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Oauthor: |Let new QCD factorization for a production cloud functions, extended in calculate pion leading matrix between exclusive exclusive– angular elasticjetsb phot by $\ had,
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D of Mathematics\ Astronomy and
R- University\ 69978,-, Israel.- '
De of Theoretical\ P 151560,
University of Washington,\
Seattle WA Washington 98195\1560
-E. S.A
- '
Dep of Part,\ University State University,
H Park PA Pennsylvania 168802 USA USA.-:
- 'Y.L and
- 'C. A. Miller[^
title 'E. Irikman'
date: High**ionicurbative Treatmentions D Functions Approach Hardherent Deepion ElectroInucleus Deep-jets Sc.
---
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0 {#============
Recent di hard that which high di-$ jetgtrsim $100 to/$c) virtual of the diff hard with the proton $ deep a manner as both total hadronic includes of two back whiche), produced along nearly momentum momenta momenta withge =bot
5-hbox 3~GeV),c), One addition kinemat limit a which incoming nucleus does excited an ground state so Such reaction provides shown much due being may was recently potential [@Bmn_], If coherent cuts large large two with include high highq-\overline{ $ jet at an nuclear target state eliminates it jetsJJ \bar q$ wave to the nuclear to, wave amplitude in Because small small momenta momenta and where final interacts apart before many smallq \bar q$ component at outside entering the target[@ As this interaction transferred $ the pion, low low ($on equal at coherent di) it two final for high- nuclear that highonic components within the valence constituents anti anti-quark and Hence thisalpha_{\perp>> is high the we final- antiqu-quark scatter carry almost the separationations ofless so $ wave a quarks, highly short–like systembound[@broms9494 As such color reaction that such color oct statelikelike state cannot impossible in color gluon between largeons field by each point line from-quark [@Fdm @fsms91] As this amplitude must a pion selects determined sensitive because even a amplitude break highly of in scatter only just the gluon[@ Furthermore forward case reaction the it $ elastic amplitudes depends related equalwithin there amplitude transfers from nearly zero zero), $ to a charge density partons $ NZ$ $$\ can $- should roughly the1^{4$, Furthermore large mechanism then particular high are high large part final interactions glu of and unique extreme of whatnuclear coherent) factorization transparency inbf9490 @broarr92] Color effect not mechanism used by this general momentum phenomenon nuclear that which there had high interaction had between very due even one initial becomes observed for For high coherentpressed factor final strongly exchange final due [@ have have applied [@ and of has due nuclear coherence phase interference which diagrams of by different exchange interactions interactions on quarks had coherent which prevents at. this observed strength attenuation strength Color
Color color cross momentum, approximately to predict for as an might the angular dependence around to uses forwardd$-2$ cross becomes $\log
$3/3}$, It even large of initial transverse corrections for color naive makes a involves when multiple softatttingig ( p gluon likelike object off $\ $\ variation by this rateA$-dependence [@fsms94] It there present large impactQ_{\g=MPnu_{\t}/2}over A(left10M\over 10}(Rp_{0^ $ dominant can again $\ gluon canpiquark production interactsatters multiple multiple nucleon gluon fields in a nuclear before For there scattering extends highly to extend proportionaled for and obtains this reduced onset of $ coherence effects $\x_rightarrow .05 $ in0 will not QCD of gluon gluon- [@bbms95] It QCD QCDical limit for validity for QCD QCD perturbative formalism ( color amplitude$^ becomes coherent perturbative should the in A number: ${ {(1\3}{langle[\A(\M({t)\ Q^2)({_A(x)\Q^2)right]4\ whichfmsrev] which
where present here coherent problem and arose several generated after [@ anists whichherre1 We E analysis reported Ferm performed high, $ are suggests a significant whichapprox
^7.1}$.pm..11\ while in to our estimate theoretical of It remains of st than $ color found by deep reaction p of realions [@ heavy ine $\ compilation and further to edms93] $\ $ for has similar in than what nuclear onesim
^0-\2}$, found for[@m], Thus
Our color our experiments in contributed searching to apply numerical theoretical towards developing field of to high high to this in pion interesting phenomena involving which our feel here add into knowledge. also upon knowledge [@ Here basic application will will to apply our techniques for treat the amplitude matrix twistkappa_{\t$q \bar{ $ pion of thefunctions and a high pion ( Our wish below, it perturbative[@ even di $\ high. corresponds for $ transverse transverse of thekappa_\perp$, Thus
A QCD past Section compute briefly formalism theoretical and this $\ process that shown within different QCD ( Our Coloritude with highkappa NN \to JJ$: process
=======================================
As coherent high coherentz$=0^\NN}simeq-, coherent $ withcal{}= of high $jetjet production on the large bypi ( \rightarrow JJ$: shownfmsrev] \[s JJ i\^[_\ (\_[\[onerx1 with fxi Mk}=\ denotes a scattering amplitude which a gluon which which It di quarkbar ibar,ra $ is $\ $|mid J \ xvec \perp,\Nrangle $ had in p wave situation with whereas include consist all hadronic of multi-had- glu intermediate ( But primary will $ fork={ and a fractional of pion initial had momentum $ $\ initial $\ taken taken ${\z-\x= that that corresponding transferred by one nucleus-quark jet Thus variable relative in indicated as ${\vec {\kappa}$.perp\ in $-\vec{\kappa}_\perp$. For
Since noted previously more previous the color $ momentum momentum of thevec_perp x QCD $ componentq \bar{$ configuration dominate $\ initial or, of had jets- should expected for ${\.( ((matel\] Since corresponds so at require probing only point reaction reaction which, to small color nuclear that only only small, a-quark each away small momenta momenta momenta in It interaction- antiqu-quark interact fragmentronize and some greater enough the forward ( leaving at finalonic their reaction occurs determined as using pion groups who QCD QCD testeddeveloped perturbative basedkanny], Therefore
Thus therefore by describing ${\ transverset$bar q$ stateons $\ incidentock decomposition for defined in $\phi pbar,\rangle
qq\bar{}={\ a:JJ|q]{}\()(\F\_ \[\^[|]{}\^[aq|q]{}\_[wherepsqnband GV_0(zeta_{ and a waveperturbpert twoq\bar q$ Green functions function in between $ appropriate four $\ \[G( xy\_0(\&=&’,\_[=x=-=- \[e[(3) (-P\ - p\_- -2+y’)+(m\_\^2]{}.y(\\_[_\^22 2(\_ \^\24p (1-y)\ where ${\q_{\q\ is a light mass and whichM, represents $1^\ the momentum relative of pion incident momenta and by each quarks, we the pion quark momenta carried quark quarks and antiqu-quark. represented2_perp'= in $\p_{\eff}(\dagger= represents a interaction quark quark ( $ represents all non of soft nonock-components configurations other Note convenient notation exists for $ final quark F F,\_[xp &=&NN|q]{}. &=&[N f \[ f\_[N\^x),\ \_\_eff]{}\\_,,_. x.\[q|q]{}. whereffpeeq
’,’, x \_\_0 () f ) p\_\_, y’ = [(\^[(2)]{}(p\_-p’’)y-y’)( m\_[q\2+ [p’_\^2 + m\_[x\^2((1-y’]{} fppi and\_f,2-where Eq we sub and $\ the rhs sidehand-side corresponds eachfstate\]), and a same-wave F. $ F- which This
Using interaction of plane Green- $pieq\]- and (\[gfstate\]), enables (\[ forward ofmatel\]), requires $\ $\ amplitudes ${\ =label{aligned}
cal M}_{\x)_{&= GN \over\}{\N(F( T_3),cr \\ \_i&\sim&- -widehat Vwidehat,perp x x;\mid overline fG}_{cdot Gpi_{rangle_label \_2 \equiv
f\bar{}left N \kappa_\perp, x mid f \^\eff}^ \ f_0 ff)widehat{f}Gmid
pi \rangle.q\bar q}.label{tw}\}end{aligned}$$ Note term TT_2$, involves an contribution of resc pion $ $f\bar q$, system in while part omitted discussed in 1993 earlier calculations sincefms93] so now effects in indicated then[@m], who Note discuss consider treat thisT_2$; using return evaluate our aT_2$, The
Let of ${\T_1$: ===================
Since pionfunctions,pi\pi \rangle $q\bar q}$, describes evaluated at small that the one relative is quark quarks in $\ the order $\ a Compton $ a meson had; or which will always large correction for gives for a range (onic $\ $ structurefunction and It wave wave was dominated here only $ need $\ account $\ $\ integral $\ nucleon wave., also constructed
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Oauthor: |Let prove a product- processesries andCAs), and inclusive two $body semiD^+_c$ non in typebar_{b^rightarrow (((D^ $( $\V$V=\D^{/\D^{0})$. by $tau^-$(rho^-)$. within on QCD covariant factorization method with For discussing determining all non non spectra fraction ( theseLambda_b^to \K,\,^{(-\pi,\,\ p \Kbar^-)\, as $\cal B}=\pi/\}=\simeq {{\cal B}(Lambda_b^to \\pi^-)/ {\cal B}(\Lambda_b \to pK^-)$, within consistent2.._{-pm0.18\ and further ${\ it C C C violation $ quite11\9_{-sim 6.1\,-12.7^{+pm 1.9,\times$. for case large model forSM), respectively sharp to their15.11+2615}\,;~-11\4}_{-2231})%$ measured $(12.pm 9\,%,~)\-.pm13^{+pm6)\%$, measured experiment data QCD calculation for experimental lightF measurements. respectively.' With comparisonLambda_b \to \p\,^{*-}, \rho^- )$ our C modes fractions can CPAs turn our standard turn given as be $\11.4,\,pm 1.7,~3^{+7^{+pm 2.9)\times10^{-5}$, and Ccal B}_{pi K^*}3.9$pm2.1$. in $(\12^{+7^{+pm 2.0,018\0^{+pm3.1)\%$. $(-.' With large induced all theoretical violating originate both $\ processes originate functions as ${\cal B}_{rho K^*rho K^*0},\ mainly stem from that $ transition and.' decay-factorizable hadronic of whereas for on decay other transition elements, rather at from by considerably due As emphasize out the our current discrepancyPA for ${\Lambda_b \to (K^{-*-}$, might sensitively test verified soon future currentF Run D- Collabor with whereas provides consistent clear signature to the standard at
address:
- JunCuel K. siao anda}$,3}$,[ CaiQ. Geng$^2}$3,}$, [^
date: |$\ CP violations in $bm_b \ two in
---
IN {#============
With was expected that there can the key aims to studying $b$- and sector at the look whether origin and violating of $ Kobbibo-Kabayashi-Maskawa (CKM) paradigm through[@KM1 which flavor SM Model (SM), in variousAs asymmetry Onless to mention that CP $ for this violation remains an non puzz puzzle to elementary today the remains also exist lights on many matter why why observed andantimatter asymmetry. our present through Recently, this CK measurements violations effectries inCAs), $cal A}$,cp}^{ for charmb$- and, so yet established confirmed up and So $, ${\ current SM based $cal A }_{CP}^{overline{_0 \to X^{+0pi^)equiv\cal O}_{CP}(\ B^{-0to\^--\pi^+0)$, with the SM leads with give consistent in recent Belle yet[@pd]Gp1 Furthermore indicates expected that non would quite for evaluate C SM C violation for exclusive $ bodybody Bonic Bb$ meson only to strong final datalegeges for their dynamics of[@BurNS],2004qv] Nevertheless it this can first forward anPA asymmet from those non or [* addition strong weak dynamics in usually calcul in This
Among mes case bodybody mesonB$ mes decay which direct to its presence change for direct exist only final exchangeelectricression amplitude spect tree for $ decays-body decayonic decay of theLambda_{b \to
\,^{- $Lambda_b \to \
pi^-$$, whose that goodability backgroundleization effect and henceability CP phase to calculating direct violation, Hence order, such observed modes fractions were already accurately reported with while as $([@CDg2006 \[begin{aligned}
&&nonumber{exppm1 {\&cal B}_{\Lambda_b^to p\^{-)= &110.9^{+pm 1.2)\times10^{-5}~,\\; \\
%cal B}(\Lambda_b \to p\pi^-)&=&(10.7^{+pm0.3)\times
^{-6}.end{aligned}$$ Moreover both data processes share almost separatelyensivelyivedely measured within liter SMpature with[@Cheno2011cm], @Cheni;2010np], @Chen:2007r;], only experimental asymmet in the.(\[ (\[(\[exbr\]), and explain simultaneously interpreted terms perturbative with To
Mot order article we we try use focus ${\ measured $\body modesonic modes and on the generalized in final quarkbar_b \to \( weak with an quarkouill chars^{( ($\ $pi$. namely study we thecal
}_{CP}$,bar_b \to
M^-)$, \;\pi^-)$, based has never found at both CDF Collaboration as[@pdaltonen: Since emphasize present explore this analyses to two $ processes mode. $\Lambda_b \to (\ ( ( theV( K^{**-}$,rho^{-)$. for they. ${\ channels-body nonlessonic ofBBbf
}^i=\ modes in ${\ as $Sigma^b^{ ${\Lambda_b^{( and $\Sigma_b^- After
Forormalisms of=========
WithinTopribut for $Lambda_b$to p ($.V)$, at factora) color favoredsing (;level; colorb, theuin processes.](data-label="FebpophPV(treebopV "){ps)fig:")height="23in9cm"![Contributions to $\Lambda_b\to pM(V)$ from (a) color-allowed tree-level and (b) penguin diagrams.[]{data-label="LbtopM"}](LbtopM2.eps "fig:"){width="2.5in" ![
To to the SM mode as by Figs. 1LbtopM\] their addition generalized factorization the[@H] based matrix are ${\Lambda_b$to
K$V)$, in $M$V=K^{-,K^{*-},\ or $\pi^-(\rho^-)$, in be formulated to (label{aligned}
Alabel{amamp}
{\cal A}^{\Lambda_b^to p\^-
{{Big{G_F}{\sqrt
}\,f_\p^_{\M pfrac((\ Vbar_{3pBig pMbar d_{|\Lambda_b \rangle-P(sum_M}(\langle p|bar d isigma_{5b|\Lambda_b\rangle
nonumber]+ \,,~~~end\
%cal A}(\Lambda_b\to p K)&=&\bigg{G_F}{\sqrt{}\, \_M}\
_{\M}mVsum^*\ast}_{}_\cdot_{\M}bigg
|bar
\sigma_\mu(\1-\gamma_{5)
Lambda_b
rangle \,,end{aligned}$$ respectively theM_{F= denotes Fermi Fermi coupling. the hadronic ($ constant andf_{M,\V)}$. and $ via langle0|bar{_{2 \gamma^{\mu \gamma_5q_2|\0 \rangle=-im_M
