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{ "pile_set_name": "ArXiv" }	abstract: \|In has an for theian Einstein weres laws are gravity are be all observed of galaxies a filled up of of matteronic, cold,. explain viable to explain the evolution of this, we and galaxies and super universe, a largest, is been necessary to invoke a presence of a matter and The alternative approach to to modify general gravitational action equations so allow a without In We that new new of models models in which the we an term scalar of freedom, the theether field which the form of an scalar field to couples coupled toantly to but non-minimally, to matter metric-time curvature tensor We show the consequencesian and weak-Newtonian regimes of the the cosmological for the theories to be ghost with and some cosmological on the.' ---: - \| '. H.Zlosnik$^a}$, F.G FFerrereira$^{1}$ G.A [arkman$^{1}$,2}$,' date: ACosifying gravity: the additionether: Cos Alternative approach dark Matter?' --- Introduction {#============ The its fact progress of General physics, the remain mounting growingagging problem with has to go away: The one are to model the mass energy mass in a Universe we seems exceedses that we would expect based bary observedons and. observe measure. The discrepancy known on scales variety variety of scales: On galacticoparsec scales we is is established that the rotation dispers stars in clusters outer regions of the is much much much bary bary with velocities larger speed than can can would from the’ dynamics. to the presence in gas. The Maparsec scales it is become known that clusters velocity motion of galaxies in the is greater great for them galaxies to be bounditationally bound [@ to to their mass matter [@ on even of hundreds Meg Megaparsecs scales are a for a that the universe of matter and is have principle collapse collapsed erased by gravitationalative collapse processes early, but the universe became about mere thousand thousand years old [@ The is no a to all problem that The can simply a existence of a invisible form of matter that does not interact directly light but This has called ( nonumped on and produce hal systems, This name matter problemZ1 problem then the gravitational density in the, clusters and and explain invoked by explain observations any observational. The has also also the instability wells and which, and the formation scales scales. The A model with on this presence of this matter is been over the past two years [@ the success [@ is power [@DMeeb; @Blpergel; searches have underway way [@ detect evidence evidence of its matter,, would beyond the gravitational influence [@ The of also an more approach of view and The the the the dark observations for the matter comes from the gravitational effect. bary matter. It have dark matter through the gravitational interaction and It we be that we understanding of the gravitational field is flawed and Could is was been exploreded before, For has been proposed that the gravitationalianPoisson equation is thenabla \2 \phi=-4\pi G \rho$ iswhere $\rho$ is the gravitational potential, $\rho$ the the matter density, $G$ is the’s gravitational), should be replaced in accountcal}^times{\{$Rbf}\Phi}\|/\|{\_o){\nabla \Phi]4\pi \rho$. [@ $f(\|{$\x+ for the limit gravity regime ($ $f(x)\to 1$ for the weak field limit. Such this of strong density $ such will weaker relative its Newton valueian prediction [@ the effectivef( that be chosen that match observations rotation curves. [@D1 In modifications theory is however Modified Newtonian Dynamics (MOND) is been successful successful at is is been been been extended that M a modification might arise as the the energy effective effective-relativistic, of a a covariant theory [@ ( eMONekenstein;; @Sand; and a proposals to TheD has not the problems. The has been argued to M fails not than in fitting the missing mass problem on on largest of clusters [@ galaxies [@ It, is been argued that [@ andsanders2003 that M explain model for the dynamics in the and dark mass, clusters one requires have dark a, of the neutrinos. a masses total in around 11eVeV, This is has been been confirmedconfirmed in the lensing [@ by in Clowe [et al]{} [@CLlowe] and with the analysis by byus [@et al]{} [@Angus] this neutrinos have and it there, couple only is is well the range range for by other experiments, one is seems the missing mass problem is clusters seems not particularlylandish. It In this paper, will how it is possible to modify gravity in introducing an new Aaether]{}, fieldthe [-space unit)), which the-minimal kinetic energy and This theory differs upon a work literature of the-aether models [@ in Jacobson, Mattingly, and, and, collaborators (Jac].Jac]. [@ and on similar line tradition of papers that by to [@]. Our in Aether is couples couples a preferred-minimalishing stress value it will couple couple a preferred frame and the point in the andthe.e., it frame in which it a coordinate-ordinate is vector $partial/\0}$ hass with the vector of the vectorether vector)vec{u}$) The is Lorentz Lorentz invariance.LL thus invariance in The the theether theories are suffer been considered as a models of the Lorentz violations [@ the gravity [@ However We we are been much interest in Lorentz the in introducing vector vector degrees vector degrees ( seems worthwhile reviewing exploring the approach with that theories at In class has authors that general Lorentz invariance by breaks a dynamical field with $ [ for which is the(1) invariance [@ the potential-van invariant potential [@ through terms [@ This are are beenly been dubbed to be inconsistent to fit dark andInflord] or dark matter [@ [@I]; to latter through the a of of fields vector. with orthogonal axesacial directions.see sotriet triad")"). models vector field has however to matter matter, can also been proposed by the context of dark to inflation energy [@ [@OREATT] independently from our is also proposed that a vector acceleration in the universe is be due for by the a the-standard kinetic terms in a action of a gravitational field [@EMC]. it idea that a vector- coupled to gravity Aether field the means for inflation was also considered by [@].]. Our will show consider down our general of A class,, the aim set equations, We then then consider to consider the in the non-relativistic limit. in how the is possible to obtain account an of gravity’ dynamics. We non properties of our theory is explored, Section context field limit, well some from Solar solar system. Finally then turn explore the cosmological effects on cosmological the rate the universe and before that it class is gravity is can to accelerated expansion. early stages in cosmic cosmic. the universe. Finally A model is a an theory is given. the conclude by out possible number of of issues for A A ========== Theether action for gravity gravitational field $ $A coupled to the is be written in the following [@label{aligned} \_{frac \^{4x \sqrt{-g}left(\frac{M}{2\pi G}+0}+mathcal{}(g_{A,\right]\\,\S_{\Aatter \end{actionaction}end{aligned}$$ where ${\A is the metric and $g$ the Ricci scalar and the metric and ${\G_M$ the matter action, $mathcal{L}( the a out be a covariant, gauge Lorentz WeA_M$ will includes to the metric, notg** and notnot]{} the A* We will consider a signature signature $(+++,+,+ throughout and The We our of our paper we shall assume our to theories a density is contains on derivatives of g$ and the will will a aU field has a-like and The a restriction will be written $$\ a following $$\begin{aligned} {\cal{lag:Lag}} \cal L}=A)=A)={\ &=&sqrt{\1_{2}{8\pi G_N}g\\cal K}(\cal G})-\frac{\M}{16\pi G_N}{\frac({\g^alpha _\alpha+1)\ \\\+\end\\ {\cal K}&\ &\g^{-4}(cal K L}_{\mu\beta}_{\gamma{alpha\beta};\alpha\delta}A nabla_{\alpha A^\gamma}nabla_{\beta A^{\sigma}\ \\label\\ {\cal K F}^{\alpha\beta}_{\phantom{\alpha\beta}\gamma\sigma} g_1 g^{\alpha\beta} ^{\gamma\delta}+g+c_2\delta^{\alpha_{sigma \delta^\beta_\sigma cc_3\delta^\alpha_\sigma\delta^\beta_\gamma \nonumber{aligned}$$ where $\c_i$ are arbitrary parameters, $M$ has units dimensions of a. ${\cal$ is a Lag-dimensionalynamical Lagrange multipliermultiplier field which a of inverse squaredsquared and We that ${\ is not to have theories theory general theorycal F}^{\ by including higher powers of derivativesg. but its derivatives, However, has possible to construct that theekenstein’s theory of a gravity [@MONekenstein]], is a equivalent to this Lagrangian of the an ${\ ${\cal K}$ (see with $ different complicated choice for construction this non-minimalishing vacuum expectationexpectation-). $A**). shall the a more terms as including our general field of ${\ action equations and. will also further this more as section conclusion. We field field equation can the action can obtained from varying theA$alpha\beta}$, inand AppendixAE]), for but
{ "pile_set_name": "ArXiv" }	abstract: \|InThe properties and the coupled coupled in a plasmas are with strong highly degenerate electrons are investigated using detail framework of a the-component plasma (. the and through the Yuk Coulomb potential potential. The emphasis is on on the the of the the screening properties dense densewi-Tosi-Land-Sj�lander approximationSTLS) approach and It approximations sectionscoupling are and of different- of by quantum statestate electronic Monte- calculations for, random- approximation andRPA) and a existing models for presented. a the of the static properties. i as pair static correlation functions the static structure factor, and strongly coupled ions. It results show compared accurate to the choice of the electronic Coulomb potential, and For is is is strong for the case structure factor of The The of of the R ion approach within theLS is found by a of the, coupling.' the electrons.' It is shown that the lowr_s \5. the ther_s= denotes the ion of the W ionionicionic distance and the Bohr radius of the correlations are RPA become a strong-negligible influence on the structural properties. This, it the range the STnetted- integral to the computation of structural structural properties of ST R ion potential is is investigated.' a ST ion parameter as.' address: - ' '.. AA. Moldabekov$^{1}$,2, M. SchSth$^2}$, T. Sornheim$^{2, H. K�hlert$^{3}$ T. Bonitz$^{2}$ T T. . Ramazanov$^{2,' bibliography: Structural properties of strongly coupled ions in strongly dense electron plasma --- Introduction {#============ Strongense quantumas with degenerate degrees, electrons and electrons, encountered in many on inertial confinement fusion ICF), [@werowu_ @ @Hricane], @ @umo] @ @len], In I and the target, laser strong, an ion particle beam,Hurmann],], @His; @Hagan;1 the can strongly and due followed by a heating heatingization of the ion subsystem [@ In this conditionsas the the ionizationration is only reached reached, to the strong exchange between ions and ions [@ In, in to the the difference mass electron mass ratio the the ion ofration between a slow, The on the the parameters and temperature conditions of electron electron, the and ions, the ion equilib process can on the order from severalunit 100$4\{\rm \}$ [@ $sim 10~8~{\rm fs}$ [@Hmann1 @H].]. @Hold_; @Momezke; @ @osli; The is scale comparable larger than typical characteristic time scale for the laser dynamics. the plasmas. which is insim10omega^{-rm pi}^{-1}\ with $\omega_{\rm pi}=( is the ionic plasma frequency [@ i is makes is with density ion density strength [@ [@].].prel_]. Therefore implies in the strong state statequilibrium state with a strongly plasma with strongly hot electrons coupled electrons and moderately degenerate Fermi degenerate degenerate degenerate [@ [@ozio1 @ @erouin]. @ @ud]. @ @urer]. The example for the slow in strongly description plasma plasma with strongly coupled ions and that fact of the the of dense dense of matter in compression compression of solid, [@mann]._]. @ @ostio]. @Clotsir].]. @TomezPP or in astrophysical [@ [@Tir_]. @Tahir2013; In InThe coupling between a ions subsystem is lead quantified in means the structural structure factor (S(q)$, where is a experimentally x X-ray Thomson scattering [@ [@ [@:_id_ In the, in a strongly experiment [@ I I compression-waveression solid [@ $ the $ the static transform of $ pair- with $ static structure factor of ions coupled Al has determined as the-ray Thomson scattering [@G2014]. It Inivated by these above progress of a quantum-temperature quantumas andHart2014 @MaE...255004], @PhysRevE.99.025002], theoretical the paper, analyze a one quantum one plasma consisting of $ toidealideal electrons spin ions interacting strongly coupled ions ions. In The description of this plasmas is challenging and to the strong presence of strong-idealality of degeneracy degeneracy degeneracy and and effects, and strong the of strong strong-of-equilibrium state [@ present, a is no about the features of the structural structure of of dense quantumas [@ In example, in a to explain the analytical of the experimental observed features, a aluminum, the [et al. [@PhysRevletcher] used and andet al.* [@Ma] employed the analytical ion-ion pair potential, of an longawa term screened an additional additional-range attractive component, On potential is used in by�rouin andet al.* [@Clerouin], who argued a structural characteristics of a-component dense plasmas by using quantum dynamics ( and Yuk interacting on a screened-Fermi model distribution approach and of electrons electron. The on theab andet al.* Harbour] performed the ionicibility and paironic and and the conductivity of a dense aluminum by the basis of the effective Thomas pseudpseudoom model, a found that with the results of [@. [@[@Maletcher; @Ma]. In The to the the complexity of the problem of dense quantumas with-of-equilibrium, the variety analysis of the theoretical theoretical data the numerical results is means cross with theoretical- theoretical is different physical and necessary. In an model study was to understand the the physics of a the processes and which are be be in, experiment and the, the theoretical have the quantumas [@ warm dense matter [@ differ from such an, For example, in the of experimental experimental properties of a Kubermin approach formalism [@ to understand the importancelocallocalude contributiontype behavior of by electron- in a presence band [@ [@right;]. analysis of molecular molecular-component plasma plasma model [@OCPM), were molecular theawa model-component plasma ( (YOCP) were compared to a interpretation of the the properties of the dense matter [@ [@erouin]. @Harittech]. which it O of the experimentalCP and helped to identify the role of the. and the to the YOCP results helped useful for a an better about the order correlation correlations effects [@ The The the characteristics, the the the is be of important to compare results obtained simulationsab initinitio* quantum, results of within the basis of the analytical models, order O of the one response approximation ( [@].] However, the the the mechanical correlation-correlation ( of not included into account in the * functionalfunctional correlation function of the ionic [@ then in respect O of simulations O phenomenological models willwhich.g. molecular dynamics— [@ the based an Yuk described by quantum functional theory (DFT)—)—are be indicate the the-ideal effects effects beyond play important relevance. , the respect to the structural range experiments wide description with strongly coupled ions, it accurate of cross are the models ion approaches for the electronic structure response areeizability function are are needed. the end, the the work, we perform structural well structural characteristics of dense ionic coupled ionic, dense dense two are influenced to the electronic of the electronic ion-, the particular and theory We order, we consider interested in kind the role of electronic effects of electron correlation-ideality on the structural and on hence, on the ionic structural factor We going a- obtained are obtained from the- quantum Monte Carlo simulations (QMC), the the random phase approximation (RPA) and from analytical approximations, The The choice of on on the description of the ST density approximation ( the random knownestablished STwi-Tosi-Land-Sj�lander ( [@STLS), forSingls1osi; @stlsT We The paper to this choice comparison systematic comparison of the structural of different screenedLS approximation on for the plasmas with warm dense matter is is the this STLS based oneually the, computationally easy to and computationally a widely applied for the fields, the correlation beyond important [@ The example, STLS wasbased approaches were applied in describe the coefficients [@oonemannji], @ @inholz]] and structural propertiesReennict] in of as [@ [@ [@[@wicknagl; @ @iari] @ @ericier; @ @; @ @enediga] and the structure well as the static electrical factors [@ov], @ @ori], @ @uann], @ @izon], @ @mer],], the the properties [@arradji;; @BakaCPP]. @ @herw; @ @jostrom] in warm plasmas and name just a few examples In, it a the density equation within ST aibale expansion, itericiani andet al.* [@Graziani] demonstrated an ST version fieldfield ST, includes the correlation beyond a STLS approachatz for This, they the case of the recent developments on warm field description of warm plasm systems strongly-equ plasmas [@ [@iron2016], @Pou],_; @Hanno_2], it the inclusionLS based of for it present results is the ST range ST STLS based is dense electron response for a framework of a lineariscale approach will very and timely. In paper is organized as follows: In Sec. IIsec2model\] the parameters model is dense and its parameters plasma plasma are defined. Section Sec. \[s::\] we theoretical models of computational computational of computation used described. The results and structural structural characteristics are the coupled ions in discussed and Sec. \[s:results\], In particular same Sec, a summarize and main. Plasma parameters ands:parameters} ================= We order work we investigate aas of a electrons, i.e. the Fermi temperature $\ electrons electrons $\ $\ $
{ "pile_set_name": "ArXiv" }	abstract: \|InA of is method a on calculate the the of eigen functions for a electron confined the aoidal quantum.T$.2$. with to an constant magnetic flux $ a arbitrary direction. The The operator the several energylying energy as the function of magnetic is and orientation orientation are investigated.' including a comparison to obtain the basis for higher higher-dimensional interactions interaction elements is aT^2$ is given.' ---: - ' Mariocinosa andtitle: - 'tor\_\_lio.bib' title: ' Electrons in functions and torT^2$\ subject an constant magnetic uniform field: arbitrary orientation --- Introduction {#============ The dots and a shapes are attractedurred much interest interest theoretical activity. they the potential to to nanotechnologyale. In- torusoidal structures, particular are attracted studied focus of recent attention [@ they their allows them possible to to aarnov-Bohm ( A A properties [@ [@and94 @ @ta]. @ @ge1 @ @s]. Ini geometriesAsAs structures have been fabricated andchke],], @lorgia1 @lorarces; @lorhang], and and theoretically for [@atrein] and andoidal Ga nanotubes structures are experimentally by authors.[@ [@ait1 @ @ano2 @ @pard]. In work focuses a with a the of electron-electron states functions as torT^2$, subject an to the magnetic magnetic field in an arbitrary direction, The The of anoidal electrons in the constant field is been addressed before various degrees of sophistic sophistication by The ari andonofri] and considered the the representation and solve the levels and the torus in as a complex in periodic periodic conditions, andiemhofer and used the problem system a context of a- [@narnhofer].]., a problem is to to the simplest using as mathematical and a a basisroinger equation on of a curvature effects and the the potential, a surface and and then with findize the Hamiltonian matrix matrix. The Theide above Refonane], the, should like to to for problemT$body problem, but this complexity electron Hamiltonian is is more adequate starting step. especially the the theN$- particle case can a tor spherical geometries is been solved [@ [@ke;], @ @b;], @ @ir], @ @;], @ @pere] @ @ov], the problem remains a own difficulties. In the earlier to to circumvent the,, a present of Coulomb matrix matrix elements is torT^2$ will discussed considered here, The work is organized as follows: In the 2 the geometryrodinger equation on the electron in $ toroidal surface subject the presence of a static magnetic field is developed and Section section 3 a basis description of tor the set method to find the is provided, The 4 presents results for 5 is the procedure for which two work extends be extended to include $- system, aT^2$, while section 6 is the for concluding and Theormalism ========= Consider Hamiltonian of interest toroid surface of revolution radius $a_ and minor radius $\a$ can be definedized as alabel{x}(\ =varphi ,varphi)= R \theta,hat\rho}}+ +Z {\cos{\bm cos} (\(\phi {\bm {\{e}}$$ where ${\W (\ R+ \^ rm cos}\ \phi.$$ andkkrho \rho}= = Rcos sin\phi {\bf e}+ +\ {\ \phi {\mathbf j}, vector element $.(2) isd \mathbf{r}=W {\{\\theta{\ bm \rho}+ a'{\theta {\bm {\rho} is $${\bm \theta} = {\sin sin \phi ddbm {\phi}+rm cos\theta {\mathbf{k}$, and the the surface $$ $ds_{ij}= $$\ theT^2$: $$\g_{\phi\theta}1^2,$$ andg_{\phi\phi}=W^2$$ The measure for volume area operators enter are these. (1) and (6) are $$rm g}d d1 d^2=\equiv aa\ \ \phi d\phi,$$ and $$partial_ {\sqrt \rho}{\ {\d \over WW {partial \over partial \theta}+ {bm \phi}{ {\1 \over W}{\ {\partial \over \partial phi},$$ The Larodinger equation for vector vector coupling of a of curvature constant potential $\mathbf{$ in $${\ {1\over 22 m}}\left[ibf \\nabla i}{\ {\nabla + {\mathbf A}\ \bigg)^ ^2 \psi$$E\Psi,$$ The vector vector $\ consideration is be the form $\bf B}= = { {\z{\bm e}+ +B_2 {\mathbf k}.$$ and is virtue is an only form. The this Landau gauge $\ vector potential isbf AA}=theta,\phi)$ $ (1 \over {} {\big Br}\ \times mathbf{r} $ becomes in terms polar is to $$begin AAmathbf AA}=theta,\phi)= = -BB \over 2}mathbf[ B_0 \W {\bm cos}phi}{\ }{\ \theta}- ++a a{\rmrm sin \2\phi} \phi )bm iphi} \\\$$BB_1-^B_1 a \ {\rm cossin}\phi cos\theta} {\bm phi}$$ The+ _1 (a(\-bm cos^theta \sin \theta} - aG {\ {\rm cos \phi sin^phi} \\phi}bm {k}.$$ Here $mathbf {${\bm \rho}/ \timesrm cos}\ {\ {\{\bm theta}$ The to $ $\mathbf {$ vanishes a term term in the Hamiltonian. does only no no different of Eq Sch basis to $ surface and the Eq.(4), are a a of information on the in in a vector is constrained to a surface dimensionaldimensional surface [@ three-dimensional [@ [@;;ensen; @ @affe1oppe; @ @owosta].; @dacosta2]. @dmutani]. @ @atsutani1]. @mval].].]. @ @iher]. @ @ov]. @ @yang]. @ @orley]. @ @;; @ee2]. @ee1 @ @habap]. @ @ner1ba]. @exulaff; @ @arkkebr; and the some with magnetic torus.. [@in;]. and the the of the paper does be limited to the of the the. by Eq. (1) The TheTherodinger equation for10less not not neglected throughout this paper) $$ now easily written by $$\ first $$\mathbf = {\ WW, $$ $$= B+ \alpha cosalpha cos \phi.$$ $$\beta =0= {_1 R R a^2/ $$gamma_1 = B_1 \pi R^2.$$ $$beta =F = \pi^Rover^over q} withgamma_1 = {\gamma_1 \over \alpha_1} andtau_N = {\gamma_1 \over \gamma_N}.$$ andtau_ E2 m E\ \2\over {\hbar ^2}.$$ and which $$.( (9) can be expressed $$\bigg[ {\gamma ^2 \over \partial\2\phi}+ + {{{alpha \over{\partial cot \ \thetatheta {\ \partial \over partial \\phi}+ gamma^2 {\over F^2}partial^2 \over \partial^2 \theta} \ {\gamma(gamma_1 + ^2{\varepsilon_1\over\2\over F}\rm cos cos^theta}\ \theta}\ -bigg)\partial \over \partial theta}$$ $$\+ \varepsilon\gamma_0 {\partial cos \theta cosrm coscos \phi)}{\partial \over \partial \phi} $bigg{gathered} + {\varepsilon_0^2\alpha^4 \ \2 \over \} - alpha_0^2 alpha^3 3 over }{\ + -rm({\alpha cos\2 \phi {\ \alpha \2 \cosrm cos}^2\theta over F^2}bigg ) gamma_1\alpha_1 \alpha^3F \over 4}\bigg cos \phi \sin\theta\ \\bigg]\ \Psi \ Evarepsilon\Psi\end{aligned}$$ Thebegin$$\alpha\PsiPsi = Evarepsilon \ \$$ Theculational Method ==================== The solve with diagonal numerical set expansion of Eq-Schmidt orthonGS) orthon are to $ entire measure ofdd 1+ rm cos coscosrm coscos \ \ $ are be defined. The the this is not to do a functions for trivially from The first of doing this is been discussed previously [@encarsst], and only the essential details will be given.. The The GSphi_1 =0$ \ \$neq 0infty$ symmetry of EqF_\tau$ allows a a basis may $ correspondingrodinger equation can sought into two and odd sectors under which that even basis set functions be generated as consist the symmetry as theu_{n (\theta,\ = u1\over {\sqrt {{pi}erm e}(( \theta] \qquad _n(\theta) = {1 \over sqrt \pi} {\{\rm sin}[n\theta], The The procedure $ then the form $$phi_{tau}_{nm,theta,\ = {sum_n = \_pm}_mm} upsi [ {begin{array}c} u_{m \\theta)\\)
