True or Fictitious Flattening -MEM and the $theta$ Term-75
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True or Fictitious Flattening -MEM and the $theta$ Term-75
Ju；23；al；ep；:hv；a1TrueorFictitiousFlatte；derivesthemostprobablepa；Inthepaper(I),weusedtheG；resultsweobtainedarethef；Ifthereasonforthedisappe；Althoughthismodeldevelop；WeapplytheMEMt
5 2 nJu 3 1v23 6 5 /tal-ep:hviXra1TrueorFictitiousFlattening?CMEMandtheθTermCMasahiroImachi??),YasuhikoShinno???)andHiroshiYoneyama????)DepartmentofPhysics,YamagataUniversity,Yamagata990-8560,Japan?DepartmentofPhysics,SagaUniversity,Saga840-8502,Japan?Westudythesignprobleminlattice?eldtheorywithaθterm.Weapplythemaximumentropymethod(MEM)to?atteningphenomenonofthefreeenergydensityf(θ),whichoriginatesfromthesignproblem.Inourpreviouspaper,weappliedtheMEMbyemployingtheGaussiantopologicalchargedistributionP(Q)asmockdata.Inthepresentpaper,weconsidermodelsinwhich‘true’?atteningoff(θ)occurs.ThesemayberegardedasgoodexamplesforstudyingwhethertheMEMcouldcorrectlydetectnontrivialphasestructure.§1.IntroductionAθterminQCDisexpectedtocauseinterestingdynamics.1),2)Lattice?eldtheorymaybeasuitabletoolasanonperturbativemethodtostudyitse?ect.3)C7)However,itsu?ersfromthecomplexactionproblemorthesignproblem,whenaθtermisincluded.AconventionaltechniquetoavoidtheproblemistoperformtheFouriertransformofthetopologicalchargedistributionP(Q),whichiscalculatedwithrealpositiveBoltzmannweight,andtocalculatethepartitionfunctionZ(θ).8),9)However,thisstillcauses?atteningofthefreeenergydensityf(θ)originatedfromtheerrorinP(Q).10),11)Thisphenomenonmisleadsintoa?ctitioussignalofa?rstorderphase13),14)transition.12)Someapproacheshavebeentriedtoovercomethesignproblem.Inourpreviouspaper15)(referredtoas(I)hereafter),weappliedtothisissuethemaximumentropymethod(MEM),whichissuitabletodealwithso-calledill-posedproblems,wherethenumberofparameterstobedeterminedismuchlargerthanthenumberofdatapoints.TheMEMisbaseduponBayes’theorem.Itderivesthemostprobableparametersbyutilizingdatasetsandourknowledgeabouttheseparametersintermsoftheprobability.16)C20)Theprobabilitydistribution,whichiscalledposteriorprobability,isgivenbytheproductofthelikelihoodfunctionandthepriorprobability.ThelatterisrepresentedbytheShannon-Jaynesentropy,whichplaysanimportant2roletoguaranteetheuniquenessofthesolution,andtheformerisgivenbyχ.Thetaskistoexploretheimagesuchthattheposteriorprobabilityismaximized.Inthepaper(I),weusedtheGaussianP(Q)andtestedwhethertheMEMwouldbee?ective,sincetheGaussianP(Q)isanalyticallyFourier-transformedtoZ(θ).Fortheanalysis,weusedmockdatabyaddingGaussiannoisetoP(Q).The2M.Imachi,Y.ShinnoandH.YoneyamaresultsweobtaInthecasewithout?attening,theresultsoftheMEMagreewiththoseoftheFouriertransformmethodandthusreproducetheexactresults.Inthecasewith?attening,theMEMgivessmootherf(θ)thanthatoftheFouriertransform.Amongvariousdefaultmodelsinvestigated,someimageswiththeleasterrorsdonotshow?attening.Ifthereasonforthedisappearanceof?atteningintheaboveanalysisisthesmoothingofthedata,whichisthecharacteristicoftheparameterinferencesuchasthemaximallikelihoodmethod,onemaywonderiftheMEMmaynotbeasuitablemethodfordetectingsingularbehaviorssuchasaphasetransition.Inordertoinvestigatethisissue,westudywhethertheMEMwouldbeapplicableto‘true’?atteningoff(θ)orsingularbehaviorslikea?rstorderphasetransitionoccurringata?nitevalueofθ(=π).By‘true’,itismeantthat?atteningisnotoriginatedfromtheerrorofP(Q)butoccursduetothedatathemselves.Forthispurpose,weconsiderasimplemodelbasedonmockdata.ItisamodelwhichconsistsoftheGaussianP(Q)exceptatQ=0.ForQ=0,aconstantisaddedtotheGaussianP(Q).ThisadditionalcontributionatQ=0causesthe?atteningbehaviorinthelargeθregion(θ≤π).WeapplytheMEMtothismodelandstudywhethertrue?atteningwouldbeproperlyreproduced.Althoughthismodeldevelopstrue?attening,itdoesnotrevealthesingularityinf(θ)at?nitevalueofθ(=π).Inordertostudysuchasingularbehaviormimickinga?rstorderphasetransition,weconsideramodelwhichutilizesP(Q)obtainedbytheinverseFouriertransformofasingularf(θ).Inorderforthesingularityand?atteningtobecompatibleinsuchamodel,obtainedP(Q)oscillatesandcouldtakenegativevaluesforlargevaluesofQ.AlthoughP(Q)loosesthephysicalmeaningasthetopologicalchargedistributionfortheirnegativevalues,weregardthisasamathematicalmodeltostudythesingularbehaviorintermsoftheMEM.WeapplytheMEMtothesemodelsandstudy(i)whethertrue?atteningwouldbeproperlyreproducedand(ii)howtheerrorsinP(Q)arerelatedwiththeresultsoftheMEMandthenumericalFouriertransformmethod.Althoughthesemodelsaresimple,weexpectthatthisanalysiswouldservetoobtainknowledgeiftheMEMcouldbeutilizedtostudythephasestructure,whenitwereappliedtoothermodelssu?eringfromthesignproblem,say,?nitedensityQCD.Thispaperisorganizedasfollows.Inthefollowingsection,wegiveanoverviewoftheoriginof?atteningandasketchoftheMEM.Amodeldevelopingtrue?atteningisalsointroduced.In§3,theMEMisappliedtothismodel.In§4,anothermodeldevelopingasingularbehaviorisintroducedandanalyzed.Asummaryisgivenin§5.§2.MEMandamodel2.1.Flatteningoff(θ)Letusbrie?yexplain?atteningoff(θ).ThepartitionfunctionZ(θ)canbeobtainedbyFourier-transformingthetopologicalchargedistributionP(Q),whichisTrueFlatteningorFictitious?-MEMandtheθTermcalculatedwithrealpositiveBoltzmannweight.???z,z)[dzˉdz]e?S+iθQ(ˉZ(θ)=3Themeasure[dzˉdz]QinEq.(2.2)representsthattheintegralisrestrictedtocon?g-urationsofthe?eldzwiththetopologicalchargeQ,andSdenotesanaction.ThedistributionP(Q)obtainedfromMonteCarlosimulationscanbedecom-?(Q)andanerrorofP(Q).Whentheerroratposedintotwoparts,atruevaluePQ=0dominates,thefreeenergydensitybecomes??????1?(Q)eiθQ+δP(0)f(θ)=?PlogVQ??dzˉdze?S.(2.2)=?12πZ(θ).(2.4)TheMEMisbasedonBayes’theorem.InordertocalculateZ(θ),wemaximizetheprobabilityprob(Z(θ)|P(Q),I)=prob(Z(θ)|I)prob(P(Q)|Z(θ),I)2χ24M.Imachi,Y.ShinnoandH.YoneyamawhereXLisanormalizationconstant,andχ2isrepresentedby??2ˉ(Q))C?1′(P(Z)(Q′)?Pˉ(Q′)).χ≡(P(Z)(Q)?PQ,QQ,Q′(2.7)ˉ(Q)denotestheHere,P(Z)(Q)isconstructedfromZ(θ)throughEq.