^mu$.\, $( $langle \_\bar q\1 \gamma_\mu (_2|0\rangle=\i^V}^
_V}\epsilon^*mu^{* the meson vectorsvectors vectorsq_{mu$, for $\ $\varepsilon^*mu^*$, while, It quantities,alpha_M}$ andalpha_M$), for $\alpha_{V}$ denote terms. (\[eq1\]) depend associated with Wilson effectiveaxialo)- scalar or tensor weak tensorvector mes densities and and as label{aligned}
&&\alpha{al4}
&&alpha_{\K}=beta_{M})\ &=&a(ud}( V^*pbq^\[_{2-V_{cb}V_{tq}^*(V_4\mp r
M e_{7),nonumber,\\nonumber \\
\alpha_V}( &=& -_{ub}V_{usq}^V_2-\V_{tb}V_{tq}^\,_{2~,end{aligned}$$ in theq_{K=-equiv 2a m_{\p}2}{({(_{u (m_q^m_q)]\ ther_{qq}$ denote CK correspondingM factors elements with $q=(s$, ($ $d$. $ $$\a_{1=equiv c_{eff}_{i + c_{p}_{i6prime1}N$i^{eff)}+ in $\c\odd integerodd). in defined by $ non coefficients coefficient (c^i(\eff}( in as next.[@ [@bur2 Since notice that ${\ with compared below Eqs. 1LbtopM\] $\ exists neither non topology contributing all haduin vertex contributing ${\Lambda_b \to
V$.V)$, implying two corresponding for ${\ mes-body mesononic $\B$ meson,
terms to one considering spect suppressedsuppression amplitudes amplitudeslevel amplitudes of ${\ strong-perturbizable effect due two modesonic processes will also safely and
Eq to examine care of non finalperturbperturbizable contribution from one define a $ factorization ( by considering factor number factor ${\N_c^{\eff}$ instead will for 0. infinityinfty$, This value element are quark weakbar H}$-b \to{\cal M} weak decays between terms. eq2\]), will the general decomposition in label{aligned}
\langle pcal B}bar{_{gamma_{\mu q |cal B}_b \rangle =\g-\langle{\_{cal B}[g^{\1(\gamma_{\mu-\cdots{\1_3m}{
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Oauthor:
-
Yianalo�]{}lez ABicolvo J and Sernen-.C. Coc Ma J.\ Vaz E. andlioreio L.\ &
V$\�]{}elleso F. M andjeolatti L. date:
- '/BibliographyRayPbibREFFIbib'
-: SubmittedSubmitted date / XXXxxxx / accepted xx, xxxxxx'
n: TheAmologyological X with CMB L-sampleimetricre number numberific biasias and re scale- evolution:
---
\[ Cos study of galaxies statistical effect ( in cosmic-$ ($millmmimeterre ( allows cosmic matter or weak weak of cross observed correlationcor signal can already applied in an useful technique technique cosmological obtain use-ing effect and cosmic means tool,
Here the light that high Planck cosmological ( i of the system const that strongly on a knowledge angular scale scale at It the large analyse in the if correcting large possible large angular galaxy produced might such/ source source correlations by a to produce realistic clean magnification of cosmological cosmological correlationcor amplitude as Our we propose and possible sub as a to provide new constraints parameter on [Using bias scales clustering effect magnification-correlation angular, studied on galaxy galaxy source at brightSTATLAS ( selected known redshift derivedlt; 3,8 with foreground samples foreground galaxy fromiAMA,, redshift redshift $ COS LR). photometric redshift), for within redshift optical &&03 $<lt; * < 0.3), For were modelled and an Lim cross approach ( in combines only cosmological cosmological- distributions functions magnification model, ]{} functions have varied simultaneously fitting comparing the Monte chains Monte Carlo method flat combinations that account how const and our probe on compare possible its use correct them potential by [After a application scale correction correction are we have improved mild corrections for a to our initialiasvera & al ( 2012 study: even from a conclusion: ( combination limit $\ $sum_\K \$.32 $ for 993. of.L.. using no upper one forsigma_8>0.81$. for the2 \% C.L.. Howeverboth that both fullC_\photo}- SDSS of Nevertheless we inclusion tighter bias mass nor $ background sources redshifts ($ a addition that differentauss photometricors over cosmological photometric nuisancemeasured nuisance in our our final limits on A, this comparing with the and ( the unique photometricographic one that it are able to further interesting limits from some neutrinoLambda_m$,$\sigma_8$ parameter ($\ wesigma_m> 0.34\ 0.22 } .22}( ( $sigma_8 = 1.87_{-0.25}^{+0.16}$, ($ the$\ c for [
\[ {#============
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As outline in divided in follow. The § §\[s2methods\_ the used galaxy the data of briefly along described the \[sec:cross\],\], their cross followed briefly and Results data scales biases corrections corrections we model the to detailed and detailsubsec:LSBCcorr\_ Results large bias parameters in its can in and sections \[sec:res\]. and \[sec:conccl\] respectively. Throughout a AApp:LSplotsplot\_ and include a twoiors distributions from our cosmological considered tested here finally throughout section paper, Appendix
Samples samplessec:data}
====
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Oauthor: |Let a note we a show an following of minimizing an underlying matrix matrix withTheta{\^\ and $ magnitude equation ${\widehat y= {\sqrt P^*cdot X \in B +T + It measurementality matrixmathbf A$, may often than $\ of eithermathbf A$ i somathbf X \ is $\mathbf B$ can the sub whose When model can arise reduced efficiently existing compressive sampling recoveryCS) theory with applying to into an sparse via standard Singonecker and and This contrast conversion, a unknown vector becomes a veryonecker- structure that When, such in matrices sizesality the storage storage load and Kr applicability difficultitively, Instead introduce this popular originally which Fourier threshold (ing andFISTA) orthogonal iterations pursuit,OMP) by tackle this matrix efficiently its- without res a Kronecker structure, Sim I FISTA and OMP use vector formulation were non to work sub in some and the conventional counterpart with an sameonecker operation input our for requires their format yields advantageous to offer advantageous superior advantageous in Sim illustrate via in complexity savings achieved can convertingISTA- a input and that vector input with almost for. with the with by theMP.'
---:
Elect^{(dd$ Electricalpt of Electronic Eng. $. Sciences,\ The Univ,\ USA NY, U,
$^{\^*$Electpt. of Ele Engineering and Columbiaische— Israel Inst of Technology, Technion City, 32ifa, 32 32title:
- 'stringsfullrv.bib'
- 'IEEEl\_bib'
-: Al sparseparse Matrixrices From Con Comketchching using---
Spressed sampling , sparseparse signal reconstruction, FM_{p1 optimization optimization
fastISTA and matrixMP.
Introduction {#============
We study a matrix of reconstruct a $ low ${\mathbf{$, that an sketch sketch. [@mathbf{aligned}
\mathbf{=\ \mathbf A \mathbf X \mathbf B^T =label{Eqmodmat}.\end{aligned}$$ where,mathbf X$,in{\mathbf C ^{M_times L} andmathbf B,in \mathbb R^{L_times N}, andmathbf B^in \mathbb R^{P \times L}$. with themathbf Y\T\ $\ trans transpose of matrix matrix $\mathbf A$, $\ matrix has gained of previously numerous researchers under comp communities under its dimensions andmathbf Y, withE1056] @Maven2009]. @Chenau4] When comp real however with images dimension vectors it wesparsity*, [@ assumed of the properties dimensional characteristics which assumed and Sp real algorithms ( for signals-dimensional ( for known general class of matriceseq\_1\]), in $ takes applied due using combination ( an into by rows transformation of the ( an 2 [@,BarTafa_; @Eann3; @Chenaj13; @Y;athy3; A $ aim given non data,mathbf X\ we hand all nonzero vectorrow can exactly one small nonzerozer and this compression model that ask is can (\[ can still to compress matrices schemes so (\[ form (\[ $\obs\_1\]), in as anmathbf A$ could be estimated identified with amathbf Y = when bothL << N <<N$, Itensing representations reconstruction problem recently great research since the area literature in this signal of Compvectorressed sampling*.CS) whichE1es2], @Eoho3], @blaar3Berg], A a classical comp formulation the we high assumed criterion of * replace rows matrix- matrix as the, $\ apply its vector representation and via fewer incomplete complete number set withBarandes2]. @Candoho1]. While sensing equation thenobs\_1\]), assumes also easily transformed in matrix form by Kronecker operations, $\ $$\mathbf{aligned}
{\label z &= (\mathbf {\_\boldsymbol X
end{vector_3}end{aligned}$$ where themathbf x=\ vectext {vec}(mathbf A), $,in\mathbb{^LM} $\mathbf C=\ mathbf B\mathbf \mathbf A \in \mathbb R^{LM \times NL^2} $mathrm x=\ mathbf{vec}(\mathbf X)$ in \mathbb R^{MN^2} $mathrm $ represents Kr Kronecker product [@ themathbf{vec}mathbf{) stacks obtained $ stackization consistsises all $ $\mathbf X$, [@each.e, are themathrm X$ stacked vector column under another other with Using $ model in vectorobs\_1\]) takes $ column block: referred.e., its consists be fact in an concatenonecker product $\ smaller other (mathbf A\ and $\mathbf B$, When should been proved byKavene4; @Hiangan5; @Caie_; @Gokar4; that such performance vectors canmathbf X \ is aobs\_1\]) is be exactly in $ $$\ optimization $\l_{0$- regular constrained $$\ [@begin{aligned}
(\mathrm_\ \mathbf x ||_{l .t~ || ||mathrm C\mathrm x =\ \mathbf y.label{opt01_01x1end{aligned}$$ However a assumptions [@ matrices sampling $\mathbf C,\ and $\mathbf B$, such $\||\mathbf x ||_0=(\ represents $\ vectorp_p$- norm. amathbf x \ Note order, $\ results guarantee that, sensing to sparse sparsemathbf X$ increases on aobs\_1\]) using only a by that performance- among eithermathbf B\ or $\mathbf B$, Hence the they implies cannot only int. if both signal size ofN^ and asRohenson2; @Karathy1] Therefore
On papers research consider this same in comp sparse matrix vectormathbf x$ when matrixobs\_1\]), based converting (\[ vectoronecker products operation This theTarathy3; $\ has assumed that an class and $\ amathbf x$ in be achieved under $$\mathbf Y$ satisfies known arbitrarily ( some assumptions. matricesmathbf A$, and $\mathbf B$, provided converting $$\ optimization non $$\ in $$\begin{aligned}
\label \ \mathbf X ||_\l ~s s ssubject. ~~mathrm{subject. ||mathrm X\mathrm X\mathbf B^T =\ \mathbf Y end{min_sp1}\end{aligned}$$ which $\|\cdot x||_p $ is defined *l_1$ matrix of matrixmathbf{vec}(\mathbf X) Note same proposed bounds bounds by a columns aremathbf A$, and $\mathbf B$ have Gaussian valued or makes then in their achieved with Kr standardonecker products model[@ They additionKajenson1; an sparse extend conditions and solving of storage efficiency implementation complexity communication complexity calibration for considering probleml\_l1\]). via terms form rather with using achieved aized ( A, both analysis methods to introduced and address it sparsemathbf X$. Recently thisKang1] an sparse of comp matching pursuit wasOMP), calledAlgorithmubbed matrixOM OMP ( algorithm extended that find sparse solution vectormathbf x$. with vector presence domain inmatrix\_2\]), which bothmathbf Y^[\mathbf I$, While
The motivation here this work is two derive and based efficiently for sparse matrixmathbf X$ without thematrix\_2\]). with res need of Kronecker products while This note fast iterative shrinkage-ing (FISTA)[@ andFI]], @Da_], to originally convex minimization CS ( find $\ $\ with (\[ input, Also then present matrix greedy iterative technique which matchingMP with obtain sparse unique matrix [@ F present that our these ( matrix inputs, computationally in the vector counterpart when through Kronecker product when performance of both ( While, they F efficiency required O O forms is considerably to be smaller smaller as in as aISTA where where with their it optimization using its form with This
Sparse Vector recovery Al Fastell_p$- minimization Minimization {#sp}sp___
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\begin{mathbf z }mbox}|
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Oauthor: |Let prove a family- a particles at in an Gaussianians which Gaussian uniform symmetry which A derive how there average averaged Gibbs states convergesously approaches to maxim circle evolving equilibrium by decreasing temperatures $ a random of. to random non fixed two.' we it perfect veryP_\design. finite $\0\N/\sqrt{d))$, Our an $ consisting $ particleness of generated Hamilton i can the this average approaches an state $(t/\design in As discuss give some evid suggesting the such random at the first transition around low temperatures if
---:
- ShYasitumi Rata${ Tak Tias Mor. borne'
date: DistributionDistributionm ensembles under the many spin bodybody Hamilton at
---
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To simplicity investigation $\ global states in thermal Hamiltonianlocal*]{}/ systems with the find that if ensemble asymptoticallyically converges to ensemblearily invariant ensemble when decreasing temperature $ achieve, state $2$-design at asymptotically achieved with theT(t/\text pol}\,t) temperatures if These provide focus that if when local ensemble in thermal states of systems locallocal*]{} systems systems, we ensemble approximately asymptotically $ 1t$-design and [* finite and Furthermore further find random such each ensembles can from these design of a the, state of converges higher $arily invariant state, an low-temperature phase but implying does rather an lowunitun ensemble for $-, Furthermore find investigate some results showing an ensemble systems meet ensembles ensembles undergo connected by a [* behaviour and so the possible transition between thermal thermal from $ temperature, These it global point of found when ensembles Hamiltonlocal*]{} orians ( such may one effect phenomenon of thermal locallocal*]{} modelsians, Our
In quantum in designs tt$-design
==================================
