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Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics

Luiz G. de Andrade Alves, Haroldo V. Ribeiro , Ervin K. Lenzi e Renio dos S. Mendes

PLOS ONE – Volume: 8; Issue: 8; Article Number: e69580; DOI: 10.1371/journal.pone.0069580; 2013

We report on a quantitative analysis of relationships between the number of homicides, population size and ten other urban metrics. By using data from Brazilian cities, we show that well-defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size. This approach has proved to be robust and useful for unveiling relationships/behaviors that were not properly carried out by the regression analysis, such as the non-explanatory potential of the elderly population when the number of homicides is much above or much below the scaling law, the fact that unemployment has explanatory potential only when the number of homicides is considerably larger than the expected by the power law, and a gender difference in number of homicides, where cities with female population below the scaling law are characterized by a number of homicides above the power law.

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Date;t.setSeconds(t.getSeconds()+this.timeoutAfter()),this.timeoutAt.set(e,t),this.injectPixel(e)})):this.state.set("",State$1.Failed)}get keys(){return this.config?Object.keys(this.config):[]}getPixelEvents(e){var t,n;return null===(n=null===(t=this.config)||void 0===t?void 0:t[e])||void 0===n?void 0:n.pixel_events}injectPixel(e){this.injectedAt.has(e)||(this.injectedAt.set(e,new Date),this.inject(e),this.watch(e))}inject(e){if(!this.providerCtor.scriptInjected){const e=document.createElement("script");e.text=this.getScript(),document.head.appendChild(e),this.providerCtor.scriptInjected=!0}this.init(e)}isTimedOut(e){return+new Date>=+(this.timeoutAt.get(e)||0)}timeoutAfter(){return this.timeoutSeconds}selectPixelEvents(e,t){const n=this.getPixelEvents(t);if(Array.isArray(n))return n.filter((t=>"term-view"===t.trigger&&"visit"===e||(!(!["term-click","ad-view"].includes(t.trigger)||"ctr"!==e)||"ad-click"===t.trigger&&"click"===e)))}}class Facebook extends Provider{getScript(){return"!function(f,b,e,v,n,t,s){if(f.fbq)return;n=f.fbq=function(){n.callMethod?n.callMethod.apply(n,arguments):n.queue.push(arguments)};if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';n.queue=[];t=b.createElement(e);t.async=!0;t.src=v;s=b.getElementsByTagName(e)[0];s.parentNode.insertBefore(t,s)}(window, document,'script','https://connect.facebook.net/en_US/fbevents.js');"}init(e){window.fbq&&window.fbq("init",e)}onPixelEvent(e,t){const n=this.selectPixelEvents(e,t);n&&n.forEach((e=>{e&&(e.custom?window.fbq("trackSingleCustom",t,e.event):window.fbq("trackSingle",t,e.event))}))}isLoaded(e){return!!window.fbq&&window.fbq.getState&&window.fbq.getState(e)}}Facebook.scriptInjected=!1;class Outbrain extends Provider{getScript(){return`!function(_window, _document) { var OB_ADV_ID = ${JSON.stringify(this.keys)}; if (_window.obApi) { var toArray = function(object) { return Object.prototype.toString.call(object) === '[object Array]' ? object : [object]; }; _window.obApi.marketerId = toArray(_window.obApi.marketerId).concat(toArray(OB_ADV_ID)); return; } var api = _window.obApi = function() { api.dispatch ? api.dispatch.apply(api, arguments) : api.queue.push(arguments); }; api.version = '1.1'; api.loaded = true; api.marketerId = OB_ADV_ID; api.queue = []; var tag = _document.createElement('script'); tag.async = true; tag.src = '//amplify.outbrain.com/cp/obtp.js'; tag.type = 'text/javascript'; var script = _document.getElementsByTagName('script')[0]; script.parentNode.insertBefore(tag, script); }(window, document);`}init(e){}onPixelEvent(e,t){const n=this.selectPixelEvents(e,t);n&&n.forEach((e=>{e&&window.obApi("track",e.event)}))}isLoaded(e){return!!window.obApi}}Outbrain.scriptInjected=!1;class Revcontent extends Provider{getScript(){return"var script=document.createElement('script');script.src='https://assets.revcontent.com/master/rev.js';document.head.appendChild(script);"}init(e){}onPixelEvent(e,t){const n=this.selectPixelEvents(e,t);n&&n.forEach((e=>{e&&window.rev("event",e.event)}))}isLoaded(e){return!!window.rev}}Revcontent.scriptInjected=!1;class Taboola extends Provider{getScript(){return`window._tfa = window._tfa || [];!function (t, f, a, x) {if (!document.getElementById(x)) {t.async = 1;t.src = a;t.id=x;f.parentNode.insertBefore(t, f);}}(document.createElement('script'),document.getElementsByTagName('script')[0],'//cdn.taboola.com/libtrc/unip/${this.keys[0]}/tfa.js','tb_tfa_script');`}init(e){}onPixelEvent(e,t){const n=this.selectPixelEvents(e,t);n&&n.forEach((e=>{if(e){const n=parseInt(t,10);window._tfa.push({notify:"event",name:e.event,id:n})}}))}isLoaded(e){return Array.isArray(window._tfa)}}Taboola.scriptInjected=!1;class Tiktok extends Provider{getScript(){return'!function (w, d, t) {w.TiktokAnalyticsObject=t;var ttq=w[t]=w[t]||[];ttq.methods=["page","track","identify","instances","debug","on","off","once","ready","alias","group","enableCookie","disableCookie"],ttq.setAndDefer=function(t,e){t[e]=function(){t.push([e].concat(Array.prototype.slice.call(arguments,0)))}};for(var i=0;i{e&&window.ttq.instance(t).track(e.event)}))}isLoaded(){return!!window.ttq}}Tiktok.scriptInjected=!1;class GoogleAds extends Provider{getScript(){return`var s=document.createElement('script');s.async=1;s.src='https://www.googletagmanager.com/gtag/js?id=${this.keys[0]}';document.head.appendChild(s);window.dataLayer=window.dataLayer||[];function gtag(){dataLayer.push(arguments)}gtag('set','allow_ad_personalization_signals',false);gtag('js',new Date);`}init(e){window.gtag&&window.gtag("config",e)}onPixelEvent(e,t){const n=this.selectPixelEvents(e,t);n&&n.forEach((e=>{e&&window.gtag("event","conversion",{send_to:`${t}/${e.event}`})}))}isLoaded(e){return!!window.gtag}}GoogleAds.scriptInjected=!1;const ADS_PARAM$1=CAFKey,MESSAGE_PREFIX="FSXDC,.aCS:",ALLOWED_ORIGINS=["https://www.google.com","https://www.adsensecustomsearchads.com","https://syndicatedsearch.goog","https://googleadservices.com"];class Pixels{static build(e){const t=unpackPHPArrayObject(e,"pixel_tracking_data");if(t)return t.useAltTikTokEventsForAdsPlatformUser=e.is_ads,new Pixels(t)}constructor(e){this.onPixelEvent=e=>{const{detail:{type:t}}=e;switch(t){case"visit":case"ctr":case"click":this.providers.forEach((e=>e.handlePixelEvent(t)))}},this.providers=[],e.facebook&&Object.keys(e.facebook).forEach((t=>{this.providers.push(new Facebook({[t]:e.facebook[t]}))})),e.tiktok&&Object.keys(e.tiktok).forEach((t=>{this.providers.push(new