <Text>BASE</Text> <Description>BASE</Description> <ParentID>23</ParentID> - <Menu> <MenuID>516</MenuID> <ITEMNMBR>2</ITEMNMBR> <Text>HYP</Text> <Description>HYP</Description> <ParentID>34</ParentID> I would need to convert this to something such as : <ul class="dropdown"> <li><a href="#">ACC</a> <ul class="sub_menu"> <li> <a href="#">BASE</a> <ul> <li> <a href="#">HYP</a> <ul> <li><a href="#">Terminal 1</a></li> <li><a href="#">Terminal 1</a></li> </ul> </li> </ul> </li> A: You will get some ideas from the following MSDN link that illustrates writing html from a dataset using xslt http://msdn.microsoft.com/en-us/library/8fd7xytc(v=vs.80).aspx