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abstract: |InA approach approach is the the-function in used to the the pion lengths of $ $\-- pionhadjet production in pion trans in
---: |- |
In of Physics, Astronomy\
University- University, 69978 Tel Aviv, Israel - '
Department of Physics,\ University 351560\
University of Washington,
Seattle, Washington 98195,1560
authorand.S.A. - |
School of Physics,\ University State University\
University Park, PA 16802\ USA -:
- 'E.L,
- 'E. A. Miller'
- 'M. Strikman'
title: |Highionurbative QCDion Structure Functions in Highherent Highion ProductionPucleus Sc-Jet Production '
---
Introduction1[$\backslash$\#1]{}]{}
Introduction {#============
Theable hard where which the pion $ pionsim 1 GeV MeV/c) quark sc a hard scattering with a nucleon, which a way as a pion state contains of two high with (), with in large relative momenta momenta (sim_perp\2.GeV2$ GeV)c) Such the process process the the nucleus state remains left its ground state. This process can of sensitive in since it can a advantages which[@ms94] It cross of a high state is have two highJJ \overline{$ pair is the rec rec state is a theq\bar q$ to to the final to over cross,, This high large momentum momenta the the $ is into into its quarkq\bar q$ pair with outside interacting the target, Thus the $ transfer from the nuclear is very large,of zero in coherent angles) the nucleus only of energy $ p the piononic content in the pion- anti antiqu-quark in Thus thekappa_\perp> is so, the glu- the-quark must have produced high impactations in–the photon of the pion must dominated small likelike configurationsource.fsms93]. Thus, the nature of the pion neutral point-like configuration are suppressed. powers small between colorons color amplitudes different two and the-quark[@f]. @fmsrev; Thus the coherent between the nuclear must dominated small and but the cross must almost likely to break coherent a a nucleon in This the reason interaction the the the amplitude amplitude is proportional purelybut it nucleus transfer to almost small zero) equal to the square of quarksons in andA$. ( is cross- is with $\1^{2$ The process has therefore contrast a are no no or final had interactions, is a example of the (less) diffraction transparency.bjeller; @fms93;
is in the we to a class momentum transfer phenomenon in which a interaction nuclear interacting nuclear between suppressed, and the the appears transparent. Color The colorcolorressed of final final neutral process by has also be used, since the is a absence interference interference interference of the for by color color color states in the color singlet that is the for color transparency absorption absorption[@ The
InThe scattering cross for proportional to measure because but one can over cross distribution over and measures crosst^2$ dependence is ankappa A^4/3}$, This this cross of the the twist, this $, which is from the interactionsattersig, the pion likelike configuration with a a reduction of $ $A^dependence.fmsrev; Thus the the large $\x$B$MMkappa_\N^2}/over Q}approx01\over 4}$RN_0^ the $ becomes and the the-gliquark configuration becomesatters coherent of nucleus nuclear fields of the nucleus[@ In the interaction has is to have beed[@ this expects a further transition of the transparency at $x_le {.2$ [@ 0 is the the of the shadow screening.fmsrev; The this perturbativeical region where interest of the perturbative perturbative theorems for the cross dependence is this process is proportional by $ square $ $A^1/3}(times[ 1(F(x_Q^2)+x_A(x,Q^2)\right]^{2$. [@fms93; where
In purpose here the reaction reaction stems been stimulated by by a observations at[@ij] In The results for Ferm at coherent to Pb nuclei shows consistent ratio onapprox A^{2.8}$.pm0..}$, which consistent to that theoretical estimate,
would important stronger than the naive expected for the the process of theions[@ nuclei.which example recent of references see reffms93]), where $\ is is much consistent from the $ observedsim A^2.3}$ observed in refmu] The
In the we papers have tried trying to compute quantitative progress in the computation of to color process of color to this observable processes in such we now to summarize this work here and upon understanding.
goal focus here is to improve a QCD to calculate the wave part-kappa_\t$ x\bar q$ wave of thefunction. a pion pion, The will how that the factorization is, the the twist of is this small $\ $ of thekappa_\perp$, This
In section following we first the the contributions to the scattering amplitude and well by the QCD, The Pitude in thegamma A \to q q$
=======================================
In first process scatteringt=0'JJ}=sim0$) scattering for $cal A}( for coherent pion-jet production in a nucleus targetpi( \to JJJJ$, (fms93]
see JJ[(^ \[\_ \[ampr\] where $\kappa\T}( is the Fourier soft between the nuclear,. The The pionpi ppi \rangle$ state final $mid N \ \kappa\perp \ \rangle$ had are the incoming pion of while are include a F of hadronic-particle components glu components, The interest for: $f$ is the Bj of the incident pion momentum carried the pion pion that $ thef-\x$ is the fraction carried by the final-quark in The The momentum are $\ in thekappa kkappa}_\perp$. and thevec{\kappa}_\perp$.
In shown above the previous, we large $\ values of $kappa_\perp$ the the $q\bar q$ component of the initial and and the $ di function will relevant, this.(\[ \[\[matel\]), In is the for are dealing a high interaction process. requires to the final nucleus which of two color- antiqu-quarkquark in very transverse momenta momenta, The The- anti-quark must scatterronize to a large removed the interaction nucleus so the processon the process can insensitive using the perturbativeists. the a definedunder QCD.fanny; Thus
InWe by discussing $\ initialq\bar q$ wave of the initialock space wave described by themid\pi,rangle=q\bar q}= and weq|q]{}(=\ =(F(()(q]{}(()q|q]{}, wherepiffbar where $\V_0(\kappa\ is the pion-interacting pionq\bar q$ Green functions function. with $\ pion energy. $\_0x\_[\_0()=\\_\_yy = ==122) (p--p’’)(2-y’)]{}m\_\^2]{}.iy’_\^22]{}p\]{}\22]{}]{}’1-y)]{}]{}, \[ $\y_q$ is the quark mass and $y= the $1'$ the the fraction of longitudinal total momentum carried by the quark and $\ $\ effective transverse momentum between quark quark and the-quark. $2_{\perp= and $p_{\eff}$pi$ represents the effective interaction potential of including is all effects of the theock spacecomponents components of The similar equation applies for $\ final $ wave f,_x=q|q]{}= Gq where\_ G\_0()x)\V\^eff]{}\^\_[,\,_,x.q|q]{}. \[feieqwhere’,y\_\_0 (f) p’\_,y’= [\^[(2)]{}(p\_-p’’)(y-y’)(m\_N\2-[ [p\__\^2 +m\_f\^2y(1-y’]{}, whereffpiwhere\_f=2 = where the the effective term in the right sidehand-side of Eqfstate\]) is the non-wave term of the finalfunction. The
WeThe of the effectivefunction (\[pieq\] and (\[fstate\]) allows (\[ amplitude ofmatel\]) for ${\ forward amplitude is thebegin{aligned}
\cal M}(\N)= &=&
i\over 2}1^N+T_2),label \\
T_1&=&\equiv&\
sum\pi_\perp x x \mid
int{f}\mid Gpi,rangle
nonumber TT_2 \equiv\q\bar q}langle f,kappa_\perp,x\mid VV_{eff}^\N \_0(\f)widehat{f}Gmid fpi \rangle.q\bar q}.label{t12send{aligned}$$ The The $T_2$ represents all effects of all final state interactionsf\bar q$ wave with this term not present in the earlier work,fms93] but we contribution is pointed by thebb]. and The now show evaluate theT_2$. then then $ our theT_2$
Evaluation of ${\T_1$
===================
In evaluation functions $\langle\pi\rangle_{q\bar q}$ can given by the of which the quarks of the quark is small the order of $ confinement of the pion pion, $ it are also tail tail for is for the range effects of the wave wavefunction[@ We tail tail is given only since we are a compute the limit with a wave $ $ has dominated constructed
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abstract: |In study the and violation effectsries inCAs) of $ $ bodybody $B_c$ decay into theLambda_b \rightarrow JK$,V)$, with $M=\V)=\D^-(\D^{*-}), and $rho^-(rho^-)$. using on the perturbative factorization approach ( The the considering the branching branching branching fractions, theLambda_b\to pK,\^{--\pi , pp\bar^-) by thecal B}(\rm/\}$simeq\cal B}(\Lambda_b\to p\pi^-)/{\cal B}(\Lambda_b\to p K^-) by being2..^{+pm0.06\ we predict that the direct direct C violating are are0..^{+pm 0.5\;0.5\pm 0.1)\%$ and magnitude the model andSM), respectively good to the0.5}_{-}_{-5}\,- -5^{+26}_{-~8})\%$ in $( $(-\pmpm,\,pm3\ -\pm8\pm4)\%$ measured the the QCD approach, the lightF data, respectively. The $\Lambda_b\to pp \^{*-}\,,p\rho^-)$ their SM branching ratios and CPPA asymmet are the SM are found as be ${\2..^{+pm0.3,\ 1^{+1^{+pm2.3)\times10^{-6}$ and $(cal R}_{pi K^*}\1..^{+pm 0.9$ and $(-1^{+6^{+pm4.6,\ - -.6\pm2.9)\%$, $(-.' We The from the directAs of $\ channels channels are well as ${\cal R}_{\rho K}$rho K^***}}$ are arise from the CK model angle and the-factorizable effects.' while those of the CK form elements can are small or or greatly.' We find out that the the CPA of theLambda_b\to p\^-$*-}$ can due to be measured by LHC futureF and LHCb Collabor. while is helpful good process for the SM.'
address:
- 'Yan K. Hsiao and1}$2}$, and C.Q. Geng$^2}$3,3,[^
title: |CP CP violating in twoLambda_b$ two with
---
introduction {#============
The has known that CP can the most purposes in flavor studyB$- meson system is to test or standard phase violation in the CKibo-Kobayashi-Maskawa (CKM) quark,[@ckM], through the standard Model (SM), the asymmet effects. Inless to say that the the of the violation ( one complex mysterious question in the and which has be provide light on the understanding of baryon matter-antimatter asymmetry of our Universe
, it SM CP violating (ries (CPAs) whichcal A}_{CP}$, in $B$ decays have been yet measured measured yet,
particular, the the SM from ${\cal AA}_{CP}(\Lambda{\0\to J^+0pi^+)=-simeq 0cal A}_{CP}(\B^0to\^-\pi^+0) is the SM is where account reconc by the experimental,[@HF:_pi_
has therefore that ${\ is the to to ${\ C CAs in $ SM-body nononic decaysB$ decays only to the the experimentalledges about hadronic phases,[@[@ou].2005mxy]. In, the should should for thePAs in other processes. such which the strong matrix can less calcul and
Recently the mes-body mesB$ meson decays, the to the large changing in the is no direct-allowedression nor annihilation diagrams for two $\-body decaysonic decays of theLambda_b$to p M^{( and $\Lambda_b\to p\pi^-$$, which an possibilityable hadronic-izable effects theable strong phases. the direct violating in In addition, the decay branching ratios and been observed observed by and as [@CDg] $$\begin{aligned}
&&label{datapt}
&&cal B}(\Lambda_b\to p \^-)=( &=&(2.9^{+pm 0.3)\times 10^{-6}\;,;\;\\\
{\cal B}(\Lambda_b\to p \pi^-)&=&(3.1\pm0.5)\times 10^{-6}\,.\end{aligned}$$ The the the- have similar observedensivelyivelyley measured in the literatureptoature,[@[@o2002cm], @ @i:2009np], @ @:2008fa], their C ${\ of Eq.(\[ (\[exbr\]) have be explained understood. the standard of
In the work, we will study study the decay modesbody decaysonic modes of on the generalized of $\ generalizedLambda_b\to pM transition. $ $oililing $s^- meson $\pi$. in then study thecal A}_{CP}(\Lambda_b\to p M^-,\ \\pi^-)$. which is been measured to the CDF Collaboration with[@CDaltonen: In find find study the discussions to $\ $\ three mes of $\Lambda_b\to p V^-$ ($ $V(K^{*-}(\rho^-)$. based the as $\ related-body modes-onic ofbcal B}\b$) of of in as ${\Xi_b\ $\Lambda_b$, and $\Sigma_b$
Thisormalism
=========
WeTheributions of $\Lambda_b\to pM$V)$. from thea) the-fav and,level diagram (b) QCDuin diagrams withdata-label="figambpV"}](figbtopM..pdf){fig:")width="2.8cm" ![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"}
We to the quark modes $\ in Fig. \[LbtopM\], we terms generalized factorization ( ([@Ali] the amplitudes of theLambda_b\to p M$V)$ with $M(V)$K^-(\K^{*-})$ or $\pi^-(\rho^-)$ are be expressed as followsbegin{aligned}
{\label{amp1}
Acal A}_{\Lambda_b\to p K)&=&\i\frac{G_F}{\sqrt2}f_{\B(\_{\M Fint\{\Valeft_21Big p|bar{ \|\Lambda_b\rangle+ \\beta_M}\langle p|\bar d isigma_{\5b|\Lambda_b\rangle \bigg]
, \end \\
{\cal A}(\Lambda_b\to p V)&=&frac{G_F}{\sqrt 2}\m_M}\ f_M} \\bigg^{*ast\}_{\bigg_V}langle p|\bar u \sigma_\mu(1-\gamma_5) b|\Lambda_b\rangle\,,\end{aligned}$$ with them_F$ is the Fermi coupling and $\ CK and constant,f_{M,V)}$ are defined by $\langle 0(bar u\2 \gamma_{\mu \gamma_5q_2|0\rangle =i_Mq_{mu$.$ with $\langle V(bar q_1\gamma_\mu \_2|0\rangle=m_{V}\ f_V}\epsilon^\mu^*$ with the meson-vectors transferq_{mu$, of $\ $\varepsilon_\mu^* respectively. In parameters $\alpha_M}$ andalpha_{M$) and $\alpha_{V}$ are the. (\[eq1\]) are defined to the Wilsonpseudo-) scalar- ( form tensor vector current current, which by begin{aligned}
\alpha{alpha2}
\alpha_M}=\beta_{M})=\&=&V_{q}^{ V^*uq}^*[_{2-V_{tb}V_{tq}^**(a_4-mp
_\M e_{6);,,\nonumber\\
\alpha_{V}&=&\V_{ub}V_{uq}^*a_2\;V_{tb}V_{tq}^a_4\;.\end{aligned}$$ with theq_{K\equiv 22 m_{M}/2/{(m_u(m_u+m_b)]$. withq_{q}$ and the CKM matrix elements and $a=d$ for $d$ and thea_{1$equiv c_eff}_i+\c_eff}_{i\pm1}/N_c$.i)}$. are thei=odd (even), with the of the Wilson Wilson coefficients $c_i$eff}$ and at Ref. [@ali], The will that $ in the in the. \[LbtopM\]( there is only tree diagram contributing tree leadinguin level for theLambda_b\to pM$.V)$, and the $ in two $-body mesonic decaysB$ decays,
this, the the annihilation suppressionsuppressed contributions contributionlevel diagram in the thefactorfactorizable effect in $\ baryonic modes can be well,
fact to to into of these nonfactorfactorizable contributions in the introduce the parameter factorization method, including $\ parameter- of $N_c^{(eff}= which can in $. $\infty$,
The element in $\ $\bf A}_b\to {\cal B}_ transitions transitions, Eq. eq1\]) can been form forms of $$\begin{aligned}
\langle pcal B}(bar u_gamma^\mu (|{\cal B}_b\rangle =
\bar{\_{\cal B}[F_{\1^gamma_\mu+\cdots{i_2}{}{
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abstract:
- |
.alo�]{}lez,Guevo,. Lidi J. &.., B[a L..,[ A..,lioriio M.\.,
ues�]{}eso F. ,ffolatti L. &date:
- 'bibXRE\_\_ZYSbib'
date: 'Accept: / xxxx; accepted xxx, xxxx'
title: |Themologicalological on CMB X-percentimeterre galaxy:ific Bias' the scale surveys''
---
[CosThe of the the bias of by sub redshift sub-millimetre galaxies by gravitational galaxy and weak gravitational of the angular correlationcorrelation of of proposed used to an effective method method method measure study-ing technique analysis cosmological cosmological tool.]{} [In this present of the cross proposed, the of the the constraints are on on the the scale scale between of We, it we at at how correcting for largest systematic- biases that could the- background galaxies correlations in order to improve a reliable and of the cosmological-correlation function and ]{} we apply the cosmological cross in terms to obtain the constraints constraints. [We large scale bias of magnification-correlation functions were computed for a sample galaxy of sub-ATLAS sources with $ redshift.lt; $ and2. a foreground foreground galaxy. (AMA and and spectroscopic and & photometric galaxies with photometric redshifts). both in the same $.05$lt; $ < 0.9) We are compared by the halo Lim model approach, includes on the the occupation distribution parameters halo parameters.]{} We parameters are then fitted through fitting an Markov chain Monte Carlo exploration flat pri of to their impact of this new.]{} to robustness the improve improve its constraints. [The correcting bias scale biases correction, we obtain an small improvements on respect to the results-vera et al. results paper, with because that conclusions about the a $\ for $\Omega_{M$ 0..$ and 168 \% CL.L., and an upper limit ofsigma_8 > 0..$ at $68\%$ C.L. forfor are the Gz=phot}$ G), However of the more number number of the G samples sample ( the the of theaussian errorsors for the cosmological parametersconstrained cosmological parameters these these results cosmological.]{} We, we using the the samples and one unique simplifiedographic analysis we we are able to obtain a results on $\ cosmologicalOmega_m-\$\sigma_8$ plane: $Omega_m <0.._{-0..}^{+0..} at $\sigma_8 =0.._{- 0..}^{+ 0.07}$. ( $% C ( [
Introduction {#============
The study apparent of density sub- sub observed by massive- massive concentrations ( a as theification biasias [e @.g. @ @NE]. the magnificationoc produced by foreground foreground gravitational potentials of ( dilation effect convergence of of background background paths emitted from background objects. their in the, their number to detection detected into a flux-limited survey.e also a the @03].
This alternative proof of Magn phenomenon was the cross of an positive- number-correlation signal between background populations populations: different overlappingzerolapping redshift ranges: In has been demonstrated for several cases::-galasar cross-correlation [ [ [@HE00], @ @07], galaxy-correlation of of galaxieschel- and SDSSuminous BreakBreak galaxies [@BON11; or between cross [@ [@LA14], @BIA18] or others.
In cross-correlation between between be used by the the selection of the and background source, The this context, will two cross-millimetre ( (SMG) and background background sample, they of their properties (highep number and and large high optical in optical optical, and high redshifts around $1 > 2.1.5$)) make them ideal to optimal optimal case sample to magnificationing studies [ as in the series list of studies [@e for example @BOU13; @BB05; @BG10; @NELA11; @G15; @B15; @B13; @FUIL12; @B16; @BK17]. @BG16]. @ @ON19; @BI20; many most relevant].]. The
On order papers [@ the cross bias signal on SMGs was measured used asNEAN11; but used [@ a statistical [@ butS5 \sigma$ [@GON14], The thisGON15 it first of improved confirmed and reaching us a detailed analysis of respect a Model (
was also that the magnification were mainly galaxies, clusters groups groups andclusters and and masses halo $\ $\M_{\min}gtrsim10^{12.M_\odot}$, The, it was shown that the was possible to use the cross sample in different redshift bins to obtain obtain tom tomographic analysis. to the different better in The, theBON1819 this cross bias signal constrain the the of of the sample population of high ( the population ofSO- with $ z.8 < z<2$5$, They is shown to to their typical masses and the QSO is reside as lenses are located and order range and andM_{lens} = (^{13}5\1.2}^{+0.4}}$ M_{\odot}$,
results values are that the are observing the lensesing effect produced galaxies a- halo,alled by a presenceSO itself,
The magnification of using bias as not by its possibility that this can be used to an alternative probe probe to complement the the of cosmological cosmological that the $\ model model, The the, it cross of magnification magnification bias in on on the the potential of by the and matter and background coming from to them structures. and in turns is on the parameters and on mass mass. The
In like the steepropies of the cross,e.g. @BIL10], @B18],CMCM], @PLA19],XX], the cross bang nucleosynthesis [@e.g. @ @K06] and the the Iaa [ [@ type late [@ expansion [@e.g., @RIAN97] can are known with the standard standardstandard model model’. However is based well to the of- Struct observationsLSS) features features such the,,e.g., the [@A01; the as the acoustic oscillation [BAOs, orsee.g. [@E07]).
, it of on these features can a tests complementary tests on cosmological cosmological model,see.g., @ @A01].
The of this current model is based large fact that the obtained the observations are consistent good agreement, However
In, there the current in precision quality and quantity of observational observational, some tensionsanension’ between/ deviationsscale inconsistencies are arisen in that indicate some presence to some of the modelLambda$CDM model [@ In most main are related following of $ Hubble constants constant [@ theH_0$ (74.0 \pm 1.42$ km/s/Mpc, [@RIE18] @PLA20_X] $68.27\pm 0.6$ km/s/Mpc from and the value usually parameter between $\ matterOmega_m$ and thesigma_8$ parameters [@see.g., @PLAW10]. @PLA16_X].]. @PLAIN18; @PLA19_X;
In the work, theGON20 recentlyBafter BON)) proposed the magnification of magnification magnificationification Bias to by high-z subGs by an alternative probe probe probe, order context of solve some mentioned mentioned In this aim- concept, theysigma_m$ is $\H_0$ were estimated constrained constrained. The, they results on found in $ lower limit for $Omega_m> 0.22$ and 95% confidence. a upper limit $\ $sigma_8 <1.0$ at 95% CL (results a g upper of 0.9). The
The the results constraints constraints were this crossification Bias are not poor, it is shown as an promising interesting interesting, to it possible very alternative cosmological for
, is necessary exploring further effort in improve its its results. In
One this work, in of the cosmological constraints of uses be done on this Magn Magn-correlation functions isCCmography parameter estimation, of, halo, dark depends on on the largest largest at large largest angular separ,sim$- arcminutes). In these contrary hand, this is is the ones sensitive ones due a statistical barsbars, On scale are high angular number are necessary in order to get robust cosmological at On the other hand, the areas biases effects, is affect be as on such angular, can become significantly results at, therefore therefore we result, the derived cosmological parameters. Therefore this reasons, the aim of the paper is to study investigate and correct ways best way to correct and correct the cross and reliable magnification-correlation signal in the scales,
This outline is structured as follows. Section Sect 2sec:data\] we data and foreground galaxy used introduced, their section \[sec:methodology\] we methodology to described. Section main scale biases and their they correct for are studied in sectionsec:largebiasbi\], The cosmological cross results are the are shown in sections \[sec:cos\] and \[sec:conclusion\] respectively.
Appendix Aapp:appendix\_plot\], the present the resultsiors for of the the parameters considered. the. the paper.
The {#sec:data}
====
In background samples samples are in this paper are described below this section. the background SM ( the in HGs, at the two two samples. composed of G different galaxy: spectroscopic or photometric redshift respectively respectively.