Tiktok({[t]:e.tiktok[t]}))})),e.taboola&&Object.keys(e.taboola).forEach((t=>{this.providers.push(new Taboola({[t]:e.taboola[t]}))})),e.revcontent&&Object.keys(e.revcontent).forEach((t=>{this.providers.push(new Revcontent({[t]:e.revcontent[t]}))})),e.outbrain&&this.providers.push(new Outbrain(e.outbrain)),e.googleads&&Object.keys(e.googleads).forEach((t=>{this.providers.push(new GoogleAds({[t]:e.googleads[t]}))}))}listenForEvents(){document.addEventListener("pixel",(e=>{this.onPixelEvent(e)}));window.onmessage=e=>{const{origin:t,data:n}=e;ALLOWED_ORIGINS.includes(t)&&"string"==typeof n&&(null==n?void 0:n.startsWith(MESSAGE_PREFIX))&&new URLSearchParams(window.location.search).has(ADS_PARAM$1)&&document.dispatchEvent(new CustomEvent("pixel",{detail:{type:"click"}}))}}listenForPixelEvents(){document.addEventListener("pixel",(e=>{this.onPixelEvent(e)}))}dispatchEvent(e){document.dispatchEvent(new CustomEvent("pixel",{detail:e}))}}var State;!function(e){e[e.Pending=0]="Pending",e[e.Loaded=1]="Loaded",e[e.Failure=2]="Failure",e[e.TimedOut=3]="TimedOut",e[e.Errored=4]="Errored"}(State||(State={}));const CAF_SCRIPT_SRC=`https://www.google.com/adsense/domains/caf.js?${GOOGLE_MV3_URL_PARAMS}`,TIMEOUT_SCRIPTS=Number(GOOGLE_CAF_TIMEOUT_SCRIPTS),TIMEOUT_CALLBACKS=Number(GOOGLE_CAF_TIMEOUT_CALLBACKS);class StateMachine{constructor(){this.state=State.Pending}transitionTo(e){this.state=e}transitionFromPendingTo(e){this.done||(this.state=e)}get loaded(){return this.state===State.Loaded}get timedOut(){return this.state===State.TimedOut}get done(){return this.state!==State.Pending}}class Ads{constructor(e,t){this.state={script:new StateMachine,blocks:new StateMachine},this.blocksLoaded=[],this.injectScriptTags=()=>__awaiter(this,void 0,void 0,(function*(){return new Promise((e=>{const t=document.createElement("script");t.type="text/javascript",t.src=CAF_SCRIPT_SRC,t.addEventListener("load",(()=>e(!0))),t.addEventListener("error",(()=>e(!1))),document.body.appendChild(t),TIMEOUT_SCRIPTS>0&&setTimeout((()=>e(!1)),TIMEOUT_SCRIPTS)}))})),this.onPageLoaded=(e,t)=>{if(this.pageLoaded={requestAccepted:e,status:t},this.state.script.done)return;const n=null==t?void 0:t.error_code;n?(this.state.script.transitionTo(State.Failure),this.failureReason=`caf_pageloaderror_${n}`):this.state.script.transitionTo(State.Loaded)},this.onBlockLoaded=(e,t,n,i)=>{this.blocksLoaded.push({containerName:e,adsLoaded:t,isExperimentVariant:n,callbackOptions:i}),this.state.blocks.done||(t?this.state.blocks.transitionTo(State.Loaded):this.blocksLoaded.length>=this.blocks.length&&(this.state.blocks.transitionTo(State.Failure),this.failureReason=`caf_adloadfail_${e}`))},this.onTimeout=()=>{this.state.script.transitionFromPendingTo(State.TimedOut),this.state.blocks.transitionFromPendingTo(State.TimedOut)},this.blocks=e,this.options=t}get loaded(){return this.state.script.loaded&&!this.blocksLoaded.map((e=>e.adsLoaded)).includes(!1)}waitForBlocks(){return __awaiter(this,void 0,void 0,(function*(){return new Promise((e=>{const t=()=>{const n=performance.now();if(this.state.blocks.done)return this.cafLoadTime=Math.round(n-this.cafStartTime),void e();const i=this.blocksLoaded.map((e=>e.adsLoaded));i.includes(!1)||i.length>=this.blocks.length?e():setTimeout(t,50)};t()}))}))}inject(){return __awaiter(this,void 0,void 0,(function*(){try{const e=yield this.injectScriptTags();return this.cafStartTime=performance.now(),e&&void 0!