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[ "Common Causes of Seattle Bicycle Accidents\n\nBy Hardwick & Pendergast, P.S. on April 29, 2016\n\nIn the past few years, bikes have become a very popular method of transport for Seattle residents. ", "More people are using their bikes to get to work, run errands, and for fun. ", "Unfortunately, riding your bike can be dangerous in Seattle.", "\n\nWhat Causes Seattle Bike Accidents?", "\n\nThere are many factors that can lead to a Seattle bike accident. ", "Hardwick & Pendergast, P.S. has handled many of these accidents cases over the years. ", "Here are the most common causes of Seattle bike accidents our clients have reported:\n\nCompensation for Seattle Bike Accidents\n\nIf you or a loved one have been injured in a Seattle bike accident, you may be able to pursue compensation for your damages and losses. ", "An experienced Seattle bike accident attorney can help you secure a settlement that covers your medical bills, lost wages, property damage, and pain and suffering.", "\n\nHow to Reduce Your Risk of a Seattle Bike Accident\n\nHardwick & Pendergast, P.S. recommends taking the following safety precautions when riding your bike in Seattle or anywhere else in Washington:\n• Always ride while wearing a helmet\n• Never ride at night without wearing bright clothing\n• Use front and rear lights on your bike\n• Be sure to use reflectors when riding at night\n• Maintain a safe distance from cars while riding\n\nContact Hardwick & Pendergast, P.S. Today\n\nHardwick & Pendergast, P.S. has guided many people to successful claims after a Seattle bike accident injury. ", "We can help you secure the settlement needed to heal and move on from this painful situation. ", "You can reach us at (888) 228-3860.", "\n\nDisclaimer: The legal information presented at this site should not be construed to be formal legal advice, nor the formation of a lawyer or attorney client relationship. ", "Any results set forth herein are based upon the facts of that particular case and do not represent a promise or guarantee. ", "Please contact an attorney for a consultation on your particular traffic accident matter. ", "This web site is not intended to solicit clients for matters outside of the State of Washington." ]

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[ "Q:\n\nExit from for loop when any jQuery Deferred fails\n\nIn the below code, whenever any one of the deferred object fails I need to quit the for loop. ", "Whenever the loop upper-case red or yellow color it fails and I want to avoid other deferreds getting executed.", "\nvar colours = ['violet', 'indigo', 'blue', 'green', 'yellow', 'orange', 'red'];\n\nvar capitalize = function(text) {\n var deferred = $.Deferred(),\n delay = (1 + Math.floor(Math.random() * 5)) * 500;\n\n setTimeout(function() {\n if (text === 'red' || text === 'yellow') {\n deferred.reject('error colour', true);\n } else {\n deferred.resolve(text.toUpperCase());\n }\n }, delay);\n\n return deferred.promise();\n}\n\nvar deferreds = [],\n result = [];\n\nfor (var i = 0; i < colours.length; i++) {\n var deferred = capitalize(colours[i]);\n\n deferred.done(function(t) {\n console.log(t);\n result.push(t);\n }).fail(function(e) {\n console.log(e);\n });\n\n deferreds.push(deferred);\n}\n\n$.when.apply($, deferreds).done(function(){\n console.log(result);\n}).fail(function(e){\n console.log(e);\n});\n\nLink to jsfiddle\nEDIT:\nI'm building a cordova based mobile application with backbone. ", "I've to use localStorage for persistence and I've to encrypt all the data before persisting. ", "Though storing/retrieving data with localstorage is synchronous, to encrypt/decrypt the data I've to call the native device API which is asynchronous. ", "I thought of using the Backbone.localstorage plugin but it is not developed for async... so not much useful!", "\nI'm developing my own plugin based on that. ", "I've nearly completed most of the code except one method i.e. findAll. ", "\nThe findAll method returns all the models that are stored in localstorage.", "\n// exiting method in the Backbone.", "Localstorage plugin\nextend(Backbone.", "LocalStorage.prototype, {\n // ...\n findAll: function() {\n var result = [];\n for (var i = 0, id, data; i < this.records.length; i++) {\n id = this.records[i];\n data = this.serializer.deserialize(this.localStorage().getItem(this._itemName(id)));\n if (data !", "= null) result.push(data);\n }\n return result;\n }\n});\n\nIn localstorage all the models are encrypted and stored as string. ", "I've to decrypt them before deserializing back to models. ", "The this.crypto class decrypt the string returned from localstorage and deserialize back to model. ", "The encryption/decryption is aysnc and so it returns a promise. ", "\n// Method in my new plugin\nfindAll: function () {\n var deferred = $.Deferred(),\n deferreds = [],\n result = [], \n errors = [];\n\n // this.records contains all the model ids\n for (var i = 0, id, data; i < this.records.length; i++) {\n id = this.records[i];\n\n // this.crypto return a promise with the backbone model as parameter\n var d = this.crypto.deserialize(this.localStorage().getItem(this._itemName(id)));\n\n d.done(function(model) {\n // I've to maintain the order in result so storing the index\n result.push({ index: i, model: model });\n }).fail(function(error) {\n errors.push(error);\n });\n\n deferreds.push(d);\n }\n\n $.when.apply($, deferreds)\n .done(function() {\n // TODO: sort the result based on i and resolve it\n deferred.resolve(sortedResult);\n })\n .fail(...);\n\n return deferred.promise();\n}\n\nThere are chances an error can occur while decrypting and in that case I've to stop the complete process.", "\n\nA:\n\nYour new findAll method will simplify as follows :\nfindAll: function () {\n var promises = this.records.map(function(record) {\n return this.crypto.deserialize(this.localStorage().getItem(this._itemName(record)));\n });\n return $.when.apply(null, promises).then(function() {\n return Array.prototype.slice.apply(arguments);//convert arguments to array\n });\n}\n\nOn success this will return a promise of an array of results in the order you want - no need to sort anything. ", "Any individual async failure will cause the returned promise to be rejected. ", "However, that rejection will be too late to prevent other async calls, which were already made. ", "\nIn order to allow a failure to inhibit further calls of this.crypto.deserialize(...), you have to perform the calls serially (in a daisy chain), thus allowing the outcome of each call to determine the next course of action.", "\nfindAll: function () {\n var results = [];\n return this.records.reduce(function(promise, record) {\n return promise.then(function(result) {\n if(result) results.push(result);\n return this.crypto.deserialize(this.localStorage().getItem(this._itemName(record)));\n });\n }, $.when()).then(function() {\n return results;\n });\n}\n\nAs before, on success this will return a promise of an array of results in the order you want. ", " \nAs each stage is executed only if the previous stage was successful, inhibition of further calls will happen automatically on async failure. ", "Although .reduce(...) built a then chain unconditionally, a rejection will force the chain down its fail path - thens to the right of the failure will be skipped (they have no fail handlers). ", "\nThings are slightly different if you need to force a failure based on testing result, but the overall pattern is essentially the same.", "\n\n" ]

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[ "On Sunday, August 22nd, 7th day on power of prog.com will feature \"Shadow Gallery: The Evolution\". ", "The band will choose 3 songs from each album that they feel best represents their music. ", "Shadow Gallery fans get to have their favorites too. ", "Choose your 3 favorite Shadow Gallery songs that YOU think best represents the SG sound. ", "We will provide your results to 7th day prior to the show\n\nYou cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot delete your posts in this forumYou cannot edit your posts in this forumYou cannot create polls in this forumYou cannot vote in polls in this forum" ]

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[ "Who Hoak?", "\n\nEver heard of Hoak Media? ", "No? ", "Me neither. ", "Not till this morning, anyway. ", "It's a Dallas-based broadcasting company that, according to its Web site, acquires and operates TV and radio stations in \"small and medium-sized markets...that rank 75 to 200,\" as ranked by the A.C. Nielsen Company. ", "Hoak Media, which offices out of the Crescent Court, is named for its chairman, Jim Hoak, whose bio is impressive: legal assistant to a commissioner at the Federal Communications Commission in the late '60s; co-founder and CEO of Heritage Communications Inc. in the early '70s, before it grew into one of the 20 largest cable television providers in the country. ", "Sold HCI to Tele-Communications Inc. for $1.5 billion in 1987. ", "Started Heritage Media Corp. after that. ", "Sold that to Rupert Murdoch's NewsCorporation for $1.4 billion in 1997. ", "Started Crown Media Inc., a cable television company that partnered with Hallmark Cards Inc. in 1991. ", "It was sold in 1995. ", "Serves as a director of three public companies: PanAmSat Corporation, Pier 1 Imports Inc., and Texas Industries Inc. Started Hoak Media in 2003. ", "Now owns seven network affiliates in such markets as Wichita Falls; Grand Junction, Colorado; and Hastings, Nebraska. ", "Only Dallas Morning News reference I can find to a Jim Hoak is the chairman of Hockaday's board of trustees. ", "Really, when did I miss all this?", "\n\nAnyway, says here the man bought three television stations and their affiliates in North Dakota and South Dakota: KVLY-TV of Fargo and KFYR-TV of Bismarck, both NBC affiliates, and KSFY-TV of Sioux Falls, which is an ABC affiliate. ", "Doesn't say for how much. ", "The deal has to be approved by the FCC; it will be. ", "Seriously, who the hell is Jim Hoak? ", "--Robert Wilonsky" ]

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[ "Cannabox shop orders are processed and shipped daily Monday-Friday (excluding holidays). ", "If your order is placed before 12pm PST Monday-Friday (excluding holidays) you can enjoy same day shipping. ", "All orders over $25 will receive free shipping within the US. ", "All orders $100 and above will require a signature and or ID at time of delivery.", "\n\nSubscription Products\n\nCannabox subscriptions are shipped to all subscribers at the same time every month (similar to a magazine subscription) This means that if you order after the 19th of the month your first scheduled box will be shipped on the next monthly shipment. ", "We schedule shipping to begin on or about the 20th of each month. ", "We schedule to conclude shipping on or around the 25th of each month. ", "If you are ordering from the US, your monthly box should arrive between the 21st and 30th of each month. ", "If you have not received it by the 30th of the month feel free to open a support ticket HERE so we may investigate further. ", "International orders will take a bit longer.", "\n\nWith Cannabox, you won’t pay less anywhere else. ", "We’re committed to providing you an excellent experience, each time you shop with us. ", "Each day, we compare the prices of our products to make sure you’re getting a great deal for a great price, without sacrificing quality.", "\n\nCannabox Price Guarantee\n\nIf you find an identical product with a lower advertised price, let us know prior to your purchase or within 24 hours after your purchase! ", "We will be happy to consider any price match request.", "\n\nGet a lightly themed monthly pack of just the essentials from Cannabox. ", "Each month, get the bare smoking accessories you need to pull up to the sesh with fresh products like:\n\nHand Pipes\n\nRolling Papers\n\nWraps\n\nCones\n\nClipper Lighter\n\nMunchie\n\nCannabox Essentials ships around the 20-25th of each month, just like Cannabox OG. ", "Get $30 worth of smoking accessories for only $13.99. ", "PRODUCTS MAY VARY.", "\n\nStill not convinced? ", "Here are some more awesome benefits of joining:\n\nFor You, By Us\n\nWe’re not some corporate scheme. ", "Just know if you met our team IRL, we’d be best buddies.", "\n\nAwesome New Monthly Themes\n\nCreative new themes every month, pertaining to pop culture and everything dope.", "\n\nDedicated Support\n\nWhatever situation you end up in, we’re there to help. ", "Customer support will answer your message usually within 24 business hours.", "\n\nSo what are you waiting for? ", "Get in with the new wave of smoking!", "\n\n*Orders of $100+ will require a signature/ID at delivery.", "\n\nShipping Times\n\nShop Orders\n\nCannabox shop orders are processed and shipped daily Monday-Friday (excluding holidays). ", "If your order is placed before 12pm PST Monday-Friday (excluding holidays) you can enjoy same day shipping. ", "All orders over $25 will receive free shipping within the US. ", "All orders $100 and above will require a signature and or ID at time of delivery.", "\n\nSubscription Products\n\nCannabox subscriptions are shipped to all subscribers at the same time every month (similar to a magazine subscription) This means that if you order after the 19th of the month your first scheduled box will be shipped on the next monthly shipment. ", "We schedule shipping to begin on or about the 20th of each month. ", "We schedule to conclude shipping on or around the 25th of each month. ", "If you are ordering from the US, your monthly box should arrive between the 21st and 30th of each month. ", "If you have not received it by the 30th of the month feel free to open a support ticket HERE so we may investigate further. ", "International orders will take a bit longer.", "\n\nLow Price Guarantee\n\nOur promise to you.", "\n\nWith Cannabox, you won’t pay less anywhere else. ", "We’re committed to providing you an excellent experience, each time you shop with us. ", "Each day, we compare the prices of our products to make sure you’re getting a great deal for a great price, without sacrificing quality.", "\n\nCannabox Price Guarantee\n\nIf you find an identical product with a lower advertised price, let us know prior to your purchase or within 24 hours after your purchase! ", "We will be happy to consider any price match request.", "\n\nCustomer Reviews\n\nThey really do rock.! ", "I mean who replaces a glass piece with no questions asked!??? ", "Cannabox does! ", "Yes for sure I contacted Customer service and explained how upset I was after my Favorite piece got broke i was devistated!! ", "They were prompt and very understanding!. ", "This just adds to my list of \"pro's\" and honestly I really don't have any cons!. ", "So thanks everyone at cannabox I will always be your biggest fan and have been ordering the subscription boxes for a couple years now.. I actually look forward to the boxes every month. ", "Just wish I could of had every one of those boxes every month. ", "But life can hit ya really hard sometimes!! ", "Thanks again guys & gals!! ", "🤗\n\nS\n\nS.s.", "\n\nBest mail day\n\nlove all your products. ", "Great company! ", "Great service!", "\n\nK\n\nK.L.\n\nAmazing\n\nWell worth the price and you get some pretty cool stuff! ", "Plus who doesn’t like a present every month!", "\n\nH\n\nH.\n\nLove Cannabox\n\nThis is an awesome subscription love it. ", "I make sure I have something to burn at that time of the month lol. ", "Amazing products Cannabox. ", "Love Cannabox it’s amazing Company.. 👍🏻👍🏻\n\nThe best in online smoke shops.", "\n\nBrowse our online smoke shop for our favorite brands like Raw, Grav Labs and Puffco. ", "Our head shop also carries the best bongs, dab rigs, vaporizers, rolling papers, rolling trays, grinders, and other smoking accessories! ", "Cannabox only picks out the best of the best, tested for stoners by stoners.", "\n\nEverything Cannabox, in your inbox. ", "Sign up to get the latest on sales, new releases and more\n\nDear Cannabox Community,\n\nDue to the current COVID-19 situation, supply chain and transit times have been severely and globally affected. ", "What this means for you is that, all Cannabox orders will be processed and delivered, but not at the speed you are used to from us.", "\n\nTherefore we cannot guarantee our monthly boxes will arrive to you on time. ", "We apologize for the inconvenience and if you have any questions or concerns please reach out to our customer support team at support@cannabox.com or open a support ticket HERE.", "\n\nCurrently we are not experiencing any delays from purchases made in the Stash store. ", "We will update you when anything changes with the current situation.", "\n\nAt Cannabox, we are focused on keeping our community and our team safe by following the most updated COVID-19 CDC guidelines. ", "At the same time, we remain committed to offering a shopping and membership experience that is accessible to all." ]