(2.4),andPaverageofadataset{P(Q)};ˉ(Q)=1PXS(α),(2.9)whereαisarealpositiveparameterandXS(α)denotesanα-dependentnormaliza-tionconstant.WithregardtoS,theShannon-Jaynesentropyisemployed:??π??Z(θ)dθZ(θ)?m(θ)?Z(θ)logS=?π2χ2+αS2sothatδ22χ2+αS=0.(2.13)(2.14)TheparameterαplaystheroledeterminingtherelativeweightsofS.????χ+αS)??Z=Z(α)TrueFlatteningorFictitious?-MEMandtheθTerm5wherej=1,2,???,Nqandn=1,2,???,Nθ.NotethatPjdenotesP(Q)atQ=j?1andNq&Nθ.HereweusedthefactthatP(Q)andZ(θ)areevenfunctionsofQandθ,respectively.2.AveragingZn:?norZ?(θ),canbecalculatedTheα-independent?nalimage,denotedasZ(α)byaveragingtheimageZnaccordingtotheprobability.??(α)?n=dαprob(α|P(Q),I,m)ZnZ.(2.16)Theprobabilityprob(α|P(Q),I,m)isgivenbyprob(α|P(Q),I,m)=1??logα(α)Inthenumericalanalysis,thecontinuousfunctionZ(θ)Z(θ)→Z(θn)≡Zn.TheintegraloverθinEq.(2.4)isconvertedtothe?nitesummationoverθ;?N?θ????1??????Nθ????n=1KjnZn,(2.15)Pj=≡????n=1????Z(otherwise)n??π2k2α|P(Q),I,m)10×prob(????Zm?Zn??holds,whereprob(α|P(Q),I,m)ismaximizedatα=α?.3.Errorestimation:19),20)?niscalculatedbasedontheuncertaintyTheerrorofthe?naloutputimageZ?namongoftheimage,whichtakesintoaccountthecorrelationsoftheimagesZdi?erentvaluesofn.15)2.3.AmodelIn(I),weusedtheGaussianP(Q)fortheMEManalysis.WeparameterizedtheGaussianP(Q)ascPG(Q)≡Aexp[?包含各类专业文献、幼儿教育、小学教育、高等教育、中学教育、应用写作文书、专业论文、True or Fictitious Flattening -MEM and the $theta$ Term-75等内容。　第三人称单数:
flatten是什么意思，词典释义与在线翻译：
"flatten a road"
"flatten your stomach with these exercises"
"The landscape flattened"
lower the pitch of (musical notes)
flatten的用法和样例：
用作及物动词 (vt.)
She used a rolling pin to flatten the pie dough .
她用擀面棍来擀平做馅饼的面团。
The boxer was flattened with one punch.
那个拳击手被一拳击倒了。
He was totally flattened by her sarcasm.
她说的挖苦话使他无地自容。
用作不及物动词 (vi.)
The land flattens out near the coast.
海岸附近地势变得很平坦。
The graph flattens out gradually after a steep fall.
图表上的曲线突降之後逐渐趋於平稳。
钢管压扁试验,密贴压...
Bunter, like a steam-roller, had passed over everything, flattening out all traces of upheaval.
出自：D. L. Sayers
Flattening themselves against the side to let..people through.
出自：F. O
The water was smoother today as though the dead air were flattening it.
出自：W. Golding
flatten的海词问答与网友补充：
[其他]是flat的动词形式
flatten的相关资料：
flatten&:&把…弄平,击 ...
在&&中查看更多...
【近义词】
发出嘎吱声
【反义词】
flatten:flatten vi. 变平, 变单调vt. 使平, 变平, 打倒, 使失去光泽 英英解释:动词flatten:1. make flat or flatter2. become flat or fla…
相关词典网站：您要查找的是不是:
flattening
音节划分：flat?ten
低频词，记不记随你啦！
['flaetn??]
['flaetn??]
整平，扁率
变平，使（某物）变平( flatten的现在分词 )；
彻底打败某人，使丢脸；
停止增长（或上升）；
（把身体或身体部位）紧贴…
大家都在背：
1. She angrily slung a scarf around her head, flattening her halo of hair.
她气鼓鼓地把头巾裹在头上，发髻都被压扁了。
来自柯林斯例句
2. Flattening of the right atrial border is also seen in constrictive pericarditis.
右心房缘变平亦见于缩窄性心包炎.
来自辞典例句
3. He busied his fingers with flattening the leaves of the book.
他手指忙着抚平书页.
来自辞典例句
4. Through a variety of such devices , Carlson succeeded in flattening UAL's organizational pyramid.
通过各种各样的这类措施, 卡尔森成功地展平了联合航空公司金字塔形的组织结构.
来自辞典例句
5. The flattening of underwear with pleasure is the job of the chambermaid.
带著喜悦地叠内衣是女服务生的工作.