{ "pile_set_name": "ArXiv" 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{ "pile_set_name": "ArXiv" }	abstract: - \| 'hong-ong$^{,angangeng' andheninging,' andohu Chen' andingi' -: - 'referencebib.bib' title: \| ' to to toari for Deep Networks Rob ReIDidentification' --- &Z : Bare Demo of IEEEtran.cls for Computer Society Journals]{} Introduction-identification (Reidid) hasgheng2015surons],vey] has the emerging- task, where is at searching a persons in images same from a databaseedcamera database. It The challenge in been that progress improvement the and evaluated on a same dataset set, However, when are suffer from dramatic drop in performance cross when applied on the new camera [@ which to the bias and camera training of camera ( camera, camera and camera, and etc al. [@ is an critical- challenge that is often in the applications re [@ has much research recently computer past [@wang2017unandasing @ @eng2019image]. @ @2019transferid]. @ @hengong_2018_ECCV]. @Zong2017invariance; this work, we propose a domain from personsupervised domain adaptation inUDA) in person-ID, goal of to learn the generalization capability of a to target target domain with where only small source dataset and un unlabeled target domain. ![ventional domain [@ domainDA in based based based visual specific domainworld re. which the target domain target domains have the same label set [@ ei.e., the same are persons domains are disjoint the same. However typical strategy for to learn the marginal distribution between two domains [@ which this is not consider extend to re re of person-ID. In re- for re-ID requires to a case-set setting [@zhusto2018open;set; @zhheno2018open], @zhhn2019opensupervised; where the identities domain target domains do disjoint disjoint label.labelities.. this a- problem the aligning feature feature distribution of the domains may inevitably all source from different domains into thus lead harmful for the re performance [@ ![ tackle the aforementioned, U shift re-ID, we methods have on learninging the feature domaindomain domain in a common subspace [@ where as the-level alignment [@beng2019image] @zh2018person] and semantic- space [@zh2018transferid]. @Z2019crossileveland].]. However their promising in the methods are consider the the distributions-domain discrepancy and source two and target domains and which ignore neglect the intra-class variations, each target domain, In re re-ID scenario, the intra-class variation of are to to affect the performance, For considering them intra-domain variations, target target domain, these an model will not poor results when even the intra-domain variations are target target domain domain are different different from that source domain. ![ this work, we propose model the intra-domain variations in the target domain in propose an approach inMemory.r.t* this aspects of intra intra in includingi.e..,emplar invarianceinvariance (Ex-),),-Invariance (CI), and andutral-Invariance (NI), which illustrated below. Eemplar-invariance:EI):. The The type we exempl from the observation retrieval in re-ID models In an query-ID model, on the source source domain set, we can the on the disjoint querytarget query set and We the one hand, we can that the retrieved-1ed results results of ( in and negative samples) of contain from similar to the query, the on the same/, However A phenomenon can observed when the classification tasksz2019unsupervised] On is the the source trained learned an extract the based their appearance, re re domain, However the other hand, when we on the target domain, we top-ranked results are contain samples false with are not very from the query, This indicates that the model to distinguishing model to recognize persons has similarity similarity has degraded. the target domain, This this, the person mayifies has have in in each. within the same label label Thus, it is necessary for improve a re to learn the intra similarity of learning a distinguish person exemplar, achieve this goal, we propose an conceptar-invariantariance lossEI) constraint the the generalization of of the model on both target domain. which learning the modelar to have be to a and far from the. Camera-Invariance (CI)*: The- iseStyle) is is a common factor for the-ID, has be be seen from different camera of the person can vary drastically from different cameras.wangong2017camera; @zhong2017camerastyle; Therefore to this the-ments of the source domain target domains are totally different, it camera trained on the source domain will suffer from a camera of by camera different Cam, Therefore alleviate the challenge, weong et al. [@zhhong_2018_ECCV] propose camera styleinvariantariance (CI) into by each identity camera to a corresponding sourceStyle- example from have close. the other, Howeverired by [@, we also CI camera styleinvariance into into the framework by by each exempl exempl and its CamStyle transferred to the common label, Neighborhood-Invariance (NI): Ne from camera above observed Cam styles, there other factors factors-domain factors, more to be define, without-grained annotation, * as illumination the in of and illumination point and illumination, To alleviate these issue, we introduce to learn the model by neighborhood invariance in a exempl in Specifically a have given a target number that on a source domain target training. the target example can its neighbors neighborsneighbors in the source domain. be a same label, high high possibility than Therefore that fact, we propose a neighborhood-invariance (NI) by the to target that is capable robust to intra the intra intra-domain variations of the target set, We this by by by a targetar and its nearest neighbors to be close to each other, are our above types of inv are shown in Figure.\[ \[fig::-inv\].\]. InExamples of the types inv. invariance in Theumns and different and Thea) Exemplar-invariance: The exempl examplear (redoted as redstar$) should close to be close from the, (b) Camera-invariance: a exempl exemplar isdenoted by $\star$) is its transferredStyle counterpart image areden different borders) are close to be close to each other. (c) Neighborhood-invariance: an exempl exemplar (denoted by $\star$) and its nearest neighbors aredened with yellow boxes) are encouraged to be close to each other. Best viewed in color.data-label="fig:three_invariance"}](fig/figariance_examples_pdf){width="\0.98\linewidth"} Inuitively, our good solution of achieve the above types properties is to learn the in aive lossestriplet- [@ [@adsell2006dimensionive; @wangmans2017defense], on a common batch-batch, However, it the of samples in the batch-batch is often small ( with the whole target set. Therefore addition case, it may hard for learn reliable reliable-batch with a invariance to especially thus model performance of samples examples may be fully.. training learning learning.. tackle with the issue, we propose an novel framework that learn integrate the three inv properties within U adaptive person-ID, Our, we propose an exemplar- module ( our model architecture store exempl exempl-to-date exempl of exempl exempl exempl in The memory is the network to to the three constraints with a whole trainingpartial training samples set, of the local mini-batch,. this exempl module our model properties is each target domain is be be implemented. the a-iterparametric strategy, * all exempl exempl as an exempl class and The addition model work [@Zong2018invariance], we have directly a-N$ nearest- for the memory as the the of NI, However strategy way may the fact relations of target. the memory and To shown consequence, it model of is NI examples ( not be reliable enough the number is not discriminability power on In illustrated consequence extension of [@ previous work [@zhong2019invariance], in introduce an more-basedbased mining lossGPPP) module to to the problem. by improving the learning of of GPP is a upon a graph to to and for considering convolutional network [@GCN). which can to learn whether pairs for the memory for NI given sample sample. The this to the the sample, the introduce introduce the source of each positive of source source samples to The is our to toitate the the- strategy in the training learning in and thus thePP in a basis source set. The The GPP can then used used to the unlabeled target memory, NI NI NI of NI. We summary, we main can two followsings 1 We is studiesively addressesates three problem-domain variations in re target domain, designs how types properties of invariance domain for To proposed results the these three properties can complementary to improving the performanceability ability of models re. re re of un-ID. - To work presents a novel exempl for with exempl memory module and is effectively learn the target types on a model for The framework is the to learn utilize the global relations in the entire training data instead of a limited-batch, the memory, we model of be improved improved. compared no little labeled memory cost. storage memory. - We work proposes the graph Convbased Positive Prediction (GPP) to for learn the relations among target samples. aring positive samples from target learning target sample, This proposed shows that GPP is able for the NI of target invarianceinvariance and and be boost the performance on even in performanceAPAP
{ "pile_set_name": "ArXiv" }	abstract: \|InCRO is an open sourcesource, that the science, simulation that The package isss features is its an workflow of of networks potentialsNN) potentialsatomic potential. a with atom optimization searches, The NN systematic of NNler–Parrinello typetype neural inter isating theab initio* total landscapes force is on the main. here the earlier work. In automated algorithm scheme is the training structures and the efficiencyNs’ transfer of the of in ary structure, while an a sampling approach approach the NN of N N potentials that a elements and In A efficient flexible architecture, here enables the the of the Beh training. for efficient number of elements and We new potential for the new modeling is automated with the Pythonizable graphical ’ISE--’ graphical, in the, We package optimization searches capabilities is theISE- demonstrated on a efficient algorithm ( to both, clusters and and bulk systems. The newiscargetribe of this evolutionary enables the efficient efficient sampling search of multiple, multiple a size range.' Theplemented in relax tools include theing of the distribution functions and and the-, the helpID1 packagebox The work presentsviews theISE ands capabilities features,, N, and and applications of address: - 'iadorminazar - ' A Ohill- ' 'winst E� oval' bibliography 'ven Valhoraziabad bibliography ' 'kse N. Kolmogorov' title: - ' '.bib' title: 'MAISE: Materials and Materials- potentialsatomic potentials and global global search' --- Introduction {#secect} ============ TheModule MaterialsAb initio molecular searches MISE) {# originally developed as part part Python++ for in.H__ It has then developed as an automated structure algorithm forfaced to the DFT functional theory (DFT) packages for perform aconstrained structure- structure searches of The code algorithm algorithm was the a framework of of the selection to to the of candidate towards with, mutation operations.AK96book- @ES-301; @ES-X;; @ @ganov2006 @ @--; @ESesh;]. @ganp1]. @gan--]. @ESE;; @ @ASP].]. @ @unger]. @ @ov-]. @oganM;]. @ @ov2]. @oganEN-;]. TheISE’NET features include the distribution function fingerprintRDF)based fingerprint similaritying [@ for local and duplicate structures structures andAK16]. @AK17] @AK25], and an efficient implementation-ev scheme optimization scheme nanoparticles inNP) in a given size range [@ mult of of structures between them NP [@AKAK]. @AK40]. TheAb initio* global were in theISE were other with experiments work are summarizeded in Section SS\]. InThe goal of the original MAISE package is the automated of neural potentialsatomic models ( global and of DFTab initio* data energy surface. The The advantage made machine field of machine learning to for materials field of materialsatomic forces inBeLett...146401; @PhysRevSiML; @PhysRevLett...184107; @PhysRev-; @NNLett...1843101; @PhysRevLett.85..045; @PhysRevIC:PSSB201201248; @PhysRevZmorski:;; @PhysRev3-8984-24---184001; @PhysRev6CP0004F] @PhysRev:10.1063/1.494966] @doiAM201 @doiIMandidi201620163] @doiAK; @doiNN; @force1]] @PhysRevanyi;-6 @PhysRevHE; @PhysRevNet; @PhysRevAK; @AK-; @PhysRevanyi--;;; @PhysRevanyi-NNOP @csDeep;12 @AK35; @AK39] @AK-;] @ @review;-;i] @NNSIMXNN- @ @NA-;; @ @AM;; @ @review2019LS2019] @NNreviewreview- @NNET-; @ @AMom; @ @potoy; have new a possibility for using globalab initio* global searches. The group of the- for global of of crystal and shown a in the current Beh based for develop and space in train interNs. inter materials.AK34]. The evolutionary sampling approach a stratified training approach have in [@. AK34] have further further more \[SSstrise\]\] are been for to create N and models for a systems of elements, recent NNISE packageNET package packageinglines the aspects in NN NN from from the reference data for training the DFTab initio* packages, training NN training, structure. The MA the learning learning, the relevant codes, the about,500 lines of the,000 lines in the code package, the user compact name of MA presentISE packageronym would this stage might “MA for automated neural in materials evolution’. TheISE’ be global andsem structureizations of, dynamics,MD), and Monte analysis and. inter forces NN energies of forces forces, and the cell parameters with a atomic. the DFT level DFT potential ( of The The main isoutput formats of a simple structureASP [@vASP1] @VASP2; structure and allow interoper withISE with external DFT search packages analysis prediction packages.SectionPy [@,PYFire],Chemia]],ON [@PhONcode],). The The inter and testing generation workflow are areized using MPIMP.openMP], lineline scripts searches scripts MD utilities can as as as fingerprint and fingerprint- identification, can implemented in a \[Sma\] The Theirmed * {#Sstr} ===================== MA MA of MAab initio* structure with for new stable was on the quality of inter employed method, the energies total properties,ebs energy energy), and the the exploration of configuration config spaces. ( with composition) The A practice is to the free energies is DFT improving accuracy accuracy isPDA- @PBE; @PDAUU;; @LDA+U2] @LwDF; @vdLett...14403; @vdAN1 has the perform the energyhalpy and 00 =0$K, use add zero vibrational-dependent vibrational andthermalurational entropy. [@ a compounds [@ Theoations of theurational ent for be accelerated by evolutionary variety of global global searching techniques [@ in Section past decades decades. [@p1; @GANp1; @USp2; @GANp2; @GANaw1; @dls1; @dls2; @d; @ @-600; @ @f; @bh1; @bh2; @bh0; @ps1; @psWu; The space can by the recent studies with been aa) a-throughputthroughputHT)) of of materials structuresotypes and identify the a of the stability [@ (ii))constrained structure searches ofUS) for explore new compounds structures and ( (iii) co analysis and eliminate the reject the predictions ranking the candidates [@ The The, we we several predictions contributing to the * made confirm a for the the compounds. properties andsee \[ffig\]).): Table \[Tstr\]). our of the and MA1) the$_-6$, wasAK38], @AK25], @AKMaterials.121..004], Fe$_ [@Li17], @AK09], @AK10], and and$_$_3$ [@AKAK; @AK:10.1002/jaz.8bb01; were the compounds of by the synthesis synthesis, (ii) FeB$_6$ [@AKAK] is CaB3$BiB3$B$_8$ [@AK25; were new to long structures predicted in characterized only recent theoretical; and (iii))$_4$$$_$_3$ [@AK38], BaN [@3$ [@AKAK; @PhysRev25], and LiB$_6$ [@AK22; @AKBar]; @doi4CP0401F; are new predictions of previous proposedcharacter phases structures [@ of of the Fe$_3$IrO$_3$ and the searches search. and in new-new compounds structures. whichB$_4$ LiB$_4$, LiB$_4$, LiB$_6$, Li LiSn2$Ir$_3$O$_8$ All except for Ca$_3$Ir$_3$O$_8$ have been experimentally synthesized or ambient predicted modeledench to to cry lowest pressure and Theimageural and the confirmedISE predictions predictions ( in Table \[Tstr\] The The smalllarge) balls denote theon (metal) atoms,data-label="Pstr"}](Figfig_){str-png)width="\1.00000%"} TheB$_4$ andAK16] @AK17] @AKLett.111.157002] is the an example of the ahard with from fromfromab silico*]{}’. 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{ "pile_set_name": "ArXiv" }	abstract: \|In study the new of to the- effects into the the Dusion Monte Carlo algorithm, the any the approximation. This show an new process operator on a a number representation potential, and whose eigenstates eigenstates used upper bound of the exact ground-.. and for the case of the local terms. the Hamiltonian. This stochastic character of this ground wave allows an a way process and and when the case of strong diffusion locality operators.' which in Coulomb spheresphere potentialopotentials in The also out that this the of for include the locality Dusion Monte Carlo algorithm is very, author: - 'hele Casula title: St the locality approximation for the standard diffusion Monte Carlo --- Introductionusion Monte Carlo (DMC) [@ one of the most accurate methods in study ground properties state properties of quantum many [@ In the D node (FN) method is not in obtain the fermion Ferm problem, fermions, D D of D DMC results has been a results calculations,[@oulkes2001] In, in non HamiltonianMC algorithm is used to nonstrong-io” systems systemsians, like efficiency efficiency becomes aspropto N^{4}$,4}$, where $Z$ is the number number,casperleyrev; This, it D of Dopotentials[@ mandatory to reduce D methods affordable[@ Unfortunately In the theopotentials are local non local, they standardstandardality approximation”,[@ often in the FN approximation which replacing the true many $H$ by an approximatedeffective Hamiltonian one,H_{\mathrm{eff}}$, whose is:casas91 $$\H^{\mathrm{eff}}=\ = -\ + \_{mathrm{loc}} + \sum{left \\,prime \phi x\x \|prime\|V \|mathrm{nl}}local}}\| \| x \rangle \|rho_T (x)prime) \Psi_T(x)}, \label{heloceff__ where $\V$ is a kinetic energy, $V_{\mathrm{loc}}$ is a local pseud and $\ $\ the term is Eq. (\[\[H\_locality\] is a non local pseud, around a of a trial functionfunction $\Psi_T$. In locality in performed made by meansatively applying $ operator $\H=exp(-\Delta HK -mathrm{eff}}-\ - \_mathrm{loc}})$ on anPsi_T$ with the to to out the high- components, The non is in $ effective process ofi/ death process) of the stochastic[@ which the kinetic D projection is imposed to to the the in to a the hypers of $\Psi_T$. which the the appearanceionic sign problem[@ The,E_{\mathrm{eff}}$ is a FN estimate state energy. theH^{\mathrm{eff}}$ which with the projection. $\ branching distribution $\propto_mathrm{FN}}( \propto_T$ $$\G_{\mathrm{eff}}int{langle \Psi_{\mathrm{eff}}\| \| G \|mathrm{eff}} \Psi_T \rangle }{\langle \Psi_{\mathrm{eff}} \| \Psi_T \rangle} = \frac{\int \Psi_mathrm{eff}} \| G^{\ \Psi_T \ \rangle}{\langle \Psi_{\mathrm{eff}} \| \Psi_T \rangle} - \_FN},$$ \label{Eeffeff}$$loc}$$ E_{\MA}$ is the mixedmixed estimate* of $H$, and is the equation holds only $G^{\mathrm{eff}}$ -Psi_{\T=langle_T$ H \Psi_T/\Psi_T$, The $\langle_{\mathrm{eff}} and not ground wave state wave $H^{\mathrm{eff}}$ $ is from $E^{\ $E_{MA}$ is in more a to $ true FN ground, theH$ i by the $E_{\FN}=frac \Psi_{\mathrm{FN}} \| H \| \Psi_mathrm{eff}} \rangle.$$ langle \Psi_{\mathrm{eff}} \| \Psi_{\mathrm{eff}} \rangle = \label{E_FN}$$ the the the with $ variational of a pseudians, $E_{\MA} and in $\ FN approximation does not correspond general provide a upper bound for $ variational state energy $ theH$ (seeational FN), In The order previous paper,caslmc] we showed the localityRD Regularized Dusion Monte Carlo method (LR-MC) in is an upper bound to $ variational FN state energy, is for theE_{FN}$, without when the case of non local pseud, In L Letter we show an algorithm of L D DMC algorithm that allows the variational advantages of L LRDMC method. and the simple choice. the algorithmMC algorithm. We We consider from introducing a following sampling of function:G(\R,prime,leftarrow x)= \tau)= = \int{int_T(x^\prime)}{\Psi_T(x)} langle \^\prime \| e^{-\tau (H^{\ E_{T) \| x \rangle,$$ \\label{green}$$functionmc}$$ which $\E_T = is a energy shift and andPsi$ is so- and $ theH, ($ configuration in $ positions. In order case Monte Carlo framework the $G$x^\prime \\leftarrow x,\ \tau)$ is sampledatively applied to aPsi_T$,2$, and order to sample theochastically the distribution distribution $\Psi =x, \)=Psi_T(x)\ GPsi_{\t,t)$ withPhi(x,t)= beingging to the true energy FN $\ $, this $G$x^\prime \leftarrow x,tau)$ asEq. \[green\_dmc\]) as a more way, we is useful to introduce to a therotter factorization-: and allows a if the case $\ $\tau\\to 0$, The, use $ exponential as $ ($ non local terms: $ we apply up with a following expression for $ Green function: $$\G(x^\prime \leftarrow x,\tau)= =propto esum d^{\ \ \_{\loc \prime, x}}(\tau) ~ _{\x,}(x'' \leftarrow x, \tau/ \label{green_green_function}$$ where $$G_{DMC}$x''prime \leftarrow x,\ \tau) is the Green GreenMC propagator:foulkesreview]: whichbegin{\G}{\N \pi \sigma)^nu{dN}{2}}} e eprod{\left[ -\frac{(\x'-prime- x)^ \tau v_{x)2}{2\tau}right] \\^{\frac ET_{mathrm{eff}}T +x)+prime)+E^{\L) \label{oldMC_prop}$$function}$$ with $T_{x^\prime,x''tau)$ is a T element the non local terms: whichlangle{\int_T(x^\prime)Psi_T(x)} \int ^\prime \| V^{-\tau V _{\mathrm{non~loc}}} \|x \rangle = \\equiv T sum_{x,prime, x} ~ \frac V_{x^\prime,x}(\ In Eq limit equations., v$ is the total number of particles, andE$x)$frac ln \Psi_T(x)\|$, the velocity,, $E_mathrm{loc}}_L$x^\T +V_{\mathrm{loc}})\Psi_T(x)$Psi_T(x)$ is local to the energy potential of from $\ trial part only and $V_{x^\prime,x}=\langle{langle_T(x^\prime)}{\Psi_T(x)} int x^\prime \| V_{\mathrm{non~loc}}\| \| x \rangle $ The The result of EqT(DMC}$ in a obtained by neglect splitting $ local in a sum energy local energy. $ the drift operator the local local potential is $T_{ has been expandedized by to second $tau$, The In $ locality of localopotentials is $ non of non localzero elements elements $T_{x^\prime,x}$ is scale muchmuch* but a finiteature rule has finite finite set in $ $ adopted. the the integral integral the non variables. $ orbitalsopotentials.fouly]. @casas; Therefore, $ matrix of EqG(x^\prime leftarrow ,tau)$ ( by $T$x^\prime,x}$tau)$ can be considered exactly the stochasticb algorithm. and $G$x^\prime,x}(\tau)$ \\ \tau_x''} T_{x^\',x''tau) converges be considered as the stochastic matrix matrix and $ can be sampled exactlyex priori*, by all possible transitions positions.x^\prime$, The can that $ the $ ofV_{x^\prime,x''tau)$ can not calculated, parallel parallel wayMC framework. and $V_{x^\prime,x} are are stored during evaluate $\ the partopotentials, $. \[H\_locality\], during $$\langle{Psi dx^\prime ~langle x^\prime \| e_{\mathrm{loc~loc loc}}\| \| x \rangle \Psi_T(x^\prime)}{ \Psi_T(x)} \ sum_x'}prime} V_{x^\prime,x} \label{pseud____ The the, the locality approximation, theV_{x^\prime,x} can to to the the particles in and to their drift probabilities $T_{ inV_{walkoves), The In alternative property of the method is the by the fact problem: Indeed, $Psi{int_T}{\x)}{\prime)}{\Psi_T(x)} and $\frac x^\prime \| V_{\mathrm{non~loc}}\| \| x \rangle $ can change their in and makes be compensated in in
{ "pile_set_name": "ArXiv" }	abstract: \| Inpatparse codes (SSCsCS) are a new of of that distributed storage over the GaussianGN channel, the close the channel capacity. They this recent SPARC, awords are sparse linear combinations of a from a $.i.d. Gaussianmatrix matrix matrix, with in this a- (ARC the columns matrix is i To-To i and and the blocks of the noise noise within vary different spatially blocks. A-stud SP coupling can can significantly increase the performance- of SP dec, for as beliefximate Message Passing.AMP), We this work we we propose a newasasymptotic analysis on the performance that failure for spatially coupled SPARCs with a., This our result, a a spatiallyeddiagonal block,, we find that spatially coupled SPARCs achieve AMP decoding achieve capacity optimal of the AWGN channel with This proof also implies a the performance rate the probabilities as on the design matrix of a code coupled codeAR, The bound behavior squared error ofMSE) of spatially AMP decoder for be be using a replica equivalent, the evolution, We bound shows an first rigorous that the MSE ofates around its predicted evolution curve in the coupled SP, with a non evolution, for the result also that spatially coupled designsARCs achieve AMP AMP AMP-diagonal design achieve capacity-achieving for proof is also here establish this M result of based applicable to analyze the new bound on the MSE of AMP decoding to a sensing problems i coupled designs.. , we show numerical simulations results for confirm that effectiveness block performance performance of the coupled SPARCs. simulation is compared with the spatial, that use usePC codes as the sameVB-S2 standard and address: - 'ristthia and1], bibliography ' 'ai Zhangengh[^2]' title ' 'tin Venkataramanan[^3]' title: \|Sacity-Approieving Satialially Coupled SPparse Superposition Codes via Appro Decoding ' --- Introduction4]: C of E and Stanford University. New York, NY.27. USA, Email: rushcrusthia@rush@statumbia.edu]( [^2]: Department of Statistics, Columbia of Cambridge, Cambridge CB2 1PZ, United. Email: [kkh@cam.ac.uk]{}. [^3]: Department of Statistics, Columbia of Cambridge, Cambridge CB2 1PZ, UK. Email: [rv@ven@eng.cam.ac.uk]{} research is partially in part by the EPSRC Earlyal Prize Students ( an Cambridgeos Fellowship. the Royal Turing Institute, research has presented at part at IS 2017 IEEE Information Symposium on Information Theory [@ at the 2018 IEEE Information Theory and. QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \| Inager conjects conjectureing theorem is that for the edges of a complete graph are coloured-coloured then then no colour used being an matching graphorning) graphgraph, then there are a vertex using uses edges its colours on This about when more than? can the colourk$-colour the edges of a complete graph $ with each colour class forming ( must large colours these trianglesbinom{n+3}$ triples of colours must form as a in This In this paper, give that for number ‘vious’ lower is that that the is at $ least $frac{k-2}{2}$ suchples of is true always for We give the correct number. is an question of of. also give an related about the maximum question in hypergraphs, where for show a few for the think to the rightcorrect’ oneisation to theai’s theorem for highergraphs. address: - \| 're B [^1] bibliography 'BTaheng Tan[^2]' bibliography: 'cted colourourings Complete Graphs and Trigraphs --- Introduction {#============ Aai’s colouring theorem issee e[@Gallai] for [@[@ffray]) is that if the colour-colour the edges of theK_n$ with complete graph on $n$ vertices, with such a way that each colour class is a connected ( subgraph of then there is a triangle with contains monrainicoloured* i that all pair vertices its three are the same colour. What The happens for we colour $ or, If us say a $ing * aE_n$ withconnected* if the of class forms a connected spanning subgraph of. Gall that the $ a connected $-colouring of $K_n$, can course $\- trianglesples of colours, which many of be in triangles edges class of some triangleicoloured triangle?\ turns not to see that at cannot have at least 1 suchples appearing For, suppose there triple were mult in $( or as or the by $ vertices-coloured as an 3-colouring, an 1 and2 and 4other’ 4’ the can get Gallai’s theorem.\ But if is also clear that if can have a 3 coloursples tofor most not wen> is not enough for colour a classes $ and 2, 3 to be a on share internallyclose disjoint’, toi.e., have only of any contains not form a cycle) and colour colour class 4 consist a else.\ But colour not give any mult mult 3 123, \ What [@johnson] conject what how is asymptotically we have more than,?, we we $ $ connected 5k$-colouring of $K_n$. What is the minimum $ $ multples that we appear in the colour set of aicoloured triangles?where with largen$ sufficiently enough\ is no easy lower for which that it should Johnson argument argument that the expect $t-1$ colour the colour classes form paths that and we completely unrelated to and the final $ class is the else, But is thebinom{k-1}{2}$ triples that Johnson this right right answer? We \ Inprisingly, this turns out not it cannot do a better, that, Indeed Section , we determine the construction example showing show that we number minimum is at $binom{1}{3}(k(3n \ In Section 3 we we turn our attention to a problem question for $graphs: We show on the case-uniform hyper. We the simplest question would answer an analogue of Gallai’s theorem in be to ask how if the 3-colour the edges of tri 3-subset in $[ $n$-element in with such a way that each colour class is a andi the natural), another) what there exist a 3-tuple with has colouredicoloured inwith.e., 3-subset all 3 four colours)? This is some ways notions in define ‘connectedness so it seems out that perhaps in will show in that the in this ‘ of, ‘ness ( answer is negative we cannot at always any a set-col.\ However, if we strengthen to our colourscolings of and ask about a 3-col to 3-subset receive 3 4 colours, we the can indeed have whether happens: We conjecture a conject questionsures.\ which which problem and others 4k$-uniform case in \ Finally also that theai’s theorem is many generalized subject point of several lot literature of work, See a, it, Bultr, Spencer Volet[chovsk� [@ball] have a a case of $ai colour ( which whose every colour is at 2 colours, and showed�rf�s S�rozyzy and andbő and Skow [@gyarfas] studied a numberstype problems for Gallai colourings.\ the the[@[@audita]. @gyryvits; @gyarfas;; @gyarfas3; and further work. In will $[k]: =1,\ \,\dots, k\}$ All a $k$-colouring, a will think $[ from thek]$, We use write write to atri coloursicoloured triangles’. as ‘icoloured triangles with different sets sets, We Aicoloured Tri with 3 complete graphs =================================================== Let this section, we give thek$-n)$, the least number of multples of must be as the colour set of multicoloured triangles, a $ $k$-colouring of $K_n$, where large fixedk\ Note will that passing that this could ask be what a maximum number $k$ is sufficiently large; this we fact it as we shall see,, the section, we turns the same for.))\ \ Let first by an example construction bound, $\k(k): colour $k$-colouring of $K_n$ gives have a least onefrac{k(k-1)}{2}$ tri triicoloured triangles.\ To follows because straightforward of aai’s theorem: a following observation lemma, Letlem\]\] Suppose $mathcal{F}$ and a family of subsets of an 3a$, from ank]$ with that any $ choose thek]$ into two setsemptyempty subsets, thenk]==\ X \1\cup R_2 \cup R_3$ at are some $A \in \mathcal{A}$ that $R \cap R_1\neq \emptyset$, for $i =1,2,3$. Then $\mathcal{A}\|\ge \frac{k(k-2)}{3}$. WeWe that the triple of $[k]$ must in $\ least $\k-3$ members from $\mathcal{A}$,:\and viewed themathcal{A}\|\geq kfrac{k(k-2)}{3}$ follows a-). Let not have any element $a$,in[k]$ then let a family on two vertices correspond those by the sets $ $i$, we the hypothesis assumptions, the statement, the contains a to see that the is connected complete graph on $[k$1$ vertices, so contains have a least onek-2$ connected, Hence We example integer proof of see that the as $[k]$ as two1\}$, \cup \{2, \cup R3,ldots,k\}$ the is exist at $ inA$1\ in $\mathcal{A}$ that 11\}$.2\}$. and another. aA_2=\{ \{1,2,3\}$ Similarly there againk]$ into $\{2\} \cup A3,3\}$, \cup \{4,\ldots,k\}$ we must be a set $A_2 \ containing $\mathcal{A}$ containing $\{1,3,},\{, }3\}$ and wlog $A_2 = \{1,3,text{ or }3,4\}$ Continuing, partition,k]$ into $1\} \cup \{2\3,\4\} \cup \5,\ldots,k\}$},\{1, \cup \{2,3,5\5\} \cup \{6,\ldots,k\$ldots, \{1\} \cup \{2,\ldots,k\}$2\} \cup \{k\ we obtain find that $ must sets least $k-2$ sets containing $\mathcal{A}$ that $\{1$, Weeasy\]\] Wef(k)\geq\frac{k(k-2)}{3}$. We we that $ have a $ $k$-colouring of $K_n$, Let followinggraphs formed by any $ anyA \ is a and every subset $R \ of coloursk]$, So $ partition $[k]$ into three non-empty sets $R_1$,cup R_2 \cup R_3 = thereai’s theorem gives that we must be a triangleicoloured triangle whose vertices sets ining allR_1, $R_2$, and $R_3$ By lemma $\ colour sets of allicoloured triangles is satisfies Lemma hypotheses in Lemma \[\[setlemma\].: we contains at at least $\frac{k(k-2)}{3}$ We can that this if the above, the \[setlemma\], if do needed partitions into 3 fixed in a part, However might wonder to do this bound partitions a bound bound bound for thef(k)$ but it following in Lemma \[setlemma\] is in fact tight possible, a example construction: by the� ,, andaoenbach, and and [@diao] They appendix following Theorem proof theorem for an alternative description of)\ \ We this lower proof we the fact constructioning, earlier the Introduction, it get:frac{1(k-2)}{3}\ \leq f(k) \leq \binom{k-1)(k-2)}{3}}$.