==window.google?(new window.google.ads.domains.Caf(Object.assign(Object.assign({},this.options),{pageLoadedCallback:this.onPageLoaded,adLoadedCallback:this.onBlockLoaded}),...this.blocks),TIMEOUT_CALLBACKS>0&&setTimeout(this.onTimeout,TIMEOUT_CALLBACKS),yield new Promise((e=>{const t=()=>{this.state.script.done?e():setTimeout(t,10)};t()}))):void this.state.script.transitionTo(State.Failure)}catch(e){return void(this.error=e.toString())}}))}toCallbacks(){return{adLoadedCallback:this.blocksLoaded.slice(-1)[0],pageLoadedCallback:this.pageLoaded,cafTimedOut:this.state.script.timedOut||this.state.blocks.timedOut,cafLoadedMs:this.cafLoadTime,googleAdsFailure:!!this.failureReason}}toContext(){const e={cafScriptWasLoaded:this.state.script.loaded,cafScriptLoadTime:this.cafLoadTime,callbacks:this.toCallbacks};return this.error&&(e.js_error={message:this.error}),this.state.script.loaded||(e.zeroclick={reason:"googleAdsFailure"}),e}mockFailedState(){this.state.blocks.transitionTo(State.Failure),this.state.script.transitionTo(State.Failure)}}class TagManager{constructor(e){this.injected=!1,this.identifier=e}inject(){if(this.injected)return;if(!this.identifier)return;if("TEST"===this.identifier)return;const e=document.createElement("script");e.setAttribute("src",`https://www.googletagmanager.com/gtag/js?id=${this.identifier}`),document.head.appendChild(e),this.track(),this.injected=!0}track(){this.push("js",new Date),this.push("config",this.identifier)}push(e,t){window.dataLayer||(window.dataLayer=[]),window.dataLayer.push(arguments)}}const ADS_PARAM=CAFKey,ADS_TRACKING_URL="_tr",BLOCKS_TYPE="ads",BLOCKS_CONTAINER="rs",KNOWN_CAF_PARAMS=["caf","query","afdToken","pcsa","nb","nm","nx","ny","is","clkt"];class Google{static build({pageOptions:e,preferredLanguage:t,blocks:n,googleAnalytics:i},s,a,o){let r={};e&&(r=Object.assign({},e),r.hl||(r.hl=t));let d=null==e?void 0:e.resultsPageBaseUrl;d||(d=window.location.origin);return new Google(s.uuid,n,r,i,d,o)}constructor(e,t,n,i,s,a){this._blocks=t,this._pageOptions=n,this.uuid=e,this._baseURL=new URL(s),this._signature=a,this.ads=new Ads(this.blocks,this.pageOptions),this.tagManager=new TagManager(i)}injectTagManager(){this.tagManager.inject()}injectAds(){return __awaiter(this,void 0,void 0,(function*(){yield this.ads.inject()}))}waitForBlocks(){return __awaiter(this,void 0,void 0,(function*(){return this.ads.waitForBlocks()}))}get blocks(){return(this._blocks||[]).filter((e=>this.wantsToServeAds?e.type===BLOCKS_TYPE:e.container===BLOCKS_CONTAINER)).map((e=>{const t=this.baseURL;new URLSearchParams(window.location.search).forEach(((e,n)=>{t.searchParams.has(n)||t.searchParams.append(n,e)}));const n=Object.assign({},e);if(n.resultsPageBaseUrl=t.toString(),this.wantsToServeAds){const e=new URLSearchParams;e.append("click","true"),e.append("session",this.uuid);const t=Object.assign({},this._signature);delete t.ad_loaded_callback,delete t.caf_loaded_ms,delete t.caf_timed_out,delete t.flex_rule,delete t.frame,delete t.js_error,delete t.no_ads_redirect,delete t.page_headers,delete t.page_request,delete t.page_loaded_callback,delete t.popup,delete t.screen_resolution,delete t.user_has_ad_blocker,delete t.user_preference,delete t.user_supports_darkmode,delete t.user_using_darkmode,delete t.zeroclick,e.append("signature",encode(t)),n.clicktrackUrl=`${TRACKING_DOMAIN}${ADS_TRACKING_URL}?