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[ "---\nabstract: |\n A broadcast on a graph $G=(V,E)$ is a function $f: V\\longrightarrow \\{0,\\ldots,\\operatorname{diam}(G)\\}$ such that $f(v)\\leq e_G(v)$ for every vertex $v\\in V$, where $\\operatorname{diam}(G)$ denotes the diameter of $G$ and $e_G(v)$ the eccentricity of $v$ in $G$. The cost of such a broadcast is then the value $\\sum_{v\\in V}f(v)$. Various types of broadcast functions on graphs have been considered in the literature, in relation with domination, irredundence, independence or packing, leading to the introduction of several broadcast numbers on graphs.", "\n\n In this paper, we determine these broadcast numbers for all paths and cycles, thus answering a question raised in \\[D. Ahmadi, G.H. Fricke, C. Schroeder, S.T. Hedetniemi and R.C. Laskar, Broadcast irredundance in graphs. [*", "Congr. ", "Numer.*]{} ", "224 (2015), 17–31\\].", "\nauthor:\n- 'Sabrina BOUCHOUIKA [^1]'\n- Isma BOUCHEMAKH \n- 'Éric SOPENA [^2]'\ntitle: Broadcasts on Paths and Cycles\n---\n\n\\[section\\] \\[theorem\\][Lemma]{} \\[theorem\\][Conjecture]{} \\[theorem\\][Observation]{}\n\n\\[theorem\\][Corollary]{} \\[theorem\\][Proposition]{} \\[theorem\\][Question]{}\n\n[**Keywords:**]{} Broadcast; Dominating broadcast; Irredundant broadcast; Independent broadcast; Packing broadcast; Path; Cycle.", "\n\n[**MSC 2010:**]{} 05C12, 05C69.", "\n\nIntroduction\n============\n\nLet $G=(V,E)$ be a graph of [*order*]{} $n=|V|$ and [*size*]{} $m=|E|$. The [*open neighborhood*]{} of a vertex $v \\in V$ is the set $N_G(v) = \\{u: uv \\in E \\}$ of vertices adjacent to $v$. Each vertex $u \\in N_G(v)$ is a [*neighbor*]{} of $v$ in $G$. The [*closed neighborhood*]{} of $v$ is the set $N_G[v] = N_G(v) \\cup \\{v\\}$. The [*open neighborhood*]{} of a set $S \\subseteq V$ of vertices is $N_G(S) = \\cup_{v\\in S} N_G(v)$, while the [*closed neighborhood*]{} of $S$ is the set $N_G[S]=N_G(S)\\cup S$. The [*degree*]{} of a vertex $v$ in $G$, denoted $\\deg_G(v)$, is the size of the open neighborhood of $v$.\n\nA [*$(u,v)$-geodesic*]{} in a graph $G$ is a shortest path joining $u$ and $v$. We denote by $d_G(u,v)$ the [*distance*]{} between the vertices $u$ and $v$ in $G$, that is, the length of a $(u,v)$-geodesic in $G$. The [*eccentricity*]{} $e_G(v)$ of a vertex $v$ in $G$ is the maximum distance from $v$ to any other vertex of $G$. The [*radius*]{} $\\rad(G)$ and the [*diameter*]{} $\\diam(G)$ of a graph $G$ are the minimum and the maximum eccentricity among the vertices of $G$, respectively.", "\n\nA function $f: V \\longrightarrow \\{0,\\ldots,\\operatorname{diam}(G)\\}$ is a [*broadcast*]{} on a graph $G=(V,E)$ if $f(v)\\leq e_G(v)$ for every vertex $v\\in V$. The value $f(v)$ is called the [*$f$-value*]{} of $v$. An [*$f$-broadcast vertex*]{} (or an [*$f$-dominating vertex*]{}) is a vertex $v$ for which $f(v)>0$. The set of all $f$-broadcast vertices is denoted $V^+_f(G)$. If $v\\in V^+_f$ is an $f$-broadcast vertex, $u\\in V$ and $d_G(u,v)\\leq f(v)$, then the vertex $u$ [*hears*]{} a broadcast from $v$ and $v$ [*broadcasts to*]{} (or [*$f$-dominates*]{}) $u$. Note that, in particular, each vertex $v\\in V^+_f$ hears a broadcast from itself and $f$-dominates itself.", "\n\nThe [*$f$-broadcast neighborhood*]{} of a vertex $v\\in V^+_f$ is the set of vertices that hear $v$, that is $$N_f(v)=\\big\\{u:d_G(u,v)\\leq f(v)\\big\\},$$ and the [*broadcast neighborhood*]{} of $f$ is the set $$N_f(V^+_f)=\\cup_{v\\in V^+_f} N_f(v).$$ The set of $f$-broadcast vertices that a vertex $u\\in V$ can hear is the set $$H_f(u) = \\big\\{v\\in V^+_f: d_G(u,v)\\leq f (v)\\big\\}.$$ For a vertex $v\\in V^+_f$, the [*private $f$-neighborhood*]{} of $v$ is the set of vertices that hear only $v$, that is $$PN_f(v)=\\big\\{u\\in V: H_f(u)=\\{v\\}\\big\\},$$ and every vertex $u\\in PN_f(v)$ is a [*private $f$-neighbor*]{} of $v$. Moreover, the [*private $f$-border of*]{} $v$ is either the set of private $f$-neighbors of $v$ that are at distance $f(v)$ from $v$, or the singleton $\\{v\\}$ if $f(v)=1$ and $PN_f(v)=\\{v\\}$, that is $$PB_f(v) = \n\\left\\{\n\\begin{array}{ll}\n \\{v\\} & \\text{if $f(v)=1$ and $PN_f(v)=\\{v\\}$},\\\\[2ex]\n \\big\\{u \\in PN_f(v) : d_G(u,v) = f(v)\\big\\}& \\text{otherwise}.", "\n\\end{array}\n\\right.$$ Every vertex in $PB_f(v)$ is a [*bordering private $f$-neighbor*]{} of $v$. In particular, if $f(v)=1$ and $PN_f(v)=\\{v\\}$, then $v$ is its own bordering private $f$-neighbor.", "\n\nThe [*cost*]{} of a broadcast $f$ on a graph $G$ is $$\\sigma(f)=\\sum_{v\\in V^+_f}f (v).$$ A broadcast $f$ on $G$ of some type is [*minimal*]{} (resp. [*", "maximal*]{}) if there does not exist any broadcast $g\\neq f$ on $G$ of the same type such that $g(u)\\leq f(u)$ (resp. ", "$g(u)\\geq f(u)$) for all $u\\in V$. Several types of broadcasts have been defined in the literature, in relation with domination, irredundence, independence or packing, leading to the introduction of several broadcast numbers on graphs, corresponding to the minimum or maximum possible cost of a maximal or minimal broadcast of the corresponding type, respectively. ", "For any such parameter, say $q(G)$, a broadcast $f$ on $G$ of the corresponding type with $\\sigma(f)=q(G)$ will be simply called a $q$-broadcast. ", "We will also say that such a broadcast is [*optimal*]{}.", "\n\nWe now introduce the various types of broadcasts we will consider in this paper.", "\n\n#### Dominating broadcasts.", "\n\nA broadcast $f$ on $G$ is a [*dominating broadcast*]{} if every vertex in $V-V^+_f$ is $f$-dominated by some vertex in $V^+_f$ or, equivalently, if for every vertex $v\\in V$, $|H_f(v)| \\geq 1$. The [*broadcast domination number*]{} $\\gamma_b(G)$ of $G$ is the minimum cost of a dominating broadcast on $G$. The [*upper broadcast domination number*]{} $\\Gamma_b(G)$ of $G$ is the maximum cost of a minimal dominating broadcast on $G$. If $f$ is a minimal dominating broadcast on $G$ such that $f(v) = 1$ for each $v\\in V^+_f$, then $V^+_f$ is a [*minimal dominating set*]{} in $G$, and the minimum (resp. ", "maximum) cost of such a broadcast is the [*domination number $\\gamma(G)$*]{} (resp. ", "the [*upper domination number $\\Gamma(G)$*]{}) of $G$.\n\n#### Irredundant broadcasts.", "\n\nA broadcast $f$ on $G$ is an [*irredundant broadcast*]{} if $PB_f(v) \\neq \\emptyset$ for every vertex $v\\in V^+_f$. Stated equivalently, a broadcast $f$ is irredundant if the following two conditions are satisfied : (i) for every $f$-broadcast vertex $v$ with $f(v) \\geq 2$, there exists a vertex $u$ such that $H_f(u) = \\{v\\}$ and $d_G(u,v) = f(v)$, and (ii) for every $f$-broadcast vertex $v$ with $f(v)=1$, there exists a vertex $u \\in N_G[v]$ such that $H_f(u) = \\{v\\}$ (note that, in this case, we can have $u=v$). ", "The [*upper broadcast irredundance number*]{} $I\\!R_b(G)$ of $G$ is the maximum cost of an irredundant broadcast on $G$. The [*broadcast irredundance number*]{} $ir_b(G)$ of $G$ is the minimum cost of a maximal irredundant broadcast on $G$. If $f$ is a maximal irredundant broadcast on $G$ such that $f(v) = 1$ for each $v\\in V^+_f$, then $V^+_f$ is a [*maximal irredundant set*]{} in $G$, and the minimum (resp. ", "the maximum) cost of such a broadcast is the [*irredundance number $ir(G)$*]{} (resp. ", "the [*upper irredundance number $I\\!R(G)$*]{}) of $G$.\n\n#### Independent broadcasts.", "\n\nA broadcast $f$ is an [*independent broadcast*]{} if no broadcast vertex $f$-dominates any other broadcast vertex or, equivalently, if for every $v \\in V^+_f$, $|H_f(v)| = 1$. The [*broadcast independence number*]{} $\\beta_b(G)$ of $G$ is the maximum cost of an independent broadcast on $G$. The [*lower broadcast independence number*]{} $i_b(G)$ of $G$ is the minimum cost of a maximal independent broadcast on $G$. If $f$ is a maximal independent broadcast such that $f(v) = 1$ for each $v\\in V^+_f$, then $V^+_f$ is a [*maximal independent set*]{} in $G$, and the maximum (resp. ", "minimum) cost of such a broadcast is the [*vertex independence number $\\beta_0(G)$*]{} (resp. ", "the [*independent domination number $i(G)$*]{}) of $G$.\n\n#### Packing broadcasts.", "\n\nA broadcast $f$ is a [*packing broadcast*]{} if every vertex hears at most one broadcast, that is, for every vertex $v\\in V$, $|H_f(v)|\\leq 1$. The [*broadcast packing number*]{} $P_b(G)$ of $G$ is the maximum cost of a packing broadcast on $G$. The [*lower broadcast packing number*]{} $p_b(G)$ of $G$ is the minimum cost of a maximal packing broadcast on $G$. If $f$ is a maximal packing broadcast such that $f(v) = 1$ for each $v\\in V^+_f$, then $V^+_f$ is a [*maximal packing set*]{} in $G$, and the maximum (resp. ", "the minimum) cost of such a broadcast is the [*packing number $P(G)$*]{} (resp. ", "the [*lower packing number $p(G)$*]{}) of $G$.\n\nat (0,0)[$f_1:$]{}; [ (1,0) to (9,0); ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[$x_1$]{}; ]{} [ at (2,0); at (2,0+0.2)[1]{}; at (2,0-0.2)[$x_2$]{}; ]{} [ at (3,0); at (3,0+0.2)[1]{}; at (3,0-0.2)[$x_3$]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[$x_4$]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[$x_5$]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[$x_6$]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[$x_7$]{}; ]{} [ at (8,0); at (8,0+0.2)[3]{}; at (8,0-0.2)[$x_8$]{}; ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2)[$x_9$]{}; ]{} at (0,-2)[$f_2:$]{}; [ (1,-2) to (9,-2); ]{} [ at (1,-2); at (1,-2+0.2)[0]{}; at (1,-2-0.2)[$x_1$]{}; ]{} [ at (2,-2); at (2,-2+0.2)[1]{}; at (2,-2-0.2)[$x_2$]{}; ]{} [ at (3,-2); at (3,-2+0.2)[1]{}; at (3,-2-0.2)[$x_3$]{}; ]{} [ at (4,-2); at (4,-2+0.2)[0]{}; at (4,-2-0.2)[$x_4$]{}; ]{} [ at (5,-2); at (5,-2+0.2)[0]{}; at (5,-2-0.2)[$x_5$]{}; ]{} [ at (6,-2); at (6,-2+0.2)[0]{}; at (6,-2-0.2)[$x_6$]{}; ]{} [ at (7,-2); at (7,-2+0.2)[1]{}; at (7,-2-0.2)[$x_7$]{}; ]{} [ at (8,-2); at (8,-2+0.2)[1]{}; at (8,-2-0.2)[$x_8$]{}; ]{} [ at (9,-2); at (9,-2+0.2)[0]{}; at (9,-2-0.2)[$x_9$]{}; ]{} at (0,-4)[$f_3:$]{}; [ (1,-4) to (9,-4); ]{} [ at (1,-4); at (1,-4+0.2)[1]{}; at (1,-4-0.2)[$x_1$]{}; ]{} [ at (2,-4); at (2,-4+0.2)[0]{}; at (2,-4-0.2)[$x_2$]{}; ]{} [ at (3,-4); at (3,-4+0.2)[1]{}; at (3,-4-0.2)[$x_3$]{}; ]{} [ at (4,-4); at (4,-4+0.2)[0]{}; at (4,-4-0.2)[$x_4$]{}; ]{} [ at (5,-4); at (5,-4+0.2)[1]{}; at (5,-4-0.2)[$x_5$]{}; ]{} [ at (6,-4); at (6,-4+0.2)[0]{}; at (6,-4-0.2)[$x_6$]{}; ]{} [ at (7,-4); at (7,-4+0.2)[0]{}; at (7,-4-0.2)[$x_7$]{}; ]{} [ at (8,-4); at (8,-4+0.2)[2]{}; at (8,-4-0.2)[$x_8$]{}; ]{} [ at (9,-4); at (9,-4+0.2)[0]{}; at (9,-4-0.2)[$x_9$]{}; ]{} at (0,-6)[$f_4:$]{}; [ (1,-6) to (9,-6); ]{} [ at (1,-6); at (1,-6+0.2)[1]{}; at (1,-6-0.2)[$x_1$]{}; ]{} [ at (2,-6); at (2,-6+0.2)[0]{}; at (2,-6-0.2)[$x_2$]{}; ]{} [ at (3,-6); at (3,-6+0.2)[0]{}; at (3,-6-0.2)[$x_3$]{}; ]{} [ at (4,-6); at (4,-6+0.2)[1]{}; at (4,-6-0.2)[$x_4$]{}; ]{} [ at (5,-6); at (5,-6+0.2)[0]{}; at (5,-6-0.2)[$x_5$]{}; ]{} [ at (6,-6); at (6,-6+0.2)[0]{}; at (6,-6-0.2)[$x_6$]{}; ]{} [ at (7,-6); at (7,-6+0.2)[1]{}; at (7,-6-0.2)[$x_7$]{}; ]{} [ at (8,-6); at (8,-6+0.2)[0]{}; at (8,-6-0.2)[$x_8$]{}; ]{} [ at (9,-6); at (9,-6+0.2)[0]{}; at (9,-6-0.2)[$x_9$]{}; ]{}\n\nThese four different types of broadcasts are illustrated in Figure \\[fig:broadcasts\\] (broadcast vertices are drawn as black vertices, non-broadcast dominated vertices as gray vertices, and non dominated vertices as white vertices): $f_1$ is a dominating broadcast, $f_2$ is an irredundant broadcast (the $f_2$-broadcast vertices $x_2$, $x_3$, $x_7$ and $x_8$ all have a bordering private $f_2$-neighbor, namely $x_1$, $x_4$, $x_6$ and $x_9$, respectively), $f_3$ is an independent broadcast, and $f_4$ is a packing broadcast. ", "Moreover, observe the following:\n\n- $f_1$ is a [*minimal*]{} dominating broadcast and also a maximal irredundant broadcast. ", "However, $f_1$ is neither an independent broadcast (the $f_1$-broadcast vertices $x_2$ and $x_3$ are both $f_1$-dominated twice), nor a packing broadcast ($x_2$ and $x_3$ both hear two $f_1$-broadcast vertices).", "\n\n- $f_2$ is a [*maximal*]{} irredundant broadcast, but is neither a dominating broadcast ($x_5$ is not $f_2$-dominated), nor an independent broadcast (the $f_2$-broadcast vertices $x_2$, $x_3$, $x_7$ and $x_8$ are $f_2$-dominated twice), nor a packing broadcast ($x_2$, $x_3$, $x_7$ and $x_8$ all hear two $f_2$-broadcast vertices).", "\n\n- $f_3$ is a [*maximal*]{} independent broadcast and a dominating broadcast, but is neither an irredundant broadcast (the $f_3$-broadcast vertex $x_8$ has no bordering private $f_3$-neighbor), nor a packing broadcast (vertices $x_2$, $x_4$ and $x_6$ are $f_3$-dominated twice).", "\n\n- $f_4$ is a [*maximal*]{} packing broadcast, and also an irredundant broadcast and an independent broadcast. ", "However, $f_4$ is neither a dominating broadcast ($x_9$ is not $f_4$-dominated), nor a maximal independent broadcast (we can increase the cost of $f_4$ by setting $f_4(x_1)=f_4(x_4)=f_4(x_7)=2$), nor a maximal irredundant broadcast (we can increase the cost of $f_4$ by setting $f_4(x_7)=2$, so that $x_4$ has still a bordering private $f_4$-neighbor, namely $x_3$, and $x_9$ is now the bordering private $f_4$-neighbor of $x_7$).", "\n\nDirectly from the definitions of these four types of broadcasts, we get the following observations.", "\n\n\\[obs:definitions\\]\n\n- Every maximal independent broadcast is a dominating broadcast, and thus $\\gamma_b(G)\\le i_b(G)$ for every graph $G$.\n\n- Every packing broadcast is an independent broadcast, and thus $P_b(G)\\le \\beta_b(G)$ for every graph $G$.\n\n- \\[obs:definitions-item3\\] Every packing broadcast is an irredundant broadcast, and thus $P_b(G)\\le I\\!R_b(G)$ for every graph $G$.\n\n- Every dominating maximal irredundant broadcast is a minimal dominating broadcast.", "\n\nBroadcast domination was introduced by Erwin [@Erw01] in his Ph.D. thesis, in which he discussed several types of broadcast parameters and the relationships between them. ", "Many of these results appeared later in [@Dun]. ", "Since then, several papers have been published on various aspects of broadcasts in graphs, including the algorithmic complexity [@BR18Alg; @HeLo06; @HeSae12], the determination of the broadcast domination number for several classes of graphs [@BHM04; @BS11; @Da07; @H06; @MW15; @Se08; @SK14], and a characterization of the classes of trees for which the broadcast domination number equals the radius [@HM09] or equals the domination number [@CHM10; @LM15; @MW13]. ", "The upper broadcast domination number is studied in [@AFSHL15; @BF16; @Dun; @Erw04; @GM17; @MR16], the broadcast irredundance number is studied in [@AFSHL15; @MR16], and the broadcast independence number is studied in [@A19; @ABS18; @ABS19; @BR18Ind; @BR18Inv; @BouZe12]. ", "Broadcast domination and multipacking are considered in [@BB18; @BBF18; @BMY19; @BMT13; @HM14; @MT].", "\n\nIn this paper, we determine all the above defined numbers for paths and cycles. ", "Ahmadi [*et al.*]{} ", "observed in [@AFSHL15] that very little is known concerning these parameters. ", "We first recall some preliminary results in Section \\[sec:preliminary\\], and prove our main results in Section \\[sec:paths-cycles\\]. ", "These results are summarized in Table \\[tab:paths-cycles\\]. ", "They confirm the conjectures given in [@AFSHL15] for $\\gamma_b(P_n)$, $\\gamma_b(C_n)$ and $\\Gamma_b(P_n)$, but disprove all other conjectures.", "\n\nPreliminary results {#sec:preliminary}\n===================\n\nThe characterization of minimal dominating broadcasts was first given by Erwin in [@Erw04], and then restated in terms of private borders[^3] by Mynhardt and Roux in [@MR16].", "\n\n\\[prop:Erwin-PB-nonempty\\] A dominating broadcast $f$ is a minimal dominating broadcast if and only if $PB_f(v)\\neq \\emptyset$ for each $v\\in V^+_f$.\n\nDunbar [*et al.*]{} ", "proved in [@Dun] the following bound on the upper broadcast domination number of graphs.", "\n\n\\[th:Dunbar-Gamma-m\\] For every graph $G$ with size $m$, $\\Gamma_b(G) \\leq m$. Moreover, $\\Gamma_b(G)=m$ if and only if $G$ is a nontrivial star or path.", "\n\nThis upper bound was later improved in [@BF16].", "\n\n\\[th:Bouchemakh-Fergani\\] If $G$ is a graph of order $n$ with minimum degree $\\delta(G)$, then $\\Gamma_b (G) \\leq n-\\delta(G)$, and this bound is sharp.", "\n\nFrom Proposition \\[prop:Erwin-PB-nonempty\\] and the definition of a maximal irredundant broadcast, one gets the following result.", "\n\n\\[cor:Ahmadi-MinDom-is-MaxIR\\] Every minimal dominating broadcast is a maximal irredundant broadcast.", "\n\nSince the characteristic function of a minimal dominating set in a graph is a minimal dominating broadcast, Corollary \\[cor:Ahmadi-MinDom-is-MaxIR\\] implies the following chain of inequalities.", "\n\n\\[cor:Ahmadi-inequalities\\] For every graph $G$, $$ir_b(G)\\leq \\gamma_b(G) \\leq \\gamma(G) \\leq \\Gamma(G) \\leq \\Gamma_b(G) \\leq I\\!R_b(G).$$\n\nMoreover, Dunbar [*et al.*]{}", " [@Dun] proved the following.", "\n\n\\[prop:Dunbar-inequalities\\] For every graph $G$, $$\\gamma_b(G) \\leq i_b(G) \\leq \\beta_b(G) \\geq i(G) \\geq \\gamma(G) \\geq \\gamma_b(G).$$ However, $\\beta_b(G)$ and $\\Gamma_b(G)$ are in general incomparable.", "\n\nIt is worth pointing out that the difference $I\\!R_b(G)-\\Gamma_b(G)$ can be arbitrarily large. ", "Indeed, Mynhardt and Roux [@MR16] constructed a family of graphs $\\{G_r\\}_{r\\geq 3}$, where each $G_r$ is obtained by joining two copies of $K_{r+1}$ by $r$ independent edges, and proved the relation $\\Gamma_b(G_r) = 3 \\leq I\\!R_b(G_r) = r$ for every $r \\geq 3$. Nevertheless, we may have $I\\!R_b(G)=\\Gamma_b(G)$, as we will prove in Subsection \\[subsec:IR-Gamma\\] when $G$ is a path or a cycle.", "\n\nDunbar [*et al.*]{} ", "observed in [@Dun] that, for any graph $G$, neither $P(G)$ nor $p(G)$ is comparable with $p_b(G)$, while we have $p(G)\\leq P(G) \\leq P_b(G)$ and $p_b(G)\\leq {\\mbox{ rad}}(G)\\leq {\\mbox{ diam}}(G) \\leq P_b(G) \\leq \\beta_b(G)$. For paths and cycles, we will prove in Section \\[sec:paths-cycles\\] that the lower bound $\\diam(G)$ for $P_b(G)$ is achieved, while the difference between $\\rad(G)$ and $p_b(G)$ can be arbitrarily large.", "\n\nBroadcast numbers of paths and cycles {#sec:paths-cycles}\n=====================================\n\nAs mentioned by Ahmadi [*et al.*]{} ", "in [@AFSHL15], it is quite surprising that the values of several broadcast parameters have not been determined yet for paths or cycles. ", "Moreover, in the same paper, they conjecture the values of these parameters. ", "In this section, we will determine the exact values of these parameters, which in some cases, but not all, correspond to their conjecture.", "\n\nThroughout this section, we will denote by $P_n=x_1x_2\\dots x_n$, $n\\geq 2$, the path of order $n$, and by $C_n=x_0x_1\\dots x_{n-1}$, $n\\geq 3$, the cycle of order $n$. Moreover, we assume throughout this section that subscripts of vertices of $C_n$ are taken modulo $n$, and that the vertices $x_1,\\dots,x_n$ of $P_n$ are “ordered” from left to right, so that by the [*leftmost*]{} (resp. ", "the [*rightmost*]{}) vertex in $P_n$ satisfying any property, we mean the vertex with minimum (resp. ", "maximum) subscript satisfying this property.", "\n\nUpper broadcast domination number and upper broadcast irredundance number {#subsec:IR-Gamma}\n-------------------------------------------------------------------------\n\nWe first consider the case of paths.", "\n\n\\[th:Gamma\\_IR\\_paths\\] For every integer $n\\geq 2$, $\\Gamma_b(P_n)= I\\!R_b(P_n)= \\diam(P_n)=n-1$.\n\nTheorem \\[th:Dunbar-Gamma-m\\] directly gives $\\Gamma_b(P_n)= n-1$. By Corollary \\[cor:Ahmadi-inequalities\\], we have $n-1=\\Gamma_b(P_n)\\leq I\\!R_b(P_n)$. We now prove the opposite inequality. ", "Let $f$ be an irredundant broadcast on $P_n$, and let $V^+_f= \\{x_{i_1},\\dots,x_{i_t}\\}$, $i_1<\\cdots < i_t$, $t\\geq 1$. From the definition of an irredundant broadcast, we get that for every vertex $x_{i_j}\\in V^+_f$ with $f(x_{i_j})\\geq 2$, there exists a vertex $x_{i_j}^p$ such that $H_f(x_{i_j}^p) = \\{x_{i_j}\\}$ and $d_{P_n}(x_{i_j},x_{i_j}^p) = f(x_{i_j})$ and, for every vertex $x_{i_j}\\in V^+_f$ with $f(x_{i_j})=1$, there exists a vertex $x_{i_j}^p \\in N_{P_n}[x_{i_j}]$ such that $H_f(x_{i_j}^p) = \\{x_{i_j}\\}$.\n\nLet $t'$, $0\\le t'\\le t$, denote the number of $f$-broadcast vertices $x_{i_j}$ that are their own bordering private $f$-neighbor, that is, such that $x_{i_j}^p=x_{i_j}$ (which implies $f(x_{i_j})=1$), and suppose that these vertices are $\\{x_{i_1},\\dots,x_{i_{t'}}\\}$. We thus have $$|V(P_n)| \\geq t' + \\sum_{j=t'+1}^t \\big(d_{P_n}(x_{i_j},x_{i_j}^p)+1\\big) \n\\geq \\sum_{j=1}^{t'} f(x_{i_j}) + \\sum_{j=t'+1}^t \\big(f(x_{i_j})+1\\big) = I\\!R_b(P_n) + t-t',$$ which gives $I\\!R_b(P_n)\\leq n-t+t'$. If $t'<t$, then $I\\!R_b(P_n)\\leq n-1$ and we are done. ", "Otherwise, every $f$-broadcast vertex is its own bordering private $f$-neighbor, which implies that $V^+_f$ is either the set of all vertices with even subscript, or the set of all vertices with odd subscript. ", "In both cases, we get $\\sigma(f)=I\\!R_b(P_n) \\le \\left\\lceil\\frac{n}{2}\\right\\rceil\\le n-1$, as required.", "\n\nWe now consider the case of cycles. ", "For that, we will use the following lemma.", "\n\n\\[lem:IR-pas-deux-H-vides\\] Let $f$ be an $I\\!R_b$-broadcast on $C_n$. If $H_f(x_{i})= \\emptyset$ for some vertex $x_i$, then $H_f(x_{i-1})\\neq \\emptyset$ and $H_f(x_{i+1})\\neq \\emptyset$.\n\nAssume to the contrary that we have $H_f(x_{i-1})=\\emptyset$, so that $x_{i-1}$ is not $f$-dominated, which implies in particular $f(x_{i-2})=0$. Therefore, there exists an $f$-broadcast vertex $x_j$, $j<i-2$, which $f$-dominates $x_{i-2}$, for otherwise we could set $f(x_{i-1})=1$, contradicting the optimality of $f$.\n\nWe then necessarily have $d_{C_n}(x_j,x_{i-2})=f(x_j)$. But, in that case, the function $g$ obtained from $f$ by setting $g(x_j)=0$ and $g(x_{j+1})=f(x_j)+1$ would be an irredundant broadcast on $C_n$ with cost $\\sigma(g)=\\sigma(f)+1 > \\sigma(f)$, again a contradiction. ", "It follows that we have $H_f(x_{i-1})\\neq \\emptyset$ and, by symmetry, that we also have $H_f(x_{i+1})\\neq \\emptyset$.\n\n[ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (9,0); ]{} [ (-1,0) to (0,0); ]{} [ (9,0) to (10,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2); ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2); ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2); ]{} [ at (3,0); at (3,0+0.2)[3]{}; at (3,0-0.2); ]{} [ at (4,0); at (4,0+0.2)[3]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**3**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2); ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2); ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2); ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2); ]{}\n\nWe can now prove the following result.", "\n\n\\[th:IR-egal-Gamma-Cn\\] For every integer $n\\geq 3$, $I\\!R_b(C_n)=\\Gamma_b(C_n)$.\n\nBy Corollary \\[cor:Ahmadi-inequalities\\], we only need to prove the inequality $I\\!R_b(C_n) \\leq \\Gamma_b(C_n)$. For this, it is enough to construct, from any non-dominating $I\\!R_b$-broadcast on $C_n$, a dominating irredundant broadcast (which is then a minimal dominating broadcast, by Observation \\[obs:definitions\\](4)) with the same cost $I\\!R_b(C_n)$.\n\nLet $f$ be a non-dominating $I\\!R_b$-broadcast on $C_n$. Then, there exists $i\\in \\{0,\\dots,n-1\\}$ such that $H_f(x_i)=\\emptyset$. By Lemma \\[lem:IR-pas-deux-H-vides\\], we have $H_f(x_{i-1})\\neq \\emptyset$ and $H_f(x_{i+1})\\neq \\emptyset$. Since $x_i$ is not $f$-dominated, we know that $x_{i-1}$ is $f$-dominated by a unique $f$-broadcast vertex, say $x_j$, $j<i-1$, such that $f(x_j)=d_{C_n}(x_j,x_{i-1})$, which implies $|PB_f(x_j)| \\geq 1$. We claim that we have $|PB_f(x_j)|=1$. Indeed, if $|PB_f(x_j)|=2$ , then we could set $f(x_{j+1})=f(x_j)$, contradicting the optimality of $f$. Now, observe that the function $g$ obtained from $f$ by setting $g(x_j)=0$ and $g(x_{j+1})=f(x_j)$ is an irredundant broadcast with $\\sigma(g) = \\sigma(f)$, such that $x_i$ is $g$-dominated, and all vertices that were $f$-dominated remain $g$-dominated (see Figure \\[fig:th-IRCn\\]) . ", "Repeating the same transformation for each vertex which is not dominated, we eventually produce a minimal dominating broadcast on $C_n$ with cost $I\\!R_b(C_n)$.\n\nWe obviously have $\\Gamma_b(C_3)=1$. For $n\\geq 4$, the value of $\\Gamma_b(C_n)$ is given by the following result.", "\n\n\\[th:Gamma-Cn\\] For every integer $n\\geq 4$, $\\Gamma_b(C_n)= 2\\big(\\left\\lfloor\\frac{n}{2}\\right\\rfloor-1\\big)$.\n\nFrom Theorem \\[th:Bouchemakh-Fergani\\], we directly get $\\Gamma_b(C_n)\\leq n-\\delta(C_n)=n-2$. Let now $f$ be the function defined by $$f(x_i) =\\left\\{\\begin{array}{cl}\n \\left\\lfloor\\frac{n}{2}\\right\\rfloor -1 & \\text{if } i\\in \\big\\{\\left\\lfloor\\frac{n}{2}\\right\\rfloor, \\left\\lceil\\frac{n}{2}\\right\\rceil +1\\big\\},\\\\[1ex]\n 0& \\text{otherwise}.", "\n \\end{array}\n \\right.$$ Clearly, $f$ is a minimal dominating broadcast on $C_n$ with cost $$\\sigma(f)=\n\\left\\{\n\\begin{array}{ll}\n n-2 & \\text{if } n\\text{ is even,}\\\\\n n-3 & \\text{if } n\\text{ is odd.}", "\n\\end{array}\n\\right.$$ Therefore, $\\sigma(f) \\leq \\Gamma_b(C_n)$. Combining this inequality with the previous one, we already infer that we have $\\Gamma_b(C_n)= n-2$ if $n$ is even, and $n-3\\leq \\Gamma_b(C_n)\\leq n-2$ if $n$ is odd.", "\n\nIt remains to discuss the case $n$ odd. ", "For $n=5$, it is not difficult to check that we have $\\Gamma_b(C_5)=2$. Suppose $n\\ge 7$ and let $g$ be any $\\Gamma_b$-broadcast on $C_n$ such that $V^+_g=\\{x_{i_1},\\dots,x_{i_t}\\}$, $i_1<\\cdots < i_t$, $t\\ge 1$. We first prove the following claim.", "\n\n\\[cl:t=2\\] $t=2$.\n\nIf $t=1$, then there is a unique $g$-broadcast vertex $x_i\\in V^+_g$, and thus $\\Gamma_b(C_n)=g(x_i) =e_{C_n}(x_i)=\\frac{n-1}{2}<n-3$, a contradiction. ", "Hence, $t\\ge 2$. We know by Proposition \\[prop:Erwin-PB-nonempty\\] that each $g$-broadcast vertex $x_i\\in V^+_g$ has a bordering private $g$-neighbor, say $x_i^p$, with possibly $x_i^p=x_i$ (and, in that case, $g(x_i)=1$). ", "Let $Q_{x_i}$ be the set of edges defined as follows:\n\n- if $g(x_i)\\geq 2$, then $Q_{x_i}$ is the set of edges of the unique $(x_i,x_i^p)$-geodesic,\n\n- if $g(x_i)=1$ and $x_i^p\\in\\{x_{i-1},x_{i+1}\\}$ is a bordering private $g$-neighbor of $x_i$, then $Q_{x_i}$ is the singleton $\\{x_ix_{i}^p\\}$,\n\n- if $g(x_i)=1$ and $x_i$ is its own bordering private $g$-neighbor, then $Q_{x_i}$ is the singleton $\\{x_{i}x_{i+1}\\}$.\n\nClearly, $g(x_i)=|Q_{x_i}|$ for every $x_i\\in V^+_g$, and $Q_{x_i}\\cap Q_{x_j}=\\emptyset$ for every $x_i,x_j\\in V^+_g$.\n\nWe now claim that for every $Q_{x_i}=\\{x_ix_{i+1},\\dots,x_{i+t-1}x_{i+t}\\}$ (resp. ", "$Q_{x_i}=\\{x_{i-t}x_{i-t+1},\\dots,x_{i-1}x_{i}\\}$), $t\\ge 1$, the edge $x_{i+t}x_{i+t+1}$ (resp. ", "$x_{i}x_{i+1}$) that “follows” $Q_{x_i}$ does not belong to any $Q_{x_{i'}}$, with $x_{i'}\\in V^+_g$. Indeed, this directly follows from the following observations.", "\n\n- Every $g$-broadcast vertex $x_i$ belongs to exactly one such path, namely $Q_{x_i}$.\n\n- Every bordering private $g$-neighbor belongs to at most one such path.", "\n\n- An end-vertex $x_j$ of such a path $Q$ is neither a $g$-broadcast vertex nor a bordering private $g$-neighbor if and only if $Q=Q_{x_{j-1}}$, $x_{j-1}$ is a $g$-broadcast vertex, $g(x_{j-1})=1$ and $x_{j-1}$ is its own bordering private $g$-neighbor.", "\n\nHence, we have $$\\Gamma_b(C_n)= \\sum_{x_i\\in V^+_g}g(x_i) = \\sum_{x_i\\in V^+_g}|Q_{x_i}| = |\\cup_{x_i\\in V^+_g}Q_{x_i}| \\leq n-|V^+_g| = n-t.$$ If $t>3$, then $\\Gamma_b(C_n)< n-3$, a contradiction. ", "Assume now that $t=3$ and let $V^+_g=\\{x_a,x_b,x_c\\}$, with $a<b<c$. Since $\\Gamma_b(C_n) = n-3$, any two of the paths $Q_{x_a}$, $Q_{x_b}$ and $Q_{x_c}$ are separated by exactly one edge.", "\n\nSuppose first that one of these $g$-broadcast vertices, say $x_c$, is such that $g(x_c)=1$ and $x_c$ is its own private $g$-neighbor, so that $Q_{x_c} = x_cx_{c+1}$. In that case, $x_{c-1}$ is neither a $g$-broadcast vertex nor a bordering private $g$-neighbor, which implies, by observation $(c)$ above, that $x_b=x_{c-2}$, $g(x_b)=1$ and $x_b$ is its own bordering private $g$-neighbor. ", "Using the same argument, we get that $x_a=x_{b-2}$, $g(x_a)=1$, $x_a$ is its own bordering private $g$-neighbor, and $x_c=x_{a-2}$, leading to $n=6$, a contradiction since we assumed $n\\ge 7$.\n\nHence, each end-vertex of any of the paths $Q_{x_a}$, $Q_{x_b}$ and $Q_{x_c}$ is either a $g$-broadcast vertex or a bordering private $g$-neighbor of the $g$-broadcast vertex belonging to the same path. ", "But since we have three paths, one of $x_a$, $x_b$ or $x_c$ must be adjacent to a bordering private $g$-neighbor of another $g$-broadcast vertex, a contradiction.", "\n\nBy Claim \\[cl:t=2\\], we can assume $V^+_g=\\{x_a,x_b\\}$, which implies $|PB_f(x_a)|=|PB_f(x_b)|$. If $|PB_f(x_a)|=|PB_f(x_b)|=2$, then $n=2f(x_a)+1+2f(x_b)+1$, a contradiction since $n$ is odd. ", "We thus have $|PB_f(x_a)|=|PB_f(x_b)|=1$, and the bordering private $g$-neighbors $x_a^p$ of $x_a$, and $x_b^p$ of $x_b$ are adjacent. ", "Moreover, if we assume, without loss of generality, that $x_{a}x_{a+1}\\dots x_b$ is a $(x_a,x_b)$-geodesic, then $b-a\\leq 2$ for otherwise the function $h$ obtained from $g$ by setting $h(x_a)=0$, $h(x_b)=0$, $h(x_{a+1})=g(x_a)+1$ and $h(x_{b-1})=g(x_b)+1$, would be a minimal dominating broadcast with cost $\\Gamma_b(h)=\\Gamma_b(g)+2$, contradicting the optimality of $g$. Hence, we have $d_{C_n}(x_a,x_b)\\leq 2$. If $x_a$ and $x_b$ are joined by an edge, we necessarily have $g(x_a)=g(x_b)$, implying that $n$ is even, contrary to our assumption. ", "We thus have $d_{C_n}(x_a,x_b)=2$, and thus $g(x_a)=g(x_b)=\\frac{n-3}{2}$, which gives $\\sigma(g)=n-3$.\n\nBroadcast independence number and lower broadcast independence number\n---------------------------------------------------------------------\n\nDunbar [*et al.*]{}", " [@Dun] noted that the upper broadcast domination number $\\Gamma_b(G)$ and the broadcast independence number $\\beta_b(G)$ of a graph $G$ are in general incomparable. ", "Erwin gave in [@Erw01] the exact value of the broadcast independence number of paths. ", "He proved that for every integer $n\\geq 3$, $\\beta_b(P_n) = 2(n - 2)$, so that, by Theorem \\[th:Gamma\\_IR\\_paths\\], $\\beta_b(P_n) > \\Gamma_b(P_n)$ for every $n>3$.\n\nOur next result proves that the equality $\\beta_b(C_n)=\\Gamma_b(C_n)$ holds for every cycle $C_n$, $n\\ge 3$ (recall Theorem \\[th:Gamma-Cn\\]).", "\n\n\\[th:beta-cycles\\] For every integer $n\\geq 3$, $\\beta_b(C_n)=2\\big(\\left\\lfloor\\frac{n}{2}\\right\\rfloor-1\\big)$.\n\nIt is easy to check that we have $\\beta_b(C_3)=1$ and $\\beta_b(C_4)=2$. Assume thus $n\\ge 5$. Clearly, the function $f$ defined by $$f(x_i) =\\left\\{\\begin{array}{cl}\n \\left\\lfloor\\frac{n}{2}\\right\\rfloor-1 & \\text{if } i\\in \\big\\{0,\\left\\lfloor\\frac{n}{2}\\right\\rfloor\\big\\},\\\\[1ex]\n 0& \\text{otherwise},\n \\end{array}\n \\right.$$ is an independent broadcast on $C_n$ with cost $\\sigma(f)= 2(\\lfloor\\frac{n}{2}\\rfloor-1)$, which implies $\\beta_b(C_n)\\geq 2(\\lfloor\\frac{n}{2}\\rfloor-1)$.\n\nWe now prove the opposite inequality. ", "For this, let $g$ be any $\\beta_b$-broadcast on $C_n$. If $|V^+_g| = 1$, say $V^+_g=\\{x_i\\}$, then $$\\sigma(g) = g(x_i) = e_{C_n}(x_i) = \\left\\lfloor\\frac{n}{2}\\right\\rfloor \\leq 2\\Big(\\left\\lfloor\\frac{n}{2}\\right\\rfloor-1\\Big),$$ and, if $|V^+_g| = 2$, then the two vertices of $V^+_g$ are antipodal, which gives $\\sigma(g)=2(\\lfloor\\frac{n}{2}\\rfloor-1)$.\n\nAssume now that we have $|V^+_g|\\geq 3$, and let $V^+_g = \\{x_{i_0},\\dots,x_{i_{k-1}}\\}$, $k\\ge 3$. Since $g$ is an independent broadcast, we have $d_{C_n}(x_{i_j},x_{i_{j+1}}) \\geq g(x_{i_j})+1$ for every $j$, $0\\le j\\le k-1$ (subscripts of $i$ are taken modulo $k$). ", "We thus get $$\\beta_b(C_n)=\\sigma(g) = \\sum_{x_{i_j}\\in V^+_g}g(x_{i_j}) \\leq \\sum_{x_{i_j}\\in V^+_g}(d_{C_n}(x_{i_j},x_{i_{j+1}})-1) = n-|V^+_g| \\leq n-3 \\leq 2\\Big(\\left\\lfloor\\frac{n}{2}\\right\\rfloor-1\\Big),$$ as required.", "\n\nWe now determine the value of the lower broadcast independence number of paths and cycles. ", "For that, we will use the following lemma.", "\n\n\\[lem:obs-i\\] If $f$ is an $i_b$-broadcast on $P_n$, $n\\ge 3$, with $V^+_f=\\{x_{i_1},\\dots,x_{i_t}\\}$, $i_1<\\cdots < i_t$, $t\\ge 2$, then we have\n\n1. ", " $f(x_{i_1}) \\geq f(x_{i_2})$ and $f(x_{i_t}) \\geq f(x_{i_{t-1}})$,\n\n2. ", " $d_{P_n}(x_1,x_{i_1})\\le f(x_{i_1})$ and $d_{P_n}(x_{i_t},x_n)\\le f(x_{i_t})$,\n\n3. ", " for every $j$, $1\\le j\\le t-1$, $\\max\\{f(x_{i_j}),f(x_{i_{j+1}})\\} + 1 \\leq d_{P_n}(x_{i_j},x_{i_{j+1}}) \\leq f(x_{i_j}) + f(x_{i_{j+1}}) + 1$,\n\n4. ", " $d_{P_n}(x_{i_1},x_{i_2})=f(x_{i_1})+1$ and $d_{P_n}(x_{i_{t-1}},x_{i_t}) = f(x_{i_t})+1$.\n\nIf Item 1 is not satisfied, then we can increase by 1 the value of $f(x_1)$ or $f(x_n)$, contradicting the maximality of $f$.\n\nIf Item 2 is not satisfied, then we can set $f(x_1)=1$, or $f(x_n)=1$, contradicting the maximality of $f$.\n\nFor Item 3, the inequality $\\max\\{f(x_{i_j}),f(x_{i_{j+1}})\\} + 1 \\leq d_{P_n}(x_{i_j},x_{i_{j+1}})$ directly follows from the definition of an independent broadcast. ", "Finally, if $d_{P_n}(x_{i_j},x_{i_{j+1}}) > f(x_{i_j}) + f(x_{i_{j+1}}) + 1$, then we can set $f(x_{i_j+f(x_{i_j})+1})=1$, contradicting the maximality of $f$.\n\nConsider now Item 4. ", "By items 1 and 3, we have $f(x_{i_1})+1\\leq d_{P_n}(x_{i_1},x_{i_2})$ and $f(x_{i_t})+1\\leq d_{P_n}(x_{i_{t-1}},x_{i_t})$. If any of these inequalities is strict, then we can increase by 1 the $f$-value of the involved $f$-broadcast vertex, again contradicting the maximality of $f$.\n\nIn the rest of the paper, for convenience, we will often define a broadcast function $f$ on the path $P_n$ (resp. ", "on the cycle $C_n$) by the word $f(x_1)\\dots f(x_n)$ (resp. ", "$f(x_0)\\dots f(x_{n-1})$), using standard notation from Formal Language Theory. ", "In particular, recall that when we write $(a_1\\dots a_k)^q$ for some integer $q\\ge 0$, we mean that the sequence $a_1\\dots a_k$ is repeated exactly $q$ times (in particular, if $q=0$, then $(a_1\\dots a_k)^q$ is the empty word $\\varepsilon$).", "\n\n\\[th:i-path\\] For every integer $n\\ge 2$, $i_b(P_n) = \\left\\lceil\\frac{2n}{5}\\right\\rceil.$\n\nLet $n=5q+r$, with $q\\ge 0$, $0\\leq r \\leq 4$ and $5q+r\\ge 2$. It is easy to check that the functions $10$, $010$ and $0101$ are $i_b$-broadcasts on $P_n$ with cost $\\left\\lceil\\frac{2n}{5}\\right\\rceil$ when $n=2$, $3$ and $4$, respectively.", "\n\nAssume now $n\\geq 5$. According to the value of $r$, we define the broadcasts $f_r$ on $P_n$ for each $r$, $0\\le r\\le 4$, as follows: $$f_0(P_n) = (01010)^q,\\ f_1(P_n) = (01010)^q1,\\ f_2(P_n) = (01010)^q10,$$ $$f_3(P_n) = (01010)^q101,\\ \\mbox{and}\\ f_4(P_n) = (01010)^q0101.$$\n\nIt is not difficult to check that each $f_r$, $0\\le r\\le 4$, is a maximal independent broadcast on $C_{5q+r}$, for each $q\\ge 1$, with cost $\\sigma(f_r)=\\left\\lceil\\frac{2n}{5}\\right\\rceil$, which gives $i_b(P_n)\\leq \\lceil\\frac{2n}{5}\\rceil$.\n\nLet us now consider the opposite inequality. ", "Let $f$ be an $i_b$-broadcast on $P_n$. If $|V^+_f|=1$, then we have $i_b(P_n)=rad(P_n) = \\left\\lfloor\\frac{n}{2}\\right\\rfloor$, which implies $n\\in S=\\{1,\\ldots,9,11,13\\}$, since otherwise we would have $i_b(P_n)=\\left\\lfloor\\frac{n}{2}\\right\\rfloor > \\left\\lceil\\frac{2n}{5}\\right\\rceil$, contradicting the inequality we have established before. ", "Observe also that we have $\\left\\lfloor\\frac{n}{2}\\right\\rfloor = \\left\\lceil\\frac{2n}{5}\\right\\rceil$ for every $n\\in S$, so that we are done. ", "The remaining case we have to consider is thus $n\\notin S$, which implies $|V^+_f|\\ge 2$. Let $V^+_f=\\{x_{i_1},\\dots,x_{i_t}\\}$, $i_1<\\cdots < i_t$, with $t\\ge 2$. The two following claims will prove that we can always choose $f$ such that $f(x_{i_j})=1$ for every $f$-broadcast vertex $v_{i_j}\\in V^+_f$.\n\n\\[cl:que-des-uns-bords\\] There exists an $i_b$-broadcast $g$ on $P_n$ such that $g(x_{i_1})=g(x_{i_2})=g(x_{i_{t-1}})=g(x_{i_t})=1$.\n\nWe first prove that there exists an $i_b$-broadcast $g_0$ on $P_n$ such that $g_0(x_{i_1})=g_0(x_{i_2})=1$. If $f(x_{i_1})=f(x_{i_2})=1$, then we set $g_0:=f$ and we are done. ", "So, suppose that we have $f(x_{i_1}) + f(x_{i_2}) \\geq 3$.\n\nIf $|V^+_f|=2$, then, by Lemma \\[lem:obs-i\\](4), we have $d_{P_n}(x_{i_1},x_{i_2})=f(x_{i_1})+1=f(x_{i_2})+1$. Using Lemma \\[lem:obs-i\\](2) and (3), we then get $$n = d_{P_n}(x_1,x_{i_1}) + d_{P_n}(x_{i_1},x_{i_2}) + d_{P_n}(x_{i_2},x_n) + 1 \\leq 3f(x_{i_1}) + 2,$$ and thus $\\sigma(f)=2f(x_{i_1})\\geq \\frac{2(n-2)}{3}$. Now, recall that the above defined maximal independent broadcast $f_r$, with $r=n\\mod 5$, is such that $\\sigma(f_r)=\\left\\lceil\\frac{2n}{5}\\right\\rceil$. Since $n\\ge 10$, this contradicts the optimality of $f$. We thus have $|V^+_f|\\ge 3$. We consider two cases, depending on the value of $d_{P_n}(x_{i_2},x_{i_3})$.\n\n[ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (8,0); ]{} [ (8,0) to (9,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**0**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[3]{}; at (3,0-0.2)[[**1**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**1**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[1]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2); ]{}\n\n\\(a) $i_2$ is even ($8$ in this example)\n\n0.8cm\n\n[ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (7,0); ]{} [ (7,0) to (8,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**1**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[3]{}; at (2,0-0.2)[[**1**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[1]{}; at (6,0-0.2)[[**1**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2); ]{}\n\n\\(b) $i_2$ is odd ($7$ in this example)\n\n1. ", " $f(x_{i_3})+1 \\le d_{P_n}(x_{i_2},x_{i_3}) \\le f(x_{i_3})+2$.\\\n Let $g$ be the mapping obtained from $f$ by replacing the $f$-values $0^{i_1-1}f(x_{i_1})0^{i_2-i_1-1}f(x_{i_2})$ of $x_1\\dots x_{i_1}\\dots x_{i_2}$ by $(01)^{\\frac{i_2}{2}}$ if $i_2$ is even, or by $1(01)^{\\frac{i_2-1}{2}}$ if $i_2$ is odd (see Figure \\[fig:th-ibPn-b\\]). ", "In both cases, we have $g(x_{i_2})=1$, which implies that $g$ is a maximal independent broadcast on $P_n$. We then have $$\\sigma(g) - \\sigma(f) = \\left\\lceil\\frac{i_2}{2}\\right\\rceil - f(x_{i_1}) - f(x_{i_2}).$$ By Lemma \\[lem:obs-i\\](2) and (4), we have $$i_2 = d_{P_n}(x_1,x_{i_1}) + d_{P_n}(x_{i_1},x_{i_2}) + 1 \\leq 2f(x_{i_1}) + 2,$$ and thus $$\\sigma(g) - \\sigma(f) \\leq f(x_{i_1}) + 1 - f(x_{i_1}) - f(x_{i_2}) = 1 - f(x_{i_2}).$$ The optimality of $f$ then implies $f(x_{i_2})=1$, so that we have $\\sigma(g) = \\sigma(f)$ and we can set $g_0:=g$.\n\n [ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (12,0); ]{} [ (12,0) to (13,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**0**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[3]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**1**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**1**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[3]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2); ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2); ]{} [ at (10,0); at (10,0+0.2)[0]{}; at (10,0-0.2); ]{} [ at (11,0); at (11,0+0.2)[2]{}; at (11,0-0.2); ]{} [ at (12,0); at (12,0+0.2)[0]{}; at (12,0-0.2); ]{}\n\n \\(a) $i_3-f(x_{i_3})-2$ is even ($12-2-2=8$ in this example)\n\n 0.8cm\n\n [ (0,0+0.5) to\\[bend right=45\\] (0-0.5,0) to\\[bend right=45\\] (0,0-0.5); ]{} [ (1,0) to (12,0); ]{} [ (12,0) to (13,0); ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[3]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**1**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**1**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[3]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2); ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2); ]{} [ at (10,0); at (10,0+0.2)[0]{}; at (10,0-0.2); ]{} [ at (11,0); at (11,0+0.2)[2]{}; at (11,0-0.2); ]{} [ at (12,0); at (12,0+0.2)[0]{}; at (12,0-0.2); ]{}\n\n \\(b) $i_3-f(x_{i_3})-2$ is odd ($11-2-2=7$ in this example)\n\n2. ", " $d_{P_n}(x_{i_2},x_{i_3}) \\ge f(x_{i_3})+3$.\\\n Let $g$ be the mapping obtained from $f$ by replacing the $f$-values $$0^{i_1-1}f(x_{i_1})0^{i_2-i_1-1}f(x_{i_2}) 0^{i_3-i_2-f(x_{i_3})-2}$$ of $x_1\\dots x_{i_1}\\dots x_{i_2} \\dots x_{i_3-f(x_{i_3})-2}$ by $(01)^{\\frac{i_3-f(x_{i_3})-2}{2}}$ if $i_3-f(x_{i_3})-2$ is even, or by $1(01)^{\\frac{i_3-f(x_{i_3})-3}{2}}$ if $i_3-f(x_{i_3})-2$ is odd (see Figure \\[fig:th-ibPn-b-1\\]).", "\n\n In both cases, all vertices are $g$-dominated and $g$ is clearly a maximal independent broadcast on $P_n$. We then have $$\\sigma(g) - \\sigma(f) = \\left\\lceil\\frac{i_3-f(x_{i_3})-2}{2}\\right\\rceil - f(x_{i_1}) - f(x_{i_2}).$$ By Lemma \\[lem:obs-i\\](2) and (4), we have $$i_2 = d_{P_n}(x_1,x_{i_1}) + d_{P_n}(x_{i_1},x_{i_2}) + 1 \\leq 2f(x_{i_1}) + 2,$$ and thus $i_3-f(x_{i_3})-2 \\leq 2f(x_{i_1})+f(x_{i_2})+1$. We then get $$\\sigma(g) - \\sigma(f) \\leq f(x_{i_1}) + \\left\\lceil \\frac{f(x_{i_2})+1}{2}\\right\\rceil - f(x_{i_1}) - f(x_{i_2}) = \\left\\lceil \\frac{1 - f(x_{i_2})}{2}\\right\\rceil.$$ The optimality of $f$ then implies $f(x_{i_2})\\le 2$, so that we have $\\sigma(g) = \\sigma(f)$ and we can set $g_0:=g$.\n\nObserve now that in both of the above cases we have $g_0(x_{i_j}) = f(x_{i_j})$ for every $j$, $3\\le j\\le t$. Therefore, using symmetry and starting from $g_0$ instead of $f$, we can similarly construct an $i_b$-broadcast $g$ on $P_n$ with $g(x_{i_1})=g(x_{i_2})=g(x_{i_{t-1}})=g(x_{i_t})=1$, as required.", "\n\n\\[cl:que-des-uns\\] There exists an $i_b$-broadcast $g$ on $P_n$ such that $g(x_i)=1$ for every vertex $x_i\\in V_g^+$.\n\nBy Claim \\[cl:que-des-uns-bords\\], we can suppose that $f(x_{i_1})=f(x_{i_2})=f(x_{i_{t-1}})=f(x_{i_t})=1$. If $f(x_i)=1$ for every vertex $x_i\\in V^+_f$, there is nothing to prove. ", "Suppose thus that this is not the case, which implies $t\\ge 5$, and let $x_{i_j}$, $3\\le j\\le t-2$, be the leftmost $f$-broadcast vertex for which $f(x_{i_j})\\geq 2$.\n\nWe will prove that we can always construct an $i_b$-broadcast $f'$ on $P_n$ such that the number of broadcast vertices with $f'$-value at least 2 is strictly less than the number of broadcast vertices with $f$-value at least 2. ", "We consider two cases, depending on the value of $d_{P_n}(x_{i_{j+1}},x_{i_{j+2}})$.\n\n[ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (9,0); ]{} [ (-1,0) to (0,0); ]{} [ (9,0) to (10,0); ]{} [ at (0,0); at (0,0+0.2)[1]{}; at (0,0-0.2)[[**1**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**1**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[3]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**1**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**0**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[1]{}; at (8,0-0.2)[[**1**]{}]{}; ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2); ]{}\n\n\\(a) $d=d_{P_n}(x_{i_{j-1}},x_{i_{j+1}})$ is even ($8$ in this example)\n\n0.8cm\n\n[ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (8,0); ]{} [ (-1,0) to (0,0); ]{} [ (8,0) to (9,0); ]{} [ at (0,0); at (0,0+0.2)[1]{}; at (0,0-0.2)[[**1**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**1**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[2]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**1**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[2]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2); ]{}\n\n\\(b) $d = d_{P_n}(x_{i_{j-1}},x_{i_{j+1}})$ is odd ($7$ in this example)\n\n1. ", " $f(x_{i_{j+2}})+1 \\le d_{P_n}(x_{i_{j+1}},x_{i_{j+2}}) \\le f(x_{i_{j+2}})+2$.\\\n Let $d = i_{j+1}-i_{j-1} = d_{P_n}(x_{i_{j-1}},x_{i_{j+1}}) = d_{P_n}(x_{i_{j-1}},x_{i_{j}}) + d_{P_n}(x_{i_{j}},x_{i_{j+1}})$, and $f'$ be the mapping obtained from $f$ by replacing the $f$-values $$f(x_{i_{j-1}})0^{i_j-i_{j-1}-1}f(x_{i_j})0^{i_{j+1}-i_j-1}f(x_{i_{j+1}})$$ of $x_{i_{j-1}}\\dots x_{i_j}\\dots x_{i_{j+1}}$ by $1(01)^{\\frac{d}{2}}$ if $d$ is even, or by $10(01)^{\\frac{d-1}{2}}$ if $d$ is odd (see Figure \\[fig:th-ibPn-c\\]).", "\n\n Observe that we have $f'(x_{i_{j-1}})=1$ and $f'(x_{i_{j+1}})=1$ in both cases, which implies that $f'$ is a maximal independent broadcast on $P_n$. Moreover, in both cases, we have $$\\sigma(f')-\\sigma(f) = \\left\\lfloor\\frac{d}{2}\\right\\rfloor - f(x_{i_{j}}) - f(x_{i_{j+1}}).$$\n\n Since $f(x_{i_{j-1}})=1 < f(x_{i_j})$, Lemma \\[lem:obs-i\\](3) gives $$f(x_{i_j}) + 1 \\leq d_{P_n}(x_{i_{j-1}},x_{i_{j}}) \\leq f(x_{i_j}) + 2.$$\n\n We thus consider two subcases, depending on the value of $d_{P_n}(x_{i_{j-1}},x_{i_{j}})$.\n\n 1. ", " $d_{P_n}(x_{i_{j-1}},x_{i_{j}}) = f(x_{i_j}) + 1$.\\\n By Lemma \\[lem:obs-i\\](3), we have $$d = d_{P_n}(x_{i_{j-1}},x_{i_{j}}) + d_{P_n}(x_{i_{j}},x_{i_{j+1}}) \\leq f(x_{i_{j}}) + 1 + f(x_{i_{j}}) + f(x_{i_{j+1}}) + 1\n = 2f(x_{i_{j}}) + f(x_{i_{j+1}}) + 2,$$ and thus $$\\sigma(f')-\\sigma(f) \\leq f(x_{i_{j}}) + \\left\\lfloor\\frac{f(x_{i_{j+1}})}{2}\\right\\rfloor + 1 - f(x_{i_{j}}) - f(x_{i_{j+1}})\n = \\left\\lfloor\\frac{2-f(x_{i_{j+1}})}{2}\\right\\rfloor \\leq 0.$$ The optimality of $f$ then implies the optimality of $f'$, and the number of broadcast vertices with $f'$-value at least 2 is strictly less than the number of broadcast vertices with $f$-value at least 2, as required.", "\n\n 2. ", " $d_{P_n}(x_{i_{j-1}},x_{i_{j}}) = f(x_{i_j}) + 2$.\\\n Since $f$ is maximal, we necessarily have $d_{P_n}(x_{i_{j}},x_{i_{j+1}}) = f(x_{i_j}) + 1$, since otherwise we could increase $f(x_{i_j})$ by 1. ", "This gives $$d = d_{P_n}(x_{i_{j-1}},x_{i_{j}}) + d_{P_n}(x_{i_{j}},x_{i_{j+1}}) = 2f(x_{i_j}) + 3,$$ and thus $$\\sigma(f')-\\sigma(f) = f(x_{i_{j}}) + 1 - f(x_{i_{j}}) - f(x_{i_{j+1}})\n = 1 - f(x_{i_{j+1}}) \\leq 0.$$ Again, the optimality of $f$ then implies the optimality of $f'$, and the number of broadcast vertices with $f'$-value at least 2 is strictly less than the number of broadcast vertices with $f$-value at least 2, as required.", "\n\n [ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (16,0); ]{} [ (-1,0) to (0,0); ]{} [ (16,0) to (17,0); ]{} [ at (0,0); at (0,0+0.2)[1]{}; at (0,0-0.2)[[**1**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[2]{}; at (3,0-0.2)[[**1**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**1**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[3]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2)[**[1]{}**]{}; ]{} [ at (10,0); at (10,0+0.2)[0]{}; at (10,0-0.2); ]{} [ at (11,0); at (11,0+0.2)[0]{}; at (11,0-0.2); ]{} [ at (12,0); at (12,0+0.2)[0]{}; at (12,0-0.2); ]{} [ at (13,0); at (13,0+0.2)[2]{}; at (13,0-0.2); ]{} [ at (14,0); at (14,0+0.2)[0]{}; at (14,0-0.2); ]{} [ at (15,0); at (15,0+0.2)[0]{}; at (15,0-0.2); ]{} [ at (16,0); at (16,0+0.2); at (16,0-0.2); ]{}\n\n \\(a) $d'=i_{j+2}-i_{j-1}-f(x_{i_{j+2}})-3$ is even ($13-2-3=8$ in this example)\n\n 0.8cm\n\n [ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (15,0); ]{} [ (-1,0) to (0,0); ]{} [ (15,0) to (16,0); ]{} [ at (0,0); at (0,0+0.2)[1]{}; at (0,0-0.2)[[**1**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**1**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[2]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**1**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[3]{}; at (7,0-0.2)[[**0**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[1]{}; ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2); ]{} [ at (10,0); at (10,0+0.2)[0]{}; at (10,0-0.2); ]{} [ at (11,0); at (11,0+0.2)[0]{}; at (11,0-0.2); ]{} [ at (12,0); at (12,0+0.2)[2]{}; at (12,0-0.2); ]{} [ at (13,0); at (13,0+0.2)[0]{}; at (13,0-0.2); ]{} [ at (14,0); at (14,0+0.2)[0]{}; at (14,0-0.2); ]{} [ at (15,0); at (15,0+0.2); at (15,0-0.2); ]{}\n\n \\(b) $d'=i_{j+2}-i_{j-1}-f(x_{i_{j+2}})-3$ is odd ($12-2-3=7$ in this example)\n\n2. ", " $d_{P_n}(x_{i_{j+1}},x_{i_{j+2}}) \\geq f(x_{i_{j+2}})+3$.\\\n Let $d'= d_{P_n}( x_{i_{j+2}-f( x_{i_{j+2}} )-2}, x_{i_{j-1}+1}) =\n i_{j+2}-f(x_{i_{j+2}})-2-i_{j-1}-1=i_{j+2}-i_{j-1}-f(x_{i_{j+2}})-3$, and $f'$ be the mapping obtained from $f$ by replacing the $f$-values $$f(x_{i_{j-1}})0^{i_j-i_{j-1}-1}f(x_{i_j})0^{i_{j+1}-i_j-1}f(x_{i_{j+1}}) 0^{i_{j+2}-f(x_{i_{j+2}})-2 - i_{j+1} }$$ of $x_{i_{j-1}}\\dots x_{i_j}\\dots x_{i_{j+1}} \\dots x_{i_{j+2}-f(x_{i_{j+2}})-2} $ by $10(01)^{\\frac{d'}{2}}$ if $d'$ is even, or by $1(01)^{\\frac{d'+1}{2}}$ if $d'$ is odd (see Figure \\[fig:th-ibPn-c-1\\]).", "\n\n Since $i_{j+2}-i_{j+1} \\leq f(x_{i_{j+1}})+f(x_{i_{j+2}})+1$ and $i_{j+1}-i_{j-1} \\leq 2f(x_{i_j})+f(x_{i_{j+1}})+2$, we get $i_{j+2}-i_{j-1} \\leq 2\\ f(x_{i_j})+2f(x_{i_{j+1}}) +f(x_{i_{j+2}})+3$ and thus $d'\\leq 2f(x_{i_j})+2f(x_{i_{j+1}})$.\n\n Hence, the mapping $f'$ is a maximal independent broadcast on $P_n$ and we have $$\\sigma(f')-\\sigma(f) = \\left\\lceil\\frac{d'}{2}\\right\\rceil - f(x_{i_{j}}) - f(x_{i_{j+1}}) \n \\le \\left\\lceil\\frac{2f(x_{i_j})+2f(x_{i_{j+1}})}{2}\\right\\rceil - f(x_{i_{j}}) - f(x_{i_{j+1}}) = 0.$$ The optimality of $f$ then implies the optimality of $f'$, and the number of broadcast vertices with $f'$-value at least 2 is strictly less than the number of broadcast vertices with $f$-value at least 2, as required.", "\n\nIn each case, we were able to construct an $i_b$-broadcast $f'$ such that the number of broadcast vertices with $f'$-value at least 2 is strictly less than the number of broadcast vertices with $f$-value at least 2, as required. ", "Repeating this construction until no such broadcast vertex exists, we eventually get an $i_b$-broadcast $g$ such that $g(x_{i_j})=1$ for every $g$-broadcast vertex $x_{i_j}$. This completes the proof of Claim \\[cl:que-des-uns\\].", "\n\nBy Claim \\[cl:que-des-uns\\], we can thus now assume that the $i_b$-broadcast $f$ is such that $f(x_{i_j})=1$ for every $f$-broadcast vertex $x_{i_j}$. It remains to prove that, for every $n\\ge 5$, $\\sigma(f)=\\left\\lceil\\frac{2n}{5}\\right\\rceil$.\n\nFor that, we first prove the following claim. ", "Let $w_f$ denote the word on the alphabet $\\{0,1\\}$ defined by $w_f = f(x_1)\\dots f(x_n)$.\n\n\\[cl:2n-sur-5\\] There exists an $i_b$-broadcast $f$ on $P_n$, $n\\geq 5$, such that $f(x_{i_j})=1$ for every $f$-broadcast vertex $x_{i_j}$, that satisfies the following properties:\n\n1. ", " $w_f$ does not contain the factor $000$, and\n\n2. ", " $w_f$ does not contain the factor $1001001$.\n\n3. ", " $0101$ is a prefix of $w_f$,\n\n4. ", " either $101$ or $1010$ is a suffix of $w_f$.\n\nIf $f(x_{i-1})f(x_{i})f(x_{i+1})=000$, then we can set $f(x_{i})=1$, contradicting the maximality of $f$, which proves Item (1). ", "Similarly, if $f(x_{i-3})\\dots f(x_{i})\\dots f(x_{i+3})=1001001$, then we can set $f(x_{i})=2$, again contradicting the maximality of $f$, which proves Item (2).", "\n\nNow, observe that we can have neither $f(x_1)f(x_2) = 00$, since otherwise we could set $f(x_1)=1$, neither $f(x_1)\\dots f(x_4) = 0100$, since otherwise we could set $f(x_2)=2$, nor $f(x_1)\\dots f(x_4) = 1001$, since otherwise we could set $f(x_1)=2$, contradicting in each case the maximality of $f$. Therefore, either $0101$ or $1010$ is a prefix of $w_f$. In the former case we are done, so let us assume that $1010$ is a prefix of $w_f$. Suppose that $w_f$ contains the factor $100$ and consider its first occurrence, that is, suppose that $(10)^k100$ is a prefix of $w_f$ for some $k\\ge 1$. In that case, we can replace the $f$-values $(10)^k100$ of $x_1\\dots x_{2k+3}$ by $0(10)^k10$ and we are done. ", "If $w_f$ does not contain the factor $100$, then we necessarily have either $w_f=(10)^{\\frac{n}{2}}$ or $w_f=(10)^{\\frac{n-1}{2}}1$, which gives $\\sigma(f)=\\left\\lceil\\frac{n}{2}\\right\\rceil > \\left\\lceil\\frac{2n}{5}\\right\\rceil$, a contradiction. ", "This proves Item (3).", "\n\nBy symmetry, using the same argument as for the previous item, we get that none of $00$, $0010$, or $1001$ can be a suffix of $w_f$. Hence, either $1010$ or $0101$ is a suffix of $w_f$, which proves Item (4).", "\n\nBy Item (3) of Claim \\[cl:2n-sur-5\\], we let $w'_f$ be the word defined by $w_f=0101w'_f$. We will now “split” $w'_f$ in factors (or blocks) $w_1,\\dots, w_q$, $q\\ge 0$ ($q=0$ meaning that no such block appeared), each of length 2 or 5, inductively defined as follows.", "\n\n- If $01$ is a prefix of $w'_f$, then $w_1=01$,\n\n- If $00101$ is a prefix of $w'_f$, then $w_1=00101$,\n\n- If $w'_f=w_1\\dots w_{k-1}w''$ and $01$ is a prefix of $w''$, then $w_k=01$,\n\n- If $w'_f=w_1\\dots w_{k-1}w''$ and $00101$ is a prefix of $w''$, then $w_k=00101$.\n\nWe then have either $w_f=0101w''$ and $q=0$, or $w_f=0101w_1\\dots w_qw''$, for some $q\\ge 1$, with $w''$ being either empty or 0 (observe that $w''$ cannot start with a 1, and recall that 00 cannot be a suffix of $w_f$), and, if $q>0$, then $w_i\\in\\{01,00101\\}$ for every $i$, $1\\le i\\le q$.\n\nObserve that if $w_i=01$ and $w_{i+1}=00101$ for some $i$, $1\\le i\\le q-1$, then the mapping $g$ defined by $w_g=0101w_1\\dots w_{i-1}.00101.01.w_{i+2}\\dots w''$ is still an $i_b$-broadcast on $P_n$. Therefore, $f$ can be chosen in such a way that there exists some $q_0\\le q$ such that $w_i=00101$ if and only if $i\\le q_0$.\n\nWe now claim that $f$ can be chosen in such a way that we have at most two blocks equal to 01, that is, $q-q_0\\le 2$. Indeed, if we add at least three such blocks, then either $1010101$ or $10101010$ is a suffix of $w_f$. In the former case, $1010101$ could be replaced by $1001010$, contradicting the optimality of $f$. In the latter case, we may replace $10101010$ by $10010101$, so that $q-q_0=2$.\n\nFinally, we get that the structure of $w_f$ (recall that $n\\ge 5$) is either $$01010,\\ 010101,\\ 0101010,\\ 01010101,\\ \\text{or}\\ 0101w_1\\dots w_{q_0}w',$$ with ${q_0}\\ge 1$, $w_i=00101$ for every $i$, $1\\le i\\le {q_0}$, and $w'\\in\\{\\varepsilon,0,01,010,0101,01010\\}$. It is now routine to check that $\\sigma(f)=\\left\\lceil\\frac{2n}{5}\\right\\rceil$ in each case, which gives $i_b(P_n) = \\left\\lceil\\frac{2n}{5}\\right\\rceil$ for every $n\\ge 3$.\n\nThis completes the proof.", "\n\nUsing Theorem \\[th:i-path\\], we can also prove a similar result for cycles.", "\n\n\\[th:i-cycle\\] For every integer $n\\ge 3$, $i_b(C_n)= \\left\\lceil\\frac{2n}{5}\\right\\rceil.$\n\nObserve first that 010 and 0101 are $i_b$-broadcasts on $C_n$ with cost $\\left\\lceil\\frac{2n}{5}\\right\\rceil$, when $n=3,4$, respectively, and that the five functions $f_0,\\dots,f_4$, defined in the proof of Theorem \\[th:i-path\\], are also $i_b$-broadcasts on $C_n$, $n\\ge 5$, with cost $\\left\\lceil\\frac{2n}{5}\\right\\rceil$. We thus have $i_b(C_n) = \\left\\lceil\\frac{2n}{5}\\right\\rceil$ for $n=3,4$, and $i_b(C_n) \\leq \\left\\lceil\\frac{2n}{5}\\right\\rceil$ for every $n\\geq 5$.\n\nWe now prove the opposite inequality when $n\\ge 5$. For that, let $f$ be any $i_b$-broadcast on $C_n$, $n\\ge 5$. Suppose first that $|V^+_f|=1$, which implies $i_b(C_n)=\\diam(C_n)=\\left\\lfloor\\frac{n}{2}\\right\\rfloor$. As observed in the proof of Theorem \\[th:i-path\\], according to the inequality we established before, this situation can only happen if $n\\in S=\\{1,\\dots,9,11,13\\}$.\n\nSuppose now that $n\\notin S$, which implies $|V^+_f| \\geq 2$ and, in particular, $n\\ge 10$. We now claim that we necessarily have $|V^+_f| \\geq 3$. Indeed, suppose to the contrary that $|V^+_f| = 2$, and let $V^+_f=\\{x_{i_1},x_{i_2}\\}$. Denote by $Q_1=x_{i_1}x_{i_1+1}\\dots x_{i_2}$, and $Q_2=x_{i_2}x_{i_2+1}\\dots x_{i_1}$ the two paths joining $x_{i_1}$ and $x_{i_2}$. Since $f$ is maximal, we can assume, without loss of generality, that $|Q_1|=d_{C_n}(x_{i_1},x_{i_2})=f(x_{i_1})+1=f(x_{i_2})+1$, which gives $f(x_{i_1})=f(x_{i_2})$. Since Item 3 of Lemma \\[lem:obs-i\\] also holds for cycles, we have $|Q_2| \\le f(x_{i_1})+f(x_{i_2})+1 = 2f(x_{i_1}) + 1$, which gives $$n = |Q_1| + |Q_2| \\leq f(x_{i_1})+1 + 2f(x_{i_1}) + 1 = 3f(x_{i_1}) + 2.$$ We then get $f(x_{i_1}) \\geq \\left\\lceil\\frac{n-2}{3}\\right\\rceil$, and thus $$i_b(C_n) = 2f(x_{i_1}) \\geq 2\\cdot\\left\\lceil\\frac{n-2}{3}\\right\\rceil,$$ a contradiction with the inequality we established before since $2\\left\\lceil\\frac{n-2}{3}\\right\\rceil > \\left\\lceil\\frac{2n}{5}\\right\\rceil$ when $n\\ge 10$.\n\nWe can thus assume $|V^+_f|\\geq 3$, and let $V^+_f = \\{x_{i_0},\\dots,x_{i_{t-1}}\\}$, $t\\ge 3$. We first claim that there exists some $j$, $0\\le j\\le t-1$, such that $d_{C_n}(x_{i_j},x_{i_{j+1}})=f(x_{i_j})+f(x_{i_{j+1}})+1$ (subscripts are taken modulo $t$). ", "Indeed, if this is not the case, we get $$n = \\sum_{0\\le j\\le t-1}d_{C_n}(x_{i_j},x_{i_{j+1}}) \\leq 2\\sum_{0\\le j\\le t-1}f(x_{i_j}) = 2i_b(C_n),$$ which gives $i_b(C_n)\\geq \\left\\lceil\\frac{n}{2}\\right\\rceil$, in contradiction with the inequality $i_b(C_n)\\leq \\left\\lceil\\frac{2n}{5}\\right\\rceil$ we established before, since $n\\notin S$.\n\nWe can thus suppose, without loss of generality, that $d_{C_n}(x_{i_1},x_{i_2})=f(x_{i_1})+f(x_{i_2})+1$, which implies that $d_{C_n}(x_{i_2},x_{i_3}) = f(x_{i_2}) +1$ (we may have $x_{i_3}=x_{i_0}$) and, similarly, that $d_{C_n}(x_{i_0},x_{i_1}) = f(x_{i_1})+1$. To avoid confusion, let us denote $P_n=y_0y_1\\dots y_{n-1}$, with $y_{f(x_{i_2})} = x_{i_2}$, and let $g$ be the function defined by $g(y_j)=f(x_{j-f(x_{i_2})+i_2})$ for every $j$, $0\\le j\\le n-1$ (subscripts are taken modulo $n$). ", "Observe that both $y_0$ and $y_{n-1}$ are $g$-dominated, since all vertices lying between $x_{i_1}$ and $x_{i_2}$ were $f$-dominated in $C_n$. Moreover, we cannot increase the $g$-value of $y_{f(x_{i_2})}$ (the leftmost $g$-broadcast vertex in $P_n$) since we had $d_{C_n}(x_{i_2},x_{i_3}) = f(x_{i_2})+1$, neither the value of $y_{n-f(x_{i_1})-1}$ (the rightmost $g$-broadcast vertex in $P_n$) since we had $d_{C_n}(x_{i_0},x_{i_1}) = f(x_{i_1})+1$.\n\nSince $f$ was a maximal independent broadcast on $C_n$, we thus get that $g$ is a maximal independent broadcast on $P_n$, which gives $i_b(P_n)\\leq i_b(C_n)$, and thus $i_b(C_n)\\geq \\left\\lceil\\frac{2n}{5}\\right\\rceil$, as required.", "\n\nBroadcast irredundance number and broadcast domination number\n-------------------------------------------------------------\n\nErwin proved in [@Erw04] that $\\gamma_b(P_n) = \\gamma(P_n)=\\lceil n/3\\rceil$. Knowing the value of $\\gamma_b(P_n)$, we can infer the value of $\\gamma_b(C_n)$. Indeed, Brešar and Špacapan proved in [@BS09] that, for every connected graph $G$, there is a spanning tree $T$ of $G$ such that $\\gamma_b(G)=\\gamma_b(T)$. Since spanning trees of the cycle $C_n$ are all isomorphic to the path $P_n$, we get the following result.", "\n\n\\[prop:gamma-path-cycle\\] For every integer $n\\geq 3$, $\\gamma_b(C_n)=\\gamma_b(P_n)=\\lceil\\frac{n}{3}\\rceil$.\n\nWe now consider the broadcast irredundance number of paths. ", "For that, we first prove the two following lemmas.", "\n\n\\[lem:MaxIrr-H-vide\\] Let $f$ be a maximal irredundant broadcast on $P_n$. If $H_f(x_{i})= \\emptyset$ for some vertex $x_i$, then $N_{P_n}(x_i)\\cap N_f(V^+_f)\\neq \\emptyset$.\n\nAssume to the contrary that we have $N_{P_n}(x_i)\\cap N_f(V^+_f) = \\emptyset$. In that case, we could set $f(x_i)=1$, contradicting the maximality of $f$.\n\n\\[lem:MaxIrrPn-et-irrPn\\] For every integer $n\\geq 3$, the following statements hold.", "\n\n1. ", " If $f$ is a maximal irredundant broadcast on $P_n$, then $H_f(x_2)\\neq \\emptyset$ and $H_f(x_{n-1})\\neq \\emptyset$.\n\n2. ", " There exists an $ir_b$-broadcast $f$ on $P_n$ such that $H_f(x_1)\\neq \\emptyset$ and $H_f(x_{n})\\neq \\emptyset$.\n\nWe prove the two statements separately.", "\n\n1. ", " If $H_f(x_2)= \\emptyset$, then $x_2$ is not $f$-dominated, and consequently $x_1$ is also not $f$-dominated. ", "We then have $N_{P_n}(x_1)\\cap N_f(V^+_f)= \\emptyset$, in contradiction with Lemma \\[lem:MaxIrr-H-vide\\]. ", "The case $H_f(x_{n-1})= \\emptyset$ is similar.", "\n\n2. ", " Let $g$ be an $ir_b$-broadcast on $P_n$. If $H_g(x_1)\\neq \\emptyset$ and $H_g(x_{n})\\neq \\emptyset$, then we let $f:=g$ and we are done.", "\n\n Suppose that we have $H_g(x_1)=\\emptyset$. By the previous item, we know that $x_2$ is $g$-dominated by some vertex $x_i$, $i>2$, such that $f(x_i)=d_{P_n}(x_2,x_i)$. We then necessarily have $|PB_g(x_i)|=1$ if $g(x_i)\\geq 2$, and $x_i\\notin PN_g(x_i)$ if $g(x_i)=1$, since otherwise we could set $g(x_1)=1$, contradicting the optimality of $g$. Now, observe that the function $h$ obtained from $g$ by setting $h(x_i)=0$ and $h(x_{i-1})=g(x_i)$ is a maximal irredundant broadcast on $P_n$, with cost $\\sigma(h)=\\sigma(g)=ir_b(P_n)$, that satisfies $H_h(x_1)\\neq \\emptyset$.\n\n If $H_h(x_{n})\\neq \\emptyset$, then we let $f:=h$ and we are done. ", "Otherwise, using the same reasoning (by symmetry), we claim that can produce an $ir_b$-broadcast $f$ on $P_n$ such that $H_f(x_1)\\neq \\emptyset$ and $H_f(x_{n})\\neq \\emptyset$. Observe first that we cannot have $|V_g^+|=2$ if $H_g(x_1)= \\emptyset$ and $H_g(x_n)= \\emptyset$, since in that case we could increase by 1 the $g$-values of $x_{i_1}$ and $x_{i_2}$, contradicting the maximality of $g$. Therefore, if $g$ was such that $H_g(x_1)=\\emptyset$ and $H_g(x_n)=\\emptyset$, then the optimality of $g$ implies $|V_g^+| \\geq 3$, so that the modification of $h$ does not affect $h(x_i)$, and thus $x_1$ is still $f$-dominated.", "\n\nThis concludes the proof.", "\n\nWe are now able to determine the value of the broadcast irredundance number and of the broadcast domination number of paths.", "\n\n[ (0,0+0.5) to\\[bend right=45\\] (0-0.5,0) to\\[bend right=45\\] (0,0-0.5); ]{} [ (1,0) to (8,0); ]{} [ (0,0) to (1,0); ]{} [ (8,0) to (9,0); ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2); ]{} [ at (2,0); at (2,0+0.2)[1]{}; at (2,0-0.2); ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2); ]{} [ at (4,0); at (4,0+0.2)[2]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**2**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2); ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2); ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2); ]{}\n\n\\(a) $x_{j'}=x_{j'^p+1}$ and $x_{i+1}$ is $f$-dominated 0.8cm\n\n[ (0,0+0.5) to\\[bend right=45\\] (0-0.5,0) to\\[bend right=45\\] (0,0-0.5); ]{} [ (1,0) to (8,0); ]{} [ (0,0) to (1,0); ]{} [ (8,0) to (9,0); ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2); ]{} [ at (2,0); at (2,0+0.2)[1]{}; at (2,0-0.2); ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2); ]{} [ at (4,0); at (4,0+0.2)[2]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2); ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**2**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2); ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2); ]{}\n\n\\(b) $x_{j'}=x_{j'^p+1}$ and $x_{i+1}$ is not $f$-dominated 0.8cm\n\n[ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (7,0); ]{} [ (-1,0) to (0,0); ]{} [ (7,0) to (8,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2); ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[2]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[2]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**2**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2); ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2); ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2); ]{}\n\n\\(c) $x_{j'} \\neq x_{j'^p+1}$ and $x_{i+1}$ is $f$-dominated 0.8cm\n\n[ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (7,0); ]{} [ (-1,0) to (0,0); ]{} [ (7,0) to (8,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2); ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[2]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[2]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2); ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**2**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2); ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2); ]{}\n\n\\(d) $x_{j'} \\neq x_{j'^p+1}$ and $x_{i+1}$ is not $f$-dominated\n\n\\[th:ir-gamma-path\\] For every integer $n\\ge 2$, $ir_b(P_n)= \\gamma_b(P_n)= \\left\\lceil\\frac{n}{3}\\right\\rceil.$\n\nBy Corollary \\[cor:Ahmadi-inequalities\\] and Proposition \\[prop:gamma-path-cycle\\], we only need to prove that $ \\gamma_b(P_n)\\leq ir_b(P_n)$. For this, it is enough to construct, from any non-dominating $ir_b$-broadcast, a dominating $ir_b$-broadcast.", "\n\nLet $f$ be an $ir_b$-broadcast on $P_n$. By Lemma \\[lem:MaxIrrPn-et-irrPn\\], we can assume that $x_1$, $x_2$, $x_{n-1}$ and $x_n$ are $f$-dominated. ", "If $f$ is dominating, then we are done. ", "Thus suppose that $f$ is non-dominating, and let $x_i$, $3\\le i\\le n-2$, be the leftmost non-dominated vertex. ", "We will prove that there exists a maximal irredundant broadcast $g$ on $P_n$, with $\\sigma(g)=\\sigma(f)=ir_b(P_n)$, such that the number of vertices that are not $g$-dominated is strictly less than the number of vertices that are not $f$-dominated.", "\n\nLet $x_{j}$, $j\\le i-2$, denote the $f$-broadcast vertex that dominates $x_{i-1}$. Since $x_i$ is not $f$-dominated, we necessarily have $x_{i-1}\\in PB(x_{j})$. Observe that we have $|PB(x_{j})|=1$, that is, the bordering private $f$-neighbor of $x_j$ is $x_{i-1}$, since otherwise we could set $f(x_{i-1})=1$, contradicting the maximality of $f$. Note also that $x_1$ is not $f$-dominated by $x_j$, that is, $x_j$ is not the leftmost $f$-broadcast vertex, since otherwise we could increase the $f$-value of $x_j$ by 1, again contradicting the maximality of $f$. Let then $x_{j'}$, $j'<j$, denote the closest $f$-broadcast vertex to the left of $x_j$, and $x_{j'^p}$, $j'^p<j'$, denote the bordering private $f$-neighbor of $x_{j'}$.\n\nSince $x_{j'^p}$ is the bordering private $f$-neighbor of $x_{j'}$, we necessarily have $d_{P_n}(x_{j'^p},x_j) \\geq f(x_j)+1$. Moreover, we necessarily have $d_{P_n}(x_{j'^p},x_j) = f(x_j)+1$, since otherwise we could increase the value of $f(x_j)$ by 1 ($x_i$ becoming the bordering private $f$-neighbor of $x_j$), contradicting the maximality of $f$. Hence, we have $d_{P_n}(x_{j'^p},x_j) = f(x_j)+1$, and thus $$d_{P_n}(x_{j'^p},x_i) = d_{P_n}(x_{j'^p},x_j) + d_{P_n}(x_j,x_i) = f(x_{j})+1 + f(x_{j})+1 = 2f(x_j)+2.$$\n\nLet now $g$ be the function obtained from $f$ by setting\n\n- $g(x_j)=0$,\n\n- $g(x_{j'^p+1})=1$ and $g(x_{j'})=0$ if $x_{j'}\\neq x_{j'^p+1}$, and\n\n- $g(x_{j+1})=f(x_j)$ if $x_{i+1}$ is $f$-dominated, or $g(x_{j+2})=f(x_j)$ if $x_{i+1}$ is not $f$-dominated (see Figure \\[fig:th-irPn\\]).", "\n\nObserve that $x_{j'^p}$ is a bordering private $g$-neighbor of $x_{j'^p+1}$, and that either $x_i$ is a bordering private $g$-neighbor of $x_{j+1}$ (if $x_{i+1}$ is $f$-dominated), or $x_{i+1}$ is a bordering private $g$-neighbor of $x_{j+2}$ (if $x_{i+1}$ is not $f$-dominated). ", "Moreover, all vertices $x_1,\\dots,x_i$ are $g$-dominated. ", "Hence, $g$ is a maximal irredundant broadcast with cost $$\\sigma(g) = \\sigma(f) - f(x_j) - f(x_{j'}) + f(x_j) + 1 = \\sigma(f) - f(x_{j'}) + 1.$$ The optimality of $f$ then imply $f(x_{j'}) = 1$, so that $g$ is an $ir_b$-broadcast on $P_n$ such that the number of vertices that are not $g$-dominated is strictly less than the number of vertices that are not $f$-dominated.", "\n\nBy repeating this modification while they remain non-dominated vertices, we eventually get a dominating $ir_b$-broadcast on $P_n$, which concludes the proof.", "\n\nUsing Theorem \\[th:ir-gamma-path\\], we can prove a similar result for cycles.", "\n\n\\[th:ir-gamma-cycle\\] For every integer $n\\geq 3$, $ir_b(C_n)= \\gamma_b(C_n)= \\left\\lceil\\frac{n}{3}\\right\\rceil$.\n\nWe already know by Proposition \\[prop:gamma-path-cycle\\] that $\\gamma_b(C_n)= \\left\\lceil\\frac{n}{3}\\right\\rceil$, so that we only need to prove that $ir_b(C_n)=\\left\\lceil\\frac{n}{3}\\right\\rceil$. By Corollary \\[cor:Ahmadi-inequalities\\], we only need to prove that $ ir_b(C_n)\\ge \\gamma_b(C_n)$ or, by Proposition \\[prop:gamma-path-cycle\\] and Theorem \\[th:ir-gamma-path\\], that $ir_b(C_n) \\geq ir_b(P_n)$.\n\nObserve that $010$, $0200$ and $00200$ are dominating $ir_b$-broadcasts for $C_3$, $C_4$ and $C_5$, respectively, with cost $\\left\\lceil\\frac{n}{3}\\right\\rceil$. It thus remains to consider the case $n\\ge 6$.\n\nLet $f$ be an $ir_b$-broadcast on $C_n$, $n\\ge 6$. If $f$ is dominating, then we are done. ", "Thus suppose that $f$ is non-dominating. ", "We claim that $|V^+_f|\\ge 2$. Indeed, if $|V^+_f|=1$, then the maximality of $f$ implies $\\sigma(f)=\\left\\lfloor\\frac{n}{2}\\right\\rfloor$, which gives $ir_b(C_n) = \\left\\lfloor\\frac{n}{2}\\right\\rfloor > \\left\\lceil\\frac{n}{3}\\right\\rceil = \\gamma_b(C_n)$, in contradiction with Corollary \\[cor:Ahmadi-inequalities\\] since $n\\ge 6$.\n\nWe thus have $|V^+_f|\\ge 2$. Since $f$ is maximal, we cannot have three consecutive vertices that are not $f$-dominated. ", "Moreover, since $f$ is non-dominating, we can assume, without loss of generality, that $x_0$ is not $f$-dominated, and that $x_1$ is $f$-dominated by some $f$-broadcast vertex $x_{i_1}$, $i_1>1$. Note that $x_{n-1}$ may be $f$-dominated or not.", "\n\nTo avoid confusion, let $P_n=y_0y_1\\dots y_{n-1}$. Let then $g$ be the mapping defined by $g(y_i)=f(x_i)$ for every $i$, $0\\le i\\le n-1$. As in $C_n$, $x_0$ is not $g$-dominated, $x_1$ is $g$-dominated by $x_{i_1}$, and $g(x_{i_1})$ cannot be increased since otherwise $f(x_{i_1})$ could be increased, contradicting the maximality of $f$. Similarly, the $g$-value of the rightmost $g$-broadcast vertex in $P_n$ cannot be increased, since otherwise its $f$-value could be increased (since $x_0$ is not $f$-dominated, while $x_{n-1}$ may be $f$-dominated or not), again contradicting the maximality of $f$. we can apply the same reasoning if $x_{n-1}$ is not $g$-dominated, which implies that $x_{n-1}$ is not $f$-dominated. ", "Hence, since $f$ is an $ir_b$-broadcast on $C_n$, we get that $g$ is also a maximal irredundant broadcast on $P_n$, which gives $ir_b(C_n)=\\sigma(f)=\\sigma(g)\\ge ir_b(P_n)$ as required.", "\n\nPacking broadcast number and lower packing broadcast number\n-----------------------------------------------------------\n\nWe first determine the broadcast packing number of paths and cycles.", "\n\n\\[th:P-path-cycle\\] For every $n\\ge 2$, $P_b(P_n) = \\diam(P_n) = n-1$, and, for every $n\\ge 3$, $P_b(C_n) = \\diam(C_n) = \\left\\lfloor\\frac{n}{2}\\right\\rfloor$.\n\nWe first consider the case of the path $P_n$, $n\\ge 2$. Observe first that the function $f$ defined by $f(x_1)=n-1$ and $f(x_i)=0$ for every $i$, $2\\le i\\le n$ is a maximal broadcast packing with cost $n-1=\\diam(P_n)$, which gives $\\diam(P_n)\\leq P_b(P_n)$. The opposite inequality directly follows from Observation \\[obs:definitions\\](3) and Theorem \\[th:Gamma\\_IR\\_paths\\].", "\n\nLet us now consider the case of the cycle $C_n$, $n\\geq 3$. Observe first that the function $f$ defined by $f(x_0)=\\left\\lfloor\\frac{n}{2}\\right\\rfloor$ and $f(x_i)=0$ for every $i$, $1\\le i\\le n-1$ is a maximal broadcast packing with cost $\\left\\lfloor\\frac{n}{2}\\right\\rfloor=\\diam(C_n)$, which gives $\\diam(C_n)\\leq P_b(C_n)$.\n\nAgain, to establish the opposite inequality, it suffices to prove that, for every $P_b$-broadcast $f$ on $C_n$, $|V_f^+|=1$. Similarly as above, if we suppose that $f$ is a $P_b$-broadcast on $C_n$ with $|V_f^+|\\geq 2$, we get $$\\sum_{x_i\\in V_f^+}\\big(2f(x_i)+1\\big)\\leq n,$$ which gives $$2P_b(C_n)+|V_f^+| \\leq n,$$ and thus $$P_b(C_n)\\leq \\frac{n-|V_f^+|}{2}\\leq \\frac{n-2}{2}< \\left\\lfloor\\frac{n}{2}\\right\\rfloor= {\\mbox{ diam}}(C_n),$$ again a contradiction.", "\n\nIn order to determine the values of $p_b(P_n)$, $n\\ge 1$, we first prove the following lemma.", "\n\n\\[lem:packing 0-1\\] For every integer $n\\ge 2$, there exists a $p_b$-broadcast $f$ on $P_n$ such that $f(x_i)=1$ for every $f$-broadcast vertex $x_i$.\n\nObserve first that $10$, $010$, $1001$ and $10010$ define $p_b$-broadcasts on $P_n$, $n=2,3,4,5$, respectively, that satisfy the statement of the lemma. ", "Suppose thus $n \\geq 6$ and let $g$ be any $p_b$-broadcast on $P_n$. If $g(x_i)=1$ for every $g$-broadcast vertex $x_i$, then we set $f:=g$ and we are done.", "\n\nOtherwise, let $V_g^+=\\{x_{i_1},\\dots,x_{i_t}\\}$, $i_1<\\cdots < i_t$, $t\\geq 1$. We first claim that we necessarily have $t\\ge 2$. Indeed, if $t=1$, we get $$p_b(P_n)=g(x_{i_1})=\\rad(P_n)=\\left\\lfloor\\frac{n}{2}\\right\\rfloor,$$ while the function $g'$ defined by $g'(x_i)=1$, $1\\le i\\le n$, if and only if $i \\equiv 1\\pmod 3$ is a maximal packing broadcast with cost $\\sigma(g')=\\left\\lfloor\\frac{n}{3}\\right\\rfloor < \\left\\lfloor\\frac{n}{2}\\right\\rfloor,$ a contradiction.", "\n\nWe thus have $|V_g^+| \\geq 2$. Let $x_{i_j}$, $1\\le j\\le t$, be a $g$-broadcast vertex with minimum subscript such that $g(x_{i_j})\\geq 2$. We will consider three cases, depending on the value of $i_j$. In each case, we will prove either that the case cannot occur, or that we can produce a $p_b$-broadcast $g'$ on $P_n$, with $\\sigma(g')=\\sigma(g)$, such that the subscript of the leftmost $g'$-broadcast vertex with $g'$-value at least $2$, if any, is strictly greater than the subscript of the leftmost $g$-broadcast vertex with $g$-value at least $2$.\n\n1. ", " $i_j=i_1$ or $i_j=i_t$.\\\n Assume $i_j=i_1$, the case $i_j=i_t$ being similar, by symmetry. ", "We first claim that we have $g(x_{i_1})\\in\\{i_1-2, i_1-1\\}$. Indeed, if $g(x_{i_1}) \\geq i_1$, then the function $h$ obtained from $g$ by setting $h(x_{i_1})=0$ and $h(x_{i_1+1})=g(x_{i_1})-1$ is clearly a maximal packing broadcast with cost $\\sigma(h)=\\sigma(g)-1$, contradicting the optimality of $g$. Now, if $g(x_{i_1}) \\leq i_1 - 3$, then we could set $g(x_{1})=1$, contradicting the maximality of $g$. We thus have two cases to consider.", "\n\n [ (-0.5,0+0.5) to\\[bend right=45\\] (-0.5-0.5,0) to\\[bend right=45\\] (-0.5,0-0.5); ]{} [ (0,0) to (4,0); ]{} [ (4,0) to (5,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**1**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[2]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**1**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**0**]{}]{}; ]{}\n\n 0.4cm\n\n [ (-0.5,0+0.5) to\\[bend right=45\\] (-0.5-0.5,0) to\\[bend right=45\\] (-0.5,0-0.5); ]{} [ (0,0) to (6,0); ]{} [ (6,0) to (7,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**0**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**1**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[3]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**1**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{}\n\n 0.4cm\n\n [ (-0.5,0+0.5) to\\[bend right=45\\] (-0.5-0.5,0) to\\[bend right=45\\] (-0.5,0-0.5); ]{} [ (0,0) to (8,0); ]{} [ (8,0) to (9,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**0**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[4]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{}\n\n \\(a) $g(x_{i_1})=i_1-1$\n\n 0.8cm\n\n [ (-1.5,0+0.5) to\\[bend right=45\\] (-1.5-0.5,0) to\\[bend right=45\\] (-1.5,0-0.5); ]{} [ (-1,0) to (4,0); ]{} [ (4,0) to (5,0); ]{} [ at (-1,0); at (-1,0+0.2)[0]{}; at (-1,0-0.2)[[**0**]{}]{}; ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**1**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[2]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**1**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**0**]{}]{}; ]{}\n\n 0.4cm\n\n [ (-1.5,0+0.5) to\\[bend right=45\\] (-1.5-0.5,0) to\\[bend right=45\\] (-1.5,0-0.5); ]{} [ (-1,0) to (6,0); ]{} [ (6,0) to (7,0); ]{} [ at (-1,0); at (-1,0+0.2)[0]{}; at (-1,0-0.2)[[**1**]{}]{}; ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**0**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**0**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**1**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[3]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**0**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**1**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{}\n\n 0.4cm\n\n [ (-1.5,0+0.5) to\\[bend right=45\\] (-1.5-0.5,0) to\\[bend right=45\\] (-1.5,0-0.5); ]{} [ (-1,0) to (8,0); ]{} [ (8,0) to (9,0); ]{} [ at (-1,0); at (-1,0+0.2)[0]{}; at (-1,0-0.2)[[**0**]{}]{}; ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**0**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[4]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{}\n\n \\(b) $g(x_{i_1})=i_1-2$\n\n 1. ", " $g(x_{i_1})= i_1-1$, and thus $i_1\\geq 3$.\\\n Let $g_1$ be the function obtained from $g$ by modifying the $g$-values of $x_1,\\dots, x_{2g(x_{i_1})+1}$ as follows:\n\n - $g_1(x_1\\dots x_{2g(x_{i_1})+1}) = (010)^\\alpha$, if $2g(x_{i_1})+1\\equiv 0 \\pmod 3$,\n\n - $g_1(x_1\\dots x_{2g(x_{i_1})+1}) = 0(010)^\\alpha$, if $2g(x_{i_1})+1\\equiv 1 \\pmod 3$,\n\n - $g_1(x_1\\dots x_{2g(x_{i_1})+1}) = 10(010)^\\alpha$, if $2g(x_{i_1})+1\\equiv 2 \\pmod 3$,\n\n where $\\alpha=\\left\\lfloor\\frac{2g(x_{i_1})+1}{3}\\right\\rfloor$ (see Figure \\[fig:lem-packing\\](a)). ", "It is then not difficult to check that $g_1$ is a maximal packing broadcast such that $$\\sigma(g_1)-\\sigma(g)= \\Big(\\left\\lfloor\\frac{2g(x_{i_1})-1}{3}\\right\\rfloor +1\\Big) - g(x_{i_1}) = \\left\\lfloor\\frac{2-g(x_{i_1})}{3}\\right\\rfloor,$$ which gives $\\sigma(g_1)-\\sigma(g)<0$ whenever $g(x_{i_1})\\neq 2$. Consequently, $g(x_{i_1})=g(x_{3})=2$ and we can then define $g'$ from $g$ by setting $g'(x_1\\dots x_5)= 10010$.\n\n 2. ", " $g(x_{i_1})= i_1-2$, and thus $i_1\\geq 4$.\\\n Similarly to the previous case, let $g_2$ be the function obtained from $g$ by modifying the $g$-values of $x_1,\\dots, x_{2g(x_{i_1})+2}$ as follows:\n\n - $g_2(x_1\\dots x_{2g(x_{i_1})+2}) = (010)^\\alpha$, if $2g(x_{i_1})+2\\equiv 0 \\pmod 3$,\n\n - $g_2(x_1\\dots x_{2g(x_{i_1})+2}) = 0(010)^\\alpha$, if $2g(x_{i_1})+2\\equiv 1 \\pmod 3$,\n\n - $g_2(x_1\\dots x_{2g(x_{i_1})+2}) = 10(010)^\\alpha$, if $2g(x_{i_1})+2\\equiv 2 \\pmod 3$,\n\n where $\\alpha=\\left\\lfloor\\frac{2g(x_{i_1})+2}{3}\\right\\rfloor$ (see Figure \\[fig:lem-packing\\](b)) . ", "Again, it is not difficult to check that $g_2$ is a maximal packing broadcast such that $$\\sigma(g_2)-\\sigma(g)= \\Big(\\left\\lfloor\\frac{2g(x_{i_1})}{3}\\right\\rfloor +1\\Big) - g(x_{i_1}) = \\left\\lfloor\\frac{3-g(x_{i_1})}{3}\\right\\rfloor,$$ which gives $\\sigma(g_2)-\\sigma(g)<0$ whenever $g(x_{i_1})\\neq 2$ and $g(x_{i_1})\\neq 3$. Consequently, either $g(x_{i_1})=g(x_{4})=2$ and we can then define $g'$ from $g$ by setting $g'(x_1\\dots x_6)= 010010$, or $g(x_{i_1})=g(x_{5})=3$ and we can then define $g'$ from $g$ by setting $g'(x_1\\dots x_8)= 10010010$.\n\n2. ", " $i_j\\in \\{i_2,\\dots,i_{t-1}\\}$.\\\n\n [ (-1,0+0.5) to\\[bend right=45\\] (-1-0.5,0) to\\[bend right=45\\] (-1,0-0.5); ]{} [ (0,0) to (8,0); ]{} [ (-1,0) to (0,0); ]{} [ (8,0) to (9,0); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**0**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[4]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{}\n\n \\(a) $2g(x_{i_j})+1\\equiv 0\\pmod 3$ ($9$ in this example)\n\n 0.8cm\n\n [ (-3,0+0.5) to\\[bend right=45\\] (-3-0.5,0) to\\[bend right=45\\] (-3,0-0.5); ]{} [ (-2,0) to (8,0); ]{} [ (-3,0) to (-2,0); ]{} [ (8,0) to (9,0); ]{} [ at (-2,0); at (-2,0+0.2)[1]{}; at (-2,0-0.2); ]{} [ at (-1,0); at (-1,0+0.2)[0]{}; at (-1,0-0.2); ]{} [ at (0,0); at (0,0+0.2)[0]{}; at (0,0-0.2)[[**0**]{}]{}; ]{} [ at (1,0); at (1,0+0.2)[0]{}; at (1,0-0.2)[[**1**]{}]{}; ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2)[[**0**]{}]{}; ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[3]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{}\n\n [ (-1,-2+0.5) to\\[bend right=45\\] (-1-0.5,-2) to\\[bend right=45\\] (-1,-2-0.5); ]{} [ (0,-2) to (7,-2); ]{} [ (-1,-2) to (0,-2); ]{} [ (7,-2) to (8,-2); ]{} [ at (0,-2); at (0,-2+0.2)[1]{}; at (0,-2-0.2); ]{} [ at (1,-2); at (1,-2+0.2)[0]{}; at (1,-2-0.2); ]{} [ at (2,-2); at (2,-2+0.2)[0]{}; at (2,-2-0.2)[[**0**]{}]{}; ]{} [ at (3,-2); at (3,-2+0.2)[0]{}; at (3,-2-0.2)[[**1**]{}]{}; ]{} [ at (4,-2); at (4,-2+0.2)[0]{}; at (4,-2-0.2)[[**0**]{}]{}; ]{} [ at (5,-2); at (5,-2+0.2)[2]{}; at (5,-2-0.2)[[**0**]{}]{}; ]{} [ at (6,-2); at (6,-2+0.2)[0]{}; at (6,-2-0.2)[[**1**]{}]{}; ]{} [ at (7,-2); at (7,-2+0.2)[0]{}; at (7,-2-0.2)[[**0**]{}]{}; ]{}\n\n [ (-1-0.5,-4+0.5) to\\[bend right=45\\] (-1-0.5-0.5,-4) to\\[bend right=45\\] (-1-0.5,-4-0.5); ]{} [ (0-0.5,-4) to (8-0.5,-4); ]{} [ (-1-0.5,-4) to (0-0.5,-4); ]{} [ (8-0.5,-4) to (9-0.5,-4); ]{} [ at (0-0.5,-4); at (0-0.5,-4+0.2)[1]{}; at (0-0.5,-4-0.2); ]{} [ at (1-0.5,-4); at (1-0.5,-4+0.2)[0]{}; at (1-0.5,-4-0.2); ]{} [ at (2-0.5,-4); at (2-0.5,-4+0.2)[0]{}; at (2-0.5,-4-0.2); ]{} [ at (3-0.5,-4); at (3-0.5,-4+0.2)[0]{}; at (3-0.5,-4-0.2)[[**0**]{}]{}; ]{} [ at (4-0.5,-4); at (4-0.5,-4+0.2)[0]{}; at (4-0.5,-4-0.2)[[**1**]{}]{}; ]{} [ at (5-0.5,-4); at (5-0.5,-4+0.2)[0]{}; at (5-0.5,-4-0.2)[[**0**]{}]{}; ]{} [ at (6-0.5,-4); at (6-0.5,-4+0.2)[2]{}; at (6-0.5,-4-0.2)[[**0**]{}]{}; ]{} [ at (7-0.5,-4); at (7-0.5,-4+0.2)[0]{}; at (7-0.5,-4-0.2)[[**1**]{}]{}; ]{} [ at (8-0.5,-4); at (8-0.5,-4+0.2)[0]{}; at (8-0.5,-4-0.2)[[**0**]{}]{}; ]{}\n\n \\(b) $2g(x_{i_j})+1\\equiv 1\\pmod 3$ ($7$ in this example) and $p=2$,\n\n or $2g(x_{i_j})+1\\equiv 2\\pmod 3$ ($5$ in this example) and $p=1$,\n\n or $2g(x_{i_j})+1\\equiv 2\\pmod 3$ ($5$ in this example) and $p=2$\n\n 0.8cm\n\n [ (0,0+0.5) to\\[bend right=45\\] (0-0.5,0) to\\[bend right=45\\] (0,0-0.5); ]{} [ (1,0) to (15,0); ]{} [ (0,0) to (1,0); ]{} [ (15,0) to (16,0); ]{} [ at (1,0); at (1,0+0.2)[1]{}; at (1,0-0.2); ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2); ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[3]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2)[[**0**]{}]{}; ]{} [ at (10,0); at (10,0+0.2)[0]{}; at (10,0-0.2)[[**0**]{}]{}; ]{} [ at (11,0); at (11,0+0.2)[1]{}; at (11,0-0.2)[[**2**]{}]{}; ]{} [ at (12,0); at (12,0+0.2)[0]{}; at (12,0-0.2); ]{} [ at (13,0); at (13,0+0.2)[0]{}; at (13,0-0.2); ]{} [ at (14,0); at (14,0+0.2)[0]{}; at (14,0-0.2); ]{} [ at (15,0); at (15,0+0.2)[1]{}; at (15,0-0.2); ]{}\n\n 0.4cm\n\n [ (0,0+0.5) to\\[bend right=45\\] (0-0.5,0) to\\[bend right=45\\] (0,0-0.5); ]{} [ (1,0) to (16,0); ]{} [ (0,0) to (1,0); ]{} [ (16,0) to (17,0); ]{} [ at (1,0); at (1,0+0.2)[1]{}; at (1,0-0.2); ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2); ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[3]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2)[[**0**]{}]{}; ]{} [ at (10,0); at (10,0+0.2)[0]{}; at (10,0-0.2); ]{} [ at (11,0); at (11,0+0.2)[0]{}; at (11,0-0.2); ]{} [ at (12,0); at (12,0+0.2)[2]{}; at (12,0-0.2); ]{} [ at (13,0); at (13,0+0.2)[0]{}; at (13,0-0.2); ]{} [ at (14,0); at (14,0+0.2)[0]{}; at (14,0-0.2); ]{} [ at (15,0); at (15,0+0.2)[0]{}; at (15,0-0.2); ]{} [ at (16,0); at (16,0+0.2)[1]{}; at (16,0-0.2); ]{}\n\n 0.4cm\n\n [ (0,0+0.5) to\\[bend right=45\\] (0-0.5,0) to\\[bend right=45\\] (0,0-0.5); ]{} [ (1,0) to (12,0); ]{} [ (0,0) to (1,0); ]{} [ (12,0) to (13,0); ]{} [ at (1,0); at (1,0+0.2)[1]{}; at (1,0-0.2); ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2); ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[0]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[3]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**1**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2)[[**0**]{}]{}; ]{} [ at (10,0); at (10,0+0.2)[0]{}; at (10,0-0.2)[[**0**]{}]{}; ]{} [ at (11,0); at (11,0+0.2)[0]{}; at (11,0-0.2)[[**2**]{}]{}; ]{} [ at (12,0); at (12,0+0.2)[1]{}; at (12,0-0.2)[[**0**]{}]{}; ]{}\n\n \\(c) $2g(x_{i_j})+1\\equiv 1\\pmod 3$ ($7$ in this example) and $p=0$,\n\n or $2g(x_{i_j})+1\\equiv 1\\pmod 3$ ($7$ in this example), $p=0$,\\\n and both $x_{i_j+g(x_{i_j})+1}$ and $x_{i_{j+1}+g(x_{i_{j+1}})+1}$ are $g$-dominated,\n\n or $2g(x_{i_j})+1\\equiv 1\\pmod 3$ and $p=1$\n\n 0.8cm\n\n [ (0,0+0.5) to\\[bend right=45\\] (0-0.5,0) to\\[bend right=45\\] (0,0-0.5); ]{} [ (1,0) to (10,0); ]{} [ (0,0) to (1,0); ]{} [ (10,0) to (11,0); ]{} [ at (1,0); at (1,0+0.2)[1]{}; at (1,0-0.2); ]{} [ at (2,0); at (2,0+0.2)[0]{}; at (2,0-0.2); ]{} [ at (3,0); at (3,0+0.2)[0]{}; at (3,0-0.2)[[**0**]{}]{}; ]{} [ at (4,0); at (4,0+0.2)[0]{}; at (4,0-0.2)[[**1**]{}]{}; ]{} [ at (5,0); at (5,0+0.2)[2]{}; at (5,0-0.2)[[**0**]{}]{}; ]{} [ at (6,0); at (6,0+0.2)[0]{}; at (6,0-0.2)[[**0**]{}]{}; ]{} [ at (7,0); at (7,0+0.2)[0]{}; at (7,0-0.2)[[**0**]{}]{}; ]{} [ at (8,0); at (8,0+0.2)[0]{}; at (8,0-0.2)[[**0**]{}]{}; ]{} [ at (9,0); at (9,0+0.2)[0]{}; at (9,0-0.2)[[**3**]{}]{}; ]{} [ at (10,0); at (10,0+0.2)[2]{}; at (10,0-0.2)[[**0**]{}]{}; ]{}\n\n \\(d) $2g(x_{i_j})+1\\equiv 2\\pmod 3$ ($5$ in this example) and $p=0$\n\n Since $g$ is a maximal packing broadcast, we necessarily have $$1\\le d_{P_n}(x_{i_{j-1}},x_{i_{j}}) - g(x_{i_{j-1}}) - g(x_{i_{j}}) \\le 3.$$ Moreover, we also have either $$d_{P_n}(x_{i_{j-1}},x_{i_{j}})=g(x_{i_{j-1}})+g(x_{i_{j}})+1,\\ \\ \n \\text{or}\\ \\ d_{P_n}(x_{i_{j}},x_{i_{j+1}})=g(x_{i_{j}})+g(x_{i_{j+1}})+1.$$\n\n We consider four subcases, depending on the value of $2g(x_{i_j})+1\\mod 3$, and on the number $p$ of vertices lying between $x_{i_{j-1}}$ and $x_{i_{j}}$, or between $x_{i_{j}}$ and $x_{i_{j+1}}$, that are not $g$-dominated. ", "Note that since $g$ is a maximal packing broadcast, we have either (i) $p=0$, or (ii) $p=1$ and either $x_{i_j-g(x_{i_j})-1}$ or $x_{i_j+g(x_{i_j})+1}$ is not $g$-dominated, or (iii) $p=2$ and either $x_{i_j-g(x_{i_j})-2}$ and $x_{i_j-g(x_{i_j})-1}$, or $x_{i_j+g(x_{i_j})+1}$ and $x_{i_j+g(x_{i_j})+2}$, are not $g$-dominated.", "\n\n 1. ", " $2g(x_{i_j})+1\\equiv 0\\pmod 3$.\\\n Let $g_0$ be the function obtained from $g$ by setting $g_0(x_{i_j - g(x_{i_j})} \\dots x_{i_j + g(x_{i_j})}) = (010)^\\alpha$, where $\\alpha =\\frac{2g(x_{i_j})+1}{3}$ (see Figure \\[fig:lem-packing-2\\](a)). ", "Since $g$ is maximal, $g_0$ is also maximal and we have $$\\sigma(g_0)-\\sigma(g)= \\frac{2g(x_{i_j})+1}{3}- g(x_{i_j}) =\\frac{1-g(x_{i_j})}{3} < 0,$$ which contradicts the optimality of $g$.\n\n 2. ", " $2g(x_{i_j})+1\\equiv 1\\pmod 3$ and $p=2$, or $2g(x_{i_j})+1\\equiv 2\\pmod 3$ and $1\\le p\\le 2$.\\\n Suppose that $2g(x_{i_j})+1\\equiv 1\\pmod 3$, and $x_{i_j-g(x_{i_j})-2}$, $x_{i_j-g(x_{i_j})-1}$ are not $g$-dominated, or that $2g(x_{i_j})+1\\equiv 2\\pmod 3$, and $x_{i_j-g(x_{i_j})-1}$ is not $g$-dominated. (", "The other cases are similar.)", "\n\n Let $g'$ be the function obtained from $g$ by setting\n\n - $g'(x_{i_j-g(x_{i_j})-2} \\dots x_{i_j + g(x_{i_j})}) = (010)^\\alpha$ if $2g(x_{i_j})+1\\equiv 1\\pmod 3$,\n\n - $g'(x_{i_j-g(x_{i_j})-1} \\dots x_{i_j + g(x_{i_j})}) = (010)^\\alpha$ if $2g(x_{i_j})+1\\equiv 2\\pmod 3$,\n\n where $\\alpha = \\left\\lfloor\\frac{2g(x_{i_j})+p+1}{3}\\right\\rfloor$ (see Figure \\[fig:lem-packing-2\\](b)). ", "Since $g$ is maximal, $g'$ is also maximal and we have $$\\sigma(g')-\\sigma(g)= \\frac{2g(x_{i_j})+p+1}{3}- g(x_{i_j})=\\frac{p+1-g(x_{i_j})}{3}\\leq 0.$$\n\n The optimality of $g$ then implies either $p=1$ and $g(x_{i_j})=2$, or $p=2$ and $g(x_{i_j})=3$. In each case, $g'$ is also optimal and the subscript of the leftmost $g'$-broadcast vertex with $g'$-value at least $2$, if any, is strictly greater than the subscript of the leftmost $g$-broadcast vertex with $g$-value at least $2$, as required.", "\n\n 3. ", " $2g(x_{i_j})+1\\equiv 1\\pmod 3$ and $0\\le p\\le 1$.\\\n In that case, $x_{i_j-g(x_{i_j})-2}$ and $x_{i_j+g(x_{i_j})+2}$ are $g$-dominated, and at most one vertex among $x_{i_j-g(x_{i_j})-1}$ and $x_{i_j+g(x_{i_j})+1}$ is not $g$-dominated. ", "Let $g'$ be the function obtained from $g$ (see Figure \\[fig:lem-packing-2\\](c)) by setting $g'(x_{i_j-g(x_{i_j})} \\dots x_{i_j + g(x_{i_j})}) = (010)^\\alpha 0$, where $\\alpha = \\frac{2g(x_{i_j})}{3}$, and\n\n - $g'(x_{i_{j+1}})=0$, $g'(x_{i_{j+1}-1})= g(x_{i_{j+1}})+1$, if $x_{i_{j} + g(x_{i_{j}})+1}$ is not $g$-dominated,\n\n - $g'(x_{i_{j+1}})=g(x_{i_{j+1}})+1$, if $i_j=i_{t-1}$ or $x_{i_{j} + g(x_{i_{j}})+1}$ is $g$-dominated, and $x_{i_{j+1} + g(x_{i_{j+1}})+1}$ is not $g$-dominated,\n\n Note that we necessarily have one of the above cases, since otherwise $g'$ would be a maximal packing broadcast with $\\sigma(g')<\\sigma(g)$, contradicting the optimality of $g$. Since $g$ is maximal, $g'$ is also maximal and we have $$\\sigma(g')-\\sigma(g)= \\frac{2g(x_{i_j})}{3}+1- g(x_{i_j})=\\frac{3-g(x_{i_j})}{3}\\leq 0.$$ (Recall that since $2g(x_{i_j})+1\\equiv 1\\pmod 3$, we have $g(x_{i_j})\\ge 3$.) The optimality of $g$ then implies $g(x_{i_j})=3$. We then get that $g'$ is also optimal and the subscript of the leftmost $g'$-broadcast vertex with $g'$-value at least $2$, if any, is strictly greater than the subscript of the leftmost $g$-broadcast vertex with $g$-value at least $2$, as required.", "\n\n 4. ", " $2g(x_{i_j})+1\\equiv 2\\pmod 3$ and $p=0$.\\\n Let $g'$ be the function obtained from $g$ by setting $g'(x_{i_j-g(x_{i_j})} \\dots x_{i_j + g(x_{i_j})}) = (010)^\\alpha 00$, where $\\alpha = \\frac{2g(x_{i_j})-1}{3}$, $g'(x_{i_{j+1}})=0$, and $g'(x_{i_{j+1}-1})=g(x_{i_{j+1}})+1$ (see Figure \\[fig:lem-packing-2\\](d)). ", "Since $g$ is maximal, $g'$ is also maximal and we have $$\\sigma(g')-\\sigma(g)= \\frac{2g(x_{i_j})-1}{3}+1- g(x_{i_j})=\\frac{2-g(x_{i_j})}{3}\\leq 0.$$ The optimality of $g$ then implies $g(x_{i_j})=2$. Therefore, $g'$ is also optimal and the subscript of the leftmost $g'$-broadcast vertex with $g'$-value at least $2$, if any, is strictly greater than the subscript of the leftmost $g$-broadcast vertex with $g$-value at least $2$, as required.", "\n\nRepeating the same transformation for each vertex with $g$-value at least 2, we eventually produce a $p_b$-broadcast $g'$ on $P_n$ all of whose broadcast vertices have $g'$-value 1, as claimed in the statement of the lemma. ", "This concludes the proof.", "\n\nWe are now able to determine the lower broadcast packing number of paths.", "\n\n\\[th:p-path\\] For every integer $n\\ge 2$, $$p_b(P_n)=\\left\\lbrace\\begin{array}{cl}\n \\frac{n}{4}& \\text{if } \\,\\, n\\equiv 0\\pmod 8,\\\\[1ex]\n 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor +1& \\text{if } \\,\\, n\\equiv 1,2,3\\pmod 8,\\\\[1ex]\n 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor +2& \\text{if } \\,\\, n\\equiv 4,5,6,7\\pmod 8.\\\\\n \\end{array}\n\\right.$$\n\nObserve first that $10$, $010$, $1001$, $01001$, $001001$, $0010010$ and $00100100$ define optimal $p_b$-broadcasts on $P_n$ for $n=2,\\dots,8$, respectively, whose costs are the values claimed by the theorem.", "\n\nSuppose now $n\\ge 9$ and let $n=8q+r$, with $q\\geq 1$ and $0\\leq r\\leq 7$. According to the value of $r$, we define the broadcasts $f_r$, $0\\le r\\le 7$, on $P_n$ as follows: $$f_0(P_n) = (00100100)^q,\\ f_1(P_n) = (00100100)^q1,\\ f_2(P_n) = (00100100)^q10,$$ $$f_3(P_n) = (00100100)^q100,\\ f_4(P_n) = (00100100)^q1001,\\ f_5(P_n) = (00100100)^q01001,$$ $$f_6(P_n) = (00100100)^q001001,\\ \\mbox{and } f_7(P_n) = (00100100)^q0010010.$$\n\nIt is not difficult to check that each $f_r$ is indeed a maximal packing broadcast on $P_{8q+r}$, $8q+r\\ge 9$, with cost $$\\sigma(f_r)=\n\\left\\{\n\\begin{array}{cl}\n \\frac{n}{4}& if \\,\\, n\\equiv 0\\pmod 8,\\\\[1ex]\n 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor +1& \\text{if } \\,\\, n\\equiv 1,2,3\\pmod 8,\\\\[1ex]\n 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor +2& \\text{if } \\,\\, n\\equiv 4,5,6,7\\pmod 8,\n \\end{array}\n\\right.$$ which gives $p_b(P_n)\\leq \\sigma(f_r)$, that is, $p_b(P_n)$ is not greater than the value claimed by the theorem.", "\n\nWe now prove the opposite inequality. ", "By Lemma \\[lem:packing 0-1\\], we know that there exists a $p_b$-broadcast all of whose broadcast vertices have broadcast value 1. ", "Let $g$ be such a broadcast. ", "For every $k$, $0\\leq k\\leq q-1$, let $$\\sigma_k = g(x_{8k+1})+\\cdots +g(x_{8k+8}).$$\n\nFrom the definition of a packing broadcast, we get that the distance between any two consecutive $g$-broadcast vertices (with $g$-value $1$) is $3$, $4$ or $5$, which implies $2\\leq \\sigma_k \\leq 3$ for every $k$, $0\\leq k\\leq q-1$. Observe also that $x_2$ and $x_{n-1}$ must be $g$-dominated, since otherwise we could set $g(x_1)=1$ or $g(x_n)=1$, contradicting the maximality of $g$, and that $d_{P_n}(x_{i_1},x_{i_2})=d_{P_n}(x_{i_{t-1}},x_{i_t})=3$, since otherwise we could increase the value of $g(x_{i_1})$ or $g(x_{i_t})$, contradicting the maximality of $g$.\n\nWe now consider three cases, depending on the value of $r$, and prove in each case that the cost of $g$ is the value claimed in the statement of the theorem.", "\n\n1. ", " $r=0$.\\\n In that case, we have $$p_b(P_n)=\\sigma(g)=\\sum_{k=0}^{q-1}\\sigma_k\\geq 2q = \\frac{2n}{8}= \\frac{n}{4}.$$\n\n2. ", " $r\\in\\{1,2,3\\}$.\\\n If $\\sigma_k=3$ for some $k$, $0\\le k\\le q-1$, then $$p_b(P_n)=\\sigma(g) \\geq \\sum_{k=0}^{q-1}\\sigma_k \\geq 2(q-1)+3=2q+1= 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor +1,$$ and we are done.", "\n\n Suppose now that $\\sigma_k=2$ for every $k$, $0\\leq k\\leq q-1$, which implies $p_b(P_n)\\ge 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor$. Suppose, contrary to the statement of the theorem, that $p_b(P_n) = 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor$. This implies $g(x_{n-r+1})=\\cdots=g(x_n)=0$. If $r=3$, then we have a contradiction since $x_{n-1}$ must be $g$-dominated.", "\n\n We thus have $r\\in\\{1,2\\}$. Since $x_{n-1}$ must be $g$-dominated and $d_{P_n}(x_{i_{t-1}},x_{i_t})=3$, we necessarily have $\\sigma_{q-1}\\in\\{00001001,00010010\\}$ if $r=1$, and $\\sigma_{q-1}=00001001$ if $r=2$. Since $g$ is maximal, we cannot have three consecutive vertices that are not $g$-dominated, which gives $\\sigma_{j}\\in\\{00001001,00010010\\}$ if $r=1$, and $\\sigma_{j}=00001001$ if $r=2$, for every $j$, $0\\le j\\le q-1$, a contradiction since, in each case, this would imply that $x_2$ is not $g$-dominated.", "\n\n Hence we have $p_b(P_n) = 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor +1$, as required.", "\n\n3. ", " $r \\in \\{4,5,6,7\\}$.\\\n Note first that we necessarily have $g(x_{n-r+1})+\\cdots +g(x_n) \\ge 1$. Hence, if $\\sigma_k=3$ for some $k$, $0\\le k\\le q-1$, then $$p_b(P_n)=\\sigma(g) \\geq \\sum_{k=0}^{q-1}\\sigma_k + 1 \\geq 2(q-1)+3+1=2q+2= 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor +2,$$ and we are done.", "\n\n Suppose now that $\\sigma_k=2$ for every $k$, $0\\leq k\\leq q-1$, and, contrary to the statement of the theorem, that $p_b(P_n) \\le 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor + 1$, which implies $g(x_{n-r+1})+\\cdots+g(x_n)=1$ since $x_{n-1}$ must be $g$-dominated. ", "If $r=6$ or $r=7$, then we have a contradiction since we must have $d_{P_n}(x_{i_{t-1}},x_{i_t})=3$.\n\n We thus have $r\\in\\{4,5\\}$. Again, since $x_{n-1}$ must be $g$-dominated and $d_{P_n}(x_{i_{t-1}},x_{i_t})=3$, we necessarily have $$\\sigma_{q-1}\\in\\{00100001,00001001,01000010,00100010,00010010\\}$$ if $r=4$, and $$\\sigma_{q-1}\\in\\{00100001,00001001\\}$$ if $r=5$. Now, since $g$ is maximal, every $g$-broadcast vertex must be at distance $3$ from another $g$-broadcast vertex, and thus we get $$\\sigma_{j}\\in\\{00100001,00001001,01000010,00100010,00010010\\}$$ for every $j$, $0\\le j\\le q-1$. We then get a contradiction since $x_2$ must be $g$-dominated and we must have $d(x_{i_1},x_{i_2})=3$.\n\n Hence, in this case also, we have $p_b(P_n) = 2\\left\\lfloor\\frac{n}{8}\\right\\rfloor +2$, as required.", "\n\nThis completes the proof.", "\n\nUsing Theorem \\[th:p-path\\], we can also prove a similar result for cycles.", "\n\n\\[th:p-cycle\\] For every integer $n\\geq 3$, $$p_b(C_n)=\\left\\lbrace\\begin{array}{cl}\n \\frac{n}{4}& \\text{if } \\,\\, n\\equiv 0\\pmod 8,\\\\[1ex]\n 2\\lfloor\\frac{n}{8}\\rfloor +1& \\text{if } \\,\\, n\\equiv 1,2,3\\pmod 8,\\\\[1ex]\n 2\\lfloor\\frac{n}{8}\\rfloor +2& \\text{if } \\,\\, n\\equiv 4,5,6,7\\pmod 8.", "\n \\end{array}\n\\right.$$\n\nObserve first that the broadcasts $f_0,\\dots,f_7$, defined in the proof of Theorem \\[th:p-path\\], are also maximal packing broadcast on $C_n$, with $n\\ge 3$, $n=8q+r$ and $0\\le r\\le 7$, which gives $p_b(C_n)\\leq \\sigma(f_r)$, that is, $p_b(C_n)$ is not greater than the value claimed by the theorem.", "\n\nWe now prove the opposite inequality. ", "Observe first that $010$, $2000$, $20000$ and $001001$ are optimal solutions for $C_3$, $C_4$, $C_5$ and $C_6$, respectively, and that their cost is exactly the value claimed by the theorem. ", "We can thus assume $n\\ge 7$. Let $f$ be a $p_b$-broadcast on $C_n$, $n\\ge 7$.\n\nWe first claim that we necessarily have $|V^+_f|\\geq 2$. Indeed, suppose to the contrary that $|V^+_f|=1$ and that $V^+_f=\\{x_0\\}$, without loss of generality. ", "Since $f$ is maximal, we necessarily have $\\sigma(f)=f(x_0)=\\left\\lfloor\\frac{n-1}{2}\\right\\rfloor$, and thus $p_b(C_n)=\\left\\lfloor\\frac{n-1}{2}\\right\\rfloor$, which contradicts the inequality we previously established when $n\\ge 7$.\n\nWe thus have $|V^+_f|\\geq 2$. Let $V^+_f=\\{x_{i_0},\\dots,x_{i_{t-1}}\\}$, $t\\ge 2$. Since $f$ is maximal, we necessarily have $$f(x_{i_j}) + f(x_{i_{j+1}}) +1 \\leq d_{C_n}(x_{i_j},x_{i_{j+1}}) \\leq f(x_{i_j}) + f(x_{i_{j+1}}) + 3$$ for every $j$, $0\\le j\\le t-1$. Moreover, if $d_{C_n}(x_{i_j},x_{i_{j+1}}) \\ge f(x_{i_j}) + f(x_{i_{j+1}}) + 2$, then we necessarily have $d_{C_n}(x_{i_{j+1}},x_{i_{j+2}}) = f(x_{i_{j+1}}) + f(x_{i_{j+2}}) + 1$ (we may have $i_j = i_{j+2}$), since otherwise we could increase the value of $f(x_{i_{j+1}})$ by 1. ", "We consider the two following cases.", "\n\n1. ", " If all vertices in $C_n$ are $f$-dominated, that is, $d_{C_n}(x_{i_{j}},x_{i_{j+1}}) = f(x_{i_{j}}) + f(x_{i_{j+1}}) + 1$ for every $j$, $0\\le j\\le t-1$, then, to avoid confusion, we let $P_n=y_0y_1\\dots y_{n-1}$ with $y_0=x_{{i_0}+f(x_{i_0})+1}$. Let now $g$ be the function defined by $g(y_j)=f(x_{j+i_0+f(x_{i_0})+1})$ for every $j$, $0\\le j\\le n-1$. Clearly, both $y_0$ and $y_{n-1}$ are $g$-dominated. ", "Since $f$ was a maximal packing broadcast on $C_n$, we get that $g$ is also a maximal packing broadcast on $P_n$, which gives $p_b(P_n)\\leq p_b(C_n)$.\n\n2. ", " If $C_n$ contains at least one vertex which is not $f$-dominated, then we can assume, without loss of generality, that $x_{i_1+f(x_{i_1})+1}$ is not $f$-dominated, which implies $d_{C_n}(x_{i_{0}},x_{i_{1}}) = f(x_{i_{0}}) + f(x_{i_{1}})+1$ and $d_{C_n}(x_{i_{2}},x_{i_{3}}) = f(x_{i_{2}}) + f(x_{i_{3}})+1$ (we may have $x_{i_0}=x_{i_2}$ and $x_{i_1}=x_{i_3}$). ", "Again, to avoid confusion, we let $P_n=y_0y_1\\dots y_{n-1}$ with $y_0=x_{{i_1}+f(x_{i_1})+2}$. Let now $g$ be the function defined by $g(y_j)=f(x_{j+i_1+f(x_{i_1})+2})$ for every $j$, $0\\le j\\le n-1$. Since $d_{C_n}(x_{i_{0}},x_{i_{1}}) = f(x_{i_{0}}) + f(x_{i_{1}})+1$ and $d_{C_n}(x_{i_{2}},x_{i_{3}}) = f(x_{i_{2}}) + f(x_{i_{3}})+1$, the values of both the leftmost and the rightmost $g$-broadcast vertex in $P_n$ cannot be increased. ", "Since $f$ was a maximal packing broadcast on $C_n$, we thus get that $g$ is also a maximal packing broadcast on $P_n$, which gives $p_b(P_n)\\leq p_b(C_n)$.\n\nWe thus have $p_b(P_n)\\leq p_b(C_n)$ in all cases and the result follows.", "\n\n[99]{} D. Ahmadi, G. H. Fricke, C. Schroeder, S. T. Hedetniemi and R. C. Laskar. ", "Broadcast irredundance in graphs. [*", "Congr. ", "Numer.*]{} ", "224:17–31, 2015.", "\n\nM. Ahmane. ", "Sur le nombre de broadcast d’indépendence de quelques classes d’arbres. ", "PhD thesis (in French), University of Sciences and Technology Houari Boumediene (USTHB), in preparation.", "\n\nM. Ahmane, I. Bouchemakh and E. Sopena. ", "On the Broadcast Independence Number of Caterpillars. [*", "Discrete Appl. ", "Math.*]{} ", "244:20–35, 2018.", "\n\nM. Ahmane, I. Bouchemakh and E. Sopena. ", "On the Broadcast Independence Number of Locally Uniform 2-Lobsters. ", "arXiv:1902.02998\\[cs.", "DM\\], 2019.", "\n\nL. Beaudou and R.C. Brewster. ", "On the multipacking number of grid graphs. [*", "Discrete Math. ", "Theoret. ", "Comput. ", "Sci.*]{} ", "21(3) (2019). ", "L. Beaudou, R.C. Brewster and F. Foucaud. ", "Broadcast domination and multipacking: bounds and the integrality gap. [*", "Australas. ", "J. Combin.*]{} ", "74(1):86–97, 2019. ", "S. Bessy and D. Rautenbach. ", "Algorithmic aspects of broadcast independence. ", "arXiv:1809.07248 \\[math.", "CO\\], 2018.", "\n\nS. Bessy and D. Rautenbach. ", "Relating broadcast independence and independence. [*", "Discrete Math.*]{} ", "342(12) (2019).", "\n\nS. Bessy and D. Rautenbach. ", "Girth, minimum degree, independence, and broadcast independence. [*", "Commun. ", "Comb. ", "Optim.*]{} ", "4(2):131–139 (2019).", "\n\nJ.R.S. Blair, P. Heggernes, S.B. Horton and F. Manne. ", "Broadcast domination algorithms for interval graphs, series-parallel graphs, and trees. [*", "Congr. ", "Num.*]{} ", "169:55–77, 2004.", "\n\nI. Bouchemakh and N. Fergani. ", "On the upper broadcast domination number. [*", "Ars Combin.*]{} ", "130:151–161, 2017.", "\n\nI. Bouchemakh and R. Sahbi. ", "On a conjecture of Erwin. [*", "Stud. ", "Inform. ", "Univ.*]{} ", "9(2):144–151, 2011.", "\n\nI. Bouchemakh and M. Zemir. ", "On the Broadcast Independence Number of Grid Graph. [*", "Graphs Combin.*]{} ", "30:83–100, 2014.", "\n\nB. Brešar and S. Špacapan. ", "Broadcast domination of products of graphs. [*", "Ars Combin.*]{} ", "92:303–320, 2009.", "\n\nR.C. Brewster, G. MacGillivray and F. Yang. ", "Broadcast domination and multipacking in strongly chordal graphs. [*", "Discrete Appl. ", "Math.*]{}, ", "in press.", "\n\nR. C. Brewster, C. M. Mynhardt and L. Teshima. ", "New bounds for the broadcast domination number of a graph. [*", "Cent. ", "Eur. ", "J. Math.*]{} ", "11(7):1334–1343, 2013.", "\n\nE.J. Cockayne, S. Herke and C.M. Mynhardt. ", "Broadcasts and domination in trees. [*", "Discrete Math.*]{} ", "311:1235–1246, 2011.", "\n\nJ. Dabney, B.C. Dean and S.T. Hedetniemi. ", "A linear-time algorithm for broadcast domination in a tree. [*", "Networks*]{} 53(2):160–169, 2009.", "\n\nJ.E. Dunbar, D.J. Erwin, T.W. Haynes, S.M. Hedetniemi and S.T. Hedetniemi. ", "Broadcasts in graphs. [*", "Discrete Appl. ", "Math.*]{} ", "154:59-75, 2006.", "\n\nD. Erwin. [*", "Cost domination in graphs*]{}. ", "Ph.D. Dissertation, Western Michigan University, 2001.", "\n\nD. Erwin. ", "Dominating broadcasts in graphs. [*", "Bull. ", "Inst. ", "Combin. ", "Appl.*]{} ", "42:89–105, 2004.", "\n\nL. Gemmrich and C.M. Mynhardt. ", "Broadcasts in Graphs: Diametrical Trees. [*", "Australas. ", "J.Combin.*]{} ", "69(2):243–258, 2017.", "\n\nB.L. Hartnell and C.M. Mynhardt. ", "On the Difference between Broadcast and Multipacking Numbers of Graphs. [*", "Utilitas Math.*]{} ", "94, 2014.", "\n\nS.T. Hedetniemi. ", "Unsolved algorithmic problems on trees. [*", "AKCE Int. ", "J. Graphs Combin.*]{} ", "3(1):1–37, 2006.", "\n\nP. Heggernes and D. Lokshtanov. ", "Optimal broadcast domination in polynomial time. [*", "Discrete Math.*]{} ", "36:3267–3280, 2006.", "\n\nP. Heggernes and S.H. S[æ]{}ther. ", "Broadcast domination on block graphs in linear time. ", "Hirsch, Edward A. (ed.) ", "et al., ", "Computer science-theory and applications. [*", "7th international computer science symposium in Russia, CSR 2012, Nizhny Novgorod, Russia, July 3-7, 2012. ", "Proceedings. ", "Berlin: Springer (ISBN 978-3-642-30641-9/pbk)*]{}. [*", "Lecture Notes in Computer Science*]{} 7353:172–183, 2012.", "\n\nS. Herke and C.M. Mynhardt. ", "Radial trees. [*", "Discrete Math.*]{} ", "309:5950–5962, 2009.", "\n\nS. Lunney and C.M. Mynhardt. ", "More trees with equal broadcast and domination numbers. [*", "Australas. ", "J. Combin.*]{} ", "61:251–272, 2015.", "\n\nC.M. Mynhardt and A. Roux. ", "Dominating and Irredundant Broadcasts in Graphs. [*", "Discrete Appl. ", "Math.*]{} ", "220:80–90, 2017.", "\n\nC.M. Mynhardt and L. Teshima. ", "Broadcasts and multipackings in trees. [*", "Utilitas Math.*]{}, ", "to appear.", "\n\nC.M. Mynhardt and J. Wodlinger. ", "A class of trees with equal broadcast and domination numbers. [*", "Australas. ", "J. Combin.*]{} ", "56:3–22, 2013.", "\n\nC.M. Mynhardt and J. Wodlinger. ", "Uniquely radial trees. [*", "Comb. ", "Math. ", "and Comb. ", "Comp.*]{} ", "93:131–152, 2015.", "\n\nS.M. Seager. ", "Dominating Broadcasts of Caterpillars. [*", "Ars Combin.*]{} ", "88:307–319, 2008.", "\n\nK.W. Soh and K.M. Koh. ", "Broadcast domination in graph products of paths. [*", "Australas. ", "J. Combin.*]{} ", "59:342–351, 2014.", "\n\n[^1]: Faculty of Mathematics, Laboratory L’IFORCE, University of Sciences and Technology Houari Boumediene (USTHB), B.P. 32 El-Alia, Bab-Ezzouar, 16111 Algiers, Algeria.", "\n\n[^2]: Univ. ", "Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400, Talence, France.", "\n\n[^3]: In their paper, Mynhardt and Roux used a slightly different definition of the set $PB_f(v)$ when $f(v)=1$ and $N_f(v)\\neq\\{v\\}$, by including the vertex $v$ in $PB_f(v)$. Moreover, they called the set $PB_f(v)$ the [*private $f$-boundary*]{} of $v$. We here use the term [*private $f$-border*]{} to avoid confusion between these two definitions. ", "However, it is easy to check that the private $f$-boundary of $v$ is empty if and only if the private $f$-border of $v$ is empty, so that Proposition \\[prop:Erwin-PB-nonempty\\] is still valid in our setting.", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "The present invention relates to a cover for a sump pump opening. ", "More particularly, the present invention relates to a sump cover which can be bolted to the floor directly above the sump crock opening for the purpose of reducing indoor radon levels in residential and commercial buildings.", "\nPrevious covers having various types of sealing arrangements are described, for example, in the following U.S. Pats. ", "Nos.: ", "2,003,770 to Goodhart; 2,358,750 to Walker et al.; ", "3,248,119 to Smith et al.; ", "4,101,236 to Meyer; 4,523,407 to Miller; and also in Canadian Patent No. ", "725,408 issued Jan. 11, 1966.", "\nBy the present invention, there is provided a sump crock cover for reducing radon levels in residential and commercial buildings, being well suited for installation on a basement floor directly over the sump pump opening, with the cover being of a generally circular configuration and including near its peripheral edge two spaced apart annular sealing rings which assist in preventing the escape of hazardous gases such as radon enriched soil gas. ", "The cover includes an integral radially extending ribbed section with a central aperture therethrough for the purpose of receiving a flexible grommet which provides a seal around sump discharge piping and electrical wiring.", "\nIn one embodiment, the cover is in the form of a 22 inch diameter reinforced polyvinyl chloride (PVC) disk which is installed directly over a standard 18 inch diameter residential sump pump opening. ", "The sump cover is constructed so that it may be bolted to the concrete slab directly above the sump crock opening. ", "The cover does not in any way hinder normal operation of the sump pump.", "\nThe primary function of the sump crock cover of the present invention is to reduce indoor radon levels in residential and commercial buildings. ", "This is accomplished by physically decoupling the barometric pressure gradient which exists above and below a concrete foundation slab. ", "A pair of rubber O-rings provide an airtight seal between the sump lid and the concrete floor, while a flexible grommet provides the seal around the sump discharge piping and the electrical wiring. ", "The cover prevents radon-enriched soil gas from being drawn from the soil beneath the slab, passing unimpeded through the sump opening, concentrating in the basement area and ultimately distributing radon throughout the entire indoor environment.", "\nIn addition to reducing the influx of soil gas radon, the sump lid has other potential benefits in residential basements or subgrade environments. ", "These benefits include: (1) reduction of injuries and/or chance of electrical shock caused by open (uncovered) sump crocks and sump motors; (2) increase in usable floor space in the vicinity of the sump; (3) reduction of indoor odors caused by standing water or storm water discharge into the sump pit; and (4) reduction of other noxious or toxic indoor pollutants such as methane or hydrogen sulfide via soil gas influx through open sump pits." ]

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[ "Minimally invasive ilioinguinal approach to the acetabulum.", "\nThe classic ilioinguinal approach is a gold standard in acetabular surgery. ", "We developed a modification, a minimally invasive method that entails a median lower abdominal approach with extraperitoneal dissection and exposure of the pubic symphysis. ", "The second incision is lateral, next to the iliac crest. ", "This allows an easy, safe and quick exposure of the anterior iliac ring as well as easy access to the posterior column and wall towards the sacroiliac joint. ", "The iliac vessels and nerves are thereby protected, and no preparation of neurovascular structures is required. ", "The technique was applied in 23 clinical cases and compared with the classic ilioinguinal approach in 9 similar cases over the same period." ]

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[ "Private Prison Secrecy\n\nCorrections Corporation of America, the largest private incarceration company in the world, today convenes its annual shareholder meeting. ", "Participants will pore over profit and revenue figures, but the more important issue is one that won’t be discussed – should for-profit prisons exist at all?", "\n\nIt’s a question that companies like CCA don’t want anyone asking.", "\n\nThey’d prefer to remain shrouded by a veil of secrecy shielding them from scrutiny, all the while raking in billions of taxpayer dollars each year and locking up nearly 130,000 men and women. ", "They want to continue to operate out of public view, and enjoy their inexplicable exemption from the Freedom of Information Act.", "\n\nDuring the past few years, CCA has voted down shareholder resolutions demanding accountability in political contributions, and management this year is seeking to kill a stockholder proposal for greater transparency in efforts to curb prisoner rape. ", "Earlier this year, CCA quietly sent officials in 48 states a letter, later leaked to the media, seeking to buy up state prisons.", "\n\nBut the taxpayers who finance private prisons, the communities where these facilities are situated, and the families whose loved ones are imprisoned in for-profit lockups deserve real answers about privatized incarceration. ", "That’s why the American Civil Liberties Union has invited CCA Chief Executive Damon Hininger to participate in a 90-minute public debate on whether his company – or any company – should be in the business of locking people up for money.", "\n\nOur view is simple: Private prisons are big government at its worst. ", "The industry’s business model depends on extracting as much public money as possible by locking up the maximum number of people. ", "While industry supporters have long touted supposed cost savings, several studies have found no significant reduction in cost.", "\n\nThe best way to cut prison spending is not to be distracted by privatization schemes but to reduce the number of people we imprison through smart criminal justice reform, including shorter sentences for minor infractions. ", "Unprecedented levels of incarceration cripple state budgets and take money away from schools and roads – to say nothing of depriving record numbers of individuals of liberty, disproportionately affecting people of color, and doing nothing to improve public safety.", "\n\nCCA was long connected with the American Legislative Exchange Council, a secretive organization recently thrust into public light for its role in pushing “stand your ground” laws. ", "The Council was also a driving force behind “truth in sentencing” statutes – the sort of laws that lengthen sentences and keep prisons full. ", "CCA denies advocating for longer sentences. ", "As CCA angles to buy prisons from state governments, however, it is noteworthy that there is a major catch: states must assure the corporation that the prisons will be 90 percent full for at least 20 years. ", "And as mass incarceration damages the country as a whole, private prisons reap lucrative rewards. ", "Mr. Hininger, as CCA’s head, received more than $3.5 million in executive compensation in 2011.", "\n\nPrivatized incarceration also presents a grave threat to human rights. ", "Last year, the ACLU of Texas sued CCA after an officer sexually abused multiple immigration detainees. ", "A CCA prison in Idaho was dubbed the “Gladiator School” due to extreme levels of violence. ", "In March, a federal judge described conditions in a private prison run by another for-profit company as “a picture of such horror as should be unrealized anywhere in the civilized world.”", "\n\nMr. Hininger no doubt disagrees with much of what has been said here, but as Upton Sinclair observed, “it is difficult to get a man to understand something when his salary depends upon his not understanding it.” ", "That is why transparency is so important, and why a public debate must occur. ", "Can CCA’s claims about the benefits of privatization, which include everything from reduced costs to high-quality facilities, survive scrutiny? ", "Or does the company reason backwards from its bottom line?" ]

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[ "Q:\n\nPast tense of “to cast” in the programming sense\n\nIn programming, to cast (also: to typecast) means to convert an object from one type to another (see Wikipedia).", "\nI'd like to know the correct past tense of to cast in this sense. ", "Is it cast or casted?", "\nI'm aware that there is already a similar question: Can “casted” be the past tense of “cast”? ", "However, that question has only one answer mentioning this particular usage of the word, and it doesn't quote any sources.", "\n\nA:\n\nOxford Dictionaries rather tersely states that past and past participle of cast is cast. ", "So:\n\nAs a novice programmer, I had blithely cast opaque pointers to\n pointers of unsigned char to access the raw bytes contained therein.", "\n\n" ]

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[ "Stuart Tyson Photography-Points of View\n\nStuart Tyson is a commercial and fine art photographer based in New York and Orange NJ, whose clients include Marie Claire, Harper’s Bazaar and Vanity Fair, to name a few.", "\n\nBorn in Yorkshire, England, Tyson studied bio-chemistry before falling in love with photography. ", "His photographs have appeared in over 50 publications worldwide and his fine art images adorn the walls of many institutions, corporations and private collections." ]

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[ "Bill Belichick and Tom Brady earned their sixth trip to the Super Bowl with a 45-7 wipeout of the Indianapolis Colts in the AFC Championship Game. ", "Jim Nantz and Phil Simms recap all the action from Gillette Stadium." ]

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[ "A desi family entertainer with super-stylized action, bouts of comedy and hi-octane drama brings back the superhit actor-director duo of Sudeep and S Krishna together for the second time after their blockbuster success of Hebbuli. ", "Directed by S Krishna, the much ambitious action drama is a universal story of a wrestler who fights for pride, love and his sport, the film also stars Sushant Singh, Aakanksha Singh among others.", "\n\nZee Studios will release dubbed-versions of the action drama in Hindi, Tamil, Telugu and Malayalam along with the original Kannada version in over 1000 screens in non-South Indian markets and the film will release in over 2500 screens across India.", "\n\nKannada superstar Sudeep shared, “A good collaboration is always a reward. ", "When it comes in the name of Zee Studios, it isn't just a collaboration, it's a strength as well. ", "It's unseen hands around the team, saying, ‘we are with you’. ", "Thank you, Zee Studios, for joining us in this Journey.”", "\n\nActor Suniel Shetty commented, “It is great news! ", "Of course, it ensures a huge release for Pehlwaan even in Hindi. ", "Zee Studios is by far one of the biggest production and distribution houses. ", "So excited and looking forward to a fantastic release. ", "5 languages itself I think is big and 2500+ screens across India, that is a huge release.\"", "\n\nDirector S Krishna commented on the announcement, “Pehlwaan has a universal theme which will connect with everyone. ", "It is a sports action drama with a lot of heart in it. ", "I am glad that Zee Studios liked the content and releasing it across North India.”", "\n\nShariq Patel, CEO, Zee Studios added, “It’s exciting to partner with director Krishna and the amazing cast on this powerful film that has the perfect mix of action, comedy and drama—a complete entertainer that you can watch with your family. ", "We want to expand into the South Indian film industry, and bringing this universal, aspirational and powerful story, Pehlwaan, to a wide-base audience is the first step towards that. ", "We will showcase the film on a huge scale by giving it the widest release for any Kannada film in non-South Indian markets.”", "\n\nProducer Swapna Krishna added, “We are overwhelmed to have Zee Studios on board as our partner for theatrical release of Pehlwaan. ", "We are also excited & looking forward to take Pehlwaan across North India, Nepal & Bhutan in all 5 languages through Zee studios.”", "\n\nThe studio will also release the film in Nepal and Bhutan. ", "Makers will announce the release date soon." ]