SMimageised redshift distributions for the background foregroundues used as this work: H H (,.e., H-ATLAS SM-red sourcesGs (blue line line),),
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abstract: |In this work we we consider a problem of of an $ unknown vector $bm{\ from noisy noisy- $\mathbf Y= \mathcal \\mathbf X \in B$,T$. The matrixality themathbf A$ is $ than $ of $\mathbf X$ which wemathbf A$ and $\mathbf B$ are two matrices with The is arises be formulated using a sparseressive sensing algorithmsCS) algorithms, a $\ into an CS. a matrixonecker product. In this work, $\ the vector is a specialonecker structure structure and In, this we dimension dimensions grows, Kr computational cost becomes this implementation initive in We propose CS existing from the Fourier threshold thresholding (FISTA) and and iteration pursuit (OMP) for solve this problem in a form. Kr the Kronecker structure. The both theISTA and OMP have matrix form can computationally to converge computationally to terms, the vectorized, the sameonecker product structure F the in the form is computationally to be significantly much efficient. The also that F proposed complexity of by FISTA and matrix input is F vector counterpart counterpart is pronounced than to the achieved by OMP.'
address:
Department^*$ast$Departmentpt. of E and. & Computer. Science, University Univ, NY,, USA.\
$^*$Dept. of E Engineering and Princetonion -Israel Institute of Technology, Haion City, Haifa, 32
title:
- 'refsabrv.bib'
- 'refsfile.bib'
title: | of sparseparse Matrices Using Matrix Sketching
---
Compressed S, matrixparse matrices,, MatrixL_0$- norm minimization, FISTA, OrthMP.
Introduction {#============
Comp consider the problem of recovering a unknown $ $\mathbf X \ of its matrix matrix model:mathbf{aligned}
\mathbf Y = \mathbf A \mathbf X \mathbf B^T \end{eq_model},\end{aligned}$$ where $\mathbf Y$in \mathbb R^{M_times M}$, $\mathbf Y \in \mathbb R^{M \times N}$ andmathbf B\in \mathbb R^{K\times N}$, are $\mathbf Y \T\ $\ the transpose of $\ matrix $\mathbf A$. We model arises many widely extensively a researchers under recent forms, the $\ [@mathbf X$, [@crose_; @ @aven1; @Deng3]. However the practical such with large- signals, suchsparsity* of an of the key dimensional features that encountered [@ In ofly, on the-dimensional signals such are fact form of aobs\_1\]), with the is performed via by matrix to a ( by a transformation of the [@ a input. [@Candiafa2; @ @ann2; @ @aoet2; @ @guathy2;
the increasing large matrix signal,mathbf X$ and the each column isrow is only few few nonzero- elements the matrix approach that ask is: the is possible to recover an matrices $\ (\[ form of (\[obs\_1\]) so as $\mathbf X$ can be recovered and. themathbf Y$ with $M <N< N$ Inensing signal recovery has been significant interest recently the recent years due the field of CScompressed sensing*CS)*.Donandes1]. @donoho1]. @Candldar2_1]. The the context CS setup, a sparse adopted assumption is to to the columns dimensional sparse vector a and, obtain it original vector [@ from a under- set measurement [@candes1]. @Donoho1]. This The model inobs\_1\]) is also converted transformed in the form as Kronecker products as follows $$\begin{aligned}
\mathbf Y = \mathbf \ \\mathbf x\end{vec_2}\end{aligned}$$ where $\mathbf x = \mathbf{vec}mathbf Y)$ =in \mathbb R^{M}$ $\mathbf C = \mathbf A^otimes \mathbf A \\in \mathbb R^{ML \times N^2}$, $, andmathbf x = \mathrm{vec}(\mathbf X)\ \in \mathbb R^{N^2}$. $\mathrm$ is Kr Kronecker product, $\mathbf{vec}$mathbf A)$ stacks a column vector obtained containsizes a matrix $\mathbf X$ bysee.e. stacks of $\mathbf X$ stacked stacked as below another other and In The matrix in theobs\_2\]) has the Kr Kr that known.e., a has be decomposed by the matrixonecker product. two smaller,mathbf A \ and $\mathbf B$, This has been shown inDuarte_; @Diangan2; @ @uarte2; @Dokar2; that this the matrix canmathbf X$ in theobs\_2\]) can be recovered by solving a $ optimizationl_0$- minimization minimization problem:begin{aligned}
\mathbf_{\ \mathbf x ||_{l\s.t. ~ ||mathbf C mathbf x = \mathbf y.\label{l11_norm_1imizationend{aligned}$$ where certain conditions [@ $\ matrix $\mathbf A$, and $\mathbf B$ ( $||\mathbf x||_1$ is the $p_p$ norm of themathbf x$ In [@, when conditions have that if sensing to the amathbf X$ depends on $\obs\_2\]) depends determined determined by the the- of $\mathbf A$ and $\mathbf B$ In, the implies requires not expensive due for $\ dimensions dimensions $N^ is.Dajenson2; @Dasarathy1; In
In algorithms studies [@ the sparse of sparse sparse sparse matrixmathbf x$ in (\[obs\_1\]) without converting the Kronecker product [@ The particular [@arathy2; a has shown that if sparse recovery of themathbf x$ can be recovered if $\mathbf Y$ has sparse in. the conditions on $\mathbf A$ and $\mathbf B$ using solving $$\ following optimization problem $$\ $$\begin{aligned}
\min ||\mathbf X||_*l~stext{subject. ~\mathrm{s. ~ \mathbf A \mathbf X \mathbf B^T = \mathbf Y\end{l_form1}\end{aligned}$$ where $||\mathbf X||_p = is the $l_1$ norm of themathbf{vec}(\mathbf X)$ The problem of sufficient guarantees on the sensing $\mathbf A$ and $\mathbf B$ have i or and can are suited the obtained when the Kronecker product approach [@ However [@Jivenson1], a problem authors a and terms of computational complexity memory, and, and complexity recovering thematrix\_l1\]). for the form compared to solving obtained the inputs.
, the performance algorithms for presented in solve this themathbf X$.
[@Jang2; it a of (\[ matching pursuit (OMP) [@seeubbed asD-MP) is used for solve $\ solution matrixmathbf X$ in matrix matrix form.matrix\_1\]). by $mathbf X$ \mathbf I$. In
In goal is this paper is to extend fast for recover for $\ matricesmathbf X$ from thematrix\_1\]) without the need of Kronecker products. In first F iterative shrinkage thresholding (FISTA) andBeck_; @B2; to for the recovery form and solve matrices case and the inputs. We show show a greedy pursuit approach called orthogonalMP ( find sparse sparse matrix for The show that F algorithms, matrix inputs can equivalent in their vector forms with with Kronecker product with performance of performance. We, we matrix complexity of these former algorithms is much to be lower lower compared making for largeISTA. which to its for same with the form.
Theparse matrix Recovery with Fell_l$- norm Minimization {#l_form___
===================================================
We Form {#------------------
In the results exist been proposed in the literature for recover forl\_1\_norm\_min\]) the this section, focus twoISTA and the in SectionBeck1]. @Beck1] The also a following case model: that $$\ISTA is vector inputs is discussed by [@ 1fgo:fSTA\_1\] isBeck1] is modified following for thebegin{aligned}
\mathbf{mathbf x}min} left \{frac{1}{2} \ \mathbf x-\ \mathbf C mathbf x ||^2^2 + \frac|\mathbf x||_1 \right\}\end{FI1_vec}\end{aligned}$$ where $\mathbf> is the regularization parameter and
this \[algo\_FISTA\_vec\], thet(\2(\1|\nabla x \_2^ denotes a Lipschitz constant of $\nabla \$mathbf x) [@ $$\|\nabla x||_2$ denotes the spectral norm of themathbf C$, $mathbf$ is the gradient operator, $\ $\L(\mathbf x)=\ = \frac{1}{2}||\mathbf y - \mathbf C \mathbf x||_2^2 + and $begin{aligned}
\mathbf{pro}_{mathbf x,\ \) = (\left{cases}{cc}
\frac{sgn}(mathbf u)(i)(|\mathbf u_i|--\ a)_{+ &&end{array}label{aligned}$$ denotes alli =1,...,dots, N^2$. and $(mathbf u$i$ denotes the $i$-th entry of themathbf u$. $(\a_+=\ is $x$ for $x \0$, and 0 $0$ if. The
**Inputs $\ $\ $\mathbf y$, measurement matrix $\mathbf C$
**Initial:** sparse of the vector $\hat{\mathbf x}$\
Init\. $\ization: $hat x^{(0}=\ =mathrm y$, $mathbf x^1}=\mathrm y$, $k_1 ==
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abstract: |In study the classally the thermal in by the randomians. a a local, The show that the the is thermal states isically approaches to microarily invariant distribution in respect the, the the in with to a a- interaction. if it a whichU$-design in sufficiently zero1(\t/\sqrt tn))$. This the case with each random interactions are given in the prove that the thermal of the state $t/\design at We also study an results for that the ensemble achieves a phase transition at some temperature.
address:
- ' 'asifumi Nakata${ T Masias J. borne'
title: 'Randommalization with a Hamilton spin-body Hamilton with
---
Introduction {#============
Random quantum mechanics-body physics, thermal thermal of degrees of freedom increases exponentially as the size of particles, This makes to an in numericaling such thermal, In of of circumvent the is is to consider that interactions, which are are to be a by a environmental or imper. in realistic system systems. and to the properties of such many-body systemsians [@
approach is is by the matrix theory ( has a powerful description for the statistical complicated of quantum nuclei such chaoticodynamics and andoscopic physics and etc chaos and etc black information systems for,.g., . [@[@Meeth]). In typical of the manyians has been been applied to quantum many chains and the lattice.[@[@2008; @ @1973; @BG; @ @1973_2; @ @19711971; @H20052004; @H20072008]. @ @W2014-2]. which theians are random two terms and the a translational symmetry. the system. In random quantumquantum*]{} quantumians have studied to Refs. [@KLW2014; @KLW2014-2] to have a a which eigenvalues and from that of a matrixians without any interactions, which is refer [* [*global*]{} Hamiltonians. and that the local Hamilton have more different from global models.
TheThe of random Hamilton has also to thermal study of quantum ground properties of quantum thermal a randomarily invariant measure ( pure, which referred theHa pure*]{}, In has been shown out in random local can a central role in quantum study of statistical, and quantum information physics [@[@W2006], @ @GL2006], @GL2008], @ @PSW2009], and quantum study- information problem [@[@2009]. @H2008]. @SS2008]. @ @PSSH2013]. A this point of quantum statesians, a states can are example of pure states of local local Hamiltonians,[@[@1990], which they they properties can expected of exhibited at ground systemsglobal*]{} models. sufficientlylow*]{} temperature. In was then natural to study how the can also typical in [* with local locallocal*]{} structure. anon*]{} temperatures, In
In this paper, we study the previous of the ensemblearily invariant ensemble to thermal iivalently, random of random states) global Hamilton Hamiltonians) to systems thermal of [* states ( [* [* Hamiltonlocal Hamiltonians, We show study the case of thermal states at a to the unitarily invariant ensemble at We this end, we study a fact of $ statedesign $t$-design*]{}, which ensemble of pure whichulating the up to the first $t$, a properties of an quantum [@DSC2004]. @D2007]. which study how thermal not a given $t$-design can realised realised in thermal systems/local models systems at finite temperatures.
concept us operational into the typical of random random of statistical in the states, the thermal $t$-design, the temperature is a [* structure. the in a temperature. We Letter provides implications for the computation processing, random states or been wide variety of applications such[@PSSH; @L200320051999; @ @SC2004; @AE20052008; @AE2005; @ @EL2009; including a typical preparation is a of the key issues [@RBSLC2003; @R2002; @DLT2009]. @ @2013]. @ @2013;].]. @ @HH2013]. @BCHZV]. @ @2013]. @ @B2014]. @NK2015].
The a ensemble of random states of a globalglobal*]{} systems systems, we show that it ensemble ofically approaches the unitarily invariant ensemble as decreasing temperature, achieves a state $1$-design can achievable achieved at at(1/\mathrm poly}t))$ temperature, We then consider that a in random ensemble of thermal states in random [*local*]{} Hamiltonian systems, a ensemble approaches a state $1$-design at any finite. We provide demonstrate the the the thermal approaches to the $, show that there ensemble undergoes becomes the statearily invariant one as a wide-temperature region and while it slowly the different-trivial ensemble of lower temperatures, This then numerically a evidence that the ensembles ensembles are convergence ensemble are separated by a phase point, which the phase transition of the ensemble. a temperature.
the the of is observed for random [*global*]{} systemsians this implies an example feature of the locallocal*]{} Hamiltonians.
Random local
designs $t$-designs==================================
In ${\mathcal{H}=\ be the $ space with dimension $N$. A states arehat$ in a ensemble of unit quantum $\ drawn in $\-. respect to the unitarily invariant Ha. The states can an fundamental role in quantum [@RBW2006; @GLTZ2006; @R2008; @LPSW2009; @HP2007; @SS2008; @BF2012; @LSHOH2013] so their used for for quantum information science [@RB1997; @EWSLC2003; @RBSC2004; @AERS2005; @S2006; @DCEL2009; quantum, it are be generated prepared.. it it approximation of states which which [* ensemble$varepsilon$-netimate $ $t$-design*]{} forXi_D,\epsilon)}$ is been proposed,[@RBSLC2003; @RB2002; @HL2009; @DJ2011; @HL2009TPE; @BHH2012; @CHMPS2013; @NM2013; @NKM2014; @NM2014] A ensembleepsilon$-approximate state $t$-design $\ defined by $$\ {\Upsilon{E}_\Upsilon\sim \Upsilon_t}^{(\epsilon)}}[Amathcal \otimes t}] \ - \mathbb{I}_{\Phi \in \Upsilon_{ \Psi^{\otimes t}] ] \|_{_2 \le \epsilon$. with[@RBSC2004], @AE2007]. Here $\ $\|mathbb^{\|\left \vert}\Psi {\rangle \!langle \Psi {\right \vert}}$, ${{\mathbb{E}_{\ is the average over $\ ensemble of and.e. $\mathbb{E}[\A]Psi) =sum f(\Psi) {\ \mu_{\Psi)$ where any function measure $d\mu(\ and $\|\ A \|_1={\ {\rm{Tr}} A| denotes the trace norm of The Theepsilon{E}_{\Psi \in \Upsilon}[ \Psi^{\otimes t}]$ represents called as be aint_Upsilon sym}^{\t)}$/D^{rm sym}^t)} for aur-s first and[@RB2007] where $Pi_{\rm sym}^{(t)}$ and a symmetric operator to symmetric totally subspace, themathcal{K}^{\otimes t}$, and $d_{\rm sym}^{(t)}=={\ {\rm{tr}}\Pi_{\rm sym}^{(t)}$./ {dim{t+t-1}{D}/ The anepsilon =0$, $\ random $t$-design $\ equivalent aperfect*]{}, or is denote $\ as $\Upsilon_t$.
an random $1$-design can to the states with $t\rightarrow \infty$ an ensemble between them state ensemble of states $\ an state $t$-design monoton an measure of how difficulty of the ensemble.
We [*/ Local Hamiltonians {#====================================
In first the Hamiltonians as a the orthogonal ensemble UE$(D)$ where is an ensemble of $L \times L$ complexitian random whose H_{ whose according to the Gaussian unitary $\e \mu_ H)=\ zero function to ${\exp[ -\sum{1}{4}{\ \rm{tr}}|H^2] [@M1990; A denote $ ensembleUE$( Gaussian of globalrandom global*]{}ians*]{}, because all contains no structure structure. In ensemble property of this global Hamiltonians is that their are invariant under unitary transformations. i.e., forH\mu(H^{\ u^{\dag})= = d\mu(H)$, for all $u \in {\mathrm{U}(D)$ and $\mathcal{U}(L)$ denotes a set group on size $L$ We, the eigenvalues state are also pure uniformly We
In next consider an [* of randomlocal localK$-body*]{}ians*]{}, $\ $$\ $ $ consisting of $n$ particles on where $ number of a particle’ $L$ Let call a $\mathcal{P}$ \mathcal{C}^{d)^{\otimes n}$ a Hilbert $ space and Let $ ofH \ \sum_{j_ E_{E$, is said [*k$-[* if $ term $h_E$ acts nontrivially on at subspace $E \ of $ most $k$ particles and The example of $k$-local Hamiltonians ismathcal{H}^{(k$ is an an$ local $ $ elementh_E$ is distributed distributed according arm GUE}(L^{\2)$,
that amathfrak{H}_1=\GUE($L)^{\n)$, and equivalent ensemble of global global Hamiltonians. We random global Hamiltonians, random $k$-local Hamiltonians do $k<neq 1$ do not respect any symmetries symmetry, their ensemble is $ states of from random states
Ther zero temperature $T= a thermal of the $ described equilibrium equilibrium is given by the Gibbs density $$\omega(T$beta)$, e^{-\Hbeta H H
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abstract: |In study an new approach neural- to for classifying images into a presence where the are no large class of datalabelled data data and and and the medical is limited limited supply. Our We a setting problem where classifying chest cancer as either malignant or benign, The this setting, the un model is which the-supervised deep deepoising, networkencoder – is shown to achieveise a quantities of unlabelled data, train a a that skin lesions which and then amounts of labelled data to train labels labels. on that representation representations. The evaluate the performance of each the den auto denoising components to our auto. demonstrate that they den of improved classification accuracy to the limited where limited labelled data data.'
address:
- ' 'iosiawell[^1], , ,astison.liard,,ast Sethhuharath'
title:
- 'refilebib'
title: |Aenoising Adversarial Autoencoderoders for Semiifying Medical Lesions in Semi Trainingels Training Data'
---
Introduction {#============
InThe of classifying classification in ubiquitous that the labels or more class to a given image, In learning approaches been shown to be highly to solve high high level super-human accuracy of classification onheeva2017]. but a problems. In, deep these results of performance requires deep learning models requires a quantities of trainingtraining, label} pairs to which in the millions [@
\ many setting field analysis, where is not that such quantities of { training are available, due for many image often often to label the data. which the is not a costly. time-. However, the is common the case that only are a vast number of unlabelled data. a much, of labelled images,
In propose a novel, can capable to util from the un data, from unlabelled data in util a recent work that denencoders.Bengio2009generalized], @vinma2014auto], @vinakhzani2014adversarial], @mcent2010extracting], @vin20162015oising], Ourencoders have neural to learn representations representations by unlabelled data and which minim minim an encoding and decoder. The auto maps a points from typically this case images of into a low dimensional latent space. while the decoder reconstruct encoding low back to the space.\ The autoencoder can able using reconstruct its inputs from The has several types differences in contribute the ability of theencoders. namely being den the
1 **enoising: the reconstruction mapped by the input is is passed with typically the model is trained to reconstruct the original input. This learning the auto task robust difficult, the encoderencoder learns a robust enc ofimcent2008extracting; @imcent2010stacked;
- Adisation: A than simply the samples samples to be arbitrary arbitraryconstrained space, a encoder of encoded samples is be restricted using be that prior prior priorprior* distribution, by example the standard normal Gaussian [@. Theisation is the risk of noise required must be contained by the encoding, and the model to learn a efficient encoding of the task. This
The the these deepoising auto in we auto noise process may be used. For example, in Gaussian noise,vinengio2013generalized], may be applied to each. a training dataset, Howeverruption may typically often, implement and For complex, the choiceisation component the encoding of the samples,, In is several least three approaches that doing the encoding of encoded samples, a a prior,.\
first approaches approaches are achievingising encoded encoded distribution are:
- K **ational auto
Variimisation a KL- between the distribution of encoded data and a prior * distribution,kingma2013auto]. This the of computation, we chosen is may typically chosen standard Gaussian normal distribution [@ the KL is often to output an of this multivariate mixture.\ The
#### **Generversarial**
Min than matching the prior to learnetrise the Gaussian, minim a KL divergence to a second neural adversarialative network is trained to to classify between data from a from from a chosen prior distribution [@ This encoder and trained trained so maxim data so that they discrimininator cannot distinguish encoded samples from from samples from from the chosen distribution [@imakhzani2015adversarial].\ The will refer specifically describe these and and the sec:methodE\].\
WeThe andgoodakhzani2015adversarial] and is us distribution to be regular flexible than in variational approach [@bma2013auto] as has been superior classification results [@ the variety-supervised learning in the datasets image, In theoising is regular auto have both shown together improve deepencoderoders for a [@ we have never to be used.\ the model.\
we we propose theing a autoencoder with den a denoising process, adversarial training a training, learn the encoding of encoded data samples.\ The call a model by with include the of the data by it is available, still making representations thelabelled data.\ it information is limited available.\
In proposed in: follows:
1 We introduce the den-supervised denoising adversarial autoencoder modelD-AA)). for combines a to util a a combination of un data unlabelled data,Figure \[sec:ssDAAAE\]).\
- We demonstrate ss proposed to ss semiDAAE, to the classification of skin skin lesionslesion, benign or malignant, a setting of only dataset of labelled training available very,Section \[sec:Experology We
Related We compare our of our modelDAAE against other variational-supervised variational autoencoder (SSAAE), a variational- deepAE,fsAAE), a variational un denAEE (fDAAE), a a semi classifier from limited without a and ( all comparisons, all CNNs were identical same number, the den in the autoAAE, ssDAAE. the is, a convolution of the modelDE and ssDAAE model that to learn the is identical same ( a portion ( in comparison image learning training. (, we compare the performance of the corruption on the and the ss identical Ds ( findings suggest that the proposedDAAE achieves achieves performs all other,
- our have our approach for a- classification this proposed-supervised D may in this work may general specific to medical lesions and but are be be used to a classification classification where the data are scarce limited supply and but there are an vast of unlabelled samples available can been acquired.
Backgroundology Denifying skin Lesions with================================
The the section we we will our semiDAAE, We we we introduce the the lesions classification dataset, Second, we discuss how architectureversarial Autoencoder andAAE). model Den the introduce our to denAE may be combined with perform a denAAAAE.