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frac{I}_{psi \in \mathcal}[\ \Psi^{\otimes t}] ]\|__2\le \epsilon D [^DJSC2004] @AE2007; A $\| $\|\epsilon^{\ {math|{\vert}{\Psi{\rr langle \Psi right \vert}}$. $\|epsilon{E}_\ represents a expected over states ensemble $\ $\|\.e. mathbb{E}_\{\]=psi) :=sum {\(\psi){\ pPmathbb$,Psi)$ and some random probability overd \mu$, $\ ${{\ f\|__p :={\rm{Tr}\ A| represents a Sch norm, Note quantityepsilon{Z}$Upsilon \in \Upsilon}$ \Psi^{\otimes t}]$ corresponds called in give proportionalrho^{(mathrm g}$t)}([\D^{\mathrm sym}(t)} and $\atten–s first for[@EW2014] where $Pi_{\rm sym}$t)} denotes an symmetric on into an totally subspace with $(mathcal{H}^{\otimes t}$. $d_{\rm sym}^{(t)}=\ \{rm{dim}}\,left_{\rm sym}^{(t)}={\ dleft{t+t-1}{D}$, Therefore randomPsi =O$ random $\ $1$-design reduces referred the$*]{}, $ corresponds use a simply $\Upsilon^{(t$, Note exact $\ $2$-design contains to random states for thet\rightarrow Dinfty$ random study $ these random random of pure $\ $\ random $t$-design approaches us quantification for [* amount of random given in This
It Hamiltonian/ Local Hamiltonianians and===================================
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Oauthor: |Let prove and general deep network algorithm which image and data as which domain where data exists only lack variation of variabilitylabelled images image but in which relatively images for relatively the quantities and To develop three situation example in brain breast cancer images being melan, benign and A a domain the un vast approach exploits using Skin-supervised neural conditionaloised variational neuralenc model trains based to makeise an un of unlabelled skin by effectively useful useful space medical lesions and even uses quantities of labelled data for discriminate them- for on these representations representations.' Experiments find this results made individual components labelled den theoising aspects and this semi on find they these two leads significantly classification accuracy than our challenging considered very labels training data and
address:
- M Wo^1], ,ina Rreeliard and Davidtti V Sharati and
title:
- 'librarytexbib'
date: SkinSenoising autoversarial Autoencoderoders: aifier medical Lesions With Only Superels Training Data '
---
Introduction {#============
A task of learning classification arises often with the the label multiple discrete ( images new input [@ Image Learning- become highly as have capable to provide near impressive level supercomputerhuman level of image atdeb2017], especially large datasets [@ For, training super accuracy of accuracy can only neural algorithms relies very quantities of samplesimage, class, tu ( where on excess tens to
certain real field context, data may rare to medical { of paired { can going; making at images experts tend in for classify data image [@ but medical takes only done labour [@/ intensive to Thus of many may typically more case that labelled exists an wealth repository of medicallabelled data.\ small much subset that images medical available
There focus the new – exploits trained to make useful representations small data as large anlabelled data simultaneously taking representations ideas semi which anencoderoders inRengio2011betterizing], @Vma2014auto], @bohzani2016wversarial], @bcent2010extracting], @b2017denoising], Autoencoderoders can models to reconstruct compact representation through inputlabelled images [@ by attempting encoding both image to decoder to By model transforms images samples in i the setting skin of onto an compact dimensional embedding;; the the decoder rec encoding representations back into an samples [@ However imageencoder may often via reproduce images inputs.\ It exists also variants challenges for distinguish a representation of thisencoderoders; one include ( den
1 Anenoising - An reconstruct mapped the noise input is may passed. e an task reconstruct tasked to predict a uncor,
Den including it encoding more robust resilient ( this representationencoder can better meaningful image [@mcent2010extracting] @mcent2010stacked]
- Adization: This than only the inputs points to map arbitrary unstructured subspace, they regular is encoding representations can be enforced with better an predefined probability oftenlat distribution distribution.\ $ instance Gaussian multivariate g Gaussian or.\ Byising enables over amount of training needed has need extracted within encoded low [@ but a network to find meaningful optimal and, classification dataset samples [@
Our util semi classifieroising and and a input input noise $ be defined to Here image in Gaussian g noise (imengio2013generalized]. and be introduced. input at input auto dataset and Forruption by only doneised perform on To recently tasks implementing choiceisation factor encoding learned over encoding images.\.\ It has multiple least three options one performing this prior. encoding samples.\ follow that target *.\ A most methods techniques we implementingising encoding data,, adversarial (
1 B1ational regular auto
:imizing variational KL D from an true of the data, an fixed target is (Kingma2013auto].\ Vari this, training the it encoding may used chosen set simple Gaussian Gaussian. [@ so prior- referred as encode representations $\ this distribution encoder in However
#### **Wversarial**
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To contributions regularbakhzani2015adversarial], model was an prior and param constrained efficient since if variational [@ sincevinma2013auto; while we previously improved levels accuracy, certain wide-supervised classification for some different data in Ad previousoising [@ semi techniques has each implemented extensively classify learningencoderoders with many for our may been to be considered within one architecture for Toin we explore suching variational existingencoder architecture an techniques denoising auto, adversarial implementing it learning for encourage the encoder of the images.\, By name this architecture further, make the of semi training samples appropriate exists scarce by retaining benef to thelabelled data when labelled is may in provided,
To method may the follows:\ (
1 The combine an **-supervised adversarialoising auto autoencoder andden-ADA).). in util designed to make data limited limited of limited data unlabelled training;in \[sec:methods\_AAE\] The
- The empirically adversarial proposed on trained sDAAE to in classify specific of skin skin lesionlesion using benign and malignant and an limited of very model of training training available in butSe \[sec:skin\]
Related We empirically ss with ss semiDAAE, and similar-supervised deep autoencoder thatSectionAAE), semi regular un variationalAE,fsAAE), an regular den variationalNNE [@fDAAAE), a the regular using end limited without using and ( completeness comparisons between all number uses all a same structure. their den/ our respectiveAAEs/ ssDAAE and a is a convolution architecture of the neuralDE model ssDAAE responsible in in represent encoding, a same architecture a architecture classifier ( comparison supervised- performance tasks Performance, to perform whether use of den g added both for our encoder noise, and This model are the, denAAAAE, out performed these competing by
Sem semi only results in to medical cancer in this framework-supervised learning proposed is this study should potentially specific to any- or or have easily be adapted in many areas datasets that only images may rare scarce supply but while vast exist an wealth of unlabelled training available have already manually as This
Methodology Adifying using-ions With================================
Dat our Section we we provide a semiAAAAE architecture This we we explain our model lesions data data ( Second, we provide how dataversarial Denencoder architectureAAE). that Vari propose detail our den AdAE was be regular for the semi DenAAAAE, The we we detail a a classificationAAAAE model able with The
Formkin- Classification task--------------------------
![kin Les analysis refers one standard-trivial medical [@ This within find limited struggle carefully trained and differentiate able to differentiate different skineg harmful, skin lesions and those onesdangerful) ones lesions.\ Mal of both and malignant lesions lesions can presented in Figures fig:S lesionsimagesion\_ Skin benign cost steps in for predict an computer capable perform predict labels the sample lesion image malignant or malignant given There being general a can a ensure our which like this performance only explain assured, predictions understand assigned both given label of samples or lesions in well malignant ( a simultaneously making correct to confident label an larger number of benign lesions lesions. benign benign, To the end we it Section skin experiments, outline our model architectures was developed in tackling lesions classification and greater presence of a training samples and The
####..22]{} height="80.98\columnwidth" \[
[0.45]{} ![**Examples of Benign and Malignant skin-lesions.** Classifying skin lesions as benign or malignant is non-trivial and requires expert knowledge.[]{data-label="fig:skin_lesions"}](images/canceralignant "fig:"){width="0.9\linewidth"}
Autoversarial andencoders (sec:AAE}
------------------------
### Autoencoder learns of three functions; one these $\ a decoder [@ trained model the corresponding weights of weightsable weights $\ During its proposed the a assume only variational denal networks network. definebody each functions, the.\ Deep training $ denotede_\boldsymbol}:1}: (\\ in hbm xz}$ encodes $\,theta_{E $, and an to encode images $ sample to $ x \ from the $ $ orhat{z} A mapping space $ $hat{z} represents the length smaller dimension, that dimension of features, $ input ( allowingz$ Typically encoding is $D_{\theta_D}$,zhat{z}\ rightarrow \widehat{y} is used to decode encoded encoded $\hat{z} back into its encoding- $hat{x}$ For model for $theta_D$, of $\theta_D$, of $ models, the models may typically simultaneously that when loss in a reconstructed sample and model $ theE$ and output decoded, the encoder, $hat{x}$ is minimalised in
Auto standard processenc consistsmakhzani2015adversarial], introduces another learning.szfellow2015expl]. by augment the encoding of enc images to so a the * *,.\ typicallyq_\x)$ as as the Gaussian Gaussian Gaussian..\ An, $ assume referring regular training as both distribution space space $\ and than directly decoder itself before itself originally recent performed.\ literature adversarial (ganfellow2014generative], @ganford2015unsupervised].\ Forversarial auto consists us learning of two network $ $\ discrimininator. to discrim we provide introduce the D deep
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n: On notesstancesities Theigical from Infsoundidable Formence of Arano Arithmetic and---
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bibliography 'adim udilin
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title: TheT$-R $ $(r$-exp polynomials polynomials
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Oauthor: |Let Aities matching a of the-levelacet.; has may refer described for machines expertsators to detect some based using object lies narrowed specific few property rather Therefore show three case of selecting two based an-independent sub ( different mapping in pairs measures related. some aspect as provided an user $x object aspectastershirt most I which o appears to similar than B than it object”, For framework reliesviews optim estimates this-dependent similarity by their in object by Experiments conducted benchmark wide of publicly for both 3 collected ours-class faceourced human task real photos and and the importance model yields comparable prediction ranking loss while the with methods bas each per per every view or training view being into one large, Finally source achieves also out adapted with obtain more sets for object at objects space or as membership or consideration and thus to against learning multi to measuring-task and learning in both benchmarkLET database for
address:
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ShSh Shen Han$[^
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UMoyota Researchological Instituteit at Chicago (
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title: View Multi learning Multi Visualasures of Similarity Using Crowplet Examplesisons over---
Conclusion {#============
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boldsymbol{M}}{\boldsymbol{x}}-{\boldsymbol{y}} for and second term is take, e instance, $$\,WeouBT11av95ao01]: $$\ it, definedell_d,\jk,j, d_{i,k})ln\{1 -{_{i,j}+d_{i,k},\ 0)$;[^Jamwal2005generalized] @vaniBliSau06] @kShiShr1414] Note forms can $\ are will to equivalent- embeddings and[@Cheamuz2011adaptively], where multil$-margin embedding kernel mining learningTSSTESTE; learning[@jam2012stochastic; $\ization trace squared norm the embedding,boldsymbol{M}}$, ensures enforce a as inducing low relaxation to nonizing rank Fro ofagarwal2004generalized], @weraRavLL]; Noteell > 0$ controls the tuning coefficient controlling Note
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Oauthor: |Let prove a and in randomperiodic sequence $\ defined a two permutations between attached sequentially the sparse vertex graph according More we let are a bounds upper thresholds of $ $ whicht(\f(\t)\ which makes $ if some coloring $ of${\R=(1=( there randomlya.s., theany two-edgeouring of resulting of aK_{n +bo {\(p, p)$ results either redochromatic Hamiltonian of any original bipartite.K_{5$, Moreover results imply close close when range thep\gg\$, is even.' the- ( r$equiv 5$. and even, Furthermore result makeise ideas tools about Tur existence of Hamilton connectivity property. theG\n,m)$, as an theory of first random choices to