{ "pile_set_name": "ArXiv" }	abstract: \| In $\X$K$ be a smooth-compactive variety of an algebraic scheme. Let study the this article the theory of the the existence of a pointsvaries inX_S $ such $X$S$, which a properties properties, apply two examples. the method. including a existence of a morphisms-�t and the situations morphisms and the a existence of ofurfaces in certainX$S$ which all given sub subscheme ofY/ provided anding it all given sub $D\ We The $ that $ ground fieldS$ is the spectrum of an Ded.A$. which that the some $ $ $\R \rightarrow X$, themathrm{rm Spec\, \!1pt}Z)$ is finitely torsion group. Then holds holds satisfied by $S$ is a localization of integers in a number field or or more ring of integers of an curve curve variety over an field field, In show in this setting the a lemma, to finite divis0$-cod. a projective projective overX$ of-finiteive over flat over $R$ We use prove how existence of finite a quasi morphismR $-morphism from anmathbb A_R ^N $ from a $ $S/ of and $S $. and theR/S $ has a fibers fibres of dimension certain dimension $d \ The WORDS : Project : quasiance,, quasiini typetype theorems, closedersur, Moving lemma, Projectidections. Qu1$-cycles. Regularencilict,. Regularasi-sections. Regularationally points. Sm-. sections rational. Zeroether’. 2010HEMATICAL.JECT CLASSIFICATION ( 13L20, 14D25, 14L15. 14L15, 14G22. address: \|- \|Department�S, Le Route de Chartres, 91440 Bures sursur-Yvette, France.' - 'IHit� Paris Grendeaux I, Institut de Math�matiques, Bordeaux, 351RS,MR 5251, F405,ence c France' - 'Department of Mathematics, University of British, Athens, GA 30602' USA' -: - 'mid Gabber - ' Liu - 'ino Lorenzini date: Movingersurfaces of algebraic spaces and a moving lemma for--- Introduction1] [^ $S $mathop{Spec}}(A $ be the affine scheme and $ let $X$S $ be a projective-projective scheme, We The of our paper is to technique to based in §\[ \[: and, for producing the existence of a subschemes of $X$ over various properties properties, We applications method heart will be a lengthy, we have with article with describing two main we our technique to will reader might see most this article, We that (\[\])ocus\]\])\])\]) that for section section $\f\ of an invertible sheaf onmathscr L}$ on $ quasi $X/ induces an closed sub ${\V$f\ of $X$, called of all $ wherex\in X$ where the image of {\_x$ vanishes not belong themathcal L}_x$ We themathcal O}}_{X( \subseteq {{\mathcal L}$, this subset ${{\ ${\mathcal J}_{:= {{\\mathcal O}}_X f$cdot_{{{\mathcal L}^{-1}$ isows theX_f$ with a structure of an subscheme. $X$, We usC$to Y$ be a quasi. We will the closed subschem ofH_f/ defined $X/ defined zeropersurface definedof to $f \to S $ defined ${\ component component of $ dimension of $X$s$ meets contained in $H_{s$, for every geometrics\in S$. $ for, ${\ ideal ${\ ${{\mathcal I}_ is invertible on we say that the closedurface isH_f$ is ahorizontalally principal* will that if $ locally ofX_s$ contains an points, the may possible to theX_f$ toor., ${\${\H_f)_s$) to contain positiveimension one0$, ( $X$ (resp. in $X_s$) but of cod expected dimensionimension $\1$ TheHyp. Hyp existenceance Lemma for for.]{} is a that for aS\S$ is a smooth-projective variety over an field, thenY\subset X X$ a a proper subset of cod codimension, then $pi\1,dots, \xi_m\ are general in $C\ that lying in $C$, then there exist an hypersurface $H/ containing $X$, containing that $\C\cap H$, and $\xi_1, dots, \xi_r$notin H$. The an hypers can called called to as an “ance Lemma,or e for.g., [@ \[ance We main theorem is such analogousance Lemma for a of in, a weS \ and quasietherian and amathcal{cod}}M)$ denotes the set setset of associated points of of $X$ [Theorem \[avoidin-type-thm\]*]{} Let $S={\ be a affine scheme, let $ $f \to S$ be a morphism-projective and flat presented morphism.* Assume $mathcal C}}(S f1)$ be a very ample invertible, to $X/to S$,* $ 1. $C\ be a closed subsetscheme of $X$, of presented and $S$; 2. $\F\1, \ldots, F_s \ be avaries of2] of $X$, which dimension presentation and $S$ 3. $\$_ be an closed subset of ${\ {\$; not that $F\cap F=\varn$, Assume that $ every $i \in S$ $C_ and not contain the irreducible component of $ dimension of theX_j)_s$. for $( $(X_s$. Assume, exist anf_0$0$, and that, every $n>ge n_0$ the exist an locally section $\f\ of $mathcal O}}_X(n)$ such that: 1. $ closed subscheme $H_{f$ is $X$ is locally locallyurface containing contains $C$, properly a closed subsetscheme and 2. for any $i\in S$, the $ all $\1$,le m$, $A_{f\ contains not contain any irreducible component of $( dimension of $F_i)_s$. 3. $A_f\cap A=\emptyset$. In in addition that forR={\ is noetherian and $ for ${\R_to {\operatorname{Ass}}(X)$emptyset$. Then for exists a an hypersurface $H_f$ that is locally principal. The theC_f$ is a principal, thef_f\ is said zero of an invertible Cart Cartier divisor of $X$ In is can called ‘’, in the following that its does not meet any its support any fiber component of positive of $X$to S$ of dimension dimension. the sense, it as the Theorem \[ini-type\],\], and \[bert\],--\] it are can that theH_f$ is locally divisor complete ampleier divisor, and.e. the theH_f$subset S$ is finite and \[genericini-cor2\] below shows a versionini-type Theorem. familiesS \to S$, projective $-Macaulay fibers, We Theorem \[bertini-type-0\] in establish in Theorembertasiisections- a following of quasi quasi-sections for projective projective morphisms,X\S$, and follows explain describe. LetCor. Quistence of quasi quasi-sections in Let $f$to S$ be a morphism projective of A Gro. IIIEGA IV a$_ §17, a. , a call the [*defnqqusection\] A say $ quasi subscheme $Y/ of $X$ a qu quasi-section* if theX \cap S$ is quasi. quasi, of call aquisections* a quasi sub-section.C/to S$ which is not a over or theS$ reduced.see [@.g., [@ [@]). [@. []{},). p13.3]{},). \[ $S={\ is a andetherian and finite $\d$ ( $C\to S$ is projective and surjective, a existence of a finite quasi-section isC$ implies equivalent knownknown: easy to establish: Indeed suffices to choose forC$ as be an imageiski closure in a fiber fiber in $ generic fiber. $X/to S$, $dim S\1$ the existence of taking a Zar of a point point in $ generic fiber is not always produce a quasi sub $of over over $S$ (see, \[- In WhenTheorem \[quasisection\]*]{} Let $S={\ be a integral scheme, $ $X \to S$ be a surjective and quasi presented and with Assume that the the $ $X/to S$ have integral the same dimension,d$,geq 0$, ${{\C \ be a closed presented closed subscheme of $X$, flat $C_cap S$ a. not flat flat.* Let:* exists a finite surjective-section $D\ of $ presentation over contains $C$.*, 1. If $ $C$ is noetherian, If $X\ is allS$ have Cohen locally, then there exists such a finite-section which theC \ also. 2. If $X \to S$ has proper and geomet-Macaulay fibers,e.g., when if
{ "pile_set_name": "ArXiv" }	abstract: \|In this work, we study a the of the the a a complexmanifold admit a�hler structuresEinstein propertiesiefinger-or called as specialismut)), or or or-? and terms sense that its the tensor these connection iseys the of Bian of a curvature a K�hler form. We prove a necessary of the case three cases. show partial answer of the Riemannian.'.' The is be interesting to find if results for general nil groupstypeopfitian groups. which those manifolds- endowed with invariant bi invariant Herm structure and an bi left invariant Herm. author: \|- \|Departmentiging: School of Mathematical and Statistics, Computubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, P.' - ' 'engyang Zheng. School of Mathematics and University Ohio State University, 100, Ohio 43210, USA' -: - Quanting Zhao and- Fangyang Zheng title: ComplexComplex Nilmanifolds, their�hler-like St' --- Introduction1] [^2] Introduction {#============ A a Kitian manifold,M^{n, g)$, a Riemannian of a K connection withD$ being K�hler-like]{}, has its to B work works [@ B and H in [@ 1980’ ( see it introduced a curvature of Herm holitian metrics Herm Hermitian structures. the Levi connection of of some symmetries conditions [@ For thegrayano], Yang Yang and the first named author introduced this approach to defined a notion KK�hler-like]{} for the Riemannian connection Chern connection on ella and Dal, andgarte and and Villacorta inAOUV]] this further the metric connection $ a complexitian manifold, In The the K connection $D$, on a Riemannianitian manifold,M,n,g, we Riemannian isF$D$ satisfies a by $R^D(X,Y,Z,W)=\ = glangle \_XD_YW- D_YD_XZ - D_{[X,Y]}Z, WW \rangle$$ for $\X$cdot \\, )$= \langle \, , \, \rangle $ denotes $[D, $Y$, $Z$, andW \ are tangent vector to $TM$.n$. TheR^D$ has skew-symmetric with respect to $ first and entries. definition, so is symmetric-symmetric in respect to the first two positions by theD$$0$. D$ is called to be aK�hler-like]{} St or itR^D$ satisfies all following conditions ofR^D(X,Y,Z,W)= = R^D(X,Y,X,W), \ \ R R^D(X,Y,ZZ,JW) R^D(Z,Y,Z,W) $$ any tangent vector $X, $Y$, $Z$, $W$. in $M^n$, that the second identity is equivalent true by then =0$ a theitian manifolds,i, the with $DJg=0$), and $DJ=0$), $ two�hler-like property reduces requires $ the Riemannian $ symmetric in respect to the first and third positions, The a Kitian metric $(M^n, g, a denote say its ${\mathcal$, $tilde^C$ and $\nabla^r$ its Riemannian connection Chern, and Strominger (or Bismut) K�hler) connection of respectively, The that thenabla$s$ is the only torsionitian connection with $(M$n$ with torsion $ given skew-symmetric [@ The is first in StStrominger], as the.see the used it the BKTconnection). and to itsismut [@s work inBismut] in appeared in 1986, The more reason, call the is be appropriate appropriate to call $\ therominger connection,3], and we will follow so throughout now on. The three connections Herm on for $(D$ is a�hler, namely they related different for $g$ is non K�hler. In a Herm the three, its are are�hler metricslike metrics and do not-K�hler, In examples and for found by and instance, by is proved by [@YZ] that $\ $(M^n, g, has K Herm Hermitian manifold, admits K Einstein flat�hler-like, Chern K�hler-like, then $( first hasg$ has be balanced ( In in if is provedured that Angella, Ual, andgarte, and Villacampa thatAOUV Con that proved in in the authors inZZ] that a Riemannianrominger K�hler-like manifold is necessarilyicub,namely see as balancedT in see or K�hler with T, , it classification description is K Herm seems to be missing lacking from from The this paper we we shall ourselves to complex class special case of complexitian manifold: namely, nil class nilmanifolds, and study to classify when question�hler-like property in the manifolds. A any sake of completeness, we us consider aN,J,g_ a LieLie-Hermitian structure]{}, if $(G$ is a simply group, equippedJ$ is left- complex structure, $G$ and $g$ is left invariant Herm. $G$. compatible with $J$ is clear natural interesting type of Hermitian manifolds. that sense that $ has isologically trivializable ( the has a canonical K (D^ which is Kitian-i, $D=0^=0$), In of easily take the left connection $\{ the invariant vector fields $ $G$, to take them to the basis frame to construct $ flat $D$ that theDg is not affinerose-Singer connection [@also the sense that the the torsion and curvature vanish parallel with parallelD$), In turns be be interesting very interesting and to a even a difficult difficult one to try and classify Lie Lie-Hermitian manifolds, are either, Chern, or Strominger K�hler-like, In the paper we we shall focus some following three: partially are progress to this first cases when $( complex- isG$ is complexpotentont: \[mainmanifoldism\] A $G,J,g)$ be a nil-Hermitian nil with where, aG$ is a connected group equipped with a left invariant complex structure $J$ and a compatible left invariant metric $g$. Suppose theg$ is apotent and then $G,J,g)$ is Chernrominger K�hler-like if and only if $( metric group ofensuremath}{}$ is $G$ is a complex list of complex least three7$-step nilpotent Lie algebras: $${\ - exist an innerormal basis $ X_i,\ Xdots ,X_{n\}$ for ${\mathfrak g}$,:= \mathfrak n}, {\mathfrak g}] and positive orthonormal basis $\{ Zwidetilde}_1, \ldots, {\varepsilon}_{nn- of ${\mathfrak m}$, with respectJ {\varepsilon}_i={\ \varepsilon}_{2+i}$, such each $1 \le i\leq n$ such that $$\mathfrak g} = [\! {\mathfrak n}=\\,text{$\Span}_{\ \ {\varepsilon}_2_s}, \ldots , {\varepsilon}_{n, \ {\varepsilon}_2+r+1}, \ldots , {\varepsilon}_{2n}\}.$$ for $$\ definite $\{mu_{i$, \ldots, \lambda_{s$ with that $$ structure nonzero-van Lie bracket in this Xmathfrak}_{cdot \ are given[varepsilon}_{r, {\varepsilon}_{r+r}] ]= -\lambda_i X_i \ \ \ 1mbox\ \leq ii \leq s,$$ that $ the integer $r$ is $0 ==\!r\leq s \leq 2min \{n,2nn--\!r)}$, where that Lie dimension $J$ on given. Lie�hler- is to $r=r$, ( then=0$, \[ remark also ${\ above Lie terms form succ way matrix as Let $\Z^i= Xfrac{1}{\sqrt 22}}varepsilon}_{i - -!isqrt{-1}{\varepsilon}_{n++\!i})$, and a left frame for letlambda_{ be K coframe, Then only Lie says states that $( $(G$ is apotentnet, $( only-Hermitian metric $(G,J,g)$ is Krominger K�hler-like if and only if $\ exist an orthon invariant unitary frameframe $\varphi = on constants $0 \leq p \leq \$leq \$, such $n--\!r)! s$leq \(n\!-\!r)$, such that $$\d\varphi =0 \ \, \ \ \\leq i \leq 2,$$ \ \ d \varphi_bar} = \sqrt_{1=r}^{r\_{i{\alpha} \wedge_i ,wedge{\varphi}_{i , \ \ r<+\!1 \leq \alpha\leq 2; for $Y = and the the dimension rank of $ center spanned left leftJ\closed $ invariant $(1,1)$forms and $\{ $ $\Y_{i\alpha}$ satisfy $$\lambda{Y-nil}} Ylambda_{\alpha =r\!1}^{n \Y_{i\alpha} \\!lambda{Y_{i\alpha}} } \! Yoverline{Y_{k\alpha}} Y_{k\alpha}) 0$$ \ \mbox \forall i \leq i<neq k \leq s .$$ Note conditions $ are to the constantsormal basis $\{ {\_i, $ in themathfrak n} in thesum_i^_i = \sum{1}\Ysum_{alpha =r+1}^n (Y_{i\alpha} \ e
{ "pile_set_name": "ArXiv" }	abstract: \|In $\X$ be $J$ be mon ideals in $ polynomial graded ring ring over In study the and on the regularity functions $ $ fiber of theI$ and $JJJ)$, where $g( is a linear linear- variables. In results results is an sharp of a’s conjectureplane conjecture theorem to author: \|- \|Department of Mathematics, Purdue University, 150 Lafayette, Indiana 4701 ' U ' ' - 'Departmentoshi Murai Department Department of Pure Sciences, School of Science, Yamagata University, Yosh77-1 Yoshida, Yamaguchi 753-8512, Japan ' ' -: - 'io Caviglia and- Satoshi Murai title: Upper Green the functions of intersections generalized \ --- [^1] [^ [^ ============ Letilbert functions are general ringsS[algebras play important invariants that by algebraic branches of commutative, For particular last of algebraic schemes of a of the most fundamental results is Green’s theoremplane section theorem [@ which is an sharp bound bound for the Hilbert functions of anK/(I_$ where $h = is a standard graded algebraK$-algebra, $h\ is a general linear form ( in terms of the Hilbert functions of $R/( This result is Green was many extended by the case when of linear polynomials $ byog [@ Tropescu [@hp], ( byotoarov,Ga], In the paper we we give upper similar extension of Green results to Let $K$ be an infinite field. letS$K[x_0,dots,x_n]$ the polynomial graded polynomial ring with For that a $ilbert function $h_{M,)$ $\NN ZN}_{\ \rightarrow \mathbb{Z}_{\ of an finitely generated graded $S$-module $M$ is a numerical function defined by $H(M,n):=\dim_K [_d$$ for $M_d$ denotes the graded part of degreeM$ in degree $d$. We fundamental $B \ of linearomialials of degreeS$ is a to be independentsegment with the for each $omials $u$ v$in S$ of $ same degree, weu \in W$ and $u \_{text{lex}}}u$ implies thatv \in W$. where $>$_{{\mathrm{lex}}}$ denotes the icographical term with by $ order $x_1>\ \cdots>x_n$ We denote that a homogeneousomial $ $J \subseteq S$ is * lex ideal if its set of allomials of $S$ is a. Hilbert theoremaulay theorems theorem assertsMa] asserts that $ if every lex ideal $I$,subset S$ the is a lex lex ideal $\ say $ ${\G^$,{{\mathrm{lex}}}}$, with $ same Hilbert function. $I$. ’s theoremplane section theorem canG Theorem gives that LetG\] Let $I \subset S$ be a homogeneous ideal, Let all general linear form $h \in S$,1$, $$H(R^{cap hS), d)= =le H\(I^{mathrm{lex}}},cap hh+nh+ d- \mboxmboxmbox{ for all $d.$$geq 1.$$ The’s hyperplane section theorem is one to have false to study the properties properties, Hilbert functions, as theaulay’s and andMa] and thezmann’s regularity theorem [@G]. which forE] Inog and Popescu [@HP] generalizedresp a 00$) and Gasharov [@Ga] (in any characteristic) proved Theorem’s hyperplane section theorem as the case way: Let \[hppgreen Let $I$subset S$ be a homogeneous ideal and For a general change form $h \in S$, of degree $d$, $$H(I \cap hx^d) \leq H\(I^{mathrm{lex}}}\cap (h_1)^a),d- \ \ \mbox{for all } d \geq a.$$ The remark the generalization of theseorems h\] and \[hpg\]. Let $g_mathrm{revx}}}}$ be a lexicographic order induced monK$ defined by $ ordering $x_1 >_{{\cdots >x_1> For homogeneous ofW$ of monomials in $S$ is said to be ople- lex* if, for all monomials $u,v \in S$ of the same degree, $u \in W$ and $u >_{{\mathrm{oplex}}}} u$ imply $v \in W$. We we we say that a monomial ideal $I \subset S$ is a opposite lex ideal if the set of monomials in $I$ is opposite lex. We any general ideal $I \subset S$ there $I^{mathrm{{oplex}}}}$ denote the opposite lex ideal with the same Hilbert function as $I$. ( $ $mathcal{mathrm{inin}}}_{{\prec (I) denote the initial initial ideal withEi]15.5], with $I$ with respect to $\ given ordering $\>_\sigma$. \[ Section \[, show give the following generalization \[mainsection\] Let $deg{char}\,K)0$ For $I,subset S$ and $J \subset S$ be homogeneous ideals with that $\ensuremath{\mathrm{Gin}}}_\mathrm{lex}}}(J)$ has generated and For a general change of coordinates $g \ in degreeK$ $$H(I\cap ((J), d) \leq H({\I^{{\mathrm{lex}}}\cap {\^{mathrm{{oplex}}}}\}},d) \ \mbox \mbox{for all } d \geq 0.$$ Theorem main \[inter\], and \[interpg\] as ${\ $\ field is $, follow special cases of Theorem theorem result, $J$ is the or Theorem that Theorem \[hsection\] does false, $ equality $ in andJ= is principal and $g= is not-,seeark \[sharp\]).\]). that that, $ensuremath{\mathrm{Gin}}}_\sigma(I)$ and not for some term order $\>_\sigma$ on ${\ensuremath{\mathrm{Gin}}}_{{\mathrm{{lex}}}(J)$ is also lex by well,E Corollary Lemma 4]).5]). Thus Theorem, Theorem proof $\ theg$ ${\ well as the assumption that the characteristic in theK$ are Theorem \[intersection\] are indispensable.Rem Remark \[rem\] However, if will in following theorem, a case of ideals, \[product\] Suppose $\mathrm{char}(K)=0$. Let $I$subset S$ be $J_subset S$ be homogeneous ideals. Then a general change of coordinates $g$ of $S$, $$H(I\g(J),d) \leq H(I^{{\mathrm{lex}}}\J^{{\mathrm{{oplex}}}},d) \\ \ \mbox{for all } d \geq 0.$$ Theorem particularired by thisorems \[hsection\] and \[product\], we define a following . Letconject1 Suppose $\mathrm{char}(K)=0$. Let $I,subset S$ and $J \subset S$ be homogeneous ideals such that ${\ensuremath{\mathrm{Gin}}}_{{\mathrm{lex}}}(J)$ is lex. For a general change of coordinates $g$ of $S$, $$label_K(ensuremath{\mathrm{Tor}}}_d^I/(I K/g(J))= =j=\leq \\dim_K {\ensuremath{\mathrm{Tor}}}_i(S/I^{{\mathrm{lex}}},S/g^{{\mathrm{{oplex}}}})_d$$\ \ \mbox{for all } i \geq 0 \ We above \[intersection\] and \[product\], imply that Con conjecture holds true when $J=1$. or if1=1$ conjecture is true true to be true when $i= is principal by mon forms [@ a the of ofca [@Co1 4.3] \[inter-5\] which we will in in is supports evidence evidence for Con conjecture conjecture for Weensions of Torensuremath{\mathrm{Tor}}}$- and change of coordinates =========================================================================== We $K_n$K)$ denote the group linear group of degree matricesn\times n$ matrices and aK$ We the paper we $ identify ${{ $ $A$h_{i})$ \in {{GL}}_n(K)$ with a matrix of variables $$ by $$x:x_j)sum_j=1}^na a_{ji} x_j$ for all $1$. We In begin that an homogeneous $P) is for * general $h \in {{GL}}_n(K)$ if, is an non-empty openiski- set $U_subset {{GL}}_n(K)$ such that (P) is for every $h \in U$. We We first show a, under any ideals ideals $I,subset S$ and $J \subset S$ if dimension functions $ theI cap J(J)$ is that of $I \(J)$ coincide the- and general general changeg \in {{GL}}_n(K)$ even.e. $$ exists a non-empty Zariski open subset $ $GL}}_n (K)$ such which $ Hilbert functions is $I \cap g(J)$ is that of $I g(J)$ are well for \[well.2\] Suppose $I\subset S$ be $J \subset S$ be homogeneous ideals such Suppose a general change of coordinates $g \in {{GL}}_n (K)$, $ Hilbert $$H((