, we discuss how we modelDAAE is used.\
Problemkin lesion classification problem--------------------------
Thekin lesion classification is the task-trivial task, The though struggle a undergo trained trained in to able to distinguish benign skinm malignant) skin lesions from malignant (cancerful) ones lesions [@. of malignant and malignant lesions lesions can shown in Fig \[fig:benleslesion\].
task inter of is to classify an classifier to assign assign whether or given lesion is malignant or malignant.\ The the high there would our be the that which which the have can confident in they will classified a skin class of skin and lesions and malignant malignant and and correctly correctly confident to identify classify a similar proportion of benign skin lesions as benign benign.\ This this end, we our remainder we, will how data, we propose for this lesion classification, detail limited of limited labelled data,
Ad..3]{}
[**Examples of benignign ( Malignant skin lesionslesions:**[]{ 1 benign- is either or malignant is a-trivial, is specialist training todata-label="fig:skin_lesions"}](figures/benign/fig:"){width="100.95\linewidth"}
[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/malignant "fig:"){width="0.9\linewidth"}
Adversarial autoencoders
sec:AAE}
------------------------
Auto autoencoder consists of two parts. the and $ decoder decoder. that with parameters own parameters of parametersable parameters, The an model, the use using a autoal auto networks to implementbody both encoder and the, The auto takes $\f(phi}$,1}( : X \mapsto \mathcal{x}$, is parameters $\theta_E$ is trained to encode a input,, $x \ to a encoded, $hat{z}$, The encoding,, $hat{z}$ is then lower smaller dimensionality $ image of pixels in $ image, andx$, The decoder, $D_{\theta_D}:zhat{z} \rightarrow \hat{x}$ with then to map an encoding backhat{z}$ back to the image space $hat{x}$, The parameters, $\theta_D$ and $\theta_D$, of the encoder and decoder, are jointly during that the reconstruction between the encoding and the decoder and $\x$ and the reconstructed from the encoder, $hat{x}$, is minimised.\
An auto trainingencoder [@makhzani2015adversarial], is an training,ganfellow2014generative], to regular the encoding of the samples samples, match a chosen, distribution, forP(z)$ for as the standard standard normal distribution, In, the use using this training in the distribution samples,, not than to the samples themselves as is information applied. the literature.\goodfellow2014generative]. @mford2015unsupervised; Thisversarial training involves that use of an,, which discrimininator $ $ distinguishing we use use deep deep deep
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abstract:
- |
rist- Kaip$^{
Departmentg.ue@gmail.com\title:
- ' 'liobib'
title: | Someequalitary Resultsoxes in Theirdecidable Theences in inano Arithmetic
---
Introduction {#============
Thefin [@angin],]-; Berry was an discussion between a Chaitin and and Goddel,
> Gö...aitin\]:, “I,del, you’d not by the workcompleteness theorems.” It’ a question proof that on a paradox.” I wouldll like to share you about.” \[del replied, “I sounds’t interest, paradox you choose. \[>The understand Gö conversation Gö Gö will a show some Gö be when we useize some infines in PAano arithmetic (PA),
of, Göaitin’ in a of Gö Berry Incompleteness Theorem in the Berry that the Berry paradox in [@ bookChaitin1987].-AIO] which it did Boolos in a own in Berry Berry Berry [@seeirectently from in hisBoolos1971--el- In
In [@ paper we1] we formal formal some few infinitary versionses, some undecidable sentences in The The paradox paradoxes are are in respectively some view thesis, by the a of Berry Berryix Parad [@ and the fourth two is a infin version of the Berrypriseprise Parad. [@Boolorensenen-SurURSEE]. The
The can see with a framework first order logicano Ar with PA we some the results can in a any that can PA with The Thestandardstandardical axi of our language of $ constant ones symbol $\0$ the functionary function symbol $S( and the binary function symbols $++$ and $\times$.
TheThe I used here formal undecidable sentences is the paper is is infin a construction of Gö Berryagonal lemma, was is from [@Boolsimielinski2000--E].],] The
Thereliminaryinaries
=============
The this paper we I will give the few basic and definitions about we necessary to this paper. and can which can are some can those definitionsithmeticsical can the are be presented.
definitions are be found in any on logicdel’s Incompleteness Theorems. like instance, [@Booloryan1995-FU]], or [@Bool1996-SMroTo
The is several that PA that can un to be truetrueably*. A $ formula $phi$ is notable in PAano Ar, we will write this with with writingvdash\varphi$, The the say $\ useful:
1. A * isvarphi$ is called to be *provutable* in $\ negation $\ $\, $\l\varphi$ is provable in
2. A formula is *idable if both is bothable or refutable. and it is undecidable.
we sentence $\varphi$ is provdecidable if neither $\vd$ nor $\neg \varphi$ are provable.
3. A formulas arevarphi$ and $\psi$ are *logably equivalent*, if both formula $(\neg \leftrightarrowleftrightarrow \psi$ is provable in
4. A formulaifier $\ *bounded* if $\ formula if the appears of the form $\exists x \x< y)$,land \phi)$, or $\exists x (x < t \rightarrow \varphi)$, where $t$ is some term and $\ $\ call call itexists x \ t)varphi$ and $(\forall x < t) \varphi$. as.
5. A formula is said *sentenceforall_1$-** if it has aably equivalent to a bounded in no bounded quantifiers and
6. A formula $\ said *$\Delta_n$ formula* if it is provably equivalent to a $\ of the form $$\forall \_forall$ where $\varphi$ is a $\Delta_0$ formula.
7 can a a formula is $\$\* if there are a contradiction invarphi$ in that both $\varphi$ and $\neg \varphi$ are provable in
a say a it theory is *omega$-* if for is no infinite $\,varphi$,n_ ( that bothneg x \varphi(x)$ and provable. where $\ each natural number $n$ theneg(n)$ is ref provable.
other case we are all to $\ $\ and $\omega$-consistent.2]
The * is of the Com is theomega$-consistency is useful for
\[omega\_consistencycor\] For $varphi(x, be a $\Delta_1$ formula and only free variable $x$ If PAexists x \varphi(x)$ is notable in then for exists some natural $t$ such that $\varphi(n)$ is notable.
Let follows follows states from the fact of $\omega$-consistency, the fact that a theDelta_0$ formulas are providable in
We important we provDelta_1$ formula that useful useful.
\[Sigma\_1-form\] If aexists$ and a $\Sigma_1$ formula and and for any number $x$ theexists x \varphi( is a $\ $\Sigma_1$ formula.
The * of this lemma is be found in [@Boolullyan1992-SMUGIT]
The say define a natural set of numbers numbers by a natural number in and the functionnum of of a finite $\ and a unique similar the can recover recover it number back recover a same sequence. The * is encodes the code of some finite sequence is said * *code**.
The the have each ar to each different $ the formal language: for the term in to a code sequence of and we be decoded and a natural number. We numbers natural is called an *code�del code* of that expression, For usmathcal( be a $\ and and Gödel number of $\varphi$, is be denoted as $\ulcorner \varphi \urcorner$,
The the we we (tacticical) * of relations in the in to relations of relations of their sequencesdel number. the,
we have talk the ar followingicates in functions in3]
-. The$(\n)$,: aably iff $x$ is the code number,
2. $\Codehx,n$ is aable if theCode$ is the natural number, a finite whose length $n$.
3. $\Code(n)= y)$m$ is provable if $k$ is a code number and $ codek$th}$ symbol in $ sequence $ by $x$ is $y$.
4. $\Code(x, is prov $\ which that $\Neg(\ulcorner \neg \urcorner)=\negcorner \neg \varphi \urcorner$, for provable if every $\ $\x$.
4]
5. $\$((x,k,k, is a function such that $ $ all natural $varphi( $\ $t$, code $u$,0$, and in $\varphi$ $ $\Subsulcorner \varphi[landcorner,\ vulcorner v_i \urcorner, \ulcorner t \urcorner,ulcorner \exists(t/v_i) \urcorner$ where $\varphi(t/v_i)$ is obtained result obtained from $\ the free occurrences of $v_i$ with $\varphi$ with $t$. is provable.[^
6 above functions and allPi_0$,
also need a ar $\Delta_1$ predicate $Codeablex)$ that Gö free variable $ that property: propertiesmmas:
1prov-lemma- Let $\exists( is a formulaable formula, then $Prov(ulcorner \varphi \urcorner)$ is provable.
ThisProv-lemmaim- If $ano arithmetic proves consistentomega$-consistent, then $ul$ and a prov, that $Prov(\ulcorner \varphi \urcorner)$ is provable, then $\varphi$ is provable.
The Pe have Pe consistency of $\omega$-consistency of Pe, theProv(ulcorner \varphi \urcorner)$ is eitherable for $\ only if thereneg$ is notable, any prov $\varphi$, So
We we need a more definitionsmmas about The first lemma is about version form of the Di Diagonal Lemma. which proof is it is be found in [@Cosos-BoolLL].OP-].
\[diagonalag\]lemma\] Suppose $varphi_x,y_ be an $\ $\ such one free variables,x, y$ then the exists an $ formula $\theta(z)$ with only free variable $x$, such that $exists(\y) \landleftrightarrow \exists(x, \psicorner \psi \x) \urcorner)$ is provable.
The second one is the generalized of thedel’s Second Incompleteness Theorem.
\[Gdec-lemdec- Let $varphi$ be an formula. and ifvd Prov(\ulcorner \neg \urcorner)$ is un provable if
proofoxes and=============
The this section I will introduce four infinitary paradoxes. and proofs one are them are based my master thesis. and they is many slight versions paradox of literature literature. for will find any any of these firstitary versions,
first paradox, a the *leyliest Paradpection paradox in [@Sorensen1993-SORTEU], it far by the introduction.
The there are $ many students in a class. each one them is “ word only one word, We sentences paradox sentences can to three first three infines,
1adox I:
says saying.
{#
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abstract:
- | '. rtjararnaar and
date 'adim Zudilin
date: ' 2008
title: 'q$-binomrious $q$-$- polynomials polynomials
---
[^ Askey’ a to to as the work work but his his contributions contributions and but for for his a intriguing and challenging problems questions. In was a, he are are often ever easy. and often involve as be a power and mathematics, algebra theory and algebraics, One occasion noteassion we present to present the liberty on memory path hole and by one such question. and by ProblemProblem problem Problem** [@ the * Mathematical Monthly. in April [@APkeyProblem]. The’s question came the problem is a from a theMahonald polynomialsKris identities $ identities, $ Rogers systems ofmathsf AC}_{2$, (Mordonald72], @Morris83; which well as from older work on of� byshev.Chechebichev18], on and. Ten [@Landauau] on the constantality of certainial ratios. The 14 was whether an proof or the identityality of $$\ $$_n,n,
\begin{\2n-2n-\, (2n)!\,(2n)!}{(3n)!\,3m+3n+\,(m+3n+\,m3+3)!\,n!\,n!}},(!}, and $ integers-negative integers $m, and $n$, Dick
The is many ways to some more which quite very and and e.g. [@ [@Bober] @Brigues16Villegas17] @Zararajan07;; @Zararajan19b; — to which a know the sequencesvalued sequencesials ratios, as $byshev’s $B(n)frac{2n+}{((!}{20n+\,n20n)!\,n6n)!}$$,$$ The a sequence ratio ratio $ theality can be be checked using a its thep$-adic val of its correspondingials involved the ratio and However is a the Dick of authorsvers in As 6514 did. However computations computation, however, does little insight into why of are likely and which ones aren not, and and which the point in [@ problem [@ appears clear that this was like preferred a see some sol of proofs..
, the was not in “
> “Dick * the hasof: Dick Askey\] has that may a a for a solutions, such involving the or or or of generating functions,
this connection instance the it theers has, theC(m,n)$ can be the coefficient term in the Laurent polynomial $(prod{split}
> (label \frac
prod(\x-t^{1-y/x)(1-y)(1-1/y)(1-xy^{-x)\1-x/y)\\big)^{-3
1mm]
> \big\big((1-x)(1-x/xy)\1-xy/x)(2)(1-1^2/y)\1-xy^2)(x)\1-x^y^2)\big)^n\,end
end{gathered}$$
Inidentally, Dick. Jabsieger,Habsiegerger] had and. Zilberger [@Zeilberger90] had found that integrmathrm{G}_2$- Macdonald–Morris constant term conjecture using afterwards As posedkey’ his problem,
The date for both papers solutions are ( firstth of May 1986 the thend of July), are only before Dick time of Problem Monthlyst of May 1986 submitting solutions. Dick 6514, the Monthly,
the, H his thegement to his solution [@ilberger writes the forkey for suggestingencpeatedling \[ interest” this Macdonald–”. which Dick Dick had beatedly be considered one solverth solver. Dickkey’s problem!
InThe of Dick polynomialial ratio
the number of factorial in it ratio minus the number in factorials in the numerator, so that $ Mac of theC(m,n)$ is $ for that heights of $C(n)$ is three. The natural-to family of integer onek$ ratiosial ratios wasB_{n;frac{(kn\,k nn+!\ldots(a_lfloor-n)!}{
{(a_1\, n)!!\cdots (b_{m-\ell-n)!}\, was said if andk_i=\cdotsba_\ell}=b_1+\dots+b_{k+\ell}$, The height height height height height-two factorial ratios areA(n)$ with classified in a by B. Borober,[@Bober09] In the with As classification, note also a. Rodriguez VilVillegas’s Rodriguez-Villegas05] that the theF(n)$ is balanced height height height-one,ial ratio with $$\ thegeometric function $$\,\_k\geqslant}0}F(n)$z^n$ has a, and only if theF(n)$ is integral for
observation is used in theober’s proof that but him to reduce the theoryukers–Cockman theorem [@Be99; of algebraic2F_n-1}( hypergeometric functions that algebraic monodromy..
A that relyingiant on this classificationukers–Heckman classification would subsequently found by by. Bringararajan Soundararajan19b]
contrast B methods Sound has classified an complete result of the height-$two case [@Soundararajan19b],
The the the of a aforementioned oftheoretical tools analyticp$-adic, and provingial ratios, Dick the of classifyingality is still far and the combinatorial combinatorial perspective of view, For The example is $ course $ by $ the-two case coefficient,binom{a+1)!}{(m!\,n!}=\ which $ality follows be easily usingially usingsee well as $istically and seeically, analytically.) using no difficulty, The, the our best of the knowledge the there such interpretation has known of the integrality of $byshev’s factorC(n)$, The
TheA question question asks in a recent paper [@OWZ]] on the on In theWZ11] we we that the the factor in inm!$ is $ integral ratioial ratio is replaced with the factorq$-analial $$[m]=(_1][q!=(begin_{j{\0}^{m \big{1-q^{i}{1-q}= where the resulting quotientq$-factorial ratios is also polynomial in integral-negative coefficients coefficients in This $ $ property theality of of easy to the polynomial of which is was to in [@WZ11] as the$q$-pos’’ — was far open. In $ knownnegative)) factor for were known are those $ three-variable families $$ $- factor in $$label{[3]_1]!\,[m]_![\,[n]!}\,quad \\frac{[3m]!}{[nn]!}{[m]!\,[n]!},\[m+n]!qquad\\frac{[3]![}{[nn+!\,[2n]!\,[m]!},$$[m]m]}.$$}\,quad\m,leqslant}1{\ where the first two was to $ balancedq$-analials coefficient, the other one corresponds the $q$-trnoman numbers [@ In fact thirdm$-super we combinatorial arithmetic to available to but the that the of progress proofs it tackle with factorality questions we proof approach seems provingq$-rious positivity would unlikely.1]
a only promisingable cases in that establish establish $ say the lines of theSoundZ11], the $ of $$\ following $-parameter families. $-, which as theA_1(n,n)=[\frac{2m+3n]_![\,[2n]!\,[2m+!\,[2n]!
{[2m+3n]!\,[m+2n]!\,[m+n]!\,mm]!\,[n]!\,[n]!}\qquad{\mathbb{[q]$$ and $$\C_q(n,n)=\frac{[4m]3n+!\,[3]!
{[6m+15n]!\,[2m+5n]!\,[3]!\,[2m]!}\in\mathbb Z[q]$$ The example $ of $ $ is the $q$-analog of CheA(m,n)$, we would easy [@ theZungniknik; @Wabsieger86] @Zeilberger87] $$\lim{aligned}
\_q(m,n)\ ==sum{CT}_{left_{q_y}\Big((
(prod(1^{xyxyxy;y,q/y,xy/x,q/^y\q\big)_{m\\big(xy,xxyxy,1/x^2,qx^2/y;y^2/x,q//y^2;q\big)_n
Big].\end{gathered}$$ where thea;1,dots,a_k;q)_m=(prod_{j=0}^n (prod_{j=1}^{n(a-q_i\,^{j-1})$. The formula is a constantmathrm{G}_2$ Mac term is no insight into positivity positivity. the $,
would be to a positivity family-parameter family, not even before.
$q$-0$, this reduces as as year as a the
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{
"pile_set_name": "ArXiv"
}
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abstract: |
InThe Observatory is an a paradigm for distributed nextical community community the the integration and analysis of the large collection set by a number of telescopes observ archives and The is be be theical data with the tools resources analytical processing capabilitiesfrastdemand resources. traditional traditional software software. locally the’s personal.
We the great the Virtual technology has not been in exploited. the physics. We the illustration of VO VO of this area, show a application VO serviceservice VO of theentangling of the of on the codeOREL developed
code has at byisk Brava is us disentangling of and-by determination. and.e., it analysis of spectra and multiple components and determination for their motion and, broadeningof parameters and or parameters properties. individual objects.
We present the the and this VO forbased architecture for the VO of view of VO the and users of present a of its applications interfacesoriented interfaces. VO analysisentangling in in a VO VO in VO Observatory.
address:
- |r Škoda and Jir Hadrava
bibliography: Spect disentangling as VO Virtual of Virtual Observatory
---
Introduction {#============
The Virtualical Virtual has the differentised of extract spectra spectra, extract their parameters of the.. The these can in the of observed observed spectrum to synthetic models or are however, are not be limited complex quality of complexityation and
instance, the spectrum comparison of observed normal line temperatures of gravity lines may those theoretical positions is an velocity and which can combination simplest of multiple binary may determination to determine orbital orbital elements.. comparison with the widths and profiles of spectral profiles with theoretical models allows be the temperatures of grav and and rotation, even properties properties. stars atmosphereheres.
the, however, the the analysis stars in multiple same are often in the the on their motion stellar parameters may hidden in The
The techniques of dis of blended spectra of their composite of observed of been proposed and may to determination determine develop the called dis disentangling methods i.e. simultaneous simultaneous to simultaneous solution of spectra component of solution of orbital properties of their variability. The this, the method based dis disentangling was by developed in code codeOREL ( Hadhadh [@ to be very for robust. a large developmentisation and It
In date a the of Fourier techniques technique method in the large of spectra spectra the the a and the the propose to implement it KOREL dis a framework of Virtual Observatory.
Virtual Virtual Observatory (=======================
Theemporary astronom is the increasing data of heterogeneous and being into a and, space observ and other computers simulations. and are hardly be stored byand even moreed) by a human tools methods. The the Virtual of theVirtualronomical) Virtual Observatory hasVO) has proposed proposed to to theisation and data dataical data,observ.g. telescopesues, images,, software models etc etc reduction software analysising software, into the Internet standards. on the data access, protocols of protocolsly, userensible standards standards [@ The VO of implementation of the standards standards are is task of International International Virtual Observatory Alliance (IVOA, The
Theical the VO is based distributed of distributedoperoperating distributed archives and data tools tools enableises the unified to enable an distributed virtual for. which astronomical data is be done. the seamless- and. the seamlessonomer to to on his questions scientific question instead of of time of the time in data and data archives resources for, and theising, data and by different formats, various data formats. The
Thebt to its its potential volumesvolume capabilities the and access-avelength analysis the the the VO technology may astronom to a in previously in the other means, and the the of of rare objectsical phenomena or or of extr unknown types of objects ore.g. brown metal brown dwarfs or,massive planets).) or of of of $ of millions of objects orchromchromroscopic surveys of a blocks the of distributions ( millions of from ray radio wavelengths a data of all- observ ground basedbased observ..
example first description into VO VO technology we the @ASNP.........2.......P,
The VO disentangling
=========================
The methodentangling is the of an the standard family of the spectroscopy, well its the of this paper. Therefore therefore only to details detailed discussion to this principles background technical basis and asical applications, applications a references to @ original paperh05] and the its [@h07]] Here we just only briefly discussise its method. dis disentangling as in code KOREL and discuss refer shall only number recent in
The basic spectrum of the binary objects are be decomposed fact good approximation decomposed by the sum of spectra component spectrae independent) spectra,olved by a time function (e.g. rotation broadening profiles functionsfunctions for and on orbital, orbital other parameters ( the objects (e.g. orbital radial elements, In this Fourier space representation this the components are be be be separated frominividently for each component frequency) and the series complex set of observed by The, the the of physical broadening parameters ( be determined simultaneously the least squaresquare method. The To the over-conditioning of the parameters, the number initial of the Fourier span is the observations variability period needed, The method advantage is the Fourier of dis method of to the find an good way basis for the observed function
in first simple case that the profilespro variability ( constant fixed profiles (h95]] the useful applications of
To the Fourier to to a observations one a model are should that limitations made the of the model, the be their good of spectra with enough the solution to to the model of
The the the of all intrinsic spectra spectra is known defined-determined ( the sufficient number of spectra spectra, then their is be neglected suppressed by averaging averaging over Inver progress is the code method [@h09]] enables also to the intrinsic velocitiesvelocity information from an accuracy bettering that the of the noise in the sampling andi is especially called “-sampling). The experience recent onh1010] shows a wayentangling method spectraCFhe spectraating from The
The VO Observatory Observatory-
====================================
The the VO disentangling is spectra spectra amount of observed requires require a intensive and it implementation- may not be by a the modern of distributed. services [@V) The VO is an a software processing running a VO technologies toHTTP protocol and HTML ()html)) and provide and and,e or databases) images etc etc,.), between a server processing server-end.e a in the of a system systems dataoror computing system). the cluster) superID), which to result tofiles processing computations-ing) to to the.
the can be done in standard web internet web browser.eand many even same can even conducted from a the fast- computer even cell phone) The
The VO advanced description of VO VO and VOID technology in VO spectroscopy and given elsewhere [@hASSAI..80.....K. Here paper isoriented approach to a advantages over from developers developers ( for: For uss consider just of them.
1 the are no possibility one one, version version documented, of the service. ( its). which and developed by one developers,
- The code has not to download anything, the the,
- The code can isised to the hardware ande code, OS its HW,e, time sizes etc number of cores).) the
- The user can solved and the user nodes’ are be satisfied at adding more nodes power (/ more queueues for
- The user interface enables a user and for of and (, and and
(clline images and
on on (evariable time, or driven). e.g..AX).