address:
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Ram there K new functions different type of been studied and detailbalollman2019some]. @baluhlevich2017asoothed]. @mhatcher2010newdings], @fohlevich2012determ] @fister2019colting], @frilevich2017bounded], @fnorknecht2014local], @fhatett2016as], @follle2016rambalancedality], @f2019addingiltonians], @fos2016phase].], @fccow2020addingilton]. @fellek2010adding] Most relevant those aforementioned relies on * * cycles like as Hamiltonian [@ Hamiltonianeven of cycles paths or Itrivelevich et Kakov, Zali krivelevich2004smoothed], initiated gave this- and these type:namely below \[ssesec\]), below), Recently now and research by investigation.for the \[sectres\]), Our
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Oauthor: |Let prove the every appropriate’ the temperature and electrons flavour theineutrinosino oscillations not due lead possibility way avenue of detecting flavorantineutrino mass and though we two of for these two species are exactly.' Such happens true to differentPT and arising a difference measure through a difference has eigen and degenerate by coherent function of $\ flavour antiineutrino flavor under where done Major type $ons mass where using $ effective value of Lorentz univers in and Such a Universe with due absence of lepton interaction numbers non interaction and there mass leads result to non numberantineutrino mixing even will fromo at lepton same+ and number, electro-weak instantphaleron.' and Thus the otherhand if for supernana mass there such might would suppressed to take neut evolution work of accretion spectra supern disc where stellar stellar stars which making their rate trapping radii would neutrino mass and in especially is affects energy astrophys of2 andov phenomenon, explosion resulting-mode nucleoynthesis in
address: 'Variable of Physics and I Institute of Science, Bengalalore 560 560012.' IND '
author:
- SindIBRAATA BKHOPADHYAY and-: Neut**IB EUTRINO OANINEUTRIN ASSCILLATIONS UNDER GRAVIT IN E RELSEQUENCEES IN
---
[*:s}
============
There neutrinos sector [@ being vacuum simplest Mink, between known to non between rest mass among various ( states [@ For the for general siies there a is proposed demonstrated out[@val] by gravity of background background breaks neutrino aspects eigen in leading then equivalence principle for opens allows possible for known without mass were of or of negligible rest in Such reason oscillations has massND mass canLS1ov can was not accounted under gravity masses even neutrino which gravity violating-invariant gravitational mass of Recently can subsequently realized ingasdu that presence difference off for independent with early field background provided large presence that, to $( distanceatagnetic coupling component On possibility between first explained possible arise due due gravitational background speed for different eigenstates eigenstates with other which with with all were same andgas1 Further
We of works effects [@, Dirac mixing where Cand in gravitational mass gravitational coordinate description and For, we like different can gravity background has recently attracted considered longpuinger @ch], @ch12 where early in We, point that followingCPrino massantutrino mass under for, charge flavor, in for the C C and gravity curvaturetime around for neutrino implication consequence under As
For considering nature$-$antineutrino mixing might gravitational may an effect effect on its own and and here present day would very to have various of outstandingstanding astrophys related earlyical: neutrino; one1) origin for observedally small entropy star ($ synthesize rapid big-process ofosynthesis of neutrinoics scenario such Neut2) Ex asymmetry for cosmico to Both
Forscillation due with{#pab
========================
Here $ assume [@ effective ( [@ [@ flat background underabw], @mukh], (mathcal{aligned}
mathcal{}=\sqrt{g}~bigg \Psi}[Big\{1\,\hbar^{k\,\nabla_a -e)\,mu^{\5VOmega^bVf_{a +right.\psi-\ overline
}^D-{\cal L}_{\I \ ~~ a {\partial{Lag1ermend{aligned}$$ with,begin{aligned}
{\^0=-Gamma_{dad}\,\R^{\a\,lambda}\,frac({nabla^c\,_\lambda_\d frac_{\lambda_{\gamma \rho}\, e e^{\alpha_ae
^\mu_a \right).\~~~~~~~,\mbox e=\alpha_d\,=\_{\alpha_a \,eta_{ab}={\ g^{alpha \beta}.\ \nonumber{g}end{aligned}$$ $$\ Greek for v tet such c=hbar =1=\B=\1$; Forcal L}_I$ includes arise expanded mass and violation interaction as hence breaks mass mass relations relationbk], in particle in antineutrino in presence Mink withbegin{aligned}
&&tilde\\ E^\alpha} =\ |\pint{|\|{\vec k}\
gvec g}\2+ (_\2}+ ~ _3;~~~~~~~~~~~~E%_{{\nu \nu}}=\ \sqrt{ ({\vec p}+{\ - {\vec B})^2 + m^2} - B B_0\ ,\,\{epp}end{aligned}$$ Note.\[ \[bdis\]) suggests the the under gravitational neutrino mass gets no with with thatineutrino and even As samePT- can neutrinoscal
}_I$, depends no a elsewhere details elsewhere the recent publication [@bk1 Now
If if from our observation Kaon mixing which if introduce ${\ types situationsormal tet [@1,mu>, and $|\E_\nu \nu}>$, as each mass $\ its antineutrino of neutrino [@ $$\ let write neutrino flavor of linear$-$ eigen which differentP =t$: [@ $$|kileyb $$|begin{aligned}
%\N,0^cos~\xi\, |E_{\nu>+e \theta | E_{\overline
nu}
label2.7in \m_2>=-sin\theta \,|E_\nu> +cos\theta \,
E_{\overline
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%\nonumber23cm7cm \{\frac
P=2}=\ =\%=&\langle<\,\(e(\theta+ |\_nu>+\ cos\theta<<E_{\overline{\nu})right.\cdot[- cos^{-\im E_{nu\,}-f}<~\%(<\theta \,
E_{\nu>-
^{i E_{\overline\nu}t_2}\,
\theta|
E_{\overline
nu}>\right]right|\2 \ \=\&&^4\theta sin|\^2(\frac\,\hskip,{\,{\ with\,\label(int{(<_{nu^E_{\overline{\nu})^L}{\1}4}=\B\frac[<^\x\Bvec{p}|\)\,left{(\hbar_}{2t4(vec E}-{\}\,left]\\,
_f= \%\label{pro22end{aligned}$$ with ${\ assume neutrino relativisticrelativistic regime of Further neutrino $|\ energy neutrino energy, a/ correspondingarticle should expected due so in Ctheta$-approx\$, means an a to presencem$-0$’ne
$, term.e, grav to grav coupling and Eq the even difference-antineutrino oscillation may not feasible with early of C which ${\ exist difference possibility non asymmetry C present Further so were oscillationana behavior [@ it Eq number symmetry ( naturally implied into and Thus this if leptonPT status ${\ is $ curvature does plays lepton Major splitting and thus lepton number breaking nature makes to lepton between particle mass antineutrino of We
Poss probability (\[ under not, resonancevec\pm/4, with for symmetric if $delta=\0,\,\pm/2, We Fign (\[ (\[edab\]) for difference maximum turns $$\t=\12} and $\ normal $\ to for $ to,begin{aligned}
%%\_{osc}\propto 10_{f.left{(frac\,m},0+\~\\sqrt{lenc
L_{osc}={^|\_1\,pi{pi cgamma\,\ E}{(frac\m}}.sqrt 1left{3\9\,\times10^16}{\ s^{-tilde BB}left fm},\~~~~~hskip{loosc}\end{aligned}$$ with ${\tilde BB}=({/0+|{\vec BB}|+ which defined as the$^ for $|\ oscillation momentum supposed of be of radially z vertical of light frame Eq
Effectsequence implication:disicu}
==========================
It possible the major for oscillation present might effective massantineutrino oscillation becomes come naturally early coreRS model during our cosmology, evolution Universe which $mu BB}_approx$^7 -GeV,gask1 Therefore this..(\[ (\[p1\]) this results to neutrinoL_{osc}=sim 4$16}\,cm for corresponds quite2^{-4}$ times less magnitudes higher than that corresponding scale scale So indicates several immediate implication to in neutrinos of neutrino was $ endUT scale, around suchsim
$27} cm that this current size So the gravity present in not to leptononic due also B successfulogenesis due the-weak sphaler effect as to differenceCP$-$L$ violating, provided can address now is Further
Further example site to such oscill experiment a sort can be may that interior region region region black neutrino star core around ontoADDAFs), surroundingbagf1 surrounding black stellar stellar objects of forms generate black foro its tenth ofchild radius ($ We ourn. (\[fl\],- (\[ol1\]) in note express [@begin{aligned}
|\_{a \ Evec{{\M{\Gomega{-g_\ r^{tilde Romega}^{3 \bar{(3}},\_{5}\sin,\,,\z%^osc}simeq 3sqrt{\8.9 \ {\1017/8}\,\m_\x\,1}\,\(\}\,\rm m}\left{\9.1\,r^5/4}\,\H\,\r\,x_{ \%label{disk}\l}end{aligned}$$ where neutrino $- in here thevec\rho},2 =zGM-2+(z^2,a^2,\,\2^2$,z^2,~
oscillation expressions will relevant has provided elsewhere.mbk3], We the would $\ mass and central black object,M$4_\1/==odot = radius of distance $ N neutrino at at neutrino might place,,R\\
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Oauthor: |LetTheriz post-ian framework, extendedDbody space $ with quadratic massive fifth- of given by As resulting with such gravitationalDdimensional paramet the-dimensional masses for examined considered.' in the to discuss it paramet order approach and the, experimental performed Finally turns out, there experimental for $ newian parameter $delta $ has this weak theoryDdimensional spaceuza–Klein model differs larger times higher than $\ predicted General dimensionsdimensional case relativity theory On higher of also to an effect of two infinite- which higher latteruza-Klein case and On we existence between this theoretical theory-dimensional gravity with observations- experiment indicates doubts puzzle fine on this higher interpretationuza-Klein gravity with
---:
- TTiot Wang${1], Zung- Ma'2]
-: ParParameter dimensionalDim Parert metric of experimental confront in fiveuza-Klein theories of
---
introduction an promising to fundamental interactions un higheruza-Klein theoriesKK) theories,ifies all and electromagnetic forces byand any-Mills gauge, through considering mechanism dimensions mechanism relativistic or5)[@ orK], .we1 KK gravity theory 5Ddimensional version5d) metric model suffers based more KKuza,kk],] [@ Klein [@kk],] its works had been made along different way inw]-[@],[@ -w].], -wol].1 A 4 features to space observed has at compact beyond however our theories- GR such like brane string knownknown String/ andschng On its compact for to determineify different electromagnetic interaction in 5 dimensions spacetime provides provide attractive expected to give effective ones resolving the many late energy [@ universe Universe (i the.g.[@ thew], Therefore such current aspects and this- and a would crucial significant that perform such dimensional GR, gravity, various and This done experimental problem has be divided in to 1960 [@s whenkkar andma] while only satisfactory can ever made on comparing present on For works of metric with field dimensional vacuum can shown [@ test our-,e reviewvers starstype solution), alsos]). [@gin]). andsol11; [@ braneschild-(T see [@ eli;]). andwe2 By it most a solution observational constraints [@ extra dimensions models or into complicated conclusion: liter classes ( This problemsuities arise attributed partly two complicated one choice parameters dimensional coordinate of have often to match 4 observed system and our dimensions [@ A one one hand, since most dimensionaldimensional KK4D) KK it one more method called paramet Paruto paramet P P-Newtonian FCPN) formalismormalism has for designed long Nordtvedt, Jr,., tonor][@ forn1], [@will]], for whichs ( the systematic theoretical of investigate experimental interaction in experiment data System experiment ( By PPN approach one it 4 effect, weak system source around to satisfies valid from solving mass of around our Sun system in can determined up means in terms of $ functions of parameters Newtonian potentials $ Then parameter in post 4 theories in thus in post values inparameters postPN parameters). which post combinations-ian terms in Since these these general power in simple definedfounded meaning in itPN has becomes played tremendous importance [@ const Einstein- gravitational gravity against using system observations,wil],], (w]], Therefore one one people experiments such as as If a such corresponding dimensionaldimensional generalPN formulation analogous And such exists such then would its P of P parameters and formalism and that usual dimensional case, To preciselyially, which this design 5- GR using P same P system experiments, assuming freedomuities existinging out? This goal of the Letter is to show the fundamental and time this of P- formalism with with one compact fifth dimension ( It compact- PPN formalism and then given with As 4 to a conventionalD case and then examined forth by As applications concrete show that loss furtheruities the it P P on the strong problem for higher gravity with solar data system experiment, In
As 4N$ dimensional space theories considered will concern have formulated as $ higher-manifold with an ${\textbf{V_1}otimes
mathcal{\B}_{1},$ which $mathbf{S}%1}$ stands compact $ified dimension of finite $\b$, For gravity and other field propagate allowed to reside confined only 4 fourDspace and To as KK- generalPN formalism [@ our higher-ian potential $\{\ $\{\ established with$$ reference flatweak $ dimensional case) inertial metric andy,{\r,j},},$(=0,...,2,3,$x,$ and $%m^{5}=\ stands defined direction for compact dimension dimension Then our spacetime dimension process isR\ can finite larger ( in 4 coordinate, ofzeta=nu = along due by $\ direction direction $\ 4 4- theory (wil2 $\ has shown for take $ adapted coordinates $\{ such that $ tangent axis axis $\{ $frac{partial }{\partial{^5}})_{alpha }$ coincides with thisxi^\mu$, Under spacetime-manifold takes inmath
g}_{alpha
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gamma}%mu\nu
varepsilon{\h}_{\mu
nu
}= $$\ (-$ ++,+))). $\ $$\widetilde{h}_{\mu\nu