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[ "Target Therapy for Esophageal Adenocarcinoma.", "\nAdenocarcinoma of the esophagus is a deadly disease and median survival of patients with metastatic disease is around 1 year only. ", "There is an unmet need to personalize treatment by identifying molecular targets and respective target therapy in esophageal adenocarcinoma. ", "There has been success in targeting the human epidermal growth factor receptor 2 (HER2) and vasoendothelial growth factor (VEGF) pathway while more failures were encountered in the clinical studies targeting epidermal growth factor (EGFR), mammalian target of rapamycin (mTOR), and mesenchymal-epithelial transition (MET). ", "Studies using immune-checkpoint inhibitors have shown early success, and we await mature data for clinical application. ", "In the chapter, the target therapy and novel treatment strategy will be reviewed. ", "In the future, it is hoped that advances in translational research in targeted therapy against esophageal adenocarcinoma will bring about new progress in clinical practice." ]

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[ "Funding clean-energy solutions\n\nThe contest, co-sponsored by Massachusetts utility NSTAR and the U.S. Department of Energy (DOE) and open to teams from any American university, is the nation’s leading student-run energy business-plan competition. ", "Past participants have gone on to raise a total of $130 million in funding.", "\n\nMore than 50 teams entered this year’s contest; 15 semifinalists made it to Monday’s grand finale. ", "One finalist was selected in each of three separate categories — renewable energy, energy efficiency, and infrastructure and resources — with each receiving $20,000. ", "The winners of the Audience Choice Award earned $10,000.", "\n\nPicasolar, a team from the University of Arkansas, developed technology that could improve the efficiency of solar panels and make them cheaper to produce. ", "This team is now automatically a finalist in the energy category of the MIT $100K Entrepreneurship Competition, whose winner will be selected on May 15.", "\n\nIn his opening remarks, CEP co-founder Bill Aulet, the managing director of the Martin Trust Center for MIT Entrepreneurship, said the contest gives clean-energy entrepreneurs the support and platform to bring their technologies to market. ", "He cited past MIT participants — such as FastCap Systems, Oscomp Systems, Levant Power and FinSix — that got their training and start in the CEP and have since grown into successful companies.", "\n\nCompetitors have often emerged from CEP, Aulet added, with a clearer understanding of what it takes to run a business and commercialize products. “", "What we’re looking to do in this competition is not to [help entrepreneurs] catch a single fish — we’re trying to teach a whole bunch of people how to fish,” he said.", "\n\nThe competition marked a culmination of the extensive clean-energy innovation and entrepreneurship events held at MIT over the course of the academic year.", "\n\nMIT power and design\n\nTwo MIT teams won in their respective categories: UPower in infrastructure and resources, and Sistene Solar in renewable energy. ", "Another all-MIT team, SunHub, took home the Audience Choice Award.", "\n\nUPower, a startup co-founded by students and an alumna of MIT’s Department of Nuclear Science and Engineering (NSE), is developing a nuclear generator to be used in places off the power grid — such as a U.S. Army base in Afghanistan. ", "Diesel generators are now generally used to supply electricity to such places.", "\n\nThe team’s transportable, solid-state nuclear generator can generate up to 1.75 megawatts of power. ", "It could, in theory, provide 12 years of energy without needing refueling, providing about a 50 percent energy savings over diesel, said UPower CEO and co-founder Jacob DeWitte, a PhD student in NSE. “", "We like to think of it as a nuclear battery,” he said, with the potential to “revolutionize energy.”", "\n\nThe startup was co-founded by Joseph Yurko, also a PhD student in NSE, and NSE alumna Caroline Cochran SM ’10.", "\n\nSistine Solar, co-founded by two students at the MIT Sloan School of Management, hopes to promote clean energy by giving solar panels a facelift with modern designs. ", "Co-founder Senthil Balasubramanian said the company aims to do for solar panels what “Apple did with cell phones” — essentially, spruce up the design to make the products desirable to the masses.", "\n\nTeam members showed renderings of their designs on well-known local buildings, such as the Genzyme Center in Cambridge and the Institute of Contemporary Art in Boston. ", "With its designs, Balasubramanian said, the company — which he co-founded with Ido Salam — aims to help “usher in a new era of clean energy.”", "\n\nSunHub — the winner of last night’s Audience Choice Award — offers solar education to homeowners, helping them make better choices when buying solar-energy systems. ", "SunHub team members are David Borrelli, a PhD student in chemical engineering at MIT, and Kevin Yates, an MBA student at MIT Sloan.", "\n\nThe winning team in the energy-efficiency category, Aeolus Building Efficiency, includes MIT mechanical engineering alumnus Michael Gevelber PhD ’88. ", "His company’s software measures airflow in a building’s ventilation and climate-control system, offering ways to reduce energy consumption by up to 20 percent.", "\n\nCEP also attracted a panel of industry experts, moderated by Aulet, who discussed topics including business strategies, carbon taxes and the effect of cheap natural gas on energy policy and renewable-energy technologies.", "\n\nPanelist Christopher Knittel, the William Barton Rogers Professor of Energy Economics at MIT Sloan, discussed, among other things, how low natural-gas prices may be distracting national policymakers from implementing clean-energy policies. ", "In the recent recession, he said, natural gas began replacing coal as fuel for electricity production, and greenhouse-gas levels dropped — possibly making policymakers complacent.", "\n\n“If you look over the past four years, you calculate the United States’ greenhouse gas emissions, it looks like we’re doing great,” said Knittel, who is also co-director of the Center for Energy and Environmental Research at MIT. “", "From that perspective, policymakers may look at the landscape and say, ‘Why do we need any additional policies?’”", "\n\n“So, we’re really at a fork in the road here,” Knittel continued, “where unless policymakers lead us down the right path, it could spell catastrophe for the climate.”", "\n\nIn her remarks, Jennifer Garson of the DOE praised CEP, saying it helps her agency promote clean-energy technologies across the United States. “", "We find such great value in being involved in these competitions,” she said. “", "MIT has been really leading the way and has proven to be an excellent model in engaging young startups.”" ]

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[ "Gyland (municipality)\n\nGyland is a former municipality in Vest-Agder county, Norway. ", " The municipality is located in the northeastern part of the present-day municipality of Flekkefjord. ", " The municipality existed very briefly from 1838 until 1839 and then it was re-created in 1893 and it existed until 1965. ", " The administrative centre was the village of Gyland where Gyland Church is located.", "\n\nHistory\nThe parish of Gyland was established as a municipality on 1 January 1838 (see formannskapsdistrikt), but it was almost immediately merged into neighboring Bakke municipality in the fall of 1839. ", " The Gyland area (population: 1,085) was separated (again) from Bakke municipality on 31 December 1893 to once again form its own municipality. ", " During the 1960s, there were many municipal mergers across Norway due to the work of the Schei Committee. ", "On 1 January 1965, the municipalities of Gyland, Bakke, Hidra, and Nes were merged with the town of Flekkefjord to form a new, larger municipality of Flekkefjord. ", "Prior to the merger, Gyland had a population of 691.", "\n\nName\nThe municipality (originally the parish) was named after the old Gyland farm (Old Norse: Gýjuland), where the Gyland Church was originally located. ", " The first element is the old name of the river that flows past the farm (Old Norse: Gýja or Gý) and the last element is land which means \"land\".", "\n\nSee also\nList of former municipalities of Norway\n\nReferences\n\nCategory:Former municipalities of Norway\nCategory:Flekkefjord" ]

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[ "Introduction {#Sec1}\n============\n\nIt has been reported that insulin resistance is associated with mitochondrial dysfunction in several tissues. ", "While mitochondria are considered central to altered metabolic pathways, leading to pathogenic processes in type 2 diabetes, the mechanisms by which mitochondrial function contributes to the disease remain to be elucidated. ", "Whether it is insulin resistance per se, chronic hyperglycaemia, or accumulation of intracellular lipid and associated alterations in metabolic pathways that affect mitochondrial function, or vice versa, is also unclear.", "\n\nIn skeletal muscle, evidence for reduced oxidative capacity in type 2 diabetes has been provided by findings of reduced oxidative enzyme levels \\[[@CR1]--[@CR4]\\] and mismatches between glycolytic and oxidative enzyme activities \\[[@CR3], [@CR5]\\]. ", "The activities of rotenone-sensitive NADH:O~2~ oxidoreductase and citrate synthase have been shown to be reduced by 40% in the skeletal muscle of type 2 diabetic patients, and transmission electron microscopy has revealed that these mitochondria have a reduced size and an altered morphology \\[[@CR1], [@CR6]\\]. ", "A decrease in the expression of genes involved in oxidative phosphorylation has also been reported in muscle of type 2 diabetic patients \\[[@CR7], [@CR8]\\] and men on a high-fat diet \\[[@CR9]\\]. ", "It has been stated that impaired muscle mitochondrial function is linked to excess intramuscular lipid accumulation and reduced fatty acid oxidation defined by rates of oxidative phosphorylation and ratios of inorganic phosphate:phosphocreatine determined by magnetic resonance studies \\[[@CR6]\\]. ", "These studies suggest mitochondrial dysfunction in type 2 diabetes; however, to date, no direct measurements of mitochondrial O~2~ flux capacity in intact cells in human type 2 diabetes have been reported. ", "We hypothesised that oxidative phosphorylation and electron transport capacity are diminished in the skeletal muscle of type 2 diabetic subjects, and that these changes are attributable to a reduction in muscle mitochondrial content. ", "In the present study we tested these hypotheses by using high-resolution respirometry to quantify oxidative phosphorylation and electron transport capacity in permeabilised muscle fibres from biopsy samples of the quadriceps in healthy subjects and patients with type 2 diabetes.", "\n\nSubjects and methods {#Sec2}\n====================\n\n**Subjects** Informed consent was obtained from all subjects. ", "The study was conducted in accordance with the principles of the Declaration of Helsinki, and was approved by the local ethics committee for Frederiksberg and Copenhagen County. ", "Mitochondrial respiration was measured in permeabilised skeletal muscle fibres obtained from needle biopsies of the vastus lateralis in men with (*n* = 11) or without (control; *n* = 8) type 2 diabetes. ", "The characteristics of the subjects are provided in Table [1](#Tab1){ref-type=\"table\"} and Fig.", " [1](#Fig1){ref-type=\"fig\"}. ", "All subjects were in good health but classified as living a typical Westernised sedentary lifestyle, participating only in routine activities of daily living (walking, gardening, etc.) ", "and not engaged in regular structured or individualised aerobic or strength training programmes or athletics. ", "None of the control subjects had a family history of diabetes and none was receiving treatment for a disease. ", "The diabetic patients were treated for their diabetes with diet or oral glucose-lowering medicine. ", "All medications were withheld 24 h prior to the experiment. ", "The patients with type 2 diabetes had no clinical signs of long-term diabetic complications and were representative of patients treated in the primary care sector. ", "Table 1Characteristics of the subjects Type 2 diabetic subjects (*n* = 11)Control subjects (*n* = 8)Age (years)62 ± 258 ± 1Height (cm)177 ± 3179 ± 1BMI (kg/m^2^)32 ± 2\\*28 ± 1Time since diagnosis (years)5 ± 2--Fasting insulin (pmol/l)61 ± 9\\*34 ± 6Fasting glucose (mmol/l)9.0 ± 0.5\\*5.4 ± 0.1Complex I activity (nmol min^−1^ mg protein^−1^)50.8 ± 6.058.3 ± 4.7Citrate synthase activity (pmol mg^−1^ s^−1^)1.6 ± 0.12.0 ± 0.2mtDNA (copies/μg tissue) ×10^3^119 ± 7\\*147 ± 12mtDNA/genomic DNA2,773 ± 2523,030 ± 185Data are means±SEM. ", "\\**p* \\< 0.05 vs control subjectsFig.", " 1Glucose (**a**) and insulin (**b**) concentrations in venous plasma before (*t* = 0 min) and during an OGTT. ", "The patients with type 2 diabetes had higher fasting glucose levels and were severely insulin resistant compared with healthy control subjects (\\**p* \\< 0.05). *", "Black and white symbols* represent healthy control subjects and patients with type 2 diabetes, respectivelySubjects were fasted overnight prior to the experiment. ", "A catheter was inserted into an antecubital vein for blood sampling. ", "After local anaesthesia of the skin and the subcutis, a muscle biopsy was taken (Tru-Core; PBN-Medicals, Stenløse, Denmark) and then a 120-min OGTT (75 g glucose dissolved in 300 ml of water) was performed. ", "At *t* = 30 min, a second muscle biopsy was taken.", "A portion of the obtained muscle tissue was frozen immediately in liquid nitrogen and stored at −80°C for later analysis (see below), and a smaller piece (2--6 mg) was placed onto a Petri dish on ice with 1 ml of relaxing solution containing Ca^2+^/EGTA buffer (10 mmol/l), free calcium (0.1 μmol/l), imidazole (20 mmol/l), K^+^/4-morpholinoethanesulfonic acid (MES) (50 mmol/l), dithiothreitol (DTT; 0.5 mmol/l), MgCl~2~ (6.56 mmol/l), ATP (5.77 mmol/l), phosphocreatine (15 mmol/l), pH 7.1, and individual fibre bundles were separated with two pairs of sharp forceps, achieving a high degree of fibre separation. ", "The fibre bundles were permeabilised for 30 min in 3 ml of ice-cold relaxing solution containing saponin (50 μg/ml) \\[[@CR10]\\]. ", "After rinsing in respiration medium (MiR05; Oroboros, Innsbruck, Austria) containing sucrose (110 mmol/l), potassium lactobionate (60 mmol/l), EGTA (0.5 mmol/l), MgCl~2~.6H~2~O (3 mmol/l), taurine (20 mmol/l), KH~2~PO~4~ (10 mmol/l), HEPES (20 mmol/l), sucrose (110 mmol/l), BSA (1 g/l), pH 7.1, the muscle bundles were blotted and measured for wet weight in a balance controlled for constant relative humidity, so that all biopsy samples were hydrated to the same degree. ", "The muscle bundles were then immediately transferred into a respirometer (Oxygraph-2k; Oroboros) containing air-saturated respiration medium at 37°C.The Oxygraph-2k is a two-chamber titration-injection respirometer with a limit of oxygen flux detection of 1 pmol s^−1^ ml^−1^. The instrumentation allows for O~2~ flux measurements with only 0.04 mg of mitochondrial protein or 1.5 mg of muscle fibres (wet weight). ", "Standardised instrumental and chemical calibrations were performed to correct for back-diffusion of O~2~ into the chamber from the various components, leak from the exterior, O~2~ consumption by the chemical medium, and sensor O~2~ consumption \\[[@CR11]\\]. ", "O~2~ flux was resolved by software capable of converting nonlinear changes in the negative time derivative of the oxygen concentration signal.", "\n\n**Analysis of muscle tissue** Citrate synthase activity and complex I activity were measured spectrophotometrically at 37°C. ", "Citrate synthase activity was determined as described previously \\[[@CR12]\\], and complex I activity was assessed by measuring the oxidation of NADH (300 μmol/l) using ubiquinone 1 (100 μmol/l) as the acceptor. ", "The complex I rotenone-sensitive activity was measured by the addition of rotenone (1 μmol/l). ", "The protein content, needed to calculate the specific activity, was measured using a commercially available assay (BCA, Sigma Chemicals, St Louis, MO, USA). ", "For measurement of mitochondrial DNA (mtDNA) content, DNA was isolated from muscle biopsy samples (∼10 mg) by proteinase K digestion at 55°C for 3 days. ", "The 100-μl digestion mix contained 50 mU proteinase K (PCR grade, Roche, Basel, Switzerland), 20 mmol/l Tris-HCl (pH 8.4) and 50 mmol/l KCl. ", "After incubation at 80°C for 45 min, the remains were spun down and the supernatant fraction diluted ×200 in triethanolamine titanate (TE) plus 1 ng/μl salmon sperm DNA (Sigma). ", "5 μl of this dilution was amplified in a 25 μl PCR reaction containing 1×Quantitect SYBR Green Master Mix (Qiagen, Hilden, Germany) and 100 nmol/l of each primer. ", "The amplification was monitored real-time using the MX3000P Real-time PCR machine (Stratagene, La Jolla, CA, USA). ", "The primers were designed to target genomic DNA (Forward: AGG TGC TGT CAG GAA GCA AGG A, Reverse: TAG GGG GAG GAG GGA ACA AGG A) or mtDNA (Forward: CCC CTG CCA TAA CCC AAT ACC A, Reverse: CCA GCA GCT AGG ACT GGG AGA GA). ", "The threshold cycle (*C*~t~) values were related to a standard curve made with the cloned PCR products.", "\n\n**Respirometry protocol** All measurements of respiration were made in duplicate, simultaneously. ", "Resting, routine respiration (state 2, absence of adenylates) was assessed by the addition of malate (1.5 mmol/l) and glutamate (19 mmol/l) as the complex I substrate supply, and then state 3 respiration was assessed by the addition of ADP (4.8 mmol/l). ", "The addition of succinate (9.5 mmol/l) provided state 3 respiration with parallel electron input to complexes I and II. ", "The integrity of the outer mitochondrial membrane was established by the addition of cytochrome *c* (19 μmol/l); no stimulation of respiration was observed. ", "We examined ADP control of coupled respiration and uncoupling control through addition of the protonophore carbonylcyanide-4-(trifluoromethoxy)-phenylhydrazone (FCCP) (0.7 μmol/l). ", "The addition of rotenone (0.1 μmol/l) resulted in inhibition of complex I for examination of O~2~ flux with complex II substrate alone, while antimycin A (12 μmol/l) was added to inhibit complex III to observe non-mitochondrial respiration with small contributions from electron leak in the uncoupled state. ", "The concentrations of substrates and inhibitors used were based on prior experiments conducted for optimisation of the titration protocols.", "\n\n**Data analysis** All values are given as means±SEM for all experiments, run in duplicate or triplicate. ", "For all statistical evaluations, a p value of less than 0.05 was considered significant. ", "Statistical analysis of differences in oxygen flux between healthy control subjects and patients with type 2 diabetes was carried out with a two-way ANOVA for repeated measures. ", "In the case of a significant main effect and interaction between the variables, the Holm-Sidak method was used for post hoc analysis. ", "All other comparisons between the two groups were performed using the unpaired Student's *t* test. ", "SigmaStat version 3.11 (Systat software, Richmond, CA, USA) was used in all analyses.", "\n\nResults {#Sec3}\n=======\n\nThe sequential addition of substrates to the muscle tissue, obtained from both groups before an OGTT, always (*p* \\< 0.05) resulted in a stepwise increase in state 3 O~2~ flux (Fig.", " [2](#Fig2){ref-type=\"fig\"}). ", "Notably, the addition of succinate (stimulating parallel electron input from complexes I+II) resulted in a marked increase in O~2~ flux in both groups. ", "The O~2~ flux per muscle mass was significantly (*p* \\< 0.05) lower in the patients compared with the healthy subjects during complex I and complex I+II respiration (Fig.", " [2](#Fig2){ref-type=\"fig\"}). ", "Further increases in flux capacity and preserved significant differences between the groups were observed with uncoupling by FCCP (109 ± 8 vs 86 ± 4 pmol mg^−1^ s^−1^ in control and diabetic subjects, respectively; *p* \\< 0.05). ", "Subsequent inhibition of complex I and III with rotenone and antimycin A blunted the O~2~ flux (Fig.", " [2](#Fig2){ref-type=\"fig\"}). ", "The addition of cytochrome *c* did not result in significant increases in O~2~ flux (data not shown). ", "Fig.", " 2O~2~ flux in permeabilised skeletal muscle fibres from patients with type 2 diabetes and healthy control subjects. ", "Data are shown as O~2~ flux per mg of tissue (**a**) and further normalised to the number of copies of mtDNA per μg of tissue ×10,000 (**b**). ", "When data are expressed relative to mtDNA, any difference between the groups disappears. ", "Data are means±SEM (\\**p* \\< 0.05). *", "Black and white bars* represent healthy control subjects and patients with type 2 diabetes, respectively\n\nThe number of copies of mtDNA and citrate synthase activity (Table [1](#Tab1){ref-type=\"table\"}) indicated a lower mitochondrial density in the patients with type 2 diabetes. ", "The O~2~ flux data were therefore recalculated relative to mtDNA content (Fig.", " [2](#Fig2){ref-type=\"fig\"}b) and citrate synthase activity (data not shown). ", "All differences in O~2~ flux between patients with type 2 diabetes and healthy control subjects disappeared following either normalisation procedure (Fig.", " [2](#Fig2){ref-type=\"fig\"}b).", "\n\nThe increase in O~2~ consumption when ADP was added (complex I respiratory control ratio \\[state 3:state 2 respiration\\]) was not different between healthy subjects and patients with type 2 diabetes (Fig.", " [3](#Fig3){ref-type=\"fig\"}). ", "Fig.", " 3**a** Respiratory control ratio for complex I (NADH supply from substrates glutamate + malate) measured as the ratio of O~2~ flux with (state 3) and without (state 2) ADP. **", "b** Electron transport capacity measured as O~2~ flux after FCCP-induced uncoupling relative to coupled O~2~ flux at state 3 with malate + glutamate + ADP + succinate (parallel electron input into both complex I and II). ", "No significant difference between the groups was noted. ", "Data are means±SEM\n\nMitochondrial respiration may be influenced by the prevailing level of glucose and/or insulin. ", "However, none of the O~2~ flux rates measured with different substrates and inhibitors displayed significant correlations with these parameters, or the changes seen during the OGTT (data not shown).", "\n\nThe glucose and insulin concentrations were markedly increased in both groups at 30 min into the OGTT (Fig.", " [1](#Fig1){ref-type=\"fig\"}). ", "However, the measured O~2~ flux in the muscle tissue obtained at this time point deviated to a lesser extent (mean +2.4 ± 3.5%) from the O~2~ flux measured in the biopsies obtained during fasting (data not shown).", "\n\nThe activity of complex I was affected by rotenone to a similar extent in the two groups (Table [1](#Tab1){ref-type=\"table\"}). ", "Furthermore, the biochemically measured activity of complex I was significantly (*p* \\< 0.02) correlated with O~2~ flux measured by respirometry during rotenone inhibition (*r*^2^ = 0.37).", "\n\nDiscussion {#Sec4}\n==========\n\nThe primary novel findings in this study are that: (1) ADP-stimulated state 3 mitochondrial O~2~ flux capacity with electron flux through either complex I or II, or with parallel electron input through both complexes I and II, is substantially reduced in type 2 diabetic patients when expressed per unit mass of skeletal muscle; and (2) when O~2~ flux is normalised for mitochondrial DNA content or citrate synthase activity, levels of both oxidative phosphorylation and electron transport capacity are similar to those observed in age-matched healthy control subjects. ", "These results provide direct experimental evidence for normal function of muscle mitochondria in type 2 diabetes and do not support other investigations reporting mitochondrial dysfunction in diabetes. ", "The reduced mitochondrial capacity per unit muscle mass observed in this study is consistent with the concept of reduced mitochondrial content and volume, oxidative enzyme levels, mtDNA and decreased levels of co-regulators of mitochondrial biogenesis-such as peroxisome proliferator-activated receptor-γ coactivator-1 (PGC-1), nuclear respiratory factor (NRF-1 and NRF-2) and mitochondrial transcription factor A (mtTFA)-in insulin-resistant states, as found in some \\[[@CR7], [@CR8]\\] but not all studies \\[[@CR13]\\]. ", "Therefore, it could be argued that specific cellular signals that alter levels of mitochondria, and thus reduce electron transport (and oxidative phosphorylation capacity) per unit muscle mass, contribute to a variety of aberrant metabolic pathways, including intracellular fat accumulation, insulin resistance and glucose intolerance.", "\n\nThe various substrate and inhibitor titrations employed in this study permitted an examination of various steps of oxidative phosphorylation and electron transport under resting respiration and maximally ADP-stimulated O~2~ flux by ADP (state 3). ", "Both resting (state 2) and ADP-stimulated (state 3) coupled respiration were substantially reduced (18--28%) in diabetic subjects, as was uncoupled O~2~ flux with parallel electron supply from both NADH (complex I) and FADH~2~ (complex II). ", "These responses indicate a blunting of oxidative phosphorylation linked to ATP synthase and a decreased maximal electron flux capacity in the uncoupled state induced by addition of FCCP, respectively. ", "The key finding, however, is that these values are comparable with those in healthy control subjects when they are normalised for mtDNA content or citrate synthase activity, both of which are used as indices of mitochondrial density per unit muscle mass. ", "The 30% reduction in state 3 O~2~ flux capacity per mg of muscle in diabetic subjects with parallel electron input (glutamate + malate + succinate) suggests an attenuation of cellular *V*O~2max~. While the prevailing view is that O~2~ delivery is a factor that influences whole-body maximal O~2~ consumption, it remains to be determined if, and to what extent, the observed decrement in muscle state 3 mitochondrial O~2~ flux capacity in diabetic patients contributes to the lower systemic *V*O~2max~ and substrate utilisation.", "\n\nThe patients with type 2 diabetes were in a chronic hyperglycaemic state and were clearly insulin resistant, but even so, mitochondrial function/mtDNA was not impaired. ", "Furthermore, mitochondrial function was also measured in the biopsy samples obtained 30 min into the OGTT, at a time when both glucose and insulin were markedly increased (Fig.", " [1](#Fig1){ref-type=\"fig\"}). ", "This acute metabolic perturbation did not have any significant effect on mitochondrial respiration in any of the subjects (data not shown).", "\n\nIt has been proposed that chronic hyperglycaemia associated with insulin resistance results in the alteration of several metabolic pathways \\[[@CR14]\\]. ", "A central hypothesis involving the mitochondria focuses on an effect of hyperglycaemia providing increased reducing equivalents to the electron transport chain, resulting in a higher membrane potential, with consequent flow of electrons between coenzyme Q and complex III, forming superoxides in the mitochondrial matrix. ", "Excess superoxide production can induce damage to mitochondrial structures, including several electron transport complexes, the mitochondrial lipid bilayer and mtDNA. ", "A role for excess superoxide production is supported by findings of reduced glutathione and metallothionein antioxidant defence systems in type 2 diabetic subjects \\[[@CR15]\\]. ", "The results of this study do not preclude these concepts, but rather suggest the possibility that many pathogenic pathways associated with mitochondrial function in cellular energetics may result from conditions leading to a reduced number of mitochondria, which in turn could place the existing mitochondria under stress with subsequent production of reactive O~2~ species, impaired metabolism of intracellular lipids, and glucose uptake.", "\n\nIt is well known that exercise training increases mitochondrial content in skeletal muscle \\[[@CR16]--[@CR19]\\], and recent work has provided evidence for increased levels of transcriptional regulators of mitochondrial biogenesis in response to exercise \\[[@CR20], [@CR21]\\]. ", "In addition, physical training can play a significant role in the prevention of insulin resistance and type 2 diabetes \\[[@CR22]--[@CR25]\\]. ", "Physical training also substantially improves skeletal muscle insulin sensitivity in patients with overt type 2 diabetes \\[[@CR26]\\], and many cellular adaptations responsible for the effect of training on insulin sensitivity in skeletal muscle have been described \\[[@CR27]--[@CR31]\\]. ", "The cellular and mitochondrial changes in response to exercise training occur in parallel. ", "In obese insulin-resistant subjects, exercise training has been shown to increase the percentage of skeletal muscle fibre volume occupied by mitochondria \\[[@CR32]\\]. ", "Thus, the present data support the hypothesis that type 2 diabetes is, to a large extent, a lifestyle disease, with insufficient exercise-induced gene expression and a surplus of energy intake contributing to its pathogenesis. ", "Accordingly, studies on the effects of 'de-training' have provided evidence of reduced mitochondrial content. ", "After cessation of an endurance training program, citrate synthase and succinate dehydrogenase activities in human muscle have been shown to decline with a half-time of only 12--14 days \\[[@CR33]\\]. ", "Cytochrome *c* protein concentration in rat muscles declines with a half-life of only 7--8 days \\[[@CR34]\\], and the activity in human muscles has a half-time of similar magnitude. ", "These decreases in the activities of cytochrome *c* and succinate dehydrogenase do not exactly follow the detraining decline in *V*O~2max~ \\[[@CR35]\\]. ", "Taken together, these studies support the notion that lack of physical activity lowers mitochondrial concentration. ", "The independent influences of exercise training and detraining, hyperglycaemia, intramuscular lipid accumulation and obesity on mitochondrial function remain to be elucidated.", "\n\nIn this study, the ability of the mitochondria to respond with increased O~2~ consumption following the addition of ADP, represented by the respiratory control ratio, was preserved in the diabetic muscle (Fig.", " [3](#Fig3){ref-type=\"fig\"}). ", "Thus, this index of mitochondrial phosphorylation capacity and coupling of electron transport to phosphorylation indicates that the respiratory chain of the mitochondria in type 2 diabetic subjects functions in a similar manner to that in the mitochondria in control subjects. ", "This view is supported by similar data reported 40 years ago, albeit mostly from patients with 'juvenile diabetes' \\[[@CR36]\\]. ", "Similarly, an increase (1.3--1.4 fold) in O~2~ flux was seen in response to uncoupling by FCCP (Fig.", " [3](#Fig3){ref-type=\"fig\"}). ", "The fact that the increase was similar in the two groups also testifies that electron transport capacity is not impaired in type 2 diabetes, and that the phosphorylation system (adenine nucleotide transporter, phosphate transporter and ATP synthase) exerts control over electron transport in patients and control subjects to the same degree.", "\n\nIn conclusion, the results of the present study provide the first direct evidence of normal mitochondrial function in the skeletal muscle of type 2 diabetic subjects. ", "An apparent impairment of oxidative phosphorylation and electron transport capacity is fully accounted for by a diminished mitochondrial content in the diabetic muscle.", "\n\nWe thank the patients and subjects who participated in the study. ", "The study was supported by The Danish Diabetes Association, Aase and Ejnar Danielsens foundation, the Foundation of 1870, the Lundbeck Foundation, Simon Fougner Hartmanns Foundation, the Novo Nordic Foundation, Jacob Madsen and Olga Madsen's Foundation, Eva and Hans Carl Adolf Holms Grant, Else and Mogens Wedell-Wedellsborgs Foundation, and Fonds de la Recherche en Santé Québec (Quebec Health Research Foundation).", "\n\n**Duality of interest** The authors attest that no conflict of interest or duality exists related to this work.", "\n\nFCCP\n\n: carbonylcyanide-4-(trifluoromethoxy)-phenylhydrazone\n\nmtDNA\n\n: mitochondrial DNA\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "Introduction {#s1}\n============\n\nThe [I]{.ul}mmunodeficiency, [C]{.ul}entromeric region instability and [F]{.ul}acial anomalies (ICF) syndrome (OMIM 242860) is a rare autosomal recessive disorder often fatal in childhood [@pone.0011364-Tiepolo1]. ", "So far, less than 50 cases have been reported worldwide.", "\n\nThe ICF syndrome is characterised by phenotypic and clinical variability, with the most consistent features being reduction in serum immunoglobulin (Ig) levels, developmental delay, facial anomalies and cytogenetic defects. ", "The normal cause of death in ICF patients is infection, usually of the pulmonary or gastrointestinal tract \\[rev. ", "in [@pone.0011364-Ehrlich1]\\].", "\n\nCytogenetic defects of diagnostic significance principally involve decondensation of the juxtacentromeric (or centromere adjacent) heterochromatic regions of chromosomes 1 and 16, and to a lesser extent chromosome 9. ", "In mitogen-stimulated lymphocytes, a wide array of aberrations can be observed, ranging from greatly stretched heterochromatic regions to multiradiate chromosomes. ", "The juxtacentromeric heterochromatic regions of chromosome 1 and 16 are mainly comprised of classical satellite 2 and 3 repeats. ", "Chromosome fusion in the ICF syndrome occurs only at regions of decondensed centromere-adjacent heterochromatin, and the alpha satellite repeats, the main component of centromeres, always remain outside the regions of multiradiate chromosome fusions [@pone.0011364-Schuffenhauer1], [@pone.0011364-Sumner1]. ", "Lymphoblastoid cell lines generated from ICF patients also show high frequencies of the same karyotypic abnormalities as those observed in mitogen-stimulated lymphocytes [@pone.0011364-Stacey1], [@pone.0011364-TuckMuller1].", "\n\nICF syndrome is also characterised by abnormal DNA methylation. ", "Although only a slight decrease in 5-methylcytosine has been observed at the overall genomic level [@pone.0011364-Xu1], the classical satellite 2 DNA sequences are significantly and consistently hypomethylated at cytosine residues in this syndrome [@pone.0011364-Schuffenhauer1], [@pone.0011364-Hassan1], [@pone.0011364-Jeanpierre1], [@pone.0011364-Kondo1]. ", "Chromosome 9 juxtacentromeric heterochromatin, which mainly consists of related satellite 3 DNA is also hypomethylated, although to a lesser extent [@pone.0011364-Jeanpierre1], [@pone.0011364-Maraschio1]. ", "A small number of other genomic regions show significant hypomethylation in ICF syndrome, most notably the non-satellite repeats D4Z4 and *NBL2* [@pone.0011364-Kondo1]. ", "Single copy loci showing heterogeneous hypomethylation comprise *SCP-1* [@pone.0011364-Tao1], the imprinted loci D15S9, D15S63 and H19 [@pone.0011364-Schuffenhauer1] and in female ICF cells a number of genes residing on the inactive X chromosome [@pone.0011364-Schuffenhauer1], [@pone.0011364-Tao1], [@pone.0011364-Hansen1]. ", "Also, some significant changes in DNA methylation patterns at promoters and CpG rich regions were recently identified within a sample of dysregulated genes in ICF [@pone.0011364-Jin1].", "\n\nICF syndrome was initially linked to chromosome 20q11.2 [@pone.0011364-Wijmenga1] and subsequently the DNA methyltransferase 3B gene (*DNMT3B*) was identified as the gene responsible for the methylation defects observed in ICF [@pone.0011364-Xu1]. ", "Along with DNMT3A, DNMT3B acts to methylate cytosine residues *de novo* and is essential for normal development [@pone.0011364-Okano1].", "\n\nMutations of *DNMT3B* in ICF syndrome are heterogeneous. ", "Analysis of fourteen patients revealed eleven different mutations, including eight different missense mutations, two nonsense mutations and a splice site mutation [@pone.0011364-Wijmenga2]. ", "Nonsense mutations always occur as compound heterozygous, highlighting that the DNMT3B protein is essential for life. ", "Most recently, a model for ICF syndrome has been engineered by generating *Dnmt3b* mutations in mice [@pone.0011364-Ueda1]. ", "Homozygous mice carrying two missense alleles of *Dnmt3b* show many ICF-like characteristics, including hypomethylation of heterochromatin repeat DNA.", "\n\nWijmenga and collaborators [@pone.0011364-Wijmenga2] also identified five ICF patients who do not carry mutations in the *DNMT3B* gene. ", "More recent investigations described further patients who did not carry a mutation of *DNMT3B* [@pone.0011364-Jiang1], [@pone.0011364-Kubota1]. ", "Intriguingly, Jiang and co-authors showed that the subset of patients carrying a mutation in the *DNMT3B* gene had alpha satellite methylation patterns comparable to control samples. ", "In contrast, the subset of patients who did not carry mutations in *DNMT3B* exhibited hypomethylation of the alpha satellite as well as classical satellite DNA. ", "These findings lead to the proposal of the existence of two distinct types of ICF syndrome, namely a Type 1, in which patients display mutations in the *DNMT3B* gene, but have normal alpha satellite methylation, and a Type 2, characterised by normal *DNMT3B* and hypomethylation of alpha satellite DNA [@pone.0011364-Jiang1].", "\n\nGlobal expression studies by microarray analysis have identified significant changes in the expression of several hundreds of genes in ICF, involved in immune function, development and neurogenesis as well as lymphogenesis, signal transduction and apoptosis [@pone.0011364-Jin1], [@pone.0011364-Ehrlich2].", "\n\nOver the years, several hypotheses linking altered gene expression to the hypomethylation of juxtacentromeric heterochromatin in ICF have been postulated by different research groups, commonly suggesting inappropriate release or recruitment of regulatory complexes by the hypomethylated satellite DNA, affecting the regulatory properties of the heterochromatin [@pone.0011364-Xu1], [@pone.0011364-Hassan1], [@pone.0011364-Hansen1], [@pone.0011364-Ehrlich2], [@pone.0011364-Bickmore1].", "\n\nThese suggestions have prompted us to investigate whether the decondensation of the juxtacentromeric heterochromatin, as observed in metaphase, and general chromosomal instability reported in ICF patients, correspond to changes in the three-dimensional properties of the heterochromatin in interphase; our working hypothesis being that disruption to the heterochromatin spatial configuration may interfere with transcriptional silencing and be indirectly responsible for some of the changes in gene expression accounting for the symptoms of ICF.", "\n\nAccordingly, we have analysed and compared in two patients (ICF Type 1 and ICF Type 2) and both related (unaffected parents) and unrelated controls the large-scale organisation and intra-nuclear positioning of chromosome 1 and 16 juxtacentromeric heterochromatin. ", "Heterochromatin organisation and positioning have been analysed in different cell lines and cultures, including, as well as ICF cells presenting different degrees of classical satellite 2 hypomethylation [@pone.0011364-Hassan1], control cells in which DNA hypomethylation had been experimentally induced by treatment with 5-azacytidine. ", "We have also carried out a comparative quantification of chromosome 1 satellite 2 and 3 repeats in ICF cells and controls. ", "Finally, we have analysed and compared the intra-nuclear positioning of four genes from chromosome 1 and one gene from chromosome 6 -- namely *BTG2* (B-cell translocation gene 2) (1q32), *CNN3* (Calponin 3) (1p22-p21), *ID3* (Inhibitor of DNA binding 3)(1p36.13-p36.12), *RGS1* (Regulator of G protein signalling) (1q31) and *F13A1* (Factor XIII; A1 subunit) (6p25-p24) - and their co-localisation with the juxtacentromeric heterochromatin of chromosome 1. ", "The expression of these genes had previously been reported to be altered in ICF [@pone.0011364-Ehrlich2]. ", "We have assessed and compared their expression levels in our patients and control cell lines, and, for three of them, we have also analysed in detail the methylation status of upstream CpG islands of their promoters using a quantitative methylation assay.", "\n\nBeyond its relevance to the ICF syndrome, by addressing fundamental principles of chromosome functional organisation within the cell nucleus, this work aims to contribute to the current debate on the epigenetic impact of nuclear architecture in development and disease.", "\n\nResults {#s2}\n=======\n\nThe large-scale organisation of chromosome 1 juxtacentromeric heterochromatin is altered in ICF B-cells {#s2a}\n-------------------------------------------------------------------------------------------------------\n\nObservations on the heterochromatin in interphase, conducted in parallel by wide-field and confocal microscopy, revealed some significant differences between ICF cells and controls. ", "Chromosome 1 juxtacentromeric heterochromatin, as defined by hybridisation with the classical satellite DNA probe D1Z1, and chromosome 16 juxtacentromeric heterochromatin, as defined by hybridisation with the classical satellite DNA probe D16Z3, were analysed and compared in B-lymphoblastoid cell nuclei of two different patients (ICF Patient 1 presenting with ICF Type 1 and ICF Patient 2 presenting with ICF Type 2) and three controls, two of which were unaffected parents of the ICF patients (respectively called Control 1 and Control 2) and one a normal unrelated B-lymphoblastoid cell line (DO208915). ", "Evaluation of the fluorescent hybridisation signals on a per cell basis on 2D fixed cells (2D FISH) allowed us to identify in each cell population the co-existence of noticeably different hybridisation patterns (Examples in [Fig. ", "1](#pone-0011364-g001){ref-type=\"fig\"}).", "\n\n{#pone-0011364-g001}\n\nIn order to quantify possible cumulative differences in the large-scale organisation of the heterochromatin of chromosome 1 in ICF B-cells and controls, we measured the intra-nuclear areas occupied by the juxtacentromeric heterochromatic regions, as defined by hybridisation on 2D-fixed interphase nuclei with the corresponding classical satellite DNA probe ([Fig. ", "2](#pone-0011364-g002){ref-type=\"fig\"}). ", "The measurements were performed as described in the [Materials and Methods](#s4){ref-type=\"sec\"}. ", "The data sets were compared using a Kolmogorov-Smirnov test, which revealed a statistically significant difference between ICF and Control cells (D = 0.3480, P\\<0.001).", "\n\n{ref-type=\"sec\"}. ", "The data sets were compared using a Kolmogorov-Smirnov test, which revealed a statistically significant difference between ICF patients and Controls altogether (D = 0.3480, P\\<0.001).](pone.0011364.g002){#pone-0011364-g002}\n\nSimilar to that observed for chromosome 1, when measurements of the hybridisation areas of chromosome 16 juxtacentromeric heterochromatin were obtained and averaged, this heterochromatic region appeared to be smaller in ICF nuclei compared to controls ([Fig. ", "3](#pone-0011364-g003){ref-type=\"fig\"}). ", "However, when the data sets were compared, no statistically significant difference was observed between ICF and Control (D = 0.1029, P = 0.076).", "\n\n{ref-type=\"sec\"}. ", "The data sets were compared using a Kolmogorov-Smirnov test and no statistically significant difference was observed between ICF patients and Controls altogether (D = 0.1029, P = 0.076).](pone.0011364.g003){#pone-0011364-g003}\n\nTo further corroborate the results obtained by 2D FISH, the large-scale organisation of chromosome 1 juxtacentromeric heterochromatin was also investigated and compared in ICF Patient 1 and Control 1 by means of 3D FISH, a variant of the hybridisation technique believed to better preserve nuclear architecture, followed by laser scanning confocal microscopy analysis ([Fig. ", "4](#pone-0011364-g004){ref-type=\"fig\"}). ", "Volume measurements were carried out as described in the [Materials and Methods](#s4){ref-type=\"sec\"}. ", "The heterochromatin was shown to occupy on average a smaller volume in ICF cells, with a mean value of 0.970 µm^3^ (SD = 0.37) (N = 202), whilst in the Control the mean value was 1.147 µm^3^ (SD = 0.53) (N = 147). ", "The data sets were compared using a Kolmogorov-Smirnov test, which revealed a statistically significant difference between the ICF and Control volume distributions (D = 0.2356, P\\<0.001).", "\n\n{ref-type=\"sec\"}. ", "The heterochromatin was shown to occupy on average a smaller volume in ICF cells. ", "The data sets were compared using a Kolmogorov-Smirnov test, which revealed a statistically significant difference between the ICF and Control volume distributions (D = 0.2356, P\\<0.001). ", "Examples of variable heterochromatin patterns as observed by 3D-FISH, confocal analysis and volume reconstruction are shown in the top panels.](pone.0011364.g004){#pone-0011364-g004}\n\nContrary to the consensual view that decondensation and stretching of the juxtacentromeric heterochromatic regions, as generally observed in metaphase in ICF, should be expected to correspond to decondensation and stretching in interphase, our findings on the large-scale organisation of these chromosomal land-marks in B-cells show that the ICF nuclear phenotype -- when compared to controls - is characterised by an apparently more compact spatial configuration of the juxtacentromeric heterochromatin.", "\n\nVariability of chromosome 1 juxtacentromeric heterochromatin organisation in interphase is not cell-cycle related {#s2b}\n-----------------------------------------------------------------------------------------------------------------\n\nIn order to establish whether the variability in the configuration of chromosome 1 juxtacentromeric heterochromatin, observed between and within cell cultures, could be related to dissimilarities in the rate of proliferation and progression through the cell-cycle between ICF cells and controls, we conducted some comparative tests to assess the existence of a temporal connection between the different heterochromatin patterns and specific stages of the cell-cycle.", "\n\nFirst, we investigated possible cell cycle stage composition differences between ICF and control cell lines by FACS analysis ([Figure S1](#pone.0011364.s001){ref-type=\"supplementary-material\"}).These investigations revealed very similar percentages of diploid cells in G1, S and G2 for the ICF Patient 1 and Control 1, and for the ICF Patient 2 and Control 2 samples analysed, ruling out significant differences in cell cycle stage composition between the patient and control cell lines.", "\n\nThen, we hybridised chromosome 1 classical satellite probe D1Z1 to BrdU pulse-labelled B-lymphoblastoid cells from ICF Patient 1 and Control 1 ([Fig. ", "5](#pone-0011364-g005){ref-type=\"fig\"}). ", "Cells undergoing DNA replication (S-phase) were visualised by antibody detection of incorporated BrdU. The different immunolabelling patterns were interpreted according to O\\'Keefe et al. [", "@pone.0011364-OKeefe1]. ", "The \"conventional\" ([Fig. ", "5A](#pone-0011364-g005){ref-type=\"fig\"}) and \"compact\" ([Fig. ", "5B](#pone-0011364-g005){ref-type=\"fig\"}) heterochromatin patterns appeared to be present indiscriminately during S phase progression and non-S phase of the cell cycle in both Control 1 (N = 91) and ICF Patient 1 (N = 70).", "\n\n![", "Heterochromatin configuration at different stages of the cell-cycle.\\\nBrdU pulse labelling (green), to visualise cells undergoing DNA synthesis (S phase), was used in conjunction with FISH with the D1Z1 probe (red) to identify a possible connection between the observed variability in the configuration of chromosome 1 juxtacentromeric heterochromatin and progression through the cell-cycle. ", "Comparative tests were conducted in both ICF and controls. ", "No differences were observed in the heterochromatin organisation when comparing B-cell nuclei in both ICF and control cells, with \"conventional\" (A) and \"compact\" (B) hybridisation patterns equally present in non-S phase and the various stages of the S phase of the cell-cycle. ", "Examples above belong to a miscellanea of informative pictures collected from both ICF and control cells. ", "S phase progression patterns as described in O\\'Keefe [@pone.0011364-OKeefe1].](pone.0011364.g005){#pone-0011364-g005}\n\nBased on both our FACS analysis and our BrdU incorporation experiments, we conclude that proliferation status and progression through cell-cycle can be excluded as factors responsible for the variability in the spatial configuration of juxtacentromeric heterochromatin observed between and within cell populations.", "\n\nThe intra-nuclear positioning of chromosome 1 juxtacentromeric heterochromatin is also altered in ICF B-cells {#s2c}\n-------------------------------------------------------------------------------------------------------------\n\nThe positioning of chromosomes 1 and 16 juxtacentromeric heterochromatin in interphase was also assessed and compared in B-lymphoblastoid cells from ICF patients and controls. ", "Preliminary observations were aimed at establishing whether chromosome 1 and chromosome 16 centromeric regions showed preferential association with the extreme nuclear periphery, and identifying possible differences between patients and controls. ", "Preferential positioning of chromosome 1 juxtacentromeric heterochromatin at the nuclear periphery was assessed in ICF Patient 1 and 2, Control 1 and 2, and DO208915.The heterochromatic signal was considered to be positioned at the extreme nuclear periphery when any part of it appeared to associate with the nuclear rim, as defined by the edge of the DAPI staining (Examples in [Fig. ", "6](#pone-0011364-g006){ref-type=\"fig\"}). ", "These observations were conducted independently from any consideration on the heterochromatin configuration, and a minimum of 100 nuclei for each experiment were scored randomly.", "\n\n{#pone-0011364-g006}\n\nOur observations on control B-cells showed no marked preferential positioning at the extreme nuclear periphery for chromosome 1 juxtacentromeric heterochromatin, with less than 25% of D1Z1 signals normally associating with the nuclear rim in all cell lines analysed ([Fig. ", "6A](#pone-0011364-g006){ref-type=\"fig\"}). ", "Interestingly, in ICF B-cell nuclei, juxtacentromeric heterochromatin positioning at the extreme nuclear periphery was less frequent, with the percentage of D1Z1 signals associating with the nuclear rim being less than 15% in all cells cultures analysed. ", "The reduction in association of the D1Z1 hybridisation signal with the extreme nuclear periphery in ICF B-cell lines compared to controls is statistically significant using a Chi-squared goodness of fit test (χ^2^ = 4.882, P = 0.027).", "\n\nSimilar observations on the intranuclear positioning of chromosome 16 juxtacentromeric heterochromatin were conducted on ICF Patient 1 and 2, Control 1 and 2, and DO208915 ([Fig. ", "6B](#pone-0011364-g006){ref-type=\"fig\"}). ", "As observed for chromosome 1, there was no evidence of preferential positioning of chromosome 16 juxtacentromeric heterochromatin at the extreme nuclear periphery in either ICF or control nuclei, but the reduction in association of the heterochromatin with the extreme nuclear periphery observed between ICF and control cell lines proved to be statistically significant (χ^2^ = 10.563, P = 0.001).", "\n\nIn order to further evaluate the observed differences in the intra-nuclear positioning between ICF and controls, the distance from the centroid of each juxtacentromeric heterochromatin signal to the nuclear rim was measured as described in [Materials and Methods](#s4){ref-type=\"sec\"}, and averaged in each cell line. ", "To obtain the mean distance of D1Z1 from the extreme nuclear periphery, measurements from two independent experiments were carried out for each cell line ([Fig. ", "7](#pone-0011364-g007){ref-type=\"fig\"}). ", "To take into consideration the varying sizes of nuclei, the measurements were normalised. ", "When performing a Kolmogorov-Smirnov test, the distance of chromosome 1 juxtacentromeric heterochromatin from the nuclear periphery was significantly greater in ICF cell lines when compared to control cell lines (D = 0.1405, P\\<0.001).", "\n\n{#pone-0011364-g007}\n\nThe distance of the D16Z3 signal from the extreme nuclear periphery was also measured in B-lymphoblastoid interphase cells from ICF Patient 1 and 2, Control 1 and 2 and DO208915 ([Fig. ", "8](#pone-0011364-g008){ref-type=\"fig\"}). ", "As for chromosome 1, the different sizes of nuclei were taken into consideration by calculating the ratios between distance from nuclear periphery and nuclear radius. ", "However, in contrast to previous observations, there was no significant difference in the distance of D16Z3 to the nuclear periphery between ICF and normal cell lines (D = 0.0558, P = 0.678).", "\n\n{#pone-0011364-g008}\n\nIn ICF B-cells, when compared to controls, the degree of association of the hypomethylated chromosome 1 classical satellite DNA signals with the nuclear periphery is lower, suggesting a specific re-positioning of the juxtacentromeric heterochromatin to a more internal location within the nuclear volume.", "\n\nChanges in the heterochromatin configuration, as observed in ICF nuclei, can be partially replicated in control cells by treatment with a demethylating agent {#s2d}\n-------------------------------------------------------------------------------------------------------------------------------------------------------------\n\nIt was previously shown that it is possible to reproduce in normal lymphoblastoid cell lines many of the cytological anomalies observed at metaphase in ICF syndrome, in particular the high frequency of juxtacentromeric rearrangements of chromosome 1, by treatment with global demethylating agents, such as 5-azacytidine and 5-azadeoxycytidine [@pone.0011364-Hernandez1], [@pone.0011364-Ji1], [@pone.0011364-KokaljVokac1]. ", "In order to investigate whether treatment with a demethylating agent was also able to reproduce in normal cells the changes to the large-scale organisation and spatial positioning of the heterochromatin observed by us in interphase in this syndrome, we conducted further observations on our cell lines after treatment with 5-azacytidine.", "\n\nWe first established the effect of the demethylating treatment on metaphase chromosomes by incubating unsynchronised B-lymphoblastoid cell lines from Control 1 and 2 with 5-azacytidine for 18 hours, following the protocol previously described by Ji et al. [", "@pone.0011364-Ji1]. ", "We compared metaphase spreads from the 5-azacytidine treated and non-treated cultures and, we observed that following the 5-azacytidine treatment, the otherwise normal control cells displayed decondensation of the chromosome 1 juxtacentromeric region in 10--15% of metaphases analysed ([Figure S2](#pone.0011364.s002){ref-type=\"supplementary-material\"} and [Figure S3](#pone.0011364.s003){ref-type=\"supplementary-material\"}). ", "We also carried out an immunostaining test with a monoclonal antibody against 5-Methylcytidine to detect changes in the chromosomal methylation patterns, with particular focus on the chromosome 1 heterochromatin. ", "We observed that, following the 18 hour treatment with 5-azacytidine, there was a significant intercellular variability in terms of extent and distribution of DNA methylation, with some metaphases and nuclei showing almost no methylation at all and others showing still substantial methylation, particularly on the compact heterochromatic areas. ", "However, most importantly, the stretched or decondensed juxtacentromeric heterochromatin appeared to be consistently demethylated ([Fig. ", "9](#pone-0011364-g009){ref-type=\"fig\"}).", "\n\n{#pone-0011364-g009}\n\nWe then proceeded with observations on the chromosome 1 juxtacentromeric heterochromatin configuration in interphase and comparative assessments of the heterochromatin areas in ICF Patient 1 and 2, Control 1 and 2 and DO208915 B-lymphoblastoid cells before and after treatment with 5-azacytidine. ", "Measurements were performed as described previously ([Table 1](#pone-0011364-t001){ref-type=\"table\"}). ", "In the Kolmogorov-Smirnov test, the control cells showed a significant reduction in the nuclear area occupied by the heterochromatin after treatment with 5-azacytidine (D = 0.1697, P\\<0.001). ", "However, the area of chromosome 1 juxtacentromeric heterochromatin is significantly smaller in non-treated ICF cell lines than 5-azacytidine treated control cell lines (D = 0.2601, P\\<0.001). ", "There was also a significant difference in the areas of chromosome 1 juxtacentromeric heterochromatin between treated and non-treated ICF cell lines (D = 01341, P = 0.001).", "\n\n10.1371/journal.pone.0011364.t001\n\n###### Heterochromatin configuration before and after 5-azacytidine treatment.", "\n\n![](", "pone.0011364.t001){#pone-0011364-t001-1}\n\n Cell Line Mean Area (µm^2^) SD (µm^2^) N\n ------------------------------- ------------------- ------------ -----\n ICF Patient 1 (5-azacytidine) 1.17 0.47 166\n ICF Patient 1 (non-treated) 1.38 0.82 322\n Control 1 (5-azacytidine) 1.89 1.08 178\n Control 1 (non-treated) 2.86 1.69 297\n ICF Patient 2 (5-azacytidine) 1.64 0.67 163\n ICF Patient 2 (non-treated) 1.78 0.75 382\n Control 2 (5-azacytidine) 2.37 1.13 197\n Control 2 (non-treated) 2.46 1.49 309\n DO208915 (5-azacytidine) 2.02 0.87 182\n DO208915 (non-treated) 2.35 0.5 262\n\nArea measurements of chromosome 1 juxtacentromeric heterochromatin, as defined by hybridisation with the classical satellite DNA probe D1Z1, were carried out on cells from ICF Patients 1 and 2, Controls 1 and 2, and DO208915, a third and unrelated control cell line, before and after treatment with the demethylating agent 5-azacytidine (SD = standard deviation; N = total number of measurements).", "\n\nTo investigate whether 5-azacytidine could also affect the positioning of the heterochromatin within the nuclear space, the average distance of chromosome 1 juxtacentromeric regions from the extreme nuclear periphery was measured and compared before and after treatment with 5-azacytidine. ", "Measurements were carried out as described previously ([Table 2](#pone-0011364-t002){ref-type=\"table\"}). ", "There was no significant difference between treated and non-treated ICF cell lines (D = 0.0708, P = 0.186) and no significant difference between the treated and non-treated control cell lines (D = 0.0727, P = 0.98). ", "However, the statistically significant difference in the distance of chromosome 1 juxtacentromeric heterochromatin from the extreme nuclear periphery previously observed when comparing ICF and control cells was maintained even after treatment of the control cells with 5-azacytidine (D = 0.1020, P = 0.009).", "\n\n10.1371/journal.pone.0011364.t002\n\n###### Heterochromatin positioning before and after 5-azacytidine treatment.", "\n\n![](", "pone.0011364.t002){#pone-0011364-t002-2}\n\n Cell Line Distance Radius Ratio SD N\n ------------------------------- ---------- -------- ------- ------ -----\n ICF Patient 1 (5-azacytidine) 4.12 10.01 0.412 2.16 208\n ICF Patient 1 (non-treated) 5.24 11.39 0.460 2.90 311\n Control 1 (5-azacytidine) 3.62 10.82 0.335 2.43 220\n Control 1 (non-treated) 4.70 11.71 0.402 2.91 328\n ICF Patient 2 (5-azacytidine) 5.53 12.55 0.441 2.70 196\n ICF Patient 2 (non-treated) 4.75 9.29 0.512 2.37 358\n Control 2 (5-azacytidine) 4.52 13.13 0.345 2.57 178\n Control 2 (non-treated) 3.22 8.87 0.364 2.27 360\n DO208915 (5-azacytidine) 4.59 14.05 0.327 2.43 201\n DO208915 (non-treated) 3.77 11.18 0.337 2.62 259\n\nThe average distance between the centroid of the chromosome 1 juxtacentromeric heterochromatin signal, as defined by hybridisation with the classical satellite DNA probe D1Z1, to the extreme nuclear periphery was measured in cells from ICF Patients 1 and 2, Controls 1 and 2, and DO208915, a third and unrelated cell line, before and after treatment with the demethylating agent 5-azacytidine (Distance = Mean Distance in µm; Nuclear Radius = Mean Nuclear Radius in µm; Ratio = Mean Distance/Nuclear Radius; SD = standard deviation; N = total number of measurements).", "\n\nComparative analysis of the nuclear architecture parameters used so far in our investigation, carried out in different cell lines before and after treatment with the global demethylating agent 5-azacytidine, shows a less conspicuous, but still significant remodelling of chromosome 1 juxtacentromeric heterochromatin, resulting in an altered configuration of this genomic region in both metaphase and interphase similar to what observed in ICF cells. ", "In contrast, positioning of the heterochromatin in relation to the nuclear periphery seems unaffected by the demethylating treatment.", "\n\nAnalysis by quantitative PCR identifies significant differences in the amount of classical satellite DNA between the different cell lines {#s2e}\n-----------------------------------------------------------------------------------------------------------------------------------------\n\nTo compare the abundance of the two classical satellite DNA families comprising the bulk of the chromosome 1 juxtacentromeric heterochromatin, Real Time PCR experiments with chromosome 1-specific satellite 2 and 3 primers were carried out in ICF cells and controls ([Table 3](#pone-0011364-t003){ref-type=\"table\"}). ", "ICF Patient 1 has about thirty times less satellite 2, and two times less satellite 3 than Control 1. ", "However, when compared to the unrelated control D0208915, ICF patient 1 seems to have two times less satellite 2, but no significantly different amount of satellite 3. ", "ICF Patient 2 has two times less satellite 2 than Control 2, but eleven times more than the unrelated control D0208915. ", "For the satellite 3, there is no significant difference between ICF Patient 2 and either control.", "\n\n10.1371/journal.pone.0011364.t003\n\n###### Relative quantitation of satellite 2 and 3 using the comparative C^t^ method.", "\n\n![](", "pone.0011364.t003){#pone-0011364-t003-3}\n\n Comparisons *SAT2* *SAT 3*\n ---------------------------- -------- -----------------\n Control 1 vs ICF Patient 1 28.9 2.02\n D0208915 vs ICF Patient 1 2.4 Not significant\n Control 2 vs ICF Patient 2 2.28 Not significant\n D0208915 vs ICF Patient 2 −11 Not significant\n\nThe amount of satellite 2 and 3 present in each patient is tabulated as --fold increase with respect to different controls. ", "Only values showing statistical significance are shown.", "\n\nWhile the abundance of the classical satellite 3 appears more or less constant, the marked inter-individual differences observed for the classical satellite 2 are consistent with the length-polymorphism of this repetitive DNA family and heteromorphism of the juxtacentromeric heterochromatin. ", "We show that both ICF patients present less satellite 2 repeats than their relative controls. ", "However, either combining the two satellites results or considering them individually, our results show no statistically significant correlation between satellite DNA abundance and heterochromatin areas measurements in interphase (Pearson Product-Moment Correlation combined: R = 0.411 P = 0.49; Satellite 2 R = 0.43, P = 0.47; Satellite 3 R = −0.206, P = 0.74 respectively).", "\n\nAnalysis by Real Time RT-PCR confirms altered expression of *BTG2*, *CNN3*, *ID3*, *RGS1* and *F13A1* in ICF {#s2f}\n------------------------------------------------------------------------------------------------------------\n\nReal-time RT-PCR was performed to compare the relative expression levels of four genes from chromosome 1 (*BTG2*, *CNN3*, *ID3*, *RGS1*) and one gene from chromosome 6 (*F13A1*) in the cell lines under investigation. ", "Relative gene expression of the above genes was compared between ICF Patient 1 and Control 1, and ICF Patient 2 and Control 2. ", "β-actin was used as a normalisation gene. ", "The results are summarised in [Table 4](#pone-0011364-t004){ref-type=\"table\"}. ", "Our Real-time RT-PCR results show altered gene expression in ICF cells, more specifically up-regulation of *CNN3*, *RGS1* and *F13A1* and down-regulation of *BTG2* and *ID3*.", "\n\n10.1371/journal.pone.0011364.t004\n\n###### Gene expression analysis by real-time RT-PCR.", "\n\n![](", "pone.0011364.t004){#pone-0011364-t004-4}\n\n Gene Primers Primer sequences Cell lines Fold-difference\n -------------------------- ---------------- -------------------------------------------------------- --------------- --------------------\n ***BTG2*** **(1q32.1)** BTG2-RT 3f/3r (5′-gaaccgacatgctccc-3′) (5′-cagtggtgtttgtagtga-3′) ICF 1 vs. C 1 −2.142 (p = 0.001)\n ICF 2 vs. C2 −5.460 (p = 0.013)\n BTG2-RT 4f/4r (5′-aataaaagccaaacct-3′) (5′-gctttccacttttctcca-3′) ICF 1 vs. C 1 −2.071 (p = 0.004)\n ICF 2 vs. C 2 −2.624 (p = 0.001)\n ***CNN3*** **(1p21.3)** CNN3-RT 3f/3r (5′-taacattacagccggtgg-3′) (5′-aggagcagcacagtatt-3′) ICF 1 vs. C 1 +2.046 (p = 0.001)\n ICF 2 vs. C2 +4.854 (p = 0.001)\n CNN3-RT 4f/4r (5′-gcaattggatagaagagg-3′) (5′-ggactcgttgaccttct-3′) ICF 1 vs. C 1 +2.104 (p = 0.001)\n ICF 2 vs. C2 +2.019 (p = 0.001)\n ***ID3*** **(1p36.12)** ID3-RT 4f/4r (5′-caaactatgccaaggcg-3′) (5′-cgcattgttacagaaagtca-3′) ICF 1 vs. C1 −2.432 (p = 0.012)\n ICF 2 vs. C 2 −2.556 (p = 0.001)\n ***RGS1*** **(1q31.2)** RGS1-RT 3f/3r (5′-acagatagtatcaagcgca-3′) (5′-gcgcctggataactttc-3′) ICF 1 vs. C1 +2.847 (p = 0.001)\n ICF 2 vs. C2 +4.512 (p = 0.004)\n RGS1-RT 4f/4r (5′-aagcgcagaaggaatg-3′) (5′-gcgcctggataactttca-3′) ICF 1 vs. C1 +2.898 (p = 0.001)\n ICF 2 vs. C2 +2.107 (p = 0.005)\n ***F13A1*** **(6p25.1)** F13A1-RT 1f/1r (5′-cgtcaacctgcaagag-3′) (5′-cgaccaatgacgtattcc-3′) ICF 1 vs. C1 +1.472 (p = 0.001)\n ICF 2 vs. C 2 +3.517 (p = 0.001)\n F13A1-RT 1f/2r (5′-cgtcaacctgcaagag-3′) (5′-acatagaaagactgccct-3′) ICF 1 vs. C 1 +5.378 (p = 0.009)\n ICF 2 vs. C2 +2.843 (p = 0.001)\n\nA relative expression study for genes *BTG1*, *CNN3*, *ID3*, *RGS1* and *F13A1* in ICF patients versus controls was performed using Real-Time Reverse-Transcription PCR (RT-PCR). ", "Relative expression levels of genes between ICF patients and controls were calculated using the equation described in [Materials and Methods](#s4){ref-type=\"sec\"}.", "\n\nAnalysis by MALDI-TOF mass spectrometry reveals no significant methylation differences in CpG islands of gene promoters between ICF and controls {#s2g}\n------------------------------------------------------------------------------------------------------------------------------------------------\n\nDNA methylation analysis of CpG islands in the promoter region of three of the genes under investigation, more precisely *BTG2*, *CNN3* and *ID3*, was performed to examine whether altered expression in ICF cells may have been caused by changes in promoter methylation. ", "No CpG islands are present in the promoters of *RGS1* and *F13A*.", "\n\nThe analysis was performed on bisulfite treated DNA from ICF Patient 1 and 2, Control 1 and 2, and DO208915 cell lines using a sequencing by fragmentation assay for quantitative methylation analysis [@pone.0011364-Ehrich1]; this assay is based on RNA transcription and base -specific cleavage. ", "Multiple CpG sites can be detected in a single experiment and altered methylation is detected as a G/A change on the reverse strand. ", "The results for all three genes show that there are no significant differences in overall promoter CpG island methylation between ICF cells and controls. ", "At all CpG sites analysed, very low and comparable levels of methylation were found for all ICF patient and control cell lines. ", "The data are summarised in the EpiGrams for each gene ([Figure S4](#pone.0011364.s004){ref-type=\"supplementary-material\"}).", "\n\nThese results show that up-regulation of *CNN3* and down-regulation of *BTG2* and *ID3* are not linked to obvious changes in the DNA methylation of their promoters.", "\n\nIntra-nuclear positioning of abnormally expressed genes and co-localisation with juxtacentromeric heterochromatin {#s2h}\n-----------------------------------------------------------------------------------------------------------------\n\nThe association of the above genes with the extreme nuclear periphery and relative positioning to the chromosome 1 juxtacentromeric heterochromatin were assessed by co-hybridising each of the four BAC clones, containing the chromosome 1 genes *BTG2*, *CNN3*, *ID3* and *RGS1*, with the classical satellite DNA probe D1Z1 to interphase nuclei obtained from ICF patient and control B-lymphoblastoid cells. ", "A BAC clone containing the chromosome 6 gene *F13A1* was also co-hybridised with D1Z1 as well as with the chromosome 6 alpha satellite DNA probe D6Z1 and the chromosome 16 classical satellite 2 DNA probe D16Z3. ", "These were control experiments designed to respectively identify: (a) possible involvement of chromosome 1 juxtacentromeric heterochromatin in inter-chromosomal associations, (b) similarity of behaviour in terms of inter-chromosomal gene-heterochromatin associations between chromosome 1 and 16, and, (c) intra-chromosomal associations involving a chromosome not specifically affected by molecular and cytological changes in ICF syndrome.", "\n\nAssociation of each gene with the extreme nuclear periphery was compared in ICF Patient 1 and Control 1, and ICF Patient 2 and Control 2. ", "A signal was considered to be positioned at the extreme nuclear periphery if any part of it appeared to associate with the nuclear rim, as defined by the edge of the DAPI staining. ", "A minimum of 250 observations were carried out per probe per cell line ([Figure 10](#pone-0011364-g010){ref-type=\"fig\"}).", "\n\n{#pone-0011364-g010}\n\nFor three of the genes under investigation, *BTG2* and *ID3* from chromosome 1 and *F13A1* from chromosome 6, the degree of association of each locus with the extreme nuclear periphery was practically negligible in both ICF cells and controls. ", "The other two genes from chromosome 1 - *CNN3* and *RGS1* - showed a higher percentage of peripheral location, although, as before, no preferential positioning at the extreme nuclear periphery were evident for either loci. ", "Statistical analysis confirmed that the intra-nuclear positioning of all genes analysed, as defined by association with the extreme nuclear periphery, is not altered in ICF cells as the differences between ICF and controls are not significant when using a Chi-squared test (χ^2^ = 1.042, P = 0.307 for *BTG2*; χ^2^ = 0.314, P = 0.575 for *CNN3*; χ^2^ = 1.010, P = 0.315 for *ID3*; χ^2^ = 1.786, P = 0.181 for *RGS1*; χ^2^ = 1.010, P = 0.315for *F13A1*).", "\n\nThe positioning of the four genes from chromosome 1, *BTG2*, *CNN3*, *ID3* and *RGS1*, in relation to chromosome 1 heterochromatin was also analysed. ", "Co-localisation was assessed by identifying on cells of ICF Patient 1 and Control 1, and ICF Patient 2 and Control 2, gene signals that showed any degree of overlap with the satellite DNA signal. ", "The co-localisation assessment was carried out independently from the heterochromatin spatial configuration and the intra-nuclear positioning of both gene and heterochromatic signals ([Fig. ", "11](#pone-0011364-g011){ref-type=\"fig\"}). ", "A minimum of 250 observations were carried out per probe per cell line ([Figure 10](#pone-0011364-g010){ref-type=\"fig\"}).", "\n\n{#pone-0011364-g011}\n\n*BTG2* and *ID3*, the two genes from chromosome 1showing low association with the extreme nuclear periphery, are also characterised by a comparably low extent of co-localisation with the heterochromatin. ", "On the contrary, *CNN3* and *RGS1*, the two genes from chromosome 1 showing a relatively higher extent of association with the extreme nuclear periphery, are also characterised by a relatively higher extent of co-localisation with the heterochromatin.", "\n\nFor the two down-regulated genes, *BTG2* and *ID3*, the extent of co-localisation with chromosome 1 heterochromatin was not significantly different between ICF cell and controls, using a Chi-squared test (χ^2^ = 0.709, P = 0.400 for *BTG2* and χ^2^ = 0.260, P = 0.610 for *ID3*). ", "However, the extent of co-localisation for *CNN3* and *RGS1*, the other two genes from chromosome 1 that appear to be up-regulated, was significantly different in ICF and control cells (χ^2^ = 6.028, P = 0.014 for *CNN3* and χ^2^ = 6.775, P = 0.009 for *RGS1*).", "\n\nThe extent of co-localisation between *F13A1*, the over-expressed gene from chromosome 6, and both chromosome 1 and chromosome 16 juxtacentromeric heterochromatic regions was negligible and there were no significant differences between ICF cells and controls (χ^2^ = 0.510, P = 0.475; χ^2^ = 0.000, P = 1.000). ", "The extent of co-localisation between *F13A1* and the chromosome 6 centromeric region, as defined by hybridisation with the alpha-satellite DNA probe D6Z1, was also assessed and showed no statistical significance (χ^2^ = 0.122, P = 0.727).", "\n\nIn conclusion, although the genes under investigation present a variable extent of association with the extreme nuclear periphery, none of them shows preferential positioning there, and, in this respect, there are no significant differences between ICF and control B-cells. ", "However, in terms of co-localisation with the juxtacentromeric heterochromatin, the inter-genic variability is more pronounced, with two of the genes from chromosome 1 -- *CNN3* and *RGS1* - showing a greater extent of co-localisation with the chromosome 1 juxtacentromeric heterochromatin. ", "Most importantly, for these two loci the extent of gene-heterochromatin co-localisation is significantly reduced in the ICF cells in which these genes appear over-regulated when compared to the control cells.", "\n\nDiscussion {#s3}\n==========\n\nThe complexity of ICF, in particular the combination of phenotypic variability and genetic heterogeneity that characterises it, has intrigued geneticists and cell biologists since this syndrome was initially identified. ", "Over the years, numerous and diverse investigations have yielded interesting insights into its pathogenesis and prompted a substantial amount of speculation on the relationship between methylation defects, chromatin abnormalities and clinical symptoms that characterise this complex disorder [@pone.0011364-Ehrlich1], [@pone.0011364-Jin1], [@pone.0011364-Ueda1], [@pone.0011364-BlancoBetancourt1].", "\n\nInvestigations on the chromosomal disturbances in ICF have been so far conducted predominantly on metaphase chromosomes and, although there has been a number of observations carried out in interphase [@pone.0011364-Stacey1], [@pone.0011364-Gisselsson1], [@pone.0011364-Luciani1], [@pone.0011364-Luciani2], [@pone.0011364-Maraschio2], [@pone.0011364-Matarazzo1], [@pone.0011364-Miniou1], [@pone.0011364-Sawyer1], our study provides the first extensive and statistically substantiated analysis on the nuclear architecture of genes and heterochromatic regions in this syndrome. ", "In particular, we have examined the large-scale organisation of chromosome 1 and chromosome 16 juxtacentromeric heterochromatic regions, their intra-nuclear positioning, and their co-localisation with five specific genes, four from chromosome 1 and one from chromosome 6, on which we have concurrently conducted expression and methylation analysis. ", "These genes express proteins with different functions, ranging from cell growth and differentiation to blood coagulation and to association with the cytoskeleton and we selected them on the basis of their chromosomal location, within a collection of genes previously reported to be abnormally expressed in ICF [@pone.0011364-Ehrlich2]. ", "The investigations have been carried out in parallel in two unrelated patients, one with Type 1 ICF and the second with Type 2 ICF, both presenting the hypomethylation of the classical satellite 2 DNA typical of this syndrome [@pone.0011364-Hassan1]. ", "One unrelated and two related controls (unaffected parents of the ICF patients) have been also included in the study.", "\n\nThe comparative analysis of the large-scale organisation of the juxtacentromeric heterochromatin, undertaken by FISH analysis on interphase nuclei, has disclosed intriguing differences between ICF and control cells. ", "To begin with, observations at the microscope on a cell-by-cell basis and 2D measurements of the areas occupied by chromosome 1 heterochromatin have revealed that these areas were on average significantly smaller in nuclei from the patient cell lines when compared to the controls, suggesting an altered intra-nuclear arrangement of this specific genomic region in ICF. ", "These unexpected conclusions were also confirmed by heterochromatin volume measurements obtained by 3D FISH, a cytological hybridisation procedure acknowledged to better preserve nuclear architecture, followed by confocal analysis. ", "A similar reduction in the size of the heterochromatin hybridisation signals in ICF cells was also observed for chromosome 16, although when analysed statistically the difference was shown to be not significant.", "\n\nBecause of the observed inter-nuclear variability, we decided to investigate a possible connection between heterochromatin remodelling and progression through the cell-cycle. ", "Based on our FACS analysis and our results on BrdU pulse-labelled cells, we were able to demonstrate that dissimilar percentages of different heterochromatin configurations within each cell population cannot be attributed to differences in cell-cycle progression.", "\n\nWe showed that a downsized configuration of the heterochromatin in interphase, similar to that observed in ICF, can be partly reproduced in control cells by treatment with 5-azacytidine. ", "This demethylating agent had been previously used to reproduce *in vitro* some of the defects observed on metaphase chromosomes in ICF syndrome [@pone.0011364-Hernandez1], [@pone.0011364-Ji1], [@pone.0011364-KokaljVokac1]. ", "Our results provide for the first time evidence that hypomethylation of classical satellite DNA sequences, as well as contributing to promote the abnormal chromatin structure of the juxtacentromeric regions in metaphase previously described in these patients [@pone.0011364-Hassan1], also affects the large-scale organisation of the same heterochromatic regions in interphase.", "\n\nOur unexpected findings of an apparently more compact configuration of the chromosome 1 juxtacentromeric heterochromatin in ICF B-cell nuclei do not concur with the consensus -- based on the generally acknowledged parallel between DNA methylation and chromatin compaction \\[rev. ", "in [@pone.0011364-Grewal1], [@pone.0011364-Richards1]\\] and also supported by earlier observations on ICF cells [@pone.0011364-Gisselsson1], [@pone.0011364-Miniou1] - that decondensation and stretching of the heterochromatin, as observed in metaphase, should also be expected in interphase. ", "However, we feel confident with the extent and variety of our investigations and the robust statistical analysis that supports our findings. ", "Interestingly, the canonical view of a direct correspondence between methylation and chromatin condensation has also been challenged by Gilbert and co-authors. [", "@pone.0011364-Gilbert1], who, by using mutant mouse embryonic stem cells completely lacking in DNA methylation, have recently shown that chromatin compaction, as assayed by nuclease digestion and sucrose gradient sedimentation, is not affected in these cells, their results underlining the complexity of the relationship between DNA methylation and chromatin structure.", "\n\nBecause of the intrinsic resolution limits of the microscopy techniques and the recurring concerns in the field of chromosome biology on the effects of cell fixation on the \"live\" properties of the chromatin fibres in the nucleus, in particular in 2D FISH procedures [@pone.0011364-Hepperger1], we are aware that any attempt to explain the observed altered arrangement of the juxtacentromeric heterochromatin in ICF nuclei should be particularly cautious. ", "However, we speculate that the downsizing of the heterochromatin signal could be partly the effect of a collapse in the folding of the chromatin fibre caused by changes in the steric properties of the hypomethylated satellite DNA and the resulting destabilization of the chromatin structure, probably rendered more obvious by the fixation procedures.", "\n\nWhile investigating the altered heterochromatin organisation in ICF, a possible linkage with the heteromorphism of the heterochromatin deserves also consideration, as the downsizing of the heterochromatic signal in interphase in ICF cells could simply occur as the result of a substantial reduction in the number of their classical satellite repeats. ", "An interesting study by Blasco and collaborators [@pone.0011364-Jaco1] has reported a reduction in centromeric repeats in mouse cells lacking the Dnmt3a and Dnmt3b DNA methyltransferases, suggesting DNA methylation at the centromeric heterochromatin to be an important mechanism to suppress \"illicit\" centromere mitotic recombination and to maintain centromere integrity. ", "The hypothesis that a variation in the amount of juxtacentromeric heterochromatin repeat DNA or satellite DNA length polymorphism may underlie the phenotypic variability observed in ICF was formulated by Luciani and co-authors in the context of their investigations on HP1 sub-cellular distribution in ICF [@pone.0011364-Luciani1]. ", "However, they speculated the presence of longer stretches of 1q or 16q repeats in the disorder.", "\n\nThe analysis of the classical satellite DNA that we carried out by quantitative PCR has indeed confirmed marked inter-individual dissimilarities and a significant difference in enrichment of classical satellite 2 repeats in ICF patients when compared to their controls, with both patients showing fewer classical satellite 2 DNA repeats than their respective controls. ", "However, our analysis has also highlighted the absence of a direct correlation between satellite DNA length-polymorphism and heterochromatin configuration. ", "Taken all together, our observations point towards an intermediate scenario in which both DNA hypomethylation and differences in the copy number of classical satellite sequences contribute to the altered spatial organisation of the juxtacentromeric heterochromatin in ICF.", "\n\nHaving established the existence of consistent and quantifiable differences in the large-scale organisation of the juxtacentromeric heterochromatin in ICF, we proceeded to investigate possible changes in the intranuclear positioning of this genomic region in this syndrome, using as a spatial reference the extreme periphery. ", "Although its role in actively regulating gene expression remains unproven, the nuclear periphery is generally considered a transcriptionally silent \"address\" within the nuclear volume, characterised in yeast by the high concentration of silencing *sir* proteins [@pone.0011364-Cockell1] and in higher eukaryotes by poor gene density [@pone.0011364-Croft1], [@pone.0011364-Shopland1], [@pone.0011364-Tanabe1] and high concentration of non-transcribed sequences [@pone.0011364-Scheuermann1]. ", "Also, repositioning of silent genes from the nuclear interior to the nuclear periphery has been observed in few instances [@pone.0011364-Dietzel1], [@pone.0011364-Hewitt1], [@pone.0011364-Kosak1], [@pone.0011364-Williams1].", "\n\nOur measurements of the distance between chromosome 1 heterochromatin and the nuclear rim have revealed that the extent of association with the nuclear periphery is reduced in ICF B-cells, suggesting a specific re-positioning of this genomic region to a more internal location within the nuclear space. ", "Based on the differential distribution of early and late-replicating chromatin within the nucleus [@pone.0011364-Ferreira1], [@pone.0011364-Sadoni1], our findings on the relocation of the heterochromatin away from the extreme nuclear periphery to a more internal position agree with the advanced replication of the hypomethylated satellite 2 previously reported in ICF [@pone.0011364-Hassan1]. ", "Evidence for a similar repositioning of the chromosome 1 juxtacentromeric heterochromatin within the nuclear volume, following treatment with the histone deacetylase inhibitor trichostatin A (TSA), was published before [@pone.0011364-BarkiCelli1].", "\n\nOur findings on the altered large-scale organisation and intra-nuclear positioning of chromosome 1 juxtacentromeric heterochromatin in ICF are particularly significant in the light of the mounting experimental evidence suggesting chromosome band 1q12 to be the core of a nuclear domain with functional significance, with earlier investigations showing physical association of this genomic region with the human polycomb group complex [@pone.0011364-Saurin1], and also with the oncogenic transcriptional regulator TLX1/HOX11 in leukemic T-cells [@pone.0011364-Heidari1]. ", "In ICF cells the 1qh satellite DNA is associated in G2 with a giant HP1-PML nuclear body [@pone.0011364-Luciani2].", "\n\nIn order to explore the existence of a possible link between altered heterochromatin organisation and changes in gene expression in ICF, we investigated the intra-nuclear positioning of four specific genes from chromosome 1 (*BTG2*, *CNN3*, *ID3* and *RGS1*), using as a spatial reference their association with the extreme nuclear periphery, as well as their co-localisation with chromosome 1 heterochromatin. ", "The genes were selected from a collection of genes previously reported to be abnormally expressed in ICF [@pone.0011364-Ehrlich2]. ", "We were also interested in identifying possible long-range interchromosomal gene-heterochromatin associations, therefore we included in the analysis *F13A1*, a gene mapping on 6p25-24, also previously reported to be abnormally expressed in ICF [@pone.0011364-Ehrlich2]. ", "In parallel to the cytological investigations, relative gene expression analysis was carried out by Real Time RT-PCR. ", "Our experiments showed comparative up-regulation of *CNN3*, *RGS1* and *F13A1* and down-regulation of *BTG2* and *ID3* in our ICF cell lines, confirming previous results obtained by microarray analysis [@pone.0011364-Ehrlich2].", "\n\nWe also tested for a direct role of methylation on gene expression changes by carrying out a comparison of CpG islands in the promoter regions of three of the genes under examination, namely *CNN3*, *BTG2* and *ID3*. ", "Our methylation analysis, carried out by base-specific cleavage and mass spectrometry, established that the genes were largely unmethylated and detected no significant changes in ICF cells. ", "The promoter regions of *RGS1* and *F13A1*, the other two genes under investigation not included in our methylation analysis due to the absence of CpG islands in their promoters, had previously shown no ICF-linked changes in the overall promoter methylation [@pone.0011364-Ehrlich2].", "\n\nIn terms of nuclear positioning, our observations show two of the genes analysed -- *RGS1* and *CNN3* -- to be not exclusively, but more frequently associated with the extreme nuclear periphery than the other three genes under investigation, for which the degree of association with the nuclear rim was negligible. ", "However, no significant differences were observed when the positioning of each of the genes in relation to the extreme nuclear periphery was compared between ICF cells and controls.", "\n\nResults that are more relevant were provided by our analysis of genes and chromosome 1 juxtacentromeric heterochromatin co-localisation, as *RGS1* and *CNN3*, the two up-regulated genes from chromosome 1, showed a significant reduction in their extent of co-localisation with juxtacentromeric heterochromatin in ICF nuclei when compared to controls. ", "Correlation between gene silencing and localisation to transcriptionally repressive heterochromatic compartments has been reported in mouse cycling lymphocytes [@pone.0011364-Brown1], [@pone.0011364-Brown2], [@pone.0011364-Grogan1], human and mouse erythroid cells [@pone.0011364-Francastel1], [@pone.0011364-Francastel2], [@pone.0011364-Schubeler1] and retinoblastoma cells [@pone.0011364-Bartova1]. ", "More recently, a link between centromeric recruitment and establishment of allelic exclusion at the immunoglobulin heavy-chain gene in mouse B-cells was also reported [@pone.0011364-Roldan1]. ", "Therefore, it is conceivable that *RGS1* and *CNN3* are normally silenced in B-cells through association with the heterochromatin and this association is disrupted in ICF.", "\n\nIn contrast to what was observed for *RGS1* and *CNN3*, the extent of co-localisation between chromosome 1 juxtacentromeric heterochromatin and *BTG2* and *ID3*, the two genes showing down-regulation in ICF but no significant changes in promoter CpG islands methylation, was negligible and there were no significant differences between ICF cells and controls. ", "These findings solicit further investigations into different aspects of nuclear architecture and other possible epigenetic mechanisms likely to affect the regulation of these two genes.", "\n\nIn conclusion, we suggest that in ICF the length and hypomethylation of the classical satellite 2 DNA, the main component of the juxtacentromeric heterochromatin of chromosomes 1,and 16, are not only responsible for the centromeric abnormalities generally observed in metaphase, but also affect the three-dimensional organisation of the heterochromatin in interphase. ", "This is based on our findings -- partly reproducible in control cells by demethylating treatment - that in ICF B-cell nuclei the chromosome 1 juxtacentromeric heterochromatin appears significantly smaller in volume and more internally positioned within the nuclear space. ", "On the basis of our observations on the changes in the extent of co-localisation of two up-regulated genes (*CNN3* and *RGS1*) and chromosome 1 juxtacentromeric heterochromatin, we also postulate that, by affecting long-range gene-heterochromatin associations, the altered intra-nuclear arrangement of the hypomethylated classical satellite sequences interferes with heterochromatin mediated gene silencing and contributes to some of the changes in gene expression observed in ICF.", "\n\nOur findings support earlier suggestions of an epigenetic impact of chromatin and chromosomal changes in ICF syndrome and present an example of how human diseases can provide ideal model systems to investigate the functional significance of nuclear architecture.", "\n\nMaterials and Methods {#s4}\n=====================\n\nCell lines {#s4a}\n----------\n\nThe ICF B-lymphoblastoid cell line GM08714A, and a control cell line generated from the patient\\'s mother, GM08728, were obtained from the Coriell Cell Repositories (USA) <http://ccr.coriell.org/>. ", "A second ICF B-lymphoblastoid cell line, LB188, and a control cell line from the patient\\'s mother, LB290, had been previously established and described [@pone.0011364-Pezzolo1]. ", "An additional control cell lines used for the study was the B-lymphoblastoid cell line, DO208915 (European Collection of Cell Cultures, UK). ", "For simplicity purposes, in the paper the ICF cell line GM08714A is referred to as ICF patient 1 and the ICF cell line LB188 as ICF patient 2. ", "The control cell line GM08728 is referred to as Control 1, and LB290 as Control 2. ", "ICF patient 1 is a compound heterozygote for mutations in *DNMT3B*, carrying a G\\>A transition at nucleotide 1807 on one allele, and a G\\>A transition within intron 22, 11 nucleotides 5′ of a splice acceptor site on the other allele, and has Type 1 ICF syndrome. ", "ICF patient 2 does not carry a mutation in *DNMT3B* and has Type 2 ICF syndrome. ", "Data on the hypomethylation of satellite 2 in both patient cell lines can be found in Hassan et al. ", "2001 [@pone.0011364-Hassan1] (wherein GM08714 is referred to as PT4 and LB188 is referred to as PT12).", "\n\nCell culture and slides preparation {#s4b}\n-----------------------------------\n\nCells were cultured in suspension in RPMI-1640 medium (Sigma-Aldrich, UK) supplemented with 10% foetal bovine serum (Sigma-Aldrich) and 1% L-Glutamine at 37°C in a 5% CO~2~ incubator. ", "Slow-growing cultures, enriched in G0/G1 cells, were obtained by incubating the cells with no serum for 72 hours. ", "For cell-cycle investigations, cells were pulse-labelled with 10 µM 5-Bromo-2-deoxyuridine (BrdU) (Sigma-Aldrich) for 30 minutes prior to cell harvesting. ", "For the demethylating agent treatment, 5-azacytidine (Sigma-Aldrich) was added to the cell cultures at a final concentration of 0.5 µM followed by incubation at 37°C for 18 hours, a wash and incubation in normal conditions for 72 hours prior to cell harvesting, as previously described [@pone.0011364-Ji1]. ", "To obtain metaphase chromosomes, thymidine (Sigma-Aldrich) was added to each culture at a final concentration of 0.3 mg mL^−1^ and incubated at 37°C for 17 hours. ", "10 minutes prior to harvest, Colcemid (Invitrogen, UK) was added at a final concentration of 0.2 µg mL^−1^. The cells were centrifuged, resuspended in prewarmed hypotonic solution (0.075 M potassium chloride) for 5 minutes and fixed in three changes of 3∶1 methanol: acetic acid. ", "Slides were prepared according to standard procedures. ", "Metaphase chromosomes obtained from cultures treated with 5-azacytidine were harvested without thymidine. ", "For interphase preparations no thymidine or Colcemid were used. ", "For 3D FISH analysis, cells were resuspended in 1× PBS at a density of 2×10^6^ cells mL^−1^. 200 µL of the cell suspension was pipetted onto a poly-lysine coated slide (VWR International, UK) and the slide incubated in a moist chamber for 1 hour at 37°C. ", "Following incubation, the slides were processed by washing in 1× PBS on ice for 5 minutes and then in CSK/TX (0.1 M NaCl; 0.3 M Sucrose; 0.003 M MgCl2; 0.01 M Pipes; 0.5% Triton X-100). ", "The cells were fixed in 4% formaldehyde/1× PBS for 5 minutes at room temperature, washed in 1× PBS and permeabilised in 0.5% Triton X-100/1× PBS for 20 minutes at room temperature. ", "The slides were again washed in 1× PBS and then incubated in 0.1 M HCl for 10 minutes at room temperature. ", "After a final wash in 1× PBS, the slides were stored in 70% ethanol.", "\n\nProbes {#s4c}\n------\n\nBAC clones containing genes *BTG2* (RP11-134p9), *CNN3* (RP4-639p13), *ID3* (RP1-150o5) and *RGS1* (RP5-1011o1) were obtained from the Sanger Institute (Cambridge, UK). ", "A DNA preparation of the BAC containing gene *F13A1* (287k15) was obtained directly from the Genomics Core Group, Wellcome Trust Centre for Human Genetics, Oxford. ", "BAC DNA extraction was carried out according to standard procedures. ", "Prior to FISH analysis, the BAC clones were verified for gene content by Polymerase Chain Reaction (PCR) amplification. ", "The primers ([Table S1](#pone.0011364.s006){ref-type=\"supplementary-material\"}) were generated using \"Primer 3\" design software (<http://frodo.wi.mit.edu/cgi-bin/primer3/primer3_www.cgi>) based on the genomic sequences of *BTG2*, *CNN3*, *ID3* and *RGS1* obtained from the Human Genome Browser Gateway (<http://genome.ucsc.edu/cgi-bin/hgGateway?org=human>). ", "Primers were synthesised by MWG Biotech (Germany). ", "Directly labeled chromosome 1 classical satellite probe (D1Z1) (Qbiogene, UK) and chromosome 16 satellite 2 DNA probe (D16Z3) (Abbott Laboratories, UK) were used to visualise the juxtacentromeric heterochromatin. ", "The chromosome 6 alpha satellite probe (D6Z1) (Qbiogene) was also used.", "\n\nFluorescence *in situ* hybridisation (FISH) {#s4d}\n-------------------------------------------\n\n80 ng of probe DNA - labeled with biotin-11-dUTP (Roche) using a nick-translation kit (Abbott Laboratories) - and 2 µg of human *C~0~t-1* competitor DNA (Invitrogen) were dried on a heating block at 65°C and resuspended in 1× hybridisation buffer (50% formamide, 1× SSC and 10% dextran sulphate) to a final concentration of 16 ng µL^−1^. Prior to hybridisation, the probes were denatured at 72°C for 10 minutes and pre-annealed at 37°C for 30 minutes. ", "The chromosome 1 classical satellite probe (D1Z1), chromosome 16 satellite 2 DNA probe (D16Z3) and chromosome 6 alpha-satellite (D6Z1) probe were denatured at 85°C for 5 minutes and cooled on ice for 5 minutes prior to hybridisation. ", "The slides were denatured in 70% formamide/0.6× SSC at 70°C for 2 minutes. ", "Following hybridisation, in a moist chamber at 37°C overnight, the slides were washed in 50% formamide/1× SSC at 42°C for 10 minutes and 2× SSC at 42°C for 5 minutes. ", "The biotinylated probes were detected with a layer of streptavidin conjugated FITC (Vector Laboratories, UK) when co-hybridised with red-labelled heterochromatin probes, or streptavidin-Texas Red (Invitrogen) when used with green heterochromatin probes. ", "Slides were mounted with Vectashield (Vector Laboratories) containing 4′, 6-diamidino-2-phenylindole (DAPI) for nuclear staining. ", "Prior to FISH, the BrdU pulse-labelled cells were treated with 0.5% Triton X-100 in 1× PBS for 10 minutes and then transferred to 0.1 M hydrochloric acid for 10 minutes at room temperature. ", "The slides were then washed in 2× SSC for 5 minutes and then equilibrated in 50% formamide/2× SSC for at least 15 minutes prior to denaturation. ", "BrdU labelling was detected using mouse anti-BrdU antibody (Roche) in 4% BSA in 1× PBS/0.1% Tween-20 and incubated at 37°C for 30 minutes. ", "This was detected using goat anti-mouse Alexa 488 (Invitrogen). ", "Slides were mounted with Vectashield containing DAPI.", "\n\nImmunofluorescence {#s4e}\n------------------\n\nMetaphase slides were denatured in 65% formamide, 2×SSC at 65°C for 30′, then dehydrated in ethanol series, and air-dried. ", "The slides were then briefly washed in 2×SSC and incubated with blocking solution (1% non-fat dried milk in PBS/0.1% Tween-20) at 37°C. ", "After 30 minutes a monoclonal antibody against 5-Methylcytidine (Eurogentec) (diluted 1∶100 in PBS/0.1% Tween-20) was applied to the samples and the slides were then incubated for 2 hours. ", "The slides were finally washed in PBS three times for 10 minutes and incubated with a secondary antibody, Texas Red goat-anti mouse (Sigma) for 30 minutes. ", "Slides were mounted with Vectashield containing DAPI.", "\n\nImage acquisition and analysis {#s4f}\n------------------------------\n\nFISH experiments were examined with a 100×, 1.3 NA oil-immersion objective lens fitted to an Olympus BX-51 epifluorescence microscope coupled to a Sensys charge-coupled device (CCD) camera (Photometrics, USA). ", "Blue, green and red fluorescence images were taken as separate grey-scale images using the 83000 filter set manufactured by Chroma (USA) and then pseudo-coloured and merged using the software package Genus (Applied Imaging International, UK). ", "Grey-scale images of the heterochromatin taken with Genus were imported into Volocity (Improvision, UK), and an image series created for each experiment. ", "Using the Classifier feature, the areas of juxtacentromeric heterochromatin were measured using the percentage mode empirically set to a lower limit of 27% intensity, an upper limit of 100%, and to exclude areas smaller than 25 pixels and larger than 500 pixels (examples in [Figure S5](#pone.0011364.s005){ref-type=\"supplementary-material\"}). ", "Nuclei were scored randomly. ", "Measurements form two independent experiments were obtained for each cell line and the mean areas calculated. ", "Measurements of the volumes of D1Z1 were also obtained using Volocity. ", "Z stacks generated by laser scanning confocal microscopy (Zeiss LSM510META) were imported into Volocity, where the Classifier feature, empirically set to threshold images at a lower limit of 14% intensity and upper limit of 100%, measured the volumes occupied by D1Z1 signal. ", "Measurements of the distances of chromosome 1 and 16 juxtacentromeric heterochromatin from the extreme nuclear periphery were imported into the software package Volocity and an image series generated for each experiment. ", "Using the VoxelSpy feature, line measurements were taken from the centroid of the juxtacentromeric heterochromatin signals to the extreme nuclear periphery or nuclear rim where the intensity value became less than one standard deviation above background. ", "The microscope used for image capture had been previously calibrated with a stage-micrometer and a conversion factor of 0.135 µm pixel^−1^ was applied to images captured using the 100× objective. ", "For the varying sizes of nuclei to be taken into account when measuring the distances of juxtacentromeric heterochromatin from the extreme nuclear periphery, the values were normalised between patient and control pairs. ", "This was done by measuring the areas of DAPI stained nuclei by the Classifier feature in Volocity, using the percentage mode set to a lower limit of 12% intensity, an upper limit of 100% and excluding areas smaller than 5000 pixels. ", "Tables of nuclear areas were exported for processing in Microsoft Excel, and the mean nuclear radius was calculated for each cell line. ", "This allowed the ratios of distance from extreme nuclear periphery to nuclear radius to be calculated. ", "The ratios for the ICF cell lines were 0.460 (Patient 1) and 0.512 (Patient 2). ", "For the control cell lines, the ratios were 0.402 (Control 1), 0.364 (Control 2) and 0.337 (DO208915).", "\n\nStatistical analysis of FISH data {#s4g}\n---------------------------------\n\nCategorical data, such as that obtained when making observations of association or non-association with the extreme nuclear periphery of juxtacentromeric heterochromatin or genes, were statistically analysed using a Chi-squared goodness of fit test. ", "For these analyses, observed frequencies from the ICF samples were compared to expected frequencies, as obtained from the controls. ", "Quantitative data from the area, volume and distance measurements, which demonstrate a normal distribution, were statistically analysed using the non-parametric Kolmogorov-Smirnov test. ", "For Kolmogorov-Smirnov test: D = the maximum difference between the cumulative distributions; P = probability of the null hypothesis. ", "A P value of ≤0.05 is generally accepted as having biological significance.", "\n\nQuantitative Real Time PCR {#s4h}\n--------------------------\n\nTotal genomic DNA was prepared from each of the samples using Qiagen Blood and Cell Culture DNA Mini Kit as recommended by the manufacturer. ", "For Real Time PCR, 50 ng of each individual DNA were amplified using the Sybr Green kit (Invitrogen) on an iCycler Bio-Rad (UK) Real-Time PCR system, using the following primers: hsSat2 (NCBI accession number X72623) 5′-ATCGAATGGAAATGAAAGGAGTCA-3′; 5′-GACCATTGGATGATTGCAGTCA-3′. S1/AS1 [@pone.0011364-Enukashvily1] 5′-AGTCCATTCAATGATTCCATTCCAGT-3′; 5′-AATCATCATCCAACGGAAGCTAATG-3′.\n\nAs a reference, primers for a single copy gene, *CENPB* (NCBI accession number NP 001801), 5′-GGCTTACTTTGCCATGGTCAA-3′ 5′-TTGATGTCCAAGACCTCGAACTC-3′ and Alu sequences (NCBI accession number D90162) were used.", "\n\n5′-CTCCCGGATTCAAGCAATTA-3′\n\n5′-CATGGTGAAACCCCATCTCT-3′\n\nIn each experiment, for each DNA sample, five replicates were run.", "\n\nThe Ct values were compared using the 2^−ΔΔCT^ formula.", "\n\nGene expression analysis by Real-Time RT-PCR {#s4i}\n--------------------------------------------\n\nTotal RNA was extracted from B-lymphoblastoid cells from ICF patient 1 and 2, and Control 1 and 2 using the RNeasy extraction kit (Qiagen, UK) as recommended by the manufacturer. ", "Reverse transcription reactions were performed to generate 2 µg of cDNA from 2 µg of total RNA. ", "First strand synthesis was set up by adding 500 µg of Oligo(dT) (Invitrogen), 10 mM dATP, 10 mM dCTP, 10 mM dGTP and 10 mM dTTP to 2 µg of total RNA and incubating at 65°C for 5 minutes before chilling on ice for 5 minutes. ", "5× first stand buffer, 0.1 M DTT and 40 units of RNaseOUT™ (Invitrogen) were added to the reactions, which were incubated at 42°C for 2 minutes. ", "200 units of SuperScript™ II reverse transcriptase (Invitrogen) were added and the reactions incubated at 42°C for 50 minutes, before inactivation at 70°C for 15 minutes. ", "The relative expression of *BTG2*, *CNN3*, *ID3*, *RGS1* and *F13A1* in ICF patient and control cell lines was analysed using the Bio-Rad iCycler system. ", "Reactions were set-up with 100 ng of template cDNA, 500 nM primers and iQ SYBR Green PCR Supermix (Bio-Rad). ", "β-actin was used as a normalisation gene. ", "Primers suitable for real-time RT-PCR ([Table S1](#pone.0011364.s006){ref-type=\"supplementary-material\"}) were designed with the LightCycler (Roche) primer design software using mRNA sequences of the genes obtained from the Human Genome Browser Gateway. ", "Relative gene expression was calculated using the following formula [@pone.0011364-Pfaffl1]:\n\nR = Relative expression ratio\n\nE = Efficiency of PCR (calculated from E = 10^(−1/slope\\ of\\ optimisation\\ curve)^)\n\nMEAN = Normalisation gene\n\nCP values were obtained from the Bio-Rad iCycler software when viewing post-run data\n\nQuantitative methylation analysis {#s4j}\n---------------------------------\n\nGenomic DNA was extracted from B-lymphoblastoid cells from ICF patient 1 and 2, Control 1 and 2, and DO208915 using the GeneCatcher™ gDNA 3--10 mL Blood Kit (Invitrogen). ", "1 µg of genomic DNA was denatured and bisulfite treated using the EZ DNA Methylation-Gold Kit (Zymo Research, USA). ", "Following this treatment, PCR was performed to amplify regions from genes *BTG2*, *CNN3* and *ID3*, using 10 µM tailed primers described in [Table S2](#pone.0011364.s007){ref-type=\"supplementary-material\"} and using Qiagen Hot Start Taq. ", "PCR products were then processed using the MassCLEAVE kit reagents from Sequenome (San Diego, USA) to generate reverse strand specific fragments for MALDI_TOF mass spectrometry [@pone.0011364-Ehrich1]. ", "Conditioning of the phosphate backbone prior to MALDI-TOF mass spectrometry was performed by the addition of 6 mg of CLEAN resin (Sequenom, San Diego, USA). ", "15 nL of the cleavage reactions were robotically dispensed onto silicon chips preloaded with matrix (Sequenom, San Diego, USA). ", "The mass spectra were obtained using the Autoflex MassARRAY mass spectrometer (Sequenom, San Diego, USA) and analysed using proprietary interpretation software tools.", "\n\nSupporting Information {#s5}\n======================\n\n###### \n\nFACS analysis. ", "Cell cycle phase composition was analysed by FACS. ", "The four unsynchronysed cell lines present similar percentages of diploid cells in G1, S and G2.", "\n\n(0.09 MB TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### \n\nEffects of the 5-azacytidine on Control 1 cells. ", "Metaphase spreads obtained from Control 1 after the demethylating treatment show variable extent of decondensation or stretching of the chromosome 1 juxtacentromeric heterochromatin (white arrows), similar to what normally observed in ICF cells. ", "Panels C, D and E show dual colour FISH images with D1Z1 in green and D9Z3 in red. ", "Chromosomes are counterstained with DAPI.", "\n\n(2.08 MB TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### \n\nEffects of the 5-azacytidine on Control 2 cells. ", "Similarly to what observed for Control 1, metaphase spreads obtained from Control 2 after the demethylating treatment show variable extent of decondensation or stretching of the chromosome 1 juxtacentromeric heterochromatin (white arrows), similar to what normally observed in ICF cells. ", "Panels B and D show dual colour FISH images with D1Z1 in green and D9Z3 in red. ", "Chromosome are counterstained with DAPI.", "\n\n(1.78 MB TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### \n\nQuantitative methylation analysis of *BTG2*, *CNN3* and *ID3*. ", "The methylation status of promoter CpG islands upstream of genes *BTG2*, *CNN3* and *ID3* was investigated using a MALDI-TOF based quantitative methylation assay on bisulphite treated DNA (for details see [Materials and Methods](#s4){ref-type=\"sec\"}). ", "The EpiGrams summarise the data from the C and T specific cleavage reactions (internal and external circle respectively), the detected methylation level is represented as colour gradient based on the percentage of methylation detected by the analysis. ", "The specific CpG sites for each gene CpG island analysed are numbered and shown in the specific base pair position within the specific amplicon: *BTG2* (A), *CNN3* (B) and *ID3* (C). ", "ICF Patients 1 and 2, Controls 1 and 2 and additional controls of DO208915, methylated control DNA (Chemicon, USA), hemi-methylated control DNA obtained mixing an unmethylated and a methylated control in equal concentration.", "\n\n(5.43 MB TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### \n\nIntra-nuclear measurements of the juxtacentromeric heterochromatic areas on 2D fixed cells. ", "The nuclear areas occupied by the juxtacentromeric heterochromatic regions, as defined by hybridisation on 2D-fixed interphase nuclei with the corresponding classical satellite DNA probes, were measured. ", "Raw images were thresholded using the Classifier feature of Volocity at a level which excluded background fluorescence with the threshold set to a lower limit of 27% intensity, and an upper limit of 100%. ", "Both limits were defined empirically. ", "Areas smaller than 25 pixels and larger than 500 pixels were excluded. ", "The resulting areas, outlined in the images by a dashed line, were measured and exported as data tables for analysis in Excel. ", "Examples of different hybridisation patterns: conventional (A) versus compact (B).", "\n\n(1.14 MB TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### \n\nPrimer pairs used for PCR and real-time RT-PCR. ", "Primers used for PCR to validate the presence of the correct insert in the BAC clones were generated from genomic sequences obtained from the Human Genome Browser Gateway and detailed in the table above. ", "Primers used for quantitative real-time reverse-transcription PCR (RT-PCR) were generated from mRNA sequences of the genes of interest obtained from the Human Genome Browser Gateway and are also detailed above.", "\n\n(0.08 MB JPG)\n\n###### \n\nClick here for additional data file.", "\n\n###### \n\nPrimers for PCR reactions prior to quantitative methylation analysis using the Sequenom mass spectrometer. ", "The sequences of the primers used to amplify the promoter CpG islands of genes *BTG2*, *CNN3* and *ID3* and the sizes of products expected from the PCR reactions.", "\n\n(0.04 MB JPG)\n\n###### \n\nClick here for additional data file.", "\n\nThe authors would like to thank Dr. Keith J. Morris for help with some of the statistical analysis.", "\n\n**Competing Interests:**The authors have declared that no competing interests exist.", "\n\n**Funding:**This work was supported by the Wellcome Trust {075491/Z/04}. ", "The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.", "\n\n[^1]: Conceived and designed the experiments: AJ SC DM GG JR EVV. ", "Performed the experiments: AJ SC DM NW MY GG. ", "Analyzed the data: AJ SC DM NW MY GG JR EVV. ", "Contributed reagents/materials/analysis tools: SC GG JR. ", "Wrote the paper: AJ EVV.", "\n\n[^2]: Current address: Department of Cardiovascular Medicine, John Radcliffe Hospital, Oxford, United Kingdom\n\n[^3]: Current address: UMR 203 BF2I, Biologie Fonctionnelle Insectes et Interactions, INRA, INSA-Lyon, Université de Lyon, Villeurbanne, France\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "In a recent interview, BLACKPINK revealed the advice and support they received from Yang Hyun Suk, and shared thoughts about their first year since debut.", "\n\nBLACKPINK recently swept international music charts with their new song “As If It’s Your Last.” ", "When reminded that they are reaching the group’s first anniversary in August, Lisa replied, “We received so much love in such a short time. ", "The pressure is growing. ", "We want to keep showing our best.”", "\n\nJisoo described her thoughts on an ideal first year anniversary, saying, “We still have a lot of hidden sides to us. ", "We hope we will be able to meet our fans and get to know each other as much as we can. ", "We hope we can make a happy first year anniversary.” ", "She added, “We still have a long way to go, but we always want to be empowering singers.”", "\n\nAlthough BLACKPINK reached mega popularity within the past year, their daily lives do not seem to have changed much. “", "Our daily routine is the same as when we were trainees. ", "We go back and forth between our home, our schedule, and the company. ", "We go to the training room to practice whenever we have time,” shared Jennie.", "\n\nThey also talked about the warm side of their seemingly strict boss, Yang Hyun Suk. ", "Yang Hyun Suk had recently showed his support for BLACKPINK on social media. ", "Jennie expressed her appreciation for his kindness, saying, “Our boss always tells us to do well by ourselves, but he secretly supports us from behind. ", "I found out about his social media post through the internet too. ", "It was touching.”", "\n\nBLACKPINK also received advice from Yang Hyun Suk. “", "Our boss always tells us to emphasize the choreography. ", "He told us that the audience trusts and listens to us more if the performance is fun to watch,” described Jisoo. ", "She further explained, “He wanted charisma in our last song, but this time he advised us to smile and try to look cute. ", "So we focused on practicing that.”", "\n\nSource (1)" ]