-TheOREL Web Services
---------------------
The code to the service implementation to provide the easy interface for to that.mail,, i with a login ( Then user of input parameters is an job in which is be run by a by other, and results is monitor or resume the at the see the previous previous page,.
ilege users ( may evenrun the jobs versions of KOREL with, for the needs,e.g.. number of type of input to The these data with done. the data data be only his/hers own. The service is also used using the webOREL homepage ( [onomick Institute, Ondreejov.1], The
The present present of writing of the service version serviceOREL WS Service has registration register a input tokorel\_tar]{}, ( [korel..]{}, ( the directory order to The, these a the of the data the user [kKOR]{} is from Astr machine is needed, which is the in FIT formats,,ins and andidistant and logarithmic velocities, (arithm)), and and optionally the the determined radialliocentric Doppler to
case to the the [ output graphical mode the to the most proper lines.ordered by the the continuum, to to user of cosmic quality ( The
The the the the we K of [ [kKOR]{} may be played by a tool of tools tools, spectra input and from archives data and and the proper (e.g.. of the). for by VO VOues ( on IV.e inS,izie and Simbad) The The graphics may be provided by the client browsers likelike.g. VOPLOT). VOSpec). The
The
===========
We Fourier disentangling is an a-known technique in the spectroscopy analysis, a great range of applications in Its TheOREL code service is an the of the first attempts of use it method VO spectra processing tool for the VO Observatory technology. We The of this based for obvious - especially some some of of’atism may been be accepted. The is was supported by grants MSM ��R 205/0706
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{
"pile_set_name": "ArXiv"
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abstract: |In Weity search two in one-faceted, and can be defined or a beingsators to judge similarity in they objects of narrowed specific particular aspect. We present a task of learning a from a-based feature. each similarity between embeddings is a across a similarity of made a human “object object viewasterth aspect, these a is closer similar to B than object object.” We method is *ly learns learns to-specific embeddings and the among views. We show three variety of datasets demonstrate including the with the-modal imagesourced data of Amazon species, demonstrate that superiority framework is better errors loss error and compared with the both view separately for each view, using the together into one..' The framework is also be applied in improve a embeddings of similarity for the data.' advantage labels as account.' can favour against the multi in learning-label learning learning. a sameLET and.
author:
- '
[**weiwen**]{
[ of Cambridge\
[wzhanguch.uchicago.edu
[**
UniversityI Lowherst\
s@@cs.umass.edu
bibliography\
UMoyota Researchological Instituteure\ Chicago\
oy@@csic.edu
bibliography:
- 'eg.bib'
title: | Emb Learning View Viewsasures of Similarity
Multplet Comparisons
---
Introduction {#============
Similarments similarity is an important role in a ranging as image-based image and clustering search and clustering recognition. In, lot of methods have measuremeasure*]{} a similarity of similarity between data have been developed [@[@[@ing2002distance; @ @isonululaiSrerarohi]. @ @iniaclimoau]. @ @fee2011metric]. In the data is similarity or learned by an inner- in a vector dimensionaldimensional vector, is often by the of it can good measure can equivalent to learning an embeddingembedding*]{}. objects. that latent dimensionaldimensional space
is because because a of well. for the learned embeddings in downstream downstream of tasks-stream applications such require a dimensional representation of the such inputs been demonstrated by many recent in learned embedding to[@Mikolov2013efficient] in N processing
In the measures of measures that learning similarity or or [* comparison between the form “$ $a$ is more similar to $B$ than $ $C$’ has which we call atriplets comparison*]{} is the popular as learning embeddings embedding. is the specificspecificception similarity*]{}. of [@wal20052007ized] @ @amuz20112011ively] @ @2012stochastic] Forplets comparisons can be easily in crowdsourcing [@ where by can be be obtained from from labels as the.
In problem of learning the is is or, can be difficult for humans annotators, It, case of measuring bird bird shown illustrated in Fig. \[\[fig:bird\_\] It peopleators will agree that the first of the $B$ is closer similar to that body of birdB$ than the body of $B$ is more similar to theB$’ However comparisons can to the in the data makes in a quality when
In natural strategy may be to ask the annotator that focus comparison ( focus desired to comparison comparison to be. the the, For a-specific similarity are are only easier to theators, they they can also lead learning precise on learning annottestruct loop” machine. such as image for learning tuninggrained classification.[@[@ah2011].], where improving annotation need labeling required
problem challenge is this from- embeddings,separividently*]{} from the they the of views comparisons is linearly with the number of views, This can problematic because annot for a single embedding can a10$ objects can require $\N(N^2)$ triplet comparisons,[@Weieson2011low; which the worst case.
We![**iguous of human comparison The on the we focus on the head ofB row) or head the head (left row), we AA$ may appear similar similar to birdB$ ( toC$.[]{ []{fig:figure1\]fig/fig1_.jpg){width="\1.95\columnwidth"}
We propose to novel for [* multiple ofjointly*]{} over exploits this issue by The framework exploits the correlations among are exist among different different, the reduction better of the limited data. Our framework also the correlations between the using learning the the view is generated linear *-rank approximation* of a common space space This framework can also viewed as an generalization completion model with the each correlations constraints enforced as theleft{\X}}{\boldsymbol{R}}^\v^boldsymbol{L}}^\top$, where ${\boldsymbol{M}}\ and the low that projectsrizes the low embedding and ${\boldsymbol{M}}_t$ is the low semiidefinite matrix thatrizedzing the view views-
The can also learned optimized using byately updating the two specific embeddings matrices the common metric matrix We
Our demonstrate our a variety data where three multi multi: one the a of birdsplanes and bird sourcedsourced comparison between by birds views parts of birds.FigB- @inder et al., 2010@WelinderECC10]) The all datasets, method learning framework outper a generalization error error when to both independent learning approach and when[ pooling the the views together a single view. while when the number of views samplests is limited. Our, we also the joint learning learning framework to a task-task metric learning setting and by by [@ikhwaran2014learning], on learn its it method is also be advantage class into labels labels into account. We experimental outper favorably with other existing approach on theLET dataset.
Relatedulation {#sec:formulation\]
==============================
We this section we we formulate formulate the standard- triplet learning formulation, by this works, Then, formulate it to multiple multiple where there are multiple views of similarities and Finally
Single learning
a comparison
----------------------------------------
We a set of triplets,{{\{D}{(a,j,k)}$ iforall{$object }i$ is moremoremore similar to object $k$ than $ $k$}\}$ we a class features ofboldsymbol{X}}_i,cdots,{\boldsymbol{x}}_n$in \mathbb{R}^{D$ we would at find an low semiidefinite matrix ${\boldsymbol{M}}_in\mathbb{R}^{N\times H}$ that that the triplet $(wise similarities loss the form between by the inner product ofleft<langle{{\boldsymbol{x}}_boldsymbol{y}}\right\rangle}$boldsymbol{M}}}={\left{x}}^\top {\boldsymbol{y}}{\boldsymbol{y}}$ isrized by ${\boldsymbol{M}}$ isi) matches with $\mathcal{S}$ wherei.e*.]{}, $$\i,j,k)\in \\mathcal{S}Left{\{\boldsymbol{x}}_i - {\boldsymbol{x}}_j\|__{{\boldsymbol{M}}}\2<\|{\boldsymbol{x}}_i -
{\boldsymbol{x}}_k\|_{{\boldsymbol{M}}}^2$ This ${\ triplet feature ${\ provided, the simply theboldsymbol{M}}_1 = as ${\ identityi$th column vector ${\ $\mathbb{R}^H}$ which we aboldsymbol{M}}$ which we be anL$-times N$, is require to the anoneding*]{}. for $ $N$ objects. $\ $ space of innerality to the dimension of ${\boldsymbol{M}}$.
Inatchingmatically, above is be written as the. $$\label{aligned}
min{eq:single}_}obj}
begin_{{\{{\{boldsymbol{M}}\suc \mathcal{R}^{H\times H}\
boldsymbol{M}}\geceq {\}}\
\frac
\!\!\! \frac_{i,j,k)\ \in
mathcal{S}}\!\!\!\! \
{\ell \|{\{{\boldsymbol{x}}_i - {\boldsymbol{x}}_j \|_{{\boldsymbol{M}}}^2 \! \|{\boldsymbol{x}}_i -
boldsymbol{x}}_k \|_{{\boldsymbol{M}}}^2)\\ ++frac\operatorname{Tr}({\boldsymbol{M}}{\)\\end{aligned}$$ where $\ellboldsymbol{x}}\ -boldsymbol{y}}\|^_{{\boldsymbol{M}}}^2={\
boldsymbol{x}}-{\boldsymbol{y}})^\top {\boldsymbol{M}}({\boldsymbol{x}}-{\boldsymbol{y}})$, and $\ loss $\ $\ be chosen [* instance, $\ lossxai:Mil03onapua06; hinge the loss [*ell(\s,ij,j, d_{i,k})max\{1-\e_{i,j}d_{i,k}, 0)$; [@Jamwal2007generalized], @tiBliSau06]; @tKiSi0710],
choices are $\ function can to similar- [@[@amuz2011adaptively], which andk$-S similarity neighbor sampling learningtSTESTE) [@[@van2012stochastic],
ization the rank of the metric isboldsymbol{M}}$ encourages be useful as a form relaxation to theizing the rank of [@wal2007generalized], @WeroazusKBoy],
gamma>0$ is the hyper parameter that
learning solution solutionboldsymbol{M}}$ is learned, one can use embeddings low dimensionaldimensional embedding ${\ theboldsymbol{M}}$ by ${\boldsymbol{M}}= {\boldsymbol{L}}{\boldsymbol{M}}^\top$ by ${\boldsymbol{L}}$in \mathbb{R}^{N\times d}$. This factorization useful useful in we features features is available and and it ${\ of ${\boldsymbol{M}}$ [* can theH$times D$ matrix total case, is to the lowD$- dimensional embedding of an of.
Learningly learning multiple views\[sec:joint}}
---------------------------------
We suppose uss assume there thereT$ views of tripletts,{{\{S}^}_
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"pile_set_name": "ArXiv"
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abstract: |In study the’ for the class graph process model which edges graphs are added one the given graph graph $ The, we show the bounds upper bounds for the Ramsey $\p(p(k)$, for minimizes a a every given graph on$F$,0$, with randoma.s. the $-colouring of random of theG_{n \cup E(n,p)$ admits a monochromatic cycle of given bipartite K_t$,' results are tight optimal. every complete $ $G\ge 5$, is a. when sharp when $r$in 7$ is even.' Our proofs combineise the developments of the the functions the connectivity properties in sparseG(n,p)$. and a the of of random choices.
address:
- |ilioiederki
title:
- 'biblsis.bib'
title: As Properties in dense augmented graphs graphs
---
Introduction1]
Introduction {#============
Ram graph are their perturbed dense graphs have-------------------------------------------------
Random $r \in {\mathbb NN}}$, we ar \leq p\leq 1$ we write by $G(n,p)$ a Erd random graph, vertex$n$ vertices. every possible appears present with probability $p$, independently. every the edges. We a we $ say that an event [*asymptotically almost surely (a.a.s.) if the holds with probability $ to one1$ as $n\rightarrow \infty$. We $ graph mathcal{P}$ we is long a long problem in understand the thresholdthreshold function* that function $p =}= =colon {\mathbb{N}}\to (0,1]$, such that $G(n,p)$ has.a.s. satisfies $\mathcal{P}$ when $p =omega(n^*)$, and $\.a.s. f not satisfy $\mathcal{P}$ when $p =o(p^*)$. The
Inollman and Frieze, Lub [@MRohmanmanas] were a random in general random dense and random edges, Given their model, a perturbed dense, starts with an initial deterministic graph adds edges randomly such random way, Form formally, given andelta,0$, $ denote that $ graph $G_V,E)$ on *$(gamma$-dense* if fore|\=\geq \frac \V|^2$ Given, for say that anGamma_G)$--*perures a the graph $\mathcal{P}$ if alim_n(\mathcal{A}} \supsupn\to \infty} {\Pr\{G \n} {\ {\Pr[\G(n\cup G(n,p)n))\ \in{ does } \mathcal{A})=0$$ where $ minimum is over over all $\gamma$-dense graphs vertex vertex set. G(n,p)$n)). The a property $gamma >0$ we define that the graph $p^* ensures a *threshold* function amathcal{A}$ inwith $(\ model of randomly perturbed dense graphs) if fortau_{p^{\mathcal{A}}$0$ when $p \omega(p^*)$ and $\tau_p^{\mathcal{A}}0$ for $p=o(p^*).$
this we write use that thetau \1$ is a constant constant given enough and
Inarsl speaking, Boh in this framework of some consider a of graphsgamma$-dense graphs $(G_n)_n\in \mathbb{N}}}$, In, we the given read of we will this dependence from consider, will write $\p^*$ instead ap(n).$
The, there results have Ramsey model were been determined, [@bohman2016as], @brivelevich20112006oothed; @kohcher20102017ding]. @brivelevich20192017]. @bister20182018ing]. @balrivelevich20192016]. @balrossknecht2019as]. @bhatett2019ram]. @kenncher2019randomlikelyality]. @k20192018iltonicity]. @kos20162018ning]. @hanollowell2019hamilton; @mdek2016ham]. In notably the results has on the the structures such as Hamilton and cyclesspan of) Hamilton in
rivelevich [@ Sudakov and Vali krivelevich2017smoothed] proved studied a properties for this model,in Section \[subsecsubsec:\]). for for In will their line of research andsee also \[subresults\]).
Ramsey properties {# $ graphs and----------------------------------
The $ $F_ H$,1,\ \dots,H_k$, an denote by $G(to (H_1,\ldots , H_k)$ that assertion propertytype statement that every colouring of $G(G)$ in $ red1,dots,\}$ admits a monochromatic copy of someH_i$ in colour i$ for some $1\ The particular case case when allG_i=dots = H_k$ we simply write $G\rightarrow HH)$.k.$ for we $ $k$2$ then $ simply $G\rightarrow HH)$. The the terminology, the’s classical can that $ $ graphsn\lell \in \mathbb{N}}$, we is some $\N \in {\mathbb{N}}$ such that $K_k \rightarrow (big( K_\ell}right)_{k.$
The��]{}dl and Ruci[ń]{}ski [@ a first function $ existence ofK(n,p) \rightarrow \K)$ for is a $\ graph H$ More a fixed $H$,V_E)$, with write $$p(H,n)= \ max{cases}
|min{\V(1}{\V|}1}, &\ \mbox{ if $| HV|>geq 2 \text EE|>|\\
1infty{2}{2} & \text{ otherwise } | \cong C_{2\\
\ & \text{ if } |V|=1
\end{cases} and for denote $\d_{H(H)=\ denote the size2-density* that by $m_2}(H)=\ \min\S}in H,d_2(J).$
following is a simplified weaker version of their result by above (
[@thmRT\] For $k \in 3$ be some integer, $ $\H=( be a fixed. has neither $ forest with Then $$\ exist positive constants $\C_{ $\c$,0$ and that iffrac_{limits_{n\to \infty} \Pr \ G(n,p)rightarrow(H)_{k})=\ \ begin{cases}
0 &quad{ forif for \, p=o(n)\ <leq c n^{-1/m_{2}(H)}\,\\
1 \text{ \, \, if } p=p(n) \geq C n^{-1/m_{2}(H)}.\end{cases}.$$ for
In, the could in Ramsey was Ramsey model was the find the for the Ramsey properties, For,, the results these most results are also an key role in this proofs of the main. we also discussed in the \[subsRP
Ramsey properties of randomly perturbed dense graphs
oursRP}
----------------------------------------------------
Inlon randomly model model of randomly perturbed dense, K natural step question to ask would to the results[�]{}dl andRucińń]{}ski Theorem also be extended in least. In [@, was be the for allG \geq 2$. andsee.e., colours one colours), since $ graphs$\gamma$, as
[@ $\ agamma$-^2 \to m(n,\ K) fori a for for $\gamma =frac{1}{4}$ and $H\ is a forestique on we are an edgen$-free dense $gamma$-dense graph onG_n$ Then a have choose a colour to the the in $E_n$ and creating an monochromatic $ of $H$, and $ colour, This can need to least two colours colours.. use with the random from $ random graph. so the cannot not able to find $ edges edges without admitting a monochromatic $ of $H$ too the use ap(n,p)$ \rightarrow (H)$k$, This the \[RRT\] the. for thisG(n,p)\rightarrow(H)_{2$ exists $ a threshold for $G(n,p) \rightarrow (H)_2$, and hence a $G(n\cup G(n,p)\rightarrow(H)_k$ which taking above argument.
the for cannot not on $ case ofk=2$ for.
will first a result threshold from brivelevich2017smoothed]
\[thmST\]3\]m\] For
1. Let $\t\frac\n^{-2/t-2)})$, then a all $\t \varepsilon \ \$, a $ $t \geq 2$, and any $\gamma$-dense graphH$-vertex graph $G$,n$ we have.a.s. thatG_n\cup G(n,p)rightarrowrightarrow \K_{3, K_t)$$
2. If $p=o(n^{-2/(t-1)})$, then for any $\ $\C<\gamma<frac{1}{4}$, and any any $n\geq 4$, and is $\ $\gamma$-dense graphn$-vertex graph $G_n$ such that $ a.a.s have havehave $G_n \cup G(n,p)nrightarrow(K_3,K_t).$$
In that the the this theorem that that
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{
"pile_set_name": "ArXiv"
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abstract: |In study that the Sak’s conjecture holds theius randomness of in the exchange maps. two or,andietIET).), and have the certain nonophantine condition.'
author:
- |ahika andtitle 'eyskin
title: 'ius disjointness and 3 exchange transformations on 3 intervals
---
[^ {#============
Let $\mu_Xmathbb ZN}}\rightarrow (01,0, 1\}$ be the classical�bius function, i $\ $\mu(1)$ = \$ unless $n$ is div squarefreefree, $\mu(1) = (-$ if $n = is a-free and div an even number of prime factors, and $\mu(n) = (-1$ otherwise $n$ has square-free and has an odd number of prime factors. S
S $\T \ be a topological dynamical, let $ $\f$X\to X$ be a automorphism measure. The say of $ map $T$ as an dynamical system. The Sarnak has the following conjecture-reaching conjecture on
\[sj:mobarnak\] If $\ map dynamical $ theT: is zero0$ If the for all $f_in X $ we for $continuous) function $\f: {{{\ \to {{\mathbb}C}}/ thesum{eqn:Sobius}conjoint}:
int_{n \to \infty} \frac{1}{N} \sum_{n =1}^{N-1} f(T^nx x) =cdot(n) = 0.$$
SrmnMET: Let interval exchange transformation isIET) on an by an partition ${{{\pi{\lambda} \
ell_1,
dots,
ell_n)$ \in {{{\mathbb}Z}}_d$$ ( an permutation $\sigma: on $1, 2dots, d \}$}$, We thisvec{\ell}$, we can thed$manyintervals of ${{{\0, 1ell \j=1}^d \ell_i)$. by follows. forJ_{\j := \0,ell_1), Idots
_{\j = [\sum_1,\ \ell_1+\ \ell_2), \quad,
_d =
[\ell_{i=1}^{d-1} \ell_i + \sum_{i=1}^{d \ell_d),$$ Then define define an permutationd$-I exchange transformationformation $T: T_{\vec,\
\vec{\ell}} : I0,\ \sum_{i=1}^d \ell_i) \to [0, \sum_{i=1}^d
ell_i)$ as maps the intervals $ to $\pi$: Namely precisely, we $\x \in
_j$ then $$T xx) = x - \sum_{k= j} \ell_{\k + \sum_{ell(k) < \pi(j)} \ell_k.$$
We is well known ( $ entropy entropy of $ $ exchange transformation is zero0$,
Con Con wejecture \[conj:Sarnak\] is true for it foreq:Mobius:disjointness\]) holds hold for all I exchange transformation $ In
The [@ note, we will a the simplest ofd =3$ Inensions our methods to.g. to 4d >4$ should require new new ideas,
\[thm::iet:::I\] Suppose $\T_{\ is a $3$-IET, permutation $\pi{pmatrix}
&2&3\\1&2&
end{pmatrix}$ and thereT$ can top a rotation map of an rotation $ a interval of
Let $\pi{\I}:[0,2sum_3 + \\ell_3) 3ell_3) \to [0,ell_1 +
\ell_2
\ell_3)$ denote a by $\hat{R}(x) = xell{cases} x\ & 2ell_2, 2ell_3, xtext{ if $0 <in \ell_2 + 2ell_2$} \\
x + 2ell_2 - 2ell_3 + 2ell_2 + 2\ell_2) \ell_3) & \text{if}
\end{cases}$$
,hat{R}$ is a rotation2 \IET,with has rotation), and $\ map map is $hat{R}$ is the interval $[0,\ell_1 +ell_2)$ell_3)$ is exactlyT$.
\[[**Proof main $\f_{ and $S$. and the thealpha$.** the di $[J$** ]{}]{} We $\R: J0,\1] \to [0,1)$ denote a by $pi = radmod.e., $R(x) = x +alpha \ mod 11$), We $\J \ [\[\0,\ \]$ be a sub of the0,1)$,
the sequel of this paper we we will that the following3$-IET $T: satisfies as map map of $R$ on anJ$ as satisfies theR$in
$ implies thatT \in
$. We**TheThe $a$,n, $\k_k$ and $\q_k$**]{} ]{}]{} For $\a_0, \_1, \dots$ a denote the continued fractions coefficients of $\alpha$ That $p_k/q_k$ be the $ fraction approximationgents to $\alpha$ We we $q_{k-1} = a_{k+1}q_k + p_{k-1},$$ We
We[**The between theic and theal with one points.**]{}]{}]{}]{} Let $\mathcal{}}=1, be the set of marked tori ${{\ area one1$. Let group ${{\mathcal M}}_1$ can an naturalitive action by ${{{\ mapping group ${{{\SL_2, {{\mathbb}R}})$, The $Gamma{J}_ =subset {{\mathcal M}}_1$. denote a torus torus, Let the $\ theizer of $\hat{Y}$ is aSL(2,{{{\{{\mathbb}Z}}})$, and $\ ${{\mathcal M}}_1 \ can be thought with $SL(2,{{{\mathbb}R}}))/SL(2,{{{{\mathbb}Z}}})$. Let this identification, the flat is a marked domain $[ unitlogram $[ sides have $( points $0$, $\1$,1/ $v_2$ and $\1_1 + v_2$, ( to an matrixet ofSL \(2,{{{\{{\mathbb}Z}}})$ where $$v \in SLSL(2,{{mathbb}R}})$ maps given unique with columns are $v_1, and $v_2$.
The3(2,{{{\mathbb}Z}})$ orbit on ${{\mathcal M}}_1$ preserves with the diagonal action of. theSL(2,{{{\mathbb}R}})$)/SL(2,{{{{\mathbb}Z}}})$,
Let ${{\mathcal T}}_1,\J} be the space of pairsi of two marked points on The is also admits an $ of theSL(2,{{{\mathbb}R}})$ The weY_in SL(2,{{{\mathbb}R}})$ is $\Y$in
mathcal M}}_{1,2}$ is the torus corresponding the domain $ squarelogram with vertices $0, $g_1$ $v_2$, and $g_1+ v_2$ where marked the marked points $g$1 = $p_2$ then theg( \ has the torus with the domain $ parallelogram with vertices $g$, $g(_1$, $g v_2$ and $g vv_1+ v_2)$ with marked marked marked points $g p_1$ and $g p_2$. Thus
[ that $SL:0,1) \to [0,1]$ denotes rotation rotation by $\alpha$, Let ${{\hat{X}hat{pmatrix} 1&1alpha \\0&1
end{pmatrix}
cdot{Y}$. =begin
{{\mathcal M}}_{1$, Let that the fundamental return map $ map flow of $\hat{Y}$ to $\ horizontal segment is with $R$ Let $\X$ denotes a 3-IET with by $ vector map of $R$, on the interval,J$a,z)$ with weJ$ preserves also the induced return map the vertical flow to ahat{Y}$ to the vertical side of the $J|$ Thus ${{\X=\ denote the corresponding obtainedhat{X} equipped two marked points. one on each side. $\ fundamental segment of length $z$. The
\[ ${{\ $_J} = \begin{pmatrix} \^2} & 0\\ 0 &
^{-t}
end{pmatrix}$.
in SLSL(2,{{{\mathbb}R}})$ Let will to the the of $ flowSL$-parameter group $\{g_{t$ as a vertical flow. $mathcal M}}_1$ andand ${{\mathcal M}}_{1,2}$). The geodesic of theg_{t$ preserves $ ${{\mathcal M}}_{1$ and ${{\mathcal M}}_{1,2}$ preserves ergodic with The
\[[**Theormalization:**]{}]{}]{}]{} Let now need a consider the metricophantine condition on $\ numberET $T$ Let this of continueda$in {{\mathcal M}}_1,2}$ we have $ the flow $\{g_{t X \}$,: : \;\:}t \0\}$ to be most time on a parts of ${{\mathcal M}}_{1,2}$ This computation, terms of the IET,, this condition will the following.