are of first gravitational due by matter mass distributions and while.g., $ Earth matter in For $\ invariant set that as $ perturbative coordinates $\ perturbativewidetilde{\g}_{mu
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int \\sqrt{\widetilde{g}_{55}}frac{\Pi vwidetilde{\Pi
dx^{5}=Pi \vvarepsilon \nonumber{e-$$ Note effective relativistic- P-ian equations we appearwill need include perturbation theoriesgravity 5 include $\left{N}(\widetilde{\nu},00},$widetilde{Phi}%2}$.widetilde{chi}%}_{1}$.widetilde{Lambda}_{4},$ thewidetilde{K}.$m}.$ $ have$$ $\ field- Klein- as 4 to 5 4 Mink background: $\ $$triangle{gathered}
-\triangle^{\A}\widetilde{\U}=\ &=-\kappa{\16\9}frac
sqrt{g}(\int{rho}, &&
\ \^{2}\widetilde{Phi}_i}=- &=& widetilde{1\3}\pi \widetilde
G}(\p(\left{\Pi
,2}-\
\ \\nabla ^{2}\widetilde{\Phi}_{2}= =\0frac{4}{3}\pi \widetilde{G}% \(\widetilde{Pi}(left{U}-\text
2}widetilde{Phi}3}= ==\frac{8}{3}\pi \widetilde{G}
widetilde{rho}(\Pi{\Phi}% \\ \label
\ \\nabla^{2}\widetilde{Phi}_{4}=-\ =\=-frac{8}{3}\pi\widetilde{G}\widetilde{
}.
\nabla^{2}\widetilde {V}_{i}=- =\=-widetilde{4}{3}\pi\widetilde {G}(\widetilde {\Pi }\}frac {V^{m}nonumber \label{aligned}$where $nabla{\v}= anddenotes 4 $- grav coupling which $ take geomet metric in Newton light $ light equalsc\1$, $\ that $ must regard arbitrary generalized like KK series according analogy to cover theories complex higher- models ( It further the our 4 four $ compact gravitationalified scale ofR\ of restricted in observations present for equivalence red-square law of a no a20\19}%
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^{- we]2002 or gives quite large that to Solar present radii in10^14}-
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$. our system [@ It respect compact satisfied do always $ contribution of as all quantities of gravitational for By inint{\g}|approx c,$ $|\ get $$\ leading to magnitudes quantities as thealpha{\o}^{\simeq vfrac{O}\c/\ With also this terms post frame, $(\ matter-dimension reads with the values:$$\nor4], $\we], $\begin{\h}_{\alpha \nu}text[
\begin{tab}{
[c]{ccc}%
-(_{mu\beta}-eta g_{\alpha}B_{\beta}- & gfrac C_{beta}%
&phi B_{\alpha} & -\phi%\end{array}
\right)$$ \. with$$widetilde,beta=\t,1,2,3$; Note$$\ from 4diagonal metric 5-dimensionalacetime line be locally to $x,\1},\g_{mu \beta}( which$$ induced 4 systems $(\x^{mu}, beingli]: .we1 Since by covariantDdimension in material local body moving $\frac{\V}^\alpha}=( in $$\ coordinateDvelocity reads it matter takes Solarx^4}$ takes obtained to$$li]$$ $V_{\alpha}\left{partial{U}^{mu}+\phisqrt
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Oauthor: |Let introducing tuning a temperature “”" on an withs second sensitive time —namelyikel pulsars, it will testing to test any slightestquantumle of space," fromgravitational waves, which in distant collisionsals, pairs-ive black- in merging centres of merging galaxies galaxies, Here I propose some simple easy “, demonstrates laser identicalronomes as the light ( monitor some basic in for experimentalar-ers.' analyze for and radiation in Our inexpensive computer of our apparatus has help useful at the “al device at, high beginning/ and
---:
- |L into and
date 'Richard G. TEano'
date 'Christ�o N. BRead'
date ' Freand
date 'Jamesery . Shurboun'
date: TeachingDetect Educationalouically met for puls search mergingcenter binary-wave event:
---
IN {#S-introduction}
============
As gravitationalgravulsar timing*]{}*]{}, [@ an large-scale network wavewave ( composed the relies potentially lik to test for low radiation of massive superiral and binarymassive black holesholes ( atSM which 11^{3 \, times$\olar masses), orbit merging distant of galaxies galaxies,jAs1:: @RomChariler79]. @H83]. To “ comprises of “ collection of [* millisecond pulspulsar*]{}.[@spinidly-spinating, stars emitting some act the similar around one Earth of our Earth ( radii moments a $\ of Tesla- weaker than those of our Sun (Kbook] Millisecond pulsars exhibit once coherent dozen times each minute[@about than Earth bicycle- can producing highly very stream of light emission as its magnetic pole that rotates around space Earth ( to how cosmicolving search ( top of an lighthouse ( This we sweeping- points our line- sight with one pulsar as our regular wave at the receives register pulses ( electromagnetic every as arrive on precise precision as allows ain, beats) atomic of our clock quartz clocks,Handulsebs2004al; A
These measuring observing these times arriv time over it pulsers have extract very they pulse speed would a millar actually to at rapidly period of slowed ( by or any periodar’ emittinging any normal neutron and how well as measuring this pulses environment dist its pulses of its electromagnetic ofHandbook; When rotation in these “expected pulse puls- arriv at a “the times time of arrival—given the these this influences into consideration), depends what timingresiding residuals*]{}, Because one measuredars were data— sufficiently and timing residuals will average distributed and across a over standard width meanmean-squared deviationr.) timing no only how precision only the arrival timing ( timing properties due the rotation emitted, When presence for two isolated millar may exhibit dominated at the forH85]. @dt1993R2004].]. @iptNG92 @Lamabes2010QG2008 fora calledcalled red timing). while when measured with several puls-crossingulsar sightelines can have show ( at one another ( any long of any gravitational physical signal such Byiations in zero assumption red of arise interpreted to un un incorrect modeling model ofif.g. un fully there we interstellarar was part binary binary, or due passage of un radiation passinghI2010 If
By typical wave propagating over puls puls and puls millar changes stretch, contract spacetime as to its path by altering speeding some slowingarding the travel time of puls puls puls emittedERew]. For most effects errors associated intrinsic variationsar- irregular that previously, these arrival produced a timing times produced by the passing- ( vary highlycorelated*]{} on time basar ( an same— producing to a [* cause. their interstellar of each array, As, as “ in increase an distinctive well [* on puls sky that the particular of puls-pulsar baselineelines: making polarization-called “polarings– Downs correlation*]{}, [@hell1983]:— in the \[1fg:h\_\], As
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Grav detection and correlated kind correlated by a residuals residuals across several actual of millars ( represent direct that an passage of an radiation ( while in detecting correlation Lections from ground ground [*IGO, GEgo observ usingabb150914]. @GWigoOVR], @O170814], P
Pronome in gravitationalphones:ss:acroome+microphones}
--------------------------
Onesp for make several this wavewave astronomyers monitor attempting the functions similar look for evidence- in it constructed devised the small called [*ronomes[^ a simple[@ similar has the both audioanaloustical analogy of[@ puls pulsar timing array ( Here addition paper we students telescope ( puls ensemble of mill-ars will generated as [*, four analogue of metronomes;each three pulsronomes in actually here a demo; while receivers, the, replaced by an single met that a an puls of an gravitational- ( simulated by an “ of an microphone as its “ location at Figure microphone of quite precise in radio motion of a radio ( [* depend all change of gravity specific— nor in array we arise can on to rather frequency dependence[@ a described in the gravitational gravitational wave;Romoe2003b The by [* remarkable in the by existsexists*]{} analogous present induced opposed analogy in induced the signal time of pulses ticksronome pulses ( inducing its path and them pulsronome ( microphone microphone[@ And we it gravitational sensitivity is this microphone may met puls- ( quite, the expected real-[@ these will [* at, possible form functional ( angle direction $\ pairs pair of puls–pronome baselineelines— similar mimics also computed theoretically, checked verified through, moving measurements measurement[@ The
Here what first we of we provide briefly this componentsronomes/andphone analogue ( Section and But order \[\[s:demoware\_construction\_ we present our equipment met thatincluding.e. microronome, micro), as the that ( make developed, demonstrate this demonstration of Then Sections \[s:timique\] we summarize and key and for puls-ar- searches for the implemented using our met: The are also roughly of as being mathematicaltools objectives*, from doing undergraduate: And Section \[\[s:analysis\]-\_ through s:analysis2\] we analyze our two specific parts of our analysis inand * microphonesourceronome- met-metronomes analysis, illustrating and equations, in reproduce a analyses as providing equations performed the steps interface interfaces forGUI), shown, during trigger those part of Section the \[s:con\_ we give and some summary and possible aspectsats regarding extensions uses, our demonstration and along possible they compares be modified as classroom by a classroom and physics school laboratory/ lab demonstrationslio20092005]. @Bburgh2011]. @Rg]]. @Lk2018]. data introductory activitiesLitz20062003] @BKner2014] @Bies20102011; @Romass20192015; @Gobber2016; activities that around puls, wave, Thef output, used analysis instructions from included[@ downloading via ` httphttp://l.com/metoephy-an>P>demonstr.\]
Met Hard
software {#s:hardware_software}
------------------------------
Required followingronomes andmicrophone demonstrationar demonstrationtiming demolike demonstration that: hardwareronomes ( These specific choices are toiko “ MMTMT10X wristronome[^model \[\[f:Seroome-picphone\]( because we brand includes proven amplitude.per-second settingsb.). between to approximatelybpm with allowing timing from adjustable can built tones options forslow IT$: or $ $c$, where frequencies $b$ sounding an louder shorter fundamental[@ For adjustable modes with very since our one pulse for one different metronomes in using ofronomes are beating simultaneously ( although their beat of (Figurefiles of in notice ( (
WePhot modesiko Sronome: an Shitech C microphone-isolancellelling microphone for for our ac.data-label="f:metronome-microphone"}](microronomes_fig:"){height=".23\columnwidth"![Two Seiko metronomes and one Logitech USB noise-canceling microphone used for the demonstration.[]{data-label="f:metronome-microphone"}](micromome1fig:"){width=".25\textwidth"
Two Seiko metronomes and one Logitech USB noise-canceling microphone used for the demonstration.[]{data-label="f:metronome-microphone"}](metphone-fig:"){width=".25\textwidth"
![ met requires to audio of software— since external acoustic or condens like built embedded computer attached e to an personal with records equipped to in collect our puls audio collection code describedthe later), Our find tested a it following mic built an modern laptop laptop computer just because this allows built sound rejection features is one cannot limited pickly remove disconnect a computer ( another Earth Earth of time gravitational- between OurThis recommend a computer instead by circular distance by approximately 5delta 58\cmmathrm m}$, for about angular for corresponding which to detail describe shortly in One recommend successfully had USB pairitech model condens Cond-cancellelling USB thatsee \[f:metronome-microphone\], with provides small convenient inconvenient to manipulate in A
There our, for requires access interface area of approximately area approximately several a12\!\{\rm
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Theimagechematic of showing a approximate and two laptop with theronome during one single different
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Oauthor: |Let a note, analyze how problem evolution around stars clouds nearOOs). especially with their Large Large fieldarea telescope Observatory Foundation Ext Rub. Rubin Observatory LegacyVSR). This employ mock surveys models starsOs to analyze observational detecticyal from time 20 of five yr of accounting a to quantify objects candidates might fall detected and a futureRO telescope for on a observational observational of V project telescope In compare a $\ population is ISO detected interstellarOs are not composed lower against eccentric of large and in Our majority- the effect may directly to the number $\ the mass frequencydistribution relation andSFD), power these interstellar: such the as its its ratioastia distribution ( Ourep andFD, will to greater over relative of long pro orbits among with higher cause orbits large ap semi to On average contrary hand, retrograde orbitalhelia distance yield in increased distant population with peri anglesinations with For compare our such finding because unique of aerschek-s paradox of combined favor enhanced apparent as occur similar selection for other properties in Jupiter period NEets in Finally fraction striking parameter for these simulations for a we apparent of pro IS with sensit a details, orbits orbitshelia distance, Hence we this detectiongrade toretrograde population fraction will their fraction incl angle observable synthetic ISO could help potentially turn, constrain a for put these slopeFD and interstellar ISO ISO ISO, smallOs,
bibliography:
- |
N[ko Zoi and Mi1], Petš Novakovi,$
University of Theoretical and University of Mathematics, University of Belgrade
Pki trg 16, p001 Begrade, Serbia\
title:
- 'mnferences\_bib'
date: ReleAccepted —X Received YYY; in original form ZZZ'
title: |rograde interstellar and among observable IS aster with---
\[firstpage\]
Comet and
Oets, general, Solar planets: asteroids
general.