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[ "Q:\n\nWhen should database indexes be rebuilt?", "\n\nI was reading about refactoring a large slow SQL Query over here, and the current highest response is from Mitch Wheat, who wants to make sure the query uses indexes for the major selects, and mentions:\n\nFirst thing I would do is check to make sure there is an active index maintenance job being run periodically. ", "If not, get all existing indexs rebuilt or if not possible at least get statistics updated.", "\n\nI'm only am amateur DBA, and I've made a few programs freelance that are basically Java desktop clients and occasionally a MySQL backend. ", " When I set up the system, I know to create an index on the columns that will be queried by, there's a varchar CaseID and a varchar CustName.", "\nHowever, I set this system up months ago and left the client operating it, and I believe the indexes should grow as data is entered and I believe everything is still working nicely. ", " I'm worried though that the indexes should be rebuilt periodically, because today i have read that there should be an 'active maintenance job'. ", " The only maintenance job I set on the thing was a nightly backup.", "\nI wanted to ask the community about regular maintenance that a database might require. ", " Is it neccessary to rebuild indexes? ", "Can I trust the MySQL backend to keep going so long as no one messes with it and the data stays under a few gigabytes?", "\n\nA:\n\nThere is no need to 'rebuild' an index. ", " They are always kept up-to-date. ", " Maybe he was referring to rebuilding the table. ", " Depending on your usage patterns and schema, you can get fragmented pages in InnoDB, and I think in MyISAM also. ", " Rebuilding the table can improve performance by getting rid of fragmentation of your data on disk. ", " I don't use MyISAM tables regularly, but I believe it is recommended to run 'OPTIMIZE TABLE' with certain usage patterns. ", " See the MySQL docs on OPTIMIZE TABLE for some good info on both MyISAM and InnoDB.", "\nI'm not as familiar with MyISAM intricacies, but with InnoDB it is true that statistics can get out of date. ", " The database keeps estimated statistics on how your data is distributed for a given index, and it's possible for those to get out-of-date, but MySQL/InnoDB has some built in functionality to try to keep statistics current. ", " You usually don't have to worry about it.", "\nSo if you are using InnoDB, the answer is no, you typically don't need to actively do anything to keep your indexes performing well. ", " I'm not as sure with MyISAM, I think it's more common to need to optimize those tables regularly.", "\n\nA:\n\nIt's usually a good idea to set up a cronjob to optimize indexes and check for errors.", "\nSee mysqlcheck. ", "A typical cron job looks something like mysqlcheck -Aaos , which checks all tables in all databases for errors, optimizes indexes, and only outputs on error.", "\n\n" ]

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[ "Estrogen receptors alpha and beta: prevalence of estrogen receptor beta mRNA in human vascular smooth muscle and transcriptional effects.", "\nEstrogens have vascular effects through the activation of estrogen receptors (ERs). ", "In addition to ERalpha, the first ER to be cloned, a second subtype called ERbeta has recently been discovered. ", "Using a reverse-transcriptase polymerase chain reaction assay that employs the same primer pair to simultaneously amplify ERalpha and ERbeta transcripts, we found that ERbeta is the ER form that is predominantly expressed in human vascular smooth muscle, particularly in women. ", "The transcriptional effects of the 2 ERs in transfected HeLa cells differed. ", "In response to 17beta-estradiol, ERalpha is a stronger transactivator than ERbeta at low receptor concentrations. ", "However, at higher receptor concentrations, ERalpha activity self-squelches, and ERbeta is a stronger transactivator. ", "Tamoxifen has partial agonist effects with ERalpha but not with ERbeta. ", "The protective effects of estrogens in the cardiovascular system of women may be due to the genomic effects of ERbeta in vascular tissue." ]

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[ "China Excursion\n\nAugust 3, 2009\n\nThere are five of us foreign teachers here in Chifeng (\"Red Peaks\"), a small Han outpost with 4.5 million people, and 200 miles north of Beijing in Inner Mongolia. ", "We have around 20 students per class. ", "The students are all junior high school English teachers and come from the Chifeng area. ", "The program is an oral English program in which we try to get the students to speak English as much as they can. ", "It means coming up with some interesting topics of conversation for each class, and breaking the students up into small groups, one-on-ones, etc. ", "We are also telling them a little about American culture and society. ", "There are opportunities to talk to students outside the classroom, either by chatting with them in their dorm rooms, or going downtown with them to shop.", "\n\nWe are living and teaching at a large vocational high school on the outskirts of town. ", "We can take a bus, or taxi downtown to sightsee and do shopping. ", "We attended a Catholic mass last Sunday, and this Sunday we will have our own service here. ", "Two of the volunteer teachers are retired clergy. ", "We noticed two of our students at the mass. ", "The church had a large crucifix on the altar surrounded by the three Marys. ", "There was a large poster of Pope Benedict on the side. ", "The liturgy seemed a standard one: readings, creeds, hymns and a ten-minute sermon on Mark 6:30-34. ", "Catholicism (Tianzhu Jiao, or \"Heavenly Master\") is considered a separate religion from Protestantism (Jidu Jiao, \"Christ\"). ", "We met with the priest after the service and he said, \"You are all Catholics, yes?\" ", "and we had to confess that we were Protestants. ", "When I said that in America, Catholicism and Protestantism are very close, they said, \"no, no, no!\" ", "Our group leader said that three of us were clergy, trying to smooth things over.", "\n\nChifeng is an amazing city. ", "In the past three years they have built an entirely new city of government, commercial, and apartment buildings, and broad avenues. ", "The \"old city\" looks new enough, probably built in the last 25 years. ", "We live in the outskirts, what Chifeng no doubt looked like 50 years ago! ", "I haven't asked why all the new construction, however, if I had to guess, it would be the government's desire to have a modern Chinese presence in what is an autonomous region. ", "It reminds me a little of (old?) ", "Montreal with all the signs in two languages, although Mongolians only make up 17 percent of the city's population. ", "We have two Mongolian students and although shy they are not at all reserved about telling the rest of the class about their culture. ", "In one childhood reminiscence, one of the students recalled riding on the grasslands on her horse and the summer days spent with her family there cutting grass. ", "A lovely image, no? ", "There is some affirmative action here, Mongolians get an automatic ten points added to all there entrance examinations to the different school levels: junior high school, senior high, and college.", "\n\nAnother lovely childhood memory I would like to relate was by another student who recalled when she was very young, and sent on her first errand to a store to buy salt. ", "On the way home, she fell and broke the plastic bag. ", "She swept up what she could and put it back into the bag. ", "When she got home, she tried to clean the salt by rinsing it under running water. ", "Alas, you know what happened, no more salt!", "\n\nOur teacher-students are wonderful. ", "They are hardworking and dedicated. ", "They are also a lot of fun. ", "It is a joy to teach them. ", "At home they work under difficult conditions, teaching more than 50 students in a class. ", "In Shandong, a far more populated region and where I taught last year, it was not uncommon for teachers to have more than 100 students in a classroom. ", "How do you teach oral English under such conditions, especially when all the examinations are geared towards reading and writing? ", "Teachers are also given a set curriculum they have to cover each day. ", "However, apparently there a new breeze is blowing. ", "The English teachers of the vocational school here went to an interesting meeting last week for all teachers in the city. ", "Apparently, there is going to be a shift in teaching goals and methods to one emphasizing spoken English, allowing the students to talk in class, and also teaching them how to learn on their own.", "\n\nWe have only one week left in the program. ", "The time has gone quickly. ", "Much faster than I remember last year when I was doing the same program. ", "For my son James, it is going more slowly, because it is his first time both in China, and teaching. ", "Although young, he is working hard. ", "He received a compliment from one of the students the other day saying how much she preferred his class to the others because he was more open, and let the students talk more! ", "Another teacher wrote in her journal, \"I like James, he is so young!\"", "\n\nJames is getting a lot of attention. ", "I have been enjoying watching him enjoying it all. ", "Every afternoon during our break he studies Chinese with two, or three of the female college-age teachers' helpers. ", "He says he is not ready to leave China. ", "I wonder why?" ]

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[ "Vaping seems like a tame variety of vice, a novelty of our time, like pipe smoking.", "\n\nBack in the distant year of 1979, 17- and 18-year-olds smoked cigarettes and marijuana, crossed into Jersey to legally drink beer and hard liquor, and had plenty of sex. ", "Sometimes all in the same night.", "\n\nAbout half of these long-ago teens had their driver’s licenses at the tender age of 16. ", "Among those who also had part-time jobs, which was most, they could purchase, for a reasonable price, an aging muscle car. ", "Maybe a 1970 Chevelle SS 454 with 360 horsepower which, legend had it, could roar from 0-60 in six seconds. ", "No air-bags. ", "No one wore seat belts. ", "Fun.", "\n\nHow did parents deal with this alien world of sex, drugs and rock ’n roll, of fast kids and faster cars?", "\n\nThey worried, no doubt. ", "Maybe they had some sleepless nights wondering where junior was at 3 a.m., for which there would be consequences. ", "And there should have been. ", "This was a time before cellphones. ", "Tracking down a teenager at that hour usually required dead-of-night phone calls to the parents of junior’s friends, or to hospital emergency rooms, or to the cops.", "\n\nEventually, junior rolled in and was punished — grounding was popular — and (usually) he never crossed the old man again.", "\n\nBy today’s standards, it’s nuts to think that responsible grownups gave teenagers that much freedom, and the knife-edge danger that came with it.", "\n\nBut those of us who were teens back then turned out OK. ", "Most of us, anyway. ", "Teen marijuana enthusiast Barack Obama, who graduated from high school in 1979, became our 44th president.", "\n\nWhich is why I can’t get worked up about vaping, the latest teen crisis according to experts, school officials and PTO-types who wring their hands raw.", "\n\nVaping is a fairly new vice. ", "The vapee inhales a nicotine-laced liquid which is heated in a small device sometimes called an e-cigarette. ", "The liquid is flavored (one fruity offering is called “Unicorn Puke”). ", "I’ve never vaped, but I suppose vaping delivers the same relaxed sense that we ex-smokers looked forward to each we lit up a Marlboro or Newport, so I get it.", "\n\nBut locally vaping is big, and no one seems to know why. ", "As we reported in Sunday’s editions, a Pennsylvania Youth Survey shows 19.5 percent of Bucks County school students vaped in the last 30 days. ", "Among high school seniors, 37.2 percent vaped over the last month. ", "That’s double the national average of 17 percent. (", "In Montgomery County it was 32.3 percent.)", "\n\nVaping’s health effects are largely unknown. ", "A report this year by the National Academy of Sciences shows vaping has no long-term health conditions. ", "However, it may contribute to a temporary condition called “wet lung,” whose symptoms include coughing, wheezing and chest pain.", "\n\nBeyond that, experts say addiction to nicotine is the most serious side effect, along with using the e-cig device to smoke cannabis. ", "There is also the danger of inhaling tiny metal particles from the heated coil.", "\n\nSchools have geared up to deal with it, experts have been consulted and students have been called to school assemblies to discuss its dangers.", "\n\n“If we have young men and women feeling the need to vape frequently during the day, that is a problem. ", "As a community, we need to talk about it,” Abram Lucabaugh, assistant high school superintendent in Central Bucks School District.", "\n\nWhile I'm sure parents appreciate the superintendent’s concern, pardon me, but it sounds like the making of a hysteria. ", "Not to dismiss legit health concerns, but in 1979, more than half of U.S. 12th graders said they had smoked weed, a high-water mark in casual drug use never reached since. ", "That was a crisis.", "\n\nNow, kids consume vape juice with names like “fruit medley” and “crème brulee.” ", "The alarms seem contrived, and it seems like vaping is getting the “Reefer Madness” spin.", "\n\nI've heard the gateway drug argument, that vaping leads, somehow, to deadly opioids. ", "That’s a stretch. ", "Not everyone who smoked weed or drank at 18 in New Jersey 40 years ago became a drunk or addicted.", "\n\nVaping seems a fairly tame vice, a novelty of our time. ", "There is only one item that should cause great concern for parents of teenagers, something that parents in 1979 didn't have to worry about: legal fun weed.", "\n\nLegalizing recreational marijuana, instead of decriminalizing it, will have a more devastating impact on the health and the well-being teenagers than all the Unicorn Puke Bucks County. ", "That's because when recreational marijuana is legal, kids who otherwise would never have tried it will indulge. ", "Some of them will have their lives altered for the worse.", "\n\nSchool districts should be sounding alarms on that one. ", "So far, I haven’t heard much.", "\n\nJD Mullane can be reached at 215-949-5745 or at jmullane@couriertimes.com." ]

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[ "Galley HF, McCormick B, Wilson KL, Lowes DA, Colvin L, Torsney C. Melatonin limits paclitaxel‐induced mitochondrial dysfunction in vitro and protects against paclitaxel‐induced neuropathic pain in the rat. ", "J. Pineal Res. ", "2017;63:e12444 <https://doi.org/10.1111/jpi.12444>\n\n**Funding information**\n\nThe study was funded by the Association of Anaesthetists of Great Britain and Ireland, the British Journal of Anaesthesia/Royal College of Anaesthetists and the Melville Trust\n\nHelen F. Galley and Barry McCormick are equally contributed to this study.", "\n\n1. ", "INTRODUCTION {#jpi12444-sec-0001}\n===============\n\nA common side effect of cancer treatment is chemotherapy‐induced neuropathic pain (CINP), which can be severe enough to require dose reduction or treatment cessation, with consequent effects on survival and the quality of life of patients with cancer.[1](#jpi12444-bib-0001){ref-type=\"ref\"}, [2](#jpi12444-bib-0002){ref-type=\"ref\"} This predominantly sensory neuropathy affects up to 68% of patients in the first month after finishing chemotherapy, with around 30% of patients still being symptomatic more than 6 months later[1](#jpi12444-bib-0001){ref-type=\"ref\"}. ", "CINP may not resolve and in some cases can worsen with time. ", "Current treatment options are based mainly on evidence from other types of neuropathic pain;[3](#jpi12444-bib-0003){ref-type=\"ref\"} duloxetine, a serotonin‐norepinephrine re‐uptake inhibitor, is one of the few agents with direct evidence of efficacy for CINP.[4](#jpi12444-bib-0004){ref-type=\"ref\"} All of the currently used agents have significant limitations both in terms of efficacy and side effects. ", "There is an urgent need for a treatment, which addresses the neuropathic mechanisms, and can prevent or alleviate CINP.", "\n\nPaclitaxel is a commonly used chemotherapeutic agent with a high incidence of CINP.[1](#jpi12444-bib-0001){ref-type=\"ref\"} It has been shown to cause mitochondrial dysfunction in vitro[5](#jpi12444-bib-0005){ref-type=\"ref\"} and in peripheral nerves and dorsal root ganglia in vivo,[6](#jpi12444-bib-0006){ref-type=\"ref\"}, [7](#jpi12444-bib-0007){ref-type=\"ref\"} associated with oxidative stress. ", "Administration of mitochondrial poisons in animals exacerbated paclitaxel‐induced neuropathic pain,[8](#jpi12444-bib-0008){ref-type=\"ref\"} whilst global radical scavengers (spin traps)[9](#jpi12444-bib-0009){ref-type=\"ref\"}, mitochondrial electron transport chain modulators[10](#jpi12444-bib-0010){ref-type=\"ref\"} and reduction in mitochondrial damage with a small‐molecule P53 inhibitor[11](#jpi12444-bib-0011){ref-type=\"ref\"} or acetyl carnitine[12](#jpi12444-bib-0012){ref-type=\"ref\"} were associated with decreases in neuropathic pain behaviours. ", "These studies support the notion that CINP induced by paclitaxel is mediated by oxidative damage to mitochondria, and suggest that targeting treatments specifically at mitochondria may be beneficial. ", "Our previous work showed that the mitochondria targeted antioxidant MitoVitE was able to reduce mechanical hypersensitivity in rats treated with paclitaxel.[13](#jpi12444-bib-0013){ref-type=\"ref\"} However, MitoVitE has not been through Phase I studies, and its use cannot be rapidly translated into the clinical arena.", "\n\nWe have previously reported that MitoVitE and melatonin are equally effective at reducing mitochondrial dysfunction and markers of inflammation in other disease models both in vitro and in animals.[14](#jpi12444-bib-0014){ref-type=\"ref\"} Melatonin, like MitoVitE, is able to accumulate inside mitochondria and is a potent antioxidant; its metabolites and reaction products are also effective.[15](#jpi12444-bib-0015){ref-type=\"ref\"}, [16](#jpi12444-bib-0016){ref-type=\"ref\"} Melatonin has been given safely to humans with no evidence of toxicity even at very high doses.[17](#jpi12444-bib-0017){ref-type=\"ref\"} We therefore hypothesized that melatonin would reduce mitochondrial damage induced by paclitaxel in neuronal cells in vitro and would alleviate, and/or limit the development of, mechanical hypersensitivity and altered peripheral nerve function in a preclinical rat model of paclitaxel‐induced painful neuropathy.", "\n\n2. ", "MATERIALS AND METHODS {#jpi12444-sec-0002}\n========================\n\n2.1. ", "In vitro studies {#jpi12444-sec-0003}\n---------------------\n\nThe 50B11 immortalized dorsal root ganglion (DRG) neuronal stem cell line was kindly donated by Professor Ahmet Hoke, from Johns Hopkins School of Medicine, Baltimore, MA, USA. ", "These cells have nociceptive properties: after differentiation, they extend neurites and generate action potentials when depolarized, express key nociceptive markers and respond to capsaicin.[18](#jpi12444-bib-0018){ref-type=\"ref\"} Culture and maintenance of these cells is described in our previous study.[13](#jpi12444-bib-0013){ref-type=\"ref\"} They were differentiated into DRGs by exposure to 75 μmol/L forskolin for 24 hours, with outgrowth of neurites starting after about 10 hours. ", "After differentiation, a range of concentrations of paclitaxel was added with and without 1 μmol/L melatonin or relevant solvent control for 24 hours.", "\n\n### 2.1.1. ", "Mitochondrial function {#jpi12444-sec-0004}\n\nMitochondrial function was determined in intact cells after 24 hours treatment, by measurement of the mitochondrial membrane potential using the fluorescent probe JC‐1 (5,5,6,6‐tetrachloro‐1,1,3,3‐tetraethylbenzimidazolcarbocyanine iodide, Invitrogen, Paisley, UK), and by measurement of metabolic activity using the rate of reduction of AlamarBlue^™^ (Invitrogen).[13](#jpi12444-bib-0013){ref-type=\"ref\"}, [15](#jpi12444-bib-0015){ref-type=\"ref\"} Mitotracker Green FM^™^ (Invitrogen) was used to determine mitochondrial volume.[19](#jpi12444-bib-0019){ref-type=\"ref\"}, [20](#jpi12444-bib-0020){ref-type=\"ref\"}, [21](#jpi12444-bib-0021){ref-type=\"ref\"} Cell viability after treatments was measured as acid phosphatase activity as we have described previously and measures of mitochondrial function were corrected for viable cell number.[22](#jpi12444-bib-0022){ref-type=\"ref\"}\n\n### 2.1.2. ", "Cancer cell cytotoxicity {#jpi12444-sec-0005}\n\nAs melatonin might affect the cytotoxic capacity of paclitaxel against cancer cells, we measured paclitaxel‐induced killing of the breast adenocarcinoma‐like oestrogen‐sensitive cell line, MCF‐7, and the ovarian carcinoma cell line, A2780, in the presence of melatonin. ", "Cancer cells were cultured for 24 hours with 0‐100 μmol/L paclitaxel, with and without 1 μmol/L melatonin or solvent control as we have described for MitoVitE previously.[13](#jpi12444-bib-0013){ref-type=\"ref\"} Acid phosphatase activity was used to assess cell viability as for DRG cells.", "\n\n2.2. ", "Animal model {#jpi12444-sec-0006}\n-----------------\n\nThe animal work was approved by the UK Home Office and carried out in accordance with Animals (Scientific Procedures) Act 1986, following applicable aspects of the ARRIVE Guidelines.[23](#jpi12444-bib-0023){ref-type=\"ref\"} Animal health and welfare was paramount throughout all studies, and animals were checked daily for any signs of distress. ", "Weight gain and cage behaviour were continually recorded. ", "All animals were handled as gently as possible, and cage bedding was ample, to provide a soft environment.", "\n\nMale and female Sprague Dawley rats weighing approximately 300 g were housed with a maximum of 6 (single sex) per cage in standard conditions, at 19‐22°C, on a 12‐hour light/dark cycle from 7 am to 7 pm. ", "Food and drinking water were provided ad libitum. ", "The rats were kept in the experimental area for a minimum of 3 days before baseline testing was started. ", "Details of the model have been published previously[13](#jpi12444-bib-0013){ref-type=\"ref\"}, [24](#jpi12444-bib-0024){ref-type=\"ref\"} and are described only briefly here.", "\n\nAs rats were group housed, treatment group allocation was undertaken by cage rather than individual animal to avoid contamination by coprophagia. ", "Rats received either 4 × doses of 2 mg/kg paclitaxel or cremophor/EL (polyethoxylated castor oil, the vehicle control for paclitaxel) diluted in saline, by intraperitoneal (i.p.) ", "injection every second day.", "\n\n### 2.2.1. ", "Behavioural assessment of mechanical sensitivity {#jpi12444-sec-0007}\n\nPseudo‐blinding of treatment allocation was achieved by mixing animals from all treatment groups immediately before testing; group allocation was only confirmed by tail number when testing was complete. ", "Prior to mechanical sensitivity testing, animals were acclimatized in 2 × 20 minute sessions on separate days and further habituated for 20 minutes immediately before testing on any given day. ", "Hind paw plantar withdrawal thresholds to von Frey filaments were determined every 2‐6 days throughout the model, using the up‐down method,[25](#jpi12444-bib-0025){ref-type=\"ref\"} as we have described previously.[13](#jpi12444-bib-0013){ref-type=\"ref\"}\n\n### 2.2.2. ", "Effect of bolus doses of melatonin {#jpi12444-sec-0008}\n\nTo assess the effect of pretreatment with bolus doses of melatonin, male rats (n = 5‐6 per group) were given 1 of 3 bolus doses of melatonin (5, 10 or 50 mg/kg, 2 μl/g body weight) or 10% ethanol vehicle control by daily oral gavage (between 10:00 and 11:00 hours) starting 3 days prior to paclitaxel or control treatment. ", "Mechanical sensitivity was measured 1, 6 and 24 hours after gavage every second or third day. ", "In a separate study, male rats were given a bolus dose of 10 mg/kg melatonin by oral gavage, then blood samples were obtained by cardiac puncture from groups of rats (n = 3 per group) at 1, 2, 6, 12, 24 and 48 hours after dosing, or untreated controls, to determine the pharmacokinetics of melatonin.", "\n\n### 2.2.3. ", "Effect of melatonin given in drinking water {#jpi12444-sec-0009}\n\nWe also administered melatonin (10 mg/kg/day) or vehicle control (0.1% v/v ethanol) in drinking water starting 3 days before paclitaxel treatment, to groups of male rats (n = 5‐6 per group). ", "A control group received saline (i.p.) ", "plus melatonin in drinking water to determine whether melatonin impacted upon baseline mechanical sensitivity. ", "To maintain 10 mg/kg/day melatonin dose, the concentration of melatonin was adjusted to account for mean water consumption over the previous 2 days, and average current weight of rats in a given cage. ", "Opaque bottles were used and changed every 2 days. ", "Levels of melatonin in drinking water were measured as described for serum below to confirm that melatonin levels were stable for at least 48 hours under these conditions. ", "The actual levels of water consumption were consistently similar to that of water with vehicle control. ", "After experimentation, blood was collected by cardiac puncture and serum melatonin levels were determined.", "\n\nThe effect of discontinuing or starting melatonin treatment after mechanical hypersensitivity had developed was also assessed. ", "Groups of rats (n = 6) received either melatonin or vehicle control in drinking water continuously starting 3 days before paclitaxel as above; melatonin starting 3 days before paclitaxel then stopping (reverting to vehicle control) at day 18 once the hypersensitivity was apparent; or vehicle starting 3 days before paclitaxel then commencing melatonin treatment at day 20 once the hypersensitivity was fully established.", "\n\nThe combination of melatonin with the current CINP treatment, duloxetine, was also assessed. ", "By targeting multiple mechanisms,[26](#jpi12444-bib-0026){ref-type=\"ref\"} we hypothesized that there would be an additive effect on paclitaxel‐induced mechanical hypersensitivity. ", "Given increasing awareness of sex differences in pain and analgesic sensitivity,[27](#jpi12444-bib-0027){ref-type=\"ref\"}, [28](#jpi12444-bib-0028){ref-type=\"ref\"} this was investigated in both sexes. ", "Male and female rats (n = 6 per group) were given melatonin or vehicle control in drinking water starting 3 days before paclitaxel as above, plus daily i.p. ", "injections of duloxetine (10 mg/kg/day; 1 μl/g body weight) or vehicle control (20% ethanol in saline), starting when the mechanical hypersensitivity had established.", "\n\n### 2.2.4. ", "Sedation testing {#jpi12444-sec-0010}\n\nPrior to behavioural testing, rats were assessed on a 5‐point scale for righting reflexes: 0, the rat struggles when placed on its side, followed by rapid forceful righting; 1, moderate resistance when the rat is placed on its side, with rapid but not forceful righting; 2, no resistance to the rat being placed on its side, with effortful but ultimately successful righting; 3, unsuccessful righting; and 4, no movements.[29](#jpi12444-bib-0029){ref-type=\"ref\"}\n\n### 2.2.5. ", "Serum melatonin levels {#jpi12444-sec-0011}\n\nRats were anesthetized by brief inhalation of isoflurane followed by overdose of 20% w/v pentobarbitone (\\~1 g/kg) given by i.p. ", "injection. ", "The chest cavity was rapidly opened, and the right atrium was punctured to collect blood for serum samples. ", "Melatonin levels were determined in serum and drinking water using a Thermo Surveyor‐TSQ Quantum liquid chromatography tandem‐mass spectrometry (LC‐MS/MS) system (Thermo Scientific, Hemel Hempstead, UK). ", "This assay has a lower limit of quantitation of 0.5 ng/ml and high inter‐ and intra‐assay precision, as we have previously described in detail.[17](#jpi12444-bib-0017){ref-type=\"ref\"}\n\n### 2.2.6. ", "8‐isoprostane F~2~α levels {#jpi12444-sec-0012}\n\nF~2~‐isoprostanes, which are one of the most reliable measures of oxidative stress status in vivo*,* [30](#jpi12444-bib-0030){ref-type=\"ref\"} were measured ex vivo in peripheral nerve tissue 19 days after paclitaxel/cremophor treatment and included experimental animals from the bolus dosing experiments receiving melatonin at 10 mg/kg or vehicle treatment. ", "Rats were decapitated under isoflurane anaesthesia and sciatic and saphenous nerve tissue were removed, placed in ice cold 0.1 mol/L phosphate buffer and homogenized, then centrifuged and frozen at −80°C. ", "Tissue was collected throughout the day with animals from different treatment groups interleaved to ensure all treatment groups were collected over comparable time windows. ", "F~2~α levels were assessed using a commercially available 8‐isoprostane F~2~α ELISA kit (Enzo Lifesciences, Exeter, UK). ", "The lower limit of detection is 40 mg/ml with median intra‐ and interassay coefficients of variation of 5.7% and 5.8%, respectively.", "\n\n### 2.2.7. ", "C‐fibre activity‐dependent slowing {#jpi12444-sec-0013}\n\nC‐fibre function was assayed by quantifying C‐fibre activity‐dependent slowing (ADS) in peripheral nerve tissue from male rats receiving cremophor or paclitaxel with and without 10 mg/kg melatonin in drinking water 14‐18 days following the start of paclitaxel or vehicle treatment. ", "Rats were decapitated under isoflurane anaesthesia, at the same time in the morning, and lumbar (L4/5) dorsal roots, minus dorsal root ganglia, were isolated and incubated at 36°‐37°C in oxygenated recovery solution for 1 hour. ", "Following incubation, tissue was transferred to the recording bath of an upright microscope (Zeiss, Oberkochen, Germany) and continuously perfused with oxygenated Krebs' solution (1‐2 ml/min) at room temperature. ", "The 95% O~2~/5% CO~2~ saturated Krebs' solution contained (in mmol/L) the following: 125 NaCl, 2.5 KCl, 1.25 NaH~2~PO~4~, 26 NaHCO~3~ 25 glucose, 1 MgCl~2~, 2 CaCl~2~ pH7.4. ", "Recovery solution was identical to Krebs' solution apart from 6 mmol/L MgCl~2~, 1.5 mmol/L CaCl~2~.\n\nCompound action potential recordings were carried out using 2 glass suction electrodes, one for electrical stimulation and the second for field potential recording, as we have described previously.[31](#jpi12444-bib-0031){ref-type=\"ref\"}, [32](#jpi12444-bib-0032){ref-type=\"ref\"} Dorsal roots were stimulated with an Iso‐flex stimulus isolator (A.M.P.I. Jerusalem, Israel), and data were acquired and recorded using a Cygnus ER‐1 differential amplifier (Cygnus Technologies Inc. Delaware, PA, USA) and pClamp 10 software (Molecular Devices, Sunnyvale, CA, USA). ", "Data were filtered at 10 kHz and sampled at 50 kHz.", "\n\nThe characteristic triphasic (positive‐negative‐positive) C‐fibre component of the compound action potential was identified, based on activation threshold and conduction velocity, which were not altered by treatment (Table [1](#jpi12444-tbl-0001){ref-type=\"table-wrap\"}).", "\n\n###### \n\nComparison of the C‐fibre electrophysiological properties in dorsal roots obtained from the different treatment groups\n\n Threshold (μA) Amplitude (mV/mm) Average CV (m/s) Initial response width (ms/mm)\n ----------------------------------- ---------------- ------------------- ------------------ --------------------------------\n Vehicle (n = 12) 121 ± 9.65 0.12 ± 0.02 0.23 ± 0.02 4.97 ± 0.2\n Paclitaxel (n = 10) 100 ± 0 0.12 ± 0.03 0.22 ± 0.2 5.57 ± 0.2\n Paclitaxel and Melatonin (n = 12) 104 ± 4.17 0.13 ± 0.02 0.21 ± 0.01 5.10 ± 0.3\n\nOne‐way ANOVA reveals that treatment group does not affect threshold stimulus intensity (*P* = .08), amplitude (*P* = .93), average conduction velocity (*P* = .75) or the initial C‐fibre response width (*P* = .23).", "\n\nJohn Wiley & Sons, Ltd\n\nTo assess the frequency‐dependent phenomenon of C‐fibre ADS,[33](#jpi12444-bib-0033){ref-type=\"ref\"}, [34](#jpi12444-bib-0034){ref-type=\"ref\"} dorsal roots were stimulated ×40 (500 μA intensity, 0.1 ms duration) at frequencies of 1 Hz and 2 Hz. ", "For each stimulus, the response width (first to last positive peak), indicative of the range of conduction velocities within the C‐fibre population, was measured and the change in width from stimulus 1 calculated. ", "Width change was normalized to the length of root stimulated, measured as the distance between the recording and stimulating electrodes.", "\n\n### 2.2.8. ", "Statistical analysis {#jpi12444-sec-0014}\n\nFor in vitro studies, 6 separate experiments with 4 technical replicates were undertaken (n = 6). ", "Data are presented as median, interquartile and full range, and statistical analysis was undertaken using Analyse‐it Add‐in for Microsoft Excel (Analyse‐it Software Ltd., Leeds, UK). ", "Kruskal‐Wallis analysis of variance was used for each in vitro treatment, with Mann‐Whitney *post hoc* testing and correction for multiple comparisons as appropriate.", "\n\nFor in vivo studies, area under the curve (AUC) of mechanical thresholds or C‐fibre ADS was first calculated; then, all data were analysed by one‐way or two‐way ANOVA with appropriate *post hoc* testing as detailed (GraphPad Prism 7 Software Inc., La Jolla, CA, USA). ", "Behavioural and C‐fibre also ADS data are shown as mean and SD; 8‐isoprostane F~2~α data are presented as median, interquartile and full range.", "\n\n3. ", "RESULTS {#jpi12444-sec-0015}\n==========\n\n3.1. ", "In vitro studies {#jpi12444-sec-0016}\n---------------------\n\n### 3.1.1. ", "Cancer cell cytotoxicity {#jpi12444-sec-0017}\n\nPaclitaxel caused loss of DRG cell viability of cancer cells such that median \\[range\\] viability in A2780 cells was 60.0 \\[52.1‐68.6\\]% in the presence of 100 μmol/L paclitaxel without melatonin and 56.6 \\[48.0‐64.3\\]% with 100 μmol/L paclitaxel plus 1 μmol/L melatonin. ", "Viability of MCF7 cells was 39.2 \\[15.8‐41.3\\]% with paclitaxel without melatonin and 36.3 \\[18.9‐55.4\\]% with melatonin, indicating that cell killing by paclitaxel was not reduced by co‐exposure of cells to melatonin in either of the cancer cell lines.", "\n\n### 3.1.2. ", "Mitochondrial function {#jpi12444-sec-0018}\n\nTreatment of DRG cells with paclitaxel without melatonin resulted in significantly reduced mitochondrial membrane potential as shown by a \\~50% reduction in JC‐1 red/green fluorescence ratio, regardless of dose (*P* \\< .0001, Figure [1](#jpi12444-fig-0001){ref-type=\"fig\"}A). ", "When cells were co‐exposed to paclitaxel plus melatonin, membrane potential actually increased except at the highest concentration of paclitaxel (Figure [1](#jpi12444-fig-0001){ref-type=\"fig\"}A). ", "Mitochondrial metabolic activity was also significantly reduced when DRG cells were treated with paclitaxel, independently of dose (*P* \\< .0001, Figure [1](#jpi12444-fig-0001){ref-type=\"fig\"}B); no such reduction was seen when cells were co‐treated with melatonin (Figure [1](#jpi12444-fig-0001){ref-type=\"fig\"}B). ", "Paclitaxel exposure of DRG cells caused a marked dose‐dependent increase in mitochondrial volume (Figure [1](#jpi12444-fig-0001){ref-type=\"fig\"}C, *P* \\< .0001), and in cells co‐treated with melatonin, this effect was not seen (Figure [1](#jpi12444-fig-0001){ref-type=\"fig\"}C).", "\n\n{#jpi12444-fig-0001}\n\n3.2. ", "In vivo studies {#jpi12444-sec-0019}\n--------------------\n\nMelatonin administration did not produce sedative effects; all rats, irrespective of treatment, scored zero on the 5‐point scale for righting reflexes (data not shown). ", "Melatonin also did not impact upon weight gain in any experimental group tested (Fig. [", "S1](#jpi12444-sup-0001){ref-type=\"supplementary-material\"}).", "\n\n### 3.2.1. ", "Bolus dosing with melatonin {#jpi12444-sec-0020}\n\nPaclitaxel administration caused a reduction in mechanical withdrawal threshold values that developed progressively over 2 weeks, as we have shown previously[13](#jpi12444-bib-0013){ref-type=\"ref\"} (Figure [2](#jpi12444-fig-0002){ref-type=\"fig\"}A). ", "Rats receiving paclitaxel plus melatonin by oral gavage had less mechanical hypersensitivity compared with rats given paclitaxel plus vehicle (Figure [2](#jpi12444-fig-0002){ref-type=\"fig\"}A and B, *P* \\< .0001). ", "AUC analysis of mechanical withdrawal thresholds revealed that melatonin limited mechanical hypersensitivity at all 3 doses given. ", "However, there was no additional effect of 50 mg/kg melatonin compared to 10 mg/kg. ", "Notably, the reduction in hypersensitivity was independent of when sensitivity testing was performed in relation to dosing, as similar effects were observed when testing was performed at 1, 6 or 24 hours after the bolus dose was given (Figure [2](#jpi12444-fig-0002){ref-type=\"fig\"}B). ", "In contrast, there was a marked increase (\\~400‐fold) in serum melatonin levels at 1 h after dosing, which had returned to baseline values by 24 hours (Figure [2](#jpi12444-fig-0002){ref-type=\"fig\"}C). ", "Six rats were allocated to each treatment group at the start of the study; however, data from 3 rats (×1 vehicle, ×1 5 mg/kg melatonin, ×1 50 mg/kg melatonin treated) were excluded as they were euthanized before the end of the study due to complications with repeated oral gavage.", "\n\n{#jpi12444-fig-0002}\n\n### 3.2.2. ", "Melatonin in drinking water {#jpi12444-sec-0021}\n\nAdministration of melatonin in drinking water facilitated longer‐term monitoring of the effect of melatonin upon paclitaxel‐induced mechanical hypersensitivity that progressively develops over 2 weeks before then plateauing at peak hypersensitivity for around 2 weeks (Figure [3](#jpi12444-fig-0003){ref-type=\"fig\"}A). ", "Melatonin alone did not affect mechanical sensitivity in naïve subjects as assessed using AUC analysis of mechanical withdrawal thresholds (Figure [3](#jpi12444-fig-0003){ref-type=\"fig\"}A and B). ", "Melatonin therefore does not appear to produce sedative effects that would confound assessment of its effect upon mechanical hypersensitivity in neuropathic animals. ", "Rats given paclitaxel plus 10 mg/kg melatonin in drinking water had less mechanical hypersensitivity than rats given paclitaxel plus vehicle throughout the time course of the model (Figure [3](#jpi12444-fig-0003){ref-type=\"fig\"}A‐C, *P* \\< .0001). ", "Comparison of the effect of 10 mg/kg/day melatonin given as oral gavage or drinking water, using AUC analysis of data from day 2‐17 after paclitaxel administration started, revealed that the melatonin effect was not dependent on the administration route (Figure [3](#jpi12444-fig-0003){ref-type=\"fig\"}C, melatonin *P* \\< .0001; interaction *P* = .49). ", "Serum melatonin levels on day 42 in animals given melatonin were significantly higher than those which received vehicle (Figure [3](#jpi12444-fig-0003){ref-type=\"fig\"}D, *P* = .001). ", "Given that administration of melatonin in drinking water was as effective, but less problematic than the oral gavage route, melatonin was administered in drinking water for the remainder of the behavioural studies.", "\n\n{#jpi12444-fig-0003}\n\nWhen melatonin was given as an intervention to rats with established paclitaxel‐induced mechanical hypersensitivity, there was no difference between AUC withdrawal threshold (day 20‐30) values of groups receiving melatonin or vehicle control (Figure [4](#jpi12444-fig-0004){ref-type=\"fig\"}). ", "Additionally, both were significantly lower than AUC values of the group receiving paclitaxel and melatonin throughout (*P* \\< .01), suggesting melatonin was not an effective intervention to the established phenotype. ", "However, when melatonin treatment was started before paclitaxel and then stopped once the hypersensitivity phenotype was apparent, AUC (day 20‐30) analysis indicated that withdrawal thresholds remained higher than rats receiving paclitaxel without melatonin (*P* \\< .0001) and were indistinguishable from those given melatonin continuously (Figure [4](#jpi12444-fig-0004){ref-type=\"fig\"}), suggesting that melatonin administration had a preventative effect that persisted beyond the cessation of treatment.", "\n\n{#jpi12444-fig-0004}\n\n### 3.2.3. ", "Peripheral nerve 8‐isoprostane F~2~α levels {#jpi12444-sec-0022}\n\n8‐isoprostane F~2~α levels were measured ex vivo in sciatic and saphenous nerve tissue collected at the peak of the model and normalized to sample protein content. ", "Increased 8‐isoprostane F~2~α levels were found in peripheral nerve tissue from paclitaxel‐treated rats (Figure [5](#jpi12444-fig-0005){ref-type=\"fig\"}A, *P* = .003). ", "Melatonin treatment was found to significantly reduce the elevated 8‐isoprostane F~2~α levels in paclitaxel‐treated rats (Figure [5](#jpi12444-fig-0005){ref-type=\"fig\"}B, *P* = .0015).", "\n\n{#jpi12444-fig-0005}\n\n### 3.2.4. ", "C‐fibre activity‐dependent slowing {#jpi12444-sec-0023}\n\nTreatment with paclitaxel with and without melatonin had no effect on C‐fibre threshold stimulus intensity, amplitude, average conduction velocity or initial response width, indicative of the initial range of conduction velocities within the C‐fibre population (Table [1](#jpi12444-tbl-0001){ref-type=\"table-wrap\"}).", "\n\nRepetitive stimulation of isolated dorsal roots produced a progressive increase in C‐fibre response width (Figure [6](#jpi12444-fig-0006){ref-type=\"fig\"}A and B). ", "AUC analysis confirmed that this C‐fibre ADS was frequency‐dependent, with stimulation at 2 Hz producing greater ADS than at 1 Hz (*P* \\< .0001, Figure [6](#jpi12444-fig-0006){ref-type=\"fig\"}C). ", "C‐fibre ADS was lower in rats treated with paclitaxel (*P* \\< .001), an effect that was prevented by melatonin (*P* \\< .0001), independent of stimulation frequency.", "\n\n{#jpi12444-fig-0006}\n\n### 3.2.5. ", "Combination treatment with duloxetine {#jpi12444-sec-0024}\n\nPaclitaxel produced mechanical hypersensitivity in male and female animals that was significantly ameliorated by melatonin administered in drinking water in both sexes (Figure [7](#jpi12444-fig-0007){ref-type=\"fig\"}). ", "Duloxetine limited mechanical hypersensitivity to an extent comparable with melatonin in both sexes (Figure [7](#jpi12444-fig-0007){ref-type=\"fig\"}). ", "Co‐treatment of paclitaxel‐treated animals with melatonin in drinking water plus duloxetine injections revealed a clear additive effect, with higher withdrawal thresholds in co‐treated animals compared to those given either melatonin (males *P* \\< .05) or duloxetine alone (males *P* \\< .0001; females *P* \\< .05).", "\n\n{#jpi12444-fig-0007}\n\n4. ", "DISCUSSION {#jpi12444-sec-0025}\n=============\n\nWe have shown that in vitro, paclitaxel treatment caused mitochondrial dysfunction in DRG cells, with reduced membrane potential and metabolic activity, and evidence of mitochondrial swelling. ", "However, when the cells were treated with paclitaxel plus melatonin, mitochondrial damage was attenuated. ", "Importantly, co‐treatment of breast or ovarian cancer cells with melatonin had no impact on the cytotoxicity of paclitaxel. ", "In a rat model of paclitaxel‐induced neuropathic pain, we found that oral melatonin pretreatment was protective, whether given as a bolus or in drinking water. ", "Furthermore, melatonin reduced paclitaxel‐elevated peripheral nerve 8‐isoprostane F~2~α levels and prevented paclitaxel reduced C‐fibre ADS. ", "When given in a prophylactic manner, melatonin significantly attenuated paclitaxel‐evoked mechanical hypersensitivity in both male and female animals, and there was an additive affect when melatonin was given along with duloxetine. ", "Melatonin treatment was well tolerated with no effects on animals' weight gain, general well‐being and sedation levels. ", "This work suggests that melatonin may be a useful preventive treatment for chemotherapy‐induced painful neuropathy in patients.", "\n\nMelatonin is known to be an effective antioxidant, and many of its reaction products and metabolites (e.g. 6‐hydroxymelatonin) also possess antioxidant activity.[15](#jpi12444-bib-0015){ref-type=\"ref\"}, [16](#jpi12444-bib-0016){ref-type=\"ref\"} Melatonin is able to cross cell membranes and is reported to concentrate particularly inside mitochondria,[35](#jpi12444-bib-0035){ref-type=\"ref\"} where it may potentially interact with mitochondrial MT1 receptors to modulate mitochondrial function.[36](#jpi12444-bib-0036){ref-type=\"ref\"}, [37](#jpi12444-bib-0037){ref-type=\"ref\"} Mitochondrial damage caused by paclitaxel has been reported previously in several cell types[5](#jpi12444-bib-0005){ref-type=\"ref\"}, [38](#jpi12444-bib-0038){ref-type=\"ref\"}, [39](#jpi12444-bib-0039){ref-type=\"ref\"}, [40](#jpi12444-bib-0040){ref-type=\"ref\"} including peripheral nerve cells.[6](#jpi12444-bib-0006){ref-type=\"ref\"} Our in vitro data show that paclitaxel caused a loss of mitochondrial membrane potential and metabolic activity in DRG cells, as previously reported[13](#jpi12444-bib-0013){ref-type=\"ref\"} and that melatonin ameliorated this damage. ", "MitoTracker^™^ Green is a marker which fluoresces inside mitochondria, regardless of membrane potential and is an indicator of mitochondrial volume, reacting with free thiol groups in cysteine residues of mitochondrial proteins.[19](#jpi12444-bib-0019){ref-type=\"ref\"} The increase in observed mitochondrial volume could reflect increased number of mitochondria, or mitochondrial swelling, the latter of which has been documented in peripheral nerve axons from paclitaxel‐treated rats.[6](#jpi12444-bib-0006){ref-type=\"ref\"} Again melatonin prevented this. ", "Moreover, these in vitro effects were in keeping with findings in vivo, where levels of 8‐isoprostane F~2~α, an end product of reactions promoted in conditions of oxidative stress,[30](#jpi12444-bib-0030){ref-type=\"ref\"} were increased in peripheral nerve tissue isolated from paclitaxel‐treated animals, an effect diminished in paclitaxel‐treated animals co‐treated with melatonin.", "\n\nAltered peripheral nerve function in the rat model of paclitaxel‐induced neuropathy has been demonstrated with in vivo electrophysiological recordings revealing that \\~30% of C‐fibres display spontaneous activity that is reduced by prophylactic treatment with acetyl‐[l]{.smallcaps}‐carnitine[41](#jpi12444-bib-0041){ref-type=\"ref\"}, which is known to limit mitochondrial dysfunction.[42](#jpi12444-bib-0042){ref-type=\"ref\"} Altered C‐fibre function can also be characterized, in both preclinical pain models[43](#jpi12444-bib-0043){ref-type=\"ref\"}, [44](#jpi12444-bib-0044){ref-type=\"ref\"} and chronic pain patients,[45](#jpi12444-bib-0045){ref-type=\"ref\"}, [46](#jpi12444-bib-0046){ref-type=\"ref\"}, [47](#jpi12444-bib-0047){ref-type=\"ref\"}, [48](#jpi12444-bib-0048){ref-type=\"ref\"} by measuring the phenomenon of C‐fibre ADS, which is a progressive slowing of nociceptive C‐fibre conduction velocity in response to repetitive stimulation.[33](#jpi12444-bib-0033){ref-type=\"ref\"}, [34](#jpi12444-bib-0034){ref-type=\"ref\"} However, to date, this had not been addressed for CINP. ", "Here, we demonstrate that in peripheral nerve tissue from paclitaxel‐treated rats, C‐fibres had significantly lower ADS, an effect that was prevented in those rats co‐treated with melatonin. ", "We have very recently reported that C‐fibre ADS alters the temporal relay of pain input to the spinal cord and that a reduction in ADS, as we have observed in the paclitaxel model, facilitates central pain processing, and likely contributes to pain hypersensitivity.[49](#jpi12444-bib-0049){ref-type=\"ref\"}\n\nThe rat model of paclitaxel‐induced neuropathy employed has been well characterized[6](#jpi12444-bib-0006){ref-type=\"ref\"}, [13](#jpi12444-bib-0013){ref-type=\"ref\"}, [24](#jpi12444-bib-0024){ref-type=\"ref\"} and features mechanical hypersensitivity as indicated by the reduced mechanical threshold of the flexion withdrawal reflex in the present study. ", "Melatonin given by oral gavage was both time‐consuming and stressful for the animal exemplified by the loss of 3 animals after multiple oral gavages. ", "Attempts to give melatonin to individual rats in jelly cubes were unsuccessful, and so we administered the melatonin in drinking water as described previously.[50](#jpi12444-bib-0050){ref-type=\"ref\"}, [51](#jpi12444-bib-0051){ref-type=\"ref\"} There was no effect of melatonin on water consumption, weight gain and no apparent sedative effect given there was no change in righting reflex activity, food or water intake, nor indeed altered mechanical sensitivity in animals given melatonin alone. ", "Furthermore, when melatonin was discontinued, the reduction in mechanical hypersensitivity persisted and when given as an intervention in animals when CINP was established, melatonin did not limit mechanical hypersensitivity, effects inconsistent with a melatonin \"sedative\" effect accounting for the attenuation of CINP. ", "Significantly higher serum melatonin levels at the end of the study were seen in animals given melatonin compared to those which did not and the magnitude of the melatonin protective effect was similar for rats given melatonin by bolus doses or in drinking water. ", "We therefore conclude that oral melatonin pretreatment, either as a bolus dose or in drinking water was effective at reducing paclitaxel‐induced mechanical hypersensitivity. ", "During these experiments, a melatonin dose of 10 mg/kg per day was used. ", "This dose has been demonstrated to be effective in reducing oxidative stress and symptom severity in preclinical models of a number of diseases, including epilepsy, diabetes, ethanol‐induced neurotoxicity and oxidative lung toxicity.[52](#jpi12444-bib-0052){ref-type=\"ref\"}, [53](#jpi12444-bib-0053){ref-type=\"ref\"}, [54](#jpi12444-bib-0054){ref-type=\"ref\"}, [55](#jpi12444-bib-0055){ref-type=\"ref\"}\n\nThe capacity of melatonin to protect against the development of paclitaxel‐induced mechanical hypersensitivity is most likely due to its antioxidant activity. ", "Oxidative stress occurs in peripheral nerves in the paclitaxel rat model[56](#jpi12444-bib-0056){ref-type=\"ref\"}, and other antioxidant strategies, including spin trap agents[9](#jpi12444-bib-0009){ref-type=\"ref\"}, mitochondrial electron transport chain modulators[10](#jpi12444-bib-0010){ref-type=\"ref\"} and the antioxidant MitoVitE[13](#jpi12444-bib-0013){ref-type=\"ref\"} reduce symptoms in this model. ", "In support, we demonstrate that melatonin limits paclitaxel‐induced elevation of 8‐isoprostane F~2~α levels in peripheral nerves in vivo. ", "Therefore, although melatonin may influence pain processing via its MT~1~/MT~2~ membrane receptors and effects on neurotransmitter systems[57](#jpi12444-bib-0057){ref-type=\"ref\"}, the protective effect we observe may be more likely to be due to its antioxidant action, perhaps via mitochondrial MT1 receptors[36](#jpi12444-bib-0036){ref-type=\"ref\"}, [37](#jpi12444-bib-0037){ref-type=\"ref\"} as firstly melatonin prevented but did not reverse established mechanical hypersensitivity; secondly, the reduction in mechanical hypersensitivity produced by daily bolus administration was stable over 24 hours yet serum melatonin levels peak at 1 h and return to baseline by 24 hours. ", "Interestingly, this antioxidant protective effect fits well with the demonstration that reactive oxygen species levels peak in the DRG during the onset rather than the peak of the paclitaxel model,[56](#jpi12444-bib-0056){ref-type=\"ref\"} although it has been demonstrated that antioxidant strategies can reduce established paclitaxel‐induced hypersensitivity.[9](#jpi12444-bib-0009){ref-type=\"ref\"}, [10](#jpi12444-bib-0010){ref-type=\"ref\"} Furthermore, the recent demonstration that melatonin limits oxaliplatin‐induced mitochondrial dysfunction and peripheral neuropathy[58](#jpi12444-bib-0058){ref-type=\"ref\"} suggests that melatonin is a potential disease‐modifying treatment for CINP. ", "However, it could also be that melatonin antioxidant capacity combines with its receptor‐mediated effects upon pain processing to collectively provide the reduction in hypersensitivity observed. ", "Of interest, given the observed additive effect of melatonin and duloxetine, agomelatine, a new class of antidepressant and a melatonergic and serotonergic receptor agonist, with evidence of antioxidant activity[59](#jpi12444-bib-0059){ref-type=\"ref\"}, [60](#jpi12444-bib-0060){ref-type=\"ref\"}, has very recently been shown to be effective against chemotherapy‐induced neuropathy.[61](#jpi12444-bib-0061){ref-type=\"ref\"}\n\nWe also found that melatonin did not inhibit the cytotoxic action of paclitaxel in 2 relevant cancer cell lines, in agreement with studies using other antioxidants.[13](#jpi12444-bib-0013){ref-type=\"ref\"}, [62](#jpi12444-bib-0062){ref-type=\"ref\"} Treatment of cancer patients with melatonin in several small studies did not impact on the effectiveness of chemotherapy[63](#jpi12444-bib-0063){ref-type=\"ref\"}, [64](#jpi12444-bib-0064){ref-type=\"ref\"}, [65](#jpi12444-bib-0065){ref-type=\"ref\"}, and a meta‐analysis of 10 randomized controlled trials of over 600 patients with advanced solid tumours reported that melatonin treatment reduced the risk of death at 1 year.[66](#jpi12444-bib-0066){ref-type=\"ref\"} Another recent meta‐analysis of 8 trials and 700 patients similarly reported that adjuvant melatonin treatment in patients with cancer resulted in improved 1‐year survival.[67](#jpi12444-bib-0067){ref-type=\"ref\"} A more recent small trial showed no difference in survival of patients with non‐small‐cell lung cancer who received 10 or 20 mg melatonin daily for 6 months, although after 22 months, only patients given melatonin had survived, with more patients surviving who received 20 mg than had received 10 mg.[68](#jpi12444-bib-0068){ref-type=\"ref\"} Other studies report mechanisms of how melatonin may potentiate chemotherapy, reduce metastatic progression and prevent resistance to chemotherapy.[69](#jpi12444-bib-0069){ref-type=\"ref\"}, [70](#jpi12444-bib-0070){ref-type=\"ref\"}, [71](#jpi12444-bib-0071){ref-type=\"ref\"}, [72](#jpi12444-bib-0072){ref-type=\"ref\"} Moreover, the ability of gliomas to synthesize melatonin negatively correlates with tumour malignancy.[73](#jpi12444-bib-0073){ref-type=\"ref\"} Melatonin appears to be without side effects, other than mild drowsiness,[17](#jpi12444-bib-0017){ref-type=\"ref\"}, [74](#jpi12444-bib-0074){ref-type=\"ref\"} and has been administered to thousands of patients without toxic effects, even at high doses, for a variety of conditions.", "\n\nOur study clearly shows the potential of melatonin as a preventative therapeutic intervention for patients undergoing chemotherapy, to limit development of neuropathic pain, with no obvious risk to the efficacy of chemotherapy or outcome.", "\n\nAUTHOR CONTRIBUTIONS {#jpi12444-sec-0027}\n====================\n\nAll authors made a substantial contribution to the conception and design, acquisition of data or analysis and interpretation of data, were involved in drafting the article or revising it critically for important intellectual content, and approved the final version. ", "They have all agreed to be accountable for all aspects of the work in terms of accuracy and integrity. ", "All authors contributed to and approved the final version of the manuscript. ", "HFG conceived of and designed the study, analysed data and drafted the manuscript. ", "BM conceived of and designed the study, conducted in vitro and in vivo experimental works and analysed in vivo data and contributed to writing the manuscript. ", "KLW: conducted electrophysiological recordings, analysed data and contributed to writing the manuscript. ", "CT conceived of and designed and supervised in vivo work and contributed to writing the manuscript. ", "DL helped conduct and supervised in vitro experimental work. ", "LC conceived of and designed study, supervised conduct and contributed to writing the manuscript.", "\n\nSupporting information\n======================\n\n###### \n\n \n\n###### \n\nClick here for additional data file.", "\n\nThank you to Professor Ahmet Hoke (Johns Hopkins, Baltimore, USA) for the gift of DRG cells and to Professor Patrick M. Dougherty (MD Anderson Cancer Center, Texas, USA) for sharing his expertise in the rat model.", "\n" ]

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[ "Q:\n\nA.P. terms in a Quadratic equation.", "\n\nThe terms $a,b,c$ of quadratic equation $ax^{2}+bx+c=0$ are in A.P. and positive. ", "Let this equation have integral root $\\alpha,\\ \\beta$. Then find the value of $\\alpha+ \\beta + \\alpha \\cdot \\beta$ ?", "\n\nplease point where I'm wrong:\nLet common difference be $d$\n$\\implies \\alpha+ \\beta + \\alpha \\cdot \\beta=\\dfrac{c-b}{a}=\\dfrac{d}{a} \\implies a|d \\ \\ \\ \\ \\longrightarrow \\ \\ \\ \\ \\ \\because (b=a+d$, $c=a+2d)$\nAlso\n, $ax^{2}+(a+d)x+(a+2d)=0$. \n$\\implies$ $\\alpha,\\ \\beta=\\dfrac{-(a+d) \\pm \\sqrt{(a+d)^{2}-4\\cdot a \\cdot (a+2d)}}{2a}$. \nFor this to be integer $\\sqrt{(a+d)^{2}-4\\cdot a \\cdot (a+2d)}$ must be perfect square.", "\n$\\implies$ ${(a+d)^{2}-4\\cdot a \\cdot (a+2d)}=p^{2}$ for some $p$.\n$\\implies -3a^{2}+d^{2}-6ad=p^{2}$\n$\\implies -3a^{2}+a^{2}q^{2}-6a^{2}q=p^{2}$ $\\because$ $a|d \\implies aq=d$ for some $q$.\n$\\implies a^{2}(-3+q^{2}-6q)=p^{2}$ \n$\\implies -3+q^{2}-6q\\ $ has to be perfect square. ", "By trial $q=7$\nBut I need to get this without trial, please help.", "\n\nA:\n\nWe have, $$p(x)=ax^2+bx+c=ax^2+(a+p)x+(a+2p)$$\nand thus, $$t+r+r\\cdot t=-\\frac{a+p}{a}+\\frac{a+2p}{a}=\\frac{p}{a}$$\nthen $p=a\\cdot k$, $k=(t+r+t\\cdot r) \\in \\Bbb Z$.\nThen our polynomial becomes,$$p(x)=ax^2+a(1+k)x+a(1+2k)$$\n$$t=\\frac{-(1+k) \\pm \\sqrt{k^2-6k-3}}{2} \\quad...(1)$$\nSo \n$$k^2-6k-3=q^2 \\Rightarrow (k-3)^2-12=q^2 \\Rightarrow (k+q-3)(k-q-3)=12$$\nand split $12$ as a product of two integer and find all possible values for $k$.\nTake for example:\n\\begin{cases}\nk+q-3=6 \\Rightarrow k+q=9 \\\\\nk-q-3=2 \\Rightarrow k-q=5\n\\end{cases}\nAdding up both equations we get $2k=14 \\Rightarrow k=7$\nAnd back to $(1)$, we get $(t,r)=(-3,-5)$ or $(t,r)=(-5,-3)$.\n\n" ]

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[ "Packers Camp\n\nPackers Camp is a locality in the Cairns Region, Queensland, Australia. ", "In the , Packers Camp had a population of 106 people.", "\n\nGeography \nPine Creek forms the northern boundary of the locality; Pine Creek Yarrabah Road forms the eastern and southern boundary of the locality; the Mackey Creek forms the western boundary. ", "Simmonds Creek traverses the locality from south to north. ", "All of these creeks become tributaries of the Redbank Creek which flows into Trinity Inlet and then to the Coral Sea at Cairns City.", "\n\nRedbank Road runs from north to the south within the locality, connecting at the south to Wrights Creek and Gordonvale and through them to the Bruce Highway.", "\n\nThe land is flat and low-lying (less than 10 metres above sea level) and almost entirely freehold. ", "The land is principally used for agricultural, mostly for growing sugarcane, with some scattered rural residences, mostly along Redbank Road. ", "There is a cane tramway passing through the locality to transport the harvested sugarcane to the Mulgrave Sugar Mill.", "\n\nHistory \nThe locality was originally known as Highclere but its name changed to Highleigh in 1896. ", "Later it became known as Packer Camp as it was the place where the horse, mule and bullock teams were loaded for the trip over the range to the goldfields.", "\n\nA postal receiving office in 1895 but closed in 1898. ", "In 1951 the Packers Creek post office opened, closing in 1971.", "\n\nReferences \n\nCategory:Cairns Region\nCategory:Localities in Queensland" ]

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[ "Chicago police say a 41-year-old woman was attacked Monday by a man after boarding CTA Blue Line. ", "View Full Caption Chicago Police Department\n\nCHICAGO — Police are on the lookout for a man they say sexually assaulted and robbed a 41-year-old Oak Park woman Monday on the Blue Line near Oak Park.", "\n\nArea North detectives said in a news conference Tuesday night they hope by spreading the man's image, someone will recognize him and come forward to identify him to police.", "\n\nA police alert released earlier Tuesday contains screen captures of the man's face from train security cameras and says the attack happened Monday around 3:10 p.m. after the woman boarded the Blue Line at Oak Park Avenue. ", "The man who attacked her had boarded the same eastbound train two stops earlier at Forest Park.", "\n\nNot long after the woman boarded the train, the man attacked her from behind, knocking her to the ground before sexually assaulting her and robbing her of an iPhone and cash. ", "The train car was otherwise empty at the time of the incident, police said Tuesday night.", "\n\nDetective Jackie Mok speaks during a news conference Tuesday night about a brutal sexual attack that took place Monday afternoon, in hopes someone will come forward with information. ", "View Full Caption DNAinfo/Linze Rice\n\nAccording to police, the man then exited the Blue Line train at Cicero Avenue, before switching directions and fleeing on a westbound train to Austin Boulevard. ", "The woman was able to use the train's help button to call for assistance.", "\n\nThe woman suffered non life-threatening injuries and was being treated at a hospital, Detective Jackie Mok said during the news conference.", "\n\nThe man is described as black and wearing a blue and grey Columbia jacket, jeans and green-laced tennis shoes.", "\n\nPolice are asking anyone with information to call Area North Detectives at 312-744-8261. ", "In the meantime, they are urging the public to remain alert, refrain from talking with strangers and to report any suspicious activity to police.", "\n\nFor more neighborhood news, listen to DNAinfo Radio here:" ]

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[ "Today's health care leaders are faced with many new and challenging decisions, from ever-changing regulations and cost pressure to growth opportunities that were nonexistent just months ago. ", "We work shoulder-to-shoulder with leaders like you to chart a course for the future and implement value-based care solutions that secure success. ", "Here are a few of the opportunities that leading systems are exploring and acting on with us today:\n\n“To build the competencies that were needed to get into everything from insurance to population health initiatives would, on our own, take us years—if we were ever able to do it.”", "\n\nMike Maiberger\n\nCOO, Premier Health\n\nTHE EVOLENT DIFFERENCE\n\nLeading health systems are succeeding in the era of value-based care by partnering with us to power, protect and scale their value business. ", "Our health system partners achieve tangible results because we work differently. ", "We integrate our teams, technology and tools across the health system enterprise to empower change from the inside out. ", "A few of the many outcomes we’ve helped our partners achieve are highlighted below." ]

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[ "Everyone has taste, yet it is more of a taboo subject than sex or money. ", "The reason for this is simple: claims about your attitudes to or achievements in the carnal and financial arenas can be disputed only by your lover and your financial advisers, whereas by making statements about your taste you expose body and soul to terrible scrutiny. ", "Taste is a merciless betrayer of social and cultural attitudes. ", "Thus, while anybody will tell you as much (and perhaps more than) you want to know about their triumphs in bed and at the bank, it is taste that gets people's nerves tingling.", "\n\nA man is known by the books he reads, by the company he keeps, by the praise he gives, by his dress, by his tastes, by his distastes, by the stories he tells, by his gait, by the notion of his eye, by the look of his house, of his chamber; for nothing on earth is solitary but every thing hath affinities infinite." ]

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[ "Q:\n\nChange UIAlertController's title fontsize\n\nI'm trying to change the title fontSize in an UIAlertController, but I can't manage how to set my NSMutableAttributedString to the title-property.", "\nSo for I've been creating the NSMutableAttributedString with the following code:\nlet title = NSMutableAttributedString(string: user.fullName)\nlet range = NSRange(location: 0, length: title.length)\ntitle.addAttribute(NSAttributedStringKey.font, value: UIFont.", "TextStyle.largeTitle, range: range)\n\nNow the tricky part for me is how to figure out how to set the new title to the UIAlertController, because it's expecting a String? ", "value.", "\nI looked around and found out that I should probably create a UILabel within the completion block when presenting the UIAlertController. ", "But how do I override the title-property in the UIAlertController with my own custom UILabel?", "\npresent(myUIAlertController, animated: true) {\n // Creating the UILabel depending on string length\n // Set the NSMutableAttributedString value to the custom UILabel and override title property.", "\n}\n\nOr maybe there's even an easier way to solve this?", "\n\nMy goal is to have like the image below:\n\nA:\n\nYou can make title and message of UIAlertController attributed by using this code. ", "You can customize as per your need. ", "You can see the result in the image. ", "I am not sure you can put it on Appstore.", "\nfunc showAlert() {\n let alert = UIAlertController(title: \"\", message: \"\", preferredStyle: .actionSheet) \n let titleAttributes = [NSAttributedStringKey.font: UIFont(name: \"HelveticaNeue-Bold\", size: 25)!, ", "NSAttributedStringKey.foregroundColor: UIColor.black]\n let titleString = NSAttributedString(string: \"Name Last name\", attributes: titleAttributes) \n let messageAttributes = [NSAttributedStringKey.font: UIFont(name: \"Helvetica\", size: 17)!, ", "NSAttributedStringKey.foregroundColor: UIColor.red]\n let messageString = NSAttributedString(string: \"Company name\", attributes: messageAttributes)\n alert.setValue(titleString, forKey: \"attributedTitle\")\n alert.setValue(messageString, forKey: \"attributedMessage\")\n let labelAction = UIAlertAction(title: \"Label\", style: .default, handler: nil)\n let deleteAction = UIAlertAction(title: \"Delete\", style: .destructive, handler: nil)\n let cancelAction = UIAlertAction(title: \"Cancel\", style: .cancel, handler: nil)\n alert.addAction(labelAction)\n alert.addAction(deleteAction)\n alert.addAction(cancelAction)\n self.navigationController?.present(alert, animated: true, completion: nil)\n\n}\n\n" ]

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[ "Players of electric musical instruments, notably electric guitars, strive to obtain particular tonal qualities from their instruments. ", "For example, guitar players often overdrive amplifiers to achieve harmonic distortion, which is desirable in various musical contexts. ", "Generally, such distortion can be generated by overloading an audio signal in a preamplifier (“preamp distortion”) and, thereafter, amplifying the distorted audio signal simply to make it louder and without further affecting its tone. ", "In addition (or in the alternative), distortion can be generated by overloading a signal in the amplifier itself (“power amp distortion”), as opposed to the preamplifier. ", "Power amp distortion usually requires an extremely high volume level to be achieved, and thus is not as practical for many players as preamp distortion, which can generate distortion at a low volume. ", "Despite the practical limitations, power amp distortion is often considered more desirable, as it produces tonal qualities having a greater dynamic range and can be controlled more effectively than preamp distortion by the player, such as by using various playing techniques. ", "Guitar players often prefer power amp distortion for being more “responsive” or “touch sensitive” than preamp distortion. ", "Further, most vintage (e.g., tube) guitar amplifiers produce only power amp distortion, and players prefer the sounds that such devices produce over more recent or modern guitar amplifiers, which rely largely or exclusively on preamp and/or digitally produced distortion.", "\nIn addition to the sounds produced by preamp distortion and power amp distortion, players of electric guitars and other electric instruments employ devices to produce other sound effects to alter tones and sounds that emanate from their instruments. ", "Referred to herein generally as “wet effects,” these devices can include signal boosters, distortion devices and equalizers, and are designed to receive a line level output signal from an instrument (e.g., guitar output) and send a modified line level signal to the input of the amplifier. ", "Wet effects can further be classified as “time-based” effects, and produce reverb (e.g., echo), delay (e.g., repeating), pitch alteration, and other sound qualities that are not intended to alter the basic sound of an amplifier, but to add sound-based functionality to an amplifier. ", "For example, a wet effects unit can produce reverb for a vintage amplifier that is not configured with that effect. ", "Wet effects can be provided in analog and/or digital devices, and can be configured in various formats, such as foot pedals, hand-held devices (including mobile computing devices), or in rackmount devices that can include rocker switches, push buttons, knobs, slider controls and/or other controls.", "\nMany players of electric instruments believe that the order in which various effects are connected, such as “in front of” or “behind” an amplifier greatly affects tonal quality. ", "For example, some wet effect units should not receive a signal from the instrument to provide a reverb effect as input to the amplifier. ", "A signal producing reverb, for example, is believed to suffer in tonal quality when it is overdriven in the amplifier or subjected to power amp distortion. ", "It is often preferred for an audio signal to be overdriven (i.e. distorted) and, thereafter, shaped to include reverb, delay or other wet effect.", "\nSome musical instrument amplifiers are configured with a preamplifier and amplifier, and often include wet effects that are positioned between the preamplifier and the power amplifier. ", "Referred to, generally, as an “effects loop,” such amplifiers are configured such that the wet effects operate on audio signals that are distorted via preamp distortion, and made louder by the amplifier. ", "Other musical instrument amplifiers are not so configured, and may not work well with effects loops because the time-based effects are positioned after the preamplifier, and the audio signals processed by wet effects get further distorted as the power amplifier is overdriven (i.e., by power amp distortion)." ]

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[ "\n“I did spend 9 years as a manager at a pizza place” - DyslexicAtheist\nhttps://twitter.com/nomedabarbarian/status/1232922661740613634\n======\nmabbo\nWhen people ask me why I moved back to Canada from the USA, knowing I'd be\npaid less and have higher taxes, I often have a hard time articulating what\nthe difference is between the two countries. ", "Why I prefer to live here.", "\n\nThis thread sums it up nicely.", "\n\nNo matter how down-on-my-luck I get back in Canada, I will always have a\nsafety net. ", "I can always walk into a hospital and be treated. ", "I can take time\noff when I'm sick. ", "I get time off if I have a kid. ", "It's the _law_ here and not\njust best effort by employers. ", "It's for everyone and not just the rich.", "\n\n~~~\nstrathmeyer\nIs it is big thing in America now to claim we don't have things we do like\ntime off when we are sick or hospitals to treat us? ", "What on earth is this post\nabout??", "\n\n~~~\njamroom\nLooks like around 40% of the US work force has no paid sick leave:\n\n[https://www.americanprogress.org/wp-\ncontent/uploads/issues/2...](https://www.americanprogress.org/wp-\ncontent/uploads/issues/2012/08/pdf/paidsickdays_factsheet.pdf)\n\n~~~\nhef19898\nDamn, that's hard. ", "In Germany we have six weeks per illness. ", "Meaning you get\nup to six weeks for your broken leg, another six for arm and so on. ", "Insurance\nto cover up to a year isn't to expensive neither if you start early. ", "Sounds\nlike paradise.", "\n\n------\ngeofft\nThis is the big reason I think we need to figure out as a society how to make\nit possible for everyone to keep a roof over their head and food on their\nplates even if they don't work at all.", "\n\nThe question of whether lazy people will take advantage of the system is not a\nlife-or-death question. ", "The life-or-death question is whether highly motivated\nand desperate people will take risks they shouldn't because we make them take\nthose risks.", "\n\n~~~\ndonatj\nI am a highly motivated person, yet if I could keep my home and health without\nworking I would stop working day 1. ", "I would target my motivation at things I\npersonally care about that don't help the economy in the least. ", "My art,\nwoodworking, finishing my stack of books. ", "I am certainly not alone.", "\n\nThis is why I think there needs to be some level of threat of destitution to\nkeep society functional. ", "Without it, this all falls apart.", "\n\n~~~\ngeofft\nWhat sort of things would you target your motivation towards? ", "Would they be\nvaluable for humanity? ", "Is \"the economy\" really the right barometer? (", "edit: I\nsee you added this - I think those are valuable for humanity! ", "I wish you could\nspend your time on art and woodworking!)", "\n\nPersonally, I spend a lot of my time keeping a hedge fund's computers working,\nbecause they pay me well for it (and I want to not only avoid destitution now,\nI want savings to avoid destitution in the future). ", "I spend about zero time on\nany of my open-source projects, which would be more valuable for humanity as a\nwhole, but I can't figure out how to get paid the same amount (or really\nanything) working on them. ", "And I know my projects are valuable to the economy\ntoo - I arrived at this job to find that another team was doing a big\nmigration onto a project I maintain (and haven't had much time for). ", "I didn't\nknow this in advance, and they didn't know I was joining their company.", "\n\nBesides - it's okay if many people lose their motivation to work, as long as\n_enough_ people still work from intrinsic motivation. ", "And you'd still have the\nmotivation of needing to earn money for luxuries. ", "Once you finish your stack\nof books, the survival stipend wouldn't cover buying any more books.", "\n\n~~~\nrichk449\nYou are payed well to do X. You can’t get anyone to pay you to do Y. Yet you\nbelieve that Y is more valuable to society than X. Why?", "\n\nIsn’t society’s willingness to pay you for something a decent signal that\nsociety values it?", "\n\n~~~\ngeofft\nNo, because as I just demonstrated, they use my open-source work - society\njust has no mechanism to monetize it.", "\n\nIt is possible that I could charge support contracts for the software now -\nbut it's just about done, and it's pretty well documented, and if anything I'd\nhave _less_ incentive to write public docs. ", "And I have no mechanism to get\npeople to fund the next thing I want to work on and think is a good idea.", "\n(Well, I could continue working at a high-paying job for a few years and then\nquit, of course... but the logical conclusion of that loophole is that nobody\nshould be paid enough that they can afford to quit, else they'd be able to\nignore the market, right?)", "\n\n------\nGhjklov\nI vouched for this post, as it's something that people need to be more aware\nof. ", "While many people here can remote into their tech job, there are many\npeople who simply do not have such privilege, and those are often the people\nwho make your food and drinks. ", "I too have mostly worked food service jobs, out\nof a job and looking for one now, and as soon as coronavirus hit the news, I\nknew that I would be eating out a lot less now because what the Twitter posts\ndescribe are completely accurate from my experience. ", "I lived it.", "\n\n~~~\nDyslexicAtheist\nthanks for vouching :)\n\nnot sure what happened here. ", "I stepped away and this blew up, so I was also\nunable to change the title into something better. ", "no idea though why this gets\nflagged (several times).", "\n\n------\nApicalDendrite\nThere are a lot of regional differences within the US. ", "In Massachusetts, it's\na lot better than this:\n\n* MA has 40 hours of mandatory paid sick leave a year\n\n* Assuming that your employer doesn't offer health insurance, if you're a single person making minimum wage in MA, working 40 hours a week, you qualify for ConnectorCare, with $15 co-pays for primary care visits and no deductible. ", "There's a $82/month premium, but you'd also qualify for a $276/month tax credit.", "\n\nThere are still plenty of situations where a person making minimum wage\nwouldn't be able to afford a doctor's visit. ", "For instance, if you miss paying\nyour premiums your health insurance can be canceled. ", "Or you could be working\nfor an employer that offers health insurance, but with a high deductible.", "\nHowever, the situation here is a lot less bleak than the thread - for many\npeople here working in the fast food industry a doctor's visit and a week's\ntime off are affordable.", "\n\n~~~\nwasdfff\nSick leave should be unlimited. ", "Have the employee skype a nurse for 10 minutes\nif you think they are faking it.", "\n\n------\nethanbond\nThis title could be better. ", "Maybe \"I spent 9 years as a manager at a pizza\nplace... Nobody in the restaurant industry goes to the doctor when they're\nsick\"?", "\n\nOr just the latter half? ", "Much more informative than the first half.", "\n\n~~~\nSilasX\nDitto. [", "1] HN seems to have a bizarre tolerance for cryptic headlines. (", "And\nthe low character limit doesn't help.)", "\n\n[1]\n[https://news.ycombinator.com/item?id=22519541](https://news.ycombinator.com/item?id=22519541)\n\n------\nwwweston\nDon't miss the re-tweet down farther in the thread:\n\n\"I'm an epidemiologist. ", "For 5 years I was specifically a flu/respiratory virus\nepidemiologist. ", "I was asked on multiple occasions what I thought was the most\neffective thing we could do to improve the severity of flu season.", "\n\nThat's an easy answer. ", "Universal paid sick leave.\"", "\n\n[https://twitter.com/Just_Eleanora/status/1233030130345246720](https://twitter.com/Just_Eleanora/status/1233030130345246720)\n\n------\nheartbeats\nThe incentives really are not in place. ", "He's just scratching the surface of\nthe rabbit hole. ", "If quarantines become compulsory, the situation will be _even\nworse_. ", "Imagine people actively covering up their symptoms and lying to\ndoctors. ", "It would be complete pandemonium.", "\n\nThe title is not great. ", "I would suggest \"I spent 9 years at a pizza place, and\nI'm terrified of COVID-19.\"", "\n\n------\nremote_phone\nIt’s in the best interest of restaurant owners to keep their customers safe\nand to monitor employees of sickness. ", "Unfortunately I doubt they have the\nforesight to do this, because they’re probably living on the edge as well.", "\n\nBut one incidence of coronavirus at their restaurant and their traffic will go\nto 0 immediately. ", "The owner will go bankrupt almost overnight. ", "Word travels\nextremely fast these days, especially over social media.", "\n\nFor example I just heard that Stanford hospital has a dozen confirmed\ncoronavirus patients there. ", "If a restaurant has a worker diagnosed no one will\ngo there immediately.", "\n\nA lot of restaurants are going to go bankrupt over the next 2-3 months\nunfortunately.", "\n\n~~~\nheartbeats\nNo, it's in the best interest of restaurant owners that there are no\n_documented_ incidences of coronavirus at their restaurant.", "\n\nTo spell it out: if a manager knows someone has the virus, they will fire\nthem. ", "Therefore, the infected will try to cover it up. ", "This will be the case\neven if healthcare is free.", "\n\n------\nWilliamEdward\nOne of the things that will shake up the US elections and put the entire\ncountry at risk is the fact that healthcare is so expensive. ", "If you cannot get\ntreated for coronavirus, you can expect the number of cases to spread and\nskyrocket.", "\n\n~~~\nConsultant32452\nI don't want to downplay the financial concerns but in the US we expect every\nhospital bed to be full by mid May. Many of those beds lack proper isolation\nfor infectious disease, and we'll have run out of proper PPE supplies for\nhealthcare workers, meaning many of those workers will cycle out of\ncommission. ", "Unfortunately every country is in a similar situation. ", "People are\ngoing to go without appropriate care regardless of copays. ", "Helping people\ncover out of pocket expenses is the easy problem to solve.", "\n\n[https://twitter.com/LizSpecht/status/1236095180459003909?s=2...](https://twitter.com/LizSpecht/status/1236095180459003909?s=20)\n\n~~~\nheartbeats\n> Undeserved panic does no one any good. ", "But neither does ill-informed\n> complacency. ", "It’s wrong to assuage the public by saying “only 2% will die.”", "\n> People aren’t adequately grasping the national and global systemic burden\n> wrought by this swift-moving of a disease. ", "23/n\n\nIsn't the best approach then to do nothing? ", "To be blunt here: if what she's\nsaying is true, most of the vulnerable groups are going to die anyway. ", "So why\nnot just ignore it completely, and spend the healthcare resources on other\nstuff?", "\n\nI mean, if the choices are:\n\n1\\. 2% of the population dies and the healthcare system and economy collapses\ncompletely\n\n2\\. 2 + ε% of the population dies\n\nThen the second option is arguably preferable.", "\n\n~~~\nConsultant32452\nI believe the unspoken plan is to let it happen but try to let it slow roll\nthrough the population at a rate I would describe as a controlled disaster.", "\nThat's why planes are still flying except to the worst spots.", "\n\n------\nsysbin\nUSA taught me how little people can have as basic rights and because they\nthink of \"equality\" without factoring in financial status; since they think\neveryone earns what they get in life. ", "Majority of US is religious. ", "So, I can\nsee why people aren't demanding basic necessities for a decent quality of life\nand when that would make them feel they haven't earned success.", "\n\nKnowing the forgoing makes me believe something like loss of life from the\ncoronavirus could possibly be what's needed to get people rallying for change.", "\nOtherwise the mentality will continue of I will get mine some day and before\nthen I don't want things to change because I'll get rich eventually.", "\n\n------\nWaterluvian\nI feel that events like this are the \"time to pay the piper\" moments with\nwhat's wrong with American society. ", "But don't expect to see the price paid. ", "I\nexpect to see a bail out in one form or another to kick the can down the road.", "\n\nIt also reminds me that \"Canada is like America put through a low pass\nfilter.\" ", "We have pretty much the same situation, but with milder extremes.", "\nWhen I worked in a kitchen I did see injuries and sickness get handled more\nproperly because a doctors visit is free and employment insurance is a thing,\nso they still got paid for being off work. ", "But I also saw the same issues with\n\"you don't get paid if you don't show up\" so people worked through short term\nillnesses. ", "I saw someone step in a pot of scalding chicken broth/fat because\nthey were so fatigued and the idiot who placed it on the floor was sick and\nfatigued and was skipping steps.", "\n\nTo each their own opinion but as I get older (and indeed pay a crap ton more\ntaxes) I'm becoming increasingly convinced that we need more socialism. ", "This\ntwitter thread is a great example of how we can all suffer when the most\nvulnerable of us suffers. ", "I say socialism because I believe we need a baseline\nsafety net where, \"if you're not conributing, at the very least you're not\ndoing harm.\" ", "I've met a lot of people where I think \"honestly I would rather\nyou just stay out of the way.\" ", "I think that's the hardest part. ", "We have a\nculture of absolutely despising the idea of free lunches and free loaders.", "\n\n~~~\nlapnitnelav\nI think America is anything but a society, more a bunch of folks that happen\nto be sharing the same tract of land, compared to other cultures.", "\n\nHyper-individualism has its shortcomings and as you framed it, the piper has\ncome to collect the money and there's been a lot interest owed.", "\n\nHope we are wrong but wouldn't hold my breath.", "\n\nDisclaimer, haven't set foot in the US yet so I'm only extrapolating from what\nI have been able to observe from far away.", "\n\n~~~\nwasdfff\nPretty spot on, actually.", "\n\n------\nSilasX\nHow did submitter conclude that \"I did spend 9 years as a manager at a pizza\nplace” is a relevant excerpt that could be used as the title?", "\n\nThe thread is about concerns about health care policy and food service labor\npractices encourage the spread of viruses, if you want a heads-up.", "\n\n------\nfoogazi\nAfter reading this I think I’m going to skip restaurants & fast food for a\nwhile\n\n------\naerovistae\nI used to love the US and I came out of the 2010s hating it instead. ", "Sigh.", "\n\n~~~\npstuart\nIt is an insane asylum, but we're not all crazy here. ", "That said, it is crazy-\nmaking watching it crumble from the inside.", "\n\n------\nblartdfdsfsd\nYou are all complaining about the system in the US but don't realize it is\nINTENTIONAL. ", "A pure capitalist society doesn't want Sick Poor People who cant\nwork. ", "You are a drain on the wealth generation engine. ", "Old Sick Poor people\nare even worse. ", "Check out the Stanford Study\n[https://news.stanford.edu/2016/04/11/geography-income-\nplay-r...](https://news.stanford.edu/2016/04/11/geography-income-play-roles-\nin-life-expectancy-new-stanford-research-shows/)\n\n------\nalexashka\nThis will boil down to the cost of a human life at the end of the day, not\nunlike the speed limit debate where we know cars kill a bunch of people every\nyear, and yet people want to get places 5 minutes faster.", "\n\nHistorically, the cost of a human life has mostly been low but was offset by a\nsense of community. ", "We've gotten rid of community by allowing people to\nmigrate in large numbers. ", "Migrate from state to state, from country to\ncountry, from job to job, from marriage to marriage, from casual sex partner\nto casual sex partner.", "\n\nAll this migration makes it difficult to create lifelong bonds and without\nthose, you really are screwed in the ways the twitter thread describes.", "\n\nIt's uncomfortable and our current political and mass media setup makes it\nimpossible to have long form conversations on these topics - so I just don't\nknow how things can possibly get better for the average citizen. ", "Sad.", "\n\n~~~\ngeofft\nOn the other hand, allowing people to migrate from marriage to marriage lets\nthem _create_ lifelong bonds that actually help them when their first partner\nturns out to be callous and uncaring. ", "And there's nothing forcing people to\nmigrate if they're happy with their current community.", "\n\nIt's true that the old system was better for some people - e.g., callous and\nuncaring partners got to have someone obligated to keep taking care of them. ", "I\nsuppose it's a tradeoff.", "\n\n" ]

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[ "A CONFERENCE to help formulate the Muslim community's response to the threat of grooming in the city will take place this week with a panel of experts lined up to discuss the issue.", "\n\nThe Professional Muslims Institute (PMI) has organised the Child Sexual Exploitation and the Muslim Community's Response conference with the intention of learning more about the issue and finding ways for that community to play a role in safeguarding those at risk from child sexual exploitation.", "\n\nAccording to the annual report from Bradford's Safeguarding Children Board, there are usually between 60 and 100 children in the city regarded as being at medium to high risk of being exploited by groomers.", "\n\nFollowing covert work between July 2013 and March this year, the authorities issued warnings to 26 individuals identified as being involved in potentially exploiting youngsters.", "\n\nCEO of the Institute Javed Bashir said: \"The Professional Muslims Institute has been shocked and horrified from recent cases and believe that we have a duty to protect and safeguard our young people.", "\n\n\"The purpose of the PMI seminar is to bring that debate into an open forum with representatives from across the social spectrum, where the underlying causes and issues could be discussed, challenged and educate us all of what the facts actually are on child sexual grooming and how our responsibility is first and foremost to recognise those victims of abuse and to seek help.", "\n\n\"Sexual grooming and child abuse afflicts all sections of society and is perpetrated by people of all ethnic groups. ", "But we as Muslims and British citizens need to play our part in protecting children and young people from such acts.", "\n\n\"Our intention is first and foremost to make Bradford a better place for all our children and keep them safe from perpetrators of gang-led crimes of which sexual grooming abuse.", "\n\n\"The event is the start of a debate in which we seek to work with others including parents, faith groups, local organisations and the business community to eradicate the practice from all communities,\" he said.", "\n\nThose who will be speaking at the conference, to be held from 6pm on Thursday at the Carlisle Business Centre, include Nazir Afzal from the Crown Prosecution Service, Shaista Gohir, of the Muslim Women’s Network UK, Imam Qari Asim from Leeds Makkah Mosque, novelist Qaisra Shahraz, Ansar Ali of Together Against Grooming, Paul Hill, representing Bradford Safeguarding Children’s Board and Superintendent Vince Firth from West Yorkshire Police.", "\n\nFor booking and for more information contact Javed Bashir on 0844 443 5652" ]

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[ "Room (15)\n\n*Please note that there is a £1.50 fee per transaction\n\nRoom (15)\n\nDirector Lenny Abrahamson (Frank, What Richard Did) has a rare talent for cutting to the heart of irreversible moral choices with this adaptation of Emma Donoghue’s Booker-shortlisted book Room.", "\n\nJack has never known life outside the room, which he shares with his mother (Brie Larson). ", "Despite their desperate limitations Jack’s mother is determined to raise him with care and imagination. ", "When the pair devise a precarious plan of escape, they are forced to return to, and discover, the wonders, horrors and choices of the world they left behind.", "\n\nHarrowing, suspenseful and wondrous, this film represents the culmination of a variety of talents, with an Oscar winning performance from Brie Larson.", "\n\n‘Astonishing’EMPIRE\n\n‘Suspenseful and heartrending’ ★★★★\nVARIETY\n\n‘One of the best movies of the decade’\nCHICAGO SUN-TIMES\n\nThe Refugee Manifesto\n\nRoom will be preceded by a screening of Catherine Cartwright’s short film The Refugee Manifesto.", "\n\nThe Refuge Manifesto was made during a 10 week art project with women affected by domestic and, or sexual abuse. ", "Artist Nicci Wonnacott and animation facilitator Joshua Gaunt supported the women to think about their personal refuge through making art in a warm and friendly environment.", "\n\nThe project was produced by Catherine Cartwright and leads on from her film with co-collaborator Joshua Gaunt, The Last Resident, a film made in the last days of the Exeter women’s refuge before it was closed down. ", "This new film explores personal refuge and puts forward a proposal for how we can collectively support each other in society." ]

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[ "What Really Grinds My Gears\n\nyou know what really grinds my gears\n\nwhen you go to a website and it asks you to share it before you've even flipping read anything\n\nthese captions aren't guaranteed to be correct" ]

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[ "General Motors CEO Mary Barra was walking the stage at the J.P. Morgan Automotive conference in New York on an early August morning, making a dramatic point-by-point case for the company she leads: that GM, despite all its challenges and varied competitors, just might be the strongest and most well-positioned business in all of automotive transportation.", "\n\nadvertisement\n\nadvertisement\n\nAnd how did the audience of investors respond to Barra’s pitch? ", "With seeming indifference. ", "Indeed, many of the attendees appeared to be more engaged with their iPhones than the CEO’s presentation. ", "It wasn’t just that lunchtime was approaching and blood-sugar levels were low, or that the meeting room’s drab brown-and-tan decor and muted acoustics had dulled everyone’s senses. ", "No, the bigger obstacle was most likely an instinctive skepticism about GM itself—and, perhaps, about Barra, too. ", "General Motors was once an acclaimed titan, the most respected company in America, but those days are long gone. ", "Decades of decline have been punctuated by bankruptcy, a government bailout, and a devastating ignition-switch design flaw that has been implicated in 139 deaths. ", "All of this solidified the notion that GM was a dysfunctional, bureaucracy-ridden has-been. ", "If any business was likely to dominate the future of auto transport, it would be a Silicon Valley darling like Uber, Tesla, Google, or even Apple—all of which have been aggressively investing in disrupting the car business as we know it. ", "They are the ones with the creativity, the talent, and the consumer passion to do something special. ", "Not old-fashioned GM. ", "As for Barra herself—dressed in a conservative brown suit, speaking with a flat, slightly nasal Michigan accent—her stage presence didn’t exactly challenge this story line. ", "The best she could do to liven up her less-than-dynamic delivery was chopping one hand into the other to punctuate her argument. ", "A 35-year lifer at GM, Barra is a product of the exact company and culture that she is tasked with transforming. ", "Perhaps it’s no surprise that GM’s valuation has dropped by about a quarter since she became CEO, the stock falling from $39 a share to a recent $32. ", "If there is anything unexpected about her as a GM leader, it’s that she’s a woman (which, unfortunately, hasn’t always been viewed as an asset in the testosterone heavy auto world). ", "But here’s the wacky thing: What if all those reasons for doubting GM and dismissing Barra as something less than a Steve Jobs–like revolutionary . . . ", "what if they are all wrong? ", "A case of prejudice and assumption that misses some larger understanding? ", "What if Barra is the perfect leader to reestablish GM as a premium, world-beating brand, outdueling all of those tech cowboys? ", "Now that would be a story for the ages. ", "GM does have some things going for it, signs that it just might be a winner in the long-haul future of transportation—if things line up the right way. ", "After Barra’s J.P. Morgan presentation, I met with her in a conference room upstairs in the bank’s offices, one of several meetings I’ve had with her and her top lieutenants over the past few months. ", "Barra, an electrical engineer, doesn’t have the shiny bravado of so many tech-world leaders, but a career spent overseeing factories, supply chains, and GM’s entire product portfolio has given her a practicality they sometimes lack. ", "She is much more at ease in person than she was on stage. ", "When she explained that her father, who spent 35 years working as a die maker in a GM factory, taught her the value of hard work, it came off as authentic, not clichéd. ", "She is keenly aware that GM’s 223,000 employees will have to behave differently if its plans for the future are to succeed; that she needs to replace a culture of blame and bureaucracy with one driven by accountability, speed, and collaboration. “", "In this area of rapid transformation, you have to have a culture that’s agile,” she said. “", "We still have a lot of work to do.” ", "GM To Top Tech Talent: Ditch Silicon Valley For Detroit By reinventing its culture, the old-line automaker hopes to attract those looking to shake things up, rather than beat them into submission. ", "GM could have gone away in 2009, disappeared. ", "Yet today it is a profit machine, with some $20 billion in cash on its books. ", "It has paid back more than two-thirds of the funds it received from the government, and for the last three consecutive quarters has reported solid results, including more than doubling its earnings in its June filing, to $2.9 billion. ", "Just as critically, over the past year, GM has leaned into ride sharing, autonomous-driving technology, and electric vehicles at a heady pace. ", "With a flurry of deals and product releases more reminiscent of its tech-industry competitors, GM has, in short order, constructed a portfolio of assets dedicated to disrupting its own core business from within. ", "What if Steve Jobs had been tasked with reviving a post-bankruptcy GM? ", "What playbook would he have adopted? ", "Looking back at Jobs’s return to Apple in 1997, he was faced with a financially strapped and dysfunctional operation. ", "His first priority was to stabilize cash flow so he would have the resources to put toward innovation. ", "This, too, was required at GM, and so far it has been successful. ", "Jobs’s other priority was to make sure he had the right team in place around him and the right culture upon which to build. ", "It wasn’t iPods or iPhones that Jobs obsessed about at that stage. ", "It was the people. ", "Only then could he turn himself to the products in earnest.", "\n\nadvertisement\n\nBarra has her own, similar obsessions. ", "In Detroit a few weeks earlier, I had watched her deliver a far more impassioned—and successful—presentation in yet another dreary auditorium, in the bowels of Tower 300 of GM’s seven-building headquarters complex. ", "This time Barra was speaking to 35 newly promoted mid-level executives, and they eagerly followed every word. “", "Remember your whole career, how you’ve been talking about them?” ", "Barra said. “", "If only they would get it. ", "If only they would work this out. ", "Well, you are now they. ", "If you don’t like something, you have to talk to yourself.” ", "Chuck Stevens [Photo: Steve Fecht for General Motors] Barra knows that she cannot succeed without turning around GM’s famously stagnant bureaucracy. ", "This is a place, after all, that has long been known for its “GM nod” (agreeing to something in a meeting and then never doing anything about it) and “GM salute” (pinning blame on somebody else). “", "Look at what came out in the Valukas Report,” CFO Chuck Stevens told me, referring to a 2014 internal investigation of the ignition-switch crisis, which delivered a scathing indictment of GM’s management. “", "No sense of urgency. ", "No accountability or responsibility. ", "A siloed mentality.” ", "That kind of culture will never compete with Google and Uber. ", "Barra has launched a slew of initiatives across the company designed to push GM in a new direction—from a program called GM 2020, which builds cross-functional “co-labs” to address all kinds of problems; to a yearlong “transformational leadership” course for senior execs; to a quarterly two-day off-site that Barra personally leads with her 16 top reports, focused not on strategy but on their own interactions. “", "Mary believes that if we change the behaviors [of top managers], people who work for us will see that and emulate it,” says HR chief John Quattrone. “", "There won’t be this dysfunction that we had before.” ", "GM started thinking about the daily experience of the 86% of Americans who commute to work by car. “", "Lots of people say they love to drive,” says Ammann. “", "But I haven’t met anyone yet who says they love their commute.” ", "Back in June, Barra had gone to San Francisco for her first test ride in one of GM’s new Bolt electric cars, which was equipped with the autonomous-driving technology of Cruise Automation, a company GM purchased earlier in the year for $581 million. ", "Barra sat in the back seat with Cruise CEO Kyle Vogt and kept her eyes trained on two things: the busy streets of San Francisco and the technician up front, who was resting his fingertips lightly on the steering wheel, as is required by California regulations. ", "Upstairs, under the broad wood beams of Cruise’s airy office, staff members gathered around a video monitor showing the car, which was marked by a flashing green light that moved around a digital map of the city. ", "If something were to go wrong and the driver needed to grasp the steering wheel and quickly take control, the light would turn red, as it had on previous drives when the Bolt had shifted lanes. ", "The crowd—and those two CEO passengers—was eager for that not to happen this time. ", "The drive was an important moment, symbolically and practically. ", "Barra says GM started down “an evolutionary path” toward re-envisioning the company soon after it emerged from bankruptcy. ", "At that point, under then-CEO Ed Whitacre, GM’s efforts at disruption had a me-too, late-to-the-party mien. ", "GM launched its first hybrid car, the Volt, in 2010, significantly lagging behind hybrid pioneers such as Toyota. ", "Still, Barra says, it was an important first step in acknowledging where the company needed to go. ", "Over the next few years, GM began incorporating aspects of self-driving technology into select models, including software that alerts drivers if they veer out of their lane or stops the car if it detects an imminent collision. ", "Many other car companies were also integrating features like this, but at least GM was in the game. ", "The evolutionary began tilting toward the revolutionary in late 2014. ", "Barra had been appointed CEO earlier that year and pulled together a new group of leaders: former investment banker Dan Ammann, whom she named president; longtime GM exec Mark Reuss, whom she appointed product chief; and CFO Stevens. ", "Together they dug into evolving data about the rise of ride sharing, the ambivalence of urban-dwelling millennials toward car ownership, and the appeal of all-electric vehicles. ", "They looked at the economics: Shared self-driving cars might cut the cost of an average trip in half. ", "And they started thinking about the daily experience of the 86% of Americans who commute to work by car. “", "Lots of people say they love to drive,” says Ammann. “", "But I haven’t met anyone yet who says they love their commute.” ", "All those trends threatened the traditional car-selling business. ", "While none of these factors were yet showing up in GM’s improving bottom line, Barra’s team concluded that without radical change, the road ahead would be rough. ", "So how to turn these looming shifts into an opportunity?", "\n\nadvertisement\n\nFrom Audi To Zoox, 17 Companies That Are Driving Change In the Car Industry Along with GM, these innovators are finding ways to improve the basics of modern transportation. ", "What Barra was trying to do in that August J.P. Morgan presentation was lay out how quickly, radically, and effectively GM has put in place the plan it started hatching at the end of 2014. ", "Spanning the arenas of connectivity, sharing, alternative propulsion, and autonomous technology, GM now has credible assets in each pillar of the business increasingly referred to as personal mobility. ", "The company has, in short order, constructed a five-part portfolio, which arguably gives it as many or more of the necessary pieces to succeed in the driving world of tomorrow as anyone else: 1. ", "The platform. ", "While most people think of wireless connectivity as the purview of Silicon Valley, when it comes to the auto world, GM’s OnStar service provides both access and data that no other competitor has available. ", "Historically, OnStar has been used by drivers to create an immediate connection to a live operator who can offer directions or help in an emergency. ", "But moving forward, that platform will be applied to providing remote diagnostics, distributing software updates, and tracking data—not to mention managing autonomous fleets. ", "2. ", "The partner. ", "On January 4, GM announced a $500 million investment in Lyft, the country’s No. ", "2 ride-share service. ", "The deal gives GM a foothold (it reportedly later passed on buying Lyft outright), allowing it to test, learn, and take advantage if ride sharing takes off even more. ", "Already this year, the companies have worked together on a program called Express Drive, which lets Lyft drivers in seven big cities rent GM cars at heavy discounts, with other collaborations in the works. ", "General Motors’ new car-sharing service, Maven [Photo: John F. Martin/General Motors]\n\n3. ", "The startup. ", "Eleven days after the Lyft investment became public, GM announced that it would launch a proprietary car-sharing service called Maven. ", "A Zipcar-like offering, Maven taps into another possible future of mobility: replacing ownership with sharing. ", "This startup inside GM has some features Zipcar doesn’t—an app that lets you book, open, and start the car; free Apple CarPlay, Android Auto, OnStar, and 4G wireless in every car—and it is already operating in seven cities, with plans to expand significantly next year. ", "At the same time, Maven lays the groundwork for a possible future when GM owns and operates a fleet of its own autonomous cars. ", "It is a testing ground that can pivot as the marketplace does, even providing a backup brand that could be tapped for ride sharing in the event of Lyft’s demise or its outright purchase by a competitor. ", "The Chevrolet Bolt EV [Photo: Steve Fecht for General Motors] 4. ", "The car. ", "Barra believes GM’s new all-electric Bolt, which goes on sale later this year, will be a landmark product. ", "When she and then-CEO Daniel Akerson initiated the Bolt project in 2013, the goal was to develop a fully electric vehicle that would be fun to drive, affordable, and practical, with a range of at least 200 miles (the minimum needed to make it viable for commuters, research shows). ", "At a cost of just $30,000 (after a $7,500 federal tax rebate) and getting 238 miles from a single charge, the new car will far surpass the specs of competing electrics made by competitors such as Ford and Nissan. ", "While the Bolt is similar in price and range to Tesla’s heavily anticipated Model 3, it will be available to consumers much earlier. ", "5. ", "The technology. ", "GM’s initial approach to autonomous driving was to incrementally add features to existing vehicles, gradually making drivers more comfortable with deferring to a computer. ", "But when Ammann nailed down the acquisition of Cruise in March, it marked an investment into the more radical all-at-once strategy being pursued by the likes of Google and Uber. ", "Launched in 2013, Cruise has built a complex array of software and hardware that uses artificial intelligence to pilot a car. ", "While in-house GM engineers were working on their own fully autonomous system, Ammann and Barra came to believe that Cruise was further ahead—and so they jumped. ", "Cruise CEO Vogt has been obsessed with self-driving cars since childhood, and designed his first autonomous vehicle for a state fair at the age of 13. ", "When Vogt started Cruise, his goal was to sell autonomous-driving kits that could be retrofitted to regular cars. ", "After he pivoted to the bigger idea of operating a fleet of autonomous cars, the shift put him right in line with the future as imagined by Ammann. ", "Now GM and Cruise are working together to implement that vision at a huge scale: millions of customers, mostly young and urban, sharing rides in autonomous Bolt EVs.", "\n\nadvertisement\n\n“[Google and Apple] generate a lot of cash, and have a lot of resources and talent, but neither one has made cars,” says Reuss. “", "A car has to work right every time, all the time.” ", "Of course, Cruise’s technology actually has to work, which is why Barra’s test drive that June morning was so significant. ", "Inside Cruise HQ, the mood was confident but tense, with little noise beyond the occasional iPhone ping. ", "As the car navigated a particularly heavy stretch of traffic, it had to make a sudden lane shift. ", "Barra and Vogt watched the driver’s hands; the Cruise staff watched the telemetrics monitor. ", "The driver never grasped the wheel; the light stayed green. ", "After the car piloted itself back into Cruise’s garage, Barra and Vogt bounded into the office, triumphant. ", "Barra stood in front of the assembled crowd. “", "If somebody [at GM] says you can’t have something, or you can’t do something, or it’s going to take this much time, and it doesn’t make sense to you, challenge them,” she told them. “", "I want to take the energy and speed and how you look at doing things and drive it into the core of GM.” ", "If there’s skepticism about GM, it is hardly without foundation. ", "The basic components of autonomous, electric, shared rides are being pursued by many of GM’s competitors. ", "Ford, for one, has announced plans to have a fully self-driving car (with no steering wheel) available by 2021, and is building its own stable of mobility-focused products and services. ", "Uber launched a trial fleet of autonomous cars in September that is already ferrying paying passengers around Pittsburgh. ", "Tesla’s ability to persuade 400,000 people to put down a $1,000 deposit on a Model 3 just from a press conference is eye-opening. ", "But what if we train that same lens of skepticism on the tech world? ", "Suddenly, GM’s aspirations may not look so far-fetched. ", "After years of development of self-driving cars and billions of dollars of investment, Google has little to show for it. ", "And Apple, according to published reports this summer, may be rethinking its approach to making a car. ", "Despite all of Silicon Valley’s astonishing accomplishments, it turns out putting together thousands of pounds of metal and plastic in a way that can safely move human beings at high speeds over great distances is, well, pretty hard to do. “[", "Google and Apple] generate a lot of cash, and have a lot of resources and talent, but neither one has made cars,” says Reuss. “", "The piece that is not well understood outside of the automotive industry is how hard it is to take technology and integrate it into a car. ", "It seems like you should be able to layer it in and have it work and that would be great. ", "Right. ", "The effort to integrate that into the car is equal to or more than the technology itself. ", "A car has to work right every time, all the time.” ", "Then there’s Tesla, which, with its high-profile Model S electric luxury car and the upcoming affordable Model 3, has been at the forefront of transportation’s transformations. ", "But the company lost nearly $600 million in the first half of 2016, and two fatal Model S accidents have raised questions about the viability of its technology. ", "While GM is sitting on some $20 billion in cash, Tesla is deeply in debt and seems likely to need a major infusion in order to achieve even its near-term goals. ", "Despite its outsize reputation, Tesla delivered just 50,580 vehicles in 2015, compared to GM’s output of nearly 10 million. ", "Elon Musk says Tesla will make 500,000 cars in 2018, but so far this year the company has missed its production goals. “", "Moving from producing tens of thousands of vehicles to hundreds of thousands of vehicles is a very significant challenge,” says Mike Ableson, who heads GM’s strategy group. “", "The Silicon Valley culture of developing fast and iterating fast can be a strength. ", "But if you’re going to put this stuff in production, sooner or later you’ve got to turn it into hardware at high volume. ", "That’s the Detroit side of the discussion.” ", "But what if that whole us-versus-them way of looking at it is wrong? ", "Maybe, as the technology improves and consumer trends solidify, GM and the tech world won’t prove to be rivals after all. ", "Perhaps they’re just different pieces of a larger puzzle—a future where Silicon Valley inspiration and Detroit know-how (and vice versa) converge in ways that yield transformative innovations we can’t yet imagine. “", "I don’t think any one company can do this all by itself, automotive or nonautomotive,” says Reuss. “", "That’s why you see acquisitions and partnerships happening.” ", "In other words, GM could still be part of the mobility of the future even if all of this year’s new ventures fall flat.", "\n\nadvertisement\n\nFor now, however, Barra isn’t thinking about that. ", "She knows the work she and her team have done so far is just the beginning of a long process with many unforeseeable turns to come, but she’s determined to be first across the finish line. ", "And like Steve Jobs and his renowned reality distortion field, the CEO believes that determination is as important as strategy. “", "Don’t confuse progress with winning,” she said while onstage at GM’s headquarters, discussing the company’s autonomous-car efforts. “", "It’s not like, ‘Check, check, check, done.’ ", "It’s, ‘Okay, the table is barely set. ", "This is a huge opportunity. ", "So what are we going to do?’ ” ", "In her vision of GM’s revved-up culture, Barra told the group, “best efforts” alone aren’t going to cut it. “", "Are you doing what you can?” ", "she asked. “", "Or are you doing what it takes to win?” ", "related video: Ford’s CEO On The Future Of Connected And Autonomous Cars" ]

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[ "Q:\n\ndataSource sql server Connection from solr\n\nHaving problem to connect to sql server from solr.", "\nI have tried following connections \n<dataSource type=\"JdbcDataSource\" name=\"ds1\"\ndriver=\"com.microsoft.sqlserver.jdbc.", "SQLServerDriver\" \nurl=\"jdbc:sqlserver://localhost;databaseName=189021-resurs;integratedSecurity=true;responseBuffering=adaptive;\" \nreadOnly=\"true\"\n/>\n\n<dataSource type=\"JdbcDataSource\" driver=\"com.microsoft.sqlserver.jdbc.", "SQLServerDriver\" \n url=\"jdbc:sqlserver://localhost\\ARBETSDATOR\\SQLEXPRESS;integratedSecurity=true;databaseName=189021-resurs\"/> \n\nIm trying to use integratedSecurity=true, is that ok?", "\ntcp/ip is enabled.", "\nI have seen variations of following part of the connectionstring, should it be:\njdbc:sqlserver://ARBETSDATOR\\SQLEXPRESS\nOr just localhost:\njdbc:sqlserver://localhost;\n?", "\nWhen using jdbc:sqlserver://localhost; i get following:\nFull Import failed:java.lang.", "RuntimeException: java.lang.", "RuntimeException: org.apache.solr.handler.dataimport.", "DataImportHandlerException: Unable to execute query: SELECT * FROM Members Processing Document # 1\n at org.apache.solr.handler.dataimport.", "DocBuilder.execute(DocBuilder.java:270)\n at org.apache.solr.handler.dataimport.", "DataImporter.doFullImport(DataImporter.java:411)\n at org.apache.solr.handler.dataimport.", "DataImporter.runCmd(DataImporter.java:476)\n at org.apache.solr.handler.dataimport.", "DataImporter$1.run(DataImporter.java:457)\nCaused by: java.lang.", "RuntimeException: org.apache.solr.handler.dataimport.", "DataImportHandlerException: Unable to execute query: SELECT * FROM Members Processing Document # 1\n at org.apache.solr.handler.dataimport.", "DocBuilder.buildDocument(DocBuilder.java:410)\n at org.apache.solr.handler.dataimport.", "DocBuilder.doFullDump(DocBuilder.java:323)\n at org.apache.solr.handler.dataimport.", "DocBuilder.execute(DocBuilder.java:231)\n ... 3 more\nCaused by: org.apache.solr.handler.dataimport.", "DataImportHandlerException: Unable to execute query: SELECT * FROM Members Processing Document # 1\n at org.apache.solr.handler.dataimport.", "DataImportHandlerException.wrapAndThrow(DataImportHandlerException.java:71)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource$ResultSetIterator.(JdbcDataSource.java:279)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource.getData(JdbcDataSource.java:236)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource.getData(JdbcDataSource.java:40)\n at org.apache.solr.handler.dataimport.", "SqlEntityProcessor.initQuery(SqlEntityProcessor.java:59)\n at org.apache.solr.handler.dataimport.", "SqlEntityProcessor.nextRow(SqlEntityProcessor.java:73)\n at org.apache.solr.handler.dataimport.", "EntityProcessorWrapper.nextRow(EntityProcessorWrapper.java:243)\n at org.apache.solr.handler.dataimport.", "DocBuilder.buildDocument(DocBuilder.java:469)\n at org.apache.solr.handler.dataimport.", "DocBuilder.buildDocument(DocBuilder.java:408)\n ... 5 more\nCaused by: com.microsoft.sqlserver.jdbc.", "SQLServerException: TCP/IP-anslutningen till värddatorn localhost, port 1433 misslyckades. ", "Fel: \"Connection refused: connect. ", "Verifiera anslutningsegenskaperna. ", "Kontrollera att en instans av SQL Server körs på värddatorn som accepterar TCP/IP-anslutningar på porten och att ingen brandvägg blockerar TCP-anslutningar till porten.\".", "\n at com.microsoft.sqlserver.jdbc.", "SQLServerException.makeFromDriverError(SQLServerException.java:190)\n at com.microsoft.sqlserver.jdbc.", "SQLServerException.", "ConvertConnectExceptionToSQLServerException(SQLServerException.java:241)\n at com.microsoft.sqlserver.jdbc.", "SocketFinder.findSocket(IOBuffer.java:2243)\n at com.microsoft.sqlserver.jdbc.", "TDSChannel.open(IOBuffer.java:491)\n at com.microsoft.sqlserver.jdbc.", "SQLServerConnection.connectHelper(SQLServerConnection.java:1309)\n at com.microsoft.sqlserver.jdbc.", "SQLServerConnection.login(SQLServerConnection.java:991)\n at com.microsoft.sqlserver.jdbc.", "SQLServerConnection.connect(SQLServerConnection.java:827)\n at com.microsoft.sqlserver.jdbc.", "SQLServerDriver.connect(SQLServerDriver.java:1012)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource$1.call(JdbcDataSource.java:149)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource$1.call(JdbcDataSource.java:129)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource.getConnection(JdbcDataSource.java:392)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource.access$200(JdbcDataSource.java:40)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource$ResultSetIterator.(JdbcDataSource.java:266)\nIts basically saying that the tcp/ip connection to sql server failed. ", "I have made sure that its enabled so that cannot be it.", "\nWhen using jdbc:sqlserver://localhost\\ARBETSDATOR\\SQLEXPRESS;\nI receive following error message:\nException while processing: member document : SolrInputDocument(fields: []):org.apache.solr.handler.dataimport.", "DataImportHandlerException: Unable to execute query: SELECT * FROM Members Processing Document # 1\n at org.apache.solr.handler.dataimport.", "DataImportHandlerException.wrapAndThrow(DataImportHandlerException.java:71)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource$ResultSetIterator.(JdbcDataSource.java:279)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource.getData(JdbcDataSource.java:236)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource.getData(JdbcDataSource.java:40)\n at org.apache.solr.handler.dataimport.", "SqlEntityProcessor.initQuery(SqlEntityProcessor.java:59)\n at org.apache.solr.handler.dataimport.", "SqlEntityProcessor.nextRow(SqlEntityProcessor.java:73)\n at org.apache.solr.handler.dataimport.", "EntityProcessorWrapper.nextRow(EntityProcessorWrapper.java:243)\n at org.apache.solr.handler.dataimport.", "DocBuilder.buildDocument(DocBuilder.java:469)\n at org.apache.solr.handler.dataimport.", "DocBuilder.buildDocument(DocBuilder.java:408)\n at org.apache.solr.handler.dataimport.", "DocBuilder.doFullDump(DocBuilder.java:323)\n at org.apache.solr.handler.dataimport.", "DocBuilder.execute(DocBuilder.java:231)\n at org.apache.solr.handler.dataimport.", "DataImporter.doFullImport(DataImporter.java:411)\n at org.apache.solr.handler.dataimport.", "DataImporter.runCmd(DataImporter.java:476)\n at org.apache.solr.handler.dataimport.", "DataImporter$1.run(DataImporter.java:457)\nCaused by: com.microsoft.sqlserver.jdbc.", "SQLServerException: Anslutningen till värddatorn localhost, den namngivna instansen arbetsdator\\sqlexpress, misslyckades. ", "Fel: java.net.", "SocketTimeoutException: Receive timed out. ", "Verifiera server- och instansnamn och kontrollera att ingen brandvägg blockerar UDP-trafik till port 1434. ", "Kontrollera även för SQL Server 2005 eller senare att tjänsten SQL Server Browser körs på värddatorn.", "\n at com.microsoft.sqlserver.jdbc.", "SQLServerException.makeFromDriverError(SQLServerException.java:190)\n at com.microsoft.sqlserver.jdbc.", "SQLServerConnection.getInstancePort(SQLServerConnection.java:3589)\n at com.microsoft.sqlserver.jdbc.", "SQLServerConnection.primaryPermissionCheck(SQLServerConnection.java:1225)\n at com.microsoft.sqlserver.jdbc.", "SQLServerConnection.login(SQLServerConnection.java:972)\n at com.microsoft.sqlserver.jdbc.", "SQLServerConnection.connect(SQLServerConnection.java:827)\n at com.microsoft.sqlserver.jdbc.", "SQLServerDriver.connect(SQLServerDriver.java:1012)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource$1.call(JdbcDataSource.java:149)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource$1.call(JdbcDataSource.java:129)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource.getConnection(JdbcDataSource.java:392)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource.access$200(JdbcDataSource.java:40)\n at org.apache.solr.handler.dataimport.", "JdbcDataSource$ResultSetIterator.(JdbcDataSource.java:266)\nSome help with this would be extremely appreciated\nUPDATE\nNew error message:\nException while processing: member document : SolrInputDocument(fields:[]):org.apache.solr.handler.dataimport.", "DataImportHandlerException: Unable to execute query: SELECT * FROM Members Processing Document # 1\nat org.apache.solr.handler.dataimport.", "DataImportHandlerException.wrapAndThrow(DataImportHandlerException.java:71)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource$ResultSetIterator.<init>(JdbcDataSource.java:279)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource.getData(JdbcDataSource.java:236)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource.getData(JdbcDataSource.java:40)\nat org.apache.solr.handler.dataimport.", "SqlEntityProcessor.initQuery(SqlEntityProcessor.java:59)\nat org.apache.solr.handler.dataimport.", "SqlEntityProcessor.nextRow(SqlEntityProcessor.java:73)\nat org.apache.solr.handler.dataimport.", "EntityProcessorWrapper.nextRow(EntityProcessorWrapper.java:243)\nat org.apache.solr.handler.dataimport.", "DocBuilder.buildDocument(DocBuilder.java:469)\nat org.apache.solr.handler.dataimport.", "DocBuilder.buildDocument(DocBuilder.java:408)\nat org.apache.solr.handler.dataimport.", "DocBuilder.doFullDump(DocBuilder.java:323)\nat org.apache.solr.handler.dataimport.", "DocBuilder.execute(DocBuilder.java:231)\nat org.apache.solr.handler.dataimport.", "DataImporter.doFullImport(DataImporter.java:411)\nat org.apache.solr.handler.dataimport.", "DataImporter.runCmd(DataImporter.java:476)\nat org.apache.solr.handler.dataimport.", "DataImporter$1.run(DataImporter.java:457)\nCaused by: com.microsoft.sqlserver.jdbc.", "SQLServerException: Drivrutinen är inte konfigurerad för integrerad autentisering. ", "ClientConnectionId:eb7b4593-8238-4d7a-92bc-7ffb520e3d9c\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.terminate(SQLServerConnection.java:1667)\nat com.microsoft.sqlserver.jdbc.", "AuthenticationJNI.<init>(AuthenticationJNI.java:60)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.logon(SQLServerConnection.java:2229)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.access$000(SQLServerConnection.java:41)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection$LogonCommand.doExecute(SQLServerConnection.java:2220)\nat com.microsoft.sqlserver.jdbc.", "TDSCommand.execute(IOBuffer.java:5696)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.executeCommand(SQLServerConnection.java:1715)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.connectHelper(SQLServerConnection.java:1326)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.login(SQLServerConnection.java:991)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.connect(SQLServerConnection.java:827)\nat com.microsoft.sqlserver.jdbc.", "SQLServerDriver.connect(SQLServerDriver.java:1012)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource$1.call(JdbcDataSource.java:149)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource$1.call(JdbcDataSource.java:129)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource.getConnection(JdbcDataSource.java:392)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource.access$200(JdbcDataSource.java:40)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource$ResultSetIterator.<init>(JdbcDataSource.java:266)\n... 12 more\nCaused by: java.lang.", "UnsatisfiedLinkError: no sqljdbc_auth in java.library.path\nat java.lang.", "ClassLoader.loadLibrary(Unknown Source)\nat java.lang.", "Runtime.loadLibrary0(Unknown Source)\nat java.lang.", "System.loadLibrary(Unknown Source)\nat com.microsoft.sqlserver.jdbc.", "AuthenticationJNI.<clinit>(AuthenticationJNI.java:35)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.logon(SQLServerConnection.java:2229)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.access$000(SQLServerConnection.java:41)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection$LogonCommand.doExecute(SQLServerConnection.java:2220)\nat com.microsoft.sqlserver.jdbc.", "TDSCommand.execute(IOBuffer.java:5696)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.executeCommand(SQLServerConnection.java:1715)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.connectHelper(SQLServerConnection.java:1326)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.login(SQLServerConnection.java:991)\nat com.microsoft.sqlserver.jdbc.", "SQLServerConnection.connect(SQLServerConnection.java:827)\nat com.microsoft.sqlserver.jdbc.", "SQLServerDriver.connect(SQLServerDriver.java:1012)\nat java.sql.", "DriverManager.getConnection(Unknown Source)\nat java.sql.", "DriverManager.getConnection(Unknown Source)\nat org.apache.solr.handler.dataimport.", "JdbcDataSource$1.call(JdbcDataSource.java:142)\n\nOne line is not in English, it says that the driver is not configured for integrated authentication.", "\n\nA:\n\nYour connection string should look like this: jdbc:sqlserver://localhost:1433;instance=SQLEXPRESS;databaseName=189021-resurs;integratedSecurity=true;\nThen also check if by default MS SQL Server Express is configured to use dynamic TCP/IP ports, like named instances. ", "Go into the Sql Server Configuration Manager\nopen SQL SERVER 2005 (this may be different for you) Network Configuration\nopen Protocols for SQLEXPRESS\nopen TCP/IP properties\non the IP ADDRESSES tab, check at the bottom if \"TCP Dynamic Ports\" has a value.", "\nif so, clear the value and leave that field blank. ", " Then change \"TCP Port\" to 1433 or whatever port you decide.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "7 = 0.", "\n-1, 0, 1\nFactor d**4/5 - 251*d**3/5 + 1238*d**2/5 - 1972*d/5 + 984/5.", "\n(d - 246)*(d - 2)**2*(d - 1)/5\nFactor -o**4 - 8*o**3 + 19*o**2 - 10*o.", "\n-o*(o - 1)**2*(o + 10)\nFactor -5*d**3/4 + 1575*d**2/2 - 165375*d + 11576250.", "\n-5*(d - 210)**3/4\nFactor 3*s**5 + 18*s**4 - 3*s**3 - 18*s**2.", "\n3*s**2*(s - 1)*(s + 1)*(s + 6)\nFactor 3*f**3 - 456*f**2 - 2337*f - 2826.", "\n3*(f - 157)*(f + 2)*(f + 3)\nFactor 35*u**3 - 160*u**2 - 95*u + 100.", "\n5*(u - 5)*(u + 1)*(7*u - 4)\nFactor -4*p**2 - 76*p - 352.", "\n-4*(p + 8)*(p + 11)\nLet 2*j**4 + 4*j**3 = 0. ", "Calculate j.\n-2, 0\nFactor -23*s**3 - 3*s**2.", "\n-s**2*(23*s + 3)\nFactor -7*b**2/3 - 1073*b/3 - 102.", "\n-(b + 153)*(7*b + 2)/3\nFactor -14*v**3 + 186*v**2 - 370*v + 198.", "\n-2*(v - 11)*(v - 1)*(7*v - 9)\nSolve -80*n**5 - 280*n**4 - 165*n**3 + 140*n**2 - 20*n = 0 for n.\n-2, 0, 1/4\nLet 4*l**4 + 8*l**3 - 8*l - 4 = 0. ", "Calculate l.\n-1, 1\nSuppose 4*l**3 - 208*l**2 - 4*l + 208 = 0. ", "What is l?", "\n-1, 1, 52\nDetermine k, given that -15*k**2 + 444*k + 180 = 0.", "\n-2/5, 30\nFactor -486*d**3/5 + 968*d**2/5 - 478*d/5 - 4/5.", "\n-2*(d - 1)**2*(243*d + 2)/5\nSolve j**3/3 + 7*j**2 - 241*j/3 - 87 = 0 for j.\n-29, -1, 9\nSolve -9*z**5 - 16*z**4 + 13*z**3 + 16*z**2 - 4*z = 0.", "\n-2, -1, 0, 2/9, 1\nDetermine d so that -d**2/2 - d/2 = 0.", "\n-1, 0\nFactor -4*b**5 - 4*b**4 + 24*b**3 + 56*b**2 + 44*b + 12.", "\n-4*(b - 3)*(b + 1)**4\nFind i such that -i**4/4 - 5*i**3/2 - 33*i**2/4 - 10*i - 4 = 0.", "\n-4, -1\nFactor f**5/8 + 5*f**4/4 + 2*f**3.", "\nf**3*(f + 2)*(f + 8)/8\nDetermine f, given that -2*f**4/7 - 80*f**3/7 + 2*f**2 + 572*f/7 + 480/7 = 0.", "\n-40, -2, -1, 3\nLet -i**5 + 2*i**4/3 + 134*i**3 - 1780*i**2/3 - 301*i + 1274/3 = 0. ", "Calculate i.\n-13, -1, 2/3, 7\nSuppose -2*i**2/5 + 262*i/5 + 1644/5 = 0. ", "Calculate i.\n-6, 137\nFind m, given that -m**4 - m**3 + 2*m**2 = 0.", "\n-2, 0, 1\nSuppose -2*l**4/11 - 245*l**3/11 - 361*l**2/11 + 22*l = 0. ", "Calculate l.\n-121, -2, 0, 1/2\nDetermine k so that 4*k**5 - 40*k**4 + 48*k**3 + 136*k**2 - 52*k - 96 = 0.", "\n-1, 1, 3, 8\nWhat is m in m**5 - 42*m**4 + 395*m**3 - 1038*m**2 - 396*m + 1080 = 0?", "\n-1, 1, 6, 30\nSolve -12*y**5 - 1216*y**4 - 5108*y**3 - 6224*y**2 - 1552*y = 0 for y.\n-97, -2, -1/3, 0\nFind u, given that -u**5/5 - 3*u**4/5 + 7*u**3/5 + 3*u**2 - 18*u/5 = 0.", "\n-3, 0, 1, 2\nFactor -2*m**3/11 - 16*m**2/11 - 10*m/11 + 28/11.", "\n-2*(m - 1)*(m + 2)*(m + 7)/11\nFactor i**3/2 - 17*i**2/2 + 31*i/2 - 15/2.", "\n(i - 15)*(i - 1)**2/2\nFactor -4*o**3 + 76*o**2 - 64*o - 144.", "\n-4*(o - 18)*(o - 2)*(o + 1)\nFind p such that -75*p**3 - 1490*p**2 - 7300*p + 1000 = 0.", "\n-10, 2/15\nSuppose t**2 + 123*t - 124 = 0. ", "What is t?", "\n-124, 1\nFactor 4*a**4 - 260*a**3 + 4956*a**2 - 21692*a - 26912.", "\n4*(a - 29)**2*(a - 8)*(a + 1)\nSuppose -g**2/7 - 8*g/7 + 12 = 0. ", "Calculate g.\n-14, 6\nLet t**3/6 - 13*t**2/6 + 7*t/3 + 44/3 = 0. ", "What is t?", "\n-2, 4, 11\nWhat is z in -5*z**3 - 50*z**2 - 135*z - 90 = 0?", "\n-6, -3, -1\nFind o, given that o**5 + 8*o**4 + 18*o**3 + 4*o**2 - 19*o - 12 = 0.", "\n-4, -3, -1, 1\nWhat is a in -a**5/3 + 14*a**4/3 - 13*a**3/3 = 0?", "\n0, 1, 13\nSolve 4*b**5 + 156*b**4 + 1960*b**3 + 6960*b**2 - 13664*b - 18816 = 0 for b.\n-14, -12, -1, 2\nFactor -45*m**2/2 - 141*m/4 + 114.", "\n-3*(5*m - 8)*(6*m + 19)/4\nFactor 2*a**2 - 22*a - 160.", "\n2*(a - 16)*(a + 5)\nSuppose 3*a**4 - 141*a**3 + 249*a**2 + 933*a + 540 = 0. ", "What is a?", "\n-1, 4, 45\nWhat is o in -o**3/9 + o**2 + 40*o/9 - 16/3 = 0?", "\n-4, 1, 12\nSuppose -16*m**4 + 1292*m**3 + 4356*m**2 + 1008*m = 0. ", "What is m?", "\n-3, -1/4, 0, 84\nSuppose 2*n**5 + 12*n**4 + 6*n**3 - 92*n**2 - 216*n - 144 = 0. ", "What is n?", "\n-3, -2, 3\nFactor -2*k**4 + 54*k**3 - 528*k**2 + 2176*k - 3072.", "\n-2*(k - 8)**3*(k - 3)\nFind l, given that 2*l**4/5 - 6*l**3/5 - 8*l**2/5 = 0.", "\n-1, 0, 4\nFactor 105*m**3 - 198*m**2 - 36*m + 24.", "\n3*(m - 2)*(5*m + 2)*(7*m - 2)\nFactor 3*k**2 - 4806*k + 1924803.", "\n3*(k - 801)**2\nDetermine l so that -2*l**5 + 40*l**4 + 134*l**3 + 92*l**2 = 0.", "\n-2, -1, 0, 23\nDetermine i so that -15*i**5 + 35*i**4 + 575*i**3 + 885*i**2 - 360*i = 0.", "\n-3, 0, 1/3, 8\nWhat is j in 3*j**4/4 - 15*j**3 + 207*j**2/4 + 303*j/2 + 84 = 0?", "\n-1, 8, 14\nLet -m**3/7 - 6*m**2/7 - 5*m/7 = 0. ", "Calculate m.\n-5, -1, 0\nLet 3*k**3 + 357*k**2 - 723*k + 363 = 0. ", "Calculate k.\n-121, 1\nSuppose n**2 - 73*n - 74 = 0. ", "Calculate n.\n-1, 74\nDetermine d so that -3*d**4/4 - 45*d**3/4 - 243*d**2/4 - 555*d/4 - 225/2 = 0.", "\n-5, -3, -2\nFactor -5*y**3 + 35*y - 30.", "\n-5*(y - 2)*(y - 1)*(y + 3)\nFactor -2*i**2/9 + 14*i/3 + 16.", "\n-2*(i - 24)*(i + 3)/9\nFactor -b**2/10 + b/2 + 7/5.", "\n-(b - 7)*(b + 2)/10\nSuppose o**3/7 - 2*o**2/7 - 11*o/7 + 12/7 = 0. ", "Calculate o.\n-3, 1, 4\nDetermine y, given that -y**2/3 + 112*y/3 - 3136/3 = 0.", "\n56\nFactor -w**4 - 659*w**3 - 107577*w**2 + 327359*w - 219122.", "\n-(w - 2)*(w - 1)*(w + 331)**2\nWhat is m in -2*m**5 + 70*m**4 - 62*m**3 - 214*m**2 + 344*m - 136 = 0?", "\n-2, 1, 34\nFactor 12*p**3 + 129*p**2 - 177*p + 36.", "\n3*(p - 1)*(p + 12)*(4*p - 1)\nFactor -5*c**3/6 - 401*c**2/3 - 950*c/3 - 316/3.", "\n-(c + 2)*(c + 158)*(5*c + 2)/6\nDetermine p so that 2*p**3 - 120*p**2 + 742*p = 0.", "\n0, 7, 53\nFactor 6*v**2/11 - 58*v/11 - 20/11.", "\n2*(v - 10)*(3*v + 1)/11\nSolve 17*u**4 - 32*u**3 - 548*u**2 + 1568*u + 192 = 0 for u.\n-6, -2/17, 4\nLet -x**2/4 - 2*x - 15/4 = 0. ", "Calculate x.\n-5, -3\nSuppose o**2 + 117*o - 1408 = 0. ", "What is o?", "\n-128, 11\nSuppose 12*w**3 - 160*w**2 + 192*w = 0. ", "What is w?", "\n0, 4/3, 12\nDetermine r so that -r**2 + 1891*r - 1890 = 0.", "\n1, 1890\nSuppose -5*c**3 - 65*c**2 + 150*c = 0. ", "Calculate c.\n-15, 0, 2\nDetermine v so that 2*v**4/17 - 12*v**3/17 + 18*v**2/17 - 8*v/17 = 0.", "\n0, 1, 4\nDetermine s so that -3*s**2/8 + 27*s/4 = 0.", "\n0, 18\nSuppose -3*y**3 - 3660*y**2 + 7329*y - 3666 = 0. ", "What is y?", "\n-1222, 1\nFind i such that i**2 - 20*i - 21 = 0.", "\n-1, 21\nFactor 4*u**2 + 6172*u.", "\n4*u*(u + 1543)\nFind d such that -d**2 - 1748*d - 1747 = 0.", "\n-1747, -1\nSolve -2*n**2/5 + 1966*n/5 - 1964/5 = 0.", "\n1, 982\nWhat is h in 20*h**5 - 448*h**4 - 1484*h**3 + 45544*h**2 + 190128*h - 83232 = 0?", "\n-6, 2/5, 17\nFactor -5*z**2 + 3335*z - 6650.", "\n-5*(z - 665)*(z - 2)\nFactor 5*m**4 + 885*m**3 + 2625*m**2 + 2615*m + 870.", "\n5*(m + 1)**3*(m + 174)\nFactor 3*s**4 + 108*s**3 + 1254*s**2 + 4212*s - 5577.", "\n3*(s - 1)*(s + 11)*(s + 13)**2\nFind c such that -5*c**2 - 950*c - 45125 = 0.", "\n-95\nLet -236*f**3/7 - 68*f**2 - 244*f/7 - 4/7 = 0. ", "What is f?", "\n-1, -1/59\nSolve -15*i**5 - 25*i**4 + 55*i**3 + 105*i**2 + 20*i - 20 = 0 for i.\n-2, -1, 1/3, 2\nFactor 2*v**3/3 - 44*v**2 + 680*v + 4624/3.", "\n2*(v - 34)**2*(v + 2)/3\nLet -3*z**3 + 14*z**2 + 155*z + 50 = 0. ", "Calculate z.\n-5, -1/3, 10\nFactor 2*w**4/7 + 8*w**3/7 + 10*w**2/7 + 4*w/7.", "\n2*w*(w + 1)**2*(w + 2)/7\nSuppose -3*l**3/5 - 6*l**2/5 + 12*l - 72/5 = 0. ", "Calculate l.\n-6, 2\nFactor -s**3/4 + 13*s**2/4 - 27*s/2 + 18.", "\n-(s - 6)*(s - 4)*(s - 3)/4\nFactor -u**4/3 + 56*u**3/3 - 320*u**2 + 1536*u.", "\n-u*(u - 24)**2*(u - 8)/3\nFind x, given that -20*x**2/7 - 1032*x/7 - 544 = 0.", "\n-238/5, -4\nFactor -21*v**5 + 1086*v**4 + 312*v**3.", "\n-3*v**3*(v - 52)*(7*v + 2)\nSuppose g**4/2 + g**3 - 13*g**2/2 + 5*g = 0. ", "Calculate g.\n-5, 0, 1, 2\nFactor 4*d**3 + 104*d**2 + 100*d.", "\n4*d*(d + 1)*(d + 25)\nSuppose -10*g**4/7 + 16*g**3/7 - 2*g**2/7 - 4*g/7 = 0. ", "Calculate g.\n-2/5, 0, 1\nDetermine h so that 665*h**4/3 - 1997*h**3/3 + 2*h**2 = 0.", "\n0, 2/665, 3\nSuppose 5*z**4 + 325*z**3 - 670*z**2 = 0. ", "Calculate z.\n-67, 0, 2\nFind k, given that -k**4/5 - 2*k**3/5 + 3*k**2/5 + 8*k/5 + 4/5 = 0.", "\n-2, -1, 2\nSolve 5*l**3 - 80*l**2 + 385*l - 490 = 0 for l.\n2, 7\nSuppose -2*o**4/15 + 14*o**3/15 - 8*o**2/5 = 0. ", "Calculate o.\n0, 3, 4\nWhat is t in 2*t**2 - 34*t - 168 = 0?", "\n-4, 21\nFind z such that -162*z**5/7 - 1206*z**4/7 - 2942*z**3/7 - 2594*z**2/7 - 768*z/7 - 72/7 = 0.", "\n-3, -1, -2/9\nSuppose -2*i**3/5 + 52*i**2/5 - 88*i + 240 = 0. ", "Calculate i.\n6, 10\nWhat is r in -3*r**5 + 237*r**4 - 1350*r**3 + 2652*r**2 - 1752*r = 0?", "\n0, 2, 73\nSuppose 5*c**2 + 40*c - 165 = 0. ", "Calculate c.\n-11, 3\nWhat is m in 2*m**4/9 - 2870*m**3/9 + 457924*m**2/3 - 219801608*m/9 + 218430704/9 = 0?", "\n1, 478\nFactor 3*q**2/2 + 1161*q/2 - 582.", "\n3*(q - 1)*(q + 388)/2\nWhat is c in 2*c**2/19 - 396*c/19 + 19602/19 = 0?", "\n99\nFactor -10*j**2/7 + 8*j + 24/7.", "\n-2*(j - 6)*(5*j + 2)/7\nFactor -8*d**2 + 5820*d + 2912.", "\n-4*(d - 728)*(2*d + 1)\nDetermine v so that -3*v**3 + 6*v**2 - 3*v = 0.", "\n0, 1\nFactor -3*l**3 - 36*l**2.", "\n-3*l**2*(l + 12)\nFind c, given that -4*c**4 + 412*c**3 - 10812*c**2 + 10404*c = 0.", "\n0, 1, 51\nLet 2*a**3/5 + 4*a**2/5 - 2*a - 12/5 = 0. ", "What is a?", "\n-3, -1, 2\nFactor -h**4/2 + 131*h**3 - 16357*h**2/2 - 52662*h - 8080" ]

{ "pile_set_name": "DM Mathematics" }

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[ "Please join me on Thursday, January 11 from 1:00 to 4:00 pm for a special \ninformation session for the Operations Management teams supporting Enron \nAmericas, Enron Global Markets and Enron Industrial Markets. ", " We will focus \non assessing, managing and mitigating operational risk. ", " Details on the \nlocation for the meeting will be sent to you early next week. ", " \n\nI look forward to seeing everyone at this meeting on the 11th. ", " The things \nthat we will discuss will be important for each and every one of you as you \ncarry out your roles in 2001. ", " I hope that you will make every effort to \nattend. ", " Please let me know as soon as possible if you have a conflict that \nwill keep you from attending the meeting." ]

{ "pile_set_name": "Enron Emails" }

[ 0.01904761904761905, 0, 0, 0, 0, 0, 0 ]