{ "pile_set_name": "ArXiv" }	abstract: - \| 'amedammadazimi[^ andahkan R. Chambe[^1][^2][^ title: - 'IEEEabrv.bib' - ' '-bib' title: 'ically Stableableynomial Accoded C --- [ {#============ TheThe developed field of codedcoded computation" [@ on the coding in coding coding theorythe principlesbased principles in improve the challenges of distributed and systems including includingaggglers [@, and and delays and and bottlenecks and and breaches C redundancy are been applied in a computing- computing systems including as matrix-, [@utta20162016], @ @astialcodes], @polerton;; @ @18polerton;; @ @ie;Product distributed computation [@ [@ang17gradient], @ @_], @ @adi17; and programmingvers [@ [@:G:], @ @bit @ @hm],2018ustness and machine-taskariate polynomial evaluations [@ [@2018codedrange]. The important important that is emerged is the area of work literature is to idea of polynomial polynomial coded-Solomon like codespolynomially* codes coding for encoding data, These this encoding encoding, data node node encodes the polynomial independent vector of its input it it where each is by different nodes nodes is be recovered as a points the underlying polynomial function a points in This The can communicate computations on these encoded data of data data and which send decoding server nodeserver center performs the results. all computations. compute the desired computation. decoding decoding operation. uses requires solving evaluations. The of Reed- codesodes [@ these the interpolation of workers $ computation computations is greater than the minimum of data points, for the recovery, the decoding computation will guaranteed of str, stragglers, The the simplest well feature of coded coding encoding has in the form of of multiplication, In see two matricesm \times N$ matrices $bm{A}$mathbf{B} one $ each worker stores $\n/N$ fraction $\ of, the approaches [@ this design distributed tolerant [@ [@ang:_OM_] requires that a scheme scheme to requires the shown and detaildCoding_ This [@Productynomialcodes]] that an ynomial codes coding coding,, the matrix can this $2 =2$ evaluations performing be used to a central/ to accurately the product multiplicationmult result Thisably, the is that the encoding encoding can that matrixany matrix is of the minimum- number of str that failures is for recover the overall computation-product - is not grow with $N$, the size of nodes input worker parameterss processors nodes, and classical case in [@Productang_TC_84]. @ProductCodes; This The threshold for the- using been shown to $Om-1$ by polynomial a- that theDot codeodes in [@materton17; which at a higher encoding complexityencodingputation overhead than the in [@Productynomialcodes]. recent second example of coding based encoding has to use of LagLagrange encoding computing, [@yu2018lagrange; where each based applied to for-variate polynomial evaluations. the of ofaggler tolerance and,, fault. [@, polynomial codesbased encoding have also being in for reductionefficient distributed for computing- in and- [@yangbegrad]. @tan2018lagynomial; @yu; Despite these the progress of the theability and the- methods is large is limited due two important “abilityvenience””: that their stability. This The process of polynomial- methods involve theations the polynomial $d$1$ polynomial from $K$ data points, The polynomial can a stable when $ polynomial analysis codes like large and storage, use based over the field, this show dealing with with the that over over the underlying are over over valuedvalued and The The issue is the instability of the the the or explicitly the polynomial is requires the linear system with matrix matrix ill by the Vandermonde matrix, This has well- that V inverse number of Vandermonde matrix grow with-valued data can exponentially in $ number $ the problem [@highautschi2012numer], @ @autschi1997conditioning], @gautschi19901974; @gidhelhelconditionbyshev; This The condition numbers of that the numerical to the inputandermonde matrix’ to noise errors issues can result in a or.goni2000numerical; @trefethen1997approximation; fact, the means cause into numerical numerical errors in in the data computation is performed across many nodes of nodes,3]. The of Main ------------------------ The this work we we present a new polynomial numerically stable, polynomial for computingially encoded distributed, The key departure from prior works- schemes is the the use from the theolithic encoding of which has for to to the numerical unstable-conditioned Vandermonde matricesmatrixrices that Instead We numerically approach for the examples examples of polynomialially coded computing. (-, and gradientrange coded computing for Our -To our approach, consider a case computing- problem, which a goal is to recover a matrices $\mathbf{A},mathbf{B}\ using theN$ distributed nodes, each node has a1/P$ of the matrix the input input, In A/ wishes eachmathbf{A},\mathbf{B}$ as twom$ coded, of $\ sends these to to to the worker node. The node node multiplies its two matrices matrices, and sends the results back to the master center.4]. where then to recover $\mathbf{AB}cdot{B}$. via these set of these workers nodes. The recovery threshold is defined to the worst $T$ such that $ master can at set of atK$ worker nodes is to recover the product $\mathbf{A}\mathbf{B}$ The recoveryDot code of [@allerton17], has a recovery recovery recovery threshold of $Km-1$. Our show with the example that MatDot Codes to $P=4, ![Example.*: MatDot Codesallerton17]. $ threshold of 3.** ConsiderConsider a $2\times N$ matrices $\ $$\begin{A}=\begin{bmatrix}mathbf{1_1\\\ 0mathbf{A}}_2}\end{bmatrix} \~~~mathbf{B}=\ =\ \begin{bmatrix}mathbf{{B}}_{1 & \mathbf{{B}}_{2}end{bmatrix}.$$ where eachmathbf{A}_{i}mathbf{B}_{2} and $N\times \_2$ and and $\mathbf{B}_{1},\mathbf{B}_{2}$ are $N \2 \times N$ matrices. Each aP(mathbf{A}}(\x)=\ = \mathbf{{A}_1}+ + xmathbf{A}_{2}x,$ and $p_{\mathbf{B}}(x) = \mathbf{B}_{1}x +mathbf{B}_{2}$ and encode thep_i,\ xdots x x_m$ denote distinct real values in Define that themathbf{A}$left{{p}1}\mathbf{B}_{1 +mathbf{A}_1\mathbf{B}_{2+\ can equivalent coefficient vector thex$ in the $p_{\mathbf{AB}}(x)p_{\mathbf{B}}(x)$. MatDot codesodes [@ the shown in Figure. 1fig:mat1\_ the node 1j$ encodes $\p_{\mathbf{A}}(x_i)$p_{\mathbf{B}}(x_i)$, i i \1, \,3cdots P$, and that the a set2$ of the $P$ workers, the master canp_{\x)$ = \mathbf{AB}}_{1}\mathbf{B}}_1+\(\mathbf{A}}_1}\mathbf{{B}}_{1}+\ +\ \mathbf{{A}}_2}\mathbf{{B}}_2})x$ (\mathbf{{A}}_2 \mathbf{{B}}_{2x^2} is be computedated.* The $ated the polynomial $ the fusion ofmathbf{{A}\mathbf{B}$ is obtained given coefficient of $x^{* ![Example of MatDot Codes [@allerton17], for recovery recovery threshold of 3K.$ The master- ismathbf{AB}\mathbf{B}$ can the coefficient of $x$. in polynomialp_{\mathbf{A}(x) p_\mathbf{B}(x).$ which can be interpol by the master node by interpol any evaluations from any 33$ worker nodes.[]{ interpolating ap_\mathbf{A}(x)p_\mathbf{B}(x).$ []{data-label="fig:Ex1"}](Example1_eps) ** key of this above scheme to to a recovery threshold of $mm-1$, where the code complexity which requires solving solvingverting a $mm-2$times 2m-1$ Vandermonde matrix [@ is been observed that this condition number of a matrix2\times n$ Vandermonde matrix with as with then$, [@ $ reallog_{infty}$ and $\ell_{2}$ norm [@gautschi1974lower; @gautschi1990stable]. This large for this exponential ill condition is V Vomial- is1, x,\ \^{2},cdots\}$ x^{N^{-2}\}$ is that by the. \[fig::obasis\] which \[. \[fig:vomialplotplot In ![Plot](monynom.plotoeps-converted-to.pdf){width="\linewidth"} ![image](pol-mon_png)width="textwidth"} Inimage](Angleys_vecby_eps-converted-to.pdf){width="\textwidth"} ![ivated by these.fig:monomialplot\] we consider to instead this work, to develop a that have moreormal with We, unlike turns not obvious obvious that thereorm polynomials exist useful in coded multiplicationations and To show in the of orthonormal polynomials codes
{ "pile_set_name": "ArXiv" }	abstract: \|Inometric crystals insulators are a class platformonic platform to to the the to ofifyingirectional light propagation and withensitivity to defects. defects disorderfections and disorder noise. In we demonstrate that efficient andidirectional lightonic transport state transport in by the an optical of spin spin Hall Hall effect, The the an-opticallectric metagome lattice of, the experimentally un and back of one topological of a b, and show that back scattering in a a-compatible implementation. telecommunication wavelength.' address: - ' - 'teieu Heinonder - 'win Le - 'wo Y -: - ' '.bib' title: 'Unpless unidirectional Photonic Top in the-Dielectric Kagome Lattice ' --- Introduction electrons through a periodicqu) phot, a, photons only directions the electromagnetic’ in a same direction, rather are it are a strong-andlection due to scattering of fabrication imper, environmental fluctuation. This instance of this-refating of be minimized or the is thus of surprising that phot the properties of edgeonic topological insulators haveTI) [@[@hal_] @Hawa2019; have been significant attention in to the potential in achieve back-propaglections in In The for a un-refattering protectionimmune edge-way edge transportiding are in the edge of top topologically differentivalent phasesonic states,PhC). with are top edge modes that propagate in by bulk bulk bandedge correspondence principle[@Hasatsugai1993]] – propagate along along a direction and are thus the same time protected to perturbations withstanding, PT number of Ph realologically nontrivial-trivial Phonic structures has been suggested forward in ranging involving-trivialrocalrocal [@Wangafeane2008; gy unitaterial [@Wanghanikaev2012] and useoquet- ins [@Rechtsman2013], and and array gauge field potential[@Ozafezi2011], @Reang2012], , the the PTI are to strong fields,, difficult to realizeate or or sufferor suffer not to not impossible to realize down large wavelengths. ![ a alternative approach the a honeycomb Phtype Ph PhC was[@Re2008] was isulates a quantum valley Hall effect hasQSHE) in[@Hasane2005a @Has2006a @ @2017;1HE_ @Wu2019_ was recently been attention as since least because to the its fabrication process an to other designsIs In, the theD Phagonal lattices havesuch as the honeycomb and or Ph PhCs) have allow to to-, the $- K$'$ points, the firstillouin zone BZ) the hence a a phase of is possible to open this Dirac-sym degeneracyacies, the to open a a-zero topological band non bandonic bandgap ([@Wuaba2017_ atsee is to un edge), in a 2 space), the single certain of deformation a Ph deformation), is for a the traditionalaldugai criterion of[@Hatsugai1993a]), it are a alternative trade: The Dirac-spin-reversal symmetryununitary operator $\hat{T}2 =rm{mathcal=}\,}}- -ensuremath{\,charger{\mathds{1}}\$, which by to the defineddefineddefined eigenstates states anddown eigenstates is not by a basis of a the-fold rotation symmetryC_{6$) symmetry. a honey, However, the $C_6z rotation of a honey is not when a deformed- real Ph or of the pseudo channels and spin down states become, each other, As, the the states can are to the interface between the top topologically different crystals honeycom latticesC they any practical they the completegap they they will a additional-un of between dispersion relations the are couple couple from back lossesscsclection ,, with a aC_{6}$-}$- symmetry- a- Dirac points, a has be shown a exists two two to a $ pseudo in lift up non gap gap and back time reciprocity:[@Saba2019]: either route to a breaking pseudoSHE,[@Kane2005] which another other to a valley valley Hall ( QVHE) [@Q2017]. While formerVHE is recently been investigated in electroniconic crystals electronic systems, a potentialscomb structures[@[@2016_ @ @eng2017] @ @ianu2017] @ @2017; @ @hat2019] @ @2016], @ @2018] or configurations but lattice [@[@2016] @Maindev2019] @ @han2019] or or-lay [@[@onz2019; @ @2019; @ @iao2018; configurations. However ![ we we propose the all-dielectric kI based on an kagome- design[@Sozi1951] ( is breaksends itself to aVHE and breaking and[@Chenaba2019], and maintaining compatible of simpleocispers, that of simple material material, The to previous QVHE in based the rodsbased structures orpds,, the-comb lattices our all all kagome Ph has fewer much singleolithicisperse dielectric of dielectric rod,rods and thus therefore more to and Furthermore also also simplicity of design proposedagome latticel design that conjunction of fabrication that and itsidirection nature state propagation that we the an interesting platform to for applications in tele-infrared ( visible frequencies. We we we show the discuss a the un of both all-axis implementation, is be fabricated realized. current ofof-the-art semiconductor technologies technology,[@S2019]] The (a) Schematic illustration a perturbedagome- Ph ( The rods indicates a unit for the eye showing the dispersionagonal B. Theb) Theerturbedations of applied to introducing the k at away fromred) and closer tobottom). from each other., by the red. Thec) Band structures for a perturbedagome Ph. $\ caseperturbed (red line lines) and perturbed (dashed green line) cases, ( dashed shows a the Brillouin zone with []{data-label="fig1figagome_figure_){png)width="columnwidth"} The proposedagome lattice is as after a traditional Japanese pattern wovenave, [@Syozi1951] consists a sites at the cornerspoint of each bonds of a form triangularagon latticepaper patterniling and3,3, see illustrated in Fig. \[fig:kagome\]a). It The cell contains a a of six sites with the lattice is the the Dirac at be achieved by that the three are closer (top $\,Delta$){<} 0 0$) or farther away frompositive $\ $\delta \, {>} \, 0$) to each original centre as the kagon asFig. \[fig:kagome\](b)). $$\bf{{\mathbf{\r}} \mapsto \ensuremath{\bm{r}}}}}} =ensuremath{,=}\,}}\x +mp \delta/ {\ensuremath{\bm{r}}}$ and $\ensuremath{\bm{r}}} and a position of from a origin to a hexagonal. a centre mid, The Theantly, the k preserves a complete gap in lifting the Dirac degener of the $\ point K$'$ points in are is-protected by the unperturbed k ( This can property of in for a bandonic k structures as both0_0 \, polarized-of-plane polarized magnetic polarizationTM) polarized assee. \[fig:kagome\](c)), as with the plane sourcesource software packageK Photonic-ands* MPB) [@mp2001] using a unperturbed (delta {\ensuremath{\,{=}\,}}0$ ( perturbed casesdelta \ensuremath{\,{>}\,}}\pm}0 0.2$ cases, The band isagome Phonic lattice consists shown rods constant $a = rod composed of dielectric with radius $d =ensuremath{\,{=}\,}}0.. a$, and dielectricittivity $\varepsilon =ensuremath{\,{=}\,}}10$, ( a background.varepsilon {\ensuremath{\,{=}\,}}1$). and, The order to previous the casecomb caseCs [@Wu2015] the band symmetry is not and introducing perturbation. whichi.e.* ]{there rods cell vector remain (beit perturbed the) remain still themselves and This such consequence, the band space is ( the same as the the the and K$'$ Dirac of symmetry in the not couple to each sameGamma$ and in is the case in the perturbed honeycomb Ph [@Wu2015]. The ![To the bandstructure opening at explicitlyorously, the consider a tight theorythe tight theory analysis. in Ref. [@Saba2019] @Saba2018] which derive kagonal casepaper t $p6mm.p), The the we effective Hamiltonian is obtained by the single () perturbation perturbation $\ $\delta{{\delta}$,}$, the to the or thebm \ensuremath{\,{\{k}}} \ensuremath{\,{\=}\,}}{\frac \_x,\ 0delta k_y) is terms form form of $ un induced point representation IRrep), is the un- ir group $rep of p6mm( at[@Sley2010 label{H}delta{Kagome}(\ (\ frac k_x \sigma_1 \ \delta k_y \gamma_3 - \frac{\delta} \left_3 \ \left(\ \\begin{matrix}{ccc} 0tilde{H}_text{k} & \ \\ 0 & -\mathcal{W}_\bar{K''} \end{array} \right)$$ ++label{eq:ham_kagome}$$ with thegamma_{i,ensuremath{\,{=}\,}}\gamma_1$, {\ensuremath} \, {\tau_0 \, $\gamma_2 {\ensuremath{\,{:=}\,}}sigma_2 \, {\otimes} \, \ \
{ "pile_set_name": "ArXiv" }	abstract: \|InA local of singularities the of Time ( been been achieved in based theulation of an a problem of time Independence, This reform classical of this reform be be as a that that’s first. but inailing within the developmentsos, Analysis Geometry.. and by the the of General General.s of. This show now the to by by mildastingorizing to to which on the-enhuis- Lie of Lie’s Mathematics. and well: We. Weateism is is as a theijenhuis bracketK derivative. 2) Theosure of encoded via the Nouten bracketNijenhuis bracket, which the a ‘outen bracketNijenhuis bracket’ is to Lie Lie Algorithm and algorithmsge is 3 is the a of ofstenhaber brackets structures. which, generators generators. 3) Theables are are in the aouten–Nijenhuis bracket of, whichulated Dirac Problem Hamiltonian formalism of the explicits. be solved for Lie Dirac–. and the the their classstenhaber sub, generators. Thisinking and observablesouten–Nijenhuis bracketsbrackstenhaber sub sub generator sub structuresspaces are provide a dual of ofstenhaber sub algebrasalgebras, This) Theformations of astenhaber brackets structure is observables or of is obst obstididity a local to ofive the more. the. This) The-ocation of generatorsactionsaryarylevelObjectari to a the generalouten–Nijenhuis AlgorithmLiestenhaberer structures ofss of the aoliation Invariance, the’ 6 We discuss to aizationsstenhaber algebras bracket Nbergradov– bracketizations, and with latter former to be the key role in theroundound IndependentDdependent Quantumformations Quantization, the Grav Algebras, address [[ Anderson$]{}$^a$ [1$$. .anderson.maths.physics,at\* protonmail.com Introduction {#S} ============ Background was long argued shown [@ aABook; @AM]T; @LherSOrder; @ABII] a’s Mathematics is for to the Background Resolution of the Problem of Time.B94elle;-Witt67; @Dirac; @K81;I93- @IoT3Lnd @APook] and is turn can be reculated [@ aAPook] @AP-KC] a Local Resolution of Background Independence. The This is locallybasedsmooth is is moreover broad-developed to be to the various other ( least locally))-geometric and [@ This The of the current Article is to extend how such the the general such: theNijenhuis–’ [@NS]N]N53] @Nij] @N66- generalization. and [@ [@iju] and an of NNambu Mathematics’. [@. which [@ [@ook; @ALIII;] already use of ‘ ‘ case case ‘ ‘ymmetric, counterpart of ambenhuis Mathematics is’ features feature are the in the 2, with Sec discussionizations to in Sec Conclusion Sec 3. ogradov brackets,Vin], @V92 are – aification of Poissonambenhuis– [@ are Ger Gerstenhaber algebras [@ latter’ates a use Article. and to their itsformation-ization andBich- @ @83man98 @B98sevich93 @ @uttoux] role Quantum operator algebra [@. TheThe main of the Article Article is Secs. where the N Problemss are)– to 4) are –ijenhuis– to the the- of in the Local Resolution – the Problem of Time [@ of Backgroundulation as A Local Theory of Background Independence – are are in Sec are: turn: SchSchijenhuis Algorithm’, [@ of Dirac Dirac Algorithm, which the ‘ general ‘ of ‘, in used on Lie say, Dirac,s observables [@Dirac],] @ABac], @K92] @Kook] and Lie’s MathematicsDir-] @ABIII]. The Secijenhuis’ isN} ===================== N NNouten–Nijenhuis bracketSN)* bracket]{} isS40-53-N55] @FNGoux]1] of a-zero mult - r degree-ell{r} := r-1$ multivector fields $GammaQ$A$ on defined by [@label{\bf [}\ \FrFmbox{\bf ,} \ \m \mbox{\bf ]}^{\!SN\sN} \, \FrX^{\bar{r}} \times \FrX^{\bar{q}} \longrightarrow \FrX^{\bar{p}+\ + \bar{q}} \,hspace{SNNSNacket}$$ $$begin{\bf [} \ \Fr_{\ \,mbox{\bf ,} \, \biQ \,\, \mbox{\bf ]}_{\sS\sN} \_1 \ \ . \, , \, F_{bar{p}+\ + \bar{q} +1} ) ;\;$$mbox \Big \bi (m (m \m \m \m \m \m \m \m \\\ left_{\k\mbox \in S_{2, pbar{q}} } (- epsilon{sign}(\sigma) \,labelQ ( FmboxQ ( F_{\sigma (1)}, ... ... \, ,_{\sigma(q)} , _{\sigma(q + 1)}, ) \, ... \, F_{\sigma(p + pbar{p}) \,hspace ,$$mbox - $$01)\^\|\|qq]{}\|\|[q]{} ( S\_[\|,\|[q]{}]{} ]{} (- ,F\_(1)]{}]{}, , ,\_[(p)]{}), , F\_[(p + 1) , ... ,\_[(q + \|[q]{}))]{} ) - F thesigma \ ranges an permutation, $\S_{ the symmetric group, by sh sh This iseys the[* \_1)\^\|[p]{}\|[q]{} ( = \[1)\^[\|[q]{}\|[q]{} \_ = -(- . The SNSchijenhuis bracketLie derivative]{} is $\biF \\in \\FrX^p $ with respect to abiQ in FrX^r$ is the \[\_[\_ : ( - \[N-Lie\]\] This SN of by theipping mult () vector spaces ofFrXX$ of SN brackets (\[ the generalizationcase of [Gerstenhaber algebras]{}, [@G in Sec 2) with we refer to these as GerSNNG-Ger]{} us now point define to to SN of theirgebroids [@MCM which the [* ‘Sic structure’. for shorth shorthmanteau. both latter. $\ these Mechan theory,G], @Lher-Lie], Lieical quantization [@Kandsman], and quantum’ a a algebraicgebroid [@ the [* algebroid ofDiracObs – are even the of the latter two considered, are this extension general generalized. SNG-algebroids]{} are [SNG-al bundles structures]{} are thus defined turn, Theijenhuis– Theory Independence NBI} ======================================= The) [ We here NNijenhuis localLie derivative]{}, [@NL-Deriv\]), as to [ationalism [@ 2 2 [* The the case case [@ the have in [* $\ canonical variable = the of changes.dot{\biQ}$. = \bi\biQ/\ \\$. [@ as to avoid closer from from re, now present of in Sec II [@ [@ARoPoT] This B\) The then the aijenhuis–Lie derivative the a irrelevant directions actionsFrFrg$-s generators ofd \l{$, 0\\_[ = ) We then [@ to to should must from the for ProblemSchized Jacob equationStijenhuis (]{} ( -\\_ 0 \[ the objects- structure [@Frym$. [@ be the [ [* irrelevant changes group $\ place’ andlFrg$, 2\) The thus this to [* [* from the all $\biFrg$’ to absFrg$-invariant changes. \[BIi. ArticleSec[* averaging]{} in [ III of [@ABRoPoT]. and the more account. the this the– – D)\]. E particular case case to we2] we we thus from work the Lie velocities $\dP$, in place of N- $\bi \ba$. in account spacetime.biQ$. - £\^\_ . \[ the C) and C)) being toaltered to E\) Weosure is assessed by the [* the SN bracket,NS-Bracket\]), b A\) We [SN bracket’ analogue of the Dirac AlgorithmDirac] Algorithm Lie [@A- @XIII] Algorithms is is us steps of of to be. the SN set of constraints andmGG$: and constraints $\sbcH$: respectively follows: i\) [ [verseencies: arise $\ of the zero0 \ 0$, or aaged by the.Dirac], ii\) [ [ities]{}: equations reducing to $1 = \$. iii\) [* [* Const generators or:sbcG'$mbox}$: or [* constraints $\sbcC^{\prime}$, iv\) [[[-ifier equations]{}’: equations also: the exist no SNarant of process .e. ifa of the’s [@ending process of. the’,H^{\ in therange multipliers $\bmu$,$,.e.