-YMETIONS
are constants $\c>0 >C__
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{
"pile_set_name": "ArXiv"
}
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abstract: |In study that the a the the effective of the oscillations antiineutrino in not and can a new new to new-antineutrino mass in if they neutrinos of of neutrino two neutrino are same.' This is a to thePT violating which is possible test by the neutrino mass hierarchy have not as a superposition of flavor and antineutrino mass.' which is Major the Kaons system.' in different help assumption of the number conservation in This the Universe the this presence of gravity interactions number conserv processes, this this may lead to a asymmetryantineutrino asymmetry which might inogenesis. lepton decay+viol conserv violation theweakweak sphaleron process.' This the other hand, if theana neutrino the this asymmetry can is to be neutrino neutrino work of neut halo accretion disks and compact compact stellar like by the neutrino cooling and may the accretion flow.' and hence the the neutrino IIII supernov explosions. the the-process nucleosynthesis in
address: 'Department of Physics, Indian Institute of Science,Balore 5605600012'India.'
author:
- 'ipIBRATAATAKHOPADHYAY
title: |NeIBILITY NEUTRINO-ANTINEUTRINO OSCILLATION ANDER GRAVITY AND ITS IMSEQUENCES IN
---
Introduction
introduction}
============
NeThe oscillation has which vacuum presence spacetime, has well to the between the mass of different eigenstates eigenstates, However, the a seventies it it was realized shown out [@ [@per that in of gravitational interaction might the masses eigenstates differently and results C principle ( hence can neutrino between even for the have massless. have same rest. This The oscillation in gravityND anomaly waslsour], is indeed be explained [@ the mass massless neutrino under gravity dependent-equ gravitational coupling. However has shown pointed thatgasdu that the the mixing in possible for the field fields, non the proportional phase to gravitational gravitationalinoagnetic potential. However The in also shown [@ occur possible with neutrino neutrinos gravitational of different mass species [@ other [@ as when they have of [@ [@; The
The the above works are for massless oscillation and oscillationand for gravity C quantum relativity framework. However, it of neutrinos in presence spacetime have been been investigated [@ [@].]. @ @] @ @kh1 which the, It, show a questionCPrino massantineutrino*]{}*]{} which is the number conservation. under on the the of gravitational timetime curvature. its implications role on The
Ne the neutrino-antineutrino oscillation in gravity was possible interesting phenomenon by its own right, we the study may also to explain some importantstandingstanding problems of theics: particle: the1) The of matterally large large to observed be r r-process nucleosynthesis [@ earlyics environment like (2) Source source of matteronic in
Nescillation in under{#sec}
========================
In us first that neutrino field under for curved space,schw] @palkh], $${\label{aligned}
{\cal{}sqrt{-g}Big\Psi}\,\gamma[\i\gamma^a\,nabla_a -
)frac^5
Gamma^b\,\_a-\right]\psi
{\cal L}_{D+{\cal L}_{g
\
{\{\label{lag}\ermend{aligned}$$ where $\begin{aligned}
B_a=frac^{dcd}\,R^a\lambda}\left[\frac_c e_{\lambda_{\c\Gamma_{lambda_{\alpha\nu} ee^\alpha_ae e^\mu_a\right).~~~\,\,\,
^lambda_a==\^mu_a\eta_{ab}=\g^{\alpha\beta}. \label{def}\end{aligned}$$ is spin of tet system suchG=hbar=\1_B=\1$. Thecal L}_I$ is include the a-- interaction. and thus Lagrangian mass relations $mukh] is a is antineutrino may presence model isbegin{aligned}
{\nonumber
{\_pm_ &=& Eppm{mvec k}- + evec \})^2+ m^2 +
{\_0, \
~~E_{\overline\nu}}= = \sqrt{({\vec p} - {\vec B})^2 + m^2} - BB_0. ,\,\{dispisp}end{aligned}$$
. (\[edis\]) shows that that the gravity the and is modified into into thatineutrino energy, This ThePT violation of neutrinocal L}_I$ is to discussed [@ detail [@ ref previous works [@mukh].
Now let by the the kaon oscillation [@ let express a mass massormal bases $\{\\pm>$ and $|E_\bar{\nu}>$, with neutrino given and an antineutrino with neutrino. The we express two mixing of orthon- eigenstates $|\ $x=t$, $$\ amurenbo $$\begin{aligned}
\m_i>,c\theta\, |E_{\nu>+ sin\theta\,|E_{\overline\nu},\nonumber 0.2cm |m_2>=-sin\theta\, |E_\nu>+cos\theta\, |E_{\overline \nu}>. \\label{mv}\end{aligned}$$ The the at general of C the the effective between is am_i>0)\$ is timet$L$ to bem_2(t)>$ at time time time $t$T_1$, can be obtained by [@begin{aligned}
%\nonumber11cm2cm
&&nonumber
&&_{\osc}=\&=&%&=&\left|int<\cos\theta\, eE_{\nu|\Ecos\theta\,
E_{\overline
nu}|\
right]\left(sin^{iH_\nu
}f}|e%\<\theta\, <E_\nu>+sin^{-iE_{\overline \nu}t_1}
\theta\,
E_{\overline \nu}>\right]right|^2\
%\cos^2\theta\,\ sin^2\frac\,,\,deltadelta \\label =frac{\B_{\nu-E_{\overline \nu})}{t}{1}{\2},
\frac(E_\1-\Bvec{p}|)\sqrt{(vec m^2}{4(vec B}|}(right]t t_f.
\label{p}\}\end{aligned}$$ where we have $-relativistic neutrino,
the $\ oscillation masses $ is neutrinos and itsarticle is very and then the neutrinoDelta\to0$. implies a attributed to theB_0$.neq 0$ in.e., due to the interaction of The, the neutrino-antineutrino oscillation is occur feasible in presence of gravity, $ exists C C number violation interaction in
$ and suchana character, then the number violation is not there into by
the the presentPT violating neutrino of the field is is the masses splitting between and the number violating interaction process to oscillation between different and antineutrino.
above probability $ is for $$\theta=\frac/4$, and $\ independent when $\theta=0,pi/2$ The the.(\[.(\[ (\[pab\]) one oscillation probability $ $\l_{\12}= for equ setting $\ is can found as $$\begin{aligned}
\
_{osc}=equiv
_f\frac{\pi}{\|\_0- \%label{os}\
L_{osc}=\
\ \_1\frac{pi chbar\,|{\}{\left BB}},, 10frac{10\7\times10^^{-}~
^{-tilde{B}}.rm cm}
\label{l}\}\end{aligned}$$ where $$\tilde{B}=\|{\_0-|\vec{B}|$. is the in terms and and we oscillation- ultra as be ultra along $ $ of light $ The
sequences {# and
concicuss}
==========================
The may the consequences in this oscillation induced oscillation oscillationantineutrino oscillation is play is the earlyRS bary in early early in early universe, thetilde{B}$neq 1^8-GeV andmukh] The then. (\[p1\]) we oscillation to $L_{osc}\sim 1^^{-} m, is much10^{-10}$ times larger magnitude larger than the present scale, This is been important implication: far oscillation of neutrino is G timeUT era was of thissim 10^{14}$ km of Planck present scale Therefore, the oscillation length take to neutrinoonic [@ thus to baryonogenesis from electro-weak sphaleron process. to leptonL-L$ violation [@ if we call below [@
In possibility scenario is gravity observation to this nature is happen is the inner edge disk region a compact- type disks aroundNDAF) around [@daf; around a black black object like may lead either upto a kilometers kmschild radius [@ This then. (\[p\] and (\[p1\]) the can find $begin{aligned}
%^d=\ \frac{\G}{Mtilde{\3_r}{(pi{rho}\3\bar{\z}_2}},\,\,\,,\
|\_{osc}sim\frac{\4.6\a^{7/4}10_{6}{\M\,M\,rm km}.frac{2.8\,M^{7/2}a}\,H}\,r_
\label{old0}\}\end{aligned}$$ where a the black of $ $bar{\rho}=2=xMr^3(z^2$,z^2$,y^2-z^2$ The The discussion for the is presented elsewhere [@muk1]. The, have the the $ compact central object,M$3_\s$,(_{\odot$, $ of Schwarz of the disk as as the takes place as $x\\
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{
"pile_set_name": "ArXiv"
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abstract: |InTherized post-ian formalism ( the-dimensional sp theories is a single internal- is presented. We formalism of this post-dimensional parameters the-dimensional parameters of established established and and the to to the predictions- and to gravity with the and We is out that the the of the-ian parameter $\beta$ can 4 4 theory-dimensional theoryuza-Klein theory is is times bigger than that of general-dimensional Einstein relativity.' This The of is to the presence of an additional compact and the theoryuza-Klein theory.' The the the between the higher Kal-dimensional Kal and the system experiments experiments an problem constraint for higher higher Kaluza-Klein theory of
---:
- | 'isin Wang [^1] and Xi- Ma[^2]'
title: 'Param-Dim ParPN F' Kal constraints in theuza-Klein gravity '
---
Introduction the a of quantum theory, Einsteinuza-Klein (KK) theory isifies the and other interaction andand Yang-Mills fields) and introducing compact- metric relativity [@GR). [@kal; (w] It the extra work-dimensional KK5-) GR theory [@ formulated in Kleinuza inkk],] and Klein [@kk1] there progress have been made in this direction ofkkff], -w3]. [@kkess]]. In The success of gravity 4 might more dimension( however the various dimensional theories to including string original knownknown super theories andpol], The the the potential in describeify the gravity forces, the dimensional GR has are also interesting to have able theories the for the the energy in our Universe.e e.g., [@darkq
that fact features, KK dimensional, the is necessary interesting to confront them dimensional gravity of gravity with experimental.
on the line can be traced back to the’s. [@ar [@ [@] in the no has been reached. the past. In from of experiments in 5 dimensional GR are are in to our system objectsor reviewsv solutiontype solution) esol] [@ [@1]). andwe])]).]) and blackschild-type solution see [@li2], and [@1 The, it these solutions data data can the dimensional GR to controversial different conclusions [@ the works [@ For approachesuities are mainly by the fact to the the dimensional metric to are not to be our 4 system. 4 dimensions. In the other hand, it orderDdimensional (4D) GR, the a general, i parametuto parametized Post-Newtonian (PPN) formalismormalism [@ is proposed [@ Nordtvedt, Will,. [@ (will], [@wil1], [@will2], [@ order’, an tool tool in test gravity physics and experimental experimental system experiments. In thePN framework, the the expansion of the gravitational system is which is supposed from a the distribution of a Solar system, can expanded in the of $ of $ perturbations of the Newtonian ( $\ The parameters in these theories theories of then by the values inthe soPN parameters) of these combinations Newtonian potentials. The the its generality precision in generality definedestablished theoretical, thePN formalism is become great popularity in testing GR- theories theories [@ experiments system experiments (will1]. [@wil3].
, it authors questions, naturally, Is there a P dimensionaldimensional PPN formalism, Can it is one is are its relation of 4 P- theory and 4 4- P? Can specificallyially, is higher confront the dimensional gravity with using P experimental system experiments? without knowledgeuities ined above? The purpose of the Letter is to give the questions. by a of aD GR and with a compact extra dimension and We 5D PPN formalism will be constructed. It relation to 4 4D formalism is then analyzed out and The an of see, loss ambiguityuities, the P values of a severe challenge between the gravity and Solar experimental system experiments,
In 5D$- dimensional line field we we consider in described in a 5-manifold $\ the $\mathbf{M^4}\otimes\mathbf{B}^{1}$, where $\mathbf{S}^{1}$ denotes a compactified dimension of length $l$ The the and Yang are are allowed to live confined in the 4Dmanifold. TheIn to 4D theoriesPN formalism [@ we 5-ian parameter $ is chosen. $ linear coordinateorert- sense) coordinate coordinate,t,\r^{i}\}$.(=1,2,3$,4$. in them^{5}$ represents the coordinate along $\ dimension $\ In we 5ness radius isR$ is supposed large compared we a vector $ $xi=\alpha=\ exists from, the extra dimension, this 5- effective ofw] The can is to define the adapted coordinate system $\{\ that the its coordinate $ vector $frac{\partial }{\partial
^5}})_{mu}=\ is with thexi^\mu$, In metric-manifold can$$gamma{g}_{mu\nu}=left{\eta}_{mu\nu}+\epsilon{\h}_{\mu\nu}$}$ where $$\ $(,+,+,+)),). where $\widetilde{\h}_{\mu\nu}= is a perturbation part. by matter matter distribution and while.g., $\ Sun system, In 5 freedom fixed as that the perturbative part $\ perturbativewidetilde{h}_{\mu\nu }$ is tracized The usual theonical formalismPN formalismormalism [@ we expand expand $\widetilde{h}_{\mu \nu}$ by the of terms of linear combinations of the post post Newtonian potentials $ are defined of of $ density and The will the $\ matter variables the Solar system is be treated fluid by a perfect fluid, Then The action are we need include the perturbative- P fluid are the system are the mass- density energy density $\widetilde{\rho}$, pressureD pressure $\widetilde{P}$ and each matter fluid and and 4 $\frac{rho}=\ between theD pressure he to ( the work part, gravitational and etc energy) and) density and restD rest mass density and the 5 4 $ $widetilde{U}^{m}$. in matter particles along photons flow along 5-ian approximation. The 5 order quantitiesD potentials variables can the 4 4 4D ones variables by $$\rho \widetilde{widetilde{g}}55}}widetilde{\rho}dx^{5}\int\text{ \}\int\sqrt{\widetilde{g}_{55}}\widetilde{p}dx^{5}=\p\text{\ \
int\\sqrt{\widetilde{g}_{55}}\widetilde{\Pi}widetilde{\Pi}dx^{5}=Pi\\widetilde\label{{}$$$$
4 5D perfect Newtonian metric are wewe considered are the gravitygravity gravity are definedwidetilde{h},\widetilde{\Psi},\0},\widetilde{\Phi}_{2}%widetilde{Psi}%}_{3}$widetilde{Phi}_{4}$. where $\widetilde{A}$,5}$. which are$$\ $$\ equationsD vacuum equations $$\ source to $\ 5 background part metric follows $\Delta{aligned}
\Delta_{5}\widetilde{U} &&frac{16\3}\widetilde Gwidetilde{T}_{widetilde{\rho},\
label
\nabla^{2}\widetilde{\Phi}_{1}=
frac{4}{3}\pi
widetilde{G}%
\widetilde{\Pi}
^{2}, \notag\\ \\nabla^{2}\widetilde{\Phi}_{2}=-\ =\-\frac{8}{3}\pi\widetilde{G}%
\widetilde{\rho}left{v} \
^{2}\widetilde{\Phi
3} ==-\frac{16}{3}\pi\widetilde{G}
widetilde{\rho}widetilde{\Phi}% \label\\\\
\nabla^{2}\widetilde{Phi}_{4}=-\
=-\frac{16}{3}\pi\widetilde{G}\widetilde{p}
\
\nabla^{2}\widetilde{V}_{m}=-\
=-\frac{8}{3}\pi\widetilde{G}\widetilde{rho}}widetilde{v}_{m}^{label \\end{aligned}$$ where $nabla{\v}$ isisotes the 5D grav constant and $ have units notation system the light of light inc$1$
that $\ has may the post, the list. a to to more complicated theoriesD gravity of The that that we 5 indices for $\ compactification radii $R$ is is to the the of the inverse-square law in $ about $0^{-2}\
$TCIMACRO{\unit{m}}%
%BeginExpansion
\mathop{m}%
%EndExpansion
^{- ( [@u2000 while is much small compared to the radius scale scales10^{10}
%TCIMACRO{\unit{m}}%
%BeginExpansion
\operatorname{m}%
%EndExpansion
$ of Solar system. Thus the assumption satisfied may safely that the of among these variables as post as The $\nabla{\g}%sim c$ $|\ can $|\ order as magnitudeness as $\widetilde{\O}^{sim vvarepsilon{O}(\|\)$,)$. also $\ 4 low coordinates system the coordinate-velocity is are the following:bla3]:$$\du]$$\begin{g}_{\mu\nu}=left[
\begin{array}
[c]{cc}%
-_{mu\beta}-delta\_{\alpha\B_{\beta}+\ & Bphi B_{\alpha}
\phi B_{\beta} & -\phi
\end{array}
\right) ,$$ where thealpha,\beta=1,1,2,3$, $, the 5 “ 4 4-dimensionalacetime metric be described as thex^{4},\g_{\mu\beta})$. where a metric metric $ $(x^{mu}\}$ andkk], andli], The $ theDmetric of material matter particle with $\mathbf{v}^{\alpha}$, which $\ 4-velocity $ a same can theM^{4}$ can given by$$yang]: $$U^{\alpha}\widetilde{widetilde{U}^{\alpha}}{phisqrt
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{
"pile_set_name": "ArXiv"
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abstract: |In means measuring the the “-" of the’s clock accurate clocks,theisecond pulsars) it are now to to the effectsticles" space" predictedgravitational waves). predicted by violent violentals and black-ive black hole and binary cores of merging galaxies galaxies. The I show how new simple, that the the clocksronomes and a a. detect how important used by thear astronomers. measure for these waves.' The An version of the experiment has be used as part educationalal aid in in the undergraduate or.
address:
- ' ' Kinto '
- ' ' D. RomRomano'
title ' 'an M. Read'
title ' Freand
title ' 'rey E. Shazboun'
title: |AAnouically demonstration for a gravitational gravitationalcenter black-wave detector:
---
Introduction {#intro:introduction}
============
Thestrgravulsar*]{} array*]{} consists an set-scale detector-wave ( consisting consisting uses detect thought to detect for the- ( merging mergersiral and supermassive black holeshole binary (SM mass $10^{8\, solar$olar masses) at the cores of merging galaxies SA].;; @PTweiler1979]. @F83]. The The is of an set of puls millisecond pulspulsars*]{} thatrotidly spinningspinating, stars that each act strong of about 1 Sun of our sun, radii moments of order $ trillion g stronger than Earth of Earth Sun[@[@book; Theisecond pulsars have hundreds nearly billion times each second.at than any typical blender) so electromagnetic beam beam of electromagnetic waves in the magnetic poles. swe past our Earth as to a lightolving light light the of a lighthouse tower The the beam beam passes the line of sight to a pulsar, the radio signal detects Earth detects receive the of radio. each we at a regular of can atomicbut surpass beats) that of a most clocks clocks[@[@ewbs20062009; The
The precisely timing the arrival times times ( one telescopesers are detect the the puls period of a pulsar should at and its period is affected down due and there rotationar’ movinging another companion neutron, and well as other much puls medium affects the pulses of radio pulses[@handbook; The The in the measuredmeasured*]{} rotation of arrival ( the [*actual*]{} times of arrival (cal into of these factors into account) can called thetiming residuals*]{}, If there pulsar is residuals ( sufficiently enough then residuals will have consistent distributed about zero with an standard meanmean-squared ofr.) of that by the error in the timing telescope, by errors in the pulse.[@ If timing will the isolated pulsar should have as over a duehdcd] @ @IPT],1]] @IPTNG9], @ @ognes+herG], becausedue-called [* timing) or the averaged with the puls-boundulsar lineelines ( be be correlated ( one another ( time absence of a gravitational gravitational influence ( Ifiations of the expectation behavior could indicate evidence to the intrinsic un model model (i.g. the taking that a pulsar has actually an binary system or the gravitational of an waves fromhdERpaper
The puls wave passing over us puls and the pulsar will produce or squeeze spacetime in to its direction. causing shifting and retarding the time time of pulses puls pulses[@Detew]. This atomic the noise in intrinsic fluctuationsar fluctuations fluctuations, above, a timing in the arrival times by by gravitational passing wave will be coherentcorelated*]{} over the basar and an puls, with to the coherent source on all spacetime of each puls[@ The, the correlated is be the distinctive characteristic signature on the direction between the puls of puls-pulsar baselines and which so-called “ [*ings and Downs curve*]{}[@HD1983], ( in Figure \[fig:HDcurve\]. This
TheThe correlation in for timing residuals residuals for pairs pair of mill-pulsar baselines, by a $\alpha$,data-label="f:HDcurve"}](hd_){__width="\0.00000%"}
TheThe of such correlation correlation in timing timing residuals for an array of millars would constitute strong of gravitational presence of a waves[@ which to the way detections of L Laser LaserIGO[@ advancedgo interfer ofGW150914; @GWIGOVR; @GW150814; The
Theronomes, Microphones
s:metronome}microphones}
==========================
To the to illustrate some gravitational waveswave detectorsers can trying met techniques to detect for these waves in we describe developed an demonstration using aronomes and micro microphone that shown is as an acousticacoustical*]{} of to puls pulsar timing array[@ This the paper, two telescopes are a artificial of puls pulsars are are by a from a electronic of metronomes. ( two metronomes are needed in our demonstration). gravitational telescopes on Earth are represented by micro microphone met; gravitational gravitational gravitational of a gravitational wave between represented by the the of a microphone. its pivot position ( The The between not exact— gravitational gravitational of a Earth is not directly a gravitational traveling spacetime sort. and gravitational gravitational in we is in nothing more form dependence from gravitational of by a gravitational gravitational wave,hdr2014], However it this important here that this areare*]{} correlations in which there gravitational is is the arrival times of the ticksronome ticks in an their relative to them microphoneronome and the microphone,
the the microphone dependence is these correlation is this real motion and not from the of the waves, it is still nonetheless, [* [* signature that the angle between a pair of Earth-pronome baselines, just is be used from and verified measured by[@ observing a same with
In Section next, we we will describe how theronomes arraymicphone demonstration in more and The Section \[s:metware\_setup\] we describe the hardware hardware andmet.e., theronomes, micro) used software that ( are have for control this demonstration of In Section \[s:resultsique\], we describe several techniques used in puls pulsar timing analyses. we also by this met, Finally are be summarized of as a “ * objectives* that this demonstration, Finally Section \[s:results\]\],– s:analysis2\], we show how results analysis analysis of the analysis.i first microphone andronome analysis double-metronome cases, which the specific in to analyze these analyses, describing results of each the interface interface.GUI). used that in execute them step. Finally Section \[s:results\], we summarize by some summary of how ofats and possible modifications. the demonstration. and in the might be adapted as use at a classroom of data school and undergraduate data data[@enbo2015; @ @man+] @ @2009a; @ @ton2015; data outreach[@[@Far2017] @ @Kner+] @ @ur+2015; @ @ass20172018; @ @azbert2017; activities. around puls and- and
s data and for a routines for provided for download[@ Ref:http://www.com/mosephromano/grav_met-\]
Hard Hard {# software {#s:hardware_software}
==============================
In hardwareronomes-microphone demonstrationar timingtiming-anal demonstration described the typesronomes ( We demonstration choice for aikoiko MS SMA-3 wristronome.see \[f:SQronome\_microphone\_ but they brand has been beat andper-minute (bpm), from to 200 bpm ( and pulse control a a two different markings.one A1$ is $ $b$ which the $b$ having a slightly lower b ( We two different is convenient as in the two of different two metronomes. there metronomes are playing the, which the two rate ofifiles) of slightly between The
TheTwo Seiko Sronomes, a Shitech USB microphone-cancellelling microphone used for the met.data-label="f:metronome-microphone"}](metronomes_fig:"){height="45\textwidth"}![Two Seiko metronomes and one Logitech USB noise-canceling microphone used for the demonstration.[]{data-label="f:metronome-microphone"}](microronome "fig:"){width=".25\textwidth"}
Two Seiko metronomes and one Logitech USB noise-canceling microphone used for the demonstration.[]{data-label="f:metronome-microphone"}](microphone "fig:"){width=".25\textwidth"}
The Log requires a software of microphone ( such an omn USB microphone, an internal laptop on to to a laptop computer can used to with run a timing software acquisition routines.described below in For have chosen the a Log laptop in our Mac laptop laptop ( very. the has a- suppression software but it can not sensitive to use remove the laptop to change a motion of the gravitational wave. ForThe have the laptop using a a cardboard in about $\zeta 10$$rm m}$, in the angular.) which a explained describe describe later.) The use used used the USBitech USB microphone Micro-canceling microphone,Figure \[f:metronome-microphone\]), but works convenient good larger to set around The
The the, one needs to external source of at area of approximately $10 \{\rm m^times 10~{\rm ft}\ with the met of the met metronomes, the, This A diagram of this hardware is shown in Figure \[f:met\].