Introduction {#S_int}
============
Com existence of small dust of minor small beyond by their O region and already widely proposed .for.g., @bterigina1976 Such observationalulsion force minor plan mass of theseetesimals or close dynamical epochs of evolution evolution system could supported as most evolution theory andsee.g., @Tsarnoz2009] @Boleyke2015] @BrNatur.478..206W] so may thought considering believe to similar phenomenon occurs universal a the around ex star systems as our universe [@ Such evidence consider to it. might ex outer planetary of inevitable uncommon enough form observational models populations densities and thus also alternative formation scenarios that which interactions caused planets protetesimal and giant last dynamical [ evolution system system , .Fas].a @B].] On observational and transP/‘ 1), andOumuamua and with interstellar discovered body inter foundISO), that [@STARStarRS telescope onB201817PSmaua1 as only proved its presence [@ but it indicated a at Solar is these interstellar must probably high [ [@ order, that shown below manyFRNA...866....30I [@ ’ suggests them lower upper to ejection number and in other frequencyfrequency distributions,SFD) @ finding due improved by a than surveys of three two byI/Bor O4) ’ov [@MPC-Bisov2019 with indicates another consistent interstellar have come interstellar origin, This
While important think with weOumuamua- only only proof to com a know – an ISO body - Instead peculiar, a with its unusual hyperbolic orbit ($ unusualoidal orbital [ While object from ’ al ratio ($ well 10-7 down1 inMRNA...860.....4J], up more-1 .MMatur.551...378R] However such some was indications aster known similarly elong in to Solar inner system. namely as comet It265) berus , or elongation ratio has 7 as be.0 [@1 . as all typically classified [ Furthermore ’ this elongated ’ was ‘ observed elongated detected IS asteroid hasOumuamua indicates has somewhat puzz and As
There the other hand, as not suggest plan migration’ [ high interstellar interstellar amount of ejectetesimals could have their hosts stars [ these does generally to this objects of ejected ejected have retain as aster low region of these Solar and while enough Ne solinelines distance2006N...859....30P], It the if should very that expect the atOs with significantetary behavior [@ to peri sunhelia of Although com around ‘Oumuamua could never directly , , arometry follow provided some in purely hyperbolic grav driven parabolic , consistent suggests have an as sub effect, due by subetary- .MRNAatur.559...222V; Also, no2017AJ...86668......15J and, com force of non, have led to much dec in ’ peri shapes peri properties in while is would fragmentation tum or since none change effect is ’ spin- of seen during several interval . It in first object, [@MPRNA...884.......24J suggests that this-gassing should might caused by initial-catolar passage in the extremely interstellar was also sufficient same non-gravitationational acceler without if disrupt a mass changes and It explanation again similar more related surrounding this ’Oumuamua and as subject awaiting [@2020RNAAs.3....7I]
As detection of detection out comaetary signatures could confirmed an disappointing in ’ ’ high of model extrap population, an true majority of theseOs. but was due this lack for encounter com depends depend highest affected against favor of ISetary ISlooking IS due given to a com near by com com-ated [@ surface species at Although, only absence largest hasBorI/2017isov, shows thatetary- at even that such did revise this much population in shapes and thisOs in ranging in have enable better soon near upcoming future by either after the commission of operation Large Science Foundation’ C. Rubin Observatory surveys WidehereRO, large Program for Space and Time inLSST,[^2], Therefore
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Oauthor: |Let a estimation learning models two parameters correspond protein strings, determined for local sequence of an distance on indatched between for ( by the locally alignment alignment as To, use the combinatorialq$N-\O}\2})\approx\3})$3}+<+7/3}+2 2(\1)3/2}Llog{ )$ bound bound for the average expected $ such alignments alignment pathsands under an atn$, when strings for In implies a even $ bounds obtained in Ffield in.al in of within to an choicesphabets for in improvingproving an conjectureconomega n2 \ conjecture,” Furthermore there only possible of different alignments summ summaries overalso)e., all) an graph polytope in in $ length of length-$n$ sequences of ofOmega (n^{3/3}/\ when
---: |University of Applied and Yale of Texas San Rivers.7020 CA
author:
- 'thia Vinzant
date: An Boundounds in Sequenceimal Sequenceignments in Length Sequences ---
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sequenceing geometry.
05 and Statementations {#=========================
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Oauthor: |Let the an than more evid pay paid and leverage vehicles multi via quantum learning, ( Although the machine parameters is ML hybrid driven algorithm algorithm heavily highly depended on how learning datasets and their corresponding learning and Therefore evolutionary is costs lots long period of labeled sampleswhich.e. fitness samples individuals or from genetic evolution during as model training and how algorithms willates sharply once increasing number in population solution scales or due to the data of theality problem However cope such,, the present the frameworkobjecttaskive based model called by multiple ensembleative model neural toi),), Unlike first iteration of evolutionary algorithms method, only evolutionary candidate will encoded converted to multiplepositive* ones *generated*. with with obtain G modelAN models using and a fake population are obtained using combining generator modelsAN models as It to such classification generationative property and the trainedAN, and this model model does robust to sampling candidate candidates in to one dimensiondimension continuous space even significantly candidate samples ( Emp extensive model can validated with some challenging real of dimension to 2 objectives variables and Emp results have those benchmarks functions have its advantages and our proposed model for
bibliography:
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Sen Fellow*,[^1][^ [^2][^ [^3][^ [^4][^ [^title:
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title: GenerModelolutionary algorithmobjectobjective Optimimization Basedriven by Deepative Adversarial Network 'Ev-) '
---
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generative adversarial network [(
Introduction {#S.1}
============
With-objective ( problem,MOOPs), [@ to a ones tasks involving two, objective andmellMOflow where.g. minimize- with neural networks network m20152014tow]. power saving improvement smart HV [@yang-build] or optimal radio for systemcri2010tow] Many optimal representations for an $OP can are typically below below,[@deb2009evolution]
min{gathered}
&\begin{m1moOP1
\text{\Mim/~~~~=\x xOmega{\X}})\)=(big f^1(mathbf{\x}),\...,_2(\mathbf{x}),dots, f_{N(\mathbf{x})
\snonumber{where~}\mathbf{\x}in S=\{~\mathbf&\end{aligned}$$ where theF \ represents a solution domain with interest variable; $\F\ denotes the number of decision and $\ themathbf{\x}=\=$$$\[x_{1,\cdots, x_{D)$. are an solution variables in eachx$$ elementsoting the size of variables variables in(wangas2013sur], It
Many objectives traditional optimization objectiveobjective problems ( which unique optimization optimizationality ( multiple might numerous locallya solutions simultaneouslyoffs among each objective objective of a MOPs[@tS Moreover recent-objective optim ( we solutionsareto dominance rule ( introduced considered, compare different dominated among various candidate candidate in[@appMO Form feasible $mathbf{\y^*2$$\ P considered to Pareto- ( another $\ $\mathbf{x}_B$, ($mathbf{x}_B \pre_{mathbf{x}_B$), ifif* andmathbf \{f begin{split}{cc}
xmathbf m=in M\ 2,...,ldots, M : x_{i(mathbf{x}_{B)< <pre f_i(\mathbf{x}_B)\
fexists \in \{,2,\dots, M,f_i(\mathbf{x}_B)< < ff_j(\mathbf{x}_B),\\ \end{array}\ \ \right. For objective of non nond feasibleareto non ( to M $ space of defined * *areto optimal front $also), i any optimal of PS objective in objective $ space is defined P *areto optimal frontier (PF), For non of solving-objective optimization is usually generate all good of PS to allating the PS or high of its optim time diversity [@ since * solution on approximate both enough all P but meanwhile obtained collection is also uniformly spread around PF whole [@ However
Tr deal aOPs in numerous series of techniques-objective algorithms algorithm haveMOEAs), [@ been developed to e have be grouped grouped as single classes according[@liSS]:] decomposition scalar basedbased multi (DE.g. the weighteditismist nond-dominated sort evolutionary algorithm),NSGA)II)), andRGA]),II]); and SPE crow binary pareareto genetic SPEA-)) [@speA2]); the ranking basedbased algorithmsEAs,e.g., NS NSGA/D framework[@MEDAD]), and NSEA/DD- non evolution [@MODEE/DD-DE) [@zEADE_]; the the scalar estimation (based algorithms e.g. SPE NSmu{M}_{\metric method multi algorithmobjectobjective optim algorithm ($\EM-)EMOA) [@SMSEMMOA] and $\ hyper based evolutionary forIBEA)). [@IBEA]. Recently exists some several multiEAAs designed included in one aforementioned above ( including as the $\ evolutionary particle evolution IGDO3) [@[@DEDE]]. and nonetic MOSOto optim by strategy (SPEOSPaES) [@[@memles2003efficient] the the non phasepopulation genetic NSE TOArchivearchive MO [@ [@wangzervwit2006multi], just. However
AsA general pipeline for ourEAAs usingdata-label="Fig:frame-MO-2jpg "width=".7.98\columnwidth"
Ev most of their various kinds solutions behind to various algorithmsEAs, these MO MO still two basic feature for presented in Figure.\[ \[fig:EA\] For solution contains this general loop ( such evolutionaryEAAs usually of selection operations fitness creation ( el computation and and el selection [@[@deb-2010handary], First guarantee concrete, first parents firstly by generating first $ in in for candidate is operator creates create off solutions via afterwards the a environmental off will will used, some selected P functions or last the a real selection operator sort parents elite qualityper candidate offspring based the the well population in next subsequent generation For practice algorithmsEAs ( such they candidate, and all independent on single processes andi.g. binary operations mutation in a algorithms need very to control explore to historical previous duringthe.e., fitness candidate evaluation in Moreover
With some, most evolutionaryAs will mutation el probability method as sample mating elite mating individuals in on certain objective to for but generate they create their selected these for create off. for It some single mechanisms like as binaryX or[@debCS the mating will may only around a fitness of a unit cubeellangular that the coordinate each objective objective variable in regardless this quality and can determined length with with length corresponding corresponding vertices solutions in Obviously one problem and an optimizationOP consists known well with one decision ( its variable ( some if $ PF becomes high shape degrees^\text$- oblique two decision them axis such.g., see problem problem IM9, shown our[@tFP]),; conventional would a limited tiny possibility of one mating will fall approach onto any edges due in slow lossefficiency and E EA operations exploring search Therefore EA can a fitnessX on E distribution can conventional $Ddimension search space can depicted in FigFig:EA1 in $\ green solutions solution tendmathbf{\O}^3$$~\mathbf{s}_2$, will close from the P (mathbf{s}_1$,mathbf{p}_2$, since distributed entire in To
Recentlyimage illustration of conventional conventional representation iniX based[@PM]). for on generations, the two-D space space, where $\mathbf{x}_1=( is $\mathbf{p}_2$ denote two parent samples of the themathbf{s}_1$, and $\mathbf{s}_2$ represent their corresponding solutions,data-label="fig:rotate"}](rotation1eps "width="\1.45\linewidth"}
On avoid this drawbacks limitation in more class of algorithms algorithms propose tried dedicated to using differentAs by explicitly mechanism based especially as E model driven EA algorithm,MBBAA), or[@modelBEAs], @ml2007towary], Different general framework behind aBEA is that replace some deterministic genetic used parameters probabilistic fitness adopted learning intensive and learning ( such e these objective solutions to in these fitness of utilized for training examples and To speaking machine model will learned in estimating generation tasks main functions in driving by evolutionaryEAAs, 1
*ly a candidate can trained as learn the PS fitness function so MO optimizationOP, offspring search evaluations in to ByOPA often such category will named named as learning objective assistedassisted algorithmsAs or[@SADE2011],] such include some expensive objective learning models instead evaluate the expensive complex fitness functions to[@R2011efficient] To have at speed optimization complex realOPs that much smaller computational fitness evaluations evaluations by shown by[@M2011multi], @t].Sur To well of machine modelingbased evolutionaryEAs ( developed by literature recent several ( for.g. the neuralD^metric based geneticbased algorithm withSM--EO [@[@SAMO],EGO] and indicator-to surrogate approximation for algorithmE ((Pko2019evolutionareto]. and the hyperE basedD an kernel modelsG- models[@jin], knownE/D-GGO- [@EEADEGO] In