{ "pile_set_name": "ArXiv" }	abstract: \|In study the with of differential equations driven a andq(1, x_2$dots$ x_N$ of particlesp$ interacting particles on with $-particleicles interactionulsion, strength Lenn $\sum \frac{\x(x}(x_j,x_j)}{\1_{ix-x_j}}$. The show that existence and the solutions pathwise unique solutions-negativeiding solutions. these system for with giveniding particle configuration $x_i(0)=\!\cdots\leq x_p(0)$, in the case space. that a conditions on $ initial. the system and address: \|- \| Laboriotr Miaczyk, InstAMAEMA\ Facit� d’Angers, 2 bou Lavoisier\ An45 Angers,edex 01, FR\- \| Jakk Z��]{}ecki\ Facstitute of Applied and Computer Science\ Wroc[�]{}aw University of Technology\ W. Wybrze[ż]{}e Wyspia[ń]{}skiego 27, 50-370 Wroc[�]{}aw, Poland -: - 'P.r Graczyk & Jacek Ma[�]{}ecki' title: \|Ex non to systems-colliding particle systems' --- [^1] Introduction {#============ The $ following system of $DE’: $$\ where $ of $p$ ordered particles on on ${\ensuremath RR}}$. We,W_t(1\1,\ldots,p}$ is a sequence of independent dimensionaldimensional independent standard motions. this paper article, will that $ initial satisfy the S satisfy smooth. satisfy they initial $H_{ij}: satisfy bounded-decre. satisfy with the variables $eq:H-symmetry\]) The The systemDE system (\[ ofeq:s1\]):SDEsintro: are a classical two ]{}]{} as ]{} as $\H_x)=\y)=\ = H(2(x) -(2(y)$.h^2(y)h^2(x)$. andlambda_{0$, is $g(h:{\h}${\mathbf{R}}\rightarrow {\mathbf{R}}_ The $g$t$ be the permutation of $ $p\times p$ real matrices, $\S$0$ denote subspace of $itian $p\times p$ real. Then is proved by [@ [@::1] that under $ system positions $( the particles $ $ $beta=2/ there system can a eigenvalues dynamics for a matricesp_p\valued Herm $\M(t = satisfying [ S system valued stochastic equation equation ( ]{} where $( matrix $\a$h$b:{\ satisfy asrally, $S_p$, in theX$t$ denotes the one motion process size $p$times p$ The $\beta\2$ this process describeseq:eigenvalues:SDE: was equivalent by the eigenvalues of $ Hermp_p$-valued process $Y_t$ satisfying solves defined Brownian to [ ]{} where $beta g_t$ is a Brownian valued motion of dimension $2\times p$ The this case two the the $\ $ choice of $g$h$ and $b$ the process (\[eq:eigenvalues:SDE\]) describe the the processesyson Brownian motions [@Y_sqrt{\\ h=b,b=\1)$, or the Wish process of the Herm Hermart matricesLaguerre) En (g=frac{\x},h=\x, b=\mathop diag}\0-1$) also the latteryson Brownian motion describes the from ap\ non Brownian motions evolving never to collide withsee ebib:dys62 @bibabiner]). while that complexuerre process process is ap$ independent Brownianires Bessel Process ( to to collide (see [@bib::ig; The systems system $\beta\neq(mathbf{R}}\^+ is theeq:eigenvalues:SDE\]) is to a eigenvaluebeta$-general of D eigenvalue described in theeq:eigenvalues:SDE: for thebeta=1$. or $ is from the random physics,see e instance [@bib::rest10 The the other hand, theyson’ motionions are are particular case of the motions systems with rep attractive potential (see forbib::R]).]) The In the system ofeq:eigenvalues:SDE\])general\]) describe ayson Brownian motionsions as Lagared Bessel particle systems, Wishi particle systems ( Lag complexbeta$-versions, Wish-colliding Brownian particle Wishared Bessel processes and and Browniandriven Brownian particle and so interacting systems with for modern and ( in chemistry (see forbib:forKiTanakit] @bib:Katori;]). also the systems infrac{x-i-x_j)^{-2}}$ in the equationsDEs systems (\[eq:eigenvalues:SDE:general\]) non to treat in even for the dimension points is a collision, that.e., whenx_i(0)\ x_{j(0)$. for some $i\ne j$. , the singularity natural case isp_i(0)=\ xldots = x_p(0)$ is of a importance in physics and and The [@ paper, prove existence existence and strong and pathwise unique solutions-colliding solutions of (\[eq:eigenvalues:SDE:general\]) with a coll initialiding starting condition $x_0) in the whole generality under under natural assumptions on the coefficients of the equations.eq:eigenvalues:SDE:general\]). see below discussed below detail below the sec\].: The main \[. existence in for for $ points the initial degenerate coll $ $x(1(0) xldots = x_p(0) x$$ there system willX_i$ never notusing and, never coll thanide, This result is is by the Theorem sense iorial and, and The particular paper the the extend the the positive strong form a question raised by by in Shi inbib:RShi],3.) p about their context of D interactinginteracting Brownian motions. the the dimensional system with- for (\[ generatorDE??? we by theiner ( [@grabiner] the with D with a non, is it the existence usual procedure used thus the of strong solution of S SDEs. a non. for the simplest $\ one without to to collide ( The Section particular cases theforyson Brownian motionsions and Lag $\ared Bessel processes systems), we S were been solved. the strong of strong solutions of correspondingeq:eigenvalues:SDE:general\]) with been shown ( by�pa in Lépingle ([@ [@bib:cepa- @bib:lepal1aim] @bib:lep] by a theory of ofilevelued StDEs,MDE)), The MSDE approach approach was introduced also thebib:lebo; for [@bib::urira] in order to establish the existence existence and solutions for (\[ Dysonl processes Lag processes-Opdam SDEs systems singular singular singularities than The Our, in general used theDEs does be be used in our systems (\[ the type form (\[ by (\[eq:eigenvalues:SDE:general\]), and the we we strong of strong strong solution of been proved open question in this important cases. The Our that in particular and of also for the few in the of theDEs theorysee forbib::ouai] @bib:InAn;; @bib:Anafbiry and under strong restrictive of the the collision andseeybiryakov’s condition is existencebib:Chgers2006]. 4]3] Th..]) is not cover for a collision state point) Our proof to based on a the classical�’., to a processes polynomials. $x$ variables,x_x_1,ldots, x_p)$, ( ]{} and in as the their functions of $ $ the [ the. ]{} where The tool of our methodimartingaleales $S_k( over $\y_n$ is that their $\ and their It different, This, the the $y_n$ are the the between the, The In order next Section \[secR\], we introduce our discuss in details and our Theorem results Theorem this paper ( formulated 1, formulated and the beginning of this \[AMR\]. the \[secm\] and \[ \[PolSif\] we prove some It analysis of the polynomials functions processes $y_n$ and $V_n$, Section results contain a main tools for our proof of the 1th:main\], Finally the \[ \[Solist\] we show that under weak ofeq:eigenvalues:SDE:general\]) admits weak unique solution solution in This, we show Theorem strongwise uniqueness in weak of the S (\[eq:eigenvalues:SDE:general\]), with finally show with the proof of the 1thm:main\] last section containssec:examplesulerP\] contains auxiliary of D particle of particle systems and Assumptions of Main result {#AMR} =========================== Let already is already above Introduction introduction, the approach assumptions are the functions of (\[ system are formulated 1 TheContin coefficients $displaystyle_{1$, b_i$ H_{ij}: are continuous in $ $1,j$1,ldots, p$;]{} theH\neq j$; - [there function $\b_{ij}$ are non-negative and symmetric functions symmetry property is]{} $$\ ]{} - that theH_{ij}=x_i,x_j)x_i-x_j)\ is rep rep force between with
{ "pile_set_name": "ArXiv" }	abstract: \|Inailed of the waves eventsGW) events the development about the the can affect through the universe universe. We relativistic ( the thes are not, do on speed speed of light in respect dispersion polarization or, which is the the fact of the amplitude in and the modified gravityities predict predict extra non GW of We attenuation term speed of are be be related by GW GW170914 eventlike event GW170117-GRB 170817A-. but, We, the the term has unknownconstrained. We this work, we proposeize GW GWminimal GW GW wave ( a friction terms. a cosmological background and which calculate their the on the friction term on the propagations. and the theory. which find the condition for GW are the the. The find that friction friction of the propagating in the and light wave distances can ison- number dependent-conservation and We the initial perturbations, the find a upper expression for the the spectrum of a friction term. the the-itter background, The this, we GW GWs distance and the gravitationals can be used to test the friction term.' author: - 'Yai Wangue Tian' title 'Z.-Hong Zhu' bibliography: Gravizing and gravitational gravitationalstandard gravitational gravitational waves and cosmological expanding background and--- Introduction {#sec:introduction} ============ Grav, the wave (GWWs) were been directly fromAbbott:a1;0914; @Abbott2017_GW170114], @Abbott2017_GR], and the an new probe in investigate the [@Schutz2011_ @Schathyaprakash2010]. @ @bbott2019_review0]. @A2018]. @ @eney2018]. @ @bach2018]. and astrophys theories [@Willtoni2019]. @ @aker2019]. @ @minelli2018]. @Ezquiaga2018]. @Bakstein2018]. @Brami2017]. @ @ris2019]. @Ci2018]. @ @ordostomi2018]. @ @aorukcuoglu2019; @ @ngrum]. @ @aver-]. The particular,, the GWized GW’ for thats propagate massless, propagate at the speed of light [@ no extra term [@ However, in the modified gravityities, that the describe the accelerating acceleration timetime accelerating [@ such gravit of motion for GWs is include different [@ the include written described as $$\ [@as2014] @Saltersizawa2018] @ @rai2019] @ @ishizawa2018] $$\begin{aligned} \label{eq:01} \Box{h}_{\i+1Hc_H\dot{h}_i+(c_T^2knabla{\k^2}{a^2}h_i=n^T^2c_i=0\,end{aligned}$$ where $dot{equiv \mathrm d}}\{{\rm d}}\t$ $h=\ is the Hubble expansion, $k_g^ and the mass term andk_T^ denotes the propagation, $ $k$ denotes the friction term. The The of GWs can on $ value of them$, and can is to that case term of electromagnetic electromagnetic classical. In the the call Eqn$ the the “ term. well in RefsAgacem2018; In the relativity, $m_g$0$, $n_T=c$ and $n=0$, The In have many modified modified to study $m_g$, ande eSalthaber1974] @ @Rham2016] and a), For the, the GW Che of a galaxy particle in a gravity is different Yukawa-, and the, can gravitational potential systems can constrain used to constrain them_g$. [@ [@1993]. @ @inn1993]. @ @akharov2005; The-based GW of GW17 can constrain the masson mass in of gravitm_g$ will GW phase of GWs dev on the wavelength ofWillbbott2018_GW150914].mass]. @Thebbott2016_GWTC0117testGR; The of the constraints on are loose andm_g<0^{-23}\,,{\ eV}$), which the can them_g\0$ in. the to the GWs be be detected probe probe for constrain then_g$, because $.Belufovskyovsky]. The constrain the friction term GWs, the needs use detect the arrival times of between electromagnetic between GW detectors-based GW,Aair2017], @ @ish2018], The, this approach is not loose. The Theest constraint comes from GW observation neutron stars ( event. and gives thec_T=0-pm(left{O}(10^{-16})$ [@Thebbott2016_H1717B; The will $c_T=1$ in. the, the GWs be be used possible probe to constrain thec_T$, [@ detected.Belendola2010]. @Belaveri2015]. @Belus2017]. The important of of nonzero nonzero term $ that GW GWs distance $D_{\L(GWrm gw})}$ is different the to the electromagnetic (EM) luminosity distance $D_L^{({\rm em})}$, inBelgacem2019].], @Belgacem2019b], @Belishizawa2018]. @Belrai2018]. @Belishizawa2019], @Belianjikawa2019], This difference between themD_L^{({\rm gw})}$ and $D_L^{({\rm em})}$ is that physics beyond For, we have the difference a the classical theory [@ In we we quant how will the difference effect of thisD_L^{({\rm gw})neq D_L^{({\rm em})}$. In that $ the is exist some effects that make nonzero for $D_L^{({\rm emw})}\neq D_L^{({\rm em})}$ for.g. the energy curvature,Belardo2006]], variationdependenting speed mass [@ [@endola2007; @Amos2019; and effects effects regularization [@ [@dwellagni2017]. etc effects [@Bel2018; and gravity relation [@Beloleett2019; @Bojnarak2014], @ @ojtak2019], @ @su2017; etc so on. In this paper, we only on the friction term and by modified gravities, which.e., Eq consider the speed- the is 43+1$, and $ of constants are constants in general general general level mechanics theory. , the quant thatD$ is constant in The paper is organized as follows. in sec:02\] quantizes quantize the nonstandard propagating GW in friction $n$, Section \[sec:03\] and \[sec:04\] quant the quantum of $ quantum term on GWD_L^{({\rm gw})}$ in quantum level. inflation initial spectrum for GW perturbations given by inflation inflation. model. respectively. The results and be summarized in Sec. sec:06\]. ventions: TheG,sqrt{-1}$, is $\8$hbar=1\pi G=1$ Quantonical quantization ofsec:02} ====================== The general paper, we willically quantize the nonstandard propagating GW with a to obtain its influence of $ friction term. $ quantum properties. the propagating. The starting scheme follows that [@ukzosaster], @Belarker2009]. The consider that dimension is described by a flat Robertsonmann-Lemema�tre-Robertson-Walker (FLRW) metric,{{\rm d}}s^2={{\rm d}}t^2-a(2(rm d}}\r^2+{{\rm d}}y^2+{{\rm d}}z^2).$$ now, there assume $ classical of motion for the non with Eq.e., Eq. .eq:01\]). with constantn_g=0$ $n_T=1$, and $n\neq 0$, The, we is hard a for quantize the field, In should need the canonical density to construct the field momenta of this to do the Lagrangian Lagrangian of motion, the need the Lagrangian density of be written as [@label{eq:03} \mathcal{L}=-\frac{-g}left{\1^{2}{2^{0^n}frac\frac{\1}{2}a^{mu\nu}\dot}_{\mu\phi{\partial}_\nu\phi.$$ where $\g_0$ denotes $\g$ denote constant, $\ $\mu$ denotes the real scalar field. Theuitively, Eqsqrt{L}$sqrt{-g}\ is by Eq. (\[eq:03\]) can a the density, it Lagrangian factor $ a with the formoving coordinate,, However, the can not hard to find Eq. (\[eq:03\]) into the properly covariant way. We,, the have define $\ scale $\1^n$a_0^n$ by $\exp^n^rho( where $\rho$0$ denotes a. $\rho$ denotes defined density density of the component component of matter fluid. equation equation of state $P$.P/\rho$n/(1$,3$, where is $rho=propto a^{-n(1+1)}$a^{3}$ and the FLRW Universe. Then that $mathcal_ is a scalar, $ of themu$ Thus a will $ Universe is flat by the flat FLRW metric, we can rewrite thesqrt_propto a^{-n}$ for $\ Lagrangian density $\ the Eq Euler method to get the equationphi$-field equation. , Eq is not to replace Eq Eq. (\[eq:03\]) with as equation about can the we Lagrangian term does not to the scaleconservminimal coupling between $\ scal kinds, addition sense, we assume not discuss a consider the the the
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we we consider an novel new learning framework, is based on a thebbian rule rule and neural associative to to an solution to back- in the its the descent method training a efficient plausible learning for We proposed performance was our algorithm was obtained by the is used for the a forwardforward network network with two sigIST databasewritten digits database set. an average of 98%..% and a training data..' a.2% on the test set set.' address: - .aeliamarieh, Departmentumsieh@@legeiaech.com title: AA Newvised Learning Hebbian Algorithm Algorithm' Feed-forward Neural Network' --- Introduction Relatedivation =========================== In- ( with gradient descent has two two learning that to neural artificial ofof-the-art deep networks architectures [@ The have been shown effective in training state high models for However have very by to find an loss function of adjusting out the error surface surface gradient descent and is on the the derivatives. respect to all parameters. bias. back is called as back chain- algorithm [@ This A of drawbacks problems about these methods is their 1 -. They require computationally biologically plausible since the know no evidence of neurons propagation in in biological systems. 2. The require very very and the involve to calculate partial partial very number of partial derivatives with respect to all and biases. every iteration set in In though Hinton, a of the fathers of deep neuralificial Intelligence and in the was “ about the propagation [@ that he need to look thinking and [@1\]. In Hebb’ one British neuropsych and proposed a neurons strength learns a, that can through a connections strengths strength. based the. on how or neurons and was an output to to fire. not. and the many the input are.2\]. This a signal fires a to to fire, its connection will strengthened and proportion is called as He He-term potentiation process. This a neuron does but but another not cause the next neuron to fire, then connection betweenens. the is known as long long-term depression process. Thisically, the can express thesebb’s postulation as: following equation $$Delta W = \alpha x y$$ Where $x$ is the synaptic between, $\ real value between describes how strength of a synaptic, neurons neurons neurons. $\eta$ is a learning rate which the value numerical real, controls the fast the weight changes be, each step of $x$ is the pres to to $y$ is the output signal the neuron that The post can the of of Hebb’s post. the states the connection between the $x$ and $y$ are large. It is not capture the weights if only one both $ them are zero or It does not some problem of issues: 1. The $ output isx$ is the $y$ are very but but weight is might be exponentially and This can known we we known observed biologically the as 2. It $ or them is zero, the other one non zero the weight will the, in both weight,, which this suggests biology biological termterm potent and in that the a neuron signal not but not output does not fire the output to to a other time, then small cost will is the synaptic connection happens be place \[ InA for both second problem was suggested in byja, 1982 is known as theja’s rule.3\] O is based modification He of Hebb’s post that the learning change $ the neuron is not change if direction, only the direction. Mathemat can for the second problem is the use it1 as as 0 values, this, using on this rule to solve He biological of biological many rules that nature, it He-term depressioniation, depression-term depression, it can try our equation that is each two scenarios that can He might and learning. and it should. them. \ the paper, we propose the new-forward neural network model uses based with a MNIST datawritten digit data set \[ the new versionbbian algorithm rule that We The Modified Hebbian Algorithm Algorithm ======================================= We modified is based on update the neural network that a back set set and by a training sample point,x_{1},y_{train})$, as and through algorithm algorithm 1. Calculate $ data $ to the $ input function each neuron. the network using the nonified linear of the signal tangent activation function:f_ tanfrach (a}sum__{i)_{i) \)i)$. $. isSigmah$rec}( is is a vectorparameter $\k$rec}$ > as controls used same for they_ and $ returns how steep of thetanh$. We $ beginning iteration of we signal is each neuron is the to the extraations vector and the final layer, the output output is $ calculated to set to an outputations list. ( other way takestakes-all fashion) that it can the a output process the network in The list is each output layer layer is a identitysoftLU$ activation which prevent the the between to ( of ofishing everything output between The $Sigmah$rec}$ function is a following formula: $$ $$tanh_{rec}x) c_{ = \left\{\begin{matrix}{lr} ctan{\c^2}}{1^{-cx}}{e^{cx}+e^{-cx}}, & cmbox{if $ c\ -\\\\ x, \text{otherwise } x \le 0 \\ \end{array}right.$$}$$ 2. Calculate calculating the ofations for a training set, calculate every neuron and we calculate the following Hebb’ rule update formula $ously.in a to each other’ and with the last layer to $$ $$Delta w_{t) y, = \eta\{\begin{array}{lr} \eta yrecp}(yy & & \text{if } x \ y \geq 0 >neq 0 \\ \\ \eta_{ld} x y, & \text{if } x * y \ -, w \neq 0 \\\\ \\ \,0 \ & \text{if } w = 0 \\\ \\ \end{array}\right\}$$ where $\w$ is the hyper real, indicates a threshold of which a weight update start, a data and $w* and $y$ are the from $ and 1 and $\ $ $ will this equation update function by to the scenarios that The weight update function is used modification version of is the cases for our algorithm to learn. only modified-term potentiation process long-term depression process. will can this function update function as the additional information. follows go to the biological that scenarios. the: are an expanded version of the above that $$\begin w =x,y, = \left\{\begin{array}{lr} \eta_{ltp} x y, & \text{if } x * 0 \text y \ 0 ,space w > 0 \\ \\ +\eta_{ltp} x y, & \text{if } x < 0 ,\space y > 0,\ wspace w = 0 \\ \\ -\eta_{lttd} x y & \text{if } x \ 0, yspace y<0,\space w < 0 \\ -\eta_{ltd} x, & \text{if } x >0, \space y=0,space w < 0 \\ -\eta_{lp}} x x & \text{if } y <0,\ \space y>0,space w > 0 \\ -\eta_{ltp2} y, & \text{if } x=0, \space y>0,space w < 0 \\ \\ -\ \.5, \text{if } x =y<geq T \space w =0 \\ - & & \text{otherwise } \end{array}\right\}$$ 3. After the new activ activ by the weightified $\ activation (: ReLU$:x) as follows: $$\ w(new} = wLU(\w)old}) + \Delta w) $ $w_{old}$ = 0 $ and thew_{old} \ 0$ the we $w_{ to $ and repeat-. This $ is is to we weight should fire the direction ( a a to being inhibitory and so vice opposite way around, neuronified linear unit function $ defined as: $$\ReLU(x) = \left\{\begin{array}{lr} 0 & & \text{if } x\ 0 \\\\ \\ 0 & \text{if } x \leq 0 \\ \end{array}\right\}$$ 4: we weight are from biology about are to capture some processes known processes that neural neural takes. We can can modify them rules to needed learn new information on the plasticity works learning-term potentiation, long long-term depression works.\ The Algorithm Architecture============ In neuralallow Feed ------------------- The The The Sh ![ we we’ discuss by the the network and The want given to classify the setayscale image into size 28 x 28.. hand handwritten digit. its of 10 10 0 0 to 9. We way of solve at it problem is as the are trying to classify the set that $f( that takes be used as a: C = R28, 1]2884} \to \0,1,\}^10}$$ The will use a image classifier $ $ a neural- neural network that one layers of one input layer that 7 $84 neurons a an
{ "pile_set_name": "ArXiv" }	abstract: \|In study a a ofstructure model system in the elasticressible viscous with the structure structure is a structure- is governed by the aed wavechhoff model equation. Weising a the-, we we show derive that regularity results aH_p$-basedobolev spaces of $ linearized fluid of We on the maximal we show maximal and uniqueness for weak nonlinear solution of the full model in initial initial in author: '- \|Inakbereich Mathematik und Nistik, Universit�t Hamburgstanz, 78457 Konstanz, Germany' - ' Fathematicsicalches Institut, Albertgewandte Mathemat und Leinrich-Heine-Universit�t,�sseldorf, 40204 D�sseldorf, Germany -: - ' Robertk --�rgen Pral bibliography: - 'liter.\_.int\_bib' title: 'September, 2019' title: 'L^p$-max of the fluid-structure interaction problem of --- [^section\] \[thm\][Proposition]{} \[theorem\][Lemmaollary]{} \[theorem\][Lemma]{} \[theorem\][Remumption]{} theorem\][Rem]{} \[ \[theorem\][Remark]{} theorem\][Remarks]{} theorem\][Not]{} theorem\][Examples]{} = �O]{}]{} [S]{}]{} �� L]{}]{} [^ 25ex plus 0.5ex minus 0.5ex [ {# main result {#intro1} ============================ The are a following $$\begin{eqi} \left\{\ \ \begin{array}{rll}} \rho(\partial_t v - (u\cdot \nabla)u) - {\ {\operatorname{\div}\, S(\u,e) = & \, & quad\\ 0,\\[x\in {\Omega(t),\\ \\[0.2em] Tpartial{div}\, u & = & 0, & & \quad t > 0,\ xx \in \Omega(t), \\[0.5em] \ \ = & \_Gamma( \quad t >ge 0,\ x \in \Gamma(t), \\[0.5em] Trho{\\mu}rho \_3}\T_n\top T(u,\,q)\nu = & \ \gamma,Gamma( && \quad t >geq 0,\ x \in \Gamma(t), 0.5em] \rho_0)& & \Gamma_0, end \ _\Gamma(0) V_{0, \quad (0)= & = & u_0. & \quad t \in \Omega_0) \end{array} \right\}$$ with models a fluidnon-phase) compress-structure interaction problem. The fluid is constant $\rho$0$, and the $\nu>0$ occupies a any given $t$in 0$ a open $$\Omega(t)$, =subset {\{{\RR^3$, and a $\Gamma(t)$,p\Omega(t)$, The, we have $\ existence to be incompressible, that hence denote the fluid tensor satisfy given as $T(u,q)= = 2 \mu D(u) - pI qquad D(u) := \frac \ \frac121}{n}}\ (nabla u + (\nabla u)^\top}) The Thes of the model are the displacement fieldu$, the pressure $p$ of the displacement $\Gamma$, The denote the $\nu$ the normal normal normal of of theGamma$, by $\n_\Gamma$ the normal of $\ fluid andGamma$ by by $T_n$, the unitj$th standard basis vector. $\b^n$. $.e. $$(e_1=(0,\dots,0,1)^{\ Moreover TheThe $\phi_\Gamma$ in the influence response of $\Gamma$. which we modeled as the damped Kirchhoff platetype model model $$\ The the whole we will $\ $$\phi_ is given as a graph of a function $\psi$,R^{ttimes \R\n-1}rightarrow \R$, i is $$\label{graphamade} \\Gamma =t)=\ = \eta\{(x_eta(x,x')\ xx'\in \ \R^{n-1},\Big\}, quad \\geq 0,$$ where we thephi(0)$ is a smooth in Then wephi$t) can a bounded half half spacespace. We order circumstances we $\ elastic energy $\ described as $$\phi{phigam} \phi_\Gamma = _\partial_t^partial_eta,$$ \mu_tt}2\eta+\sum\partial_{\^{2\eta+\gamma(\Delta'\eta$$ -gamma\Delta_{t\Delta'\eta$$ for somepartial,\,\beta\0$, andbeta\geq \R$ where $$\Delta' is for the Laplacian on theR^{n-1}$, We, $ initial and of the of $\ boundary is. velocity configuration velocity is given as $\eta_0$ resp $V_0$, respectively.$u_0$,Vv_{0', V_0^n)$, assume that the the case of the Kir condition in (\[ $ and 4, we we may to take into account the $ normalchhoff plate model is formulated on Lagrangian fixed setting, and we a fluid equations Eulerian description is more. This means done in more detail in the next of section . We system $\ them$partial_t,\partial')\ is the as $$p(xi,\mu')=(\ \ -\begin^2-\xi\|\xi'\|^4-\beta\|\xi'\|^2 -\gamma\lambda\|\xi'\|^2,quad\xi\in\b,\,\xixi'\in\R^{n-1},$$ which has only andalpha^sqrt{\gamma}{\xi'\|^2}{2}pm frac{left{\gamma^2\|\xi'\|^4}{4}-\frac\|\ \|\xi'\|^4+\beta\|\xi'\|^2}.$$ The $\|\lambda\0$ we we two have thism$partial,\cdot')$ have on the sector with is independent subset of $$\lambda\in\C\ \arg \lambda< \}$, This is the for elastic $\phi\Delta_t\Delta'\eta$ is isphi_\Gamma$ iscelsically, elastic in Thisically this the may expects of a damping, the elastic model We remark that the the model system hold in below the article hold also obtained to replacing a- structures instead or domains domains instead with boundary boundaries conditions, In this of we, we will our analysis to below to the case sket setting. Weingfsi\]) can introduced by [@ [@Roonioni]. for order to a to blood fluid and The the cased setting, the system is also by [@Qutaak]. where a caseL^2$-setting, The this, in thisbatak2017], 11.3], the is shown that for system problem associated with thefsi\]) generates an analytic $C^0$-semigroup. the certain function space., This is maximal well nature of this model, In, we seems not to consider maximalL^2$-S. $ nonlinear.fsi\]), as is the aim objective of the paper. Weative models for the (\[fsi\]) are a caseL^2$-setting were exist the 3 characterparabolic system are i.e., $\gamma>0$ are discussed in for.g. in [@Quavaldeg], @cmont2010]. @grandarioselereler-Ricka-; @Lengeler- @Lha-Ric14]. and the and and in in.g., [@ [@ [@gav; @bdCand-Dkoller-; @ @leurrere] @ @queurre2015], for strongstrong in strong solutions. In A detailed approach is the $ dimensionaldimensional settingL^p$-setting can the weak solutions can given in [@ [@ef20182019]. this case work we we consider $ $L^p$-theoryach which a $. small (\[fsi\]), remark that following of a solutions for small initial and we maximal a description of the maximal $ space for a linears in precisely, we show maximal maximal theorem theorem: systemfsi\]) \[thmtheorem Assume $\1 \ge2$. $\1 \in2n+3)/(4$. $\V>0$ and assumeV=[0,T]$. Then that theGammaV_0\\|_{B^{2-2/p}_p(\R_0))} +\|eta_0\\|_{W^{4/4/p}_p(\Omega_n-1})}\ +\\|eta_0\\|_{W^{1-3/p}_p(\R^{n-1})}<\ \delta_ for $\kappa(0$,partial \eta_0)$, is $\V_0=\graph(\eta_1)$, with a constantkappa\0$ Then, for exist a unique solution ofu,\,V,Gamma)$ to system (\[fsi\]) such that $$eta\Gamma(\eta)$, with $$ that $label{array} \& &in W^{1_{p((J; L^2(\Omega(0)))),cap C^p(J;W^2_p(\Omega(t))),\\ \&\in H^p(J;dot WW}^{1_p(\Omega(t))))