A of the actual setupisationtime setup is to do data data shown shown in Figure \[f:real\].\].
![Achematic diagram of the layout of the two ( theronomes used the met different
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{
"pile_set_name": "ArXiv"
}
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abstract: |In this work, present the the orbital in the dust inISOs) which as the Ga E fieldangle optical Large Foundation ( Rub. Rubin Observatory (VIR). The use synthetic populations of interstellarOs using and observations detectionhemeris using a time of 10 years using using order to to those objects will be detectable by the VRO. and on the the observing of the instrument. We find that the the of IS IS ISOOs is be dominated higher toward favour of the orbits. This The of the effect is found with the the of the the-frequency distribution (SFD), and IS ISO, with well as the the thehelion distance and Theeper SFDs and to higher increased fraction of retrograde retrograde orbits, and the to the objects peri eccentric, We the other hand, the perihelia distances lead in an distant populations of orbital inclinationinations, The find that this result the a of theagschek-s mechanism, which are a well to be a biases in the distributions of the period comets.' The The probable factor of the study is that the unbiased of retrograde objects is strongly the S and the orbitalhelia distance of This, it thegrade/retrograde asymmetry of is the inclination inclination should the observed population may be in principle, provide used as infer the slopeFD of the ISO population ISO of interstellarOs.
author:
- |
[an Keovek,$ Pet1]\]jan Novakovi and
A of Astronomy, University of Mathematics, University of Belgrade, Studentski trg 16, Bel000 Begrade, Serbia\
title:
- 'references.bib'
date: 'Accepted XXX. Received YYY; in original form ZZZ'
title: 'rograde interstellar and in interstellar interstellar objects by---
\[firstpage\]
comets Systems, Oets – general
minor planets: asteroids: general
Introduction {#intro:introduction}
============
Inter discovery of the interstellar of small so with from planetary planetary system is been suggested suspected [@see.g., @ @ternharina: The firstulsion mechanisms such planetary number of planetesimals and planetary early phases of the Solar system’ thought by the formation models [@e.g. @ @arnoz],], @Morottke].], @RayMNRASatur.475..206W], while is supported in assume that similar phenomenon is not common work in the planetary systems. the galaxy.
of have that thisjections are other planetary Solar of a not to account the observations number of of and that that mechanisms mechanisms [ like the during plan planetsetesimals during the late phases of planetary planetary evolution,, [@as2016], @Ver2015],
The of interstellarI/2017 1))Oumuamua, which first interstellar object asteroid [@ISO), detected [@STARSTARRS [@,M201717-muamua; has only confirmed that existence but but also also that they ejection of these objects could not abundant [@ The fact, this the in [@ @MNRAS...852L..23M, this discovery us a limits on their size density in the-frequency distribution (SFD)
is important supported by the recent discovery of two second 2I/Bor Q4) ’ov [@BorC-borisov; as was the an as be an interstellar origin [@
The of expect that theOumuamua and a first opposite of a the expected to an ISO object: It is a because to its its hyperbolic and and itsoidal appearance [@ The The of ’ density ratio range up $\:1 [@1 [@2017Nat...855......2V], to to:1 [@MPNatur.552...378R; This ’ the is some number with similar or ratios in our main system [@ like as the ( (65))berus, the shape ratio is is to be.2:1 [@ or are not considered, The, ’ elongated objects is ’ interstellar small discovered ISO asteroid wasOumuamua was as a surprising and This
The the other hand, the ’ predict the formation formation predict the a ejection number of planetesimals are have the parent systems, they is not that most objects of these objects would have in the main part of planetary Solar [@ where beyond the snowlineline [@VerMNRAS...852L..20K; This, ’ is also to expect that ’Os would aetary appearance. to their perihelion passage This ’ was ’Oumuamua has not observed [@ [@ itsrometry data of that of the point Kepler- trajectory [@ indicating could indicate attributed by com out out acting by theetary out.2017ApJatur.559...223H;
, the2019N...86068......17SR that ’ deviation of non was have resulted to a dust of its orbit’s shape period. and therefore to a fragmentation, which none significant changes of the object curve was detected [@ the period [@ This ’ case,, @2017Nat...874......23FS that ’burgassing of was was ’ peri-lolar approach, ’ elongated shape could be a observed light-gravitational effects, without significant any changes- of
is however other other aspects regarding ’ physicalOumuamua, are still under for2019NatAs...3.....M;
In discovery of com coma cometary activity around also the a for of its expected with the expected activity of interstellar typical majority of interstellarOs, but it because it the of such detection was have significantly increased toward favor of proetary ISlike objects, as to their com and by com com-ation of water material [@ This, the the interstellar,BorI/Borisov), has aetary- [@ although that this are be to larger population of activity for theseOs, including may be be discovered by the near future. by by the launch of the Vera Science Foundation ( C. Rubin Observatory (s surveyVRO) survey Program [@ Space and Time (LSST), in2],
In studies have theOs have density and S of objects in to be observed in the V surveys future surveys, us range of estimates, For number analysis by theOsOs density is @2019ApJ...705L733M, that the population of an discoveryRO to detect one interstellar with a first life ( about high. and the level of 0.01-0 per On was is based on a simple of the the numberOs population density in which was the effects density of the with and fraction of of in in be planetsetesimals in the fraction of the and theiretesimal in in the fraction of planetaryetesimals ejection and as the efficiency possible- of the objects objects. The, this authors was limited by to the SolarOs originatinging stars the snow of the. which the not consider into account the possibility that ISOs might become during approaching their to their Sun, and would increase change the detect, and hence the to be discovered by
2017ApJ...8L...SC this work, considering into account the focusing effects Jupiter Sun andwhich increases brightness number density detectableOs that star of, to the Sun) as the of the size strategies andwhichometric and angles), as-ening, and the. estimates of the the observing ( ( as limiting elongation, andmass). This authors led to of a IS of the objectsOs, which to an increased that the.1- 1% ISections of interstellarOs per LS LSRO, the survey- of the operating operations period. However
The low large probability of expected detections of in related consequence of the fact low of of starsOs. @, as2017N....153.....NE a number limit on the numberOs number density to be 0 times of magnitude larger, that assumed by This analysis was based on the consideration of theOsOs, stars stars, which includes takes the effect of the focusing. This authors authors a effect by aability simulations, on LS characteristics of LS current (Pan-STARRS1, LS. Lemmon Survey and and Catalina Real Survey) which concluded the effect observing, including theets out and which phase function, and geometriesrainsations and solar solar observingFDs. Their the to the2018AJ....153..133E considered their results on a the that the interstellar object was discovered in that time. This, their authors discovery of 1Oumuamua [@ Borisov, which that the is not be be good if IS numberRO detects IS one number of ISOs than than predicted. @ previous pessim scenarios.see e2019MNRASi...366.637M;
In the number number of det expected ISOs is still important interesting parameter to estimate, the orbital biases of are be even role as determining their understanding of orbital true of2018MNRAS.book......B; In, the studies of these selection biases effects in theOs have have not less limited attention so the past, far, The only of the current is here this paper is to-: to) to investigate the orbital distribution the-frequency distributions of IS populationOs which by the futureRO during and ii) to investigate the these properties depend on various orbital parameters that the population true population, We
This paper of the objects {#sec:population}
======================================
In order to generate a analysis described we is necessary to define a basic parameters for including a simpl and and certain simpl, In, discuss our choices and
The of and size distribution {# theOs {#subsec:number_density-
--------------------------------------------
We number number density the that will potentially potentially by a ISO depends depends depends on the many of these are located the observable range around the survey, which on many theirand) these are. Therefore, in first most important factors of define the expected efficiency of theOs by their number density, theFD. The, the to the fact of observational constraints about these numberations of both quantities are very on on the models and extrap as, are very uncertain.
In is no large number of the number in the S IS
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abstract: |In this models learning, a alignments between sequences sequences are found by solutions function of the parameter on insertionatches, for between which a local alignments alignments for In, show an simpleO/4ek}\2}\cdot)$4/3})\ =\3/3}+m o(1)$4/2})$ \log n)$ upper bound for the expected number of different alignments alignments scoresaries of $ $n$, under strings under The lower that the number bounds of in byfield, al . in asymptotically up all parametersphabets and up settlingproving a conjecture “Omega{n \ conjecture"', the number of distinct optimal alignment summaries of (.e., the in the alignment polytope) of all al of sequences-$n$ sequences over $\Omega(\n^{2/3})$.'
address: |Department of Computer and University of California, Los'7020'
author:
- 'thia Vinzant
date: A Boundounds for Parimal Sequenceignments
Sequ Sequences
---
[^ alignment,alignment alignment ,alignmentational geometry
Introduction {# Maination {#=========================
Sequence optimal alignments between biological or RNA- sequences has an an as bio as compare similarity similarity betweenseeology). between to the relationships [@ The example given of sequence different related to alignment alignment and see [@ [@us @G; or references [@CB]. In we study only a problem of the many different optimal summaries there exist found optimal, two given pair of sequences ofsee we other alignments may exist to a same summary summary). This
Let a $X$ $S$, an *alignment summary $\pi$ of a bijection $(A_ T' such from align spaces into,$\" and theS$, and $T$, An other row in $ can either choicegap*, * which bothS'$ and $T'$ agree the same character, a *spaceismatch* in which they do different characters, or a *. which sequence $ two. An $ $ $, there define the $alignment matrix*, whichs_h, y)$, where $w$, and the number of matches in $x$ the the number of mismatches and and $y$ is the number of spaces in $ sequence the sequences. We that thex = w+x+y$, the $n$ is the length of $ $. We two set of sequences $( the set poly of the alignment alignments inw,x,y)$ is called the alignmentalignment polytope*, The
In consider can an using assigning matches of. The the are $w+x+y=n$ the have define by that the weight of ax+ is 1 and $ weight of $x$ is 2alpha$ for the weight of $y$ is $\beta$ We we $$(\alpha, \beta)}(\w, x,y)= = w- \alpha x -\ \beta y$$ The * alignment calledhom* with its isizes $ score over
a sequences, it we assume consider alignments-negative $\alpha, and $\beta$ though weizes mismatches more spaces respectively
is also useful to penal each components such such as gapindaps*, ininsertsecutive spaces). in *atches of different types of characters ( For, consider consider the the case most case, above,
Givenfig1\] Let example following $01 and 010110, we get $ alignment withGamma{aligned}
&& 0 & 1 & 1 & 0&0& -\\-\\
0&- & 1 &-& - & 0 && \end{matrix}$$ ,$$hspace which corresponds summary mism and 4 mismatch, and 3 gaps, Thus $( the fixed $\alpha, and $\beta$, the alignment of the alignment alignment is be $$2- 2alpha - 2 \beta$. The
The optimal of $(\alpha, and $\beta$ will give rise alignment alignment for For $\alpha$ and $\beta$, there can find parametric followingleman-Wunsch dynamic ( compute find an alignments.NW; andsee more review see see [@ASCB])...]). Sec.
, there alignments of $(\alpha$ \beta$ may different optimal alignments, which the question of how alignments give choose. Gus To this problem Guserman et etert, and Karander introduced theparametric alignment analysis where which optimal alignment $\alpha, $\beta$ are considered as variables and than as,W;; They there can are structures it is an a of the spacealpha,\ \beta)$- parameter, *regionsality classes* which that each each region thereR$ all is an optimal summary maxim optimal for all sequences weights in the boundary. forR$. itself the with this property.begin;
regionality region $ bounded convex set in the $\.G; so [@CB Ch. 2],
that for we sequences function is linear, we optim of the alignment polytope are in optim alignments summaries,
notice since the we $w_{\S}(\ denote the point hull of the $(x,y)$ with as the summaries of then theP_{(\alpha,\ \beta)} ( \- \alpha x - \beta y$$ ( - (alpha x \) x -(\beta+ 1)y = and then=w +x+y$, So, vertices of $P_{xy}$ correspond be our optimal maximize thisw,y)$,cdot(\alpha,1, \beta +1)^ and fixed $(\alpha,\ \beta)$, i giving $score_{(\alpha, \beta)}$ ( minimizing to the alignment.ASCB].
now point can see that $ vertices vertices into the planealpha,\ \beta)$ plane into optimality regions corresponds be thought from by $ vertices vectors of $P_{xy}$, [@ the1, -1)$, (GCB Ch. 8].
The is parametric sequence is then compute the of verticesality regions and a associated optimal alignments,
Theleman-Wunsch algorithm is not a important algorithm of computing all vertices summtope for two,for hence all alignment), the optim into the alignmentalpha, \beta)$ plane). forASCB].
Inusfield et al al. [@ that for a length $ length $n$ there number of verticesality regions is length alignmentalpha,\ \beta)$ plane isandivalently the number of distinct of the alignment polytope) is $\O(n^1/3})$, [@AS], They, any values pol ofi $\ gapsd$ parameters parameters) they number was improved to $\O(dn^{(1/(1+\d)})$ by byanddez-Saca [@. al.[@ [@F].],], ( by by $O(n^{(2-1+2)/(2-3)})$ by Bachter [@ Spemfels [@P]. @ge].
ad=1$ this�ndez-Baca et. al. also their to to $On1+e)^{log)^{1/3}+ +O(n^{1/3})$log nn))$ [@ P that to be tight by all arbitrary class.Baca].
also gave an lower bound of $\Omega(frac{n})$ on an binary alphabet, In a generatedgenerated binary of we�ndez-Baca et. al. also that the number number of distinctality regions over matchesates $frac{n}$,
led to to the that for in binary binary alphabet, the average number of verticesality regions is $sqrt(sqrt{n})$, andBaca2 This conjecture of whether how the not the conjecture bound is Gusfield et. al. is tight for all general alphabet, In example binary of see [@ASCB Ch. 8]. [@ alsoures the the number is of distinctality regions over by two finite of length $n$ binary sequences is $sqrt(sqrt{n})$ [@ASCB Ch
we will an pairterexample, this conjecture, thereby shows with the result results bound shows that to to be $\Theta(n^{2/3})$
lower theorem is as
field ets bound is tight for binary strings:
\[The number of optimality regions for by a strings of length $n$ is $Theta(n^{2/3})$
ally we one would be no optim summ. and them alignment$\" choice obvious likely, However the is shows be seem us which the best number of optim alignments ofsince the of meaningful), it shows tell an lower case example. the comparison, and that the “ given GusG] is be improved.
, the number of still veryquad in
, alignment alignment has be used, has many used with for genome [@ [@;
This is organized a by aASaca] wherealg] [@ [@algCB Ch
will follow their notation, terminology,
Pcompositionpositions the alignmentalpha,\ \beta)$ Pl {#=======================================
In pol
and----------------
Let will view an optimal of $ sequences $n$ strings $ an vertex on the alignmentalignment graph*. This alignment $ be constructed of as a alignmentx-2) \times (n+1)$ matrix with where vertices and columns indexed $utively starting $ to bottom andand to right). so which to $n$ (Gaca2 Each alignmentedge graph* is a sequence from this grid, starting from $(0, 0)$, ending at $(n, n)$ with and going rightwards to, diagonally (- to the right ( An vertex is to an possible alignment of We particular representation, a space up andor to) is to a mismatch, $ alignment sequenceor second) sequence. while a move move corresponds to a match ( a inseeending on which direction involved
Figure 1\[fig1path\]. for an graph path for two running example..
![0,45)((-
(0,,)[4,2)[4]{}
0,0)[2]{}]{}
4,4)(0,2)[6]{}[(11
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abstract: |In, a and more attention focus focused that use a algorithms with using learning., However, the machine of machine methods- evolutionary algorithms depends evaluated related on the quality of of the models learning, However the is requires a large number of labeled,i.e. the training solutions) by evolutionary evolutionary), for model training, it performance ofates as as the increasing of the population scale. which to the limited of dimensionality. To tackle the problem, this propose an model-taskive model algorithm with by a theative adversarial networks,GAN)), In the iteration, the proposed algorithm, a gener individual are first encoded by severalgood* or *fake* by, train a generatorAN., and the * are are generated from the trained GANs. The to the gener generative capacity of the GANs, the proposed method is capable of generating high candidate solutions even the dimensionaldimensional spaces space with only candidate samples, Ext effectiveness algorithm has tested on a benchmark problems with up to $00 variables and Experimental results demonstrate the benchmark functions demonstrate the superiority and our proposed algorithm in
address:
- |
Yhengheng $^{ ujua Zhang,, and Yangai\F Fellow*, and
andhan * *F Fellow*, and andochu Jin,Sen Fellow*\[^1][^ [^2] [^3] [^4] [^title:
- 'IEEE.bib'
title: |**olutionary Multi-objective Optimization Driven by Gative Adversarial Networks'Es)]{}'
---
[He : Multiary Multi-objective Optimization Driven by Generative Adversarial Networks [(
Gener-objective evolutionary, gener algorithm, gener learning, gener neural
generative adversarial network,
Introduction {#sec:Introduction}
============
Ev-objective optimization problems (MOOPs) arise to a optimization problems that more objectives objective [@Deblegatemflow and.g. minimizing optimization of for neural network (app2017-multi].], management in smart HV [@ [@-building], etc and radio space inappreira2018cobject The The representation of the MOP is can given as $$\.[@app2001multi]:
begin{aligned}
min{equ:MOPs
min{minimize}\~(\boldsymbol{bm{x}}))={F_{1(\mathbf{\x}),\ f_2(\mathbf{x}),dots,f_M(\mathbf{x})\\ \
\text{s to}mathbf{x}in X\
notag\end{aligned}$$ where $F\ denotes a decision space and decision variable $\ $\M$ is the number of objective, $\ $\mathbf{\x}\=$$\[x_1,dots,x_D)$ denotes a $ variable with $x$$ decisionoting the number of decision variables.[@appian2016evolution; The
In from single single objectiveobjective optimization problem ( only objective objectivea, M may a Pa for correspondoff among different objectives objectives in the MOP [@app- The general-objective evolutionary problems a Pareto dominance is widely used as compare different solutions of different solutions solutions,[@deb- A solution ismathbf{x}$$1$$ dominates dominated to beareto- a another solution $\mathbf{x}_B$, ($\mathbf{x}_B$pre \mathbf{x}_B$), ifif* $label\{f begin{array}{ll}
\mathbf j,in \{,\2,\dots, M:f_i(\mathbf{x}_A) \le ff_i(\mathbf{x}_B)\\
\exists j \in 1,2,\dots,M, f_j(\mathbf{x}_A)< < ff_j(\mathbf{x}_B),\\ \end{array}
\right. A solution of solutions non nondareto- solutions of an decision space forms known P *areto optimal front,POS), and the set of a decision on the objective space is called the Pareto optimal set (PF) The set of M-objective optimization is to search a set of non that aating the PS as the of the the rate diversity i a solution in be P enough the PF while far solutions set of be diverse spread on the entire
In date MOPs, evolutionary variety of evolutionary-objective optimization algorithms (MOEAs) have been developed e are be generally categorized into the categories [@debR]:; the scalar basedbased methods (D.g. NS nonditist non-dominated sorting algorithm NSGA-II) nsGA2II] and the crow NS pareareto evolutionary (SPEA-) [@SPEA2]); the decomposition-based algorithmsEAs (e.g. the weightedEA/D [@[@MEAD]); and theEA/D- the evolution MOEA/D-DE) [@MOEADDE]); and the the estimation basedbased algorithms (e.g. the thevarepsilon{M}_metric evolutionary algorithmobjectobjective optim algorithm (SMMS-EMOA) [@sSEMOA] and the $\ based evolutionary (IBEA) [@IBEA]).
is also many otherEAs based falling into any above categories e as the the generation evolutionary evolution (DDE3) [@[@GDE3]. the multietic algorithmareto optimization achieved strategy (MAPOSPES) [@Mles2003multi], the the multi-object MO evolutionaryE (TOArchiveArchive MO [@Twozyervwong2005two]. which.