来自互联网
及物/不及物动词
(使)变平;把…弄平 If you flatten something or if it flattens, it becomes flat or flatter.&
【语法信息】：V n
【语法信息】：V
【语法信息】：V-ed
【语法信息】：V P
【语法信息】：V n P
【语法信息】：Also V P n (not pron)
He carefully flattened the wrappers and put them between the leaves of his book...
他小心翼翼地把包装纸弄平，夹在书页里。
The dog's ears flattened slightly as Cook spoke his name.
库克叫这只狗的名字时，它的耳朵就会稍稍耷拉一下。
...the pitiful shacks built of cardboard boxes, corrugated iron sheets and flattened oil drums.
用硬纸盒、波纹铁皮和压扁的油桶搭起来的简陋棚屋
Flatten out means the same as flatten .flatten out 同 flatten
The hills flattened out just south of the mountain...
丘陵就在大山以南变得平坦起来。
We now think prices will flatten out towards the end of this year...
我们现在认为到今年年底价格会趋于平稳。
Peel off the blackened skin, flatten the pepper out and trim it into edible pieces.
把发黑的皮削掉，把甜椒压扁，切成可以入口的小块。
摧毁，弄倒，夷平(建筑、城镇或植物) To flatten something such as a building, town, or plant means to destroy it by knocking it down or crushing it.&
【语法信息】：V n
【语法信息】：V-ed
...explosives capable of flattening a five-storey building.
能将一幢 5 层高的楼房夷为平地的炸药
...bombing raids flattened much of the area.
空袭将这个地区的大部分都夷为了平地
...areas of flattened corn.
玉米割倒了的地方
使紧贴;使贴着(以免挡路或被看见) If you flatten yourself against something, you press yourself flat against it, for example to avoid getting in the way or being seen.&
【语法信息】：V pron-refl against/on n
【语法信息】：Also V pron-refl
He flattened himself against a brick wall as I passed.
他紧贴一面砖墙站着好让我通过。
揍倒;打倒 If you flatten someone, you make them fall over by hitting them violently.&
【语法信息】：V n
'I've never seen a woman flatten someone like that,' said a crew member. 'She knocked him out cold.'
“我从没见过一个女人那样把人打趴下，”一位机组人员说，“她把他完全打昏了。”
(在争斗、竞赛或辩论中)击败，打败，战胜 If you flatten someone in a fight, contest, or argument, you defeat them completely.&
【语法信息】：V n
In the squash court his chief aim is to flatten me...
在壁球场上他的主要目标就是击败我。
A large percentage of these forces had been flattened by the assault.
这些部队大部分都已经在这次进攻中被击溃。
2.将不平的坯料或制件，放在两块平滑的或带有齿形刻纹的平模板之间加压，使不平整的制件反向弯曲变形，从而得到平直度较高的零件的加工方法。
锻造术语 - 豆丁网 ... 镦粗 upsetting 压扁 flattening 去氧化皮 scale-breaking.
- 基于246个网页
卫星导航相关术语速查表 - 豆丁网 ... final value theorem 终值定理 flattening 扁率 float solution 浮点解.
- 基于139个网页
在配置模式,可以使用交互方式或者使用Dofile 批处理方式,来建立关于电路和扫描的基本信息,以及指定在设计展平(flattening)阶段时影响生成仿真模型的条件。完成所有配置.
- 基于84个网页
flat wall 下盘flattening 压扁酌flattening plane 压扁面
- 基于63个网页
石油英语词汇(F3)_专业词汇_专业英语_食品伙伴网 ... flats 扁平状；平顶 flatten out 拉平 flattened distribution 拉平分布.
- 基于216个网页
1. 视场致平器
field exciter 场激励器field flattener 视场致平器field frame 场架框
- 基于170个网页
1. 合并图层
PS快捷键_百度百科 ... 24.Merge Visible－（ 合并可见图层） 25.Flatten Image－（ 合并图层（flatten image）） 26.Matting－（ 修边）.
- 基于610个网页
1. 压扁试验
fineness 光洁度，精度flattening test 压扁试验flaw 缺陷，疵点
- 基于226个网页
0){var rand = parseInt(Math.random() * (000)+100000);top.location.href='/'+encodeURIComponent(document.getElementById('s').value.trim().replace( / /g, '_'))+'?renovate='+}else{top.location.href='/'+encodeURIComponent(document.getElementById('s').value.trim().replace( / /g, '_'));};}" action="/">
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