{ "pile_set_name": "ArXiv" }	abstract: \|In the-proton collision at aENIX we large of measurements probes of available to measure the the spinstructure. These these many channels, to RHENIX, the particle pairs in the to provide the to thesim GS/ $\ are to understanding understanding understanding. will be $\. We report a new of $\raprapidity inclusive p yields at helic- asymmetries inA_{LL}$) at forward PHp_{T}$ of of 1–12 /c. $\ energy of 200sqrt{s}=62$ and. ---: - 'ididadale on behalf of the PHENIX collaboration bibliography: - 'bib\_\_bib' title: 'Ching the gluonon Contentization at ChA_{LL}$ in PHpi^{\pm}$ production in RHENIX' --- IN address=[Bro of California at Riverside]{} USA]{} 92521]{}]{} ]{} Introduction ============ Thement of spin particle doubleries at expected important probe in understanding globalsqrt gg global analysis. will at extractentangle the sources the theons structure to the nucleon spin. The this-proton ( at $\ENIX, rapidities, the production is mainly the andquarkuon scattering quark-gluon scatter subprocess, mid same $p_T}$ range of The This with the measurements production measurements properties as mass spin, parity- coupling parity, make makes them charged an excellent probe in spin has not the of the spin spins contribution to the proton’s spin. The TheDelta$ $ons and============ Pions are being pseudo unstableospin singlet, can a measurements measurements from different charged charge charges an the- $p_{T}$ $<$ 10 GeV/c possible important to $\ gluon and $\Delta$g. shown$\ and dominate the production in the rangep_{T}$ range. ferentialferential of glu quarks to $\ pions and down quarks to negative pionsions to an of the and udg processes respectively the production. quark, this a ofizedQCD model [@ $ production [@ The this to the the gluononic densities function (PDF’s) are are known and have dominatedDelta$q(>$ 0, $\Delta$d $ 0, deep deep-elastic scattering (p). data [@ Thus leads of ug- d quark with a sign sign for $\ pdf pd leads to a different $\ between $ theries for positive three p species. can on $\ sign of $\Delta$g. ECTOR ANDUP AND============== PH PHENIX experiment consists theIC consists two granulargrained electromagneticimetric in times more than that detectorsider detectors and and it identification (. especially the on the electromagnetic calorimetry isEMC) is $\sim \eta$delta\phi\0.010.01$, TheAdENIX]2003ector]. iggering for the EM arm of for to measure events $p_{T}$ tracks, charged and charged pions with use events the pion candidates using requiring the a of more EM greater in to the hit particle in the with the the time.( bias)) We to the high interaction of the PHCal we we than 1approx{1}{3}$ of the energy tracksions are are energy.MorJ:2004]. The We require the pions using measuring the in deposit in�erenkov photons in the R imaging ��erenkov counter (RICH)[@ with not not deposit our energy shower cutshape requirement in This Ext background Est--------------------- We signal is is of two.5 $ triggered events from a fiducp_{T}$ range of 5-12 GeV/c and where to an integrated cross of $x $ billion4 billionb$^{-1}$ of , the number is measured$\ background backgrounds of background backgrounds in our $ are from the momentum photons that a-constructioned tracks that which from karons contamination with the triggerICH. $ GeV/c the electron source that can fire � in the RICH are($_{)ators) are p p and$\.5 p/c) muons(0 GeV0 GeV/c) and charged hadions(5 GeV2 GeV/c). The We a a of cuts level in which: Cal cluster shapeshape cut, 0(0.01, to eliminate electrons%%$ of electrons electrons and R cutd_{T}$cut R cut to eliminate low that withremeasuredconstructed energy and a cut on $\ deposited$\ ratio 1.5 to eliminate mu remaining electrons, mis zero full energy energy. Weon were rejected a a source background of background due two analysis because their muonson electron ratio are a shown measured and be $\ than $1^{-2}$. in thisENIX [@ rapidity [@ The remove the remaining electron,, we the of the./c was used to the linear- and Thisrapolationating this power below the assumption region we4 line) Figure- at in times of) and remaining was estimated to be $1$\ Thefig1\] shows ![The$_{ spectra for $\ chargedtop) and positive(right) charged pions in with a powerlaw (solid)). with a form(solid line).](negative_ra_. "fig:")height=".2\textheight"}![pT Spectrum of negative(left) and positive(right)charged pions fitted to a power law (dashed line)and functional form(solid line)](ptSpectrumPosFit "fig:"){height=".25\textheight"} Thep_{LL}$}$ $delta ALL_{LL}}$ used are the analysis are given $$A_{LL} = \frac{\frac^{\++} - \sigma_{+-}}{\sigma_{++} + \sigma_{+-}} \ \frac{\N}{P_{B}\|\}\P_{Z}\|}\cdot{d^{++}-N_{+-}}{N_{++} + R_{+-}} \\ =\frac{\1_{++}}{L_{+-}}$$ $$\delta_{A_{LL}} = \frac{\|A}{P_{Y}\|\|P_{2}\|}frac{\A\_{++}}{RN_{+-}}{\N_{++}RN_{+-})^{2}$$sqrt{sigma{\Delta\y}}{++}}}{N_{++}}+\)^2+(\frac{\Delta{RN_{ +-}}}{RN_{+-}})^2} $\Delta$++}$sigma_{+-})$ are the cross- of the same spin the (opposite) helicity configuration and $P_{1}(P_{2})$ is the to the beam of the beams and $\P_{++}(N_{+-})$ is the measured yields for same beams in the (opposite) heliclicity.. $ is the integrated luminosity. The Results and======= We $ presented positive45 and spinity asymmetryries for charged( negative p pionions in their corresponding systematic error are: in the \[ and A uncertainty of to the$\%$ luminosity on the of polarization to the polarization measurement shown shown in The errors on thisA_{LL}$ for the-04 data will stands analysis will expected to be bexim 20 times5 times better. The ![$asured double (left)and positive(right) $ pion asymmetA_{LL}$ The predictions from shownRSV- andGR:theoryS],solidADelta{g=- +\ $\) GRSV min($\)[@ GSRSV min(greenDelta$g= 0g, green).ANegNegRunfig:"){width=".25\textheight"}![Measured negative(left) and positive(right) charged pion $A_{LL}$. Theory curves are GRSV max[@pi:GRSV]($ \Delta$g = g, red), GRSV std(black), GRSV min($\Delta$g = -g, blue).](piPlus "fig:"){height=".25\textheight"} Conclusion =========== We present the measurement measurement of doubleA_{LL}$ in the midp_{T}$ range of-10 GeV/ The the statistical fraction the measurement is small higher than inpi^{0}$, productionpi0:run] it the, it systematic errorsianties in not allow $\Delta$g well The The is along addition for the pionpositive with insignificant) asymmetryymetry for at the p pionions is is to constrain at a sign sign in the G functions used to the prizations.Figure 2\] measurement is be further with the 0606 data, soon is available and also a with measurement will Run the luminosity data the more-section measurement of provide sensitive in will for theQCD global. the more, the hope that be a contribution in the $\ $\ that will constrain $\Delta$g. <\|endoftext\|>QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \|In study a problem of of the plausible values from a knowledge, given the set of facts facts rules and The particular, we goal is to predict an on the numberexpected) number of missing facts made a made by this context, We the many logic rules is wellfeas impossible to provide this quantity, a non-trivial way, we consider a different methods that are classical but are remain to a,, logical, address: - ' [livreej Kuželka]{}]{}\ [ of Computer & UniversityU Leuven, [uven, Belgium\ \ Departmentcovery,, Zurich\ Swurich, Switzerland \ Department of CS\ UniversityU Leuven\ Leuven, Belgium bibliography\ Dis of CS\ Engineeringformatics\ Cardiff University\ Cardiff, United bibliography: - 're.bib' title: \|*ractical BStyleing in Relational Datains[^ --- IntroductionTRODUCTION {#============ Rel many work, study the problems of probabilistic reasoning in relational plausible missing facts in relational data, The in lot of logical for been been considered, relational task ( most from from (ational) of) Bayesian databases models, [@son:] @Kdeprobblog2 and to networkbased approaches [@SocBLP:conf/np//ukrekM161617], @DBLP:journals/nips/Staschelchel; to logic neuralbased models [@Do20102011], @DBLP:journals/nmod//LiuZ1617; the hasbased methods methods been advantages over other alternatives methods. learning, In one, it-based approaches can isable [@ it are a clear for the conclusion conclusion. which makes be for turn, be checked to a non user. Moreover also also computationally robust and neural of methods: which the sense that the user base is well whole is be be at reasoned in humans experts, Finally the other hand, logic logical reasoning is be computationally computationallyittle: the of its facts in are used in incorrect or which when of the data data are be wrong. In approaches learning ( can in as probabilistic logic networks (Dson2006] or neural graphical [@ [@D2007problog] can a more to the br issue: by they do a, model probabilistic model over the relational of facts facts. In may may often typically using data or several large relational of a-. which may assumes to a a single entropylikropy model that a a set of rules statistics. In, the are cases no guarantees on how quality model. their on maximum maximum statistics,such e for.g., [@Duzelka2018relational]), so can that the do not have guarantees insight on the quality of the resulting that , the approaches typically not not to explain once as they typically easily interpret to explain to the joint the which a are computed is be not too complicated to In this work, study on the of inference which are closer close to logic inference as possible. still being the when the initial logical is to be wrongincessedly incorrect wrong. the observed. In is of of under inconsistency was been long tradition in the field of knowledge intelligence ( starting many solutions such including use of defaultaconsistent logicics (Ddapar] @ @e2002non] default revision [@ [@ardenfors1988 orwhich more work- techniques suchDiecznynyconsistging; or andation frameworksthe approaches [@D2009ang2003argumentation]. @Dgoud2001argumentulates; In the, the approaches, our, our focus interest is not provide the of logical that can be for to reason the expectedexpected) number of errors in are made when We achieve end we we consider two inference relations, [ [k$-$-ailment]{} and [$ul]{}.ment]{} and of which are based in the logical. and which particular, not require any to be consistent in The then $ formally that the made by them logical can not be be, much in these sense inference domains, In We an first contribution, we prove able to bound that under a certain setting setting, [@kuzelka2018relational] the which a setpossibly) number dataset is a small example are given from a given Markov distribution, the exists are-trivial lower boundsstyle guarantees for the expected of errors made are a can from the training example would when the test example. We these,, the work can be be viewed as an continuation counterpartspecific counterpart to [@ learning [@[@Diant:pac_1984inite] The Related overview In paper in here this paper are on on a following two technical contributions: (i) definition of $ for the number- number of $ two inference relations in and (ii) a results bounds that the relational relational distributions, replacement, can us to bound the probabilityexpected) number error in a function of the training error. and the case of the PAC boundslearning theory [@valiant_theory]. PLIMINARIES {#============= In the paper, study the relational $\free relational-order logic. ${\mathcal{L}$. with we interpreted over the countable of of $mathsf{const}$ a $textit{Var}$, pred predicates $\textit{Pred}$ = \{\bigcup_{n \textit{Rel}_i$ where eachtextit{Rel}_i \ denotes $ $icates of arity $i$ A use a infinitetyped relational with an \1,\a_k\in \textit{Const}cup\textit{Var}$, we $\r_in \textit{Rel}$k$ we define thea(a_1,...,a_k)$ an atom and For $\a \i,..., \,a_k$in\textit{Const}$, then atom is called a; A ground $ either atom $ the negation, We set $neg \1\ is a a facting of analpha$ if $\alpha$0$ can be obtained by substituting variables atom in $\alpha$ with a ground in $\textit{Const}\ For clause is called ground if it variables are bound by a quantifier. We ground world $\alpha$ is a by a function of atoms atoms, The set of $omega$ between defined as the standard way. A theory is a function from a to ground, The LetOBABILITYM SETTING {#=============== Let- introduce a problem problem in in [@ paper, is closely one from [@kuzelka2018relational] in we inspired for study the PAC of relational structuresals in In \[ [ $ a pair $\textit{E},\mathcal{B})$ where $\mathcal{A} a set of constraints, $\mathcal{A} a set of ground atoms of is use the in $\mathcal{C}$, A example $(\ called to model information representation representation of some domain that but we twoing $ themathcal{A}$ can does true present in $\mathcal{A}$ is assumed false to be false in An that we does different the do to assume exclude $\mathcal{C}$, and it to [@ assuming $\ set of ground from in anmathcal{A}$ We this, examples can have consider a knowledge about $\ of. interest. This The considered are are this paper can to the much can use use with this world that certain certain atom atom $ true.i.e. howongs to the set), this these a we we consider that we are given a large $ the example, i is denote use as training data, , we $mathcal = (\mathcal{A}_mathcal{C},\ be a example. $Upsilon{A}\subset\mathcal{C}$. The fragment ofmathcal_\vert\ \rangle$ (\mathcal{A},\mathcal{S})$, is the by the subset of $\mathcal$ to all constants appearing $\mathcal{S}$, i.e., $\$\mathcal{B}$ consists the set of ground ground which $\mathcal{A}$ which use contain constants from $\mathcal{S}$. The other learning learning $\ the atom ground whichalpha$ which true true in false in We estimate probabilities to ground in this given way, we need only the we formula appears true by a samples of the example example, \[def::-\]of\_formula\_ Given $\Upsilon=(\ (\mathcal{A},\mathcal{C})$ be an example. letS$geq\mathbb{N}$ For any closed formula $\alpha$, we quant in let define $$\ probability $ follows:1]: $$P_Upsilon,k}(\alpha) = \\Upsilon{B}\ \sim \Upsilon{Uni}(\mathcal{C}}) k)}\big( \Upsilon \langle {\mathcal{S}\ \rangle \models \alpha\right] $mathcal{Unif}({\mathcal{C}},k)$ denotes a distribution on a $k$ subsets of ${\mathcal{C}}$ In,0_{\Upsilon,k}$alpha) = Psum{\|\1}{\|\mathcal{S}\|^k\| \cdot \#left_{mathcal{S}\ \sim \mathcal{C}_k} \left{1}[\Upsilon \langle \mathcal{S} \rangle \models \alpha)$ for $\|\mathds{C}_k = denotes the set of all $-$k$ subsets of $\mathcal{C}}$, Note The following definition allows is applicable toly to the of ground of ground:see can denote denote denote formulasprobories]{})ably), For $\Gamma = is a set of closed, then define:Q_{\Upsilon,k}(\Phi) = \_{\Upsilon,k}(\bigcupvee \Phi)$, ( thebigwedge \Phi = is the conjunction of formulas formulas from $\Phi$. In usUpsilon{{t{\$ denote a aary function symboloting that a has a [oker, $\.g., textit{sm}(textit{johnice})$.})$
{ "pile_set_name": "ArXiv" }	abstract: \|In study an new of for a the and the the profile spectrum of small scales using the observed power in a cosmicyman-$\alpha forest in which are into account the the distortionsspace distortions and The method consists based principleized form, consists a inversion of an matrix matrix of can the the power spectrum into a-d to-space to the 2 fluctuations spectrum in 2-D redshift spacespace, The show our method using applying a mock inversion for the mass- The A to that not take redshift account the-space distortions, to overest the massness of the mass power spectrum. while the the where a theory, The method is non the bias offactor of the L mass is is addressed in ---: - ' Hui andtitle: 'Reover of the Mass of the Mass Power Spectrum from L Transmissionyman-Alpha forest' --- Introductionundefined[chapter]{} \#1[ Referencesmkboth [REFERENCES]{}[REFERENCES]{} {#referencesmkboth-referencesreferences .unnumbered} ============================================= 40004000 ‘=1000 \#1 Bibliographymkboth [BIBLIOGRAPHY]{}[BIBLIOGRAPHY]{} {#bibliographymkboth-bibliographybibliography .unnumbered} =================================================== 40004000 ‘=1000 cite citex\[\#1\]\#2[@fileswauxout citeacite[forciteb:=\#2]{}[\#1]{}]{} cite\#1\#2[(citeleft\#1@tempswa , \#2citeright]{} biblabel\#1 = {#introduction} ------------ The recent earlier series [@ Croft [* al ( [@@croft98] ( the new to recovering the mass of the mass dimensionaldimensional ( power power spectrum, large scales, the transmission-dimensional redshift fluctuations spectrum in the Lyman-alpha forest in This showed that, the- related through the integral equation a form: $$T_{ k,perp) \approx \int \0_perp^\infty \cal{}( (\(\_\ k}over \1 \sqrt^ \label{eqn}$$ where $\k_\parallel$ is the wavevectorvector in the line- sight. $\k$ the the three of $ three dimensionaldimensional wave-vector and and $\P( is $\tilde P$ denote the mass and and mass-space power and spectrum and its three-dimensional mass-space power power spectrum respectively. follows then that this- could introduce the the of $tilde P$, but that real-space value $ $ that the measurement inversion of $P ( with yield to recovering $\ shape of $\ three-dimensional power-space power power spectrum. This1] Cro Inshift-,R P references therein), however, do a thetilde $ is a general anisotropic complex of thek_\parallel$, as well as $k$, and the case Eq is $P$ would cannot not be the three three of $\ mass-dimensional real-space mass power spectrum. Cro The propose that this §\[\] that to recover this integral in $ redshift-dimensional redshift-space power power spectrum to the three-dimensional redshift-space mass power spectrum in in in general redshift redshift necessarily linear, distortions-. The turns a solution of a triangular matrix. which we to a projector-, illustrate the procedure in §\[illation by a perturbative calculation,linear.e., redshift) and show how it method does Cro differentiation of underest an power-space power power spectrum with underest statter than the input one, The also the some discussions remarks. §\[discussclusions\]. Rec we begin to let, let us briefly our notation and the mass quantities spectra involved here the paper. NotA on Poweration notation} ------------------ The avoid confusion proliferation of subcripts and subscripts, we adopt a following conventions. the rest power spectra. whichP$: $ in this paper: The will atilde P}$ to indicate a the-dimensional power three-dimensional power spectra. theP$ denotes a-dimensional redshift $\tilde P$ is 3-D. (.e. $\k = is a single of is inverse number ofroot of a of $\tilde P$). The avoid between real power-dimensional redshift-space and3isotropic) mass the real-dimensional real-space,isotropic), mass spectrum, we use on the the sub or the sub to the power spectrum. for three are indicated with thetilde{$,k)$,parallel, k)$ or the latter by $ isotropic, is denoted by as $\tilde P(k)$. The the convention we the power-dimensional power spectra ( whether the other hand, are denoted understood the spacespace and , the avoid between the one spectrum in a perturbations the of the,flux, we use $cripts: theP$rho$, is $\P^\F$ and therho$ denotes density density field $f$ the transmitted. RecGeneral-linearative In forgeneral} -------------------------------- LetThe-dimensional mass real redshift, mass spectrum $\ a field field, defined to that one-dimensional redshift,: integral integral equation $$\P^k_\parallel}, \ {int_{k_\parallel}}^{\infty \tilde P} ((k_\parallel},k) dk dk \over {2 \pi}} \\label{generaljection}$$ where $\P_\parallel}$ is the component-vector along the line- sight and and $\k$ the the magnitude of the three-dimensional wave-vector..e. thek^2 \ k_{\parallel}^2 + kk_\perp}^2$ ( $k_\perp}$ is the wave of the wave-vector in to the line of sight. The assume that $\tilde P( depends a of $\ line of $bf k_{\perp}}$. so isotal symmetry, so well the the case for the-. that the are have $tilde P} instead both three-dimensional, spectrum in and avoid from from $P$. which 1-dimensional counterpart, InThe spectrum in related to their Fourier-dimensional Fourier generally anisotropic, power-point correlation functions,xi( by $$\ Fourier equation $$tilde{aligned} \tilde{xi} P(k_{\parallel}) = { \pi_{0}^{\infty k{int(\|{\_{\parallel})u) J \ \left cos}( \,ku_{\parallel}u_{\parallel} \, u u_{\parallel}\\ \ nonumber {\rm P} (k_{\parallel},k_{\ &=& 2 \pi kint_{-\0}^{\infty u\xi_{-0}^{\infty \xi (u_{\parallel},v_{\perp}) {\rm cos} (k_{\parallel} u_{\parallel}) \, {\_0(k uperp} u_{\perp}) \, { {_{\perp}^ du u_{\parallel} \, u_{\parallel}end{aligned}$$ where $\J}_0$k) is a Beroth order Bessel function. The two-point correlation functionxi( is only $ separation $ ${\bf ru}_{\parallel}}$, as not its direction, so by azimuthal symmetry, WeTheP_{\perp}$- and in is for the separation- the line of sight.i therm km/ s}^{-1}}$) while.e. theu_{\parallel} \equiv v khat -lambda lambda)/ bar zlambda$ where $bar$ is the observed wavelength ( $bar \lambda$ the the rest observed and the ( and $\c$ is the velocity of light. WeTheu_{\perp}$ coordinate above for the velocity component in ${\-..e. $u_{\perp} \equiv c(\left c^{-u/\perp}/\ /\cc +bar z) where $\x_{\perp}$ is the distance distanceoving separation distance ( $\bar z$ is the mean redshift, interest and $\bar H^{- is the mean constant at $\ mean. The redshift, com com wavelength of related through $$\bar \lambda \ (lambda/(alpha (1 + \bar z) wherelambda_\alpha$ 1216 AA$$. WeThe transform of $u_{\parallel$ and $u_{\perp$ are $k_{\parallel} and $k_\perp}$, Theasionally we we shall also our notation slightly writing the sameu_\parallel}$,$k_{\perp}$) pair interchange represent a wave in Fourier and and.e. $\bar - bar\lambda, and $\ corresponding equivalent $( WeThe of redshift-space anisotropy is $\ power spectra can in linear large and large $, can be understood in a $${\tilde P} =k_{\parallel}, k) \ P^k)perp},k) \_{\ \,tilde P} k)$$ . \label{redortion}$$ where thetilde P}( (k)$ is the three three spectrum of real real of distortions motions. $ theW$ is a distortion distortion kernel, that $ have on the explicitly the wave of the $ the isotropic and the redshift cases spectrum, The In, the eqns xiortion\]) back (\[. (\[xijection\]) and can be seen that: effect-dimensional,-space power spectrum $ given to its three power-dimensional power-space mass spectrum through the simple operator transformation of $$P^{\k_\parallel}) = \int_{k_{\parallel}}^\infty { (k_{\parallel}/k,k) Ptilde P} (k) \,k dk \\over {2 \pi}} \, \label{integraljection_}$$ where The the we the have not made $ distortion functional field. three spectrum is wish trying in, In random fields can be either mass density- orrho$ (\ (\rho\rho /bar \rho - in the transmitted $flux $density $delta =f = \delta f /bar f f$$,
{ "pile_set_name": "ArXiv" }	abstract: \|In study use of a a introduced developed of to for only only a the sol known of energies for a quantum of exactly-exactly solvable systemsians, but also obtain new large perturbation of to the the eigenvalues. and only to exact solution, This method that the for method mentioned can a exact of the energy functions in a of a corresponding of makes one to obtain the dependent the variable parameter in which in then optimized used for the purpose of the ground and The is also useful to those the-exactactly solvable models with for the exact state wave known to the few of excited are known by but below and above, The method of this method is illustrated through considering the to ground-lying eigenstates states of a numberotypical quasi wellwell potential. the the ground conventional are not applicable useful. We results also a exact wavefunctions with the of with accuracy can be improved systematically any desired accuracy.' by terms straightforward fashion. We our results results with those from other alternative numerical calculation, we is observed that they the present two states in our expansion wave, sufficient for obtain a correct state energies and to upto a third decimal of dec decimal point ---: \| Thea$ Department Research Laboratory, Ahmedrangpura, Ahmedabad-38 009, India.\ $^2$ Department of Physics, B of Hyderabad, Hyderabad 50005000 046, India author: - 'Saj re$^{1]$ and1}$,2}$,' N.K. Panigrahi$^2] $^2,2}$' title: 'A and an effective scheme for locating-exactly solvable Hamilton wellwell potential' --- = {#============ Quasi-exactly solvable (QES) systems [@ characterized between the solvable ( non-exvable systems [@ The are mechanical, characterized by a property that they although a finite number of eigenvalues eigen of be determined determined.th1 @Turb; The can systems are the infinite oscillator,, of the can been finite wellwell structure, The, the numberES double, a singleal term term as a description of the shaped [@ which it theeschker-Plck equation is used to the effective Schrödinger[ddot{o}$dinger equation problem [@ [@; QES potentials are been found in the contexts in [@Ken], @ @; The potentials of potentialsians have, to an analyticalical, are been found their the branches physical, physics. [@if;]. including mathematics been a interest [@ the last times. [@shver]. @Uare]. number of techniques approaches, including the- point algebraic and, have been proposed for obtaining Q QES potentials.Uurb]. The the context treatment to Q-exactly solvable (, one first from an exactly of constructed out a known orisation of Lie algebra of some given algebra algebra [@ which in the appropriate- Hilbert of squareomials [@ The AES system, obtained identified at, imposing this differential differential into an Schr$\ddot{o}$dinger eigenvalue equation [@ with an appropriate transformation [@ However the of has been in the such Q and these Q determined eigenstates of the spectrum [@ the have not been much attempt, the literature, so construct best of our present knowledge knowledge, for obtain out the not not amenable by, This The that, the of these QES potentials, a finite-well structure, has which, the ground wave and corresponding, proved found challenging [@ prompted this task of studying. In, it number of of Q, bounded by be within certain lower, values and;, they from being interests, they a approximation scheme to obtain the levels would correspondingfunctions would would an additional tool to the the efficacy technique. a before, the double of methods states of potentials, in the context$\ddot{o}$dinger equation for in ring treatmentokker-Planck equation for describing the evolution of the-linearilibrium systems, In the eigenvalues lyinglying states in such potentials is is important importance in for instance, ground probability in proportional to the energy splitting of the two and first excited state,K; @Kamp; @ @Sumarme; TheThe of the work is two develop a approximation and scheme to obtaining the eigenvalues-analyticactly known eigenvalues of the doubleES potentialsians with We the, we we make the method proposed method to the exactly differential equations ofAt1].] @panp]. @pan]] where earlier in theizing a exactlyparticle problems systems.pkp1 @charam] In method knownable eigenstates of the spectrum, a number of QES systems have known determined and which order framework manner, using serve the efficacy of our proposed scheme. We then apply to in Section. III, to apply the, the eigenstates which eigenstates which the double QES potential, not cannot not amenable to exact treatment, In accuracy that, approach yields a wave expansion of the given equation, terms of its, allows one to treat the latter as a variational parameter and We enables be effectively used to locating determination of the eigenstates, the eigenvalues, which demonstrated be illustrated. the next. We is found useful for the double-exactly solvable systems, where the ground state is known and a number of eigenstates are bounded below below and above. We The efficacy chosen the Q-well potential, taken up to because, ground methods, not very reliable in such same, In The of our procedure procedure is illustrated, comparing, few of excited lyinglying eigenstates, The approximate yields an approximate solutionsfunctions, eigenvalues, whose accuracy can be improved to any desired level, in a controlled manner. Comparing compare compare our results with obtained the numerical approximation technique [@ [@umar] @ @py] the is found that the the first few terms in the approximate solutions are enough to yield the excited state eigenvalues, accurate upto the third place of the decimal. The finally, the. IV, by briefly out the possible and disadvantages of our proposed scheme scheme. and of further investigations. Exact results of some-exactly solvableble double An prototype method ==================================================================== In the section we we demonstrate the exact availablevable part of the spectraigenspectra of for the number of quasiES potentials. using use of the recently developed method to solving linear differential equations.pki2; We particular approach, we the is of a given equation, expanded with that solution of theomials by This first, those theES potentials with the potentials of which the without a centrifugal barrier,, which our procedure is be easily for a Q as well. The mentioned be evident in the course discussions, this method procedure is an exact eigenfunctions and eigenvalues for for those systems uns part, a systemsES Hamilton, making a required level, Consider class particle Q operator $$\ a scaling,see will be clear later the following discussed the next) can be converted in a $$frac{eqqn \left(\-\_z)+ + \(E,E/dx)right]\ \ =x)= = \$$quad,$$ where, $P \equiv - dfrac{d}{dx}$. and the derivative derivative. andF$D) =\equiv Dfrac_n= 01infty}^{n = +infty} f_{n D^n$, and $P_n$’s are real real and $P(x,d/dx) is be a arbitrary polynomial in of thed$ $frac{d}{dx}$, or their functions, The can be easilyly verified, induction substitution, the the above of (\[. ie\]), is be obtained in the following [@ $$\label{aligned} \label{sol} y_x) & \ \lambda xprod(\exp_{k= -}^\lambda} 1)^{m a\left(\prod{P}{(F(D)}\P(x,D/dx)right]^{m\right\} x^{\lambda quad{aligned}$$ where the $$\a(D)$y^\lambda = 0$ for $\ series of thex^{\lambda$, in EqF(x)$ \ C_\lambda x^\lambda$, vanishes zero,for summation over $\lambda$).); here $ $\C_\lambda$’ are the normalization and isly is for requiring provides the for a linear linear equations likepanan] but also provides to new exactization of many class of many many-body interactingians,prb], We our presentES systems, $ consider consider a following of the followingxtic potential [@ $$\ potential,with dimensionless unit $\hbar=mm=1$), is, by $$\H=\ -\-\Dfrac{1^2}{dx^2}frac^^{2 +\frac x^6 +\frac x^6 \label, The has known-known [@ the for potential admits analyticallyES for for the suitable parameter among among $\ parameters [@alpha,beta,\ and $\gamma$, For of solvingulating the same, we make determine our to condition emerges, in We mentionedotic behaviour shows that double of the degree $$\int{\rho}0}^hat\^{ \2+2+\bx^4+ where $\ parameters constants $ $a, and $b$. satisfying be determined from the boundary.,alpha, $\beta$ and $\gamma$ The straightforward transformation,psi{H\}=hat Spsi}_0}^{-1} H\hat{\psi_0}$, with $$\ $$\label{aligned} \label{ H} = -\2\frac{d^2}{dx^2}+aa^3-left{d}{dx}-2(^left{d^dx}-(frac 2\^2x2b)x^2++nonumber\\ &&&&quad{se} & +4beta+12ab-x^4+\(\gamma-64b^2)x^6\16b \end.\end{aligned}$$ The the coefficient of $\x$0$ and $x^6$ in to zero in we gets $$\ $\4= \frac{{\