[ "---\nabstract: 'Advanced gravitational-wave detectors are limited by quantum noise in their most sensitive frequency band. ", "Quantum noise suppression techniques, such as the application of the quantum squeezed state of light, have been actively studied in the context of homodyne readouts. ", "In this paper, we consider quantum squeezing schemes for the heterodyne readouts. ", "This is motivated by a successful suppression of the higher-order-mode content by stable recycling cavities in advanced detectors. ", "The heterodyne readout scheme requires precise tuning of the interferometer parameters and a broadband squeezing source, but is conceptually simple and elegant. ", "We further show that it is compatible with the frequency-dependent squeezing, which reduces both the shot noise and the radiation-pressure noise. ", "We propose a test of the heterodyne readout with squeezing in Advanced LIGO. ", "This can serve as a pathfinder not only for the implementation in future detectors, such as Einstein Telescope and Cosmic Explorer, but also for general high-precision optical measurements.'", "\nauthor:\n- Teng Zhang\n- Denis Martynov\n- Andreas Freise\n- Haixing Miao\nbibliography:\n- 'bibliography.bib'\ntitle: Quantum Squeezing Schemes for Heterodyne Readout\n---\n\nIntroduction {#sec:introduction}\n============\n\nThe Pound-Drever-Hall heterodyne technique [@DreverPDH; @Black_PDH_2001; @Takahashi_2004; @Sigg_2008; @LIGO2015; @Acernese_2006; @Acernese_2014; @Dooley_2015; @PhysRevA.57.3898] is a powerful tool for stabilisation of optical cavities in modern precision instruments, such as frequency references for optical atomic clocks, passive laser gyroscopes, and gravitational-wave detectors. ", "In the heterodyne readout, phase modulated light probes the motion of the optical cavity and produces the signal on photodetectors at radio frequencies (RF). ", "After demodulation, the residual signal is proportional to the cavity motion or the laser frequency noise. ", "The heterodyne technique circumvents laser technical noise by upconverting the signal detection to frequencies where the laser light is shot-noise-limited (a few MHz) [@Rakhmanov:01] but couples technical noises of the modulation oscillator [@Ward_THESIS_2010]. ", "In this paper, we do not focus on the technical noises of the heterodyne readout scheme and only consider the fundamental quantum noise.", "\n\nQuantum noise in the heterodyne readout techniques has been previously studied in Refs.", " [@PhysRevA.43.5022; @PhysRevD.67.122005] in the context of gravitational-wave detectors. ", "As it turns out, there are additional vacuum noises at twice the RF modulation frequency $2\\omega_m$ away from the carrier frequency $\\omega_0$, which leads to 50% higher shot noise compared to the homodyne readout. ", "The squeezed state of light can be used to suppress this additional noise, and in general, we need to have squeezing near the carrier frequency $\\omega_0$ and the two RF sidebands frequencies $\\omega_0\\pm 2\\omega_m$[@PhysRevA.44.4693; @PhysRevD.23.1693; @PhysRevA.57.3898]. ", "In this paper, we further advance these studies and consider application of quantum noise suppression techniques to the heterodyne readout in advanced gravitational-wave detectors, *i.e.*, a single squeezer is not only sufficient to improve the shot noise[@Gea-Banacloche1987], but also can be made compatible with frequency-dependent squeezing, which reduces the quantum radiation-pressure noise. ", "As discussed in Sec \\[sec:Sqz\\] and \\[sec:FD\\], we find that quantum squeezing works for the heterodyne readout if (i) the source of squeezed states of light has a bandwidth at least twice the RF modulation frequency ($\\omega_m$), (ii) the filter cavity for the frequency-dependent squeezing is tuned the same as in the current homodyne readout scheme, and (iii) the power imbalance of the upper and lower RF sidebands which are on phase quadrature is less than 10 % for 12dB broadband squeezing.", "\n\n![", "Schematics of the balanced homodyne readout and the heterodyne readout which requires a broadband squeezer with bandwidth at least twice the modulation frequency $\\omega_m$. []{data-label=\"fig:GWD\"}](GWD_new.pdf){width=\"1\\columnwidth\"}\n\nThe main advantage of the homodyne readout scheme is that its quantum shot noise is a factor of $\\sqrt{1.5}$ smaller compared to the one in the heterodyne readout for the same level of squeezing and optical losses. ", "The price paid for this improvement is complexity involved in the balanced homodyne readout scheme which requires an additional local oscillator field and optical cavities to filter the carrier field from the RF sidebands[@Fritschel2014; @PhysRevD.95.062001; @Sebastian2015; @Zhang_2018]. ", "In Advanced LIGO, an additional local oscillator field is derived by offsetting the interferometer from its operating point. ", "This scheme, known as DC readout [@2015; @Hild_2009; @Fricke_2012; @Grote_2010], is also the current readout scheme in Advanced Virgo[@Acernese_2014], KAGRA[@Akutsu:2019aa], and GEO600[@Hild_2009]. ", "It has been very successful and allowed direct observation of gravitational waves for the first time [@GW150914; @GW170817; @PhysRevX.9.031040]. ", "However, the offset couples technical noise sources and will not allow future gravitational-wave detectors to reach their design sensitivity at low frequencies [@PhysRevLett.120.141102].", "\n\nThe heterodyne technique is ideal for coupled optical resonators and is already used in the Advanced LIGO detectors to stabilise auxiliary degrees of freedom and for initial stabilisation of the gravitational-wave channel. ", "In this paper, we explore optical parameters when quantum noise in heterodyne and homodyne readout schemes are identical but heterodyne readout is conceptually simpler as shown in Fig.", " \\[fig:GWD\\]. ", "This study is motivated by successful operation of the stable recycling cavities [@Arain_RECYCLING_2008] in the Advanced LIGO detectors which has significantly suppressed higher-order-mode (HOM) content in the RF sidebands due to misalignments in the cavity [@Gretarsson:07] and is also good for suppressing the HOM content from contrast defect. ", "In Sec \\[sec:aLIGO\\_test\\] we show quantum noise of the Advanced LIGO detectors with the heterodyne readout and discuss steps for further improvements.", "\n\nSqueezing for Heterodyne readout {#sec:Sqz}\n================================\n\nIn this section, we will show the resulting quantum noise level for the heterodyne readout with a broadband squeezing. ", "We choose the demodulation phase such that the photocurrent is proportional to the phase quadrature $\\hat Y$, which is given by: $$\\label{eq:HRp}\n\\hat Y(\\Omega)={\\hat Y_0}(\\Omega)+\\frac{{\\hat Y_{+2}}(\\Omega)+\\xi \\,{\\hat Y_{-2}}(\\Omega)}{1+\\xi}\\,,$$ where $\\xi$ denotes the amplitude ratio of two RF sidebands which are on phase quadrature (more details are presented in Appendix\\[sec:AHR\\]). ", "Here ${\\hat Y_0}$ and ${\\hat Y_{\\pm2}}$ represent the phase quadrature of three modes around the carrier frequency $\\omega_0$ and the RF sidebands frequencies $\\omega_0\\pm 2\\omega_m$, which are linear combinations of their audio sidebands, as illustrated in Fig.\\[fig:bd\\_sqz\\]. ", "The last two terms contribute to the additional noise of the heterodyne readout compared to the homodyne readout. ", "The quantum noise level is quantified by the single-sided spectral density, which is defined for any operators $\\hat A(\\Omega)$ and $\\hat B(\\Omega')$: $\n \\langle \\psi |[\\hat A \\hat B^{\\dag} +\\hat B^{\\dag}\\hat A]/2|\\psi \\rangle \\equiv \\pi\\, S_{AB}(\\Omega) \\delta(\\Omega-\\Omega')$. In the absence of squeezing, the quantum state $|\\psi\\rangle$ is in the vacuum state $|0\\rangle$. Using the fact that $\\langle 0| [\\hat Y_{i}(\\Omega)\\hat Y^{\\dag}_{j}(\\Omega')+\\hat Y^{\\dag}_{j}(\\Omega')\\hat Y_{i}(\\Omega)]/2|0\\rangle = \\pi\\delta(\\Omega-\\Omega')\\delta_{ij}$ $(i, j =0, \\pm2)$, we have $$S_{YY} =1+\\frac{1+\\xi^2}{(1+\\xi)^2}\\,.$$ Considering the balanced case with $\\xi=1$, $$\\label{eq:vac_balanced}\n S_{YY}|_{\\rm balanced}=\\frac{3}{2}\\,,$$ which is 50% higher than that of the homodyne readout.", "\n\n![", "Schematics of a broadband squeezer in the sideband and the quadrature picture. ", "In contrast for an audio band squeezer, the sidebands are entangled only for $\\Omega$ up to kHz.[]{data-label=\"fig:bd_sqz\"}](broadband_squeezer.pdf){width=\"1\\columnwidth\"}\n\n Audio band versus broadband squeezing {#sec:BS}\n--------------------------------------\n\nWith the introduction of squeezing, the quantum noise level will be different, depending on the squeezing bandwidth. ", "For the audio band squeezing, the squeezing is limited to the audio frequencies. ", "The audio sidebands around the carrier frequency are entangled, which can be mapped to the (anti-)squeezing of the corresponding amplitude quadrature $\\hat X_0$ and the phase quadrature $\\hat Y_0$[@SCHNABEL20171]. ", "For the phase squeezing, the spectral densities of the quadratures satisfy the following covariance matrix, $$\\mathbb{V}_{o}=\n\\begin{bmatrix}\ne^{2r_0}&0\\\\0&e^{-2r_0}\n\\end{bmatrix}\\,,$$ where $r_0$ is the squeezing factor at the audio frequencies. ", "However, the sidebands around frequencies $\\omega_o\\pm 2 \\omega_m$ are still in the vacuum state and are uncorrelated. ", "Therefore, the audio band squeezing results in the spectral density for $\\hat Y$: $$\\label{eq:SYYnarrow}\nS_{YY}=e^{-2r_0}+\\frac{1+\\xi^2}{(1+\\xi)^2}\\,.$$\n\nIn contrast, as illustrated in Fig.", " \\[fig:bd\\_sqz\\], for the broadband squeezing with a bandwidth up to RF, the sidebands around frequencies $\\omega_0+2\\omega_m$ and $\\omega_0-2\\omega_m$ are entangled. ", "Their corresponding quadratures also form the Einstein–Podolsky–Rosen (EPR) entanglement[@Gea-Banacloche1987; @PhysRevA.67.054302; @Ma:2017aa; @SCHNABEL20171; @Danilishin2019], and for the phase squeezing, their spectral densities satisfy the following $4\\times4$ covariance matrix: $$\\label{eq:Vepr}\n\\mathbb{V}_{\\pm} = \\begin{bmatrix}\n\\alpha &0 & \\beta & 0\\\\\n0 &\\alpha &0& -\\beta \\\\\n\\beta&0 &\\alpha & 0\\\\\n0& -\\beta &0 &\\alpha\n\\end{bmatrix}\\,,$$ where $\\alpha=\\cosh2 r_{2\\omega_m}, \\beta=\\sinh 2r_{2\\omega_m}$ with $r_{2\\omega_m}$ denoting the squeezing factor at twice of the RF. ", "As we can see, the uncertainties of the individual quadratures are larger than that of the vacuum, namely $S_{Y_{+2}Y_{+2}}=S_{Y_{-2}Y_{-2}}=\\alpha\\ge1$. However, the sum of their phase quadratures, $\\hat Y_{s} = (\\hat Y_{+2}+\\hat Y_{-2})/\\sqrt{2}$, has uncertainty less than 1, namely, $S_{Y_s Y_s}={\\alpha-\\beta}=e^{-2r_{2\\omega_m}}$. With a broadband squeezer, the spectral density for $Y$ reads $$S_{YY}=\\frac{3}{2}e^{-2r}+\\left(\\frac{1-\\xi}{1+\\xi}\\right)^2\\frac{e^{2r}}{2}\\,,$$ where we have assumed $r_0=r_{2\\omega_m}\\equiv r$ for simplicity. ", "If two RF sidebands were balanced with $\\xi=1$, $$\\label{eq:SqzSyy}\nS_{YY}|_{\\rm balanced}=\\frac{3}{2}e^{-2r}\\,.$$ The additional noise due to the fluctuations around $\\omega_0\\pm2\\omega_m$ is smaller by a factor of $e^{2r}$ comparing with Eq.. Fig.", " \\[fig:imba\\] shows $S_{YY}$ as a function of the sidebands imbalance. ", "With 10% imbalance in the sideband power, *i.e.* $\\xi = \\sqrt{0.9}$, there is still around 10dB quantum noise suppression for 12dB input broadband squeezing.", "\n\n![", "Quantum noise level in dB for the heterodyne readout as a function of the power imbalance of two RF sidebands, considering different broadband squeezing lever.[]{data-label=\"fig:imba\"}](Simba.pdf){width=\"1\\columnwidth\"}\n\nFrequency-dependent squeezing\n-----------------------------\n\nFrequency-dependent squeezing has been proposed to simultaneously suppress the shot noise and the quantum radiation-pressure noise in gravitational-wave detectors[@kimble2001]. ", "It uses a Fabry-Perot cavity as the filter cavity to transform the squeezed light, and will be implemented in, e.g., the Advanced LIGO plus upgrade. ", "In this section, we will show the suppression of the additional noise with the broadband squeezing also holds for the frequency-dependent squeezing.", "\n\n![", "Plot shows the level of the additional noise from $\\omega_0\\pm 2\\omega_m$ in the phase quadrature at the reflection port of the filter cavity for different RF $\\omega_m$. The broadband squeezing level is assumed to be 12dB. The optical parameters of the filter cavity are the same as A+ design. []{", "data-label=\"fig:saddF\"}](SFilter.pdf){width=\"1\\columnwidth\"}\n\nThe filter cavity imprints different phases on the sidebands, which effectively creates a frequency-dependent rotation of the quadratures. ", "Mathematically, the rotation is described by the following transfer matrix[@SD2012]: $$\\mathbb{R}=e^{i\\Phi}\\begin{bmatrix}\n\\cos \\theta & -\\sin \\theta \\\\\\sin \\theta &\\cos \\theta\n\\end{bmatrix}\\,.$$ Here the phase $\\Phi$ and rotation angle $\\theta$ are $$\\Phi=\\rm{atan} \\frac{2\\gamma\\Omega}{\\gamma^2+\\Delta^2-\\Omega^2}\\,, \\theta=\\rm{atan} \\frac{2\\gamma\\Delta}{\\gamma^2-\\Delta^2+\\Omega^2}\\,.$$ The frequency $\\gamma$ is the filter cavity bandwidth. ", "The frequency $\\Delta$ is the cavity detuning, and is different for the three modes: $\\Delta \\equiv \\Delta_0$ for the mode around the carrier frequency; for RF modes around $\\omega_0\\pm 2\\omega_m$, $$\\Delta_{\\pm2}\\equiv \\Delta_0\\pm\\rm{mod}(2\\omega_{m}, \\rm{FSR})\\,,$$ where FSR is the free spectral range of the filter cavity.", "\n\nIn the balanced case, the spectral density of the additional noise due to fluctuations around $\\omega_0\\pm 2\\omega_m$ is $$S_{Y Y}^{\\rm add}=\\frac{1}{2}\\left[\\alpha-\\beta\\cos(\\Phi_{+2}-\\Phi_{-2})\\cos(\\theta_{+2}+\\theta_{-2})\\right]\\,,$$ where $\\Phi_{\\pm 2}$ and $\\theta_{\\pm 2}$ are the phase and rotation angle for quadratures of $\\omega_0\\pm 2\\omega_m$. Ideally, we want $\\Phi_{\\pm2} = \\theta_{\\pm2} = 0$, so that $S_{YY}^{\\rm add} = (\\alpha-\\beta)/2 = e^{-2r_{2\\omega_m}}/2$, which leads to the minimum additional noise. ", "This can be approximately achieved when $\\Delta_{\\pm 2}$ is much larger than the filter cavity bandwidth $\\gamma$, namely having $2\\omega_m$ away from any FSR of the filter cavity. ", "As an illustration, in Fig.", " \\[fig:saddF\\], we show the additional noise as a function of the distance of $2\\omega_m$ away from the FSR (normalised by $\\gamma$). ", "We assume a filter cavity parameter the same as the A+ design, namely, the cavity bandwidth $\\gamma/(2\\pi) = \\Delta_0/(2\\pi)=45.8\\,{\\rm Hz}$. Indeed, when $2\\omega_m$ is offset from $N\\times {\\rm FSR}$ by 200 times of the filter cavity bandwidth, the additional noise level is close to $e^{-2r_{2\\omega_m}}/2$ for the entire frequency band relevant to gravitational-wave signals. ", "Here $N$ is an arbitrary integer.", "\n\n![ ", "Figure shows the ratio of the quantum noise spectral density of the heterodyne readout over the that of homodyne readout as a function of the OMC loss ($\\zeta_{\\rm OMC}$) in homodyne readout and HOM content ($\\zeta_{\\rm HOM}$) in heterodyne readout in the unit of dB. The contour line of $0$dB denotes the cases when the two noise levels are equal. ", "12dB input squeezing is assumed.[]{data-label=\"fig:HM\"}](HomOMC.pdf){width=\"1\\columnwidth\"}\n\nHigher-order-modes and Schnupp asymmetry {#sec:FD}\n========================================\n\nIn comparison with the homodyne readout, there are two new quantum-noise related issues associated with the heterodyne readout. ", "The first issue is the higher-order-mode content leaking through the dark port due to the absence of output mode cleaner, which shall be traded off with the benefit of removing the output mode cleaner that induces the mode mismatch and misalignment loss. ", "The second issue has to do with vacuum fluctuations around $\\omega_0\\pm 2\\omega_m$ which transmit from the bright port to the dark port due to the Schnupp asymmetry. ", "They act like additional optical losses.", "\n\nIn the absence of output mode cleaner, the high-order-mode content at the carrier frequency and in the RF sidebands will both introduce additional quantum noise at $\\omega_0\\pm\\omega_m$, which are in the vacuum sate. ", "We define the ratio of the power of the higher-order-mode content to the total sideband power as $\\zeta_{\\rm HOM}=\\zeta_{\\rm HOM}^{0}+\\zeta_{\\rm HOM}^{\\omega_m}$, in which $\\zeta_{\\rm HOM}^{0}$ represents carrier frequency components and $\\zeta_{\\rm HOM}^{\\omega_m}$ represents RF components. ", "In the case of balanced RF sidebands, the total quantum noise spectral density of the heterodyne readout is $$S_{YY}^{\\rm Heterodyne}=\\frac{3}{2}e^{-2r}+\\zeta_{\\rm HOM}^{0}+m\\zeta_{\\rm HOM}^{\\omega_m}\\,,$$ where $m$ is between 1 and 1.5 depending on the mode coherence between upper and lower RF sideband. ", "For the homodyne readout, the output mode cleaner loss, quantified by $\\zeta_{\\rm OMC}$, also leads to a degradation of the squeezing, namely, $$S_{YY}^{\\rm Homodyne}=(1-\\zeta_{\\rm OMC})e^{-2r}+\\zeta_{\\rm OMC}\\,.$$ In Fig.\\[fig:HM\\], we show the ratio of these two spectral densities in dB as a function of $\\zeta_{\\rm HOM}$ and $\\zeta_{\\rm OMC}$. We take the the lower bound shot noise contribution from HOM content in RF sidebands, *i.e.* $m=1$.\n\nThe Schnupp asymmetry allows the RF sidebands from the bright port to transmit to the readout port (dark port) as the local oscillator for the heterodyne readout. ", "However, it also couples the vacuum noise from the bright port to the dark port, which is equivalent to introducing optical loss to the broadband squeezing near twice of the RF. ", "Such a loss is determined by the transmissivity of the coupled power and signal recycling cavities, which depends on the optical properties of three components: the power recycling mirror, the signal recycling mirror, and the central Michelson. ", "In particular, the effective amplitude transmissivity and reflectivity of the central Michelson is, according to Ref.[@Izumi_2016], $t_{\\rm MI}=-\\sin\\omega_m\\Delta L/c\\,,r_{\\rm MI}=-\\cos \\omega_m\\Delta L/c$, where $\\Delta L$ is the Schnupp asymmetry and $c$ is the speed of light. ", "In advanced LIGO, the 45MHz sidebands resonate in both power recycling cavity and signal recycling cavity. ", "The resonate condition in power recycling cavity builds on the accumulated phase $\\pi+2N\\pi$ of the 45MHz sidebands traveling through round macroscopic length of power recycling cavity and $\\pi$ phase shift acquired from the arm cavity, in which the 45MHz RF sidebands are anti-resonance. ", "In signal recycling cavity, the 45MHz sidebands accumulate phase $2N\\pi$ traveling round trip of signal recycling cavity under *Resonate Sidebands Extraction* mode. ", "The resonance condition of 90MHz filed is different, it still resonates in signal recycling cavity but anti-resonates in power recycling cavity. ", "The effective optical loss for 90MHz and the transmissivity for 45MHz are shown in the Fig.", " \\[fig:Schnnup\\]. ", "As we can see, in current aLIGO configuration, the optical loss for 90MHz squeezing fields is around $0.2\\%$. And the transmission of 45MHz sidebands can be adjusted significantly by tuning the Schnupp asymmetry or the signal recycling mirror transmissivity without boosting the optical loss at 90MHz significantly.", "\n\n![", "The top panel shows the transmissivity for 45MHz sidebands. ", "The bottom panel is the equivalent optical loss for squeezing around 90MHz as a function of the Schnupp asymmetry and the SRM transmissivity. ", "The stars are rough estimates for the current situation of Advanced LIGO (aLIGO).[]{data-label=\"fig:Schnnup\"}](SidebandsT.pdf){width=\"1\\columnwidth\"}\n\nHeterodyne in Advanced LIGO {#sec:aLIGO_test}\n===========================\n\nIn this section, we illustrate our findings in Sec.", " \\[sec:Sqz\\] and Sec.", " \\[sec:FD\\] on the example of the Advanced LIGO detectors which currently operate with squeezing and homodyne readout [@Tse_SQZ_2019]. ", "The source injects $7.2 \\pm 0.3$dB of squeezing and the maximum observed level is $3.2 \\pm 0.1$ dB. The discrepancy between the amount of injected and observed squeezing comes from the optical losses in the interferometer. ", "According to Ref.", " [@Tse_SQZ_2019], around $25\\%$ of the signal is lost on the Faraday isolators, on the output mode cleaner, and photodiodes. ", "Another 10% of the signal is lost on some optical components yet to be identified.", "\n\nIf switched to the heterodyne readout, the quantum noise level in the Advanced LIGO detectors would be $$\\label{eq:adv_ligo_shot}\n\\begin{split}\nS_{YY}^{\\rm total} =& (1-\\epsilon_0)e^{-2r_0} + \\epsilon_0+\\\\ &\\frac{1}{2}\\left[(1-\\epsilon_{2\\omega_m})e^{-2r_{2\\omega_m}}+\\epsilon_{2\\omega_m})\\right]+\\zeta_{\\rm HOM}^{0}+\\zeta_{\\rm HOM}^{\\omega_m}\\,,\n\\end{split}$$ where $\\epsilon_0$ and $\\epsilon_{2\\omega_m}$ are optical losses of the interferometer near the carrier frequency and RF sidebands at $2\\omega_m$, respectively. ", "For the current Advanced LIGO configuration, according to Ref.", " [@Araj_OMC_Scan_1988], $\\zeta_{\\rm HOM}=0.12$ and the higher-order-mode content is dominated by the 02 modes of the RF sideband. ", "The bandwidth of the LIGO squeezing source is $\\sim$10MHz [@Oelker_THESIS_2016], which is much smaller than $2\\omega_m = 90$MHz, and therefore, we have $r_{2\\omega_m} \\approx 0$. Furthermore, the loss from the mode matching and alignment of the output mode cleaner which is 5-15% in the homodyne readout scheme is negligible in the heterodyne readout, as it does not require output mode cleaner. ", "Using the parameters discussed above and Eq.(\\[eq:adv\\_ligo\\_shot\\]) we estimate the final observed squeezing is around $1.7 \\pm 0.2$dB for the heterdoyne readout in the current Advanced LIGO detectors.", "\n\nThe LIGO parameters can be optimised for the heterodyne readout as discussed in Sec.", " \\[sec:Sqz\\] and Sec.", " \\[sec:FD\\]. ", "First, we need to increase the bandwidth of the squeezing source above $\\sim100$MHz. ", "Achieving this milestone will make $r_{2\\omega_m}=r_0$. The observed squeezing level will be increased up to $3.9 \\pm 0.2$dB. Finally, if we can suppress the 02 mode of the RF sidebands at the antisymmetric port, we will reduce the higher-order-mode content down to $\\zeta_{\\rm HOM}=0.02$, and the Advanced LIGO detectors will reach the observed level of squeezing equal to $4.7 \\pm 0.3$dB.\n\nThe corresponding shot noise amplitude spectral density is only a factor of $\\approx 1.02$ larger than the current shot noise in the Advanced LIGO detectors, which is much smaller compared to a factor of $\\sqrt{1.5}\\approx1.22$ for the case of the same optical losses in both readouts. ", "Moreover, higher input squeezing will further shrink the gap between the homodyne and heterodyne readout in our model since we remove the output mode cleaner for the heterodyne readout. ", "Performing a test described in this section has a strong potential to help the Advanced LIGO detectors to estimate losses and technical noises of the output mode cleaner. ", "The test will also demonstrate that squeezing of the quantum noise in the heterodyne readout works according to our model and can be considered for future gravitational-wave detectors.", "\n\nSo far, we have been focused on the cases with RF sidebands having nearly equal power. ", "The imbalance was treated as an imperfection, which is the case for gravitational-wave detectors, as the imbalance usually introduces undesired technical noises. ", "If the technical noises can be suppressed, we can consider more general heterdyne readouts with strongly imbalanced sidebands, or even a single sideband. ", "However, a single broadband squeezing will not be able to suppress the additional quantum noise from $\\omega_0\\pm 2\\omega_m$, and we would need three-mode squeezing schemes shown in Appendix \\[sec:TM\\].", "\n\nConclusion and discussion {#sec:conc}\n=========================\n\nTo summarise, we have investigated squeezing schemes for the heterodyne readout in advanced gravitational-wave detectors. ", "Our research shows that the heterodyne readout is compatible with frequency-dependent squeezing by using a broadband squeezer and a filter cavity the same as the one for the homodyne readout. ", "We have studied the problem of the higher-order-mode content leaking to the dark port and the vacuum noise coupling from the bright port to the dark port around frequencies $\\omega_0\\pm 2\\omega_m$ due to the Schnupp asymmetry, which turns out to be negligible. ", "Taking Advanced LIGO for instance, there is a promising path to reduce the higher-order-mode content with the stable signal recycling cavity and the suppression of the dominant 02 mode. ", "The heterodyne readout requires less auxiliary optics, and its sensitivity can be made comparable to that of the balanced homodyne readout.", "\n\nThe strategies of incorporating quantum squeezing into general heterodyne readout can be applied to a broad class of optical measurements that use RF sidebands as in the Pound–Drever–Hall technique. ", "Therefore, our findings will not only have impacts to the gravitational-wave community but also the general high-precision measurement community.", "\n\nAcknowledgements\n================\n\nWe would like to thank Roman Schnabel, Ken Strain, Stefan Hild, Joseph Briggs, Lee McCuller and Daniel Sigg for fruitful discussions. ", "T. Z., D. M., A. F. and H. M. acknowledge the support of the Institute for Gravitational Wave Astronomy at University of Birmingham. ", "A. F. has been supported by a Royal Society Wolfson Fellowship which is jointly funded by the Royal Society and the Wolfson Foundation. ", "H. M. is supported by UK STFC Ernest Rutherford Fellowship (Grant No. ", "ST/M005844/11).", "\n\nDescription of heterodyne readout {#sec:AHR}\n=================================\n\nIn heterodyne readout, the RF sidebands are generated by modulating the phase of the carrier field with a RF sinusoidal signal $\\left[m+\\delta m (t)\\right]\\cos\\left(\\omega_m t+\\delta \\phi (t)\\right)$, where $m$ is the modulation index, $\\omega_m$ is the modulation frequency, $\\delta m (t)$ is the modulation index fluctuations and $\\delta \\phi (t)$ is the modulation phase fluctuations. ", "When $m\\ll1$, the laser field can be described approximately as $$\\label{eq:E}\n\\begin{split}\nE(t)=&E_0(1-\\frac{m^2}{4})e^{i\\omega_0t}+\\\\\n&E_0\\left[\\frac{i m}{2}+\\frac{i\\delta m(t)}{2}\\right]e^{i\\omega_0t}\\left(e^{-i\\omega_mt}+e^{i\\omega_mt}\\right)+\\\\&E_0\\frac{m\\delta \\phi(t)}{2}e^{i\\omega_0t}\\left(e^{-i\\omega_mt}-e^{i\\omega_mt}\\right)+h.c.\\,,\n\\end{split}$$ where $E_0$ is the amplitude of the carrier field, $h.c.$ denotes the hermitian conjugate. ", "According to Eq.", " , we symbolise RF local oscillator as $$\\label{eq:L}\n\\begin{split}\nL(t)=&\\left[L_{+}+ l_+(t)\\right]e^{i(\\omega_0+\\omega_m)t}+\\\\&\\left[L_{-}+ l_-(t)\\right]e^{i(\\omega_0-\\omega_m)t}+h.c.\\,,\n\\end{split}$$ where $L_+,L_-$ are the upper and lower RF sidebands with $L_+=L_-=i\\frac{m}{2}E_0$. $l_+,l_-$ are the fluctuation terms of the local oscillator beam. ", "Their classical parts have the amplitude,\n\n\\[eq:dl\\] $$\\begin{aligned}\nl_+(t)=\\left[\\frac{i\\delta m(t)-m\\delta \\phi(t) }{2}\\right]E_0\\,,\n\\\\\nl_-(t)=\\left[\\frac{i\\delta m(t)+m\\delta \\phi(t) }{2}\\right]E_0\\,.\\end{aligned}$$\n\nWe define the signal field $Z(t)$ and specify only three modes around frequencies $\\omega_0$ and $\\omega_0\\pm2\\omega_m$, which will eventually contribute to the final output. ", "There is $$\\label{eq:o}\n\\begin{split}\nZ(t)=&\\left[\\overline{Z}_0+Z_0(t)\\right]e^{i\\omega_0t}+\\\\\n&Z_+(t)e^{i(\\omega_0+2\\omega_m)t}\n+Z_-(t)e^{i(\\omega_0-2\\omega_m)t}+\\\\&h.c.\\,,\n\\end{split}$$ where $\\overline{Z}_0$ is the amplitude of the carrier that leaks to the dark port of the interferometer, $Z_0(t)$ represents the fluctuations around frequency $\\omega_0$, including both signal and noise. ", "$Z_+(t)$ and $Z_-(t)$ represent the fluctuations around frequencies $\\pm \\omega_m$, respectively. ", "Ignoring the second order terms and the terms at irrelevant frequencies, the beat between local oscillator and signal field can be calculated as $$\\label{eq:phc}\n\\begin{split}\n\\left[L(t)+Z(t)\\right]\\left[L(t)+Z(t)\\right]^{\\dagger}=\\\\\n2\\left[L_++l_+(t)\\right]\\left[\\left(\\overline{Z}_o+Z_o(t)\\right)^{\\dagger}e^{i\\omega_m t}+Z_+^{\\dagger}(t)e^{-i\\omega_mt}\\right]+\\\\2\\left[L_-+l_-(t)\\right]\\left[\\left(\\overline{Z}_o+Z_o(t)\\right)^{\\dagger}e^{-i\\omega_m t}+Z_-^{\\dagger}(t)e^{i\\omega_mt}\\right]+\\\\\nh.c.\\,.", "\n\\end{split}$$ This photocurrent is then demodulated by the sinusoidal signal $\\left[m'+\\delta m' (t)\\right]\\cos(\\omega_m t+\\phi'+\\delta \\phi' (t))$, which is from the same source of modulation signal. ", "It can be written approximately as, $$\\label{eq:m}\n\\left[m'+\\delta m'(t)\\right]\\cos(\\omega_m t+\\phi')-\\delta \\phi'(t) m'\\sin(\\omega t+\\phi')\\,,$$ where $m'$ and $\\delta m'(t) $ represent the amplitude of demodulation signal and its fluctuations; $\\phi'$ and $\\delta \\phi'(t)$ represent the demodulation phase and its fluctuations. ", "After applying a low pass filter with audio bandwidth to the product of Eq.", "  and  , we can get the demodulated output.", "\n\nIt is convenient to describe the output in frequency domain using quadrature operator base on the relation[@PhysRevD.67.122005] $$A\\hat{Z}^{\\dagger}_{-\\Omega}+A^{\\dagger}\\hat{Z}_{\\Omega}=\\sqrt{2}|A|\\hat{Z}_{\\zeta}(\\Omega),$$ where $A=|A|e^{i\\zeta}$ is an arbitrary complex amplitude. ", "The quadrature operator $Z_{\\zeta}$ is defined as $$\\label{eq:b}\nZ_{\\zeta}(\\Omega)=\\hat{X}(\\Omega)\\cos\\zeta+\\hat{Y}(\\Omega)\\sin{\\zeta}\\,,$$ with $$\\hat{X}(\\Omega)=\\frac{\\hat{Z}_{\\Omega}+\\hat{Z}^{\\dagger}_{-\\Omega}}{\\sqrt{2}}\\,,Y(\\Omega)=\\frac{\\hat{Z}_{\\Omega}-\\hat{Z}^{\\dagger}_{-\\Omega}}{\\sqrt{2}i}\\,,$$ representing amplitude quadrature and phase quadrature, respectively. ", "Eventually, the demodulated output can then be calculated as\n\n$$\\label{eq:I}\n\\begin{split}\nI(\\Omega)&=\n\\sqrt{2}m'\\left[|L_0|{Z_0}_{\\zeta_0}(\\Omega)+|L_+|{Z_+}_{\\zeta_+}(\\Omega)+|L_-|{Z_-}_{\\zeta_-}(\\Omega) \\right]\n+\\sqrt{2}m'|\\overline{Z}_0|\\left[{l_+}_{\\alpha_{+}}(\\Omega)+ {l_-}_{\\alpha_{-}}(\\Omega)\\right]\\\\\n&-2m'\\delta\\phi'(\\Omega)\\left[|L_+||\\overline{Z}_0|\\cos\\beta_++|L_-||\\overline{Z}_0|\\cos\\beta_-\\right]+2\\delta m'(\\Omega)\\left[|L_+||\\overline{Z}_0|\\cos \\psi_++|L_-||\\overline{Z}_0|\\cos \\psi_-\\right]\\,,\n\\end{split}$$\n\nwhere $$|L_0|={|L_+e^{-i\\phi'} +L_-e^{i\\phi'}|}\\,,$$ and\n\n$$\\begin{aligned}\n \\zeta_0&={\\rm arg}\\left(L_+e^{-i\\phi'}+L_-e^{i\\phi'}\\right)\\,, \\\\\\zeta_\\pm&=\\pm\\phi'+{\\rm arg}L_\\pm\\,,\\\\\n\\alpha_{\\pm}&=\\pm \\phi'+{\\rm arg}\\overline{Z}_{0}\\,,\\\\\n\\beta_+&= {\\rm arg}\\left(L_+e^{-i\\phi'}\\right)-{\\rm arg}\\overline{Z}_0-\\frac{\\pi}{2}\\,,\\\\\n\\beta_-&= {\\rm arg}\\left(L_-e^{i\\phi'}\\right)-{\\rm arg}\\overline{Z}_0+\\frac{\\pi}{2}\\,,\\\\\n\\psi_+&= {\\rm arg}\\left(L_+e^{-i\\phi'}\\right)-{\\rm arg}\\overline{Z}_0\\,,\\\\\\psi_-&= {\\rm arg}\\left(L_-e^{i\\phi'}\\right)-{\\rm arg}\\overline{Z}_0\\,.\\end{aligned}$$\n\nWhen $\\overline{Z}_0=0$, considering balanced RF sidebands which are on phase quadrature and $\\phi'=0$ for phase measurement, there is $$\\begin{split}\nI(\\Omega,|L_+|=|L_-|)=\n\\\\\\sqrt{2}m'|L_0|\\left[{Y_0}(\\Omega)+\\frac{{Y_+}_2(\\Omega)+{Y_-}_2(\\Omega)}{2}\\right]\\,,\n\\end{split}$$ where $Y_0$ and $Y_{\\pm2}$ represent the phase quadrature of three modes around frequency $\\omega_0$ and $\\omega_0\\pm 2\\omega_m$. If, $|L_+|\\ne|L_-|$, $$\\begin{split}\nI(\\Omega,|\\frac{|L_-|}{|L_+|}=\\xi)=\n\\\\\\sqrt{2}(1+\\xi)m'|L_+|\\left[{Y_0}(\\Omega)+\\frac{{Y_+}_2(\\Omega)+\\xi{Y_-}_2(\\Omega)}{1+\\xi}\\right]\\,,\n\\end{split}$$ where $\\xi=|\\frac{L_-}{L_+}|$ denotes the ration of amplitude of two RF sidebands on phase quadrature.", "\n\nThree modes squeezing schemes {#sec:TM}\n=============================\n\n![", "Different three-mode squeezing schemes to produce independent squeezing fields near $\\omega_0-2\\omega_m$, $\\omega_0$, and $\\omega_0+2\\omega_m$ for general imbalanced heterodyne readouts. ", "Scheme (a) coherently combines the squeezing from three independent sources. ", "Scheme (b) uses three longitudinal modes of a single cavity, which are separated by the free spectral range equal to $2\\omega_m$. It works when the crystal squeezing bandwidth is smaller than $2\\omega_m$. Otherwise, a more sophisticated scheme (c) with three cavities coupled together can be an option. []{", "data-label=\"fig:3mode_sqz\"}](three_mode_sqz.pdf){width=\"1\\columnwidth\"}\n\nIn this appendix, we introduce squeezing schemes as shown in Fig.", " \\[fig:3mode\\_sqz\\], which produce three independent squeezing modes around $\\omega_0$ and $\\omega_0\\pm2\\omega_m$.\n\nScheme (a) uses three audio band squeezing sources which are coherently combined through two optical cavities that properly reflect and transmit the fields using their frequency selectivity. ", "Scheme (b) uses a single cavity with three pumps interacting with the non-linear crystal. ", "The longitudinal mode frequency of the cavity coincide with that of three squeezing modes. ", "The squeezing bandwidth of the crystal, however, needs to be smaller than $2\\omega_m$ to avoid the EPR entanglement between neighbouring modes. ", "If it is challenging to achieve, we can consider scheme (c) which uses coupled cavities and two nonlinear crystals.", "\n\nIn scheme (c), we define the optical modes of the three cavities as $a$, $b$ and $c$ with identical frequency $\\omega_{E}$. The power transmissivities of the mirrors between cavities $a$, $b$ is defined as $T_1$; the power transmissivities of the mirrors between cavities $b$, $c$ is defined as $ T_2$. The cavities lengths are defined as $L_a, L_b, L_c$. They should satisfy that the cavity coupling frequencies between each pair of adjacent cavities are identical. ", "So the coupling frequency $\\omega_c$ can be calculated as [@PhysRevD.66.122004] $$\\omega_c=\\frac{c\\sqrt{T_1}}{2\\sqrt{L_a L_b}}=\\frac{c\\sqrt{T_2}}{2\\sqrt{L_b L_c}}\\,.$$ In the interaction picture, the optical part of the hamiltonian of the three coupled cavities can be written as $$\\mathcal{H}_{\\rm opt}=\\hbar\\begin{bmatrix}\na^{\\dagger}&b^{\\dagger}&c^{\\dagger}\n\\end{bmatrix}\n\\begin{bmatrix}\n\\omega_E &\\omega_c & 0\\\\\n\\omega_c &\\omega_E & \\omega_c \\\\\n0 &\\omega_c &\\omega_E\n\\end{bmatrix}\n\\begin{bmatrix}\na\\\\ b \\\\ c\n\\end{bmatrix}\\,,$$ The decoupled eigen-modes of the three coupled cavities, $n_0$, $n_{\\pm}$, can be derived by diagonalising the matrix above, which gives $$\\begin{bmatrix}\na \\\\ b \\\\ c\n\\end{bmatrix}=\n\\begin{bmatrix}\n\\frac{1}{\\sqrt{2}} &\\frac{1}{2} &\\frac{1}{2}\\\\\n0 &-\\frac{1}{\\sqrt{2}} &\\frac{1}{\\sqrt{2}}\\\\\n-\\frac{1}{\\sqrt{2}} & \\frac{1}{2} &\\frac{1}{2}\n\\end{bmatrix}\n\\begin{bmatrix}\nn_{0} \\\\ n_{-} \\\\ n_{+}\n\\end{bmatrix}\\,.$$ The three eigen-modes have eigen-frequencies, $\\omega_E$ and $\\omega_E\\pm\\sqrt{2}\\omega_c$. For our purpose, we need $$\\omega_c=\\sqrt{2}\\omega_m\\,.$$ The hamiltonian describing the interactions in the system can be written as [@walls2007quantum] $$\\label{eq:Hamiton}\n\\begin{split}\n\\mathcal{H}_{\\rm I}=&-\\frac{i\\hbar}{2}\\Big[ \\chi_0^a\\frac{{n_0}^2+n_+n_-}{2}+{\\chi_-^a}\\frac{{n_-}^2}{4}+\\chi_+^a\\frac{{n_+}^2}{4}-\\\\\n&\\sqrt{2}\\chi_0^b n_+ n_- +\\chi_-^b\\frac{{n_-}^2}{2}+\\chi_+^b\\frac{{n_+}^2}{2}\\Big]+h.c.\\,,\n\\end{split}$$ where each constant, $\\chi_0^a, \\chi_-^a, \\chi_+^a, \\chi_0^b ,\\chi_-^b, \\chi_+^b$ is proportional to the second-order nonlinear susceptibility of crystal in cavity $a$ and $b$ and the amplitude of the pumps. ", "By designing the power of pumps and crystal features satisfying $\\chi_0^a=2\\sqrt{2}\\chi_0^b$, the correlations between mode $n_+$ and $n_-$ can be coherently cancelled. ", "Thus Eq.", "  can be rewritten as $$\\label{eq:Hamiton2}\n\\begin{split}\n\\mathcal{H}_{\\rm I}=-\\frac{i\\hbar}{2} \\left( g_0 {n_0^{\\dagger}}^2+g_- {n_-^{\\dagger}}^2 + g_+{n_{+}^{\\dagger}}^2 \\right)+h.c.", "\n\\end{split}$$ where $$g_0=\\frac{\\chi_0^a}{2}\\,,g_-=\\frac{\\chi_-^a+2\\chi_-^b}{4}\\,,g_+=\\frac{\\chi_+^a+2\\chi_+^b}{4}\\,.$$ It is then straightforward to see the three pairs of independent interactions, which will give three modes of single mode squeezing.", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "Antibiotic concentrations in saliva of purulent parotitis.", "\nIn patients with unilateral acute purulent parotitis treated with penicillin and doxycycline the antibiotic concentration was determined in plasma and saliva from both the healthy and the affected parotid gland. ", "The results show that the penicillin concentrations in purulent saliva of the diseased gland is considerably higher than in non-purulent saliva of the healthy parotid gland. ", "There was no such marked difference in concentrations of doxycycline. ", "The possible mechanisms behind these observations are discussed as are the conclusions that can be drawn concerning treatment of acute purulent and chronic recurrent parotitis." ]

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[ "/*\n * Copyright 2002-2018 the original author or authors.", "\n *\n * Licensed under the Apache License, Version 2.0 (the \"License\");\n * you may not use this file except in compliance with the License.", "\n * You may obtain a copy of the License at\n *\n * https://www.apache.org/licenses/LICENSE-2.0\n *\n * Unless required by applicable law or agreed to in writing, software\n * distributed under the License is distributed on an \"AS IS\" BASIS,\n * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.", "\n * See the License for the specific language governing permissions and\n * limitations under the License.", "\n */\n\npackage org.springframework.messaging.simp.config;\n\nimport java.util.", "ArrayList;\nimport java.util.", "Arrays;\nimport java.util.", "List;\n\nimport org.springframework.lang.", "Nullable;\nimport org.springframework.messaging.support.", "ChannelInterceptor;\nimport org.springframework.scheduling.concurrent.", "ThreadPoolTaskExecutor;\n\n/**\n * A registration class for customizing the configuration for a\n * {@link org.springframework.messaging.", "MessageChannel}.", "\n *\n * @author Rossen Stoyanchev\n * @since 4.0\n */\npublic class ChannelRegistration {\n\n\t@Nullable\n\tprivate TaskExecutorRegistration registration;\n\n\tprivate final List<ChannelInterceptor> interceptors = new ArrayList<>();\n\n\n\t/**\n\t * Configure the thread pool backing this message channel.", "\n\t */\n\tpublic TaskExecutorRegistration taskExecutor() {\n\t\treturn taskExecutor(null);\n\t}\n\n\t/**\n\t * Configure the thread pool backing this message channel using a custom\n\t * ThreadPoolTaskExecutor.", "\n\t * @param taskExecutor the executor to use (or {@code null} for a default executor)\n\t */\n\tpublic TaskExecutorRegistration taskExecutor(@Nullable ThreadPoolTaskExecutor taskExecutor) {\n\t\tif (this.registration == null) {\n\t\t\tthis.registration = (taskExecutor !", "= null ? ", "new TaskExecutorRegistration(taskExecutor) :\n\t\t\t\t\tnew TaskExecutorRegistration());\n\t\t}\n\t\treturn this.registration;\n\t}\n\n\t/**\n\t * Configure the given interceptors for this message channel,\n\t * adding them to the channel's current list of interceptors.", "\n\t * @since 4.3.12\n\t */\n\tpublic ChannelRegistration interceptors(ChannelInterceptor... interceptors) {\n\t\tthis.interceptors.addAll(Arrays.asList(interceptors));\n\t\treturn this;\n\t}\n\n\t/**\n\t * Configure interceptors for the message channel.", "\n\t * @deprecated as of 4.3.12, in favor of {@link #interceptors(ChannelInterceptor...)}\n\t */\n\t@Deprecated\n\tpublic ChannelRegistration setInterceptors(@Nullable ChannelInterceptor... interceptors) {\n\t\tif (interceptors !", "= null) {\n\t\t\tthis.interceptors.addAll(Arrays.asList(interceptors));\n\t\t}\n\t\treturn this;\n\t}\n\n\n\tprotected boolean hasTaskExecutor() {\n\t\treturn (this.registration !", "= null);\n\t}\n\n\tprotected boolean hasInterceptors() {\n\t\treturn !", "this.interceptors.isEmpty();\n\t}\n\n\tprotected List<ChannelInterceptor> getInterceptors() {\n\t\treturn this.interceptors;\n\t}\n\n}\n" ]

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[ "Q:\n\nhardware upgrade\n\nCan any one explain this\n\"My feiend is using a Windows xP O.S. & a 2x2gb=4gb RAM but on the DXDIAG it onlt shows 3gb\"\nAlso \n\"I have Windows Vista 64 bit & 2 gb RAM, So is it OK if I get another 2 gb RAM, I mean It\nwouldnt show only 3 gb insted of 4 gb\"\n\nA:\n\nOK... It could be a few things, but the most common thing is...\nYour friend either has the 32 bit edition of Windows which can only see ~3GBs of memory, or he has the 64bit edition, but 1GB is reserved for graphics.", "\nIf you have the 64bit edition, you should not have a problem seeing the full 4GBs unless again, you have memory reserved for your graphics card.", "\n\n" ]

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[ "\n\n What cha think of my startup: PocketLoot - darkxanthos\nhttp://www.pocketloot.com\n\n======\nbrianwillis\n>Your beta registration could not be processed for some reason. ", "Maybe you\ndidn't type in one or more of the fields or your internet connection hiccuped?", "\nMessage: error\n\nAll the fields are filled out correctly. ", "I did forget to fill out the comments\nsection the first time I hit \"send\", maybe that's behind it. ", "Why is the\ncomments section even a required field?", "\n\n~~~\ndarkxanthos\nHey thanks for trying to sign up I see the issue in my logs.. working on it.", "\n\n" ]

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[ "We’ve all got that friend who says they can’t pay you back for dinner, but when you show up at their house you discover they just bought a brand new big-screen TV.", "\n\nNow imagine that dinner cost you $12 billion, and that new TV was worth $66 billion. ", "You might be a little frustrated.", "\n\nA new study released Thursday suggests that’s exactly what’s going on with a major chunk of private-industry pensions across Canada. ", "The study, by the Canadian Centre for Policy Alternatives, found that of the 90 companies listed on the TSX Composite Index that have defined-benefit pension plans, just a handful completely funded their workers’ pension funds in 2017. ", "At the same time, they were busy paying out billions of dollars in dividends to shareholders.", "\n\n“I’m not against companies paying dividends. ", "But if they can afford to pay the shareholders, they can afford to fund the pensions,” said report co-author David McDonald, senior economist at the CCPA.", "\n\nThe study found that in 2017, the 90 defined pensions were collectively underfunded by roughly $12 billion. ", "The companies responsible for those pensions, meanwhile, paid out $66 billion in dividends to shareholders — more than five times the amount it would have cost to fund the pensions.", "\n\nThose shareholders usually include the very senior executives and board members who decide how free cash is used.", "\n\nThe biggest single reason pension-funding deficits aren’t been cleaned up, argues McDonald, is that the companies don’t have to. ", "Pension regulations dictate that funds must have at least 85 per cent of the money required to meet all their obligations, in the event that the plan is wound up. ", "Regulators don’t look at whether the company’s been paying out dividends or hefty executive bonuses.", "\n\n“All they need to do is look at whether they meet the statutory minimum. ", "That needs to change. ", "It’s pretty clear that without regulatory changes, those deficits are going to be there forever,” said McDonald. “", "Shareholders are supposed to take on the firm’s risk. ", "Instead, that risk is being shouldered by workers whose retirement security is compromised by outstanding pension deficits.”", "\n\nRetired Sears employee Ken Eady, who worked at the now-bankrupt retail powerhouse for three decades, agreed that regulators should be able to take a broader approach.", "\n\n“I think (the regulators) should be looking at the financial health of the company. ", "The dividends. ", "Executive bonuses. ", "Those are all things that should matter,” said Eady, who’s now a vice-president of Sears Canada Retirees Group, an association of company pensioners.", "\n\nSears pensioners sued after their pensions were cut, saying that the company shouldn’t have paid a $509-million dividend to shareholders in 2013. ", "At the time that dividend was paid, the pension fund at Sears Canada was short by $133 million.", "\n\nWhile Eady says he and his wife have been able to survive on a pension that only pays about 80 per cent of what it was supposed to, other former colleagues haven’t been so fortunate.", "\n\n“For me and my wife, we’re OK. ", "For some people, particularly outside of Ontario, it’s been really tough. ", "It’s not the ability to take vacations to Florida. ", "It’s the difference between being able to stay in your own apartment or having to move in with your kids,” said Eady.", "\n\nBut pension expert Malcolm Hamilton says occasional underfunding is a side effect of the way defined benefit pensions usually work — contributions from workers and companies which are then put into investments like stocks and bonds. ", "When markets take a tumble, as they did after the global financial crisis in 2008, pensions will look underfunded. ", "But that’s only a problem, says Hamilton, if the company itself is actually in financial trouble. ", "Otherwise, the company and its workers will keep paying in, and there will be plenty of money for pensioners to collect.", "\n\nLoading... Loading... Loading... Loading... Loading... Loading...\n\n“From time to time, the investments are going to perform badly,” said Hamilton, a pension industry consultant and former actuary at human resources consulting giant Mercer.", "\n\n“As long as the company’s in good financial shape, that’s what matters more. ", "I’d rather have something that’s 85 per cent funded by a strong, financially healthy company than something that’s at 102 per cent but is with a company that’s in trouble.”" ]

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[ "\nAsk HN: What is the real difference between Terraform and Ansible? - ", "ejanus\nI am beginning to learn these tools and I noticed that Ansible is used to configure servers and Terraform does something similar but I can&#x27;t figure what makes Ansible poor choice when doing provisioning? ", "\nNB: I am still learning please bear with my poor use of technical terms.", "\n======\ndigitalsushi\nTerraform is for building infrastructure, you know foundations, skyscrapers,\nstreets. ", "Build an empty restaurant with a giant yellow excavator (Terraform)\n\nAnsible, Chef are for building configuration, you know menus, staff schedules,\ngrocery lists. ", "Ensure a restaurant is configured correctly to serve customers\nwith its wait staff (Ansible)\n\nYou can use an excavator to configure the stuff inside the restaurant. ", "People\ndo it. ", "It's just not generally the most efficient way to do it. ", "And you could\nhave the wait staff at a restaurant pouring concrete for their second place a\ntown over. ", "You could do that too, but a lot of people would use the excavator.", "\n\nSo what really makes these tools effective is when you start using them at\nscale. ", "They start to become helpful once you realize how much you can do with\nhow little, and they each have this same strength solving different levels,\nand their strengths become weaknesses at the other end.", "\n\n~~~\ngitgud\nThat's a great analogy. ", "Breaking down concepts like this helps a lot more than\nmost people realise...\n\n------\njaejae\nThere are five broad categories of IAC (Infrastructure as a Code) tools:\n\na)Ad hoc scripts\n\nThe most straightforward approach to automating anything is to write an ad hoc\nscript. ", "You take whatever task you were doing manually, break it down into\ndiscrete steps, use your favorite scripting language (e.g., Bash, Ruby,\nPython) to define each of those steps in code, and execute that script on your\nserver\n\nb) Configuration management tools Chef, Puppet, Ansible, and SaltStack are all\nconfiguration management tools, which means that they are designed to install\nand manage software on existing servers.", "\n\nc)Server templating tools An alternative to configuration management that has\nbeen growing in popularity recently are server templating tools such as\nDocker, Packer, and Vagrant. ", "Instead of launching a bunch of servers and\nconfiguring them by running the same code on each one, the idea behind server\ntemplating tools is to create an image of a server that captures a fully self-\ncontained “snapshot” of the operating system (OS), the software, the files,\nand all other relevant details.", "\n\nd)Orchestration tools Server templating tools are great for creating VMs and\ncontainers, but how do you actually manage them? ", "Handling these tasks is the\nrealm of orchestration tools such as Kubernetes, Marathon/Mesos, Amazon\nElastic Container Service (Amazon ECS), Docker Swarm, and Nomad\n\ne)Provisioning tools Whereas configuration management, server templating, and\norchestration tools define the code that runs on each server, provisioning\ntools such as Terraform, CloudFormation, and OpenStack Heat are responsible\nfor creating the servers themselves. ", "In fact, you can use provisioning tools\nto not only create servers, but also databases, caches, load balancers,\nqueues, monitoring, subnet configurations, firewall settings, routing rules,\nSecure Sockets Layer (SSL) certificates, and almost every other aspect of your\ninfrastructure\n\n~~~\nForHackernews\nThis is a good overview, but notice how hazy these different categories are\naround the edges.", "\n\n> not only create servers, but also databases, caches, load balancers, queues\n\nThese things are, I would say unquestionably \"infrastructure\".", "\n\n> firewall settings, routing rules, Secure Sockets Layer (SSL) certificates\n\nThese things are more or less configuration, basically files that exist on the\nabove.", "\n\nAnd yet, as you say, it's common to manage them using provisioning tools like\nterraform.", "\n\n~~~\nethbro\n> > firewall settings, routing rules, Secure Sockets Layer (SSL) certificates\n\n> These things are more or less configuration, basically files that exist on\n> the above.", "\n\nPart of the different perspective feels like managed cloud vs on prem.", "\n\nIn the former, these are all actually things to be created, albeit as an\nabstraction on the underlying implementation. ", "Which you don't have access to.", "\n\nIn the latter, they're configurations on things you have access to.", "\n\n------\noneplane\nIf you are new to both and to IaC and DevOps as a whole:\n\nAnsible is for 'inside' virtual machines or computers, Terraform is for\n'outside' virtual machines or computers.", "\n\nInside a machine you might have software, configuration, assets. ", "Outside a\nmachine you might network connections, firewalls, disks, dns etc.", "\n\nThis isn't a comprehensive comparison, but when you start from nothing, it\ndoesn't really help to do a syntax, provider or imperative vs. declarative.", "\n\n~~~\nbryogenic\nAnsible also does 'outside' virtual machines.", "\n\nSee\n[https://docs.ansible.com/ansible/2.3/list_of_cloud_modules.h...](https://docs.ansible.com/ansible/2.3/list_of_cloud_modules.html)\n\n~~~\nscoot_718\nMy advice would be to avoid Ansible for that sort of thing like the plague.", "\nAll the nice things like idempotency and having the same script for setting\nthings up and tearing them down no longer function when using those modules.", "\n\nEssentially you need to 1. ", "do the checks to ensure your playbook won't just\ncreate a new set of VMs every time it's run if they already exist 2. ", "maintain\na teardown playbook alongside your setup one because Ansible is entirely\nprocedural and the steps would be reversed in that case and 3. ", "do queries\nfirst to determine what actually exists in the cloud and do lots of jinja\nmanipulations to work on the right things. ", "Did you know EC2 has default\nsubnets and routing tables? ", "Did you know that the Ansible module will error\nout if you try to delete those objects?", "\n\nIf only there was a thing like Terraform that could just rely on a single\ndescription of the setup you'd like. ", "Seriously. ", "There's an Ansible module that\nwill run a Terraform .tf file, and there's a provider for terraform that will\nrun Ansible on the servers it provisions.", "\n\n~~~\nPaywallBuster\nI think you're exagerating.", "\n\nI use Ansible to provision dev environments on each PR, it works fine, every\ntime a deployment occurs Ansible will deploy if required, otherwise proceeded\nwith the deployment.", "\n\nDestroying the environment is done separate, triggered by a webhook once the\nPR is closed.", "\n\n~~~\nscoot_718\nIf you're just provisioning software on an individual server, then sure. ", "I\nagree. ", "It kinda works okay.", "\n\nWhat I'm talking about is using the cloud modules to spin up servers, and god\nhelp you, entire VPC set ups.", "\n\n~~~\nPaywallBuster\nEach PR will provision a new server and then configure/deploy.", "\n\n~~~\nscoot_718\nSo wait, you make a playbook per individual server instance? ", "Why?", "\n\n~~~\nzufallsheld\nHe didn't say that. ", "He presumably uses one playbook that creates vms and\nprovisions the software for every PR. ", "With ansible this can be idempotent and\ncreating vms is by default idempotent.", "\n\n------\ngazoakley\nTake a look at this talk - it explains what both tools do and how they can\nwork together well:\n\n[https://www.hashicorp.com/resources/ansible-terraform-\nbetter...](https://www.hashicorp.com/resources/ansible-terraform-better-\ntogether/)\n\nTLDW; You can do resource management (e.g. creating EC2 instances in AWS) and\ndeployment (e.g. installing packages on an instance) through both Terraform\nand Ansible. ", "Terraform is best used for resource management - the\ndocumentation states using the \"provisioning\"/deployment function is a last\nresort. ", "Ansible is great at deploying packages but less so at resource\nmanagement for the reasons you'll see in the other comments. ", "Either use them\ntogether for what they're good at, or use Terraform to do resource management\nand other techniques (such as prebuilt images) for deployment:\n\n[https://www.terraform.io/docs/provisioners/index.html](https://www.terraform.io/docs/provisioners/index.html)\n\nAlso useful:\n\n[https://blog.gruntwork.io/why-we-use-terraform-and-not-\nchef-...](https://blog.gruntwork.io/why-we-use-terraform-and-not-chef-puppet-\nansible-saltstack-or-cloudformation-7989dad2865c)\n\n------\nbusser\nAnsible connects to remote servers to configure them, while Terraform calls\ncloud provider API’s to provision resources.", "\n\nFor example, you can use Terraform to provision virtual machines, database\ninstances, or Kubernetes clusters on AWS. ", "Terraform does this via the AWS API.", "\n\nIn my opinion, Terraform is better for provisioning because of the way it\nmanages its own state. ", "Terraform remembers what resources it created the last\ntime it ran, and can edit or delete them according to any change in your\nTerraform code.", "\n\nI like Ansible, but not for managing cloud resources. ", "Ansible has no memory.", "\nFor example, if I ran a playbook that installs MySQL, Ansible has no built-in\nway to undo this change and bring me back to my previous state.", "\n\n~~~\nuser5994461\nAnsible has full integration with cloud providers API. ", "It's actually better\nfor managing instances and highly dynamic resources because it has much better\nstate management than Terraform.", "\n\nIf you (re)create some EC2 instances with Terraform. ", "Terraform save the ID the\nfirst time they are created (in a state file that needs to be shared and keep\nin sync). ", "It goes mental the next time it runs if any of the instances are not\nfound, or the state file is missing, or some of the instances were modified or\ndied.", "\n\nAnsible always lookup what's actually running, instances with the intended\nname/tags and match versus what's expected. ", "It skips when it's already there,\nit's much less accidentally destructive and never run out of sync.", "\n\n~~~\nlawik\nHow does the coverage of APIs compare. ", "Just AWS is a gigantic set of APIs. ", "I\nsee most of what I'd need in the Ansible Module Index but it doesn't seem like\nit covers all that is available.", "\n\n~~~\nakvadrako\nTerraform has way more coverage. ", "I used ansible for aws a couple years ago and\nneeded to rewrite many of the modules myself.", "\n\nTracking AWS apis is a fulltime job and ansible for clouds just isn’t popular\nenough.", "\n\n~~~\ngazoakley\nUnfortunately this is true - the Terraform AWS provider has thousands of PRs\nclosed (and hundreds still open) as proof. ", "Nevertheless, things seem to get\nsupport quicker in Terraform than in CloudFormation.", "\n\n------\nthraxil\nI know I'm late to comment, so this will probably get buried, but I think a\nkey to understanding Terraform and why it is different is to understand that\nit's an implementation of the Reconciler Pattern. ", "This is a more useful\ndistinction than the usual declarative vs imperative contrast that is usually\nbrought up.", "\n\nThe Reconciler Pattern basically means:\n\n* there is some notion of \"expected\" state, which is what you define (declaritively) in the configuration\n\n* there is some \"actual\" state, which is basically what is running at whatever cloud service, etc. ", "you are dealing with.", "\n\n* the reconciler's job is to query the actual state, compare it to the expected state, calculate the difference (usually in terms of a graph), then make whatever changes it needs to to bring \"actual\" in line with \"expected\".", "\n\nKubernetes, SaltStack, and others implement the same pattern (just on\ndifferent levels of resources) and it's becoming increasingly common and\nimportant to understand if you're working with cloud stuff.", "\n\n[https://www.oreilly.com/library/view/cloud-native-\ninfrastruc...](https://www.oreilly.com/library/view/cloud-native-\ninfrastructure/9781491984291/ch04.html)\n\n------\nstyluss\nTerraform is a declarative way of setting up your cloud infrastructure. ", "You\nspecify the state you want your cloud to be in.", "\n\nAnsible is an imperative way of setting up your cloud. ", "You tell it to do\ncertain things, install this package, copy this over there.", "\n\nHope it helps\n\n~~~\nPaywallBuster\nAnsible is mostly declarative.", "\n\nby default you use Ansible modules/roles and specify the desired state.", "\n\nE.g. have these packages installed, have these directories created/deleted.", "\n\nUse cases not covered by modules can fallback to using shell commands\n\n~~~\npiroux\nTo define something as declarative or imperative, it is important to compare\nthe definition model to the execution model.", "\n\nSo I would rather say that Ansible is much less declarative than Terraform,\nbecause Ansible tasks (the different steps of an Ansible Playbook) are\nexecuted sequentially.", "\n\nThe tasks of Ansible are its statements, so yeah we would say that each\nAnsible task is declarative. ", "And still, a requirement for that would be for\nthe task to use a module/role which is idempotent, right? ", "Another proof,\nAnsible natively offers loop, blocks, and conditional to control the execution\nflow throughout its tasks.", "\n\n(This is not a critic of Ansible. ", "I am happy to use it as is, as a high-level\nscripting mechanism.)", "\n\n------\nuser5994461\nAnsible is really SSH on steroid across multiple hosts, with extra commands\nthat bash never added. ", "It can configure servers and services. ", "It can also\nconfigure cloud products and it's a better choice than Terraform for many\nthings because it's more flexible.", "\n\nTerraform can only provision cloud resources on AWS/GCP/Azure/other. ", "Usually\nit gets support first for new products they release. ", "Terraform is very static\n(see issues with sharing the state file) so it's more indicated to configure\nvery static stuff, like networking and subnets.", "\n\n~~~\ndynamite-ready\nThis is not a bad high level description. ", "I asked myself almost the exact same\nquestion as the OP a year ago, though I had prior experience with Ansible, so\nknew what I was getting into.", "\n\nMy advice to the OP, as it's all new to you, is to learn Ansible. ", "It will\nrequire more work than Terraform, but Ansible can be made to perform the same\nfunctions as Terraform, and a heck of a lot more stuff that will prove useful\nto you, if you're looking into how to provision cloud instances.", "\n\nThat makes Ansible sound like it's hard work, but it's actually quite the\nopposite. ", "It's surprisingly easy to do something useful with it.", "\n\nAnsible is probably best described as a scripting environment / DSL\ncombination to help you control multiple machines remotely for build and\nprovisioning purposes.", "\n\nYou have 2 separate remote machines, and want to install Postgres on both of\nthem? ", "Use Ansible.", "\n\nWant to install GIT and then pull your project repo onto two machines? ", "Use\nAnsible.", "\n\nPerhaps you have 3 machines, want git on all 3, but Postgres on only one of\nthem? ", "Ansible again.", "\n\nWhere there is an overlap with Terraform, is that Ansible can also be used as\nan interface to control AWS/Google cloud/Whatever services, which is\nTerraform's sole purpose. ", "Terraform provides a cloud platform agnostic\ninterface to allow you to spin up new cloud instances, and perform some\nprovisioning tasks, but it will only skim the surface of what you can do with\ndedicated Ansible scripts.", "\n\n~~~\nejanus\nI learnt a bunch ...I will build up my knowledge from Ansible first.", "\n\n------\nForHackernews\nVery crudely, Ansible is like a YAML frontend to SSH, Terraform is like a TOML\nfrontend to AWS CloudFormation.", "\n\n~~~\nlawik\nNot quite accurate but very funny :)\n\n------\njonahbenton\nThere are a lot of answers but none are geared to the beginner. ", "I read the\nquestion as asking for an answer like the below-\n\nTo a large degree expressing something is a \"poor choice\" is an opinion, maybe\nexpert, about optimizations, not about capabilities.", "\n\nWhen one is learning, adopting the value judgements of experts is a form of\npremature optimization that actually prevents learning.", "\n\nThe only way to build your own opinions is through your own experience. ", "You\nwill need to have your own problems, and solve them using a variety of tools,\nto build your own opinions.", "\n\nTry both tools in real problems, and the mental model that accrues in your\nexperience will start to guide your opinions about ways to optimize your work.", "\n\nAlso- everybody is just making it up. ", "And all tools suck.", "\n\n~~~\nejanus\nOkay...and thanks for being frank\n\n------\nXophmeister\nTerraform is best at provisioning \"hardware\" (physical or otherwise); Ansible\nis best at provisioning software.", "\n\n------\ntoyg\nTerraform is very good when it comes to _declaring topologies_ : “there should\nbe N items of this type, in this network, with these characteristics”. ", "It\nremembers state; as you add or remove stuff to your topology, it will take\ncare of doing all the necessary work to go from topology A to topology B, and\ndetect any inconsistency.", "\n\nI don’t know Ansible much, but I believe it’s more of a procedure-oriented\nsystem, where you declare the steps necessary to reach A, then again to go\nfrom A to B. This can be an issue if any item is actually not in the state you\nexpected.", "\n\n------\nacd\nTerraform tracks and provisions cloud provider state. ", "Ansible you need to pass\nand parse Ansible output around which can take considerable time.", "\n\nTerraform tells how your Infastructure should look like. ", "Ansible what software\nshould be on your infrastructure/servers.", "\n\nI tend to use Terraform to describe how the underlying Cloud infrastructure\nshould look like. ", "I use Ansible to describe and configure what software should\nbe running on those servers.", "\n\nUsage cases:\n\nSimply put Terraform cloud infrastructure provisioning. ", "Ansible server\nsoftware and configuration files provisioning.", "\n\n~~~\npeterwwillis\nTechnically Terraform tracks and provisions its own state. ", "The cloud\nprovider's state at any given time may be different, and Terraform may find it\nimpossible to resolve the difference, leaving you to manually fix it.", "\n\nAnsible (mostly) does not refuse to do anything just because the state\nchanged. ", "If you need to make sure something happens, you can be more confident\nAnsible will do it, because it doesn't care what the state was before now.", "\n\n------\ntarun_anand\nI like both of them. ", "One thing interesting in Terraform is the ability to say\nI want to go from X to Y and see what will be the impact _without_ actually\ndoing the steps.", "\n\nOtherwise both are quite good.", "\n\n~~~\npintxo\nCheck mode in ansible\n\n> \\--check\n\n------\nspeedgoose\nYou can use Ansible to provision servers, it works, but if you do that a lot\nit's better to use Terraform. ", "With Ansible you are a bit at a lower level and\nyou need to manage the state of your system yourself. ", "It's fine for 4\npermanent VMs but not for more complicated infrastructures.", "\n\n~~~\neusebius\nI'm not very familiar with Ansible but consider it to be somewhat\ninterchangeable with Puppet (which I use extensively at work). ", "You can\ncertainly use Puppet to manage thousands of hosts but it entirely depends on\nother practices and technologies (an external node classifier in Puppet's\ncase) to keep things manageable. ", "I assume the same is true for Ansible.", "\n\n~~~\nlukevp\nAnsible is agentless, so the management of endpoints is entirely based on your\nserver doing the scripting. ", "It can use a static inventory file (text) or a\ndynamic one which can be served from anywhere (eg, sql query). ", "Whenever you\nwrite playbooks you target groups of hosts based on tagging that’s done\nthrough inventory.", "\n\n------\nsadjunky\nAnsible is primarily used for provisioning resources, on the other hand,\nTerraform is used for managing and deploying cloud resources. ", "This\ndifferentiation falls fairly well in the concept of immutable infrastructure.", "\n\nIf you're familiar with Packer, then Packer is responsible for creating\nidentical VM images which can be integrated to a CI pipeline and provisioned\nand baked using Ansible. ", "This baked image is then deployed using Terraform.", "\n\nBe advised that provisioning in Terraform during VM deployment is not\nrecommended since it increases startup time of the machine. ", "To perform ad hoc\nconfiguration management, you use Ansible.", "\n\nYou could very well use Ansible for managing and deploying cloud resources,\nbut that's not what it's meant to do. ", "Moreover, Ansible does not support the\nconcept of state as does Terraform.", "\n\n------\nborplk\nThey somewhat compliment each other, they are not really alternatives to each\nother.", "\n\nUsually Ansible is used for declaring the desired state of the individual\nservers for example you may use it to manage installed packages and\nconfiguration files on the servers.", "\n\nWhereas with Terraform you declare the desired state of cloud resources for\nexample you may ask Terraform to give you 5 EC2 instances, 1 RDS instance for\nDB and 1 S3 bucket for storage.", "\n\nThere's some overlap between them but what I've said is largely accurate.", "\n\n------\nphedoreanu\nHave a look at Pulumi - a modern infrastructure as code platform.", "\n[https://www.pulumi.com/docs/intro/vs/terraform/](https://www.pulumi.com/docs/intro/vs/terraform/)\nand\n[https://www.pulumi.com/docs/intro/vs/chef_puppet_etc/](https://www.pulumi.com/docs/intro/vs/chef_puppet_etc/).", "\n\n------\njake_morrison\nThe fundamental model behind Terraform is declarative. ", "You use the Terraform\nlanguage to define resources for your target system, e.g. a load balancer in\nAWS. ", "You then run Terraform and it checks the desired configuration vs the\nrunning configuration, and it shows the differences. ", "If the new config is what\nyou want, you apply the changes, and it updates the production system.", "\n\nAnsible is much more of an imperative system, sort of \"executable YAML\". ", "You\ndefine a series of tasks in a YAML file. ", "There are predefined tasks for\nstandard things that you need to do when configuring a system, e.g. creating a\ndirectory or generating a config file by merging Ansible configuration\nvariables with template. ", "You can and should make these tasks idempotent, but\nas the system gets more complex, it becomes difficult and runtime can be slow\nas it compares tasks one by one to the running system.", "\n\nBoth systems suffer somewhat from difficulty in writing code. ", "The fundamental\ntask is to transform configuration variables and templates into running\nresources. ", "To do that, you need loops, if/then/else logic, etc. ", "Ansible has\nsome constructs, but it is basically string manipulation, with a backdoor of\nbeing able to write modules in python. ", "Terraform has a better syntax to define\nresources. ", "Logic is generally things like ternary operator and list\ncomprehensions. ", "Terraform 0.12 improved this tremendously, but it is still\nsomewhat weak. ", "Ansible has a bit better management of config variables.", "\nTerraform tends to make you serialize things through environment vars, and\nit's awkward to define structure sometimes. ", "Both would benefit greatly from\nfirst class functions and programming logic, even as they are \"functional\",\njust transforming data.", "\n\nI love them both, and I hate them both. ", "Terraform is best for provisioning\ncomplex infrastructure. ", "Ansible is great for setting up instances, and it's\neasy for everyone to understand, dev and ops. ", "Here is a complete example of\ndeploying a complex, full-featured app to AWS using Terraform and Ansible:\n[https://github.com/cogini/multi-env-deploy](https://github.com/cogini/multi-\nenv-deploy)\n\nI feel like we are suffering through a period where the tools are immature.", "\nPeople are focusing on syntax, but we are missing fundamental parts of the way\nthe system should work. [", "https://www.cogini.com/blog/is-it-time-for-lisp-in-\ndevops/](https://www.cogini.com/blog/is-it-time-for-lisp-in-devops/)\n\nThe exact same thing is going on in the Kubernetes world. ", "Back in the .com\ndays, we would laugh at the \"HTML programmers\", but now we are \"YAML\nprogrammers\".", "\n\nThere are a couple of fundamental ways of managing the new cloud systems, all\nof which are better or worse depending on what you are doing. ", "There are\ndeclarative systems like Terraform or CloudFormation. ", "There is imperative with\ntasks, like Ansible. ", "There are things that talk directly to the API like boto.", "\nThere are tools like Pulumi which take a library approach in a general purpose\nprogramming language. ", "Dockerfiles are crying out for higher level solutions,\nwhich are being developed. ", "Ultimately I like the approach of a dedicated\nsyntax like Terraform, but with more programming capability, or Pulumi.", "\n\n~~~\nspecialist\nYour description of Ansible makes me think of the Apache Ant build system.", "\nJames Duncan Davidson's post mortem was illuminating. ", "He never intended to\ncreate executable XML scripting.", "\n\nAm noob. ", "Have done a wee bit of CloudFormation, Docker, k8s. ", "And once\ncompleted a Terraform howto. ", "I've never touched Ansible, Chef, Puppet, etc.", "\n\nI'd love a feature comparison matrix. ", "Or maybe a decision flowchart on how to\nchoose which tool for which job.", "\n\n\\--\n\nUpdate: This comparison was linked upthread. ", "It's pretty good.", "\n\n[https://blog.gruntwork.io/why-we-use-terraform-and-not-\nchef-...](https://blog.gruntwork.io/why-we-use-terraform-and-not-chef-puppet-\nansible-saltstack-or-cloudformation-7989dad2865c)\n\n~~~\njake_morrison\nBig fan of terragrunt.", "\n\n------\npiahoo\nterraform manages infrastructure (e.g. creating VM). ", "ansible manages\nconfiguration (e.g. installing tools on fresh VM)\n\n~~~\nh91wka\nTo be fair, one can manage infrastructure with Ansible too.", "\n\n~~~\ntoyg\nAnd one can manage configuration with Terraform too, via null-resource blocks\nand so on.", "\n\n------\nrad_gruchalski\nObligatory plug, you can use both together:\n[https://github.com/radekg/terraform-provisioner-\nansible](https://github.com/radekg/terraform-provisioner-ansible) I’m the\nauthor.", "\n\n" ]

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[ "1964 Humboldt State Lumberjacks football team\n\nThe 1964 Humboldt State Lumberjacks football team represented Humboldt State College during the 1964 NCAA College Division football season. ", "Humboldt State competed in the Far Western Conference (FWC).", "\n\nThe 1964 Lumberjacks were led by head coach Phil Sarboe in his 14th year at the helm. ", "They played home games at the Redwood Bowl in Arcata, California. ", "Humboldt State finished with a record of eight wins and two losses (8–2, 4–1 FWC). ", "The Lumberjacks outscored their opponents 181–81 for the season.", "\n\nSchedule\n\nTeam players in the NFL\nNo Humboldt State players were selected in the 1965 NFL Draft.", "\n\nNotes\n\nReferences\n\nHumboldt State Lumberjacks\nCategory:Humboldt State Lumberjacks football seasons\nHumboldt State Lumberjacks f" ]

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[ "The Institute is presided by a dean who is in charge of its management. ", "He may appoint attending deans or assisting deans to help him accomplish his duties after consultation with His Beatitude and the president of the university." ]

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[ "Top 10 Best Billiards and Pool Table Covers Reviews In 2019\n\nPlaying billiards is always a lot of fun when you are with your companions. ", "However, your pool table needs a lot of maintenance. ", "Especially, It needs to be protected from dust to keep it in fine condition. ", "But how can you do that? ", "Well, the answer is pretty simple. ", "You need to opt for the billiards and pool table covers. ", "Manufactured from only nonpareil materials, these covers protect your board from all kinds of damage and keep it ready for playing at all times.", "\n\nHowever, all sorts of confusion always linger in our mind. ", "Thus, a researched solution is at your reach. ", "Go through our list where we have reviewed the top 10 billiard and pool table covers in detail. ", "Give no second thoughts and get to know about its authenticity.", "\n\n10. ", "Iszy Billiards 8ff Heavy Duty Pool Table Billiard Cover\n\nA perfect fit for 8-foot pool tables, this cover would be of great help when you want to preserve the expensive pool table at your club or man cave. ", "Constructed of tough vinyl, it can withstand the onslaught of various elements like dust and moisture while keeping your table out of harm’s way. ", "Best for indoor pool tables, this cover would last you for ages.", "\n\n9. ", "GSE Games & Sports Leatherette Billiard and Pool Table Cover\n\nPets have sharp claws and your pool table isn’t immune to drink spills either. ", "The pool table covers from GSE is created of vinyl that is heavy duty and strong enough to resist all that damage as well as keep your pool table nice and safe. ", "The material is even wrinkle-free, so you don’t have to worry too much about maintenance either.", "\n\nKey features\n\nThe corners are weighted and fabric joints are machine sewn.", "\n\nImprovised durability.", "\n\nGreat for 8 feet and 9 feet tables.", "\n\n8. ", "Imperial Billiard and Pool Table Fitted Naugahyde Cover\n\nInstead of vinyl, Imperial has decided to use Naugahyde for manufacturing this cover. ", "Naugahyde with superior quality is always better than vinyl due to its better potency in handling abuse. ", "It properly covers the top and even the side aprons, giving all-round protection for your prized table. ", "It is available in various sizes for various pool tables so that you can buy this excellent product without needing to settle for inferior options.", "\n\nKey features\n\nHas a weight of only 1.4 pounds.", "\n\nNearly 2-inches thick.", "\n\nThe pool table cover fitting is excellent.", "\n\n7. ", "Billiard Depot Leatherette Pool Table Cover & Billiard Table Cover\n\nDue to the leatherette finish, this exquisite quality vinyl cover gives off a very premium and luxurious feel. ", "It hangs 7.5-inches at the sides covering both the top surface and all the important portions on the side. ", "Furthermore, it has high-durability and will last you for an undefeated time since it has seams that are reinforced and boast double stitch. ", "Its backing isn’t ordinary either since it doesn’t spoil your felt with the occasional shedding that other covers go through.", "\n\n6. ", "Boshen Heavy Duty Leatherette Billiard Pool Table Cover\n\nThis billiard table cover for sale comes with a lot of promise and expectation. ", "If you have a pool table of 7, 8 or 9 feet, you can buy this cover without worries to give your table its deserved protection. ", "The leatherette cover has a backing made of cotton fleece to last you for prolonged periods with minimal maintenance. ", "With the cover on, your furry friends won’t be damaging the felt top either.", "\n\nKey features\n\nIt weighs 6.08 pounds\n\nSudden spills, damage or dust will cause no harm.", "\n\nDrape size is 8 inches.", "\n\nWill not wrinkle or get crushed.", "\n\n5. ", "Yves Empire USA Deluxe Dark Brown Leatherette Pool Table Cover\n\nAvailable for 7 ft, 8 ft and 9 ft pool tables, this aesthetic cover is a true piece of art that adorns your pool table and accentuates its beauty. ", "This cover is thick enough and made of heavy-duty materials to tolerate a lot of abuse and protect your table.", "\n\nKey features\n\nLimited warranty of 1 year.", "\n\nThe backing is smooth and doesn’t leave scratches on the cover.", "\n\nBoasts good quality cross stitching.", "\n\n4. ", "Brown Leatherette Billiard Table Cover by Felson Billiard Supplies\n\nFelson has been a trusted brand in the billiard industry and has created an amazing product tailored to your requirements. ", "The Naugahyde construction resists all sorts of unwanted damage that might be afflicted on the table. ", "Moreover, the weighted corners keep a firm position over the table and hang nicely. ", "You might be a business owner or an individual but the cover will awestruck you nonetheless.", "\n\n3. ", "CueStix International Pool Table Cover\n\nCueStix has made this product with great innovation while keeping the average consumer in mind. ", "Their cover protects your billiards table from cats, dust and other daily mishaps that your table has to endure. ", "Being 100-inches long and over 50-inches wide it appropriately fits your 8-inch pool table.", "\n\nKey features\n\nUnbelievably lightweight, being just 3 pounds.", "\n\nManufactured from durable Naugahyde that works better than plastic and vinyl.", "\n\n2. ", "GSE Games & Sports Expert Billiard Pool Table Cover\n\nYou don’t need to worry about unfortunate scratches, dust spills and other daily damage to your pool table with this cover. ", "Your 7ft pool table will have all-around protection as long as it has this cover on. ", "From the top, the drape hangs 7-inches to give a perimeter protection.", "\n\nKey features\n\nWeighted corners for a nice hang.", "\n\nSeams are exceptionally well-sewn to render it more durability.", "\n\nJust over 5 pounds.", "\n\n1. ", "Black Leatherette Pool Table Cover – 9 Foot Billiard Table Cover\n\nJust from sewing at the seams and feel of the cover gives you a rough gauge over the top quality manufacturing process behind this product. ", "It drapes over your 9-inches table to form a protective shield against various elements. ", "Apart from the drape, it extends over 110-inches in length and over 60-inches in width. ", "The drape forms a 7.5-inches deep periphery around your table protecting your treasure to the best of its capabilities.", "\n\nKey features\n\nSeams have a double stitch.", "\n\nMatches the look of your home.", "\n\nMuch better than plastic alternatives in the market.", "\n\nThe billiard pool table cover quality must be excellent in order to guarantee the users of the same quality service." ]

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[ "It is an indication of the pressure on Steve Mounie’s shoulders that Huddersfield Town were just the 14th highest scorers in the Championship last season. ", "For all their organisation, spirit and frenzied pressing, goals proved hard to come by.", "\n\nMounie is the man tasked with fixing the problem. ", "An £11.5 million signing from Montpellier, the ­Benin international arrived in West Yorkshire knowing he would be ­expected to adapt quickly to Huddersfield’s high-octane style of play and the rigours of English football.", "\n\nOn the evidence of 90 eye-opening minutes, he appears to have done so already. ", "It is early days yet, but Mounie’s double against Crystal Palace suggests the 22-year-old’s broad frame might well be capable of shouldering the burden of being Huddersfield’s Terrier-in-chief.", "\n\n“Now people know who I am,” he said. “", "I could not imagine a better start.”", "\n\nMounie celebrates with his Huddersfield team-mates credit: REUTERS\n\nIn truth, it was not just the goals. ", "Mounie led the line throughout, while the only real blemish was that he could and should have scored a hat-trick. ", "He dreams of emulating another powerful African forward who barrelled his way into the ­Premier League following a move from France.", "\n\n“My idol is [Didier] Drogba,” he said. “", "Sometimes I just watch video clips of him, scoring goals over here. ", "I think I have a similar style to him. ", "I am big like him.” ", "In a curious quirk of Premier League history that will presumably not be lost on Mounie, Drogba’s first goal for Chelsea also came against Palace at Selhurst Park. “", "What he did here is an inspiration to me,” Mounie said. “", "He is also African, like me, and we almost have the same story. ", "He was born in Africa and came to France and then to England. ", "I will try to follow in his footsteps.”", "\n\nFor now, though, he is still finding his own feet. “", "I am learning English and getting used to my new life over here,” he said. “", "The players call me Steve. ", "An English name.”", "\n\nMounie made an impact on his debut credit: Getty Images\n\nThe comment prompted a laugh from David Wagner, his manager. “", "When someone mentioned his name to me for the first time I said OK, he’s excellent, because his first name is English,” Wagner said. “", "The good thing is he speaks English, so we can communicate, which is always important for a manager if you like to give him our thoughts.", "\n\n“He is very open-minded, so he will ask if something is unknown for him and he is not sure what he has to do. ", "He has a great working attitude, a real Terrier attitude, which is unusual for a striker, for a goalscorer.”", "\n\nMounie’s brace, alongside an own goal from Palace’s Joel Ward, ensured a scarcely believable start to Huddersfield’s life in the Premier League and prompted chants of “We are top of the league” from their delirious supporters.", "\n\n“I know we have a real chance to stay up,” said Wagner. “", "I knew this before this game. ", "As a sportsman, a footballer, you only like to have a chance, and we have a chance. ", "What we will do out of our chance is up to us, and nobody knows.”", "\n\nFor every Huddersfield fan who dares to dream, there will be a ­Palace fan cursing this nightmare start. ", "Frank de Boer, the new ­manager, who blamed a chaotic 15-minute spell in the first half for changing the game, clearly has work to do.", "\n\nView more!", "\n\n“It is a very big lesson for us,” he said. “", "Before, we analysed the ­opponent so when they do certain things we have to have an answer on that, and we had the wrong ­answer in those 15 minutes. ", "That is football. ", "It’s hard. ", "You have to learn from this kind of thing. ", "There are still 37 games left.”", "\n\nDe Boer’s arrival was supposed to herald a new era of attractive, passing football. ", "But within 40 minutes, nervousness was coursing through Selhurst Park as the Palace defenders became increasingly shaky in possession. ", "At one point, there were even ironic cheers when goalkeeper Wayne Hennessey punted an aimless hoof downfield. “", "You have to recognise when you have to play it on the ground and when you don’t,” said De Boer. “", "In those 15 minutes, everybody saw, we played it on the ground and they pressed us. ", "It is a very expensive lesson.”" ]

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[ "IL-4-dependent IgE switch in membrane IgA-positive human B cells.", "\nIgE responses by human B cells, separated according to membrane Ig classes, were analyzed in a clonal assay using EL-4 thymoma cells as helper cells, T cell supernatant, and rIL-4. ", "In cultures seeded by means of the autoclone apparatus of the FACS, IgE responses were generated frequently by either IgM (mu+/gamma-alpha-) or IgA (alpha +/mu-)-positive B cells (16 and 14% of the Ig producing wells, respectively), but rarely by IgG (gamma +/mu-)-positive B cells (1.3% of Ig producing wells). ", "The total amounts of Ig secreted by IgM-, IgG-, or IgA-positive cells and the total proportions of responding autoclone wells (23-27%) were comparable. ", "All IgE secretion was IL-4 dependent. ", "When the Ig secretion patterns from alpha +/mu- vs alpha +/mu-epsilon- B cells were compared, most autoclone wells from both types of cells produced IgA only, and similar proportions of IgA producing wells (6.2 and 6.0%) also secreted IgE. In addition, IgE restricted responses occurred 6 times more frequently with alpha +/mu- than with alpha +/mu-epsilon- cells, which suggests that membrane IgA+E double-positive, IgE committed B cells occur in vivo. ", "The isotype pattern generated by alpha +/mu-epsilon- B cells cannot be explained by a chance assortment of separate IgA and IgE precursors or by cytophilic antibody. ", "Thus, IL-4 dependent switch to IgE occurred frequently in IgM- or IgA-positive, but rarely among total IgG-positive, B cells. ", "This could be relevant to IgE production in mucosal tissues rich in IgA expressing B cells." ]