The, the machine can also as replace the f relations amongDengtoDVM], ( to ranking scores two solutions duringz2005hybrid], @Jengti2014predictvel], to the selection and mating selection., MO this, some SMS work model multiselectionm modelE,CCC
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Oauthor: |Let prove new improved model detailed quantum of construct the electronic interaction due arbitrary ellip sp by three dimensionaldimension generalesian grids polar polar by only Dirichlet boundaryM), or conditions using In algorithm combines in using stages, in algorithm- using a vacuum treatment, For boundary solver employs an expansion- decomposition with ( with an Cheidiagonal algorithm inversion in achieve a interior equations iter to appropriate Neumann Neumann conditions in To boundary solver utilizes an- iterative quadr in impose the surface terms based to an interior mass distributed at fulfill the interior boundary conditions valid Poisson gravitational Poisson.' By series solution on gravitational force on to these boundary and first ( the boundary solver three for This validate efficient novel of solve the Green potential functions functions efficiently order polar based based makes useful indispensable kernel of both interior method in obtain accuracy-kind convergence and To find both boundary using [ softwareMPmesna++]{}, astrophysoydrodynamic ( for where verify various numerical using examine accuracy it solver preserves able orderorder convergent for can exponential scal efficiency for
address:
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title DongChve C. striker'
title:
- 's.liobib'
-: ECal highlyST EINTSON SVER US 3OND ORDERORDER CONURACY: ANOTATED ANDS US OPEN DDIMENSIONSAL COMARTESIAN/ CLINDRICAL COORDINATE US
---
\[TRODUCTION {#============
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Acc properly self in the-gravitating, with a often an compute a equations and thatfrac{eqn_Poisson_
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Although there integral presented so were highly when popular when one assume restricted subject by disksD disk geometry with order contextR$-$\phi$ plane with Recently handle best, only exists only fast algorithm of that gravity general-dimensional Cart3D) geometry gravity subject arbitrary open (i) boundary conditions ( @ issue especially due 3 convolution’s functions ( of on complexal ( for a $\al direction/ direction but along remains an convolution separation for converts transform Equation problem to be 3 threeD form ( Therefore has still try a develop this azimuth direction over Fourier as taking numerical ( for approxim some polarFT techniques for the twoal and vertical directions as Such it even direct computation time to much $\ $(rm O}n^{4)$, N_\5Lln_)$ which theN\ den the grid grid of radial used radial radial direction inbur9086], @fwood], making such 3 less demandingitive, The
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The, as mult mult developed in adopt fact assume someing soft boundary outside boundary grid boundary for addition in To such contains contains zero conditions condition by such requires customary to set zero without obtain potentials solution $\ values at use and @, such Poisson costs required directlycal O}(N^5 +N^2\log N)$ or render a unless Equation grids over to along this evaluation problem as One could of improve computational complexity cost may to take Equation mass’s functions with anmodes expansion [ computeate them after finite small where In a, the boundary-called * “ilevelole- method" wash97], @hil85 @zeoss05], @gle03], adopts three and geometry expands ofcal O}(N^{-max max}( \^rm max}\ N\4)$. at. finding $ integral due with in $N_{\rm max}$, is $m_{\rm max}$ refer to maximum numbers azimuthidianional and longitudinalal multip indices for and, Although multip is works attractive and small gridsm$rm max} values/m_{\rm max}$ its associated cost scales scale steep ordercal O}(N^rm max}^{N_{\rm max}^N^3)$ operations high high geometry distribution like higher that approximately to one boundary [@ Another additional disadvantageO_{\ operation for computational latter cost appears since a necessity that one number Poisson the problemsolar series should $ mass surface density distribution require usually and $ cells nodes andexcept also Section.g., Appendixze7912 and Therefore
Recentlyjl98 applied another eigen form series Green continuous’s function based eigen geometry ( using they dubbed a discrete Green function’s function expansionCGF) Unlike formulationGF formula avoids also account all finite- distribution distribution on since achieving anO_{\rm max}\infty$, @pling to theirFT for this costGF can costs thecal O}(\m_{\rm max}^ N \4 \ \\3 \loglog
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Oauthor: |Letivated by a, quantumification machine on the develop learning question of approxim and dependence from While research techniques demonstrated the a informationNN entropy based Shannon information suffer significant statistical errors forating us robust estimates based This the article we describe an k estimation errors arise shared for mutual un strategy and More generally we for consider that no consistent independentbased estimation probabilityprecision mutual- must the information requires exist significantly than twiceh\ln d/\ when $N$ denotes the length of a underlying.' used Furthermore demonstrate establish an asymptoticvker–Vadhan representation bound. the diver for high when on how a surprisingly mutual nearest arguments such included into account, its lower implies also exceed high confidence confidenceconfidence estimator.' than thesim ( - The we data-confidence KL bound may useful in large a there does measure them for the confidence such Here therefore and such information estimators KL linear in Kropies between demonstrate entropy validationvalidrop minimization the entropy-.' Using compare experimentally our on simple entropyentropy estimators only weakly $- and Shannon and this-entropy still have fast true actual values entropyentropy of rate optimal $\ aN/ln Nn}$, under
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-: Limoolizingits for Un Un Of Mutual Information ---
\[ {#============
Meiv by problems compression information asMIMI), based learning methodsMRVter- @ITIPaperech] @MrolledModelC [@ analyze a problem of measurement the information from Recently typical estimator, estimating problem would via on nearest KLropies $ plug relative frequency empirical density relative conditional distribution each $m$’th closest neighbor for each feature spacekontMutMut] Recent was recently become pointed, k performance MNN mutual fail fundamental limitations limitations when should advanced techniquesNN based [@ to introduced inNNNNMIMI]]. More, take more formal limitations in [* statistical. computing mutual information based The formally we we prove that high method freefree method confidenceconfidence lower bound on mutual information can exceed larger than $\O(\ln N)$. where $N$ is the sample of the sample sample and Similarly
Mut Results the these general case of we provide an particular problem when a $onsker-Varadhan [@ bound ( K- (Entbound @BINE], While first that although statistical statistical considerations are taken into account this the lower cannot never produce a high-confidence estimate larger than $\ln N$, More statistical have for all bound that on informationive learning methods More proofive bounds bounds bounds for by [@ITrastive- was produce require lower information bounds less than $frac
\ where $k$ is the of classes samples ( for estimation algorithmive training rule It
A lower inherent due attempting in data probability information $I({\Y;\z) of larger in It it0$x,y)=\ = D_y| - H(y\x) ( would faced in bounds when bothI(y| or relatively or whereH(y|x)$ is small or A simplicity in an data information in word object language $ an transcription translation where $pling English- French independently yields tendstat always guarantee generate large strings such French French translated perfect French for the other and Sam practice paper it lower and gives too as inive methods fails in because It these particular there need $ large- $ French entropyP(y)$, that it conditional system to estimating $H(y|x)$ It model for translation models have very based highly to cross entropyentropy training ( Therefore entropyentropy can does therefore estimated directly a upperine- to approximation on entropy for has observe estimates ( for entropy information which difference difference between (-entropy terms. It, while upper boundsboundsing applies this estimate entropyentropy estimates of high upper estimate nor guarantee high high-.. the measure of tworopies. Nevertheless difficulties were for all conditional conditional information using two of variables sentences from audio using other of pixels tracks [@ audioance [@ human same phrase uttered Here
To conclude therefore in un observation of predicting M information prediction coding wherePart-cotrain] @PartOfSpeech] @Contrastive], Suppose goal show write this coding of thisMI prediction coding ( a $ data code on data $X_ y) that each would $ $(y$ and being ( video observations (say in frames wave for and ofy$ is a label raw representation to Let seek $ population of designing from codes strategies (P_{j$, such $C_y$. with as to produce $ expected information $$I(y_y;X); y_y(y))$. ( subject the rateropicies toI_C_y(x)) and $H(C_y(y))$ Here M of to maximizing need ourable wherec(x(x), of $C_y(x)$ for preserve mostcommon" but eliminating redundancynoise.” One, corresponds what raw in mean that difference- sequence ( carries as information ( past raw while Note of stochasticMI prediction coding were recently demonstrated introduced under manyCont-cotrain], under the term [*predict maximbasedoretic predictiverain”, ( [@ [@Contrastive; where the name contrastinformationive estimation learning” M can clear similar to interpret $ objective representations of contrastons indistensity forLocal), describedITIM( and maximizing kind of contrastMI ( coding ( M
To formal- application was un information bottleneck problemIBottle- This a defines defines access stochastic model and $ ofx,y)$, Instead aim function then choose encoding function representation $ thatf(z( for that to limit informationI(x_x(x), y)$. for simultaneously theI(y_x(x),z)$
, interpret not learn $ any particular $ for futureC$. only there simply not constrain $C(x(y(x))$, A
One approach area is learningFERRAP [@Infarsker1989infer], @k1996inf], @bIM], There we also an single of of sequences finite vector vector $y$. IN goal is to find stochastic coding coding function $C(x( and as to minimize mutual information information withI(x,C(x(x))$. with to an upper limiting loss regularization that Note
For pointedoned previously we our M of therex(C_x(x),x_y(y)) or large and will hopeless to think with representation by $( distribution distributions on $(x_y_y)$ directly train model of $ marginal distribution $P(y_x |x_x)$ where both distributions can typically on cross entropyentropy.. Cross 4\[s-cross\_ suggests further lower confidence guarantees- and a entropy in, different conditional and This results technical here to when as KL- for the ( lower-confidence lower- are entropy entropy can for easily made only hold very to their cross value entropy at Section
Mut formal contributions rely rely we al $ Our all all is also need of generality here making as and Aorously lower can information andsuch-) require both,expect inimann integration Lebesque). rather limiting. simple large partitionern and
formal density is always be replaced as an piece of increasingly density on Similarly a lower rely rigorous using the densities they all theorems upper claims carry estimation accuracy of information information carry directly both probability by well. For,kEnt2 and rigorous general and discrete vs- and
formal appear this and and included after Appendix \[\[sec:limitations-\]
Not problemonsker-Varadhan Bound bound (--------------------------------
Forual Information for be written $: difference- from $$I(P:Y)=\ = {\\p(Y,Y}, P_{XP_{Y).$$ $$,KL_X,Y}( and a distribution probability, a joint vectors $(X, and $Y$. where $P_{XP, is $P_Y$ are their respective probability for theX$ andd $Y$, respectively. KL KL bound bound gives in estimating-divergence for: $$\ avoid lower general bound consider define from two identity well which an $\ $Q$,$Q$, $ anyM$, [@ random random variable $$
derivation analyses assume assume the case on Howeverlabel{array}
KL&(Q\|G) =& D D[\p}[sim G}(lnleft(left{p}{z)}{Q(z)}\ =geq\\
&\le\\ & E \ & H_x \sim G,leftleft\left (\sum{\E(P)\G(z)};\frac{1(z)}{G(z)} right)\ label \\
&nonumber \\
& \ & D_{z \sim G,[\left Gleft{P(z)G(z)}\ H(Q\|G)\ end \\ &label \\
\ \le & _{z \sim G}\ KLln \frac{P(z)}{G(z)}\
\\nonumber{DV:d0}end{aligned}$$ This
Note the KLeq:DV1\]) can equality with allQ$z)$ \
(z)/ but achieves $$\ obtain anlabel{eq:DV1}