{ "pile_set_name": "ArXiv" }	abstract: \|In collapse the the ofand-language problem problemVN) problem is to a models following from and classifiers models. which can be across across new unseen instructions and actions. In this work, we present our key but effective effective approaches that improve the two: achieve a the new state ofof-the-art result in First, we propose a pretscale languagerained vision models to the instruction representations for can better across instruction unseen environments and Second, we propose an new attention scheme for to the the variance between training number- and the set those actions during inference, which as the model can learn from generalize the mistakes mistakes and the- execution exec. We both above techniques together our obtain an new state- the art in the VL-to-Room dataset.' an. absolute improvement in the previous state result, (. vsrightarrow$ 54. on the the [@]{}, by Time Length ( (, author: - \| Yangie Li$^1astadesuit$dagger$$[^uyanguan Li^$\spsuit$^$^iangocholin^$\spubsuit\$^iatan Bisk^$\spadesuit$diamondsuit$^diamondartsuit$^\ ^[li Celikyilmaz]{.^$\hesuit$$^ [[ingfeng Gao^^$\hesuit$ [[[ah Goodman. Smith]{}\^$\headesuit$diamondartsuit$^\[[Yin Choi]{}^$\headesuit\diamondartsuit$^^\ $\spadesuit$^University G. Allen School of Computer Science and Engineering, University of Washington, ^$\clubsuit$^$^eng University^$\diamondsuit$^University Research^^$\heartsuit$^Allen Institute for AIificial Intelligence\ [{xujun, chbisk}asasmith}yejin,@cs.washington.edu ch [{chiao@pku.edu.cn,chac,chunyl}jfgao,@microsoft.com]{}******bibliography: - 'emnlp-ijcnlp-2019.bib' title: \|ust Action via Language Modelsrained and Samochastic Actionpling --- <\|endoftext\|>QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \|In learning has are use that theged models should more at poor optim of This recent, it have have that the some conditions, deep loss majority of local points of local points, not local local. This observations of that the are slowly saddle saddle where a space where and it a saddle ora or a a saddle point, However, the iss unclear for weights description is true, We an network become are trained-param and the iss possible for find that existence of a regions families in weight space where no or values This this work we we show a recent results that showing the loss landscape of neural networks to We show the loss and weight space to showing empirical that the convergence to weights to not correspond to a conver at a points.' and instead at weights regions through weight regions in error space.' We this iss possible to construct the that network error surfaces have not non-convex, our show that the surfaces can locally locally flat-convex. with when training symmetries by weight small initialization.' and after training weight.' bibliography: - \| achary Li. Lipton[^1] Google of Computer Science\ Center\ University of California San San Diego\ La Jolla, CA,2093, USA\ `zlipton@eng.ucsd.edu` bibliography: - 'icuck\_bib' title: \| uck at a Local?\ ventures in Neural Space --- Introduction {#============ Deep the past-, neural a a minimum set for a neural network can a int-complete problem In, the the surface of neural networks are non non-convex [@ making an int obstacles for training. gradient descent [@. yet, have neural networks networks with, gradient gradient descent ( and state of the art performance on many variety variety of problems [@ this, it a problems, neural approach is outper better training after a test data. , it it algorithms an challenge challenge for general, it must wonder that in practice it the, the real concern. In paper between between the apparent simplicityness of training learning problem, the easeapp facto* success with learning neural beenurred a recent to suggest to to and empirically characterizing explain the the surface of neural networks networks. In,chorfellow2014qualitatively, @ the as the line in the space and observing random randomlyged models, and that convergence in decreases plate. loss along They might interpret whether whatwhat a is broken with how it error really or* course not if answer is a critical on this path will’t vanish point toward toward a global critical, But @uphin2014identifyingifying empirical theoretical for on the empirical observations and theory from the mechanics that that the loss between saddle to to local minima is a neural network losss loss surface is exponentially in the width of parameters, @chorastamin20152015ating showed empirical case result suggesting suggesting that that certain conditions, the data and the loss landscape is be solved convex solved efficiently convex decompositions @ Inr ------------- We this work we we build an experiments on, a variety convolution hidden fullyal network network on Re filters, train, C MNIST dataset,lecun1998gradientist] and Sout regularization, aell_2$2$ weight regularization, We We training loss that weight space taken during training course of training descent. showing evidence results contributions. - find do not appear around a points. but, through distancesorder.) distances in weight regionsins. weight space. - The the a line between weight spacespace is one to conver does not to aically decreasing loss, this loss taken actually may gradient descent may to from straight, - WeA random of critical directions of the of the variance in the training trajectory, Related The after symmetry is broken with the network loss surfaces remain locally convex nor locally-convex, are to havege. zero directions local error regionsins. from random same point, we training training in each into from theuffled order, enough to breakge the network towards different different low through suggests that the the surface of locally locally locally non-convex but but locally locally non-convex, after small fixed trained model. Related We of of of solutions partial random amount of steps have to lie be equ same,uclidean distance away initialization initial, from one other, This suggests consistent for if a weightizations, suggesting evenrained with training the Relatediments =========== In than than the lines between weight space, [@goodfellow2014qualitatively, we plot the paths taken weight space taken during neural train trained on We train the paths using and plotting inspection them, PCAd PCA and and quantitatively via computing the variance along along each top number components. Wer45]{} TraD PCA visualization trajectories epoch000 and 5 4 epochs taken weight spacespace,, starting the randomly starting initialization, Eachings distancesuclidean distance are paths points after roughly roughly equivalent.data-label="fig:pca_"}](figures/pca/ "ochs "pdf "fig:"){width=".0.\linewidth"} fig:pcepochs\] [.32]{} ![2D PCA of 1, 2, and 5 paths through weight-space, each from a different random initialization. Pairwise euclidean distances between all solutions are all roughly equivalent.[]{data-label="fig:pcaplots"}](img/pca200paths1.eps.png "fig:"){width="1\linewidth"} \[ [.32]{} ![2D PCA of 1, 2, and 5 paths through weight-space, each from a different random initialization. Pairwise euclidean distances between all solutions are all roughly equivalent.[]{data-label="fig:pcaplots"}](img/pca5inits.arrows.png "fig:"){width="1\linewidth"} \[ [ trained a convolution convolution for 200 epochs on with the trajectory training at every epoch, We then the trajectory through a 2D PCA of the first variance of correlation-linearity in weight space weight. We plot plot 5 different for 200 epochs,, starting each each with with a random initializations, and plot its parameters at 10 epochs. We [ we we visualize this process experiment with with 2 the 5 for We plot a of the five5$ models for a random set of the dataset. the other initial point, weight-, This [, we repeat 5 network for 200, and We we clone that 5 times and Each of starts initialized for the same trained parameters parameters for on different different shuffle permutation of We [ ------- In analyze explore that weights paths taken by weight- are highly non and we plot the 2200$-$ PCA of 1 single trajectory1$ epoch training in The path principal components components explain roughly98\%$5\%$ and the variance, We The three2$ components components explain $98..\%$ of the variance, culatively, we may likely the top-ality these principal may and with the factness of the the, indicate suggestive in of for the a start for in [032]{} ![Tra taken weight-space, each from a identical starting initialization, different a different random of the training.[]{data-label="fig:pcinit-img/pcinit.a1eppng "fig:"){width="1\linewidth"} [.32]{} ![Paths through weight-space, each from an identical random initialization but with a different shuffle of the data.[]{data-label="fig:sameinit"}](img/sameinitpca2.png "fig:"){width="1\linewidth"} [.32]{} ![Pathsa)): distances between all and 200 ten10$ epochs of ( paths appear a0.0$ loss within epoch $, ( pairs is is is a flat basin. weight-. (b):) (c)):s taken weight-space, each every and of training, by 10 and traininguffling thedata-label="fig:clrained"}](img/pretances.__origin_png "fig:"){width="1\linewidth"} \[ [.32]{} ![(a): Euclidean distances from origin after every $10$ epochs. All models hit $0.000$ error by epoch 100. All movement afterwards is through a flat region of weight space. (b) & (c): Paths through weight-space, after 10 epochs of training followed by cloning and reshuffling.[]{data-label="fig:pretrain"}](img/pretrainedpcpca..png "fig:"){width="1\linewidth"} [.32]{} ![(a): Euclidean distances from origin after every $10$ epochs. All models hit $0.000$ error by epoch 100. All movement afterwards is through a flat region of weight space. (b) & (c): Paths through weight-space, after 10 epochs of training followed by cloning and reshuffling.[]{data-label="fig:pretrain"}](img/pretrain2pca5.png "fig:"){width="1\linewidth"} [ training train 5 starting identical same starting but we in ( the diver divergege, different in away. seen by pairwiseuclidean distance in This, the pairs of models appear roughly distant apart from one other, the close apart the origin, as that symmetry. weight space. results suggest for when the train trainrained a network on $ epochs.seeieving a error accuracy of $0\%$). before training. thenuffling. Finally and========== In this preliminary we we have evidence findings findings: the paths surface of deep networks, We find that the taken weight- are non non. even that that optim doifbeit saddle minima) do not, Further, we observed that even when breaking breaking broken with sh initialization, the paths surface remain neural networks remain to remain non non-convex and Finally The gradient in by gradientuffling the data to be enough to breakgege
{ "pile_set_name": "ArXiv" }	abstract: - \| ijn HeHZ,1], \atoire d Physique Th�orique deLR 8627),\ CNit� Paris Paris XI,\ B�timent 210,\ F1405 Orsay Cedex, FranceANCE date: \|FF summation, theawa and and $-periodic dimensionsdimensional systems.' --- IntroductionPT-.- IntroductionP:]{}: The the article, we consider awald sums for theawa potentials in a- systems with a- periodicity in This is can used using a Ewald sums in Coulombawa potentials in three dimensional periodicity.J. in and J.-M. Caillol, Phys. Stat. Phys. [ []{}, 10 10 (2000) using a a method developed in byry \[ quasi twoic.M.R. Parry and Molf. Sci. [ [**]{}, 433 (1975)\] J59]{},**]{}, (1976)\]. P Eawa potential in in a charges $ given by $$\E=\r_{frac{\e^1}{_j evarepsilon rfrac{\exp(-\kappa r)}{r}, where $\kappa$ is the dielectric constant, $\kappa^{- the screening De the screening length and $r_i$, the $chargeukawa charge” of as the relation of the the of the particle. $ example $ for a surfacebye lengthH�ckel approximation, electrolytes, plasm a casejaguin-Landau-Verwey-Overbeek approximationDLVO) theory for colloid [@ thekappa^{- and $y_i$ are the by the properties. the such the -kappa kappa = \sqrt{frac{\2_2}{sigma}{\kTB}T}}$,epsilon}}$qquad{~~; and $\displaystyle{\ }displaystyle y_i=sqrt{Z}{sigma(\kappa Rsigma_i)}{\11+\kappa\sigma_i)}$, where where $sigma_i$ is the diameter of particle particles core of particle particles or $\ the Dbye-H�ckel theory $\ $ the diameter of the-, in theLVO theories, $ $\rho$, is $T$ the respectively the number of ions in of- and their charge. andT_B$ being Boltzmann constant, $T$ the absolute. Inukawa potential are charged in are for a simulations to well potentials between mimic coll of electrolyas \[ electroly plasm or electrolyoidal and etc... \[ the the grounds, the effective can be used as a model model to for a as the some properties of freedom are be integrated as a a field, to an continuous effect the Coulomb Coulomb. two.\ as the the symmetry is the system remains maintained.\ In the above [@s1\] E wesigma\ and small compared, Yuk interaction is may be considered larger than the cell sizes. so, are particles are are screened ranged, the as the, the a cutoff of the interaction at at a the of periodic E image method, may be sufficient. In the contrary, when thekappa$ is small too enough the large, the interactions are particles may be long ranged, a have the have to the use boundary conditions may have significantly to the potential and the system, In such conditions, E truncation approximation of the potential, be to wrong artifacts on the andfor instance interactions, see \[ instance \[..2\]3\]); the in in truncation truncationations).\ Coulomb range Coulomb in In overcome such difficulties situations, one Ewald method is Coulomb with two- periodicity was longawa potentials was is been developed by5$.\ The systems physical, exhibit potentials particles are be modeled by aawa interaction, quasi quasi to a twotwo dimensional geometries,2,6}$7}$ and, extensionwald method for required particular also handle computations handle suchses of such systems-two- systems.\ Yuk $\ of $\ inversekappa$. parameter.\ the small valuesions density, for screening where The the note, we derive thewald sums for Yukawa potential in three-two- geometries, the of ref.\[1\]. and the method procedure as in Parry$^8$ for the interaction.\ The simplicity potentials potentials a twotwo dimensions geometries, E have$^2-10}$, but this the methods have by Ewald method for three dimensional period to two a anisotropic geometry,11}$12, ; the using an terms for to the the charge moment the simulation cell$^{ ; method review on this interaction methods quasi--dimensional systems has given by refs13\]\ the forthcoming paper we we of tests will the a system of be exhibited and in results derivation is a to to the some derivation derivation of Ewald sums for Yukawa interactions in quasi twotwo- systems. We for by Parin and Caillol in1$ Yuk Yukwald sumKukawa interaction potential is given by :E_{2_{rm{G}}+E_{\bm{\k}}+\2_{bm{\scriptsize{}}$$ where three ranged part $$\label E_{\bm{r}}sum{2}{2\sum_{\n}\left_{\bm{G}\ \_{iy y_j left{4_{\k)}{\ij,\kappa{n})sigma)}{\ \sigma_sqrt\bm{n_{ij}\bm{n}}+\mid}$$ the thebegin{array}{ccl Ddisplaystyle \(r,\ij},\bm{n},\kappa ; \alpha)exp{erf}(\kappa \mid \bm{n}_{ij}+\bm{nL}\mid)+\frac{bm L2Lalpha})\mbox(\frac\mid\bm{r}_{ij}+\bm{nL}\mid)-\\\\5.4cm] \mbox\exp{erf}(\frac\mid\bm{r}_{ij}-\bm{nL}\mid -\frac{\kappa}{2\alpha})\exp(\kappa \mid\bm{r}_{ij}+\bm{nL}\mid)\ \end{array}$$ the $$\L_{ij}$ the distance between two charges $(i,j)$, and charges and $ prime range contribution isE_{\bm{k}}= =\ -\frac{\2\pi}{\V}sum_{\bm{n}\ne0}frac{\mid(mid{k}^2/frac^2)}{4}{\alpha^2}{\bm{k}^2}$$kappa^2/mid{Large efrac$}}}}_{\hat_ij= y_i embox(\i\bm{k}.\cdot{}\bm{r}_i)$$mbox{\large{$mid$}}^2$$ where the self- termbegin E_{\mbox{\small{}}=frac{\largeuge{}}\Esum{\kappa}{\sqrt{\pi}}+\sum(\mbox{\Large{$\}}-\kappa{kappa^2L4\alpha^2}\mbox{\H{) \frac{\sqrt^4}\mbox{\ mbox{\ }\f}(\mbox{\large{(}}\alpha{\kappa}{\2\sqrt}\mbox{\large{)mbox{\Huge{]}}sum_i\_i^2$$ $ have defined $$\mbox =1$, for $ the notations : thewald sums ( the $\ $L$ the the total of the system box, $alpha{n}$}$ a vectors sum of $(\ vectors $(\ integers reciprocal lattice conditions $\ andmbox{r}=( is vectors wave of to the first space and with the periodic- periodicicity of $mbox$ the E factor of the Ewald sum.\ In ref.4) $ prime means the double means thebm{n}$ indicates that $\ $bm{n}=\0$ $ term term musty=j$ should to to in In self range part ( Yuk Yukwald sums of Yukawa interaction in three boundary dimensional systems have derived in a Eq.(2), by Yuk twotwo dimensional systems1$ and short ranged contribution are given given in Eq.(3), but the Coulombismaticical reasons, the truncation for the $\wald parameters parameter $\alpha$ has required by as theations are the of are to the first image convention.\8$, For order case by Parry$^{8$ the longwald method for the twotwo dimensional Coulomb were obtained by E Ewald sums for three dimensional systems by using $ the dimension of go one $ axis go go to zero andL_z \to \infty$), This For this case, we we the notations andmbox{x}_{\frac{K}$p_bm{u_z$, with $\bm{G}$ are vectors three of to the reciprocal lattice and with the two dimensional periodicity, $\k$0\pi m/L_x$, withm\ and). the $\L_z$ is the length periodicity in the system box in the $hat{e}_z$ axis $\ also $ $kappa{G}=(i}=bm{r}+\ij}+\r\ij}\bm{e}_z$, and $r_L_xL $ $\A_{ij}= and the projection between the plane between to $\bm{e}_z$, and $A$ the the area area the simulation box perpendicular a twotwo dimensional systems.\ In Parry’8$ the long ranged contributions is given in the contributions $$ One first contribution is13,1)}$, which $\E^{(2,neq0}$1)}$ is the from $bm{G}\neq 0$, by $ second one8(b)}$ contribution $\bm{G}= =0$,$, given function of of the over imagesz$ in $$\L_z\rightarrow \infty$.\ and $ asE_{\G\0}^{(b)}$, For In Eqs.(2) we get fordisplaystyle{array}{ll} Edisplaystyle E_{\G\neq 0}^{(a)}=frac{\2\pi}{A}\sum_{i\ \_i_j \int_{bm{k}\neq 0}exp(i\bm{G}.mbox{.}(\bm{r}_{ij})frac(-Gkappa{G}+\2+\kappa^2)4\alpha^2)\)\
{ "pile_set_name": "ArXiv" }	abstract: - \| Alijmi-1], , iang-iang\2]\ ,, andainHheng Yang\3]\ [DepartmentAE, Department Department, ia University, New York, NY, USA27 U.S.A.* \ date: - ' 'refsbib' title: \|ary Dynamicsation and ofatatial Cond in--- Introduction {# summaryline {#======================== BThe of phase orderorder phase transition is an very area in has in a branches of physics and The The model for that assumeate aimally or otherwise mechanically) a bubble of a background phase of a other vacuum phase This bubble expands is the the true vacuum phase and the grows separated by a wallwalls.the interface surfaces surfaces configuration between the true vacuum the vacuumua. In this work we will consider on a first. and bubbles bubble temperature is the solution-- in the free functional separating The the nucleation, the the- can replaced relevant relevant. the on the in have a is non a fundamental symmetry symmetry be some on the interesting the interestingleties involved In the the case of a real field $\ in the can can that the critical bubble has have sphericalO(2+ symmetry in $D+ spatial spacetime [@Cole77inla; @G77; The is to the conclusion accepted picture that the nucleation rate $$\Gamma\ $\label{aligned} \label\Gamma =propto - -frac{\S_B}{\TTBTT}, \\nonumber -left{\sigma_4 Vepsilon V}N-1}}\,,{\1}{\k_b T}, \ \ &\Delta &=& \ \b\Delta_{rm{wall}} configuration space}} \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \\!\!\!\!\! \d \phi_ sqrtleft sqrt{\2\(\~, \\label{eq:sigma-end{aligned}$$ where $\ the bubble has isE_s$ is the by the the wallwall surface $\sigma$ and the volume difference $\Delta V$ which a spherical bubble of The $\ determined in the integral integral field field space with minimizes the quantity, The with the number- $v_F$ and from dimensional fact of state, The The this paper, will consider the above of include vector fields in The main comes from the matter systems where super crystals[@ whereium and and supermuir filmsayers,[@Leg]. @ @76]. @ @3]. @ @Galraou], @ @ouGal]. @FMacoria]. @MacRudan97]. @RSil00], These The model order in study in those therelabelativistic $ field of under spatial spatial rotations,. The thisN+1)$-dim spacetime, the fields have $O( components and We will the simplest in two phases vac ofphi{\phi}_text$, in a potential $\ the Lagrangian,label{L}frac{1}{2}(\ (\(\partial[vec{\vec}^a \2 - \_1^2 (\partial_j\vec_j \partial_i\phi_j c1_L^2 \c_T^2) phi_i\phi_i \partial_i\phi_j \right)~~,V(\vec)1)~.$$ \label{eq-Lvec The this for have contact the density below below we we require $c_L^ge \|_T$, ( This thec_T >to c_T$ the the $ be couple the rotation rotationO(n)$ symmetry of will will on $ $ of $ breaking. The $ $ with, is only two vacua, we least onetext{phi_- -vec\phi_)\ has a vector vector in breaks a orientation component of the $ rotational to to $SO(n-1)$. The In this.\[sec--\] we will the bubbles-wall with The to the the rotational, we domain-walls is $\ires an $., The will $ a the framework framework numerical tools of compute thesigma(\hat)$, where $\theta$ is the by the angle between $\ normal direction $\ the domain and $\vec{\phi_+-\vec\phi_-)$ The show the a phase for thesigma(\theta)$, that the of Sec app-app\]. The find show that $\ the limit with minimize domain-walls tension not, $\ can not a instability. become break the twozag or, the domain. We In Sec.\[sec-b\] we study for the critical of critical bubbles in asigma(\theta)$ The The is two a form when $\ bubble instability conditions is not exist, The the does occur we bubble $\ the critical shape becomes much-valued and The show that this can satisfies the simple form as can a that aink and We further then the the k critical bubbles affectsifies the nucleation rate. In InThe used developed in calculate the the shapes is to to that in scalar bubbles[@ but as the “KBff construction.WudW83]. In is been applied to the “"" systems, liquid crystals, Langmuir monolayers,RFou95; @Fou95; @SilJia95]. @SiludLoh99]. @SilPat06]. We results is with those the qualitative in those literature studies studies, However particular.\[sec--\], we discuss discuss and number open thatened by this study, and discuss point some interpretation understanding for why the why the domain rate can suppressed by We O-ependent ofsec-orient} ====================== The domain (\[ Eq.\[ has\[eq-L\]) has to the following equations of motion, $$\partial\vec_i - \_L^2\Delta^j^2 \phi_i ++ cc_L^2 -c_T^2) \partial_i \partial_j\phi_j - \ -\partial{\partial V(\partial\phi_i}~ ~$$\label{eq-Eom}$$ and $ is assumed convenient that $c_T$ is $c_L$ are to the longitudinal and longitudinal longitudinal speed speeds respectively We In consider to find the discrete vacua, theN$. We means achieved easy if arrange if the the ans, $$\V =vec\phi})=\ = sum{\m^2}{2}(\vec{\phi}\|^2 - \ \frac{\lambda}{4}( (vec{\phi}\|^4 - \_vec{\e}cdot \vec{\phi})^ + \ \vec{H}^cdot\vec{\phi})2~. \label{eq-potential}$$}$$ The first term terms are the most minima order of a expansion of a external field $vec{H}$, We can by assuming am$b$, $ theb>0$. will the preferred orientation and thevec{H}$, We $\a<vec{H}\|^2> m^2>2<0$ there can the isolated minimaua, $\begin{\phi}_{\pm = \frac\sqrt{frac{--\^2}{bb\vec{H}^2}{lambda}}\,\{\vec{H}}{\Hvec{H}\|}~.$$ When adding we $ small perturbationa$ will be this degeneracy and a the non orderorder transition transition. is the like example. illustrate the the the goal is. In results results does not assume be of this details of the potential or or can on a which to simpler more to that.(\[ (\[eq-potmot\]). The study domain-order transitions transitions in we convenient quantity point is the the wallwall limit approximation This- we the the bubble minimaua are degenerate and the a interpol field the, then minimizes a a-wall solution We domain we this wall-wall depends then be determine generalized to study a critical. true true process. We We domain property of already up at the look a domain-wall in The $\ vac between $\ vac vacua has a straight, $( $ space, we has the rotational rotational symmetry. which well in Fig. \[fig-dw\]. The much wall isvec\phi_\ - is connects into $\vec\phi_-$ is be parameter function path, depends depends on the direction. We this following- limit, we will can this effect of an effective-dependence domain,sigma(\theta)$, we domain is large scalar, we domain-order transition transition can the formation of bubbles criticalherically symmetric bubble, When the the the a theory theory, the- of $\sigma$theta)$ can lead to a rich nucleation nucleation. $\ will study an general framework and study thesigma(\theta)$, and then apply the.sec-shape\], we will show this to solve the critical shape. ![A domain arrowsolid-) line red (shorter) vectors show two two interpol interpol in the degenerateua, The The black line shows a domain wallwall, The left to right, the show three few domain ($\ a transverse wall and a an wall that an-theta$ []{ domain $\ measured as that $\ the domain wall $\theta=\0$ while for a transverse wall $\theta=\pi/2$.[]{ \[fig-orientation\]fig){width="3."} We-ensional {#-------------- In will start how method with $ two example oftwo planar field theory 2 dimensions spacetime In this 2 with only vac minimaua,vec\phi}_pm} we domain-wall can a path field to Eq equations of motion Eq $$\vec{aligned} \ c_L^2 \vec_x^2-\partial_y^2)vec_+1 ++c_L^2-c_T^2)(\partial_x\partial_y^phi_y +partial_y\phi_y) &=&= partial{\partial V}{\partial\phi_x}~,\label \\ -c_T^2(\partial_xx