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[ "Emergency cerclage: literature review.", "\nThis article reviews the use and effectiveness of emergency cerclage for women who present with a dilated cervix in the second trimester of pregnancy and seeks to identify predictors of favorable emergency cerclage outcomes. ", "We searched PubMed and the Cochrane Library for the period January 1995 to April 2012 and used the terms \"emergency cerclage,\" \"emergency stitch,\" \"rescue cerclage,\" and \"rescue stitch.\" ", "Thirty-four studies in which transvaginal emergency cervical cerclage was performed in women with a dilated cervix were identified and included. ", "Predictors of poor outcome were prolapsed membranes, evidence of intra-amniotic or systemic infection, symptomatic presentation, cervical dilatation greater than 3 cm, or cerclage after 22 weeks. ", "According to observational and limited randomized controlled trials, the cerclage group did significantly better than the bed-rest group in mean randomization-to-delivery interval, preterm delivery before 34 weeks, and compound neonatal morbidity. ", "The current data suggest that emergency cerclage is associated with a longer latency period and, most often, with better pregnancy outcomes when compared with bed rest. ", "Many of the predictors of adverse outcomes appear to be associated with evidence of inflammation or infection. ", "Obstetricians and gynecologists, family physicians After completing this CME activity, physicians should be better able to review the use and evaluate the effectiveness of emergency cerclage for women who present with a dilated cervix in the second trimester, to identify predictors of favorable emergency cerclage outcomes, and to compare emergency cerclage versus bed rest." ]

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[ "Efficacy and long-term patency of fenestrated amplatzer devices in children.", "\nNovel transcatheter techniques to control interatrial communications exist. ", "Devices with restrictive fenestrations can be implanted to maintain patency of an atrial septostomy, or reduce an interatrial communication. ", "Experience with these devices in children is limited. ", "Fenestrated atrial septal devices were implanted into 10 children (5 male, age 1.5-15.5 years). ", "Devices were modified by the manufacturer (MM, n = 6), or by a modification of an atrial septal occlusion device by the operator (OM, n = 4). ", "Seven devices were implanted after atrial septal puncture and septostomy for severe symptomatic pulmonary hypertension (PHT) [4 heart failure, 3 syncope], according to World Health Organisation Guidelines. ", "Two devices were implanted to reduce left to right shunting through large atrial septal defects with associated PHT. ", "One device was implanted acutely to offload the left atrium during extracorporal circulatory support prior to heart transplantation. ", "Warfarin (n = 5), aspirin (n = 4), or heparin (n = 1) were used for prevention of fenestration thrombosis. ", "Symptoms in all patients with PHT improved after implantation; syncope recurred with fenestration occlusion in one patient. ", "Nine patients were followed up to a mean of 26 months. ", "Five devices (all MM; warfarin n = 4, aspirin n = 1) remained patent on echocardiography. ", "Fenestrations occluded in 4 children after median follow-up of 10 months (MM n = 1, OM n = 3, warfarin n = 1, aspirin n = 3). ", "Implantation of fenestrated atrial devices is feasible and effective; but the occlusion rate is high. ", "Further research on fenestrated atrial septal devices with better long-term patency, and effective antithrombotic drug treatment is necessary." ]

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[ "Induction capacity and influence of dThdMP on thymidine kinase activity of type 1 and 2 strains of herpes simplex virus.", "\nThe thymidine kinase inducing ability of 104 strains of herpes simplex virus was studied comparatively. ", "A pronounced relationship was established between induction of the enzyme and the serotype of the strains. ", "As a rule, the strains of serotype 2 are weaker inducer of dThd- and dCyd-kinase activity than serotype 1 strains. ", "A certain parallelism exists between induction of both enzymes, however the activity of the thymidine kinase increases after infection with herpes simplex virus 4--5 times more than that of the dCyd-kinase. ", "Adaptation of the strains to cell cultures only slightly modifies the inducing ability of the herpes simplex virus strains. ", "The thymidine kinase activity induced by HSV-1 and HSV-2 differ from each other and are different from the cell enzyme with respect to their thermal stability at 40 degrees C. These differences are expressed more clearly in the presence of 480 muM dThdMP during inactivation. ", "dThdMP stabilizes the type 1 but not the type 2 enzyme." ]

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[ "Lü Yang\n\nLü Yang (; born 26 November 1993) is a Chinese rower. ", "She competed in the women's double sculls event at the 2016 Summer Olympics.", "\n\nReferences\n\nExternal links\n\nCategory:1993 births\nCategory:Living people\nCategory:Chinese female rowers\nCategory:Olympic rowers of China\nCategory:Rowers at the 2016 Summer Olympics\nCategory:People from Luohe\nCategory:Asian Games medalists in rowing\nCategory:Rowers at the 2014 Asian Games\nCategory:Asian Games gold medalists for China\nCategory:Medalists at the 2014 Asian Games\nCategory:World Rowing Championships medalists for China" ]

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[ "1. ", "Introduction {#sec1}\n===============\n\nReal-time ultrasound-guided central venous cannulation has been associated with higher success rates, faster access times, and a reduction in mechanical complications when compared to landmark techniques, especially for the cannulation of the internal jugular vein (IJV) \\[[@B1]--[@B6]\\]. ", "The ultrasound-guided method via a longitudinal approach has been favored since it offered another view to visualize the needle tip in the lumen and the back wall of the vein \\[[@B6]\\]. ", "However, the transverse axis approach has been the standard monoplanar ultrasound view since the introduction of the above technique \\[[@B7]\\], but it was rather problematic in visualizing the cannula and thus controlling its depth without arterial puncture or transfixion of the vein \\[[@B8], [@B9]\\]. ", "This may be particularly relevant to the intensive care unit (ICU) setting as the clarity of two-dimensional (2D) ultrasound images is oftentimes affected in critical care patients by the presence of various factors such as obesity, subcutaneous air and/or edema, trauma and mechanical ventilation, while complications may occur even under ultrasound guidance \\[[@B6]--[@B12]\\]. ", "Cannula visualization is fundamental to the safety and efficacy of all ultrasound-guided methods, but no single technology meant to improve cannula echogenicity has been widely adopted or studied in the ICU setting \\[[@B13]--[@B20]\\]. ", "Recently, a vascular cannula (VascularSono, Pajunk, GmbH, Medizintechnologie, Geisingen, Germany) incorporating \"Cornerstone\" reflectors on the distal 2 cm, to increase echogenicity, was developed based on technology previously used in regional anesthesia cannulas \\[[@B16]\\]. ", "We hypothesized that the use of an echogenic vascular cannula (EC) would improve visualization when compared with a nonechogenic vascular cannula (NEC) (Arrow Howes, PA, USA) during real-time ultrasound-guided internal jugular vein (IJV) cannulation via a transverse approach.", "\n\n2. ", "Materials and Methods {#sec2}\n========================\n\nDuring 2011, eighty patients who required central venous access were prospectively enrolled in this randomized study that was conducted in two medical-surgical ICUs. ", "Forty patients underwent EC and 40 patients were randomized to NEC. ", "The procedure was ultrasound-guided IJV cannulation via a transverse approach. ", "All patients were sedated and mechanically ventilated. ", "Randomization was performed by means of a computer-generated random-number table and patients were stratified with regard to age, gender, and body mass index (BMI). ", "Block randomization was used to ensure equal numbers of patients in the above groups \\[[@B6]\\]. ", "All physicians who performed the procedures had at least five years of experience in central venous catheter placement. ", "The study was approved by the Institutional Ethics Committee, and appropriate informed consent was obtained. ", "Chest radiography was used to assess catheter placement after the procedure. ", "Mechanical complications were defined as arterial puncture, hematoma, hemothorax, pneumothorax, and catheter misplacement \\[[@B6]\\].", "\n\n2.1. ", "Real-Time Ultrasound-Guided IJV Cannulation {#sec2.1}\n------------------------------------------------\n\nAll patients were placed in Trendelenburg position and were cannulated as described in detail by Karakitsos et al. ", "\\[[@B6]\\]. ", "Triple-lumen catheters were used in all cases and all procedures were performed under controlled, nonemergent conditions in the ICU. ", "Standard sterile precautions were utilized. ", "The EC and NEC were both 18-gauge cannulas specifically intended for use in vascular access. ", "Ultrasonography was performed with an HD11 XE ultrasound machine (Philips, Andover, MA, USA) equipped with a high-resolution 7.5--12 MHz transducer, which was covered with sterile ultrasonic gel and wrapped in a sterile sheath (Microtec medical intraoperative probe cover, 12 cm × 244 cm). ", "Vessels were cannulated using the Seldinger technique under real-time ultrasound guidance.", "\n\n2.2. ", "Data Acquisition, Study Protocol, and Outcome Measures {#sec2.2}\n-----------------------------------------------------------\n\nThe cannulation was performed by a single operator and was observed by a second physician. ", "The operators and observers were blinded to the cannula used. ", "Following each procedure, the operator and the observer were asked to score the percentage of time they were able to continuously visualize the cannula; a 10-point scale was used (ranging from 1 = 0%--10%, to 10 = 90%--100%). ", "The observer measured access time, number of attempts, and complications. ", "Access time was defined as the time between penetration of skin and aspiration of venous blood. ", "Data was collected using a standardized form and was entered in a database. ", "We documented baseline patient characteristics, side of catheterization, the presence of risk factors for difficult venous cannulation, previous difficulties during cannulation, previous mechanical complications, known vascular abnormalities, and untreated coagulopathy (international normalization ratio \\> 2; activated partial thromboplastin time \\>1.5; platelets \\<50 × 109  litre − 1) \\[[@B6]\\].", "\n\n3. ", "Statistical Analysis {#sec3}\n=======================\n\nData were expressed as mean ± standard deviation (SD). ", "The Student\\'s *t-*test for independent mean, *χ* ^2^ analysis, or Fisher\\'s exact test where appropriate were used to identify differences between the two groups. ", "A *P* value (two-sided in all tests) of \\<0.05 was considered significant. ", "Study power was based on data from a previous cannula visibility study, which were adjusted for our intervention \\[[@B19]\\]. ", "Assuming data to be nonparametric, power sample analysis gave a minimum sample size of 40 cannulations. ", "Wilcoxon rank sum test was used to compare cannula visibility data for the 2 groups. ", "The agreement between the operator and observer cannula visibility results was evaluated by Cohen\\'s weighted kappa, while 2.5th, and 97.5th percentiles of 5,000 bootstrap replicates estimated 95% confidence intervals. ", "The bootstrap is a resampling method used for estimating a distribution, from which various measures of interest can be calculated \\[[@B21]\\]. ", "Statistical analysis was performed using SPSS, version 11.0 (SPSS Inc. Chicago, IL, USA).", "\n\n4. ", "Results {#sec4}\n==========\n\nBaseline characteristics of the study population are presented in [Table 1](#tab1){ref-type=\"table\"}. ", "There were no significant differences in age, gender, body mass index (BMI), and presence of risk factors for difficult venous cannulation between the NEC and the EC groups; moreover no cases of preexisting thrombosis were identified.", "\n\nResults of cannula visibility are presented on [Figure 1](#fig1){ref-type=\"fig\"}. ", "Operators reported improved cannula visualization in the EC group when compared to the NEC group (88% ± 8% versus 20% ± 15%, resp.; *", "P* \\< 0.01). ", "Also, operators reported that when using the NEC via the transverse approach they might have visualized it, but surely have noticed its acoustic shadow ([Figure 2](#fig2){ref-type=\"fig\"}). ", "In contrast, the echogenic vascular cannula could be clearly identified, even if the insonation angle was slightly modified ([Figure 2](#fig2){ref-type=\"fig\"}). ", "Finally, the agreement between the operators and observers was statistically significant (kappa = 0.9; 95% confidence intervals assessed by bootstrap analysis = 0.87--0.95; *P* \\< 0.01).", "\n\nResults of the secondary outcomes are presented in [Table 2](#tab2){ref-type=\"table\"}. ", "Access time (5.2 s ± 2.5 versus 10.6 s ± 5.7) and mechanical complications, notably hematomas (0% versus 10%), were both decreased in the EC group compared to the NEC group (*P* \\< 0.05).", "\n\n5. ", "Discussion {#sec5}\n=============\n\nOur study demonstrated improved cannula visibility with the use of EC during ultrasound-guided IJV cannulation via a transverse approach. ", "The latter has been the standard monoplanar 2D view since the introduction of the ultrasound technique \\[[@B7]\\]. ", "Intrinsically, cannulation of a vessel using the transverse approach often limits cannula visibility; hence controlling the trajectory of the cannula may be problematic, especially when the 2D image is of low quality due to various factors (i.e., subcutaneous air and/or edema, trauma, etc.) ", "\\[[@B1]--[@B12]\\].", "\n\nNevertheless, we found that the use of EC statistically increased the likelihood of continued successful cannula visualization. ", "This could be attributed to the fact that the EC is brightly echogenic as it incorporates \"Cornerstone\" reflectors mainly arranged at the distal 2 cm of the needle. ", "These reflectors guarantee the visibility of the cannula shaft, independent of the puncture angle according to the manufacturer. ", "The principle is the same as that used in bicycle reflectors, where light is reflected back to its source regardless of the angle at which it approaches \\[[@B16]--[@B19]\\]. ", "The present results demonstrated that using the EC resulted in significantly reduced access times and mechanical complications. ", "Notably, once IJV cannulation is pursued via a transverse approach, the adjacent carotid artery may be a potential \"target\" for the cannula, especially if the operator cannot fully control its trajectory \\[[@B3]--[@B9]\\].", "\n\nThe present methodology was designed to test EC in actual clinical practice in the ICU, where image acquisition is affected or limited by the presence of various factors such as obesity, subcutaneous air, edema, trauma, and mechanical ventilation \\[[@B1]--[@B12]\\]. ", "The use of EC may improve image acquisition and success rates in technically challenging cases of vascular access. ", "Moreover, we should underline that the transverse approach is less technically demanding compared to the longitudinal one under ultrasound guidance, and thus can be easily applied by inexperienced operators \\[[@B1]--[@B12]\\]. ", "This technical \"advantage\" can be further enhanced by the implementation of echogenic cannulas, and hence resulting in a simpler ultrasound-guided method but with optimal cannula visibility results. ", "There is no definitive method for objective assessment of cannula visibility. ", "Previous studies used scoring systems with skilled observers rating static images \\[[@B14]--[@B19]\\]. ", "We aimed to examine cannula visibility during IJV cannulation, under real-time clinical conditions. ", "Although interpretation of dynamic 2D ultrasound images remains subjective, we used an analytical 10-point scale along with a dual evaluation model of operators and observers. ", "We demonstrated that high operator and observer agreement existed between the subjective estimations of cannula visibility rates. ", "The study has several limitations. ", "Despite the fact that the operators were blinded at the initiation of the procedure, the two vascular cannulas inherently exhibited different ultrasonographic appearance, and could possibly be differentiated. ", "Although we demonstrated a significant reduction in hematoma formation, we failed to find a significant reduction of major mechanical complications. ", "This may be due to the fact that our baseline mechanical complication rate was extremely low (given the fact that our study group is highly skilled in ultrasound-guided vascular access) and that the sample size was rather small. ", "Concluding, the present investigation demonstrated that echogenic technology significantly improved cannula visibility and decreased access time during real-time ultrasound-guided IJV cannulation via a transverse approach. ", "Our data provide clinical rationale to study the evolving field of enhanced echogenic ultrasound technology. ", "Further studies are required to determine if EC is cost-effective and changes overall outcomes in the ICU.", "\n\nThe authors declare that they have no financialor other interest in the echogenic vascular cannula nor do they have any financial or other affiliation with pajunk.", "\n\n{#fig1}\n\n{#fig2}\n\n###### \n\nBaseline characteristics of the study population; values are presented either in percentages or as mean ± SD.", "\n\n Characteristics EC group (*n* = 40) NEC group (*n* = 40)\n ---------------------------------------------- --------------------- ----------------------\n Age (years) 45 ± 9.5 46 ± 10.9\n Gender (male/female ratio) 0.49 ± 0.4 0.5 ± 0.5\n APACHE II score 20.6 ± 2.1 20.8 ± 2.4\n Diagnosis upon admission \n  Trauma without brain injury 15 (37.5%) 15 (37.5%)\n  Trauma with brain injury 15 (37.5%) 15 (37.5%)\n  Burn 1 (2.5%) 0 (0%)\n  ARDS 2 (5%) 2 (5%)\n  Sepsis 5 (12.5%) 7 (17.5%)\n  Postsurgical complications 2 (5%) 1 (2.5%)\n Side of catheterization (left/right) 14/26 12/28\n Body mass index (kg/m^2^) 21.1 ± 3.6 21.8 ± 3.9\n Prior catheterization 7 (17.5%) 5 (12.5%)\n Limited sites for access attempts 5 (12.5%) 5 (12.5%)\n Previous difficulties during Catheterization 9 (22.5%) 7 (17.5%)\n Previous mechanical complications 6 (15%) 4 (10%)\n Known vascular abnormality 1 (2.5%) 1 (2.5%)\n Untreated coagulopathy 1 (2.5%) 1 (2.5%)\n Skeletal deformity 1 (2.5%) 1 (2.5%)\n\nAPACHE II score: acute physiology and chronic health evaluation score II; ARDS: acute respiratory distress syndrome; NEC: nonechogenic cannula, EC: echogenic cannula.", "\n\n###### \n\nSecondary outcome measures in the EC group versus the NEC group.", "\n\n Outcome measures EC group (*n* = 40) NEC group (*n* = 40)\n ---------------------------- ------------------------- ------------------------\n Access time (sec) 5.2 ± 2.5 (4.5--12.4)\\* 10.6 ± 5.7 (8.1--17.3)\n Success rate (%) 40 (100%) 40 (100%)\n Average number of attempts 1 ± 0.2 (1--1.3) 1.1 ± 0.4 (1--1.7)\n Artery puncture 0 (0%) 1 (2.5%)\n Hematoma 0 (0%)\\* 4 (10%)\n Pneumothorax 0 (0%) 0 (0%)\n Hemothorax 0 (0%) 0 (0%)\n\nEC: echogenic cannula, NEC: nonechogenic cannula; Comparisons between the NEC and the EC group of patients; *P* \\< 0.05\\*; Access time and average number of attempts are expressed as mean ± SD (95% confidence intervals).", "\n\n[^1]: Academic Editor: Apostolos Papalois\n" ]

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[ "#!", "/bin/sh\n# Copyright 2009 The Go Authors. ", "All rights reserved.", "\n# Use of this source code is governed by a BSD-style\n# license that can be found in the LICENSE file.", "\n\nCOMMAND=\"mksysnum_plan9.sh $@\"\n\ncat <<EOF\n// $COMMAND\n// MACHINE GENERATED BY THE ABOVE COMMAND; DO NOT EDIT\n\npackage plan9\n\nconst(\nEOF\n\nSP='[ \t]' # space or tab\nsed \"s/^#define${SP}\\\\([A-Z0-9_][A-Z0-9_]*\\\\)${SP}${SP}*\\\\([0-9][0-9]*\\\\)/SYS_\\\\1=\\\\2/g\" \\\n\t< $1 | grep -v SYS__\n\ncat <<EOF\n)\nEOF\n" ]

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[ "A Weekend in Rügen Island\n\nWhat a beautiful island it is Rügen! ", "The largest island of Germany, located off the coast in the Baltic Sea and 300 km away from Hamburg. ", "Statistics say most of the German people still spend their vacation in Germany and Rügen Island is clearly one of their favourite destinations.", "\n\nFriends of mine rented an apartment in Sellin, one of the seaside resorts of Rügen Island, and had a spare room. ", "They invited me to stay with them over the weekend. ", "My answer was yes, obviously…\n\nRügen is a big island with a total area of 974 km² with lots of attractions. ", "From all the things one can do in the island, I picked a couple for the weekend. ", "Here are my highlights for you, in case you find your way to Rügen.", "\n\nSellin Pier\n\nMy tour started in Sellin which is a very beautiful town indeed. ", "The 394 meters long pier is the most famous landmark of Sellin, which is also famous with its beautiful resort villas with Art Nouveau architecture.", "\n\nSellin is located directly at a long wide sandy beach and there are many cafés and restaurants which make this town perfect as base for the stay in Rügen.", "\n\nPhoto by Ingmar Sörgens – check out his Flickr profile for more\n\nProra\n\nOn our way to the white chalk cliff in Jasmund National Park we first drive by Prora which is one of those ugly faces of the history. ", "It was build (not fully completed) by Nazi Germany as a resort planned by the “Strength through Joy” organisation.", "\n\nSince 2004 the local government started to sell the ugly cement blocks to investors and today there are already hotels and apartments for tourists. ", "Driving around here was really not a joy at all and I would never ever understand the people who would want to stay in such a horrible ugly place with even more horrible and ugly history.", "\n\nI didn’t take photos of Prora. ", "Here is a photo of the beautiful magical forest instead.", "\n\nWhite Chalk Cliffs\n\nI quickly forgot about my bad mode as soon as we arrived in Jasmund National Park. ", "We parked the car in Hagen and walked 3 km till Königsstuhl (King’s Chair) through a beautiful forest.", "\n\nKönigsstuhl lies at 118 m above sea level and from here you have breathtaking views of the Baltic Sea. ", "The white chalk cliffs of Königsstuhl can be best seen from Victoria View. ", "The legend says the person who first climbed the cliff became the king.", "\n\nAdmission fee: 8,50€\nFrom/to Königsstuhl you can also take the bus from/to Hagen or Sassnitz.", "\n\nWe ended our tour for that day in Sassnitz which is famous for its port, not away from the Jasmund National Park.", "\n\nRasender Roland\n\nJep, this is the first train I heard of with a nickname: Rushing Roland. ", "With its 100 year old locomotives it is also the cutest train I drove with. ", "The steam-powered narrow gauge railway is definitely a highlight and perfect medium to get to some of the main destinations in Rügen.", "\n\nWe drove with the Rushing Roland with a speed of 30 km per hour (not sure why they call it “rushing”) through breathtaking landscapes till Lauterbach which has a beautiful harbour and “swimming” houses.", "\n\nYellow Fields\n\nWho followed me in Instagram during my stay in Rügen already know how flashed I was with the bright colours of these fields. ", "The green of the trees, the blue of the sky, the white of the clouds and the yellow of the rape plants (canola) just took me away in a happy world for a while.", "\n\nThe views of these endless fields were so beautiful that I couldn’t stop taking pictures of them." ]

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[ "class DwarfFortress < Formula\n desc \"Open-ended rogelike game\"\n homepage \"http://bay12games.com/dwarves/\"\n # The final PowerPC-compatible release\n url \"http://www.bay12games.com/dwarves/df_28_181_40d_m.zip\"\n version \"0.28.181.40d\"\n sha256 \"12c0ef27ef87bcdbb47d02cb9f3285351986c4ebfca3ebd3374b70b55ee4debe\"\n\n depends_on :x11\n\n def install\n (bin/\"dwarffortress\").write <<-EOS.undent\n #!", "/bin/sh\n exec #{libexec}/Dwarf\\\\ Fortress.app/Contents/MacOS/Dwarf\\\\ Fortress\n EOS\n rm_rf \"sdl\" # only contains a readme\n libexec.install Dir[\"Dwarf Fortress 0.28.181.40d/*\"]\n end\nend\n" ]

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[ "\"What you doing?\" \"", "You said clean up.\" \"", "I'm cleaning up.\" \"", "You can't just throw everything in the closet.\" \"", "Hey, you can tell me what to do or you can tell me how to do it, but you can't do both;\" \"this isn't sex.\" \"", "What if someone looks in there?\" \"", "They're just coming over for dinner.\" \"", "No one's gonna look in the closet.\" \"", "Well, you don't know that.\" \"", "What if someone's looking for the bathroom and they open that door?\" \"", "Could work out.\" \"", "For all we know, there's a toilet in there somewhere.\" \"", "Fine.\" \"", "But after tonight, we need to get a handle on this mess.\" \"", "You know what we should do?\" \"", "We should show the closet to Sheldon.\" \"", "Why?\" \"", "Are you kidding?\" \"", "He's like a savant at organizing.\" \"", "Everything in his apartment has a label on it.\" \"", "Including his label maker, which has a label that says \"Label Maker.\"\" \"", "And if you look really close at that label maker label, you'll see a label that says \"Label.\"\" \"", "He's our guest;\" \"we can't just ask him to straighten our closet.\" \"", "No, we wouldn't ask him.\" \"", "We'd just show him the closet and let the goblins in his head take it from there.\" \"", "Hey, guys, come on in.\" \" ", "Hi.\" \" ", "Hi.\" \" ", "Ooh, it smells good.\" \" ", "Thanks.\" \"", "And, Sheldon, I know tonight's the night you eat Thai food, so I went to the Asian market, got all the ingredients and made it from scratch.\" \"", "Oh, you shouldn't have.\" \"", "Oh, it's my pleasure.\" \"", "No, you really shouldn't have.\" \"", "I brought my own.\" \"", "You stopped and got him takeout?\" \"", "I had no choice.\" \"", "He kept kicking the back of my seat.\" \"", "Sheldon, I've been cooking all day.\" \"", "Well... now don't you feel silly.\" \"", "Show him the closet.\" \"", "♪ Our whole universe was in a hot, dense state ♪\" \"♪ Then nearly 14 billion years ago expansion started...\" \"Wait!\" \"", "♪\" \"♪ The Earth began to cool\" \"♪ The autotrophs began to drool, Neanderthals developed tools ♪\" \"♪ We built the Wall ♪ We built the pyramids ♪\" \"♪ Math, Science, History, unraveling the mystery ♪\" \"♪ That all started with a big bang ♪\" \"♪ Bang!\" \"", "♪\" \"♪ The Big Bang Theory 6x19 ♪ The Closet Reconfiguration Original Air Date on March 13, 2013\" \"== sync, corrected by elderman == Resync for WEB-DL by Norther\" \"These spring rolls are amazing.\" \"", "Good job, Bernadette.\" \"", "That's the takeout that Sheldon brought.\" \"", "Oh, well, I'm sure they wouldn't have tasted nearly as good if I hadn't tried your food first.\" \"", "Howard, did you want your clothes arranged seasonally or by color?\" \"", "Color's fine.\" \"", "Wrong, they'll be arranged seasonally.\" \"", "Sheldon, aren't you gonna spend a little time with Amy?\" \"", "Oh, it's okay, I'm used to it.\" \"", "The other day at Whole Foods, he spent an hour optimizing the cheese aisle.\" \"", "Yeah, and some thanks I got.\" \"", "The assistant manager chased me out with an artisanal salami.\" \"", "His quirks just make you love him more.\" \"", "Someone please agree with me.\" \"", "Sheldon, come on.\" \"", "It's getting late.\" \"", "Time to go.\" \"", "Oh, five more minutes.\" \"", "That's what you said five minutes ago.\" \"", "Amy and Penny are already in the car.\" \"", "Let's move it.\" \"", "How come I never get to do anything I want to do?\" \"", "You know, if he really wants to stay and finish,\" \"I can give him a ride home.\" \"", "Please, Leonard!\" \"", "He said it's okay!\" \"", "Sheldon, it's\" \"Wait, I can go home without you?\" \"", "Bye!\" \"", "Howard, I have a few questions.\" \"", "I found three bowling pins.\" \"", "Now, do you juggle these, or are you missing seven?\" \"", "Juggle.\" \"", "You health nuts kill me.\" \"", "Oh, my God, it's beautiful!\" \"", "Look, he found the juggling pins I hid.\" \"", "Uh, just a couple more items.\" \"", "Howard, I found this letter from your dad in a box.\" \"", "Now, based on the content, it could either be filed...\" \"Whoa, you opened this?\" \"", "Well, I had to find out if it was personal correspondence or memorabilia.\" \"", "Now, as I was saying, based on the content...\" \" I couldn't be less interested.\" \"", "Now, come on, I'll take you home.\" \"", "Howard, don't you want to know what's in the letter?\" \"", "If I wanted to know, I would've opened it years ago.\" \"", "The closet looks great.\" \"", "Let's get out of here.\" \"", "Wait, can I bring this box of extra shirt buttons to sort on the ride?\" \"", "Do whatever you want.\" \"", "Thanks.\" \"", "Oh.\" \"", "Great party.\" \"", "You know, when I first met Howard, he would pull his scrotum out of his shorts and say, \"Oh, I sat in gum.\"\" \"", "What is your point?\" \"", "Well, it's just kind of weird how grown up he is now.\" \"", "Happily married guy throwing dinner parties.\" \"", "Really?\" \"", "You couldn't just say that?\" \"", "You had to tell the scrotum story?\" \"", "Trying to paint a picture.\" \"", "Yeah, it was a nice change of pace not eating takeout around a coffee table.\" \"", "Mm, you know, we could throw a dinner party, too.\" \"", "Maybe even ask everyone to get dressed up.\" \"", "Sure.\" \"", "Just, when you say \"dressed up,\" you mean nice clothes, right?\" \"", "Not, like, capes and tights and crap?\" \"", "Yeah.\" \" ", "Although...\" \" No!\" \"", "Howie, you okay?\" \"", "Yeah, I just...\" \"couldn't sleep.\" \"", "Told you you shouldn't have espresso after dinner.\" \"", "I know the little cups make you feel big, but it's not worth it.\" \"", "It's this stupid letter.\" \"", "Did you read it?\" \"", "No.\" \" ", "You must be curious.\" \" ", "Of course I'm curious.\" \"", "I haven't seen the man since, oh, I was a little kid.\" \"", "And a letter shows up on my 18th birthday?\" \"", "What's that about?\" \"", "Why don't you read it?\" \"", "Maybe he apologizes or explains why he left.\" \"", "He abandoned me and my mother.\" \"", "Why does he deserve a chance to explain anything?\" \"", "I get that.\" \"", "So, what do you want to do with it?\" \"", "Something I should've done a long time ago.\" \"", "Really?\" \"", "Are you sure?\" \"", "Yep.\" \"", "Feel better?\" \"", "I do.\" \"", "Great.\" \"", "Neither one of us is tall enough to reach that.\" \"", "I can't believe he set it on fire.\" \"", "Yeah, just seeing that letter really freaked him out.\" \"", "And he was already having a tough day 'cause he accidentally wore my pants to work.\" \"", "I don't know why he was upset.\" \"", "They were bigger on him than me.\" \"", "Boy, I'm really curious what's in that letter.\" \"", "Me, too, but I guess now we'll never know.\" \"", "Well, you said Sheldon read it.\" \"", "Why not ask him?\" \"", "I can't do that.\" \"", "What kind of wife would I be if I didn't respect my husband's privacy?\" \"", "What if I ask Sheldon, you just happen to be in the room?\" \" ", "That works.\" \" ", "Okay.\" \"", "Blech.\" \"", "Like cleaning out the entire building's belly button.\" \"", "Hey, Sheldon.\" \"", "Oh, hello.\" \"", "What can I do for you ladies?\" \"", "You have something we want.\" \"", "Oh, dear.\" \"", "My mother warned me this is what happens to pretty boys in the big city.\" \"", "No, we just want information.\" \"", "Oh.\" \"", "Oh, I've got that in spades.\" \"", "Ravage me.\" \"", "We heard you read the letter from Howard's father.\" \"", "I did.\" \" ", "What did it say?\" \" ", "Yeah...\" \"I can't tell you that.\" \"", "I'm bound by closet organizer/ organizee confidentiality.\" \"", "Sheldon, that's not a real thing.\" \"", "Well, neither is the rule that you have to hold your girlfriend's hand at the movies.\" \"", "You know.\" \"", "That doesn't stop you from pawing at me like you're a bear and I'm a trash can full of sweets.\" \"", "Why do you even care?\" \"", "Just tell us what it says.\" \"", "Control over the information contained in that letter belongs to Howard.\" \"", "By happenstance, I came to know it.\" \"", "That doesn't give me the right to disseminate it freely.\" \"", "Come on.\" \"", "Look, the letter was found in Bernadette's closet.\" \"", "Doesn't that count for something?\" \"", "Are you pointing out that California is a community property state, and since Howard and Bernadette are married, the intellectual property contained in that letter is jointly owned by the two spouses?\" \"", "Yeah, obviously.\" \"", "Well played.\" \"", "Sometimes I don't give you enough credit, Penny.\" \"", "Dude, you made the right choice coming to me for help with this party.\" \"", "Actually, all I did was invite you.\" \"", "Well, put your mind at ease.\" \"", "I'm here to make sure your dinner party kicks Howard's dinner party's ass.\" \"", "Now, the first thing we need is a theme.\" \"", "I'm thinking... ah, turn-of-the-century Moulin Rouge.\" \"", "I'm thinking you need a testosterone patch.\" \"", "Penny and I just want to do something low-key.\" \"", "You know, cocktails, light jazz music, hors d'oeuvres.\" \"", "So your theme is \"I saw a rerun of Mad Men and bought some crab puffs from Trader Joe's\"?\" \"", "Hate to miss that.\" \"", "Hey, where have you been?\" \"", "Oh, Leonard.\" \"", "If I was prone to sarcasm,\" \"I'd say I was pulling off a major heist at the museum of laundry baskets.\" \"", "One, two, three, four, five, six, seven, eight, nine, ten.\" \"", "I meant, \"Golly, Sheldon, you've been gone a long time.\"\" \"", "Oh.\" \"", "Yeah, well, I was waylaid by Penny, Bernadette and Amy.\" \"", "They made me reveal confidential information about Howard's father.\" \"", "What information?\" \"", "I can't tell you that.\" \"", "I am bound by closet organizer/ organizee confidentiality.\" \"", "Well, come on, we won't tell anyone.\" \"", "Sorry, badgering me won't work.\" \"", "What you should have said is, \"It's pointless to keep this a secret because Penny will tell us.\"\" \" ", "Fine, then that.\" \" ", "All right, I'll tell you.\" \"", "My goodness, everyone's on their game today.\" \"", "This is really fun.\" \"", "Yeah, it's nice to get dressed up once in a while.\" \"", "Yeah, and hors d'oeuvres are delightful.\" \" ", "As is the company.\" \" ", "Aw.\" \"", "My shirt is itchy and I wish I were dead.\" \"", "Hey, uh, listen, everybody.\" \"", "Before Howard gets here, let's all just agree to not bring up the letter from his father.\" \" ", "Of course.\" \" ", "Sure.\" \" ", "Absolutely.\" \"", "If I say yes, can we turn off that Latin orgy music?\" \"", "Ridiculous that we still have to walk up all these flights of stairs.\" \"", "Yeah, try doing it in heels.\" \"", "I am.\" \"", "Wait.\" \"", "There's something I have to tell you.\" \"", "What?\" \"", "I know what was in your dad's letter.\" \"", "Sheldon, I swear to God, I'm gonna kill you!\" \"", "Hey!\" \"", "I made him tell us.\" \"", "What? \"", "Us\"?\" \"", "Who else knows?\" \" ", "I know.\" \" ", "Me, too.\" \"", "Same here.\" \"", "Shame on all of you.\" \"", "You know, too.\" \"", "Couldn't leave him with one friend, could you?\" \"", "So everybody knows what's in that letter except for me?\" \"", "Yes, it's six against one.\" \"", "Stand down, sir.\" \"", "How could you do this?\" \"", "I'm sorry.\" \" ", "If you want, we could tell you.\" \" ", "No, I don't want to know!\" \"", "I mean,\" \"I do, but...\" \"I got to go.\" \"", "Used me as a human shield?\" \"", "I panicked.\" \"", "He looked taller than usual.\" \"", "Howard?\" \"", "In here.\" \"", "I'm sorry.\" \"", "I should have left it alone.\" \"", "It's okay.\" \"", "Sorry I ran off like that.\" \"", "What are you looking at?\" \"", "Uh, pictures of my dad and me when I was a kid.\" \" ", "That's nice.\" \" ", "I got to tell you, as angry as I am at Sheldon for blabbing, he did a hell of a job organizing this closet.\" \"", "Look at this.\" \"\"", "Photos of Wolowitz family before father left forever.\"\" \"", "Check out nine-year-old Howie with cornrows.\" \"", "Neither race was happy to see me with those.\" \"", "Think you could take a break?\" \"", "Why?\" \"", "Got a little surprise for you.\" \"", "Come on.\" \"", "Oh, honey...\" \"I am in no mood to have sex tonight.\" \"", "I mean, I'll lay there if you absolutely have to have it, but...\" \"Oh.\" \"", "What are you guys doing here?\" \"", "When you left, you weren't sure whether or not you wanted to know what was in your dad's letter, so we came up with kind of a cool solution.\" \"", "Oh, yeah, what's that?\" \"", "It's simple, really.\" \"", "It occurred to me that knowing and not knowing can be achieved by creating a macroscopic example of quantum superposition.\" \"", "The-the principle that a physical system exists partially in all its possible states at once.\" \"", "We were all thinking it, really.\" \"", "It was kind of the elephant in the room, so...\" \"Anyway, um, I realize if we each present you with an account of what your father wrote to you, only one of which is true, and then we don't tell you which one it is, you will forever be\" \"in a state of epistemic ambivalence.\" \"", "Yeah.\" \"", "And I said if it wasn't epistemic, we might as well not do it.\" \"", "Sit down, honey.\" \"", "Raj, you're up.\" \"", "Okay, um...\" \"It was a card for your 18th birthday.\" \"", "Inside it said,\" \"\"Happy birthday, Howard.\" \"", "I love you.\" \"", "Dad.\"\" \"", "Oh, and it was a Far Side card, the one where the frog has its tongue stuck to the underside of an airplane.\" \"", "Thinks it's a fly.\" \"", "Silly frog.\" \"", "So funny.\" \"", "Sheldon.\" \"", "It was a map leading to the lost treasure of famous pirate One-Eyed Willy.\" \"", "Nice try.\" \"", "That's the plot for Goonies.\" \" ", "Told you.\" \" ", "Don't.\" \"", "Amy.\" \"", "You didn't know it, but your father was in the auditorium at your high school graduation.\" \"", "And he cried because he was so proud of you.\" \"", "Really?\" \"", "Or that's complete poppycock which Amy made up.\" \"", "It still could be the map.\" \"", "Penny.\" \"", "It was a letter explaining that your dad wasn't who he said he was.\" \"", "Eventually, his other life caught up to him, and the only way to keep you and your mom safe was to leave.\" \"", "I would like to change mine.\" \"", "The pirate's name was Peg-Leg Antoine.\" \"", "Now it's completely different from Goonies.\" \" ", "No, it's not.\" \" ", "Don't.\" \"", "Okay, my turn.\" \"", "Your dad wrote about how family is the most important thing, and that you should never throw it away like he did.\" \"", "Hmm.\" \"", "Bernadette.\" \"", "Inside the envelope was a picture of your dad holding you the day you were born.\" \"", "On the back he wrote,\" \"\"Howard, my son, my greatest gift.\"\" \"", "You okay?\" \"", "Yeah.\" \"", "I'm terrific.\" \"", "So...?\" \"", "Which one do you think it is... matey?\" \"", "Actually, I don't want to know.\" \"", "I... want all of them to be true.\" \"", "Well, one of them is.\" \"", "That's pretty cool.\" \"", "Thank you, guys.\" \"", "Hey, it's still early.\" \"", "Why don't we go back and have that party?\" \" ", "Yeah, cool.\" \" ", "Okay?\" \"", "Good.\" \"", "You know, surprisingly, uh, the letter from your father wasn't the most interesting thing\" \"I read in the closet.\" \"", "Bernadette's diary has some saucy passages.\" \"", "Sheldon, don't you dare!\" \"", "Th-There's nothing to worry about.\" \"", "Your secret's safe with me.\" \"", "That's more like it.\" \"", "Although copyright law would allow me to quote snippets in the context of a review.\" \"", "Glad you're feeling better.\" \"", "Me, too.\" \"", "If I'd known we were gonna be dancing, would have worn my flats.\" \"", "This turned out pretty well, huh?\" \"", "Yeah, I think so.\" \"", "I agree.\" \"", "That is, if you've never been to or heard of a party before.\" \"", "If you'd let me pierce your brain with a hot needle in the right place, you'd be happy all the time.\" \"", "Uh, Penny,\" \"I-I have a couple of questions about your closet.\" \"", "Is there any reason you're keeping this dead goldfish?\" \"", "Damn, I forgot to feed him.\" \"", "And that I had him.\" \"", "Well, now, did you also have a dog?\" \"", "Because I found what appears to be a battery-operated chew toy.\" \"", "Party's over!\" \"", "Party's over!\" \"", "== sync, corrected by elderman == Resync for WEB-DL by Norther\"" ]

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[ " United States Court of Appeals\n FOR THE EIGHTH CIRCUIT\n _____________\n\n No. ", "97-3344\n _____________\n\nPatricia Peters, *\n *\n Plaintiff - Appellant, *\n *\n v. *\n *\nMarvin Runyon, in his official *\ncapacity as Postmaster General of the *\nUnited States, *\n * Appeal from the United States\n Defendant - Appellee, * District Court for the\n * Western District of Missouri.", "\nPat Barba, in her individual and *\nofficial capacity as Manager of * [UNPUBLISHED]\nCustomer Service, Kansas City Area *\nUnited States Postal Service; James *\nWood, in his individual and official *\ncapacity as Postmaster, Kansas City, *\nMissouri; Phil Stabler, in his *\nindividual and official capacity as *\nManager of Customer Service, Kansas *\nCity Area, United States Postal Service, *\n *\n Defendants. ", " *\n _____________\n\n Submitted: March 10, 1998\n Filed: March 18, 1998\n _____________\n\fBefore BOWMAN, FLOYD R. GIBSON, and MORRIS SHEPPARD ARNOLD,\n Circuit Judges.", "\n _____________\n\nPER CURIAM.", "\n\n The District Court1 dismissed plaintiff's employment-discrimination complaint\nfor lack of subject matter jurisdiction. ", "Plaintiff appeals. ", "Finding no error of law, we\naffirm on the basis of the District Court's thorough and well-reasoned opinion. ", "See 8th\nCir. ", "R. 47B.\n\n A true copy.", "\n\n Attest:\n\n CLERK, U.S. COURT OF APPEALS, EIGHTH CIRCUIT.", "\n\n\n\n\n 1\n The Honorable Dean Whipple, United States District Judge for the Western\nDistrict of Missouri.", "\n\n -2-\n\f" ]

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[ "Authorities in Rowan County have arrested a convicted felon after a search of his home turned up a loaded .22 revolver and two long guns.", "\n\nArea media outlets report that after a search of 56-year-old Anthony Worth Wyrick's home in Gold Hill turned up the firearms as well as prescription pain medication, a second search warrant for a bank safety deposit box turned up more than $16,000 in cash.", "\n\nWyrick is charged with one count of felony possession of a firearm. ", "He was being held in the Rowan County Detention Center under a $10,000 secured bond. ", "It's not known if he has an attorney.", "\n\nWyrick, who was arrested after last Friday's search, has been convicted for a number of crimes, including felony second-degree rape and felony breaking and entering." ]

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[ "There are people who believe that in Spongebob Squarepants' laugh they can hear the eternal dance of the infinite, collapsing solar systems, new planets being forged in unimaginable furnaces of the stars." ]

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[ "The examination of mushroom poisonings at Akita University.", "\nIn the past 10 years from 1991 to 2000, the number of consultations to the Japan Poison Information Center were 947 concerning mushroom poisonings. ", "However, those from the hospital cases were not analyzed toxicologically. ", "We examined toxicologically 20 cases (35 patients) of mushroom poisonings from 1993 to 2001. ", "Investigation of amanita toxin poisoning was requested in 19 cases. ", "We could detect the amanita toxin, amanitin, and phalloidin, in two cases, which resulted in concluding the cause of death. ", "A fatal case by the magic mushroom poisoning was analyzed in the blood, urine, and mushroom, and we detected the hallucinogenic substances from the body fluids and ingested mushrooms. ", "We report the results of our examinations, and point out the usefulness of the examination of the mushroom itself and biological samples toxicologically for forensic practice." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Apple is today introducing an Apple Music plan aimed at students. ", "The service is identical in features to the standard plan but rather than paying $9.99 per month, qualifying students can subscribe to Apple Music for $4.99 per month. ", "The offering is rolling out today in the United States, the United Kingdom, Germany, Australia and more countries (via TechCrunch). ", "Prices vary per region but the discount should be around 50% of the normal Apple Music price.", "\n\nTo qualify, students must be currently attending an eligible university or college and gain the discount for up to four years. ", "Apple has partnered with UNiDAYs to verify people who sign up to the student plan are legitimate students attending a school.", "\n\nExisting Apple Music subscribers can migrate to the cheaper student tier if they qualify. ", "Check Apple Music settings to change tiers. ", "The addition of the student tier brings Apple Music in lockstep with Spotify which offers a similar discounted plan for customers in education (again representing a 50% discount from their normal Spotify Premium plan).", "\n\nApple announced it has reached 13 million paying Apple Music subscribers as of last week. ", "No doubt a new student plan will entice further sign ups. ", "Apple Music is expected to receive a significant design overhaul with iOS 10 with a new black and white theme, larger artwork and more. ", "9to5Mac has also reported that the company will partner with labels to add automatic lyrics support to most songs.", "\n\nThe company continues to offer a three month service trial, so new users to the service can try out Apple Music for free without a monetary commitment. ", "Subscribe to Apple Music for $9.99 per month … or $4.99 per month with the student discount, which is rolling out today. ", "The company also offers a generous Family Plan, allowing up to six people to use Apple Music for $14.99 per month.", "\n\nFTC: We use income earning auto affiliate links. ", "More.", "\n\nCheck out 9to5Mac on YouTube for more Apple news:" ]

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[ "New microscopic pushbroom hyperspectral imaging system for application in diabetic retinopathy research.", "\nTo aid ophthalmologists in determining the pathogenesis of diabetic retinopathy and in evaluating the effects of medication, a microscopic pushbroom hyperspectral imaging system is developed. ", "40 healthy Wistar rats of half gender are selected in this study. ", "They are divided into three groups (six rats failed to be models). ", "10 normal rats as the normal control group, 12 diabetic rats without any treatment as the model control group, and another 12 diabetic rats treated with LCVS1001 as the LCVS1001 group. ", "The microscopic hyperspectral image of each retina section is collected and processed. ", "Some typical spectrum curves between 400 and 800 nm of the outer nuclear layer are extracted, and images at various wavelengths are analyzed. ", "The results show that a small trough appears near 522.2 nm in the typical spectrum curve of the model control group, and the transmittance of it is higher than that of the normal control group. ", "In addition, the spectrum of the LCVS1001 group changes gradually to the normal spectrum after treatment with LCVS1001. ", "Our findings indicate that LCVS1001 has some therapeutic effect on the diabetic retinopathy of rats, and the microscopic pushbroom hyperspectral imaging system can be used to study the pathogenesis of diabetic retinopathy." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Q:\n\nHaskell lifetime of memoized function bound to record instance\n\nFirst of all, I'm a beginner in Haskell so be kind :)\nConsider the following example:\n{-# LANGUAGE RecordWildCards #-}\n\ndata Item = Item {itemPrice :: Float, itemQuantity :: Float} deriving (Show, Eq)\ndata Order = Order {orderItems :: [Item]} deriving (Show, Eq)\n\nitemTotal :: Item -> Float\nitemTotal Item{..} = itemPrice * itemQuantity\n\norderTotal :: Order -> Float\norderTotal = sum . ", "map itemTotal . ", "orderItems\n\nIs it possible to memoize the function orderTotal so it only execute once per \"instance\" of an Order record and, this is the tricky part, the cache entry bound to this instance is eliminated once this order is garbage collected? ", "In other words, I don't want to have a cache that keeps growing forever.", "\nEdit after comments:\nIndeed, in this simple example the overhead of memoization probably doesn't pay off. ", "But you can imagine a scenario where we have a complex graph of values (e.g. order, order items, products, client...) and lots of derived properties that operate on these values (like the orderTotal above). ", "If we create a field for the order total, instead of using a function to compute it, we have to be very careful to not end up with an inconsistent order.", "\nWouldn't be nice if we can express these data interdependencies declaratively (using functions instead of fields) and delegate the job to optimize these calculations to the compiler? ", "I believe that in a pure language like Haskell this would be possible, although I lack the knowledge to do that. ", "\nTo illustrate what I'm trying to say, look at this code (in Python):\ndef memoized(function):\n function_name = function.__name__\n\n def wrapped(self):\n try:\n result = self._cache[function_name]\n except KeyError:\n result = self._cache[function_name] = function(self)\n return result\n\n return property(wrapped)\n\nclass Item:\n def __init__(self, price, quantity):\n self._price = price\n self._quantity = quantity\n self._cache = {}\n\n @property\n def price(self):\n return self._price\n\n @property\n def quantity(self):\n return self._quantity\n\n @memoized\n def total(self):\n return self.price * self.quantity\n\nThe class Item is immutable (kind of), so we know that each derived property can be computed only once per instance. ", "That's exactly what the memoized function does. ", "Besides that, the cache lives inside the instance itself (self._cache), so it will be garbage collected with it.", "\nWhat I'm looking for is to achieve a similar thing in Haskell.", "\n\nA:\n\nA relatively simple way of memoizing a calculation on a value of a particular type is to bring the calculated result into the data type and use a smart constructor. ", " That is, write the Order data type as:\ndata Order = Order\n { orderItems :: [Item]\n , orderTotal :: Float\n } deriving (Show, Eq)\n\nNote that the orderTotal field replaces your function of the same name. ", " Then, construct orders using the smart constructor:\norder :: [Item] -> Order\norder itms = Order itms (sum . ", "map itemTotal $ itms)\n\nBecause of lazy evaluation, the orderTotal field will be calculated only the first time it's needed with the value cached thereafter. ", " When the Order is garbage collected, obviously the orderTotal will be garbage collected at the same time.", "\nSome people would pack this into a module and export only the smart constructor order instead of the usual constructor Order to ensure that an order with an inconsistent orderTotal could never be created. ", " I worry about these people. ", " How do they get through their daily lives knowing that they might double-cross themselves at any moment? ", " Anyway, it's an available option for the truly paranoid.", "\n\n" ]

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[ "Thursday, 3 October 2013\n\nCongratulation to Megan and the Vice Captain's team who were the 2013 winners of the Hattersley Cup. ", "It was a very close run competition with the Vice Captain's team beating the Captain's team by just 6 points to 5. ", "There were 42 players taking part, making ten pairs matches and one singles match. ", "The day started in sunshine but the later pairs were left to battle out their matches in the rain. ", "As usual on big competition days, the cup was presented as the Ladies enjoyed afternoon tea, with a delicious selection cakes provided by Joel and his team." ]

{ "pile_set_name": "Pile-CC" }

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[ "// Copyright 2014 beego Author. ", "All Rights Reserved.", "\n//\n// Licensed under the Apache License, Version 2.0 (the \"License\");\n// you may not use this file except in compliance with the License.", "\n// You may obtain a copy of the License at\n//\n// http://www.apache.org/licenses/LICENSE-2.0\n//\n// Unless required by applicable law or agreed to in writing, software\n// distributed under the License is distributed on an \"AS IS\" BASIS,\n// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.", "\n// See the License for the specific language governing permissions and\n// limitations under the License.", "\n\npackage logs\n\nimport (\n\t\"bufio\"\n\t\"os\"\n\t\"strconv\"\n\t\"strings\"\n\t\"testing\"\n)\n\nfunc TestFiles_1(t *testing.", "T) {\n\tlog := NewLogger(10000)\n\tlog.", "SetLogger(\"multifile\", `{\"filename\":\"test.log\",\"separate\":[\"emergency\", \"alert\", \"critical\", \"error\", \"warning\", \"notice\", \"info\", \"debug\"]}`)\n\tlog.", "Debug(\"debug\")\n\tlog.", "Informational(\"info\")\n\tlog.", "Notice(\"notice\")\n\tlog.", "Warning(\"warning\")\n\tlog.", "Error(\"error\")\n\tlog.", "Alert(\"alert\")\n\tlog.", "Critical(\"critical\")\n\tlog.", "Emergency(\"emergency\")\n\tfns := []string{\"\"}\n\tfns = append(fns, levelNames[0:]...)\n\tname := \"test\"\n\tsuffix := \".log\"\n\tfor _, fn := range fns {\n\n\t\tfile := name + suffix\n\t\tif fn !", "= \"\" {\n\t\t\tfile = name + \".\" ", "+ fn + suffix\n\t\t}\n\t\tf, err := os.", "Open(file)\n\t\tif err !", "= nil {\n\t\t\tt.Fatal(err)\n\t\t}\n\t\tb := bufio.", "NewReader(f)\n\t\tlineNum := 0\n\t\tlastLine := \"\"\n\t\tfor {\n\t\t\tline, _, err := b.ReadLine()\n\t\t\tif err !", "= nil {\n\t\t\t\tbreak\n\t\t\t}\n\t\t\tif len(line) > 0 {\n\t\t\t\tlastLine = string(line)\n\t\t\t\tlineNum++\n\t\t\t}\n\t\t}\n\t\tvar expected = 1\n\t\tif fn == \"\" {\n\t\t\texpected = LevelDebug + 1\n\t\t}\n\t\tif lineNum !", "= expected {\n\t\t\tt.Fatal(file, \"has\", lineNum, \"lines not \"+strconv.", "Itoa(expected)+\" lines\")\n\t\t}\n\t\tif lineNum == 1 {\n\t\t\tif !", "strings.", "Contains(lastLine, fn) {\n\t\t\t\tt.Fatal(file + \" \" + lastLine + \" not contains the log msg \" + fn)\n\t\t\t}\n\t\t}\n\t\tos.", "Remove(file)\n\t}\n\n}\n" ]

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[ "Q:\n\nJavascript Nested Function Evaluation\n\nHi I am confused with this Javascript function:\nvar currying = function(a) {\n return function(b){\n return function(c){\n return function(d){\n return a + b /c * d;\n };\n };\n };\n };\nvar a = currying(4)(8);\nvar b = a(2)(6);\nconsole.log(b);\n\nIt outputs 28 but I am not sure how did Javascript evaluated the function. ", "I also have learned that a = 4, b = 8, c = 2 and lastly d = 6. ", "Thank you for somebody that will be able to explain the function.", "\n\nA:\n\nWhen you use currying you are writing a function that takes one argument, that will return a function taking the next argument until all arguments are supplied. ", "\nIn this case you need to call the returned function 4 times until you get to the last function and evaluate all the arguments.", "\nThis is good because you can pass in arguments at different times during the execution of your code and you can create new functions with arguments already set within the closure of the final functions. ", "eg.", "\nconst fourPlusTwo = currying(4)(2)\n\nnow you can use the new function fourPlusTwo anywhere in your code and you will have those arguments baked in the closure of the remaining two functions.", "\nThe code you have is a non standard example but maybe if you needed to calculate tax throughout your app you could do something like.", "\n\nconst inclusiveTax = rate => amount => {\r\n return '$' + (amount * (rate / (100 + rate))).toFixed(2)\r\n}\r\n\r\nconst norwayIncomeTax = inclusiveTax(60.2)\r\nconst strayaIncomeTax = inclusiveTax(32.5)\r\nconst muricaIncomeTax = inclusiveTax(31.5)\r\n\r\nconsole.log(\r\n norwayIncomeTax(50000),\r\n strayaIncomeTax(50000),\r\n muricaIncomeTax(50000)\r\n)\n\nUsing just one function you have curried the tax rate for 3 separate countries and returned functions waiting for the amount.", "\n\nA:\n\nYou should know the difference between function object and function call.", "\nlike: var a = function(v){return v + 1;} a is a function object. ", "Then a(2) invokes function a.\nTry to understand the procedure step by step.", "\n\ncurrying is a function which return another function.", "\nso currying(4) returns a function(a is given value 4):\nfunction(b){\n return function(c){\n return function(d){\n return 4 + b /c * d;\n };\n };\n };\n};\n\nthen currying(4)(8) also is 'var a' returns another function:\n function(c){\n return function(d){\n return 4 + 8 /c * d;\n };\n };\n };\n\ninvoking a(2) returns a function object: \n function(d){\n return 4 + 8 / 2 * d;\n };\n };\n\nfinally a(2)(6) returns 4 + 8 / 2 * 6 which is 28.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "y**4 - 1518*y**3 - 23520*y**2 + 37950*y + 586125 = 0. ", "What is y?", "\n-15, -5, 5, 521\nDetermine y so that -2*y**5/3 - 3260*y**4/3 - 1769854*y**3/3 - 320040772*y**2/3 + 589952*y + 106681344 = 0.", "\n-574, -528, -1, 1\nFactor 5*d**2 + 4843195*d - 4843200.", "\n5*(d - 1)*(d + 968640)\nSolve -r**2/6 - 2734555*r/3 - 7477791048025/6 = 0.", "\n-2734555\nFactor 2*p**4/3 - 4228768*p**3/3 + 2235322535978*p**2/3 - 4470594326884*p.", "\n2*p*(p - 1057189)**2*(p - 6)/3\nFind v, given that v**4/2 + 1251*v**3 + 738441*v**2/2 + 29636766*v + 85621050 = 0.", "\n-2175, -162, -3\nSolve -3*n**4/2 - 77393*n**3/2 + 283863*n**2 + 206440*n = 0.", "\n-25805, -2/3, 0, 8\nLet 3*n**2 - 144258*n - 1009953 = 0. ", "Calculate n.\n-7, 48093\nWhat is h in -4*h**4 + 97300*h**3 + 97312*h**2 - 194608*h = 0?", "\n-2, 0, 1, 24326\nLet -2*y**3/7 + 527026*y**2/7 + 9491004*y = 0. ", "Calculate y.\n-126, 0, 263639\nSolve -20*v**5 - 6068*v**4 + 29596*v**3 + 389668*v**2 + 489544*v + 135520 = 0 for v.\n-308, -5, -1, -2/5, 11\nFactor 2*b**2/9 + 81920*b/9 + 17763512/9.", "\n2*(b + 218)*(b + 40742)/9\nDetermine g, given that 2*g**4 - 85328*g**3 + 4346724*g**2 - 8437472*g + 4176074 = 0.", "\n1, 49, 42613\nLet 2*z**2/25 - 264564868*z/25 + 8749321172482178/25 = 0. ", "What is z?", "\n66141217\nSuppose -2*v**5/7 - 7606*v**4/7 - 7189438*v**3/7 + 79823134*v**2/7 - 174833760*v/7 - 261838728/7 = 0. ", "Calculate v.\n-1907, -1, 6\nLet -2*v**4 + 3828*v**3 + 120272*v**2 + 618060*v + 875250 = 0. ", "Calculate v.\n-25, -3, 1945\nFactor 5*c**2 - 78710105*c + 78710100.", "\n5*(c - 15742020)*(c - 1)\nDetermine h, given that 3*h**3/5 - 4743*h**2/5 - 176016*h/5 + 446292 = 0.", "\n-46, 10, 1617\nSolve -5*h**5 - 20150*h**4 - 6782910*h**3 + 76671920*h**2 - 132914485*h + 63045630 = 0 for h.\n-3658, -383, 1, 9\nLet 7*n**3/2 - 73085*n**2/2 + 1336877*n + 384948 = 0. ", "Calculate n.\n-2/7, 37, 10404\nDetermine q, given that -2*q**2 - 30106*q - 30104 = 0.", "\n-15052, -1\nSuppose -2*b**2 + 6696436*b - 60267762 = 0. ", "What is b?", "\n9, 3348209\nFactor 846053569*q**2/5 - 814436*q + 980.", "\n(29087*q - 70)**2/5\nFactor -22050*a**2 + 28286580*a - 9071775602.", "\n-2*(105*a - 67349)**2\nSolve -4*j**2/7 - 216862568*j/7 - 2939335837472164/7 = 0 for j.\n-27107821\nSuppose 5*i**4 + 55505*i**3 - 333185*i**2 + 277735*i + 666420 = 0. ", "What is i?", "\n-11107, -1, 3, 4\nFactor 4*a**3/9 + 3327736*a**2/3 - 2218492*a + 9983216/9.", "\n4*(a - 1)**2*(a + 2495804)/9\nFactor -5*z**3 + 15925*z**2 + 6219000*z + 574290000.", "\n-5*(z - 3545)*(z + 180)**2\nLet -2*u**4/9 + 87256*u**3/9 - 951439388*u**2/9 - 1903664152*u/3 - 951962978 = 0. ", "What is u?", "\n-3, 21817\nLet 4*d**5 + 1028*d**4 + 32024*d**3 + 211792*d**2 + 495456*d + 383616 = 0. ", "What is d?", "\n-222, -27, -4, -2\nFactor -h**3 - 5974990*h**2.", "\n-h**2*(h + 5974990)\nLet -5*x**4 + 76140*x**3 + 76170*x**2 - 380740*x + 228435 = 0. ", "Calculate x.\n-3, 1, 15229\nDetermine t so that -2*t**4/7 - 35534*t**3/7 - 161687698*t**2/7 - 4863101998*t - 100670911932/7 = 0.", "\n-8773, -218, -3\nFind q, given that -10625*q**3 - 88700*q**2 - 157980*q - 49680 = 0.", "\n-6, -828/425, -2/5\nFactor c**4 + 384*c**3 + 1119*c**2 - 9116*c + 10668.", "\n(c - 2)**2*(c + 7)*(c + 381)\nLet -3*w**4/5 + 9048*w**3/5 + 109137*w**2/5 - 390702*w/5 + 54504 = 0. ", "Calculate w.\n-15, 1, 2, 3028\nFind k, given that -368*k**3 - 360*k**2 + 29*k + 21 = 0.", "\n-1, -21/92, 1/4\nLet -3*l**5 + 15219*l**4 - 5105562*l**3 + 443509434*l**2 + 5105565*l - 443524653 = 0. ", "Calculate l.\n-1, 1, 177, 4719\nSuppose 2*p**2 + 9463530*p = 0. ", "What is p?", "\n-4731765, 0\nSuppose 2*w**3/5 - 3990*w**2 + 55006494*w/5 - 25481013554/5 = 0. ", "What is w?", "\n577, 4699\nLet 3*l**4/4 - 1023*l**3/2 + 276879*l**2/4 - 3057273*l + 31972995 = 0. ", "Calculate l.\n15, 74, 519\nSolve 2*x**3 + 2446*x**2 + 165884*x + 2649600 = 0.", "\n-1152, -46, -25\nFactor u**3/3 + 341083*u**2/3 - u/3 - 341083/3.", "\n(u - 1)*(u + 1)*(u + 341083)/3\nFactor -4*g**2 + 142892*g + 68482832.", "\n-4*(g - 36196)*(g + 473)\nDetermine n so that 2*n**4/3 + 13702*n**3/3 - 661526*n**2/3 + 5366738*n/3 - 1572972 = 0.", "\n-6899, 1, 9, 38\nDetermine i, given that 1125*i**3 - 1074794325*i**2 - 286611880*i - 19107460 = 0.", "\n-2/15, 955373\nWhat is b in -3*b**2 + 49770*b - 17813952 = 0?", "\n366, 16224\nDetermine k so that -k**5 - 6111*k**4 - 9121080*k**3 + 662528132*k**2 + 5736473760*k + 11763259200 = 0.", "\n-3090, -4, 77\nFactor i**3 + 4935*i**2 - 1219657*i + 3614529.", "\n(i - 233)*(i - 3)*(i + 5171)\nLet -5490*y**5 + 12489*y**4 + 84810*y**3 - 199800*y**2 + 48480*y - 384 = 0. ", "What is y?", "\n-4, 1/122, 4/15, 2, 4\nSolve 8*o**5 + 3310*o**4 - 215172*o**3 + 257954*o**2 + 370924*o - 105504 = 0 for o.\n-471, -1, 1/4, 2, 56\nFactor 2*y**3/5 - 1235704*y**2/5 + 31134978*y - 4903508988/5.", "\n2*(y - 617726)*(y - 63)**2/5\nSolve 3*c**2 - 415323*c + 39013854 = 0 for c.\n94, 138347\nSolve 28*t**5 + 84764*t**4 + 63524492*t**3 - 948732428*t**2 + 3351225384*t + 1036421568 = 0.", "\n-1521, -2/7, 7, 8\nFactor -2*p**3/7 + 5930*p**2 - 200691950*p/7 - 154995153750/7.", "\n-2*(p - 10715)**2*(p + 675)/7\nFactor 2*n**2 + 1478*n - 499464.", "\n2*(n - 252)*(n + 991)\nFactor r**2 + 44757294*r - 134271891.", "\n(r - 3)*(r + 44757297)\nLet -o**2/2 - 7457*o + 6782820 = 0. ", "Calculate o.\n-15774, 860\nLet -21*i**3 + 22719*i**2 + 163134*i + 235224 = 0. ", "What is i?", "\n-36/7, -2, 1089\nDetermine j, given that 2*j**4/7 - 4328*j**3/7 + 1598280*j**2/7 + 854786816*j/7 + 961968640 = 0.", "\n-280, -8, 1226\nDetermine z, given that 3*z**5 - 5580*z**4 - 659766*z**3 - 5568216*z**2 - 9179469*z - 4265436 = 0.", "\n-103, -7, -1, 1972\nFactor -4*s**3 - 18912252*s**2 - 37824492*s - 18912244.", "\n-4*(s + 1)**2*(s + 4728061)\nFactor -2*l**4/3 + 21296*l**3/3 + 1694866*l**2/3.", "\n-2*l**2*(l - 10727)*(l + 79)/3\nSolve -2*w**3/9 + 11240*w**2/9 + 169022*w/9 + 157780/9 = 0.", "\n-14, -1, 5635\nSolve 5*j**4 + 1805*j**3 + 38865*j**2 - 526525*j + 1432250 = 0 for j.\n-337, -34, 5\nFactor 2*m**4 - 728*m**3 - 22360*m**2 + 159936*m.", "\n2*m*(m - 392)*(m - 6)*(m + 34)\nLet z**3 - 1117*z**2 + 404240*z - 47761700 = 0. ", "What is z?", "\n310, 497\nFactor 2*c**2 - 558252*c.", "\n2*c*(c - 279126)\nSolve 25*d**5 + 50930*d**4 - 707065*d**3 + 1087150*d**2 + 246120*d = 0 for d.\n-2051, -1/5, 0, 2, 12\nSolve t**5 + 127883*t**4 + 4086788547*t**3 - 110424766955*t**2 + 376302266300*t = 0.", "\n-63955, 0, 4, 23\nFactor -f**3/4 - 16974*f**2 - 303937845*f - 529507637212.", "\n-(f + 1948)*(f + 32974)**2/4\nFind j, given that j**2/8 - 70267*j/2 - 9838605/8 = 0.", "\n-35, 281103\nDetermine t, given that t**2/2 + 16547425*t + 273817274130625/2 = 0.", "\n-16547425\nFactor 54*a**2 - 40225137*a - 2234730.", "\n3*(a - 744910)*(18*a + 1)\nFactor 5*o**2 - 46459180*o - 46459185.", "\n5*(o - 9291837)*(o + 1)\nLet -4*v**4 + 1709776*v**3 - 80352748*v**2 + 902660160*v + 984722688 = 0. ", "Calculate v.\n-1, 24, 427397\nFactor -5*o**2 + 1073420*o + 1073425.", "\n-5*(o - 214685)*(o + 1)\nFactor -3*m**4/2 + 105333*m**3 - 1849700034*m**2 + 18486468540*m.", "\n-3*m*(m - 35106)**2*(m - 10)/2\nDetermine c, given that -c**2/6 - 1809*c + 337435/6 = 0.", "\n-10885, 31\nFind a such that -a**4/3 - 54290*a**3/3 - 242264651*a**2 + 272999219440*a/3 - 25286174303296/3 = 0.", "\n-27329, 184\nLet 5*t**2 + 1137181930*t + 64659137095926245 = 0. ", "Calculate t.\n-113718193\nSuppose 2*v**2 - 6790*v + 201900 = 0. ", "Calculate v.\n30, 3365\nLet 20*g**5 - 3903*g**4 - 15255*g**3 - 13544*g**2 + 2388*g = 0. ", "What is g?", "\n-2, 0, 3/20, 199\nFind n, given that -190*n**4 + 468735*n**3 - 259194185*n**2 - 37793685315*n + 994750155 = 0.", "\n-119, 1/38, 1293\nLet -c**5 + 6*c**4 + 935*c**3 + 1488*c**2 - 30940*c = 0. ", "Calculate c.\n-26, -7, 0, 5, 34\nFactor -3*i**2/5 + 16662*i/5 + 10935513/5.", "\n-3*(i - 6147)*(i + 593)/5\nFactor 11*l**2 - 286882*l + 52160.", "\n(l - 26080)*(11*l - 2)\nLet 4*b**4 - 63368*b**3 - 443772*b**2 = 0. ", "What is b?", "\n-7, 0, 15849\nFactor -o**3/2 + 364111*o**2 - 132595752065*o/2 + 3446505067850.", "\n-(o - 364085)**2*(o - 52)/2\nSuppose -2*x**5/15 - 788*x**4/5 - 734888*x**3/15 - 7067652*x**2/5 - 2341630*x/3 + 16399000 = 0. ", "Calculate x.\n-575, -31, -4, 3\nFactor -68*o**2 - 52949580*o.", "\n-4*o*(17*o + 13237395)\nFactor v**2 - 7083*v - 5085180.", "\n(v - 7740)*(v + 657)\nDetermine u, given that 21*u**2 + 38316*u - 54780 = 0.", "\n-1826, 10/7\nFactor v**3 - 1844942*v**2 + 7379756*v - 7379752.", "\n(v - 1844938)*(v - 2)**2\nDetermine u so that -2*u**3/11 + 879552*u**2/11 - 3518184*u/11 + 3518176/11 = 0.", "\n2, 439772\nDetermine d so that 3*d**2/4 + 4622985*d/4 + 2311491/2 = 0.", "\n-1540994, -1\nDetermine v, given that -143*v**3/4 - 412*v**2 - 825*v/4 = 0.", "\n-11, -75/143, 0\nFactor -2*o**3 + 28756572*o**2 - 57513138*o + 28756568.", "\n-2*(o - 14378284)*(o - 1)**2\nFactor 144*a**3 + 3010224*a**2 - 59242844*a + 29134" ]

{ "pile_set_name": "DM Mathematics" }

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[ "An increasing number of data security threats exist in the modern computerized society. ", "These threats may include viruses or other malware that attacks the local computer of the end user, or sophisticated cyber attacks to gather data and other information from the cloud or server based infrastructure. ", "This server based infrastructure includes real and virtual computing devices that are used to provide a variety of services to user computing systems, such as data storage, cloud processing, web sites and services, amongst other possible services. ", "To protect applications and services, various antivirus, encryption, and firewall implementations may be used across an array of operating systems, such as Linux and Microsoft Windows.", "\nFurther, some computing environments may implement security information and event management (SIEM) systems and other security detection systems to provide real-time analysis of security alerts generated by network hardware and applications. ", "In particular, SIEM systems allow for real-time monitoring, correlation of events, notifications, and console views for end users. ", "Further, SIEM systems may provide storage logs capable of managing historical information about various security events within the network. ", "Although SIEMs and other security identifying systems may generate security alerts for devices within the network, administrators may be forced to translate each of these alerts into particular actions, and may further be forced to gather additional information about the alert before taking the action. ", "Thus, time and resources that could be used on other tasks may be used in researching and determining an appropriate course of action to handle a security threat." ]

{ "pile_set_name": "USPTO Backgrounds" }

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[ "In his 1970 recording “Space Captain,” Joe Cocker sent out a message of cross-cultural peace when he sang the lyrics “learning to live together ’til we die.”", "\n\nRecent social research indicates that coexistence with our out-groups has never been more critical. ", "The United Kingdom is on track to become the most ethnically mixed country in the Western world in fewer than 40 years, according to the Migration Observatory at the University of Oxford. ", "In fact, Whites are now a minority in London, according to UK census figures.", "\n\nThe foreign-born populations in cities like Amsterdam, Singapore, Sydney, and Toronto range from 40%–50%. ", "And the US Census Bureau projects that the national population of non-White racial groups will exceed that of Whites before the middle of this century.", "\n\nWith rising immigration and declining birth rates, we are indeed witnessing a seismic shift in the ethnic and cultural makeup of many nations in the developed world. ", "Racial and ethnic majorities are slowly transitioning toward minority-group status. ", "In the United States, Canada, and parts of Europe, Whites may still comprise the single largest racial group, but their numbers are on the verge of shrinking below the combined populations of other ethnic groups.", "\n\nAlthough some embrace the concept of racial and cultural diversity, large pockets of people in the traditional majorities are far more averse to it. ", "A British government survey, for example, indicated that almost a third of White Britons believe ethnic minorities receive preferential treatment, even though unemployment among minority groups remains disproportionately high. ", "In Greece and Spain, animosity toward foreign-born residents — particularly Muslims — has been stoked by massive unemployment. ", "And many Singaporeans have been complaining about foreign workers putting a strain on housing, jobs, and infrastructure.", "\n\nSeveral psychological theories — including power threat theory, first proposed by Hubert Blalock in 1960 — have attempted to explore the deepest drivers of the resistance to these demographic shifts. ", "Expanding on Herbert Blumer’s theory that racial prejudice arises from the way racial groups view themselves in relation to other groups rather than individual feelings or attitudes, the power threat theory posits that the majority group perceives a threat to its hold on economic, political, and even cultural resources when a minority group’s size increases.", "\n\nFears About Status\n\nAccording to power threat theory, the majority responds to these status threats by creating or tightening state control in racialized ways; one example is the support for intensifying immigration laws. ", "In the United States, that support primarily has targeted Mexicans. ", "In Europe, it has focused significantly on Muslims — now fueled by Islamic extremists’ recent terrorist attacks in Paris.", "\n\nHow might these intergroup dynamics change once a historically dominant ethnic group no longer constitutes a majority?", "\n\nTo examine the effect this shift may have on White Americans’ racial attitudes, Maureen Craig of New York University and Past APS Board Member Jennifer Richeson of Northwestern University set up an experiment to determine whether making this majority–minority shift salient to White participants would increase their pro-White and/or antiminority feelings. ", "They first primed participants with either an article about the aforementioned Census Bureau’s projections or an article about current racial demographics, then measured subjects’ explicit racial bias with the Evaluative Bias Scale. ", "They also used Implicit Association Tests to measure implicit racial bias and found that subjects primed with the information about the impending majority–minority shift exhibited greater implicit pro-White and antiminority biases, compared with control subjects to whom projected increases in the ethnic minority populations in another country (the Netherlands) were made salient.", "\n\n“These findings suggest that rather than ushering in a more tolerant future, the increasing diversity of the nation may actually yield more intergroup hostility,” the authors wrote.", "\n\nTo test the potential repercussions of these demographic changes on overall political views, Craig and Richeson conducted another study in which White American participants read a text either about the US majority–minority shift or about a shift toward increased geographic mobility. ", "They found that participants who read about the impending majority–minority racial demographics expressed support for more conservative policies than did those who read about geographic mobility — even on race-neutral issues, such as the environment — and were more likely to identify as conservative.", "\n\nChanging Archetypes\n\nSome of this effect may be rooted in the threat that shifting demographics pose to a nation’s prototypicality. ", "The label “all-American,” for example, emerged in the 1930s as a descriptor bestowed only on those in the White majority. ", "What does it mean to be all-American when Whites no longer represent that majority?", "\n\nPsychological scientists Felix Danbold and Yuen J. Huo of the University of California, Los Angeles, explored this question in a study published in 2015. ", "Across two studies involving White American adults recruited through Amazon Mechanical Turk, they asked participants questions designed to measure their attitudes toward ethnic diversity and cultural assimilation. ", "In Study 1, participants indicated the extent to which they expected the racial makeup of the US population to change between the present and 2050. ", "They also were asked to rate their feelings about their status as prototypical Americans and about how much other ethnic groups should adopt American values. ", "As they expected, Danbold and Huo found that Whites who viewed their racial group as prototypically American, and who felt threatened by their numerical decline in the population, were the most resistant to diversity and were most likely to want people from other cultures to assimilate.", "\n\nIn a second experiment, also employing Mechanical Turk, Danbold and Huo found that simply showing White participants information about their relative population decrease lowered their endorsement of diversity — especially when they viewed their status as prototypical Americans as under threat.", "\n\nStudies in other industrialized countries, including Germany, the Netherlands, France, Belgium, Russia, and Australia, have shown that the more people perceive an increase in the number of foreigners moving into their borders, the greater the antiforeigner sentiments they express.", "\n\nFor example, psychological researchers Daniel Johnson, of the Queensland University of Technology, Australia, and Deborah J. Terry and Winnifred R. Louis, of the University of Queensland, Australia, found similar reactions among Australian Whites toward Asians. ", "The scientists recruited 255 White adults and had them complete questionnaires designed to measure their feelings about obedience, discipline, and conformity and their perceptions of Asian Australians. ", "They also had the participants rate the status of White Australians compared with Asian Australians. ", "Results showed that the higher White Australians scored on authoritarian beliefs, the more signs of prejudice they showed toward Asian Australians. ", "But of particular significance was that Whites who viewed their status as high but unstable and porous showed the strongest anti-Asian bias, particularly when they felt their privileged position to be deserved.", "\n\nA Matter of Resources\n\nAnxiety over economic resources can be heard in calls for immigration restriction, which are often invoked alongside the specter of job and public-resource scarcity for native citizens. ", "In fact, there is evidence that minority racial markers become more salient during economic downturns: Subjects perceived Black faces to be “darker” and “more stereotypically Black” under scarcity conditions in a 2014 study by Amy Krosch and APS Fellow David Amodio of New York University. ", "Subjects in that study also allocated less money to Black recipients in a money-splitting task, suggesting the kind of real-world effect these economically moderated perceptions can have.", "\n\nIn a series of experiments, an international team of psychological researchers demonstrated the ways that these feelings of exclusion can fuel intolerance toward minority groups. ", "In one of those experiments, the researchers, led by Nilüfer Aydin of the Alpen-Adria University of Klagenfurt in Austria, assigned a group of students in Germany to imagine themselves as new employees in a workplace environment. ", "Some participants were told that their colleagues avoided them by refusing to have lunch with them or to help them with new or difficult tasks. ", "Others imagined being welcomed by their coworkers, while still others were told to picture a neutral new-job situation. ", "The participants then filled out a questionnaire designed to measure anti-Muslim attitudes.", "\n\nNext, the participants were asked to support the construction of a mosque in Munich. (", "Unbeknownst to the students, the mosque project was fictitious.) ", "As the researchers predicted, the participants who had imagined being outcasts at work scored higher on anti-Muslim attitudes compared with the other participants. ", "They also were less likely than their peers to support the mosque project.", "\n\nIn a second experiment, Aydin and her colleagues showed a way to buffer the xenophobia that feelings of social exclusion kindle. ", "They had another pool of students imagine the same workplace scenario as in the earlier experiment, then had a subset of participants write essays about a time when they felt particularly powerful and in control of their lives. ", "Another group wrote about a time when they felt powerless and out of control. ", "The participants then were asked about their views on the social and economic costs caused by immigrants. ", "Specifically, they rated their level of agreement with statements ranging from “Foreigners increase crime rates” to “Foreigners are good for the economy.”", "\n\nIn analyzing the results, the researchers found that participants in the social-exclusion condition were less apt to report anti-immigrant attitudes if they’d been prompted to recall being in control of their lives.", "\n\nIn fact, many psychological scientists have turned their focus to examining the factors that promote positive intergroup relations.", "\n\nOther research has shown that having strong objectives and principles douses resistance to heterogeneity. ", "In a 2014 study, for example, Cornell University psychological scientist Anthony L. Burrow and colleagues recruited White adults via Mechanical Turk and used a variety of measures to capture not only their personality traits, emotions, comfort with diversity, awareness of current racial issues, and connectedness with people from other ethnic groups, but also their sense of purpose in life. ", "Burrow and colleagues found evidence that, among White adults, having a sense of purpose in life bolsters comfort with living in an ethnically diverse community — no matter what the individual’s overall affect and connections with people from other ethnicities.", "\n\nGetting Together\n\nThe idea that increased diversity leads to more positive intergroup relations draws largely on the contact hypothesis, first developed by Gordon Allport in 1954. ", "This theory posits that increased contact and communication between groups can bring about increased understanding and decreased stereotyping and prejudice. ", "However, several conditions are required for this theory to hold, two of which are equality of status between groups and a lack of competition between them.", "\n\nIt also may be true that intergroup contact does indeed positively influence attitudes about outgroups, but that these positive changes are mitigated by the effects of perceived group threat. ", "A 2009 study of Dutch subjects examining the two theories simultaneously found evidence that both group threat and intergroup contact mediated changes in attitudes toward immigrants. ", "An inflated perception of the number of immigrants predicted an increased perception of group threat, which in turn predicted disapproval of immigrants; at the same time, the increased intergroup contact associated with surging immigrant populations predicted a decrease in perceived group threat and was negatively associated with disapproval of immigrants, the researchers discovered.", "\n\nOther interventions, such as those based on the common ingroup identity model, seek to expand individuals’ conception of “us” to include others formerly categorized as “them.” ", "This model, first proposed by APS Fellows John F. Dovidio and Samuel L. Gaertner, draws on the process of social categorization, or how people perceive group boundaries and identities. ", "Because individuals generally will favor the ingroup over the outgroup, the key is to encourage people to identify with a group superordinate to their racial or ethnic group such that their conception of “we” includes other groups. ", "For example, in the wake of the September 11, 2001, terrorist attacks, many found their racial and political group identities superseded by their identification as Americans; on a smaller scale, affinity for a common sports team can cut across even robust racial and social lines.", "\n\nStudies examining this model have found that White subjects rated Black confederates more favorably when they were positioned as members of the same work group rather than as separate individuals, as well as when the Black confederates displayed the same university affiliation as the subject. ", "Common ingroup identification also has been observed in majority populations after a natural disaster.", "\n\nAs many Western countries come to face these demographic changes, it is difficult to predict what lies ahead. ", "Conditions that previously had to be artificially created within the confines of a lab will soon prevail outside of it as the norm. ", "Whether this change will usher in a new era of cultural harmony or sharpen the spears of intergroup hostility remains to be seen. ", "In the meantime, psychological scientists continue to seek out mechanisms for studying and ultimately reducing the intergroup tensions and hostilities that this shift could exacerbate. ", "Their work echoes the words of Dr. Martin Luther King, Jr.: “We must learn to live together as brothers or perish together as fools.” ", "œ\n\nJennifer Richeson will sit down for an “Inside the Psychologist’s Studio” interview at the 2016 APS Annual Convention, May 26–29 in Chicago, Illinois.", "\n\nReferences and Further Reading\n\nAlba, R., Rumbaut, R. G., & Marotz, K. (2005). ", "A distorted nation: Perceptions of racial/ethnic group sizes and attitudes toward immigrants and other minorities. ", "Social Forces, 84, 901–919.", "\n\nAllport, G. W. (1954). ", "The nature of prejudice. ", "Reading, MA: Addison-Wesley Publishing Co.\n\nAydin, N., Krueger, J. I., Frey, D., Kastenmüller, A., Fischer, P. (2014). ", "Social exclusion and xenophobia: Intolerant attitudes toward ethnic and religious minorities. ", "Group Processes & Intergroup Relations, 17, 371–387. ", "doi:10.1177/1368430213510569\n\nBlalock, H. M. (1960). ", "A power analysis of racial discrimination. ", "Social Forces, 39, 53–59.", "\n\nBlumer, H. (1958). ", "Race prejudice as a sense of group position. ", "Pacific Sociological Review, 1, 3–7.", "\n\nBobo, L., & Hutchings, V. L. (1996). ", "Perceptions of racial group competition: Extending Blumer’s theory of group position to a multiracial social context. ", "American Sociological Review, 61, 951–972.", "\n\nBurrow, A. L., Stanley, M., Sumner, R., & Hill, P. L. (2014). ", "Purposes in life as a resource for increasing comfort with ethnic diversity. ", "Personality and Social Psychology Bulletin, 40, 1507–1515. ", "doi:10.1177/0146167214549540\n\nCraig, M. A., & Richeson, J. A. (2014). ", "More diverse yet less tolerant? ", "How the increasingly diverse racial landscape affects White Americans’ racial attitudes. ", "Personality and Social Psychology Bulletin, 40, 750–761. ", "doi:0146167214524993\n\nCraig, M. A., & Richeson, J. A. (2014). ", "On the precipice of a “majority–minority” America: Perceived status threat from the racial demographic shift affects white Americans’ political ideology. ", "Psychological Science, 6, 210–218.", "\n\nColeman, D. (2013). ", "Immigration, population and ethnicity: The UK in international perspective. ", "Retrieved from http://www.migrationobservatory.ox.ac.uk/briefings/immigration-population-and-ethnicity-uk-international-perspective, The Migration Observatory at the University of Oxford.", "\n\nDanbold, F., & Huo, Y. J. (2014). ", "No longer “All-American”?: ", "Whites’ defensive reactions to their numerical decline. ", "Social Psychology and Personality Science, 6, 210–218. ", "doi:10.1177/1948550614546355\n\nDasgupta, N., & Greenwald, A. G. (2001). ", "On the malleability of automatic attitudes: Combating automatic prejudice with images of admired and disliked individuals. ", "Journal of Personality and Social Psychology, 81, 800–814.", "\n\nHooghe, M., & de Vroome, T. (2015). ", "The perception of ethnic diversity and anti-immigrant sentiments: A multilevel analysis of local communities in Belgium. ", "Ethnic and Racial Studies, 38, 38–56.", "\n\nKoopmans, R., & Schaeffer, M. (2013). ", "Statistical and perceived diversity and their impacts on neighborhood social cohesion in Germany, France, and the Netherlands. ", "Social Indicators Research, 125, 853–883.", "\n\nKrosch, A. R., & Amodio, D. M. (2014). ", "Economic scarcity alters the perception of race. ", "Proceedings of the National Academy of Sciences, 111, 9079–9084.", "\n\nNier, J. A., Gaertner, S. L., Dovidio, J. F., Banker, B. S., Ward, C. M., & Rust, M. C. (2001). ", "Changing interracial evaluations and behavior: The effects of a common group identity. ", "Group Processes & Intergroup Relations, 4, 299–316.", "\n\nPlant, E. A., Devine, P. G., Cox, W. T., Columb, C., Miller, S. L., Goplen, J., & Peruche, B. M. (2009). ", "The Obama effect: Decreasing implicit prejudice and stereotyping. ", "Journal of Experimental Social Psychology, 45, 961–964.", "\n\nSchlueter, E., & Scheepers, P. (2010). ", "The relationship between outgroup size and anti-outgroup attitudes: A theoretical synthesis and empirical test of group threat- and intergroup contact theory. ", "Social Science Research, 39, 285–295.", "\n\nSchmidt, K., & Nosek, B. A. (2010). ", "Implicit (and explicit) racial attitudes barely changed during Barack Obama’s presidential campaign and early presidency. ", "Journal of Experimental Social Psychology, 46, 308–314.", "\n\nSemyonov, M., Raijman, R., Tov, A. Y., & Schmidt, P. (2004). ", "Population size, perceived threat, and exclusion: A multiple-indicators analysis of attitudes toward foreigners in Germany. ", "Social Science Research, 33, 681–701.", "\n\nTaylor, M. C. (1998). ", "How white attitudes vary with the racial composition of local populations: Numbers count. ", "American Sociological Review, 63, 512–535.", "\n\nUnited States Sentencing Commission. (", "1995). ", "Special report to the Congress: Cocaine and federal sentencing policy. ", "Washington, DC: Author.", "\n\nVezzali, L., Cadamuro, A., Versari, A., Giovannini, D., & Trifiletti, E. (2014). ", "Feeling like a group after a natural disaster: Common ingroup identity and relations with outgroup victims among majority and minority young children. ", "British Journal of Social Psychology, 54, 519–538." ]