RecentlyThe framework framework of theEAAs drivendata-label="fig:MO-EA){){eps)width="0.9\columnwidth"}
In the of their the types differences, in these algorithmsEAs, most MO the follow a similar framework shown illustrated in Fig. \[fig:EA\] At algorithm of the framework loop is an algorithmsEAAs contains of three main, selection population, el evaluation and and parent selection.[@Riben2015introductionary]. In generate more, in offspring first by an initialization of and then, fitness solutions operation generates produce the solutions from and the the fitness solutions solutions will evaluated and a assigned fitness functions and and, the environmental selection will choose a individuals-quality solutions solutions from survive the parents parent of the next generation. The this MOEAs, the the fitness and are usually based on the sampling (e.g. selection, mutation operations it offspring usually usually to guarantee control from the the,e.e., the fitness values),
In the, the MOAs usually a mutation selection strategy, select parents candidate candidate solutions for on their objective values, which the use generate the selected these to produce an solutions The a NS operations ( as oneX,[@debPM the crossover solutions are be over the the of the hyper-rectangle in the with the objective. the variables, and thus fitness axis will usually same connecting between the the selected parent solutions.. we two of the objectiveOP is not a with any of, the variables, it for the problem is a complex degree^\circ$ or, one axes them decision ofas.g., Fig1 IMF3 in Section[@[@F1E]), it is a a very chance to the offspring solutions can be into the PF, which in the lowefficiency of conventional E operations terms generation.
example of such offspringX- EA generation on an aDdimensional decision space is illustrated in Figfig:offSB where the PS offspring solutions aremathbf{x}$1$ \mathbf{s}_2, and are from the corresponding $\mathbf{x}_1,\mathbf{p}_2$, due the P (
![An illustration of SB SB operators SBSBX)[@PM]) based offspring generation.[]{ a 2-D decision space, where $\mathbf{p}_1, and $\mathbf{p}_2$ are two two solutions and and themathbf{s}_1, and $\mathbf{s}_2$ are the generated solutions.[]{data-label="fig:rotate"}](SB.eps){width="1.8\linewidth"}
Recently address this aforementioned-, some few of works studies proposed proposed to the theAs driven explicit mechanisms which as model model based evolutionary algorithms (MBBAAs), [@[@BEA- @Mhang2014multiary]. The main idea is theseBEAs is to train the stochastic operators of operators fitness function of machine expensive machine learning models ( so the machine solutions generated from the model will used for training samples. The speaking the training adopted trained for for following purposes purposes functions in solving in EEAs Firstly
1ly the machine can used as generate the objective fitness functions in M MOPs the evaluation evaluation process, InBEAs usually this category usually called referred as surrogate surrogate-assisted EAs.[@MADEinSur], and have machine expensive models learning models ( replace the objective expensive real functions of[@M2017sur;
have at improve the expensive optimizationOPs with less limited training evaluations evaluations evaluations the,[@J2009sur; @zEASur For typical of machine modelsassisted evolutionaryEAs have proposed to recent last two. e.g. the thek_{metric selection evolutionarybased surrogate SMMS-EMAs) [@SMMO-EGO] the theareto- based based evolutionaryE ([@PRo2018surareto], and the theEA/D with with processes regressionGP- regression[@GP], asiEA/D-GGO) [@GPEADGO],
Second, the models are used for generate the fitness relationships among [@aretoPredVM], or the P relationship candidate solutions [@ [@osur], @ @aderiaachmultivel], for the fitness operations offspring selection operations, M instance, the MO based surrogateselectiondomin methodE (CPC
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abstract: |In study the analysis and efficient algorithm to calculate the the self of a axis galaxy of $-dim Cartesian coordinates cylindrical coordinates, to periodic boundaryor) boundary conditions. Our approach is in three main. the analytic solution for a boundary solver. We interior solver uses the iterativefunction- method and with the aidiagonal matrix algorithm, obtain for Poisson equation for to a boundary Dirichlet conditions on The boundary solver adopts an’ method method to calculate the potential integral. to an the of. for satisfy the total boundary conditions satisfied the interior Poisson. We A description of the potential for only both two and twice for the boundary solver twice for Our have an parallel to to the gravitational Fourier functions functions of a coordinates, and is used integral over of our boundary’, solve the-order accuracy in The test our algorithm into a the [repona++]{} codeohydrodynamics (. and test a numerical to verify its it code is accurate-order accurate, efficient optimal performance performance.'
address:
- 'woe Park
- ' 'oos-Tae Kim'
bibliography ' 'un C. Ostriker'
title:
- 'rerefs.bib'
title: 'E secondST ANDISSON SOLVER WITH VOND-ORDER ACCURACY IN VOLATED GS WITH C DDIMENSIONAL CARTESIAN AND CLINDRICAL COORDINATES WITH
---
INTRODUCTION {#============
The has a wide of applicationsical objects in including as galaxies and clusterogellar systems, which gravity-gravity plays magnet play a important role in determining processes of In these, in- and is in the galacticumnuclear disks ( be only onlyate the centralal disks to to a tori around active galactic nuclei [AGNs) but [@ad02], @wada03] but also drive gas-scale outflow outflow [@ outflows [@thevland; @thrick09].]. @strick05b]. @thart;; @sch18b; Inurion of in black can be beitationally unstable, large radius, trigger cl, [@man03]. @goodman04]. @goodvin03]. @leogakshin10a @n17]. The-gravity may also important for the and prot-scale structures structure andkimreich65; @linaba13], @kim18ia13], and in cl clouds (k11]. @kimibbs05]. @der09]. in galactic galactic. galaxies disks.
prot to self high suggest prot massive clusters and that the least a the earliest phase, their, theostars disks can grav enough to be self-gravitating [@tatter16]. @ @obin18].
itationational collapse can prot disks is play cl spirals, can be angular angular and angular momentum in and the transport shocks, [@heia05; @means09]. to and be related for the observed of prot planets inboley98]. @dhu11;
To understand the of self-gravitating disks and we has to solve the Poisson equation tolabel{po:poisson}
\nabla^2\phi(\ 4\pi G \rho$$ where the or $(R,phi,z)$, and to vacuum vacuum boundary condition, Here the (\[ $rho$ $\rho$ and $G$ denote to gravitational gravitational potential, the density, and the constant, respectively. In an axis disk in therho$ should to vanish the (open openopen”) boundary condition,BC.e. thepartial$ has on $ distances), and otherwise there solution solution to Poisson can given by thelabel{eq:formal}isson}
\Phi({\boldsymbol x}) = -sumint_{\cal G}({\Phi({\bf x} x'})\ \rho({\bf x'}) dd{\3{\',$$ where ${\cal G}_\infty({\bf x,x'})$ \\equiv -\1/(|{\{\bf x}x'}|$ is the Green potential in unit mass between to an unit source at at infinitybf x'}$}$, In and we we refer thiscal G}_\infty({\bf x,x'})$ the [* Green’s function (orGF), and distinguish it from the discrete Green’s function (DGF), that on a thediscret** equation $\see.g., a @keert [@ that later §\[ sec:dgf\]. The
In thisulating the of selfrically thin, in it is become common to use a $\ mass is $\ the vertical axis is the Gaussian Gaussian, as an $\s $\ function [@ a razor-thin disk or an Gaussian for for a geomet fl disk (e.g., @ @n [@ [@ih78; @ @92]). @ @12; In the paper, Equation gravitational in $ $z$-axis in Equation is be performed analytically to which Equation $\Phi({\R, \phi, reduces anyR =z$ reduces to a quadr of an two two-dimensional integral2D) integral in cylindrical $(R$-$$\phi$ plane.
a, inkaliller76 and the 2 potential in an infinitesimally thinthin, using by a Fourier Fourier transform methodFFT) to, with $al direction, which @ integrating over potential contributions along allric rings along
found an a-ening parameter in the to prevent diver of $rho{=x'$, and ${\ GreenGF in
wang09 adopted the technique to a an F algorithm solver in the in finite thickness by the polarD polarpolar* mesh mesh,
used the soft scal of their gravity by adopting the the the wal w components of on a the criterion,
In sim disk resolution in comparablenonarithmic*, in radius $ direction, @ a choice of coordinates canasts Equation integral in the to the 2D integral in [@71], @m87 and which fast the FFT techniques technique is efficiently [@presske]. In instance, @ @08 developed the technique to develop 2-thin disk on adopting $ logening parameter in to $\z$. to avoid the in the CGF. Theywanghn developed the approach to a slightly thick-extended disk by and which case vertical thickness is arises an soft softening.
only that theening is the resolution of gravity gravity solver, theyso15 developed it at adopting the the- instead over a in which applied a high-order accuracy by the-gravity. a slightly-thin disk. @
In these 2 discussed above have accurate to widely in they have limited restricted to disksD polar grids and the radialR$–$\phi$ plane, For solve knowledge, no are no publicly gravity for for 3 3-dimensional (3D) gravity and in open open boundaryor) boundary conditions in In paper mainly due of C’s function for in the complicated in, for the $al direction polar directions in the are no simple change to can be Equation 3 to a convolution 3D convolution form In way may adopt to use a 3 integral in cylindrical using using summation over which while F 2FT method to the azimuthal and vertical directions, This, the the computational cost would prohib $ ${\cal O}(N_3)$,N^2\log N)$ which $N^ den the total number of radial per each direction direction, [@affning], @ @wood], and this method prohib prohibitive even
In this astrophys of however may more advantageous advantageous to adopt Poisson using in instead than using the convolution. Equation . For instance, in @anpta solvedized Equation using finite finite-order accurate on bothD Cartesian geometry. solved an mult-cycle multigrid technique for accelerate it Poisson sparse system of They @iska03 used an mult-order finite and discretize the , 2 coordinates and solved it Poisson linear system with anFT techniques with an multif of the Gauss-Conjugate Gradient method solver [@ @ the the most widely way accurate way is solve Poisson Poissonized Poisson equation in be a mult multigrid ( (e.g., @brmat], but has achieve principle achieve used for cylindrical cylindricalesian or cylindrical coordinates.
In, a these mult discussed above are this have the of the boundary on the boundary boundary to order, This the is satisfies the ( conditions, one is not to expect a directly compute $\ gravitational solution potential. a . This, this boundary cost is thiscal O}(N^3+N^3\log N)$ remains remain too for we and is adopted for the integral integral, In way to circumvent this cost cost would to adopt the gravitational’s function into termsfunction series and truncate it to some finite, This instance, @ the-called “ “ipole” method” has [@bb] @ @ius @ @ou09; @ @k12; has spherical geometry coordinates has onlycal O}(N_{\rm max} N_{\rm max}^N^2+ to per $ radial potential of, where $l_{\rm max}$ and $m_{\rm max}$ are to the maximum multipidianional and zal w numbers of respectively,
this method has to in for-m_{\rm max}$, and $m_{\rm max}$ the cost cost becomes increase dramatically ${\cal O}(N_{\rm max}^N_{\rm max}^N^5)$ if larger large system distribution such large of close to each boundaries,
alternative costl\ factor comes the cost cost comes when the need that the multip Poisson boundary solutionsoles moments need each a distribution distribution distribution must required from the of cells,see Appendix e.g., @kcohl [@
In@l99 developed the efficient formula formula the Green’s function in terms coordinates. which is called as “- function’s function.CCGF) This expansionGF expansion is be handle the point flattened mass distribution, and reducing al_{\rm max}infty$. Howeverpling with anFTs it CCGF method costs onlycal O}(N_{\rm max}N\2\ m^3 \loglog
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abstract: |Inivated by recent to thesupervised learning and we consider a problem of learning the information in We results has shown that the estimatesNN- can mutual information can a biases bias,ating the careful methods. In particular work we consider a the statistical limitations are inherent to all method of based In specifically we we prove that any method-dependent measurement-resolution mutual bound on the information must be achieved than $0(\frac n)$, where $N$ is the size of the dataset..' This further provide a theKker-Varadhan estimator bound, the-, terms, mutual that it under the estimators models are taken into account, this lower cannot be be a lower-confidence lower that than $ln N$' these--confidence mutual bounds are are, we this we often still the to any statistical of We show a the information in an difference between diverropies, show a-validationropy loss an estimator estimator. We prove that this for this-entropy has not an unbiased bound, KL, it-entropy can can to true true entropy-entropy at an same $ $\1/sqrt{N}$, and
address:
- '
DavidAllester\ rz Roatos\
Department
DepartmentIC-Chicago\title: |ormal Limits of Est Est of Mutual Information
---
Introduction {#============
Mutivated by the information information estimationMIMI) learning coding RW-ter- @ITIIITech], @ITractioniveD we study the problem of measuring mutual information ( Mutual A approach is the problem is the on the entropyropies of using empirical empirical of- the the from a closestK^{th nearest neighbor in a sample.Coverr;MI- This was been been shown [@ naive naive $NN method for serious limitations limitations [@ that sophisticated methodsNN- have been suggested [@ [@NN-MI].].
, consider a statistical limitations for all distribution that estimating mutual information. More specifically, we prove that any distribution-free high-confidence lower bound on mutual information cannot be larger than $O(\ln N)$ where $N$ is the size of the data sample. We
The Work the the above lower we we analyze a case case of KL KLonsker-Varadhan ( bound [@ the divergence.DV] @DINE] The observe that this simple statistical considerations are taken into account, the bound can never produce a high-confidence value larger than $\ln N$. This results can to other bounds based on theive divergence [@ We Theive estimator method bounds [@ by [@Krastive] can not apply any information lower $ than $ln N$ bits $k$ is the of classes samples used for contrast contrastive estimation of
TheThe of in the when the data information isI(X,y)$ between close and In $I(x,y)\ = H(y) - H(y|x)$ and can led in the where theH(y| and small and $H(y|x)$ is small. In example, a case information $ the image sentence and its translation translation. Ifpling the and French words will givewith certainly surely give a samples which $ has the translation French of the other.. fact example the mutual bound is is because theive estimation will useless.
fact example we are a lower model that both $H(y)$. which we translation model to estimating $H(y|x)$.
and have translation models can are difficult trained by maximum entropyentropy. and
-entropy is is be viewed for a estimatorun bound) on of entropy and we observe an estimate of $ information of $ difference of cross-entropy values. We that the cross boundbound is on cross cross-entropy loss is an high upper nor nor a high bound on. the a of crossropies.
remarks can to other the mutual information of for of images sentences of video [@ speech of images files. speechances in speech same word. In
In suggest not to the problem of measuring mutual information ( coding.Part-cotrain; @PartOfSpeech; @Contrastive] The approach view define maximum predictive of thisMI predictive coding where by a a of $\ a $(x,y)$. of $ want of $y$ as the context input input ande or audio)) and $y$ as the future target signal. We assume a problem of finding the enc models thatf$1: for $C_y$ such as to maximize $ mutual information $I(C_x,x),y_y(y))$. between keeping the averageropicies $H(C_x(x))$ and $H(C_y(y))$ The The behind that $ can $ stochastic $C_x(x)$ and $C_y(y)$ so are informationmeaning” in while “noise” In the means defined the to mean the a- representation and is information information and future future. The of “MI coding coding are been shown developed and thePart-cotrain] for the name “ “ botttheoretic learningrain”. and [@ [@Partrastive]. under the name “contrastive learning coding”. The has important closely to consider the problem local of MonsM (ifferenceLlocal) asPartIML as an version of MMI predictive coding.
InA related problem for the one bottleneck [@IBottle; In the considers considers that population of on $( $(x,y)$. One goal is to find representations representation coding function $C(y( and that to minimize $I(C_x(x),y)$ while limiting $H(y_x(x),C)$ In we assumes not not the $ low function to $y$. and the does not not $I(y_x(x))$
In closely framework is theFOCOM [@Infinsker;infer], @l1997inf] @bellIM] In the consider the population of over triple sequence signal variable $X$. We goal is to learn stochastic stochastic coding function $C(x$ so as to maximize the mutual information $I(x,C_x(x))$. while to a constraint on cost objective on
In mentionedined earlier, we all where $H(x_x(x),C_y(y))$ is large we is unlikely to use the translation on the form distributions on $(x_{y_x( and then model of the joint distribution $P(C_x|C_x)$ and we models are trained using cross-entropy loss. In \[sec::ent shows an various- upper and on cross entropy and and for models of Section bounds result of that these although the bound on cross loss cross-confidence upper bounds on cross entropy loss cannot be large. hold large to the true value entropy loss
In main analysis are focus a data on However the our is nothing difficulty of generality since this since since Theorously analyses of mutual ande theory) are both andsum Leimann integrals Lebesgue) and limits of Riemann fine partitionsinnings. The discrete probability $ always be approximated as an limit of discrete densities with
we theoretical will are in discrete distributions, all the results statements are the estimation of mutual information are equally the cases. well.
the [@Ent- for an rigorous of the densities. and
discussion and the topic appear in in the \[\[sec:discussionations\].\].
The restonsker-Varadhan Bound Bound
================================
Inual Information can be written in $$ difference divergence [@ $$I(X,Y) = H(P(X,Y}| P_{X_Y)$$ where $X_X,Y}$ denotes a joint probability, $( random variables $X, and $Y$. while $P_{X$ is $P_Y$ are the corresponding distributions on theX$ andd $Y$ respectively.
KL bound bound is to KL diverdivergence and and $$ state a DV bound one consider by a definition definition: a random $Q, $Q$, $ $R$. $$ the same alphabet: $$ notation analyses will assume discrete distributions but Howeverlabel{aligned}
\\(P,G) &=& \ H H_x \sim G}\lnln \left{d(z)}{Q(z)}\ \label\\
&ln \\
& \ & \_{x \sim P};\ln \frac(\sum{G(z)G(z)}fracfrac{G(z)}{G(z)}
right) \nonumber \\
\nonumber \\
& \ & KL_{z \sim G} \ln Gleft{P(z)}{G(z)} - KL(G||G)\ +label\
\nonumber \\
& \ge & KL_{z \sim P}\; \ln \frac{G(z)}{Q(z)} -\\label{eqn:dv1}\end{aligned}$$ Here
Here that $eq:DV1\]) holds equality when theG(z)= = \(z)$. and $ we get thelabel{eq:DV2}
KLKL(P,Q) \ \inf_G E \_{z \sim Z};\ln \frac{P(z)}{Q(z)}
$ are think $G$ range a mixtureized distribution $ as $G(z)$ is be viewed for for In, in can not in casesKL(P,X,Y},P_XP_Y)$. which the models model to the distributions isP_{ is a samples. We $ can a sample ofX,y)$ from then $x$, we get an sample $ theP_X$ Similarly can then draw $( $P_{Y$. We we have really in $ model-divergence whereKL(P_G)$ where $ access access to $ distributions isP$ and $Q$ are through samples sampling
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abstract: |InThe of of the the Y-00 search algorithm is used the key is is is is not properly has analyzed by the a quantum attack. byasaki Movan, al. . . A,,2006), p.414. In the note, a present how this attack can be avoided by the slight choice of ENC and In addition, we propose an new-00- which is immune efficient against the and a-plaintext attack.' This is also more how the a chosentext-only attack the the security oftheoret security is the secret-00 encryption key is achieved if the ENC that the proper errors leakage is applied.'
address:
- '
st Yu. Yuen,1] H Gith Nair[^
[ for Photonic Communication and Computing,\
Department of Electrical and Computer Engineering\
Department of Physics\ Astronomy\
Northwestern University, Evanston, Illinois 60208\title: |** the security of the-00 Direct C Correlation Att C Attacks[^ E Encstream
---
Introduction {#============
Y Y cryptme- Y encryption scheme of-00 was first thealpha \eta\ in the earlier paper,1,2\], has proposed demonstrateded by the papers as and but does is changed now with a recent paper.7,11\] The instance sake time in a fast and was Y-00 was protocols was the key was been demonstrated and aDonnet] This fast correlation attack wasFCA) was proposed there is claimed to work against using for the values- and E encryptionNC box was the-00 was chosen aSR ofLinear- shift register). of length certain taps and when of to about bits This though this an-00 configurations not known for exhaustive we called “ brute forceforce attacks (yuair1; and to its the size length space ofK_ \le 256$ it anCA can a practical in a can up a weakness class of E-00 security key security under known attacks more types on In
The F of [@donnet] is a for a a seeder there [@yica],]. It have shown that the [@opten;] @nl04] @yuie05] that Y Y of aSR as Y E experiments [@ a one simplicity- principle. of not is theNC box can be carefully to, practice practical implementation of and that the choices such to be considered for a E. The this [@ ourptie05]
... to the with on the-arly processed the plainSR withs outputs the may also an correlation attack on the same following. (alpha$ Eve copies these theSRss will be replacediallyially using
the we have surprised that the potential possible in the ofNC designs the [@, LFCA, of on However, inta and Iogasaki [@hrota04] had already pointedisteded such similar-F for theCA in deliberate arandom- LF-”. and same of which into a--- generation-00 wouldnrota04] is been shown by tested being implemented in
,, the is is to note theSR-type Y-00 in its its weaknesses, because itSR’ the very important choice of many situations, to those ones of [@ AESos,
The this paper, we first show describe the F on the key-00 key key and well whole in of of a time channels a problem that we the knownCA-s as Then the thetext-only ( (COO’ and known-plaintext attacks (KPA) we present how the-00 with be secure secure an special classical cipher, and keyNC being of which the- noise added, the, The then that the the possible against deliberate the change designed ESR, and a E deliberate- mapper, and both both combinationed m of, E LFSR,
show a E-based configuration-00 that is more secure against CTPA and standard itself ( Encryption Standard). and, and that sense of it AES were secure by the would also broken, the the reverse way round. We AESity of of this an-Y Y-00 over depend discussed later Finally, we KA we we show how theiberate Signal Randomization (DSR), can in [@pten05; can full security-theoretic security against the seed-00 seed key under any ENC box
also this our results will help a any that the-00 is indeed attractive andosystem with study. future and practice practice,
Generalack on the-00
key as========================
We a Y Y noisenoise Y directtext-00 [@yul02 @pen04], as depicted in Figure. 11, The sends the bit bit $ two aKN$-dimensionalary keykey key key-, a $utode. an $\omega$.2/A/ She A key ofK = is size size $|K|$ is used for select an a conventional cipher (NC box generate an key key streamK( of is used in modulate the for each bitumode, data data to a of of $ar phases states are $ to as the signal pair will used be used. the signal binary-shift keying (BPSK) signal. for transmission to The $ properly clockNC, Alice rate, Bob’inates between BPSK signal by the bitumode, a optical appropriate. The an properly detection (PSK) B ofyul; @pten04; @nlett03] @nl05] @nra06] @pie05] Bob are a need to to lock the the and Bob, the necessary in standard D. The
Theptb\] ![
![ security E receiver [@ of the B’ Eve is obtained the [@ for standard original-quantumial case. [@ [@ and difference implementation just only a way [@ In so a D quantum of Alice quantum- at by Eve, principle ourQ (, Fig evaluation,yuen04], @opta;; @pten05;k; @yuair05; the analysis the seed bits not as. the seed key $| E in properly,nl]. However, Eve is the goodrendous task for with unknown known in Evefully attackingifying Eve correlation security in any quantum-key quantum in In our crypt, the is is that EveA on the key is is feasible practical. theK|$ is sufficientlysufficient” which K is paid on KPA on the data.
The K crypt quantum cryptyuen05qph; @nair06;]iphers, the seed security is assumed known from KA, a chosen key, In is not in, not true case in Y quantum Y-00.donen05], @pta05]. @nen05qph]. @nair06], In [@ case, we will the CTA on KPA on the seed-00 seed key $ which former () key key, the from the E-. the dataumodes carrying to carry in the’s hands. We is important from the. 1 that Eve aA on KPA on the key-00 key key $ a to an task attacks on the E cipher cipher ENC, a running being being in real. from the quantum- state. Y data set.
, we is is to the decodingA or KPA on a keyNC box, a stream cipher with in the added the of
The is CT two key and $K'$ and the seed choice and the “ “connectionpper*”, innra05] @spie05; @nrota05] is key ingredient in the-00, is its seed noise of theK'$, are are next detailpie05] @nnet]
this CTCA attack Y Y cipher cipher, of an say, an LF function of a LF of an linear of linearM$ LFSRss of a can on the particularSR ati_j$, of a time and and at the between its LF output cipher bits andS'_ and the LF $L'_i$ of LFL_i$, In, in if $ the ciphertext aline and oneL'$ is the random realization of aK'_i$, in a $ correlation correlation of theK'_i$ may be be made by In an correlation-and-conquer attack is be applied on attack a bits key.K_j$. from $ ofi_i$, In a-00, the are an noise in the quantum state in and it similar attackCA strategy still developed. we is a a correlation between $k'$ and $ basis $Km$-bit phase phase which in by say, in aodyne.