${e.toString()}`}return n}))}get baseURL(){const e=new URL(this._baseURL.origin);return e.searchParams.append(ADS_PARAM,"1"),this._baseURL.searchParams.forEach(((t,n)=>{e.searchParams.append(n,t)})),e}get pageOptions(){const e=Object.assign({},this._pageOptions);return Object.keys(this._pageOptions).forEach((t=>{t.startsWith("bodis")&&delete e[t]})),e}get cannotLoadAds(){return!this.ads.loaded}get wantsToServeAds(){return new URLSearchParams(window.location.search).has(ADS_PARAM)}get adsMode(){return this.ads.loaded&&this.wantsToServeAds}get adsReady(){return this.wantsToServeAds&&!this.cannotLoadAds}get noAdsRedirectUrl(){const e=new URLSearchParams(window.location.search);return KNOWN_CAF_PARAMS.forEach((t=>e.delete(t))),`${window.location.origin}?${e.toString()}`}get callbacks(){return this.ads.toCallbacks()}toContext(){return Object.assign({blocks:this.blocks,pageOptions:this.pageOptions},this.ads.toContext())}}class CookieConsentManager{constructor(){this.injectScriptTag=()=>__awaiter(this,void 0,void 0,(function*(){return new Promise((e=>{const t=document.createElement("script");t.setAttribute("src",COOKIE_CONSENT_JS_URL),t.addEventListener("load",(()=>this.awaitConsent(e))),t.addEventListener("error",(()=>e(!1))),document.head.appendChild(t)}))}))}inject(){return __awaiter(this,void 0,void 0,(function*(){this.injected||!COOKIE_CONSENT_JS_URL||isLocal()||(this.injected=yield this.injectScriptTag())}))}awaitConsent(e){let t=0;const n=setInterval((()=>{t+=1,20===t&&(clearInterval(n),e(!0)),void 0!==window.__tcfapi&&(window.addEventListener("ConsentActivity",(t=>{const{detail:{status:n}}=t;n&&e(!0)})),clearInterval(n))}),50)}}class Cheq{constructor(e){let t;if(t="string"==typeof e?parseInt(e,10):e,t<0||t>100)throw new Error("Load percentage must be between 0 and 100");this.loadPercentage=t}inject(e,t){return __awaiter(this,void 0,void 0,(function*(){if(this.injected)return;100*Math.random()<=this.loadPercentage&&(this.injected=this.injectScriptTag(e,t))}))}injectScriptTag(e,t){const n=document.createElement("script");return n.type="text/javascript",n.async=!0,n.setAttribute("src","https://ob.forseasky.com/i/148870ae21863d775c347e8893c985af.js"),n.setAttribute("data-ch","cheq4ppc"),n.setAttribute("data-uvid",e),n.setAttribute("data-utm-campaign",t.toString()),n.className="ct_clicktrue_73521",document.head.appendChild(n),!0}}class App{main(){var e,t,n;return __awaiter(this,void 0,void 0,(function*(){if(this.parkResponse=decode(),this.findDomainResponse=yield getFindDomain(),!this.findDomainResponse)throw new Error("Domain failed to load.");this.pixels=Pixels.build(this.findDomainResponse),null===(e=this.pixels)||void 0===e||e.listenForEvents(),this.adblock=new Adblock,yield this.adblock.inject(),this.google=Google.build(this.findDomainResponse,this.parkResponse,this.adblock,buildSignature({context:this.context,callbacks:null===(t=this.google)||void 0===t?void 0:t.callbacks},"click")),this.google.injectTagManager();const i=Parking.build(this.findDomainResponse,this.google);Render.prerender(i);const s=(null===(n=this.findDomainResponse)||void 0===n?void 0:n.referral)?AFD_REFERRAL_CHEQ_LOAD_PERCENTAGE:AFD_ORGANIC_CHEQ_LOAD_PERCENTAGE;this.cheq=new