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[ "Hurricane Lester (1992)\n\nHurricane Lester was the first Pacific tropical cyclone to enter the United States as a tropical storm since 1967. ", "The twelfth named storm and seventh hurricane of the 1992 Pacific hurricane season, Lester formed on August 20 from a tropical wave southwest of Mexico. ", "The tropical storm moved generally northwestward while steadily intensifying. ", "After turning to the north, approaching the Mexican coast, Lester attained hurricane status. ", "The hurricane reached peak winds of 85 mph (140 km/h) before making landfall on west-central Baja California. ", "The system weakened while moving across the peninsula and then over northwestern Mexico. ", "Not long after entering Arizona, Lester weakened to a tropical depression, and degenerated into an extratropical low on August 24, 1992, over New Mexico. ", "The storm's remnants later merged with the remnants of Hurricane Andrew and another frontal system on August 29.", "\n\nIn Mexico, the hurricane resulted in $3 million in damage (1992 USD, $4.7 million 2011 USD). ", "It also left 5,000 people homeless, and was responsible for three fatalities. ", "The remnants of Lester also produced moderate rainfall and minor flooding across southern California, Colorado, Arizona, and New Mexico, as well as rare August snow in the Rocky Mountains.", "\n\nMeteorological history\n\nA weak tropical wave moved off the coast of Africa on August 7. ", "It tracked across the Atlantic Ocean and Caribbean Sea without development due to strong wind shear. ", "The wave then split into two, with the northern portion dissipating over Cuba on August 15 and the southern portion continuing westward. ", "The wave crossed Central America and entered the Pacific Ocean on August 16. ", "Deep convection increased over the wave upon entering the Pacific, and early on August 19 it started to become better organized. ", "After the development of a low-level circulation, the system organized into Tropical Depression Fourteen-E on August 20 while located about 275 miles (445 km) south-southwest of Manzanillo, Colima.", "\n\nThe depression gradually tracked northwestward at 15 mph (24 km/h). ", "Although the center of the depression was initially uncertain, it slowly strengthened and steadily organized. ", "The depression attained tropical storm status late on August 20, upon which the storm was named Lester. ", "The cyclone continued to the northwest, and passed directly over Socorro Island on August 21. ", "By early the next day, an eastward moving trough weakened the ridge to its north, resulting in a to turn to the north. ", "Around this time, forecasters at the National Hurricane Center predicted the storm would not strengthen to hurricane intensity before making landfall. ", "Despite this, Lester intensified into a hurricane late on August 22 while located about 240 miles (385 km) west of La Paz in Baja California Sur.", "\n\nThe hurricane continued to organize and banding-type eye soon formed. ", "Early on August 23 it attained peak winds of 85 mph (140 km/h) with a minimum central pressure of 985 mbar (hPa; 29.09 inHg). ", "Lester weakened steadily as the storm turned to the northeast, and made landfall as a minimal hurricane near Punta Abreojos, Baja California Sur about ten hours after reaching peak intensity. ", "It degenerated into a tropical storm while crossing the Baja California Peninsula. ", "After passing through the northern Gulf of California, it made a second landfall near Isla Tiburon in the state of Sonora. ", "Lester entered Arizona as a tropical storm on August 24, the first time since Hurricane Katrina in 1967 that an Eastern Pacific tropical cyclone entered the United States with winds of at least tropical storm intensity. ", "Lester maintained tropical storm status until it weakened into a tropical depression near Tucson, Arizona. ", "Later that day, the low-level circulation dissipated over New Mexico, and Lester ceased to exist as a tropical cyclone. ", "The storm's remnants transitioned into an extratropical cyclone, as it continued to the north-northeast, ahead of an approaching trough, and later merged with the remnants of Hurricane Andrew and another frontal system on August 29, over Pennsylvania.", "\n\nPreparations and Impact\n\nMexico\nThe Government of Mexico issued tropical storm watches and warnings for Baja California on August 21. ", "The following day, a hurricane warning was issued for the peninsula from Punta Eugenia southward to Cabo San Lazaro. ", "The government of Mexico also issued a tropical storm warning for the Sonora and Sinaloa mainland from Cabo Tepopa to Los Mochis. ", "All watches and warnings were discontinued as the storm weakened and dissipated. ", "The threat of the hurricane prompted the evacuation of about 10,000 residents.", "\n\nNo observations exist for the duration when Lester, as a tropical depression, moved over Socorro Island, while winds were estimated to have reached 37 mph (59 km/h). ", " However, a station reported winds of 23 mph (37 km/h) six hours after Lester passed over Socorro Island. ", "Several ships came in contact with Lester, with one in the eye reporting hurricane-force winds for 11 hours on August 22. ", "The ship in the eye reported rough seas, causing it to roll 33° to each side and thus was responsible for a large amount of cargo to go overboard.", "\n\nHurricane Lester produced heavy rainfall across its path through the Baja California Peninsula and Sonora. ", "Peak rainfall occurred in Mulege with . ", "A weather station in Presa Rodriquez reported 8.66 inches (203 mm) of precipitation, with several other locations reporting over 2 inches (50 mm). ", "The heavy rainfall caused extensive flood damage to the west of Hermosillo, destroying some entire communities and flooding a large highway. ", "Roads were washed out, and power lines were knocked out. ", "Waves up to were recorded. ", "Flash flooding from Lester caused 10,000 people to be evacuated from their homes. ", " In addition, mudslides killed three people, and left 5,000 homeless. ", "The storm resulted in $3 million (1992 USD), equivalent to $4.7 million (2011 USD). ", "The Mexican Army provided relief efforts to residents after the storm.", "\n\nUnited States\nThe remnants of Lester produced heavy rainfall across the Southwestern United States. ", "In Arizona, rainfall amounted to over 5 inches (125 mm) near Phoenix and Tucson, with much of the rest of the state reporting over 1 inch (25 mm). ", "Moderate rainfall was also reported in western New Mexico and southern Utah, while one location in southwestern Colorado reported over 5 inches (125 mm) of precipitation. ", "In the later location, rains caused flash flooding of arroyos and a mudslide along U.S. Route 180. ", " Additional rainfall caused moderate flooding in Denver. ", "In addition to the rainfall, moisture from the remnants of Lester dropped 2 to 4 inches (50 to 100 mm) of snow across portions of Colorado, causing traffic problems in mountainous areas. ", "A weather station on Mt. Harvard recorded about 4 inches (100 mm) of snow during Lester's passage through Colorado. ", "Moisture enhanced from a cold front, the remnants Lester extended through the eastern United States, with Mattoon, Illinois reporting a peak of . ", "In all, rain from Lester caused rainfall records in Minnesota, Nebraska, Colorado, and North Dakota.", "\n\nSee also\n\nOther storms of the same name\nList of Baja California Peninsula hurricanes\nList of Pacific hurricanes\n\nReferences\n\nLester\nLester 1992\nLester 1992\nLester 1992\nLester 1992\nLester 1992\nLester 1992\nCategory:1992 natural disasters in the United States\nLester" ]

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[ "FORT LAUDERDALE, FLA. (", "WSVN) - Broward Sheriff Gregory Tony has announced that a deputy was fired after surveillance video showed him punching a detainee.", "\n\nOfficials said Deputy Kevin Fanti was in the process of booking 19-year-old Kyle Paul at the Main Jail on June 26 when he dropped a paper.", "\n\n“It’s unacceptable. ", "There isn’t any excuse for it,” Tony said. “", "There isn’t a policy that I need to see to tell me that that’s wrong.”", "\n\nFanti could be seen on surveillance picking up the paper, shoving Paul and throwing several punches.", "\n\n“One of my deputies decided that they were going to respond with slamming a piece of paper into his chest and inciting further violence and punched him several times, as you witnessed,” Tony said. “", "Too many of our good deputies’ reputation continue to get tarnished because, like in every organization that exists here on this planet, there will be a bad seed that make it through the recruitment and application process. ", "The expectations and the standards that are here in this organization now are at the highest level.”", "\n\n7News showed the video to Paul’s mother. ", "She is not in contact with her son but said she is disgusted by the way he was treated.", "\n\n“It is sad. ", "It is really sad,” she said.", "\n\nTony praised his command staff for reporting the incident to him.", "\n\n“These are my men and women that’s holding this place accountable,” he said at a press conference. “", "This is my messaging, and we’re changing the culture that exists here. ", "Too many of our good deputies’ reputation continue to get tarnished because, like every organization that exists here on this planet, there will be a bad seed that makes it through the recruitment and application process.”", "\n\nAfter reviewing the video on Thursday, Tony fired Fanti on the spot.", "\n\nThis is not the first time the now fired deputy has generated headlines.", "\n\nBefore he was hired at BSO, Fanti worked at Gun World of South Florida in Deerfield Beach. ", "In the aftermath of the shooting at Marjory Stoneman Douglas High School in February 2018, it was revealed he sold the shooter an AK-47. ", "The shooter was of legal age to buy a gun.", "\n\nThe deputy was hired in April 2018 and had still been on his probationary period.", "\n\n“What’s unique here is that this young man is on probation,” Tony said, “and he has failed to meet the standards that I have for all these deputies. ", "He’s been terminated. ", "He will not have any opportunity to be interviewed by my investigators because he didn’t deserve it.”", "\n\nThe deputies union said they are not defending Fanti.", "\n\nBecause Fanti was still on probation, there will be no appeal process, and his termination is effective immediately.", "\n\nCopyright 2020 Sunbeam Television Corp. All rights reserved. ", "This material may not be published, broadcast, rewritten or redistributed." ]

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[ "Q:\n\nHow to detect whether users have accepted terms?", "\n\nBasically I am writing a PHP and MYSQL script that will check whether a user has accepted the terms and conditions or not. ", "In the databse every current user that has signed up is set to \"unaccepted\". ", "When they log in the first page that they are directed to should have a scirpt on it that detects whether or not the status of the tos column in the users table is set to \"accepted\" or \"unaccepted\". ", "If it is accepted they can continue, and if it is not they they will be forced to go to a page and accept them before they can continue to use the rest of my site. ", "This is the code so far but it doesn't seem to be working. ", "Any suggestions help.", "\n<?", "php\n\n$username=$_SESSION['username'];\n$connect = mysql_connect('**', '**', '**', '**');\nif (!", "$connect) \n{\n die('Could not connect: ' . ", "mysql_error());\n}\nif (!", "mysql_select_db('**')) \n{\n die('Could not select database: ' . ", "mysql_error());\n}\n$toschecker = mysql_query(\"SELECT `tos` FROM `users` WHERE `username` = '$username'\");\nif (!", "$toschecker) \n{\n die('Could not query:' . ", "mysql_error());\n}\nmysql_close($connect);\n$unaccepted='unaccepted';\n\nif ($toschecker === $unaccepted)\n{\n header('Location: accepttos.php');\n} \n?", ">\n\nFor some reason this isn't directing them to the accepttos.php page. ", "Thanks in advance.", "\n\nA:\n\nChange MySQL to MySQLi. ", "Explanations are in the comments.", "\n<?", "php\n\n$username = $_SESSION['username'];\n$connect = mysqli_connect('Host', 'Username', 'Password', 'Database');\nif (!", "$connect) \n{\n die('Could not connect: ' . ", "mysql_error());\n}\n\n$toschecker = mysqli_query($connect,\"SELECT `tos` FROM `users` WHERE `username` = '$username'\"); /* SELECT TOS COLUMN */\n\nwhile ($row = mysqli_fetch_array($toschecker)) \n{\n $tos = $row['tos']; /* STORE TO A VARIABLE THE FETCHED TOS */\n}\n\n$unaccepted = 'unaccepted';\n\nif ($tos == $unaccepted) /* COMPARE THE TOS VARIABLE IF UNACCEPTED */\n{\n header('Location: accepttos.php');\n}\n\nelse {\n header('Location: acceptedTOS.php'); /* IF TOS IS ACCEPTED. ", "CHANGE THE LOCATION */\n}\n\nmysqli_close($connect);\n\n?", ">\n\n" ]

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[ "How To Know What Others Think\n\nCommunication is most commonly believed to be an activity of verbal language, but words can often deceive and mislead. ", "For maximum understanding of human behavior that transcends social falsehoods, you may learn to pick up body cues and signals that are sure to get to the heart of the truth every time.", "\n\nThe art of reading body language is a discipline that requires a lot of time for study, no different than learning a verbal language. ", "The unique feature of body signals is that they transcend all verbal languages and most cultures, for an accurate reading almost anywhere in the world. ", "To begin a study of the movement of man, try to focus on simple situations such as sitting down for an employment interview or reading the cues given in a personal relationship.", "\n\nSome simple cues to watch for to ensure the party you are speaking with is truly responsive to you include:\n\nCrossed legs. ", "When the crossed leg is pointing in your direction, you have their favor. ", "When its crossed away from you, they have retreated.", "\n\nWhen sitting across from someone, watch to see if their upper body leans forward when speaking to you. ", "This indicates that they are engaged and are moving towards you.", "\n\nFolded arms across the chest. ", "This gesture is a subliminal way of shutting you out. ", "The crossed arms have long been thought to be a simple stance of relaxation, but be sure it is not. ", "It’s a defense mechanism that screams, \"I don't accept you or what you are saying\".", "\n\nOne valuable signal is to know when someone is lying to you, and this may be best observed by what the person does, rather than what they say. ", "Be on the lookout for eyes that dart away when they affirm a statement to be true. ", "Also, you will find them to touch their nose or face at the moment of deception, as this is a sign of an uncomfortable moment and a way to divert from their verbal language.", "\n\nAnd finally, if you really want to know if that guy or gal is attracted to you, watch closely for the movement in the pupil of their eyes. ", "If you see them dilate when they look at you, it is a surefire signal that they like what they see.", "\n\nThe study of body language is an art that everybody can benefit from, from simple daily life situations to work relationships. ", "Learn the tricks of the trade and zero in on your sales client's behavior to give yourself the upper hand during a presentation. ", "In addition, many gestures are picked up unaware by people, and you may wish to hone your skills to send out positive messages, whether it is for a desired relationship or the opportunity to close a deal." ]

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[ "Alisa Valdes\n\nSet your calendars for Jan. 29! ", "Best-selling author Alisa Valdes is\ncoming to campus to discuss her transition from Pulitzer-nominated\nreporter at The Boston Globe and Los Angeles Times to author of \"The\nDirty Girls Social Club,\" which spent 21 weeks on\nthe New York Times best-seller list. ", "She was named one of Time\nMagazine's 25 Most Influential Hispanics in America and now writes\nwomen's fiction and teen fiction.", "\n\nAlisa will be here from 3:30 to 5 p.m. on Tuesday, Jan. 29 in BLB 170. ", "Her new book, The Feminist and the Cowboy, will be on sale.", "\n\nIn THE FEMINIST AND THE COWBOY: An Unlikely Love Story (Gotham Books, Hardcover, E-book, January 7, 2013) Alisa Valdes meets (and falls in love with) a man who teaches her to look at love from an alternative perspective; taking a closer look at the ways women and men approach love and romance in a post-feminist America. ", "Once included in an anthology of the nation’s top young feminist writers, Alisa, thanks to a manly cowboy, is standing up and saying, “Hang on ladies, we’ve got some of this wrong.”", "\n\nFeminism was a religion in Alisa Valdes’ childhood home, and her hippie, academic Marxist parents raised her to believe that she was cut out for better things than playing with Barbie dolls and learning to bake. ", "For her 12th birthday gift from her mother, she got a cardboard box full of feminist works by Erica Jong, Betty Friedan and Gloria Steinem. ", "Her resume reads like a testament to the success of her liberal feminist upbringing: graduate of Berklee College of Music (as a jazz saxophonist) and Columbia Graduate School of Journalism; writer for the Boston Globe where she was nominated for three Pulitzers and recognized as one of the nation’s top feminist writers by age 30; author of the bestselling debut novel, The Dirty Girls’ Social Club; named by Time magazine as one of the “25 most influential Hispanics in America.”", "\n\nBut in spite of so much professional success, at age 42, Alisa found herself bitter and divorced and came to the harsh-realization that some of the same “skills” that made her successful in business, were ruining her in her personal relationships. ", "After trying online dating and many painful first dates with less than ideal men, Alisa found herself falling head-over-spurs in love with the last man she ever expected to date: The Cowboy, an honest-to-goodness conservative rancher who drives a pick-up with a gun rack and a pistol under the front seat.", "\n\nAfter several exchanges with The Cowboy, Alisa realized the guy she thought she wanted (liberal, well-educated, corporate, etc.) ", "was not the guy she wanted at all. ", "Alisa was suddenly aware of the damage her extreme feminist upbringing had wreaked on her personal and sexual relationships.", "\n\nFrom their very first date, The Cowboy makes her pulse race and her blood boil, forcing her to reevaluate everything she thought she wanted in a man. ", "Alisa finds her entire belief system turned\nupside down by The Cowboy, and realizes that maybe to let go, relax and trust, as a woman isn’t so bad after all. ", "She has finally met her match in intelligence, insight, and wisdom, and it doesn’t hurt that he has the rugged good looks of someone who just stepped out of a Ralph Lauren ad.", "\n\nAfter learning and loving with The Cowboy, Alisa found ‘Difference Feminism’; which simply put means men and women are different, and being different makes us complementary and equal versions of the same species, and that together, men and women must “form a communion of persons to exist mutually one for the other.” ", "After a lifetime of strict feminist ways, Alisa advocates for relationships grounded in difference feminism.", "\n\nAs Alisa says, “If you want to feel fulfilled in love, if you want to find true, lasting romantic love with a man worthy of you, you’re going to have to get it through your head that all the tricks feminism taught us that get us ahead at work will doom us in love if we bring them home.” ", "Through butting heads (and falling in love!) ", "with the conservative cowboy, Alisa realized the idea that liberated her most: Women (and men) will never find happiness in love until they stop thinking everything has to be fair and equal. ", "It’s not about fair. ", "It’s not about equal. ", "It’s about nature.", "\n\nTold with humor and candor, THE FEMINIST AND THE COWBOY is the true love-story of a tough, progressive city chick who reclaims her womanhood and learns to love with her guard down.", "\n\nTHE FEMINIST AND THE COWBOY: An Unlikely Love Story\nGotham Hardcover || On-sale: January 7, 2013\nALSO AVAILABLE AS AN E-BOOK\n\nAbout the Author:\nAlisa Valdes is the New York Times and USA Today bestselling author of commercial women’s fiction and teen fiction, including her bestselling debut novel The Dirty Girls Social Club, which spent 21 weeks on the New York Times bestseller list. ", "Named one of Time magazine’s 25 Most Influential Hispanics in America, she has a Master’s in Journalism from Columbia University and is a Pulitzer-nominated award-winning former staff writer for the Boston Globe and Los Angeles Times. ", "She is also a graduate of Berklee College of Music (as a jazz saxophonist).", "\n\nAbout Gotham Books:\nGotham Books, a nonfiction imprint of Penguin Group (USA), was launched in 2003 by industry veteran William Shinker. ", "Penguin Group (USA) Inc. is one of the leading U.S. adult and children’s trade book publishers, owning a wide range of imprints and trademarks, including Berkley Books, Dutton, Frederick Warne, G.P. Putnam’s Sons, Gotham Books, Grosset & Dunlap, New American Library, Penguin, Penguin Press, Philomel, Riverhead Books, and Viking, among others. ", "Penguin Group is owned by Pearson plc, the international media group.", "\n\nVisit Us:\n\nFrank W. and Sue Mayborn School of Journalism\n\nGeneral Academic Building, Room 102\n\nMail us:\n\nMailing Address for U.S. Mail:\nMayborn School of Journalism\nUniversity of North Texas\n1155 Union Circle #311460 Denton, TX 76203-5017 USA" ]

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[ "---\nabstract: 'Cyber literacy merits serious research attention because it addresses a confluence of specialization and generalization; cybersecurity is often conceived of as approachable only by a technological *intelligentsia*, yet its interdependent nature demands education for a broad population. ", "Therefore, educational tools should lead participants to discover technical knowledge in an accessible and attractive framework. ", "In this paper, we present *Protection and Deception* (*P&G*), a novel two-player board game. *", "P&G* has three main contributions. ", "First, it builds cyber literacy by giving participants “hands-on experience with game pieces that have the capabilities of cyber-attacks such as worms, masquerading attacks/spoofs, replay attacks, and Trojans. ", "Second, *P&G* teaches the important game-theoretic concepts of asymmetric information and resource allocation implicitly and non-obtrusively through its game play. ", "Finally, it strives for the important objective of security education for underrepresented minorities and people without explicit technical experience. ", "We tested *P&G* at a community center in Manhattan with middle- and high school students, and observed enjoyment and increased cyber literacy along with suggestions for improvement of the game. ", "Together with these results, our paper also presents images of the attractive board design and 3D printed game pieces, together with a Monte-Carlo analysis that we used to ensure a balanced gaming experience.'", "\nauthor:\n- 'Saboor Zahir, John Pak, Jatinder Singh, Jeffrey Pawlick, Quanyan Zhu[^1]'\ntitle: 'Protection and Deception: Discovering Game Theory and Cyber Literacy through a Novel Board Game Experience'\n---\n\nCyber literacy, security awareness, cybersecurity, deception, board game\n\nIntroduction\\[sec:Introduction\\]\n================================\n\nCybersecurity has been directly in the limelight of contemporary media. ", "The Sony Pictures Entertainment hack over the controversial film *The Interview*, the infamous debut of the Snowden Revelations and ensuing debate, and important security breaches at The Home Depot and Target Corporation have made national news at all levels of society. ", "The U.S. Federal Government’s commissions of reports on big data and privacy [@key-2] and bulk collection of signals intelligence [@key-4] - together with the surging interest in cybersecurity from academic and commercial perspectives - suggests an intense effort to combat cybercrime from the top-down. ", "But cybersecurity is an interdependent phenomenon. ", "This interdependency demands cyber literacy that branches out from technology companies and computer science schools to consumers of the technology that they develop. ", "It also requires a grassroots effort at igniting interest in cyber-careers as an investment in tomorrow’s human capital.", "\n\n*Serious games* offer a promising means to overcome the intimidating nature of learning about cybersecurity. ", "Because it is difficult to perceive how security threats affect individuals, and because cyber experience and vocabulary are not well-integrated among those in non-technical fields, cybersecurity can seem to pose a high barrier to entry [@key-3]. ", "Serious games employ the entertainment value of games towards accomplishing distinct educational objectives. ", "They sit upon an intersection between engineering, science, and education. ", "Our work is a serious game with the objectives of answering such basic questions as “What is a masquerading attack?” ", "and “How is a local area network different from the internet?”", "\n\nSeveral recent educational efforts have promise for technical professionals or aspiring STEM students. ", "Proliferating *Capture the Flag* (*CTF*) competitions have placed security education in a non-technical environment. ", "An application of *gamification*, they leverage the enjoyable properties of games in a real-life security challenge. ", "But they may not be appropriate for novice participants. ", "They do not (at least yet) especially represent an outreach of security education beyond the STEM fields and into populations underrepresented in technical fields. ", "Games are needed that feature a gentle introduction to cyber-security; one that helps build cyber literacy without intimidation and teaches other concepts relevant to cybersecurity only implicitly.", "\n\nIn this work, we present *Protection and Deception* (*P&G*), a two-player board game that combines a turn-based chess-like structure with elements such as infrastructure configuration that are characteristic of real-time strategy games. ", "The basic gameplay is simple and follows a storyline related to cybersecurity. ", "In *P&G*, both players configure local area networks (LANs) and allocate attack and defense packages. ", "They hide “critical information” on one of their computers. ", "Then, gameplay evolves in a sequence of turns in which players deploy attacks and navigate them through the network. ", "Throughout the game, players learn about attack capabilities. ", "They also face trade-offs between brute strength and maintaining information-assymetry - as when deciding whether to surveil an opponent’s LAN with a weak attack. ", "Players achieve victory when they destroy the opponent’s computer containing the critical information.", "\n\n*P&G* offers a gentle introduction to cyber literacy. ", "Explicit cyber-jargon is limited to various types of cyber attacks: *e.g.*, viruses, Trojans, masquerading attacks and worms. ", "The rest of the gameplay has parallels in traditional board games - although there are some parallels to collectable card games (*e.g. Magic: The Gathering* and *Yu-Gi-Oh!*). ", "In this way, *P&G* attempts to lower the learning curve for serious security games so that they can reach populations outside of corporations or the university.", "\n\nIndeed, we tested this game at a community center on the lower-east side of Manhattan. ", "We found both encouraging results - in terms of interest in the game and acquired knowledge - and elements of the game that need to be improved and further simplified in order to attract young players. ", "We were also inspired towards future work in digitalizing the game or providing game instructions in the form of a *YouTube* video.", "\n\nThe rest of the paper proceeds as follows. ", "Section \\[sec:Gameplay\\] describes the gameplay of *P&G* in detail. ", "We were especially intrigued by one aspect of the gameplay design: attempting to balance the capabilities of cyber-attacks and defense packages. ", "Towards this end, we created a Monte-Carlo simulation which we describe in Section \\[sec:Simulation-for-Design\\]. ", "Section \\[sec:Playtesting\\] describes our playtesting proceedure and observations. ", "Finally, we conclude the paper in Section \\[sec:Conclusions\\].", "\n\nGameplay\\[sec:Gameplay\\]\n========================\n\n*Protection and Deception* (*P&G*) is a two-player board game. ", "The goal is of the game is to locate and destroy the opponent’s computer that holds his *critical information*. ", "This task is achieved through a combination of effective local area network (LAN) design, intelligent deployment of attacks and defenses, and quickly routing attacks and defenses to their intended target. ", "This requires balancing strength with maintaining the ability to deceive the other player. ", "The first stage of *P&G* consists of LAN configuration.", "\n\nLAN Configuration\n-----------------\n\nEach player controls the following pieces:\n\n1. ", " 4 routers\n\n2. ", " 8 computers\n\n3. ", " 8 mesh points\n\n4. ", " 16 links\n\n5. ", " Deck of attack and defense cards\n\nThere are three components to the platform of the board game as shown in Fig. ", "\\[fig:Basic-board-layout.\\].", "\n\n![", "\\[fig:Basic-board-layout.\\]Basic board layout. ", "Each player configures her own local area network, and connects via routers to the public internet. ", "Network configuration is an optimization experience in which players need to make trade-offs between capabilities to defend critical information, utilize deception (hide critical information in unexpected computers), and rapidly deploy attacks.](Fig1_edit){width=\"0.8\\columnwidth\"}\n\nEach player will have a Local Area Network (LAN), which is essentially her base. ", "The players configure these LANs. ", "The board that is in the middle of the two LANs is the public Internet, which has static configuration.", "\n\nThe game begins with each player setting up her own LAN. ", "A network topology consists of routers, computers, mesh points, and links. ", "A mesh point is essentially a way to link two computers directly. ", "Fig. ", "\\[fig:Basic-board-layout2\\] represents a sample network topology for Player A of three computers connected with the use of three mesh points.", "\n\n![", "\\[fig:Basic-board-layout2\\]Basic board layout with three computers connected via mesh points and links](Fig2_edit){width=\"0.8\\columnwidth\"}\n\nEach player creates a network topology that consists of 8 computers, at least 4 mesh points and at most 8 mesh points, and 4 routers, which are accompanied by 4 routing links and must be connected to at least four mesh points. ", "A router is used to connect computers to the public Internet. ", "The 16 links are used in order to connect a computer to a computer, a computer to a mesh point, or a router to a mesh point. ", "Each computer must use 2 to 3 links to connect to another computer or mesh point. ", "Fig. ", "\\[fig:Sample-configuration-of\\] is a sample network topology. ", "The routing links are represented with the green lines. ", "In Fig. ", "\\[fig:Sample-configuration-of\\], the computers are linked to other computers or mesh points with the use of red links. ", "After each player sets up his or her network topology, each player must designate one computer out of the eight computers as the computer that holds critical information. ", "In Fig. ", "\\[fig:Sample-configuration-of\\], the computer that holds the critical information is colored in red.", "\n\n![", "\\[fig:Sample-configuration-of\\]Sample configuration of $\\text{LAN}_{1}$. The red computer holds critical information. ", "The routing links are represented with green lines, while the computers are linked to each other or to mesh points with red lines.](Fig4_edit){width=\"0.8\\columnwidth\"}\n\nEach router is connected to the public Internet with the use one link (in yellow in Fig. ", "\\[fig:Sample-configuration-of\\]). ", "Once each player has set up her network topology and decided on the computer that holds critical information, each player allocates the deck of attack and defense cards. ", "Each computer, besides the computer that holds critical information, is assigned one attack card and one defense card. ", "The next two subsections describe the attacks and the defense packages.", "\n\nAttacks\n-------\n\nEach attack card features a different type of attack. ", "These attacks can be spawned from the computers equipped with the attack card. ", "Fig. ", "\\[fig:Sample-attack-card:\\] depicts an image of one of the attack cards.", "\n\n1. ", " *Worm* - takes down a piece and then replicates if a host is taken down\n\n2. ", " *Masquerading Attack/Spoof* - propagates throughout a network without attacking a particular piece\n\n3. ", " *Denial of Service* (*DOS*) *Attack* - stops traffic within a mesh point.", "\n\n4. ", " *Virus* - attacks a computer and then the piece is reset\n\n5. ", " *Replay* - captures a packet and does not let it propagate throughout the network\n\n6. ", " *Trojan* - reveals the defenses that a particular computer has installed. ", "A Trojan is also coupled with a weak level virus\n\n7. ", " *Modification Message* - changes the type of message/attack a computer sends. ", "If this attack comes across the opponents attack at a node in the Internet, it can randomly select a different type of attack\n\n![", "\\[fig:Sample-attack-card:\\]Sample attack card: *Worm* Attack](Fig5_edit){width=\"0.8\\columnwidth\"}\n\nDefense Packages\n----------------\n\nPlayers also equip computers with a defense package. ", "The defense packages differ in terms of which attacks they block. ", "We have counterbalanced these packages in order to prevent any one attack from becoming exceptionally powerful. (", "See Section \\[sec:Simulation-for-Design\\].) ", "Fig. ", "\\[fig:Sample-defense-package\\] depicts one of the defense package cards.", "\n\n1. ", " *Defense Package 1* - Blocks worm, replay, and masquerading attack/spoof\n\n2. ", " *Defense Package 2* - Blocks worm, denial of service (DOS), and modification message attacks\n\n3. ", " *Defense Package 3* - Blocks worm, virus, and Trojan attacks\n\n4. ", " *Defense Package 4* - Blocks worm, modification message, and masquerading attack/spoof\n\n5. ", " *Defense Package 5* - Blocks worm, Trojan, and DOS attacks\n\n6. ", " *Defense Package 6* - Blocks virus, replay, and masquerading attack/spoof\n\n7. ", " *Defense Package 7* - Blocks Trojan, replay, and DOS attacks\n\n8. ", " *Defense Package 8* - Blocks Trojan, replay, and modification message attacks\n\n![", "\\[fig:Sample-defense-package\\]Sample defense package card: *Defense Package 1*](Fig6_edit){width=\"0.8\\columnwidth\"}\n\nOn every turn, each player is allowed to make one move. ", "A move is defined as either spawning an attack or moving an attack one unit. ", "An attack piece is represented as a ring. ", "When a player spawns an attack piece, she simply places the ring on top of the appropriate computer. ", "An attack that is in a LAN follows the configured links. ", "An attack that is in the public Internet moves along the sides of the squares. ", "The attack is allowed to move either horizontally (left or right) or vertically (up or down). ", "Each player does not know what the other players moving attacking is. ", "An attack is revealed under one of two conditions:\n\n1. ", " A player attacks the opponent’s attack\n\n2. ", " A player attacks the opponent’s computer\n\nA defense package is revealed if an attack is conducted on a computer. ", "Below is a sample gameplay:\n\n1. ", " Player A has a worm attack. ", "Player A attacks Player Bs computer.", "\n\n2. ", " Player B reveals the Defense Package that is assigned to the particular computer that is attacked: Defense Package 1.", "\n\n3. ", " Defense Package 1 is able to defend against a Worm, Replay, and Masquerading Attack/Spoof. ", "Therefore, Player As worm attack is destroyed.", "\n\nIf an attack attacks a computer and the computer is successfully able to defend against the attack, the attack is destroyed. ", "However, although the attack is destroyed, it can still be spawned from the starting point, which is the computer that the attack originated from, on another turn. ", "If an attack attacks a computer and the computer is unable to defend against the attack, the computer is destroyed. ", "The game ends once one player discovers and destroys the opponents computer that holds the critical information.", "\n\nSimulation and Strategy\\[sec:Simulation-for-Design\\]\n====================================================\n\nEvery game requires fairness for a balance of good gameplay. ", "No single attack should dominate to the point where the game ends quickly. ", "In this section, we first describe the results of a simulation that we used to balance the capabilities of the attacks and the defense packages, and then we describe a strategy that might be employed based on insight from this simulation design process.", "\n\nSimulation for Design\n---------------------\n\n*Flow* is a notion developed by psychologists to describe a mental state in which one is completely involved in an activity for its own sake [\\[]{}1[\\]]{}. ", "It is characterized as an activity where time flies. ", "Fairness in a game is essential to induce flow [@key-6]. ", "We wanted to allocate defense capabilities such that no single attack was able to dominate. ", "In order to do this, we simulated virus and worm attacks against a fixed network topology for different allocations of defense packages[^2]. ", "This gave us a mapping from (number of defenses with the ability to block viruses) to (number of computers that a virus would likely destroy), and it gave us a similar mapping for worms. ", "We then used the inverse of this mapping to allocate the capabilities of defense packages such that viruses and worms would be likely to destroy the same number of computers.", "\n\nFor the Monte Carlo simulation, we used the following topology in Fig. ", "\\[fig:LAN-topology-used\\], one that is within limits and is symmetrical in nature.", "\n\n![", "\\[fig:LAN-topology-used\\]LAN topology used for Monte-Carlo simulation. ", "In this simulation, we ran different attacks against different possible configurations of the defense packages. ", "We ultimately designed the defense packages based on the configurations that created the most equal performance for the different attacks.](Fig7_edit){width=\"0.8\\columnwidth\"}\n\nFor the random simulations, a random routing point was chosen from a uniform distribution. ", "The virus was simulated such that it would not revisit nodes if it had the potential to explore unvisited nodes. ", "The worm had the capability to visit all nodes. ", "For each number of defenses ranging from 0 to 8, 1000 simulations were done to average the number of nodes destroyed. ", "Figs. ", "\\[fig:Number-of-computers-destroyed\\] and \\[fig:Number-of-computers-worm\\] depict the results of these simulations.", "\n\n![", "\\[fig:Number-of-computers-destroyed\\]Number of computers destroyed by virus attack versus number of defenses equipped with the ability to block the virus. ", "For instance, if four defenses were to be configured with the capability to block the virus, then the average virus attack would destroy approximately one computer.](Fig8_edit){width=\"0.8\\columnwidth\"}\n\n![", "\\[fig:Number-of-computers-worm\\]Number of computers destroyed by worm attack versus number of defenses equipped with the ability to block the worm](Fig9_edit){width=\"0.8\\columnwidth\"}\n\nFigs. ", "\\[fig:Number-of-computers-destroyed\\] and \\[fig:Number-of-computers-worm\\] show that to give the virus and worm similar strengths, the number of defenses that protect against viruses should be less than that of worms. ", "Based on the figures, four defense packages should be equipped with the ability to block worms and two with the ability to block viruses. ", "This makes each able to destroy approximately 2.5 computers on average[^3].", "\n\nBased on the results of this simulation, the next subsection describes a sample strategic consideration that players might use to build a LAN and allocate defense packages.", "\n\nStrategy\n--------\n\nClearly there are some implicit guidelines for making a topology. ", "For instance, it seems unwise to leave a direct path without worm defense to the critical computer. ", "Such topologies arise in automatic wins if the correct attack is carried out. ", "One particular defensive strategy that could be used is to create two *communities*.", "\n\n![", "\\[fig:A-topology-robust\\]A topology to robustly protect against worm attacks](Fig11_edit){width=\"0.8\\columnwidth\"}\n\nThe topology in Fig. ", "\\[fig:A-topology-robust\\] is an example of a dual-community topology. ", "A community could be defined as a concentration of nodes with a high degree of inter-connectivity. ", "This dual-community topology in Fig. ", "\\[fig:A-topology-robust\\] also has the property that it forces attacks through certain computers on the way to computer number 8, in which the critical information is maintained. ", "As a result, there are no short routes to get to node 8.", "\n\nWe conducted a simulation to analyze the effectiveness of this topology. ", "The results of this simulation are shown in Fig. ", "\\[fig:Computer-casualties-with\\], which shows that fewer computers were eliminated on average for the same defensive configurations for the long dual-community strategy than for the default strategy.", "\n\n![", "\\[fig:Computer-casualties-with\\]Computer casualties with default versus robust defense configurations](Fig12_edit){width=\"0.8\\columnwidth\"}\n\nFrom an offensive standpoint, an attack strategy might be to send out 4 attacks simultaneously. ", "The attack that has the least probability of being defended against will attack a node. ", "Once this node is attacked the defenses of that node are now known. ", "If it successfully defends against one attack, the player has at least one other attack to take out this node. ", "In fact, this method of attack is very effective when using the first attacker to be a virus because there are only two defenses against viruses.", "\n\nImplicit Game-theoretic trade-offs\n----------------------------------\n\nBesides explicitly teaching players basic cyber literacy, *P&G* also aims to give them implicit experience in game-theoretic optimization. ", "This optimization is apparent in network configuration for defense and selecting optimal attack strategies.", "\n\nThe defensive network strategy embodied by the dual-community strategy depicted in Fig. ", "\\[fig:A-topology-robust\\], for instance, involves a trade-off. ", "The advantage of the configuration is that it strongly protects computer number 8, which can be used to store the critical information. ", "Unfortunately, this also reveals the likely location of the critical information to the opposing player! ", "A more “flat” and network topology would have the advantage of more effectively disguising the location of the critical information. ", "Such deception is heavily studied in the area of security in general [@key-13; @key-14; @key-15], and is especially important in cybersecurity [@key-16; @key-17]. ", "In terms of game theory, choosing a flat topology amounts to preferring information asymmetry to brute force.", "\n\nInformation asymmetry is also important in selecting attack strategies. ", "Initially, an attacking player has no knowledge of her opponent’s allocation of defensive packages. ", "She has the option to use initial attacks primarily as “scouts” in order to ascertain the allocation of defense packages. ", "Of course, this may involve sacrificing the turns that it takes to regenerate attacks. ", "We are excited to see how players develop strategies that leverage these concepts - possibly without explicit knowledge of the scholarship behind them.", "\n\nPlaytesting\\[sec:Playtesting\\]\n==============================\n\nThe initial target audience of *Protection and Deception* (*P&G*) ** was any person over the age of six. ", "The game was tested out among various ages ranging from ages six to 21 years old. ", "The testers were from two groups. ", "The first was a combination of children who frequented a community center located in the Lower East Side of Manhattan, New York. ", "The second consisted of mostly college students. ", "Our initial tests at the community center were conducted with four children.", "\n\nWe initially considered implementing structured pre- and post-play surveys that would have enabled statistical analysis. ", "Encouraged, however, by advice from the educational community, we eventually opted for less structured observation that would not discourage students. ", "Essentially, we collected evidence by open-ended observation.", "\n\nQuestions to the children before the game lasted no more than five minutes per player. ", "We asked the players their age, what they know about cyber security, what academic subject they preferred, and what interests they pursued outside of school. ", "The questions about favorite subject and interest were a means to figure out their backgrounds. ", "We had children who were interested in math, science, basketball, painting, and other activities. ", "These children at the community center did not have any explicit knowledge about cybersecurity. ", "We asked whether they had heard of “hackers,” but they had not. ", "We also tested the game with two high school students, one of which expressed interest in business and another in engineering. ", "Finally, our second pool of testers were college students looking to pursue careers in the fields of engineering, medical, and art.", "\n\nIn the post-survey, all players were asked what they learned about cyber security, what they liked and disliked about the game. ", "One 7-year old girl from the community center said, I like the cards the most. ", "A 10-year old boy said, I forgot which card I put down for the different computers - which indicated to us an aspect of the board design that we can improve so that it is obvious which attack and defense cards have been allocated to each computer. ", "A 20-year old college student studying medicine had a brief understanding about cybersecurity before the game, but after playing learned how different attacks such as the worm worked and learned about cyber attacks that I didn’tt know existed like masquerading. ", "A 17 year old in high school who expressed an interest in business said he would play the game if more of his friends knew about the game and how to play. ", "He was asked a follow-up question if there was anything in the game he wanted to learn more about. ", "He said he plays video games on his *PlayStation 4* console a lot and realized he had an experience of denial of service when a group of hackers took down the *PlayStation* online network and I could not log on or use the network for a few days. ", "We were encouraged by this rather comical realization that cybersecurity concepts are especially embedded in non-academic activities.", "\n\nFor all age groups, the instructions seemed rather complex; many times during the game, players would ask the testers whether moves were legal or ask about the results of particular actions. ", "Importantly, we learned that it was helpful to follow the instructions with a quick demonstration of the game play. ", "This adjustment in our introduction of the game decreased the difficulty of learning, although did not remove the learning curve completely. ", "Based on this expressed difficulty, we are considering including video instruction or other means to make the game easier to learn. ", "We describe these briefly in Section \\[sec:Conclusions\\].", "\n\nFinally, we noted that the game seemed enjoyable to players once the rules became clear. ", "Players were excited when their attack successfully destroyed a computer or when their computers successfully repelled the opponent’s attacks. ", "Among the older players, we noted a competitiveness that emerged from the freedom allowed to choose different strategies. ", "From observing the various age groups, it appeared that the testers that were around or over the age of 13 enjoyed the game the most. ", "We will seek a much larger subject pool for further testing in order to refine the target age for *P&G*.", "\n\nRelated Work\n============\n\nIn the introduction, we described various classes of games from which *Protection and Deception* (*P&G*) derives its framework. ", "Namely, *P&G* is a serious game - a game which teaches concepts which have actual value outside of serving the entertainment purpose of the game. *", "P&G* aims to build cyber literacy, as well as to implicitly teach about trade-offs between strength and information revelation. ", "Furthermore, *P&G* represents an effort in the vast category of security education, a critical area of study in the light of intense regional and international conflicts in cybersecurity. ", "Finally, *P&G* builds upon a tradition of games-based learning.", "\n\nWe can see similarities to *P&G* in at several recent games. ", "From last year’s *3GSE,* Microsoft’s *Elevation of Privilege* [@key-7] is a card game based on concepts from information security with a fascinating purpose: it is played between developers in order to discover security flaws of a system. *", "Elevation of Privilege* is an example of gamification, since it employs motivations from game-playing for a serious task. ", "Developers in this game draw cards which prompt them to name vulnerabilities, and thereby accomplish a technical objective. *", "Elevation of Privilege* is obviously not geared towards a novice population.", "\n\n*Control-Alt-Hack* [@key-8] is a card game from *3GSE’14* which is geared towards a novice population. ", "This game seeks to give participants an social experience related to hacking, rather than teaching specific concepts. ", "The network security game called *[\\[]{}d0x3d![\\]]{}* [@key-9] is also a similar effort to ours. ", "It is a board game with changeable configuration achieved by tiles which are arranged at the beginning of gameplay. ", "Players in *[\\[]{}d0x3d![\\]]{}* deploy special abilities on their way to collecting digital resources (“*[\\[]{}loot[\\]]{}*”). ", "Both games are attractively designed, and represent efforts to intelligently deploy and commercialize or test security games. ", "They both use existing games re-skinned in cybersecurity concepts and terminology, whereas our game is an entirely new design.", "\n\n*Control-Alt-Hack* and *[\\[]{}d0x3d![\\]]{}* both seem to feature a higher degree of security vocabulary than *P&G*. ", "Indeed, *P&G* represents an effort to reach out to non-technical, underrepresented, and young players. ", "We are concerned not only about players who may not have the technological background to understand security concepts, but also players who may not have the attention span to learn a complicated game. ", "In our own playtesting, we observed that even with the simple mechanics of our game, there was some learning curve. ", "Thus, we aim to keep the security lexicon in *P&G* to a minimum. ", "This will help us achieve the goal of engaging a diverse population in security awareness.", "\n\nConclusions and Future Work\\[sec:Conclusions\\]\n==============================================\n\nOur initial work on *Protection and Deception* (*P&G*) opens up vast possibilities for future development. ", "In terms of basic elements of gameplay, we have considered several options. ", "First of all, the connection between security challenges and economic questions has been extensively noted in the literature [@key-10; @key-11; @key-12]. ", "Because of this, we are considering incorporating money or budgeting resources into the gameplay. ", "We are also considering allowing players to elect to build up their LAN capabilities instead of deploying attacks. ", "This trade-off pits myopic against farsighted strategies, and allows implicitly teaching the present value of future rewards. ", "Finally, we have noted that a visual demonstration of play seemed to lower the learning curve for our participants. ", "Because of this, we are considering deploying video instructions online that can be used to learn the game. ", "On the more extreme end, the entire game could be digitized, or a hybrid board game and digital game combination could be considered.", "\n\nIn its present version, *P&G* is a board game designed to engage young, non-technical, and underrepresented players in the world of cyber security. *", "P&G* features a completely new design which relies on probabilistic simulation to ensure fair gameplay. ** ", "The game offers three major contributions. ", "First, by exposing participant to various types of cyber-attacks such as *denial of service* and *masquerading attacks*, it builds cyber literacy in an inviting way. ", "Second, it teaches aspects of game theory such as information asymmetry and deception implicitly. ", "Finally, *P&G* engages players with little or no previous introduction to cybersecurity. ", "Indeed, we conducted an initial set of tests with such a population at a community center in the Lower East Side of Manhattan, New York. ", "Encouraged by these initial results, we hope to continue to improve *P&G* so that it can contribute to the important and vast contemporary challenge of cybersecurity education.", "\n\n[10]{} M. Robert, 10 Biggest Data Breaches of 2014 (So Far), *CreditUnionTimes*, 06-Oct-2014. [", "\\[]{}Online[\\]]{}. ", "Available: http://www.cutimes.com/2014/10/06/10-biggest-data-breaches-of-2014-so-far. [", "\\[]{}Accessed: 16-May-2015[\\]]{}.", "\n\nPresidents Council of Advisers on Science and Technology, Chairs: J.P. Holdren and E.S. Lander, “Report to the President, Big Data and Privacy: A Technological Perspective,” 2014.", "\n\nCommittee on Responding to Section 5(d) of Presidential Policy Directive 28, Bulk Collection of Signals Intelligence: Technical Options, National Research Council of the National Academies, 2015.", "\n\nS. Payne, Developing Security Education and Awareness Programs, *Educause Quarterly*, Nov. 2003.", "\n\nJ. Nakamura, M. Csikszentmihalyi, The concept of flow, in *Handbook of Positive Psychology*, 2002.", "\n\nS. Baron, Cognitive Flow: The Psychology of Great Game Design, *Gamasutra*. [", "\\[]{}Online[\\]]{}. ", "Available: http://www.gamasutra.com/view/feature/ 166972/cognitive\\_flow\\_the\\_psychology\\_of\\_.php. [", "\\[]{}Accessed: 18-May-2015[\\]]{}.", "\n\nA. Shostack, Elevation of Privilege: Drawing Developers into Threat Modeling, presented at the *Summit on Gaming, Games. ", "and Gamification in Security Education*, San Diego, CA, 2014.", "\n\nT. Denning and T. Kohno, Practical Lessons From Creating the Control-Alt-Hack Card Game and Research Challenges for Games In Education and Research, presented at the *Summit on Gaming, Games. ", "and Gamification in Security Education*, San Diego, CA, 2014.", "\n\nM. Gondree and Z. N. Peterson, Valuing Security by Getting [\\[]{}d0x3d![\\]]{}, presented at the *Workshop on Cyber Security Experimentation and Test*, Washington, DC, 2013.", "\n\nN. Chachra, D. M. S. Savage, and G. M. Voelker, Empirically Characterizing Domain Abuse and the Revenue Impact of Blacklisting, presented at the *Workshop on the Economics of Information Security*, Pennsylvania State University, 2014.", "\n\nM. H. R. Khouzani, V. Pham, and C. Cid, Incentive Engineering for Outsourced Computation in the Face of Collusion, presented at the *Workshop on the Economics of Information Security*, Pennsylvania State University.", "\n\nY. Pu and J. Grossklags, An economic model and simulation results of app adoption decisions on networks with interdependent privacy consequences, in *Decision and Game Theory for Security*, Springer, 2014, pp. ", "246265.", "\n\nU. Fischbacher and F. Föllmi-Heusi, Lies in Disguise - An experimental study on cheating, *Journal of the European Economic Association*, vol. ", "11, no. ", "3, 2013.", "\n\nS. Hurkens and N. Kartik, Would I Lie to You? ", "On Social Preferences and Lying Aversion, *Experimental Economics*, vol. ", "12, no. ", "2, 2009.", "\n\nA. Vrij, P. A. Granhag, S. Mann, and S. Leal, Outsmarting the Liars: Toward a Cognitive Lie Detection Approach, *Current Directions in Psychological Science*, vol. ", "20, no. ", "1, pp. ", "2832, Feb. 2011.", "\n\n*Cyber War and Cyber Terrorism*, ed. ", "A. Colarik and L. Janczewski, Hershey, PA: The Idea Group, 2007.", "\n\nJ. Pawlick and Q. Zhu, “Deception by Design: Evidence-Based Signaling Games for Network Defense,” to be presented at the *Workshop on the Economics of Information Security*, Delft University of Technology, the Netherlands, 2015.", "\n\n[^1]: Department of Electrical and Computer Engineering, Polytechnic School of Engineering, New York University, Brooklyn, NY 11201. {", "sz903, jp3122, js6160, jpawlick, quanyan.zhu} @nyu.edu\n\n This work was supported in part by the New York University Prototyping Fund, a collaborative program offered by the *Greenhouse at NYU* and the *NYU Entrepreneurial Insitute*.", "\n\n It was also supported in part by an NSF IGERT grant through the *Center for Interdisciplinary Studies in Security and Privacy* (*CRISSP*) at NYU.", "\n\n[^2]: We simulated virus and worm attacks because they have least and most powerful special attack properties, respectively. ", "The virus has no special attack power, while the worm has the power to continue to propagate if it is not destroyed. ", "We allocated defenses against the other attacks by assuming that their special attack properties lie somewhere between those of the virus and worm. ", "Thus, we configured between two defense packages (the number which were endowed with the ability to block viruses) and five defense packages (the number configured with the ability to block worms) with the ability to block the other attacks.", "\n\n[^3]: The first iteration of defense packages used preliminary simulation results. ", "Thus, in the allocations discussed in Section \\[sec:Gameplay\\], there are five rather than four defense packages equipped with the ability to block worms.", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "Q:\n\nHow to identify NAMESPACE, METHOD_NAME, URL and SOAP_ACTION from WSDL and SOAP message\n\nI have some problem in parsing a SOAP web service. ", "How can i identify the NAMESPACE, METHOD_NAME, URL and SOAP_ACTION from WSDL and also how can i handle using SoapObject.", "\nI want to call the soap in android. ", "\nBelow are the WSDL AND SOAP REQUEST XML.", "\nWSDL:\nhttps://e1jas01.domain.cssus.com:8091/DV910/RI_AddressBookManager?WSDL\nThanks,\nGowtham.", "\n\nA:\n\nFirstly, downloading SoapUI will help you a lot, when you create a new project there and import that URL, you will see namespaces and method names properly. ", "For the Soap action; for each operation there is 1 soap action. ", "From that link first you should find the operation which you want to use then you will see soap action of that operation.", "\nhttp://www.c-sharpcorner.com/UploadFile/88b6e5/how-to-call-web-service-in-android-using-soap/\nHere, there is a tutorial about creating soap objects etc.", "\n\n" ]

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[ "// Copyright 2015 the V8 project authors. ", "All rights reserved.", "\n// Use of this source code is governed by a BSD-style license that can be\n// found in the LICENSE file.", "\n\n#include \"src/compiler/graph-assembler.h\"\n\n#include \"src/code-factory.h\"\n#include \"src/compiler/linkage.h\"\n#include \"src/objects-inl.h\"\n\nnamespace v8 {\nnamespace internal {\nnamespace compiler {\n\nGraphAssembler::GraphAssembler(JSGraph* jsgraph, Node* effect, Node* control,\n Zone* zone)\n : temp_zone_(zone),\n jsgraph_(jsgraph),\n current_effect_(effect),\n current_control_(control) {}\n\nNode* GraphAssembler::IntPtrConstant(intptr_t value) {\n return jsgraph()->IntPtrConstant(value);\n}\n\nNode* GraphAssembler::Int32Constant(int32_t value) {\n return jsgraph()->Int32Constant(value);\n}\n\nNode* GraphAssembler::UniqueInt32Constant(int32_t value) {\n return graph()->NewNode(common()->Int32Constant(value));\n}\n\nNode* GraphAssembler::SmiConstant(int32_t value) {\n return jsgraph()->SmiConstant(value);\n}\n\nNode* GraphAssembler::Uint32Constant(int32_t value) {\n return jsgraph()->Uint32Constant(value);\n}\n\nNode* GraphAssembler::Float64Constant(double value) {\n return jsgraph()->Float64Constant(value);\n}\n\nNode* GraphAssembler::HeapConstant(Handle<HeapObject> object) {\n return jsgraph()->HeapConstant(object);\n}\n\n\nNode* GraphAssembler::ExternalConstant(ExternalReference ref) {\n return jsgraph()->ExternalConstant(ref);\n}\n\nNode* GraphAssembler::CEntryStubConstant(int result_size) {\n return jsgraph()->CEntryStubConstant(result_size);\n}\n\nNode* GraphAssembler::LoadFramePointer() {\n return graph()->NewNode(machine()->LoadFramePointer());\n}\n\n#define SINGLETON_CONST_DEF(Name) \\\n Node* GraphAssembler::Name() { return jsgraph()->Name(); }\nJSGRAPH_SINGLETON_CONSTANT_LIST(SINGLETON_CONST_DEF)\n#undef SINGLETON_CONST_DEF\n\n#define PURE_UNOP_DEF(Name) \\\n Node* GraphAssembler::Name(Node* input) { \\\n return graph()->NewNode(machine()->Name(), input); \\\n }\nPURE_ASSEMBLER_MACH_UNOP_LIST(PURE_UNOP_DEF)\n#undef PURE_UNOP_DEF\n\n#define PURE_BINOP_DEF(Name) \\\n Node* GraphAssembler::Name(Node* left, Node* right) { \\\n return graph()->NewNode(machine()->Name(), left, right); \\\n }\nPURE_ASSEMBLER_MACH_BINOP_LIST(PURE_BINOP_DEF)\n#undef PURE_BINOP_DEF\n\n#define CHECKED_BINOP_DEF(Name) \\\n Node* GraphAssembler::Name(Node* left, Node* right) { \\\n return graph()->NewNode(machine()->Name(), left, right, current_control_); \\\n }\nCHECKED_ASSEMBLER_MACH_BINOP_LIST(CHECKED_BINOP_DEF)\n#undef CHECKED_BINOP_DEF\n\nNode* GraphAssembler::Float64RoundDown(Node* value) {\n if (machine()->Float64RoundDown().IsSupported()) {\n return graph()->NewNode(machine()->Float64RoundDown().op(), value);\n }\n return nullptr;\n}\n\nNode* GraphAssembler::Projection(int index, Node* value) {\n return graph()->NewNode(common()->Projection(index), value, current_control_);\n}\n\nNode* GraphAssembler::Allocate(PretenureFlag pretenure, Node* size) {\n return current_effect_ =\n graph()->NewNode(simplified()->Allocate(Type::Any(), NOT_TENURED),\n size, current_effect_, current_control_);\n}\n\nNode* GraphAssembler::LoadField(FieldAccess const& access, Node* object) {\n return current_effect_ =\n graph()->NewNode(simplified()->LoadField(access), object,\n current_effect_, current_control_);\n}\n\nNode* GraphAssembler::LoadElement(ElementAccess const& access, Node* object,\n Node* index) {\n return current_effect_ =\n graph()->NewNode(simplified()->LoadElement(access), object, index,\n current_effect_, current_control_);\n}\n\nNode* GraphAssembler::StoreField(FieldAccess const& access, Node* object,\n Node* value) {\n return current_effect_ =\n graph()->NewNode(simplified()->StoreField(access), object, value,\n current_effect_, current_control_);\n}\n\nNode* GraphAssembler::StoreElement(ElementAccess const& access, Node* object,\n Node* index, Node* value) {\n return current_effect_ =\n graph()->NewNode(simplified()->StoreElement(access), object, index,\n value, current_effect_, current_control_);\n}\n\nNode* GraphAssembler::DebugBreak() {\n return current_effect_ = graph()->NewNode(machine()->DebugBreak(),\n current_effect_, current_control_);\n}\n\nNode* GraphAssembler::Store(StoreRepresentation rep, Node* object, Node* offset,\n Node* value) {\n return current_effect_ =\n graph()->NewNode(machine()->Store(rep), object, offset, value,\n current_effect_, current_control_);\n}\n\nNode* GraphAssembler::Load(MachineType rep, Node* object, Node* offset) {\n return current_effect_ =\n graph()->NewNode(machine()->Load(rep), object, offset,\n current_effect_, current_control_);\n}\n\nNode* GraphAssembler::Retain(Node* buffer) {\n return current_effect_ =\n graph()->NewNode(common()->Retain(), buffer, current_effect_);\n}\n\nNode* GraphAssembler::UnsafePointerAdd(Node* base, Node* external) {\n return current_effect_ =\n graph()->NewNode(machine()->UnsafePointerAdd(), base, external,\n current_effect_, current_control_);\n}\n\nNode* GraphAssembler::ToNumber(Node* value) {\n return current_effect_ =\n graph()->NewNode(ToNumberOperator(), ToNumberBuiltinConstant(),\n value, NoContextConstant(), current_effect_);\n}\n\nNode* GraphAssembler::DeoptimizeIf(DeoptimizeReason reason, Node* condition,\n Node* frame_state) {\n return current_control_ = current_effect_ = graph()->NewNode(\n common()->DeoptimizeIf(DeoptimizeKind::kEager, reason), condition,\n frame_state, current_effect_, current_control_);\n}\n\nNode* GraphAssembler::DeoptimizeIfNot(DeoptimizeKind kind,\n DeoptimizeReason reason, Node* condition,\n Node* frame_state) {\n return current_control_ = current_effect_ = graph()->NewNode(\n common()->DeoptimizeUnless(kind, reason), condition, frame_state,\n current_effect_, current_control_);\n}\n\nNode* GraphAssembler::DeoptimizeIfNot(DeoptimizeReason reason, Node* condition,\n Node* frame_state) {\n return DeoptimizeIfNot(DeoptimizeKind::kEager, reason, condition,\n frame_state);\n}\n\nvoid GraphAssembler::Branch(Node* condition, GraphAssemblerLabel<0u>* if_true,\n GraphAssemblerLabel<0u>* if_false) {\n DCHECK_NOT_NULL(current_control_);\n\n BranchHint hint = BranchHint::kNone;\n if (if_true->IsDeferred() !", "= if_false->IsDeferred()) {\n hint = if_false->IsDeferred() ? ", "BranchHint::kTrue : BranchHint::kFalse;\n }\n\n Node* branch =\n graph()->NewNode(common()->Branch(hint), condition, current_control_);\n\n current_control_ = graph()->NewNode(common()->IfTrue(), branch);\n MergeState(if_true);\n\n current_control_ = graph()->NewNode(common()->IfFalse(), branch);\n MergeState(if_false);\n\n current_control_ = nullptr;\n current_effect_ = nullptr;\n}\n\n// Extractors (should be only used when destructing the assembler.", "\nNode* GraphAssembler::ExtractCurrentControl() {\n Node* result = current_control_;\n current_control_ = nullptr;\n return result;\n}\n\nNode* GraphAssembler::ExtractCurrentEffect() {\n Node* result = current_effect_;\n current_effect_ = nullptr;\n return result;\n}\n\nvoid GraphAssembler::Reset(Node* effect, Node* control) {\n current_effect_ = effect;\n current_control_ = control;\n}\n\nOperator const* GraphAssembler::ToNumberOperator() {\n if (!", "to_number_operator_.is_set()) {\n Callable callable =\n Builtins::CallableFor(jsgraph()->isolate(), Builtins::kToNumber);\n CallDescriptor::Flags flags = CallDescriptor::kNoFlags;\n CallDescriptor* desc = Linkage::GetStubCallDescriptor(\n jsgraph()->isolate(), graph()->zone(), callable.descriptor(), 0, flags,\n Operator::kEliminatable);\n to_number_operator_.set(common()->Call(desc));\n }\n return to_number_operator_.get();\n}\n\n} // namespace compiler\n} // namespace internal\n} // namespace v8\n" ]

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[ "The diagnosis of pulmonary embolism.", "\nAlthough clinical diagnosis of pulmonary embolism (PE) is not sufficiently reliable to determine management, it is valuable for stratifying patients into high, intermediate, and low clinical suspicion of embolism. ", "Clinical assessment can then be combined with lung scanning to identify groups of patients with a sufficiently high or low probability of PE that a decision to anticoagulate or withhold therapy can be made. ", "Approximately half of patients with suspected PE will fall into one of these categories. ", "Thrombosis in the deep veins of the leg (DVT) can be detected by noninvasive tests in approximately 50%, and by bilateral venography in approximately 70% of patients with PE, and provides grounds for anticoagulation of some patients with nondiagnostic combinations of clinical and lung scan assessments. ", "Failure to detect DVT makes it less likely but does not exclude the possibility that the patient had a PE. ", "Preliminary evidence suggests that the majority of patients with nondiagnostic combinations of clinical assessment, lung scanning, and negative noninvasive tests for DVT can safely be managed without anticoagulation, provided serial noninvasive tests for DVT remain normal over a 2-week period. ", "Pulmonary angiography may be advisable in patients with nondiagnostic combinations of the above tests in whom (a) the probability of PE remains high (e.g. 30-80%), (b) cardiopulmonary reserve is poor, (c) serial follow-up is not feasible, or (d) future management (e.g. subsequent pregnancy) would be influenced by the result. ", "D-Dimer measurements are sensitive but nonspecific for PE and therefore may have a high negative predictive value, further simplifying the diagnostic approach to PE." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "The Military Racquetball Federation released a new promo video today. ", "The MRF does important work with rehabilitation of injuries both mental and physical by introducing veterans to racquetball. ", "Please consider supporting their work, either with your time, your social media presence, or your money.", "\n\nFacebook\n\nWebsite\n\nGoFundMe" ]

{ "pile_set_name": "OpenWebText2" }

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[ "Researchers Closer to Uncovering a New Feature in Heart Failure\n\nAuthor Information (click to view)\n\nPerelman School of Medicine at the University of Pennsylvania\n\nPerelman School of Medicine at the University of Pennsylvania (click to view)\n\nPerelman School of Medicine at the University of Pennsylvania\n\nAdvertisement\n\nA team of researchers from Penn Medicine, in collaboration with the University of Connecticut, published their findings today in the Journal of the American Heart Association, building on a methods paper which was published recently in Nature Protocols. ", "The team is the first to have developed a method for measuring the length of telomeres using human heart tissues.", "\n\n“Once we had established the method for measuring the telomeres in heart cells, which was tricky because human cardiac cells are rarely taken from a living person, we acquired heart tissue samples from patients receiving heart transplants and organ donors in order to evaluate telomere length,” said the study’s lead researcher, Foteini Mourkioti, PhD, an assistant professor of Orthopaedic Surgery and Cell and Developmental Biology, and co-director of the Musculoskeletal Regeneration Program in the Penn Institute for Regenerative Medicine. “", "Using samples from the Penn Heart Tissue Biobank meant we were also able to acquire patient data for the samples, so we knew useful information like the patient’s age, sex, and heart function.”", "\n\nResearchers were able to measure the telomeres in the samples of patients who had heart disease and those who did not, and group the findings into categories based on patients’ age. ", "They found that in the samples for healthy people, age did not play a role in telomere length, since the telomeres of both young and old healthy individuals were not affected. ", "However, patients with heart failure had shorter telomeres regardless of their age. ", "In comparing diseased and healthy samples, researchers were able to draw a correlation between shorter telomeres and the presence of heart failure. ", "Patients with the shortest telomeres in their cardiac cells also had the most severely decreased cardiac function. ", "The team also found that the cardiomyocytes were the only heart cells affected by the telomere length in disease samples, but the telomere length of other cells within the same diseased heart samples were not different.", "\n\n“This human tissue research is critical as it may open the door for future telomere preserving therapies to help protect heart failure patients” said co-author Kenneth B. Margulies, MD, a professor of Medicine and research director for Heart Failure and Transplantation. “", "While there is a need to better understand howheart disease induces telomere shortening, this is an important step in the research process, one that brings us closer to a better understanding of heart failure”" ]

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[ "Q:\n\nRegex - Validate an account number with two different patterns\n\nI need to validate an account number. ", "\nA valid number could be either a sequence of exactly 11 digits or 3 groups of digits separated by hyphens (2 digits - 3 digits - 6 digits)\nI tried this :\n/^([0-9]{11})|([0-9]{2}-[0-9]{3}-[0-9]{6})$/\n\nBut it only works for the second rule . ", "The first rule doesn't work as it allows numbers of more than 11 digits\nThis is how I use the regex in my js function :\n var re = /^([0-9]{11})|([0-9]{2}-[0-9]{3}-[0-9]{6})$/;\n if (re.test(txtNumber.value)==true) {\n return 1;\n }\n else {\n alert(\"Invalid Account Number\");\n return 0;\n }\n\nAny advise or guidance would be greatly appreciated\nVALID NUMBERS:\n12345678912 (11 digits)\n12-345-678912 (11 digits separated by hyphens) \nINVALID NUMBERS:\n1223 (less than 11 digits)\n111111111111 ( more than 11 digits) \n123-23-678912 (11 digits , but not separated correctly, it should be 2 digits-3 digits-6 digits)\n\nA:\n\nAs | regex operator precedence is the lowest, it should be written like this:\n/^(?:[0-9]{11}|[0-9]{2}-[0-9]{3}-[0-9]{6})$/\n\n... so that alternation pattern is bound both to the beginning and the end of the string.", "\nAs it stands in your code, pattern checks for either sequence of 11 digits at the beginning of the string, or sequence of 'two digits, hyphen, three digits, hyphen, six digits' at its end - but never really bind the rule to both ends. ", "And that's easy to prove:\nvar patt = /^([0-9]{11})|([0-9]{2}-[0-9]{3}-[0-9]{6})$/;\npatt.test('acdbdfdsfsf22-333-666666'); // true\n\nAs a sidenote, as you don't need to capture anything with that grouping expression, I've prepended it with ?:. ", "Actually, it can be optimized even more:\n/^[0-9]{2}(?:[0-9]{9}|-[0-9]{3}-[0-9]{6})$/\n\n... as the less you alternate, the better. ", "But in this case it really won't matter much, I suppose.", "\n\nIn short, the problem can be illustrated with these two patterns:\n/^a|b$/\n\nThis reads as 'match either a at the beginning of the string, or b at its end.", "\n/^(?:a|b)$/\n\nThis reads as 'match the beginning of the string, followed by either a or b, followed by the end of the string'.", "\n\n" ]

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[ "Q:\n\nAdding a fade effect to an image slider\n\nI have a working image slider.", "\n\nvar sliderIndex = 0; // start with the first image\r\nvar autoSlideHandler; // for the reset\r\nvar activeDuration = 3000; // each picture is active for 3 seconds\r\n\r\nstartImageSlider();\r\nfunction startImageSlider() { // Initialize the slider\r\n sliderIndex++;\r\n updateImageSlider();\r\n autoSlideHandler = setTimeout(startImageSlider, activeDuration);\r\n}\r\n\r\nfunction changeSliderImage(direction) { // change images manually by pressing the buttons\r\n sliderIndex += direction;\r\n updateImageSlider();\r\n clearTimeout(autoSlideHandler);\r\n autoSlideHandler = setTimeout(startImageSlider, activeDuration);\r\n}\r\n\r\nfunction updateImageSlider() { // switch the images\r\n var sliderImages = $(\".sliderImg\");\r\n\r\n for (var i = 0; i < sliderImages.length; i++) {\r\n sliderImages[i].style.display = \"none\"; // hide the current image\r\n }\r\n if (sliderIndex > sliderImages.length) {\r\n sliderIndex = 1;\r\n }\r\n else if (sliderIndex < 1) {\r\n sliderIndex = sliderImages.length;\r\n }\r\n sliderImages[sliderIndex - 1].style.display = \"block\"; // show the next image\r\n}\n#containerImageSlider {\r\n width: 200px;\r\n height: 100px;\r\n position: relative;\r\n top: 50%;\r\n left: 50%;\r\n transform: translateX(-50%) translateY(25%);\r\n}\r\n\r\n.sliderImg{\r\n width: 100%;\r\n height: 100%;\r\n}\r\n\r\n.sliderBtn {\r\n width: 64px;\r\n height: 64px;\r\n top: 50%;\r\n position: absolute;\r\n}\r\n\r\n#sliderBtnRight{\r\n left: -200px;\r\n /* background-image: url(\"../../Resources/slideImageLeft.png\"); */\r\n}\r\n\r\n#sliderBtnLeft{\r\n right: -200px;\r\n /* background-image: url(\"../../Resources/slideImageRight.png\"); */\r\n}\n<script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js\"></script>\r\n\r\n <div id=\"containerImageSlider\">\r\n <button class=\"sliderBtn\" id=\"sliderBtnLeft\" onclick=\"changeSliderImage(1)\"></button>\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg1.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg2.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg3.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg4.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg5.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg6.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg7.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg8.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg9.jpg\">\r\n <img class=\"sliderImg\" src=\"Resources/SliderImages/sliderImg10.jpg\">\r\n <button class=\"sliderBtn\" id=\"sliderBtnRight\" onclick=\"changeSliderImage(-1)\"></button>\r\n </div>\n\nSo when calling the function updateImageSlider() I want the current Image fading out and the next image fading in.", "\nExample\n$(currentImage).fadeOut(1000, function () {\n // hide the image\n});\n\n$(nextImage).fadeIn(1000, function () {\n // show the image\n});\n\nBut when trying to put this code into my existing code it doesn't seem to work fine.", "\nI thought about writing\n var currentImage = sliderImages[i];\n $(currentImage).fadeOut(1000, function () {\n currentImage.style.display = \"none\";\n });\n\nand\nvar nextImage = sliderImages[sliderIndex - 1];\n$(nextImage).fadeIn(1000, function () {\n nextImage.style.display = \"block\";\n});\n\nbut this does not fit into my code. ", "The current Image is fading out while the next image is already fading in below the current container...\n\nA:\n\nTry to change your updateImageSlider() function as like below and check,\nfunction updateImageSlider() { // switch the images\n var sliderImages = $(\".sliderImg\");\n\n for (var i = 0; i < sliderImages.length; i++) {\n $(sliderImages[i]).fadeOut(1000); // hide the current image\n }\n if (sliderIndex > sliderImages.length) {\n sliderIndex = 1;\n } else if (sliderIndex < 1) {\n sliderIndex = sliderImages.length;\n }\n\n setTimeout(function() {\n $(sliderImages[sliderIndex - 1]).fadeIn(1000); // show the next image\n }, 1000);\n}\n\nCheck this fiddler for reference.", "\n\n" ]

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[ "Genetic characterization of a new astrovirus in goslings suffering from gout.", "\nSince early 2016, the Chinese goose industry has experienced severe outbreaks of gout; however, the etiological factor of the disease is still unclear. ", "Here, we investigated the possible involvement of viral infection in the disease. ", "Using sequence-independent PCR amplification, astrovirus sequences were generated from a gout case. ", "Full-length genomic sequencing and sequence analysis of three goose astrovirus (GoAstV) strains revealed that they belong to a new avastrovirus most closely related to viruses classified within species Avastrovirus 3. ", "The GoAstV was detected in 16/16 gout cases collected from two provinces, supporting a pathogenic role for the new avastrovirus." ]

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[ "Big US markets, especially Silicon Valley, get a lot of attention. ", "I would imagine it distorts the view of what it's really like outside these big markets. ", "So what's the situation like for the average developer outside the big US markets in terms of ease of getting a job (or switching jobs), perks, salary, quality of work?", "\n\nI ask as an average grad entering the industry in a non-top-tier, non-US city." ]

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[ "Q:\n\nGetting SupportFragmentManager without extending FragmentActivity\n\nI want to use Fragments in my application, but I cannot extend FragmentActivity because my application already extends an activity that is part of a library. ", "Since this means that I cannot call getSupportFragmentManager(), I am looking for a workaround that would allow me to use Fragments without having to extend FragmentActivity. ", "Is it possible?", "\n\nA:\n\nYour library is going to need to extend the FragmentActivity.", "\nI would be concerned about a library that requires you to use their base activities anyway.", "\nAs mentioned (where possible) grab the library source code and add it as a library project to eclipse and make its activities extend the FragmentActivity class.", "\n\n" ]

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[ "70 years ago the CIA didn’t exist. ", "Know it is one of the most powerful organisations in the world. ", "With an estimated budget of 5,000 billion dollars annually and 25,000 people working for it, the CIA has more money and power than most developing countries.", "\n\n​\n\nThe CIA first enemy was the Soviet Union. ", "They recruited Reinhard Gehlen (3 April 1902 – 8 June 1979) was a German general who was chief of the Wehrmacht Foreign Armies East (FHO) military-intelligence unit, during World War II. ", "He became a spy of the anti–Communist Gehlen Organization for the U.S. (1946–56).The CIA bought hundreds of Hitler’s officers back to the USA after the war. ", "At secret bases, they were trained how to be spies and then sent back to Germany to spy on the Russians. ", "Nikolaus \"Klaus\" Barbie was an SS-Hauptsturmführer and Gestapo member. ", "He was known as the \"Butcher of Lyon\" was hired by Gehlen. ", "The CIA didn’t question Gehlen on his hires as he was considered to valuables.", "\n\n​\n\nAfter a brief stint with Gehlen, Barbie was recruited by the Pentagons Counter Intelligence Division, known as CIC. ", "In the late 1940’s French intelligence learn Barbie’s assignment in Germany and calls for his extradition. ", "When this became came a political issue in France the CIC decided to smuggle Barbie out of the country to Bolivia where he lived comfortably for the next thirty years.", "\n\n​\n\nIn 1948 the Soviets over through the Czechoslovakian government and installed a puppet Communist government in its place. ", "Gehlen over exaggerated the strength of the Soviet forces when reporting back to Washington. ", "He did this to keep the focus on the Soviet’s strength and maintain his importance in the role of the CIA. ", "The CIA were so interested in the Soviet control over Germany, they overlooked Gehlen’s hiring policies. ", "Gehlen’s organisation was infiltrated by Soviet spies who blackmailed the operatives because of what they did in the war.", "\n\nThe CIA believed the Russians had developed a way of controlling people’s minds so the CIA started on their MK Ultra experiments.", "\n\n​\n\nIn 1953 Alan Dulles sent aside $1 million to get rid of Iranian democratically elected Prime Minister Mohammad Mosaddegh elected in 1951. ", "The British wanted control of Iran’s oil fields and the US wanted control of the 1000 mile border with Russia. ", "In 1953 the CIA bought newspapers, periodical, they bought Army Officers and they organised protests against Mosaddegh. ", "Mosaddegh was overthrown by a group funded by the CIA and loyal to Mohammad-Rezā Shāh Pahlavi, the Shah of Iran to take over power. ", "The CIA had successfully overthrown its first government.", "\n\n​\n\nThe CIA efforts in the Democratic Republic of the Congo was to stop the Russian from getting a stronghold in there. ", "Within days of independence, the Congo was in disarray. ", "Prime Minister Patrice Lumumba had asked the Russians for help. ", "This was unacceptable to the CIA, so they started to look for a replacement Lumumba. ", "They found one in Joseph Mobutu, Mobutu was Lumumba's chief of staff and head of the army. ", "In 1961 Lumumba was murdered by troops loyal to Mobutu. ", "Mobutu chased the Soviet’s out of Russia and he was managed for the next three decades by the CIA. ", "The Congo became Mobutu’s backyard. ", "Over his lifetime it was reckoned that Mobutu took $4 billion from the Congo equivalent to half of the Congo’s GDP. ", "Mobutu was also extremely cruel if you crossed him you were a dead man. ", "In spite of all of this, the CIA continued to support him.", "\n\n​\n\nIn the Bay of Pigs the CIA mercenaries to invade Cuba. ", "The CIA put together a fighting force of about 1,500 ex-Cubans they weren’t army men but trained them and then they sent them off to fight the 35 thousand strong Cubans army. ", "The result was a complete humiliation for the United States.", "\n\nThe CIA then turned its attention to Indonesia the CIA did believe President Ahmed Sukarno to be at least indirectly involved with the Indonesian Communist Party (PKI). ", "The CIA turned to Black Operations. ", "Black Ops are illegal operations performed by the CIA for the US Government. ", "On 30th September 1965, a low ranking soldier kidnapped and murdered six Indonesian generals. ", "The solder claimed he’d carried out the attack to prevent the Generals taking over the country in a CIA-sponsored coup. ", "In the confusion that followed the murders General Suharto blamed the Indonesian Communist Party and mounted a coup to get rid of President Sukarno the CIA had gotten what they wanted and Sukarno was driven from power. ", "After the coup, the CIA worked with General Suharto to make sure every communist in Indonesia was killed.", "\n\nThe CIA gave General Suharto a list of people they suspected were communists, Suharto’s men then started massacred between half a million and a million people. ", "The United States government supplied money, training, and ammunition to the Suharto government so they could carry out the massacres.", "\n\n​\n\nThe CIA invented a gun that mimics the effects of a heart attack. ", "The bullet made of ice can be shot into a person and only leave a tiny red mark. ", "The ice then melts and leaves a poison in the body, the poison dissolves and a heart attack is the only thing that is detected in an autopsy." ]

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[ "Debate over health reform's insurance tax heats up\n\nMedicare actuary Rick Foster has testified that the law will increase national health expenditures by $311 billion through 2019. ", "But the administration says Foster undervalues cost-containment measures and that many Americans will still save money thanks to the federal subsidies they'll be entitled to in 2014.", "\n\nThe new estimate comes as health insurance trade associations are again drawing attention to the tax after focusing much of their efforts for the past year on the law's implementation.", "\n\n\"We've really had our hands full just making all the considerable changes,\" said Alissa Fox, senior vice president of policy and representation with the Blue Cross Blue Shield Association. \"", "This tax is going to add hundreds of dollars to the cost of insurance for individuals and small employers. ", "And that's something we are raising concerns with.\"", "\n\nKaren Ignagni, president and CEO of America's Health Insurance Plans, called it an \"unprecedented\" tax that would \"hit individuals and small business.\"", "\n\n\"That moves in the wrong direction, because anything that increases cost beginning in 2014 is going to be something that individuals and small employers look at very very carefully and are going to be concerned about,\" she told The Hill. \"", "We're talking about (the tax and other provisions) again now so people (in Congress) can examine the issues between now and 14 and make changes for this to work, basically.\"" ]

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