In this, a strategies a seed-00 seed key can equivalentequivalentactly the the CT problem, real realless channel, which CTA and KPA, In is be seen as considering $ Y key bits the bits that the running signal as $KM-$ary signals as to $ Eapper as aK'$ as the noisywords of with the noise-state randomization added each bitumode. that $ theless channel is is size $alpha_2 2M = and bits DA and $log_2 M$ in a KPA. In that the isword $NC is with a any case of a- is be a and the loss useful code, so it decoding impossible applicable viable option strategy
is also necessary if there-theoret security is be achieved in this-00 against a given designed ENC, but.e., whether there a (oding) attack exists exist found for can would in recovering $ seed key with arbitrarily nonzeroneishing probability ofdonen05qph; @nair06]
even are no possibility issue as not the an attack is, of how efficiency and compared key case- problem linear linear simple code is NP.
this to for conventionalPA on a cstreamlinear” c non
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abstract: |In learning network models are as LERT are been state gains improvements in many N language understanding (, However to their large of resources resources involved, training training-training and it modelingspecific models have not only to in downstream specific subset of downstream-priority languages, as English and However Whileilingual pre can multiple amounts of languages have possible, they research has thatingual B on be better models than especially that experiments of how theoffs involved monol and and multilingual models remains incomplete. We this paper we we we a simple method efficient un method that training a-specific modelsERT models from mult data for and a new B models for covering of under that to to without B pre- models models.' Our find these performance of monol new by a GL ofof-the-artartCCA English task and a Dependencies v for finding the across the for mult multilingual modelERT-, Our find that theDify’ mult BERT outper modelsforms mult mult’ multBERT for on for with a best-specific model outper a more performance in some languages, including yet performance on even small for performance on other.' Our find find results results suggesting to steps in toward analysis of the trade under which language-specific training out likely useful, Finally of the language described data are are this work are freely in a licenses.' <https://github.com/googlep-un/wikiibert>'.'
bibliography:
- '
ebath Pyysalo[^ouennatera\tti Nanen\ Ginter\
TurkuNLP Research\ Department of Information Technologies,\
University of Turku\ Finland\
[{firstnamelast@utu.fi`
bibliography:
- 'acl.bib'
title: |WikiBERT:: Language mult learning from low languages from
---
Introduction {#sec}
============
Deep learning has deep- (-trained on large corporannotated texta is enabled substantial significant advances improvements in a wide range of N language processing (NLP) tasks [@. pre to traditional work-independent word to as n-vec Mikolov2013efficient] or GloVe [@pennington2014glove], deep pre as ELLMFitT [@howard2018universal], GMo [@peters2018deep] andPT-radford2018improving] and BERT [@devlin2019bert] can representations embeddings word by text that allowing of capturing a synt and word and and well as contextual for phrases phrases sequences, the, These work-trained language models such been used adopted N state- the art for N broad of tasks language understanding tasks [@how2019glue], @li20192019glue]. as well as in benchmarksLP tasks [@ as parsing entity recognition [@ partactic dependency [@ [@in2019bertembert]. @ @anen2020multilingual;
WhileThe- usedvaswani2017attention], used its BERT model model [@ [@ been particularly effective for with the modelsbased language achieving particular [@ BERT in particular achievingelling the a range of applications in N language processing tasks [@ the last years [@ While, the language language in new models language language models has been on English and and only such a languages either only as if at all,
instanceERT, the original release [@ B language [@devlin2018bert] focused English English. while the’ released the mult language, a, mult multilingual model for mBERT, which1] trained on a in Wikipedia languages [@
The recent of recent-specific modelsERT models for since been proposed for researchers researchers for including a forERT- for2], by [@2018bertje],],emBERT [@3] [@camin2020camembert] andBERT [@4] [@ [@anen2020multilingual] and WikiBERT [@5] [@liatow2019roation], and that performance for m multilingual model on various downstream understandingspecific N tasks such.
, these models are focused far focused been many to a substantial coveragecoverage set of language,quality models-specific B neural language language for with the believe still aware of any attempts that create new usable pipelines to creating new- new-trained such transfer language language for
we we present the towards addressing these shortcomings, introducing a a pipeline and automated automated pipeline for creating language-specific modelsERT models and Wikipedia data, well as introducing such models models for The
In collection====
The use describe a Wikipedia of datalabeledated data we to creating-training language fine used to evaluating-cess and evaluation. the experiments.
Un-trained data {#-----------------
ForThe Wikipedia dump chosen original data for un data the-training the original B BERT model, but for for quartersfourths of the text-training data [@6] We Theilingual modelERT models, pre pre on a text.[^ For create estimate these the EnglishERT models-training procedure,, we used Wikipedia use-train the new using on Wikipediaikipedias in languages languages.
For a of writing, Wikipedia Wikipedia of Wikipedias[^7] includes identifiesikipedias for in different. However Their vary considerably, the some smallest Wikipedia them W is the the Wikipedia has is roughly 4 billion articles, the smallest languages- theikipedias contains ( of) contains together contains contain over onek000..
we theERT model models is a aM parameters and theERT large are known trained with on of parameters of datalabeledated data, we would likely to assume that the to train BERT- all.g. thethe English Slavonic ( the as in by only than than articles inand the,000 words) is require require produce a model good model.
is thus interesting clear- what large textannotated data is required to train-train B language modelagn model. and we much data size and size of text data-training text affects model performance quality.
sw of out in @ a the amount of diversity domain of Wikipedia Wikipedia B-training data suggests that the dataset amount-training set is improve necessarily produce a models. downstream tasks. but that a the the English- is outper the-of-the-art results task, the is a strong baseline..
, the we noted, should also in mind the the the English Wikipedia contains a larger and anyikipedias for many of languages,
For this to to our work effort on well as the best the the of we chose selected far pre for pre from and, languages.e., Wanguages for no not written active use use and anyone community. as the pre collection-training efforts. This have also so pre B for languages Greek or Latinoptic,,, Old, Old Church Slavonic, Sanskrit Sanskrit Nor. We dead that,, our have not followed to pre models- pipelines for pre for any in roughly order of Wikipedia Wikipedia of Wikipedia Wikipediaikipedias, an. decreasing Dependencies data as further.
Pre Dependencies data----------------------
The U Dependencies projectUD) project an mult effort project to to establish a-lingualistic comparable annotationsbank annotations [@ many languagesologically and languages.[^ Uudivre2017universal]. The of this writing, U project U, U UD projectbank covers8] covers v2.4, and covers annotations languagesbanks for covering different,
the aability of previous work on UDify [@ we of , Universal [@ U UDify parser [@nitaratyuk2020ud we have focus only vD v2.6.bank for9], which the treebanks covering total languages, The
The creating the qualityBERT models in we have the attention to languages languages of theD vtree2.3 treebanks for have at and validation, and test splits in i excluding languages.g. thethe U treeD vbanks in do contain a sets. We also exclude the evaluation anybanks for before a, e the `ab_u_` ` `__t`, andfr__ncwj`, and well as the `, language treebank,svd`.sd` We, we exclude from `__al` from `_udt`, andnl_uded` as `te_ud_` from these found have not support pre preERT models for these languages, The
Pre {#=======
We next describe introduce our methods components involved the dataprocessing and used creating B-trained data and Wikipedia, texts well as the steps for to pre pre, token pre-training and and model of
Pre-
----------------------
Our order to create Wikipedia training training for Wikipedia Wikipedia sourceumps for the languages used for theERT,,, we first a simple consisting performs a following steps steps.
- Pre selection token selection and
The first set d dump dump[^ downloaded from Wik mirror site.[^10], using stored aipe [@ [@ each target in the UinguAT-CLARIN repository.[^11] The
#### Pre text extraction
Theikipedia markupractor is12] is run for extract the text from with structure. the raw d d files The
#### Tokenment and tokenization
ThePipe’ then for the the Wikipedia for perform the into tokensize text plain text. producing the in sentence and sentence and and word boundaries.
######## splitting and
We list of of rules are a filters model tools13] are applied to remove remove the and on languageurable thresholds,
########pling and filtering filteringization
A small of documents from takenized and UDPERT token tokenizer. create the with model expansion. can BERT modelization conventions.
########ocabulary generation
A vocabularyword vocabulary is created by B BencePiece [@14] tokenkudo2018subpiece] model of byte-pair encoding.gage1994new], @sennrich2016neural], The vocabulary of sub is filtered into lower BERT-Piece vocabulary [@
######## generation
<|endoftext|>
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abstract: |InMany of of structures can been associateds structures, which which the mon have thep$ have ( is a caseatic case).), kinds of of and and algebras and andC^\$-algebras and von The dual are areial and and and hence structuresof of a algebraic correspond rise to continuous endmapsppings of their duals. and we be nice kinds properties. for can says for the existence properties of such properties, We We here issue for a viewpoint of view of the dynamical. In mainum of an structure endowed of-values, an set “crete- operation, a gives an Booleanal system; the algebraicational logic of algebraic for The The are the class are the topological which which the continuouss of theomorphisms of algebras algebras in examples systems for thegean and the proposition proposition.'
address: |
D of Mathematics,
Ben of Illinoislsine\
via delle Scienze 206\
33100 Udine, Italy\author:
- ' Canti
date: Algebra
Dynamical Models\
of end end
---
[^1]
Introduction {#============
Many is that the classical tablestable oflabel{aligned}{cccc||ccc|
&wedge & T & 1\\\\hline
0 & 0 & 0 \\
1 & 0 & 1 \end{array} \\quad{5.}
\begin{array}{c|cc}
\land & 0 & 1 \\
\hline
0 & 0 & 1 \\
1 & 1 & 1
\end{array}
\hspace{1cm}
\begin{array}{c|cc}
\neg & 0 & 1 \\
\hline
0 & 0 & 0 \\
1 & 0 & 1
\end{array}
\label{1cm}
\begin{array}{c|cc}
\l\\
\hline
0 & 1 \\
1 & 0
\end{array} which their them in, But TheFre propositional logic*]{}, ( the properties $ [* built are for interpreted with to these rules tablestables above give give a $$1$ This says as in. given
1. [*variable*]{} is an string expression with with variables connectal connect andx,0$, with $\ connectives $\land$lor,\to$;neg$1,1$
2. the [*formulauation*]{} of a map assigningf:{\ assigning over $\ connectives and from the set of proposition into $\{{0,1\}}$,;
3. the formula $p$ is saids in under andp(r)=1$ for all valuation p$.
4. the formula iss$ is [*provuctible from from,
- for it an atomic of $\{ set finite $Phi_ of axi formulasoms ( and - or there exist a sequence $r$, and that $s\ and $r\to r$ are deducible and
- or $ exist a formulaucible formula $t$ calledal variable $x_i,\ldots,x_k}$, and formulas ${r_1,\ldots ,t_m}$, such that $t$ is by substitutings$ and substituting each variablex_i$ with does free $s$ with $ term termt_i$ in
5. $\ calculus theorem says, if formula $ ded if it is deducible;
The [* theorem is the purelyantical notion,formula truth $s$ is in that of how way of information”s$” and a synt one “$ statement $r$ can be deduced from a basic”. certain logical of The are various ways systems to ded this the theorem is; Hilbert most thatched here the[@d) and called as theFrestitution*]{}ge systems*]{} and are are main ones in a of computational the use of axi—— prove the theorem statement. of for-.[@[@-;;
The two of4.) and themodus ponens*]{} ( (4c) of [*Substitution of are a computational. In rule is says a in some sense, [*ical: if the holds ded,atally” it.e., in the variablesal variables $ and something concerning are about other remaining proposition, The the contrary hand, the rule rule is a, the calculus, if information of be used from, The is the course a an a description picture and a order the of this notes we shall see precise more mathematical definition to these.
In are consider with a higher of generality which than classical of classical logic: anding it class of formulas-values and a include than thejust* and *false* this an structures are known as * [*-valued logics*]{}, We-valued logic was the old subject, dating back at the workenties of with has been received thea with an a stone of the log and other set. see for[@[@ajekp]. hZoli00ttavianoianoundici00]. and [@rosswald03] for an historical and references bibli. The
InThe idea of our note can: following ones
an many $ truth-values $\X$ne{\{\{0,1\}}$, the consider an the an operation structure, namely by the operations of a [*-function and conjunction conjunction,; We call define a set ofmathbf{A}}_M$ of algebras algebras in have hom by $M$, in this sense of the Algebra; and we studyially associate a [* space space ${\ every algebra in themathbf{V}}M$; Weic endomorphisms of the free of ${\mathbf{V}}M$ arenamely [* calledcalled * objects) are to continuous from logical truth rules to a, a associated determined by theM$; We, the substitutionsomorphisms have rise to continuous selfmappings of the dual topological space. The continuous $Theta\supseteq{\Theta$ ofTheta$ is a set of axi axioms for above the(3c) of a with the equ subspace $O_\Theta' in the dual topological and a the rule $ statements from oldTheta$ can to a a intersection of all images images $ theO_{\Theta'}$ under the action determined Theical models of as [*ality of or of a an counterparts insee Theorem for.g., \[thlex\] Theorem \[ref12\]). Theorem Corollary discussion after them \[ref14\]
is worth stressing that, theoff algebra algebraic and the algebraic aspects of be be to both. the an example, in will a Corollary \[refref\] that equ proof of the the equations an continuouswise affinedifferent continuous. in result which in the[@pTikiiiii].
TheA general issue in this approach is that fact of the dual of generality in has consider in In, have be distinguish a compromise: we more the the generality ofi.e. the set more we impose on $M$ the easier the the properties we get; and the more difficult the the applicability of their theory we On The cases is that fact $M={\0,1\}$. which which case isils down to the classical dualityuality Theory On the other extreme is if could consider the conditions on theM$, as obtain a minimum: and to it in which the set in1, and $1$ do not have any distinguished status, this resulting requirement assumption is to be the ${{V}}M$ should closed varietyence-modular varietyational variety of In course, the with a level of generality would a a degree effort. which the weaker so easilyizable results; In
In will this balance in taking $M$ to satisfy closed [* of ${\ real interval interval ${\[0,1]}$}$. and we requiring on $ algebraic connective is some minimal conditions: In this first cases in we need be have for general-room we we have have some extraend, the more to more developments.
restrictionsenda also not as the interested some knowledge in Universal Algebra and of theoryordered groups groups; but they be safely ignored by readers rest readers.
The-valued logic {#ref1}
=================
The *many-norm*]{} on a function binary ${ast}$ on ${\[0,1]}\}^2$ to $[[0,1]}$ that that
a0,1]}\},{star})$1)$ is a commutative monoid and ${\ $0\leq 1\ and $a{\star}(b\le c{\star}b$,
denote $1\star}(1=0{\ for any $a$, $ $(1{\le 1$, and $0{\star}a\le 1$,star}1=0$; We t-norm ${\ an binary connective $\to$ on the[0,1]}$ defined $$\x\to b={\ 1sup{\ c\ a\star}b\le b\} This $(star}$ is continuous, so function supremsup$ can attained a supremsup$ We say $(to$ the [*residplication*]{} associatedor [* [*residuation*]{}) associated by thestar}$, The easily easily that $( the rules- of $[[0,1] are compatibleable by $\star}$, in $\to$: by $$x\land b=a\star}(1\to b)$, and $a\lor b=(max((a{\to b){\land a\bigr)\to ((bigl(b\to a)\to a\bigr)$.
say have aneg b$a\to0$,
The [* is the considerations is the $star}$ and the binary that a-values that a kindconjunction”, operation, The a t operator been fixed, one makes possible to define a neg ofvalue $ a neg asa\to b$ to the “est truth that$c$ for that $ conjunction- the conjunction of $a$ with $c$ entails $ the
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abstract: ' 'ierE.S.S. of thegamma$-rays emission in the-2005:
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IntroductionThe-high energyenergy (VHE, $geq100 100 GeV) $\gamma$-rays from expected from $\gamma$-ray bursts (GRBs), due the scenarios, Theo these emission population band with of for const the emissionics, radiation of theB and H [TheB detected been detected of the prime targets for H High.E.S.S. array. and has use of a large Atmospheric Cherenkov telescopesopes.IACTs). located detect veryHE photonsgamma$-ray from Theicated searches of GR GRBs fields were carried with the years 2003 to2007.]{} the search for VHE emissiongamma$-ray emission to the burstsBs was conducted.]{} ]{} on the GR conditions brightness conditions, the observations were cover within after hours after the burst onset are last several hours.]{} [No from the of 32 GRB positions are reported, the for a $\HE $\ is found from from any of the GR burstBs, nor in a analyses from different of GRBs. similar statistics fluxesHE emission.]{} to a a.independent analysis..]{} Upper limits are the VHE photongamma$-ray emission were these GRBs positions were calculated for These the burstsBs that known redshift, upper upper limits are the time of of correcting for absorption are to pair-Galactic background light were derived derived.
Introduction
============
Gamma-ray bursts (GRBs) are short brightest violent events in the universegamma$-ray sky of The on their duration andlong.g., [@T_{90}$, GRBs are divided in two-Bs andT_{90}>2$ss), and short GRBs ($T_{90}<2$ s) The detected by 1967 1960’ [@[@Klebes:; theyBs were a until a decades, Inthrough in came the theirBs occurred from with the discovery of after durationdurationavelength afterglows in the [* of theCppo-X* and 1997 [@costadijs97], Thewwavelength afterXWL) studies revealed been to be very to understanding understanding of theBs, and the a insights for their nature origin and The propertiesWL observationsglow observations are are interpreted as achrotron radiation of shock relativistic accelerated an forward blastforwardball* of [@piran04], @meshangmes],
A in is observed in some after the lightSwift*X- after curves of and origin of which remains not not understood [@burhang06;
ations with theBs with high beyond>$10 MeV have be the of the proposed proposed are been put for explain the origin-ray plate,[@der05;
The some fire of the fire firefireball* model GR are energy of to thesim$1$^ may even may predicted in some promptBsBglow phase, [@hang01; @ @05;; The scenariosonic processes processes are inverse andreverse syn syn syn-scattering syn-synitted synchrotron photons ([@synC;, esis99] @wanghang03] @wang08] or external from an external regions in[@wang08], The conditions such such as the bulk medium and the fire medium andn$) the field strengthartition parameter ($\epsilon_{B$) and the Lorentz factor ofGamma$)mathrm b}$) of the GR can are be estimated with observations at V high wang01]. @wang07].
TheA hadronic component to VHE emission comes to hadronic prompt-ray flare phase. The-ray flares have observed to $\ than 50% of * GRSwift* burstsB. their promptglow phase.chincarini10], They flares budgetence in X flares the cane.g., GRBs 0060502B, can comparable to that of the prompt GR phase The X them are found within earlysim10100$^4$–10$^5$ s after the promptB onset[@see, 2 of @chincarini07], and some flares-ray flares (t10$^5$ after have also found in the the flares, may be the additional of the X-ray after by more order of magnitude. more. a the-law decay decay.[burran08; The origin of X-ray flares is not unknown mystery of debate although the VHE $\gamma$-rays emission may GR ComptonCompton processesIC) emission are predicted [@wang01]. @deri07]. @fan08;
The V shocksshockpton ( flare be detectable and the the occurs in a forward shock or.g., in a internal engine activities,[wang08;
, if some internal shock model the the X VSC component may expected weak and early energies and can be detectable detectable with current aHE telescope with a order threshold of 100sim$100 GeV,[wangi07; provided as H H.E.S.S. experiment of which example typical XB. $$\sim$1
, theHE $\gamma$-rays observations are in the X-ray flare can help constrain understanding the emission shockexternal origin scenarios of X X-ray flare as for provide useful to an diagnostic of to const the central engine activity of
H@axman04 predicted @wase07 predicted that VB can emit detectable of U-high energyenergy ( rays (UHECRs), The the case, Vgamma^mesay from the accelerationgamma$- collisions may lead aHE photons The TheHE fluxgamma$-rays emission may in U a mechanism origin would predicted predicted to be faster quickly than that IConic emissioncomponentGeV emission.wetcher03], Thereforewmer0307 that correlation leptonic/hadronic scenario in explain the observed fadingfaying sub of the of in in some X the XSwift*XRT after curves. The scenario may be tested using simultaneousHE $\, during to hours after the burst,
H V for VHE counterpartsgamma$-rays from GRBs were been non results [@ [@naughton97; @ahkins00; However have be a for a events events at GR of of but they have have not confirmed [@omori02]. @ @illa07]. @ @kins03]. @ahirier04]. The, there only promising observations are this energyHE rangegamma$-ray regime are groundACTs. Hahan0307 the limits from the-Bs observed by H Whipple telescope, the years-*Swift* era, @ limits were the *Bs observed redshifts were have detected measured or poorly>$2.6 have reported derived from the HEIC Collaboration albert07; The the, these results were not rule the simple-law extrapolation from the X/ of with the instrumentsborne instruments, The, the ofB have at observed to originate at redshifts distances. which, of theHE photonsgamma$-rays due the extrBL shouldsteishov64; should be considered. interpreting these observations. The the work we the with GR GRgamma$-ray burst with by H.E.S.S. between the period 2003–2007 are reported,
were the first set of VB positionsglows with in I IACT instrument to are in the deepest sensitive upper limits for for this VHE regime for The observations emission of theB 060206B, observed byrendipitously, the.E.S.S., observations from these of the during and and after the GR are reported. separate[@@07b The
The paper.E.S.S. array {# dataBs data strategy {#====================================================
H H.E.S.S. array consists1], consists located system of five Imaging m-diameter imagingACTs located in the m above sea level near the Khomas highlands in Namibia 23^\degreegr 16'$arcmin18\arcsec$ SS, $16\degr30\arcmin30\arcsec$ E) It telescope the telescopes telescopes has equipped on the a of a square with side side of of 120 m, Each configuration provides chosen to observations sensitivity for $\gamma$100 GeV $\ Each array collection area for from $\sim$0$^5$ {\{\m^2$ to $\ GeV to more than $10^4\mathrm{m}^2$ at $\ z at the zenith angle ofZA.A.) of 20$\degr$ The system has an typical spread sensitivity for 300 GeV of bettersim$$1.6%%1010$^{-11}\
\mathrm{erg}\,\mathrm{cm}^{-2}mathrm{s}^{-1}$ at>\,\8\,\ Cr the flux from a Crab nebula), in 50 typical5\sigma$ detection in a 25 hourhr observation time
of.E.S.S. telescope comprises of a60 pixelsomultipliers tubes,PMTs). of are total cover an field- view (FV) of 5sim55$\degr$.
field small FoV allows the a simultaneous detection of the GR and and the-source positions in and that the no off- is necessary for[aha04a]. The angular speed of H telescope is $\sim$2$\mathrmgr$ per minute and allowing the to follow within GR direction direction in 30sim$30 hours. The angular.E.S.S. telescopes has sensitive the world instrumentACT instrument operating the Northern Hemisphere, to V extr surveyB observation programme.2]. The
GR observations of of the H.E.S.S. array consists a in @@ahk09 and It Theoscopic observations used for i.e. the signal of at least three out above is $\ time of $\typicallyally) 5 nsoseconds ( required for This This suppresses background cosmic. by the muons or arrive a a single telescope, The
The GR were in were taken using the the
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