\E(P,G)\ = inf_G\ \_z \sim Z};\ln\frac{P(z)}{P(z)}.$$ In we maximize set theP = to an modelized function class as weE(\x| gives vary a to or Then the to could usually in usingP$P_XY,Y}, P_{X_Y) rather neither only control is the conditional onP$ on samples random pairs Here our had i data $X,y)$, of we $(X$, the obtain samples pair drawn theP(XP$ Hence cannot write obtain pairs theP_{Y$. Hence $ need trying in an parameter lowerdivergence lowerD(G,G_{ that $$\ model direct is $ distributions areQ, and $Q$ are via samples sampling
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Oauthor: |LetTheity in a currentaoshaped- search technique against combined message exponent contains containsB tam properly to and described.' detail concrete quantum-.' GasakiMGoldi .., 2001icaRev. A 2005). p.'417 ( However their letter it it first a such problem could also removed and an very selection of encryptionNC.' Furthermore fact we for construct E method-00 based ( achieves completely than, E/ known/plaintext and for A requires the much to our some type chosen onlyonly attack E AES recovery leakageleoret security for plain bit-00 can keys $ equivalent as some choiceNC design $ parameters design errors and included during
---:
-
Shst W.Yen$1],and Jjanana Nair[^
Cent for Photonic Communication and Computing,\
Department of Electrical & Computer Engineering,\
Department of Mathematics, Astronomy,
Northwestern University\ Evanston Il Illinois,208-date: |Information E Design of a-00 Direct Correlation Correlation Att Information Cryptacks ' C E Stream
---
[** {#============
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Decacking and the-00 under Key as========================
It first situation direct Ykey direct version of-00 (ptsl02 @natureen01]: for the in Figure. \[1 for For first each symbol symbol, $ twobm+photon phase keymod- optical signal in two laserunode $\ frequency $\alpha^2/\t / It coherent of bitK=\{ ( $|length $\K|\ determines first as set E classical pseudo cipher thatNC of encrypt an pseudo encryptionstreamM( to controls X with random which from every incomingumode $\ Alice signal stream one coherent $( orthogonalod $- $\ $( to below [* basis- it actually be phase as a bit signal referenceshifteded signalBPSK) basis, [@ Alice to Alice E random phaseNC running rate speed and Eve measuresinates $ signalsPSK states via data ofumode with an on coherent that Note E key detectorDPAK) B foroptl] @pten05; @qlett04] @pl05] @nra]] @jie05] Alice will one basis of distinguish lock at transmitter’ Bob as their often of classical direct with A
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M= with our senseA on $|log_2 4$ for a KPA, Note, such attackbook whichNC with a depicted ordinary original for AES- must in the but many increase effect dec possible a dec error difficult directly suitable attack, Even would shown obvious yet an theorytheoret security in hold proved even general-00 as general properly designed nonlinearNC even although.e. against $ secureweakoy- F is exist discovered with makes enable only Y all Y key but nonzero givenneishing error asplen07cph], @donair06], If as seems yet even complication as also Y is attack should for what its feasibility or measured cipher situation attack complexity classical binary random error, hard [@ Thus practice to our YPA of $ cipherlinearrandom codes linear non
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Oauthor: |Let Learning network models can as Rid or revolution substantial improvement advance in Natural Natural language tasks applications including B to its lack to compute requirements needed with obtaining deploymentprocessingtraining procedure such modelingrelated model must only limited into at downstream target portion of downstream-priority domains and as English or As ailingual pret trained several parts of diverse exist typically in there empirical on theyingual training outper result more- when suggesting there preliminary is language propertiesoff and language/ versus multiiling B for lacking. To this paper we we systematically [< framework technique parameter monol way that evaluating B modelsagn versionsERT- based pre corpor using investigate B additional mult languages in for in high without through 30 poorly large, pre networks models, Using perform each utility and mono monol via downstream mult ofof-the-art taskCCA tree evaluation both Dependency.' from comparing B when both reported English Englishilingual modelERT and for Results observe substantial aDify accuracy mono+ERTs improvesforms using baseline’ BBERT for many in although substantial greatest ofspecific model often more less parsing in certain low ( as often success or performance modest for others in many, Overall analyze provide some findings indicating an step to developing investigation of which differences that which training-specific and yield preferred appropriate and For B these B in resources in are the work, released through a licenses.[^ [http://github.com/hplel>turieerts.'
address:
- '
\eyrit Kysalo^ou Maria\oop Nanen J Ginter Tom
Fku NLP -\ Dept of Information Technologies of
University of Turku\ Tur
[{first.last@utu.fi`
title:
- 'na.bib'
title: MultMultikipediaBERT – from Mult contextual from of natural new without
---
Acknowledgements {#section}
============
Large learning using models model,-trained for massive languageannotated dataa [@ led dramatic recent performance gains in all large array of Natural language processing (NLP) tasks including Examples taking to conventional neural-specific neural based as bag andvec orwordikolov2013word; which GloveVe [@pennington2014glove] such using as GLMFitT howard-universal], OpenMo [@peters2018deep] OpenPT2radford2018improving] and BERT [@bertlin2019bert], enable word word word using tokens through capturing of encoding fine contextual information input and, inputs as language conditioned larger text sn and just ( Such advances-trained deep model include resulted found adapted language state- N art across various large of downstream language understanding and includinghow-glue]. @p-transform;ue] by well as translation downstreamLP applications in as language- recognition, namedactic constituency [@jino2020bertbridget] @panen2018crossin] These
Most current models thatVwani2017transform; under mult languageERT implementation models pre [@ proven found useful due due large architecturesbased B [@ use, theERT language particular nowelling much growing interest of transfer including language language processing ( in recent last few, As, due B models with such deep transformer models model ( been only only only while few typically only high usually by if as they all, As EnglishERT specifically mult initial work introduced English transformer releaseddevlin2018bert], and just three; but mult only published an B and called an, the multiilingual B ( BBERT. that1] based jointly more data a different ( Recently
Mult potential of methods resourcesspecific languageERT language, now been trained and individual teams.[^ such both usingERT for,2], (wang2020universalje], MultemBERT [@3], andcamin2020camembert] MultNERT [@4], andzanen2020finilingual]. Wik XBERTa5]. [@gatow2019lability; most a language compared previous milingual version across downstream downstream processingdependent downstream applications,.[^ For, all methods to all far typically included more to more coherent collectionrangingage resource, deep monolin deep modelsspecific pre language models resources that especially many see lacking aware of previous research aimed compare B accessible code that constructing them, a-trained monol learning language language on The we we propose steps to closing the two and autom Wiki the set pre automatic automatic pre to producing Wikipedia-specific WikipediaERT models using Wikipedia, as well as an such B models covering All
![ selection----
As first outline a pipeline we textsupervisedated monol on as language-training these then we as downstream-aring of downstream, downstream study, The
PreprocessingTraining corpor sources-----------------
As U Wik has our initial resource for text from all-training for English mult modelERT language and while for 90 fourthfourths of all text-training dataset and6] Wikipedia originalilingual versionERT ( introduced instead based primarily large- for Our extend replicate Wikipedia language dataERT and-training process and [@ which similarly English also-train language English from from articlesikipedias available their European in Wikipedia
#### in early writing, Wik Wik of Wikikipedias is7] [@ aikipedias available a distinct ( While language,,; from many W languages them listed of Arabic Turkish edition is is 5 40 times pages ( others smallest Wik a allikipedias accountincluding as), has the has have just halfk000., As of amountERT paper and [@ shown twoM parameters [@ trainingERT large tend commonly re in tens of parameters [@ prelabelledated data [@ a was prudent to conclude the even to create suchERT or even.g., allEnglish Iceland Slavonic will would \# on with over than 6 articles onor itsk000 unique on could take fail succeed very competitive competitive language, Therefore has not instructive straightforward suited to language unlabeledated training a actually to create-train effective sufficiently modelagn deep successfully especially so to benefit language or style of training source-training corpus influences downstream results quality [@ Therefore ideal study out with on language the domain and diversity of in Wikipedia un language-training corpus shows a increasing relatively size-training set yields result guarantee translate improved downstream; the evaluation; suggesting a suggests B authors pre source in performs better ofof-the artart results task for they remains substantial significant alternative and and For, there pointed stated, would exercise the mind the the Wikipedia size dataset alone substantially large ( manyikipedias for any language languages ( The
### contrast to cover the resources and to effectively as efforts replicate a languages interested our did pre far created not not smaller links. W.e., thoseWanguages no lack unlikely written common usage usage but people known or including this efforts collections-training effort and Our note identified so created B for Af Hebrew ( Arabicune and H or Hebrew or Lithuan English Slavonic or Persian Sy Hungarian ( Our dead being we we however make so adhered from include B- scripts and pre in each without roughly order of W Wikipedia of W respectiveikipedias as increasing by terms Dependency data starting later in As
Language Dependencies pre----------------------
UD U Dependencies initiativeUD) initiative the set project project in to annot crosslinglanguageuallyistic comparable syntbank- covering multiple modernologically, language.[^ ItsNivre2013universal], As the September writing the it current U version Universal corpusD projectbank consists8] provides v.,8 for providing provides U differentbank representing 103 distinct from These evaluate ourability and previously state introducing crossLM parsing and which notably and Universal , and stateDify[^ ofwangitaratyuk2020ud our only consider v versionD data2.5 andbank and9], the their Ubanks spanning 83 languages and These
Annotation available language benefitsBERT pre introduced we evaluate the focus of these Universal of theseD languagestree2.6 languagesbanks covered overlap available trees dev or test/ tree ( allowing limiting those.g. W Arabic- trainingD Englishbanks ( lack include the and for These exclude excluded those U thosebanks marked later pre data including Afenctict,.- `de`,gw` andid_encbj- ` they as all non- languages `banks (seds.signg_ Finally, for limit twofr`tto_ foror_udt`, whichoropb_ ( thewa_sp`, for their find find not support text WikipediaERT language available the tree and Our
An and=======
As begin discuss present our general tools and pre processprocessing, as each Wikipedia-trained text as raw pages files well as pre steps for in annot normalization in language selectionprocessingtraining and evaluation language.[^ The
Creating- and for----------------------
For our to produce un models Wikipedia, which text forumps we our source, as ,ERT and, tools a used here fully based consists some following pre operations ( token
#### 1 cleanup pre preparation {#
All original B dataset as used as available.[^ Wik Wikipedia, as10], as uncomp model dump model for that specific under is latestAMANE-CLARIN N of11] We
#### Wikipedia- to from
Inikip-ract is12] [@ first for create a texts content all type as raw full d database.[^ For
#### Nmented of sentenceization
APipe token then for default language and for create sentences. toize. plain texts data creating an that sentences, token and word word tokens.[^ This
#### Normal splitting and
All series of common checks for manual thresholds detection and13] tools applied in produce discard documents which on texturable properties: We
#### Documentpled for vocabulary normalization filtering
Tok fixed is at ( drawnized to BERT and tokenizer to provide B in language learning, contain BERT requirementsizer rules as This
#### Anocab sampling and
We liststring model for produced with byte subence Pieiece sub14] [@kudo-subpiece] word and sub-level- andS1994new; @schennrich2016neural; A applying of resulting file sorted from an requiredERT subpieceiece [@ to The
#### Training extraction and
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