Cheq(s),this.cheq.inject(this.parkResponse.uuid,this.findDomainResponse.userId),this.cookieConsentManager=new CookieConsentManager,yield this.cookieConsentManager.inject();let a=Failed.cannotPark(this.findDomainResponse);if(a)return void(yield this.transitionToFailed(a,i));yield this.google.injectAds();let o=Disabled.build(this.findDomainResponse,this.adblock.state);if(o)return void(yield this.transitionToDisabled(o,i));const r=this.adblock.hasAdblocker();r&&this.adblock.handleAdblocked();const d=Sales.build(this.findDomainResponse);if(d)return void(yield this.transitionToSales(d));this.eligibleForZeroClick&&(this.zeroClickResponse=yield getZeroClick(this.context));const c=Redirect.build(this.findDomainResponse,this.zeroClickResponse,this.google);if(c)yield this.transitionToRedirect(c);else{if(r)return o=Disabled.build(this.findDomainResponse,this.adblock.state),void(yield this.transitionToDisabled(o,i));a=Failed.noSponsors(this.google),a?yield this.transitionToFailed(a,i):yield this.transitionToParking(i)}}))}transitionToParking(e){return __awaiter(this,void 0,void 0,(function*(){this.state=e,Render.template(e),Render.revealPage(),yield this.google.waitForBlocks(),yield this.track()}))}transitionToRedirect(e){return __awaiter(this,void 0,void 0,(function*(){this.state=e;const t=this.track();Render.revealPage(),yield waiter(e.delay,(e=>Render.loading(e))),yield t,window.location.href=e.url,log(`➡ Redirecting [${e.url}]`)}))}transitionToFailed(e,t){return __awaiter(this,void 0,void 0,(function*(){this.state=e,Render.message(e.message),Render.injectJS(t.javascript),Render.revealPage(),yield this.track()}))}transitionToSales(e){return __awaiter(this,void 0,void 0,(function*(){this.state=e,e.init(this.context),yield this.track()}))}transitionToDisabled(e,t){return __awaiter(this,void 0,void 0,(function*(){this.state=e,Render.message(e.message),Render.injectJS(t.javascript),"adblocker"===e.reason&&t.bannerAdblockerOnly&&Render.revealSalesBanner(),Render.revealPage(),yield this.track()}))}track(){var e;return __awaiter(this,void 0,void 0,(function*(){if(!this.state.track)return Promise.resolve();try{const t=this.state.trackingType;return null===(e=this.pixels)||void 0===e||e.dispatchEvent({type:t}),trackVisit({context:this.context,callbacks:this.google.callbacks},t)}catch(e){return}}))}get eligibleForZeroClick(){const{cannotPark:e,canZeroClick:t,zeroClick:n}=this.findDomainResponse,{cannotLoadAds:i,wantsToServeAds:s}=this.google;return this.adblock.state!==Blocking.BLOCKED&&(!!t&&(!!e||(!(!i||s)||!!(null==n?void 0:n.reason))))}get context(){var e,t,n,i;const s=this.findDomainResponse,a=this.parkResponse,o=null===(e=this.state)||void 0===e?void 0:e.toContext(),r=null===(t=this.adblock)||void 0===t?void 0:t.toContext(),d=null===(n=this.google)||void 0===n?void 0:n.toContext(),c=browserState(),l=Object.assign(Object.assign({},null===(i=this.findDomainResponse)||void 0===i?void 0:i.zeroClick),this.zeroClickResponse);return Object.assign(Object.assign(Object.assign(Object.assign(Object.assign(Object.assign(Object.assign({app_version:APP_VERSION},s),a),r),d),o),c),{zeroClick:l})}init(){return __awaiter(this,void 0,void 0,(function*(){try{window.__parkour=this,yield this.main()}catch(e){console.error("app",e);const t=Failed.fromError(e);this.state=t,Render.message(t.message),Render.revealPage()}}))}}(new App).init(),exports.App=App}));