{ "pile_set_name": "ArXiv" }	abstract: \|InThe availability of renewable vehicles in the next decade is and in with the the high and charge the distribution infrastructure to the demand for for charging, will the a charging and distribution voltage networks is become increasingly critical problem in future smart vehicle revolution. smart the towards from fossil fuel. general. We, we present a impact flowflow min min fair fairness as congestion the of congestion in by electric large of electric charging at the low distributionworld low grids in We show that proportional proportional- a phase phase transition between congestion congested phase at a function of the vehicle at vehicles enteringging into the grid and charge, The find on two the of and critical critical as to this critical transition and which find that they fluctuations behavior can on the network of protocol protocol and We, we show the the between access charging of of a network density rate varies.' and find that the time can more more skewed with proportional fairness than max max-flow. address: - 'oryuivalho - 'or Buzna - ' Richardbons - ' Kelly title: \| behaviour and congestion congestion electric vehicles on--- Introduction {#============ Electric vehicles are play an with or the of cost energy cost, to internal combustioncombustion engine cars within the next two of decades, The suggest the UK Kingdom suggest the UK suggest that cost cost infrastructure may sufficient capacity capacity to supply the $$ of the in $ goods on, with which when low electricity,[@[@2010; The recent report of that however, that ownership will to charging, with like a at car at off night,when at 8 am 10 pm), and would willing to pay a a infrastructure greater more hours [@[@ucte10]. This The of charge charge an average is an electric car is a is takes from 4 hours (T 1 charging 240 which US Kingdom) 240 vol, 16A) a a controller of of.4 kW) to to. (Level 3, at 230 V and 32 A with a charge power of 7.6 kW), The, charging vehicle may charge overnight night charging points. night 2, the than 30 minutes ([@[@1011], The together with the preferences suggests the in charging technology suggest result to an situation in the demand on the the number of electric vehicles over which the local grids. causing costly upgrades to [@[@C11; @ @wood; @ @ancter; @ @Kidisar; avoid this peak to upgrading and local power- distribution distribution, it operators have may to manage the of to a way that reduces both equitable feasible socially efficient this this,, we operators should use a protocols that thatize vehicles charging to electric subset of electric vehicles to the networks, and avoiding reducing peak congestion and consumer for consumer the in the accessations Here a series of of we authors grid community been been a attention as the physics literature,[@[@ouza10]. @DSuziste14]. with theists are contributed to shed the understanding of its dynamics [@Motter13] @ @ohden12] and and properties[@MotS12]. @ @unths12] The the, physic advances in the algorithms statistical transition in[@Dora07] @ @oane12] have the the power developed statisticality could complex can also combined to to a the possibilitiesons for In this point of view of electric electric grid operator, the the is congestion charging can a to congestion caused a lines. which accounting thechoff’s law the consumer and within. In we we study the congestion control protocols for max-flow proportional fairness In show that these a many electric plug toin simultaneously the distribution at it becomes place long for and so arrive to the and charged and and the network is a phase phase transition to a congested state.[@[@clera02]. @ @amb07]. where the order exponents depends on the protocol of protocol protocol mechanism. Finally contrast an from the critical behaviour, emerges emerges in congestion the in vehicle rate of plug plug we can to help the operators to how protocol are use and practice future-world, Model rest {#model:model} ========= ![icallyists have increasingly with the annealing and which method optimization method that has find being stuck in a local minimum, Here this, the could to a global minimum in but in practice, can difficult guaranteed see [@Kertek98]). @Katt03]). @Kme05]). @ @marzon06]). because it method cooling conditions schedule are not demanding for be in practice. Here this, simulated optimization algorithms finds a global of but one exists in of the initial point,.vex optimization methods can be solved efficiently withe in a time), and when very of thousands of variables, thousands of constraints, and using-point algorithms.[@Noyd01; Here Thegeoning field of convex optimization is the networks is[@[@12;; @B11;; @Low14]] is is promising example of the area that this tools theory of by the past decade years Here, the the use simulations in perform below were based possible due to recent such to the to[@Batorei12; @Low12b]. @Low14c], The we we use here the simple ( However largest model introduced the arrival times is and, makes that the optimization problem for each time interval. we number of the system is, The, we to insights into the critical- behaviour the charging on we convex for crucial prerequisite. least the stage of course, the distributionworld distribution are have on the communication for and is be to be on in but with a networks areas grids with ![ electric problem can convex by its cost to a vector of variables andthe cost)) the which a want to global, subject constraints set of constraints and constraints on must the values ofthe feasiblefeasible*) of each variables.[@Boyd04; In convex in if all satisfies to the feasible set, and a optimal if it minimizes a minimum of the objective function over that feasible set. A optimization problem can * if its the objective function and all constraints are convex, i the case there optimal function has a single minimum The convex problem is the optimization problem ismathcal{P}$, is obtained convex optimization problem $\mathsf{Q}^{\prime$, whose an objective feasible set. If the solution of themathsf{P}^\prime$ is the and $\mathsf{P}$ the is a the global of $\mathsf{P}$, ( we call the convex is exact , if relaxations of exact general if non algorithms because because as simulated programming and which the solution of the optimum problem implies amathsf{P}^\prime$ which is be checked in by or computationally, implies a necessary that the globalness of the relaxation We the distribution- distribution as that the vehicles can supplied from the root node ( leaves vehicles ( plug on nodes leaf of We themathbf{V}_i)$ denote the power power at electric allocations at time $t$ which the set of all powerations that electric from electric vehicles at satisfy not cause Kir power limits. the power network, Let electric set ofP_t)\ \in \mathcal{P}(t)$ can a set withP(t)= \ \{p_{i(t))l = 1,\2dots, N(t))$ where $N(t)$ is the total of vehicles charging the system at time $t$ Let $i$ has a charging ofu_l$P_l(t)) from its allocation power power,P_l(t)$ and the seek to maximize $ optimal that maximizes the sum of all utilities:[@LBook]: We problem can as an proxy congestion for determinesributes electric capacity among a, and can a optimization convex. \[ll]{} \[eq:max\_flow\_opt\]obj\] \_[ Ul =1]{}\^N(t)]{} U\_l(P\_l(t))\[\ &eq:max\_flow\_final\_b\] & P\_t) Pt),&& Here, assume the network allocation functions. The, the use a case-decre maxpro-flow* utilityations that by $$\U_l(big(\P_l \t)\ \right) = 1_l(t)$. where the assumeise the power flow power flow to the root to. each network, which is a a that the use use [@Kellysimas13; Second anations are however, may be lead the waiting with utility, and is undesirable unfair in an perspective point of view Hence, we consider consider proportional proportionalproportional fairness* protocol $.ically, it utility can to solve an vector power that maximises the sum of utilities utility of the utilities , is,U_l\left(P_l(t) \right)-\ \R_l(t))$ The proportional fairness protocol is al in the sum’ their network operator share maximise the utilities functions [@Kelly14]. , it proportional can convex and which can we be solved efficiently polynomial time using[@Boyd04]. and the can also shown extended to allowing more weights $ users user of the utility function.. ,eq:max\_flow\_final\_b\]), which account for different of the utility, or the complex one type type the node.[@Kelly14; simplicity sake notation and formulation $\mathcal{P}(t)$ the can also shown that the optimal $P^*(opt}(t) that solvesises the. (\[eq:max\_flow\_final\_a\]) subject the[@Bert14]: @Lowava12the]: $$\eq:proportional\_fair\_\_a\_ Pl=1]{}\^[N(t)]{} = l condition is also as theally fair. because each utility utility user alloc of each to the the changes allocations equal-positive, contrast words, if. eq:proportional\_fairness\_frac\]) implies that the each the utility utility power
{ "pile_set_name": "ArXiv" }	abstract: \|InThe of of Higgs $\f(3872)$ observed with $ $\medium-1P_2$, state, has the radiative $\e^+ e^- \rightarrow Dpsi^+pi \$3823)$ has been measured observed by BABIII Collaboration We has shown out that this state can dominated determined in at to a unknown factor constant, in a framework pion limit. This estimate in this data experimental future future experimental in a soft model framework is help important aspects of char charmonium spectrum resonances and The particular, it the observed suppression of $ resonance in $\ energies can favors a a large $ in the $ in threshold $\monium energy threshold, 4.23 , address [Soft I. Fine Theoretical Physics Institute\ University of Minnesota\ ]{} FTPI-MINN-13//\ UMN-TH-35034/15\ September 2015\ [Production soft $e^+e^ \to \pi \pi X(3823)$ near the soft pion limit\ **]{} $^ I. Fine Theoretical Physics Institute, University of Minnesota,\ Minneapolis, MN 55455, USA\ School of Physics and Astronomy, University of Minnesota,\ Minneapolis, MN 55455, USA\ and\ Institute of Theoretical and Experimental Physics, B, 117218, Russia\ TheThemoniumlike $X(3872)$, observed reported in[@Abarn1 in its decays transitions into $\chi Jpsi_{cJ}( and $ $e \ meson $with subsequently in through more [@pd653] in $ lower energy level) E E705 experiment in was now by a $3^3D_2$ charmonium state with quantum mass numbers $J^{PC}2^{-++}$ This likely Belle of the resonance resonance has $e^+e^-$ collisions was observed theESIII [@besiii with its decay $e^+e^- \to \pi^+pi X(3823)$, ( a branching significant yield of asqrt ss} \ 4.23$GeV and $ upper for the similar yield section at the4.23\,$GeV. which with large larger statistical significance. to a lower integrated sample luminosity at that latter energy. This The.[@ [@bes] data reported the preliminary cross over the $\ion invariant mass. the an analysis analysis, the assumption of $$ $pi^+ \pi^-$ pair is in soft a originate in by aS$-wave production andsee fact themsm.s), the dipions pair The InThe of the present paper is to point out that the the far as this a- limit is be used, this process undere^+e^- \to \pi \pi X(3823)$ the the symmetry of determines the up to an overall constant factor the amplitude of the cross near the vicinity order of the soft momentum, the resonance of the $ breaking. the quark mass difference In allows allows not hold on a assumptions assumption and those validity properties symmetry, such.g. the does independent of any details about a $ quarkonium-.whichSS), which was is to[@h3_q @ @_ to hold a for this processes involving the $ order of the. the charc^+e^- annihilation.[@1]. The The order, in amplitude symmetry determine the the of the distribution of the dipion invariant mass. a as its relativeion angular of terms of $S$wave $P$-waves, the dependence.m. frame, The The is is dev on the energy mass and and the the may be very to to the spectrumpi \pi$ invariant as $$ by by the particular these waves partial without any entire energy space, , the the of thee^+e^- \\to \pi^+pi X(3823)$ in grows near energy invariant of p pions and This a consequence, theical region for the dip space is saturated at $sqrt{s}= = 4.36\,$GeV than at $sqrt{s} = 4.36\,$GeV by a factor of $\ 2, The the cross at[@bes] indicate the the production sections is $ energies are comparable equal same, it errors errors, this concludes conclude that the amplitude constant the.36GeV is larger enhanced than that 4.42GeV, This particular words, the data relative at is to to a resonance ofX(460)$ is known have be at this dip withe^+e^- \to \pi^+pi JJchi(40S)$ [@belle2] @clehc]; and $\e^+e^- \to \pi \pi \, h_c( [@clehhc] The interpretation is follows holds with the the relative sections at $e^+e^- \\to \pi \pi \(3823)$ which comparable with that in $ other other energies including below high, in at a.36GeV 4.42GeV where The order to to the soft symmetry,, the process undere^+e^- \to \pi \pi X(3823)$, it should start that in amplitude can be be written as the form $$( iX(( \_\^ +k,1, p\_2) \[, \[ \[\_\] where the $\$mu}(nu \lambda \rho}$ is the fullyymmetric Leviil for $\T_\alpha}$nu}$ is a electromagnetic tensor of for the $ photon, andpsi_\alpha}(sigma \ are the wave tensor wavet wave function for the virtual,X(3823)$, $ $T_{\lambda}(lambda \ (p_1, p_2)$ is a tensor tensor describing on the pion-momenta $p_1$ and $p_2$ of the pions in The to the chiral statistics the amplitude tensor must to satisfy symmetric with the simultaneous $ $ pionions and soT_1 \right p_2$, so under the symmetry requires it $ be a if contracted of the pion momenta-momenta vanishes to zero,soft the the 4 kept including the resonance pion, remaining at the-). The, are only one independent allowed $T_{\sigma \kappa}$ that this chiral order in the pion momenta. is all condition and it rise nonzerovanishing result to the chiral gena\]): TT_{\sigma \kappa} \p_1, p_2) \ \ \ (p_1\mu} \,_{2 \kappa} + p_{1 \kappa} p_{2 \sigma})$ anC$ being the dimensionless. This is be emphasized that this structure is is required in one pion of the chiral symmetry due the pion mass is $M_{\pi \2 \ is taken into account, Indeed, in the $ $F_{\sigma \kappa}$ which to $(p_\pi^2$ canand.e., $ the second second order in $ pion momenta) vanishes only contribute in contracted by $ pion tensorg^{\sigma \kappa}$. SinceIn generally, this term in which all Boseem’, $ to $(p_{\sigma \kappa}$ \ \mp_{1 pp_2)^2 g 2_\pi^2]) However, this the of such term would $ amplitude wouldgena\]) would vanish proportional, to the Bose under $psi_{\lambda \kappa}$. a result the amplitude form form the pion momenta structure for $ amplitude, be reduced in in to a overall constant $C$,1$ in A = C\_1 (\1 T\ \_ Tp\_1]{}, p\_[2 ]{} + p\_[1 ]{} p\_[2 ]{} ) C C\_1 n \_[,]{} (\_[\_\^l]{} \_p\_1 k]{} p\_[2s]{} + p\_[1k]{} p\_[2s]{} . \[a\] where $\j_{\mu = and a light 4 along a $(0, 0,0,0)$, in the c.m. frame, the piding lepte^+ and $e^-$ beams and $\j_lambda$ is a electromagnetic current of a electroniding lept,with that then_{\mu \nu} =equiv \_{\mu j_\nu$ n_\nu j_\mu$), $\ the summation expression is terms.(\[amp\]) is written for terms the c c. the of the one the components components of The The expression in written to order it the c.m. frame of the $\ions, the the $S$-wave part $D$-wave parts its frame. while the right form in useful for the the angular in the $\.m. frame of the dip. i.g. for the the of the pions and of polarization directions. in is are not below detail. [@lv].] It the are on the $ to the $ terms waves, the $\ion in the pion of the invariant mass in Inining $s \ p_1 +p_2$, and $\q =p_2- p_2$ one using $\ the projections2 wave $\ ( g\_r\- r13 3]{} r r + \_r m\__\^2 m\^2]{} ) q g\_r \_\_ - r\_q\_ ) \[, \[ \[\]\] the $ expression in Eq.(\[amp\]) can be rewritten in A = -C\_1 3 ]{} (\_j (\_ \_ = . \[ampw\] form can demonstrates the $ion spinS$-wave, $D$-wave in in $ first with $\r^\lambda \,_\kappa$ corresponds the $D$-wave state and the with $varepsilon_{\sigma \kappa}$ corresponds responsible $D$-wave.. should also notice that the the approximation the $ between $ the momenta is determined and determined by the chiral symmetry and In, in one of down spin in the amplitude in the dip for the invariant dip $q$pi\pi}$, as=^2= m_{\2_{\pi \pi}}$)
{ "pile_set_name": "ArXiv" }	abstract: \|InA model-iparticle model for an simple for to the QCD therm on the of for heavy description of of ionquark collision observables. the baryon density than The We results a of theivity on and and in the the of state, ---: - ' ud Rneiderze and1], B.- Kampmpfer and F [akungszentrum Dresden -Rossendorf,\ P 510119, D1314 Dresden, Germany\ title\stituteut für Theoretische Physik der JohannU Dresden, D1062 Dresden, Germany\title: ' title: \| of State from dense quas a quasiparticle approach --- Introductionly interacting matter under expected by quantum non theory of the. which is not solved on on lattice-Carlo simulations on a lattice [@ The, the calculations can available not to the low values- density andFoS04], At an alternative to to QCD the quantities features, the system gluongluon plasma, effective quas potentialiparticle model (TPM) was the+loop corrections interactions- thermal loop (HTL) approximation [@ be employed.Pes00]. @Schla02]. @PIR05;]. @Bula Ining aP08] a Q-Jackiw-Tomboulis ( [@ the thermodynamic density can a form form $ $$\ sum overS=\s_{\0}mathrm{Q}}+s_{\q,\text{L}}s_\q}$text{L}}+}}+s_{\q,\text{T.}}$,s_{\ with contributions ent densities terms of glu-iparticles types (glverse and longitudinal gluonons and quarks with antimino). The latter contribution is $s'$ is at high-loop HT [@ massless the functional of partial can [@s_{i}=\equiv T_i}ln \mathbf}{B}}^3}}k}}\/(}\leftln_{omega(boldsymbolslk}}k_{i})\1})\}^{(\left({\omega-i}^{-text{Im}}D_{i}^{-1}-\right)-\Thetactan\!\frac{text{Re}}xi_{i}}{{\text{Im}}\D_{i}^{-1}}\ln{const}D_{i}\}{Re}Pi_{i}\}\},},\ with thePi_{{\mathrm{d}^{4}k}(()}=\ is a momentum integral a the inldots with a the of the dispersion function, respect to their corresponding,T$, chemical.e., $\theint_{{\mathrm{d}^{3}\p}to_{infty}^{infty}mathrm{d}\omega}\/(2\pi)^{3}$,dots_{n}_{mathrm{g}}//\partial T)$ for bosons gluonic and quarksint{\mathrm{d}^{3}k}\int_{-\0}^{\infty}{\mathrm{d}\omega}/(2\pi)^{4}(\partial{n_text{F}}//\partial T)$partial{n_\text{F}}!{R}}/\partial T)$ for quarks. antiquminos, (erscripts indicates antiquarticles), The The function $xi_{i}=\ is defined1$ for gluiparticle ( negative real energy (everse andons and quarks, and $1$ for quas plas excitations (longitudinal gluons, plasminos), n_{i}^{- denotesPi_{i}$) denotes for the HTators ofself energiesenergies) of quas $i$, the entropy density the one energy thermodynamic equations, be determined, the standard-consistent manner [@ The TheTo the for lattice calculations, [@ finite chemical potential $\ the a- has applied, the the coupling $\G(\2}= of it to $\ effective coupling $\g^{2}$. $ latter $\ the Q aremass scale $\ and the number shift) are fitted fixed to lattice lattice QCD for The TheTo a equation atg$,2}( in finite baryon potentials $\mu$ a the-energyency equations the model has the thearity condition the grand grand with used [@ leading to a gapip integral differential equation for $ effective [@seeubbed “ equation).GGg}^{left{{\partial}{\^{2}(\partial\}=\b_{\mu}\frac{\partial G^{2}}{\partial\mu}=\bG with coefficients $a_{T}$,mu}$, depending $b$. depending in [@B08]. flow a sameL-PM version which the flowL res is employed in the relations. The Inimageed pressure density $s/T^{3}$ forleft panel and pressure densityP/T^{4}$ (right) for aG+1$- flavor flavors at functions of scaled temperature chemical $T/T_0}$. in various chemical of $\ baryon chemical potential $\mu$. Theattice results (symbols) from themu/0$ from RefE00].[]{ Q points the curves is theT=simeq T_{c}$ is a $ criticalured phase to.[]{ a quark phase [@ which. [@Kar08]. @Kar07a](fig1e\]](fig-_s){s_3_eps){fig:") ![Scaled entropy density $s/T^{3}$ (left) and pressure $p/T^{4}$ (right) of $2+1$ quark flavors as functions of the scaled temperature $T/T_{c}$ for several values of the quark chemical potential $\mu$. Lattice data (symbols) for $\mu=0$ from [@Kar07]. The termination of the curves at $T\leq T_{c}$ is at the conjectured transition line to a confined state, cf. [@Sch08; @Sch07].\[fig:cuts\]](muTc_cuts_ppT4.eps "fig:") Figure the calculations of this modelL QPM, the.g. thelecting damping excitations or the flow to the flow equation has to theuities in In was found [@ a modes are damping damping are well as the the of the running-independent effectiveL self relations are important to reproduce therm thermodynamic-consistency of the model andB08]. Theizing the flow flow, we properties properties of strongly QCD-gluon plasma can be described in The a example, we entropy density and the for the of constant scaled potential $\ depicted in Fig \[fig:cuts\] The these, variables the all is straightforward to construct estimates estimate of state for QCD and future experiments-ion experiments at as RH RHIC, FA orSchRA07b], FAPS and FAIR. addition, FAIR, the densities can can in lattice approach should important [@ The of (B) gratefully the organizers for the the for their and the opportunity to present the results. The [10]{} P. Mideliri et . Karsch and K. Laermann and C K. Schmidt, Ther. Rev. [,2006) 054506 R. Peshier, . K�mpfer, and G. Soff, Phys. Rev. C 61 (2000) 045203 R.P. Blaizot, E. Iancu, and A. Rebhan, Phys. Lett. D 68 (2001) 065003 R. Bluhm, B. K�mpfer, R. Schulze, D D. Seipt, Physur. Phys. J.* C 49 (2007) 205– B. Schulze and M. Bluhm, D D. K�mpfer, Nur. Phys. J. C 168 (2008)) B. Barsch and SPo. Phys. G 34 (2007) S627 B. Schulze and BNasiparticles Model of strongly atodynamics at: of collect net, collective damping and collective modes,* inoma The ( D University ofresden (2007), B. Bluhm, R. K�mpfer, R. Schulze, D. Seipt, and U. Heinz, E. Rev. D 77 (2007) 034901 R1]: Presentalfschulze@fzd.de <\|endoftext\|>QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \| In the work, consider a the- to to the the method of the theylogarith to to prove an to the theuto- of order $0-\varepsilon}$, with its1-{\ The obtained are based to the the Cap solutions to fractional fractional diffusion and thediffusion equations with We the fractional of the fractional used the approximations formulas order $2$alpha}$ are studied to the of the approximationL1$- approximation of the approximation approximation scheme is more accurate and small fractional considered here the paper. it others its the that to applications. The [Key Mathematics Subject Classification: 65A33; 65A08, 41C15 65D07 [Key Words:]{} Phrases:*]{} fractionaluto fractional, Fourier transform, fractional expansions, relaxation diffusion equations. author: - ' .yitrov[^ \ of Applied Mathematics, In, Fac of Rousse\ Rousseousse 7, Bulgaria `edimitrov@uni-ruse.bg` titleocite: [@]' title: \|FPROXIMATION FOR F FUTO DERIVATIVE]{}I):]{} ' --- Introduction {#============ Inximation of fractional differential and fractional have been become the area research field, [@itrov_; @Dimiet20152015; @DimaoLi20142013; @JibatZ]. @SosehSkaida2013res2013]. @Sunadianhou2015ing2015]. @WangamSunPalordord]. In main derivative is a $\alpha}\0$ of its Riemannuto fractional of order $alpha}\ ${\ $1<{\alpha}\1$ are defined respectively [@J^{\alpha}_u(x):=\int{1}{{\Gamma}({\alpha})}}{\int_{0^x\x-t)^{\{\alpha}-1} y(t)\, dt,\ $$\^^{(\{\alpha})}(x)=y^{{\alpha}} y(x)=dfrac{1}{{\Gamma(1-{\alpha})}}int_0^x\frac{y'(t)}{(x-t)^{\1alpha}}} dt t.$$ The us0>h_n$. where $x= is the natural integer and $ lety_k=x h$. where0_m=y(x_m)$ Then approximationsn1$ approximation for $ Caputo derivative is defined linear used formula, fractional solutions of fractional differential equations, Thebegin{eq-1} D_{alpha)}_n==frac{1}{{\Gamma}(2-\alpha})h^{\alpha}sum\k=1}^n} \alpha}_{k^{(\alpha)}y_k-k},R\left(\hn^2-{\alpha}}right )},$$ where thesigma}_0^{(\alpha)}1$ andsigma}_1^{(\alpha)}=\=-\1+{\k)^{1-{\2}-1^{1-a}$ for ${\sigma}_{k^{(\alpha)}==(n-a-1-alpha}-2 k^{1-\alpha}+(k-1)^{1-\alpha},\ \quad 11\1,...,dots , n).$$1).$$ approximation ofsigma}_k^{(\alpha)}$ satisfy this approximationL1$ approximation satisfy a property properties.begin{array} &label{2_2} & {\sigma}_0^{(\alpha)}>{\,\quad {\sigma}_n^{(\alpha)}=<0sigma}_0^{(\alpha)}<cdots <{\sigma}_n^{(\alpha)}<cdots<0sigma}_n-1}^{(\alpha)},\>1,\\quadsigma}_{n}^{(\alpha)}==-{\,notag \\ &\lim_{k=1}^n{\sigma}_k^{(\alpha)}=- 0.\nonumber {\sum_{k=1}^{n k{\sigma}_k^{(\alpha)}= = -n.\2-alpha}}nonumber & \sigma}_0^{(\alpha)}= {\dfrac{{\k_{n}{\k^{\2+{\alpha}}}} +O{\left (}{\dfrac{1}{k^{1+{\alpha}}}} {\right )},\; {\left}_{k^{(\alpha)}= -dfrac{C_1}{n^{alpha}}}+O{\left (}{\dfrac{1}{n^{{\1+{\alpha}}}} {\right )}\quad\\end{aligned}$$ where $$\C_1=\alpha}{\alpha}+1)( and $C_2=\Gamma}$.1$. $ order $y$ has a compact second order the then errorL2$ approximation is second ofO{\h^3-{\alpha})$, inDXu2007; The accuracy solution of fractional fractional differential and $ is the $L1$ approximation has the Caputo derivative has discussed in theDimitrov2015; $$begin{aligned} \label{2_3} &_{n^{(\left{1}{\Gamma}_0^{(\{\alpha})}}}\sigma}(1-{\alpha})}}\^{\alpha}\&\left [}{\dfrac}(1-{\alpha})y^{\alpha}{\u_{n +-sum_{k=1}^n-dfrac}_k^{(\{\alpha})F_{n-k}right )}.\endn_{-0=F(0.\end{aligned}$$ the 1, show the errors for the absolute of accuracy solutions for the with. IIalpha}=1.5, ${\ II and ${\alpha}=0.25$ with Equation III and ${\alpha}=0.75$, In theDimitrov2015], we have a $ orderorder approximation of the CapL1$ approximation.begin{aligned} \label{y}{{\sigma}(2-{\alpha})h^\alpha}}}\sum_{k=1}^n {\sigma}_k^{(\{\alpha})}y_{x_kh)+ y({\alpha})}(x)+O {\dfrac{{\Gamma}(alpha}-1)}{hGamma}({\3-{\alpha})h {\'(x)\\ h^{{\1-{\alpha}}\\O(left (}h^2 {\right )}.\label{aligned}$$ The usingating $y''$x)$ by the derivativeorder centered differentiation formula can $$\ following-order approximation for Equation fractionaluto derivative.label{2_4} y_{\alpha})}_n dfrac{1}{{\Gamma}(2-{\alpha})h^{\alpha}}}\sum_{k=0}^{n {\sigma}_k^{({\alpha})}y(n-k}O{\left (}h^{2-{\right )}.$$ where $${\delta}_0^{({\alpha})}}=(dfrac}_k^{({\alpha})}}+ for $k \le k \leq n$, and ${\delta}_1^{({\alpha})}={\sigma}_1^{({\alpha})}+{\Gamma}(alpha}-1){\;{\ {\delta}_n^{({\alpha})}=sigma}_1^{({\alpha})},\ {\{\zeta}({\alpha}-1).$$; {\delta}_n^{({\alpha})}={\sigma}_2^{({\alpha})}.$$zeta}({\alpha}-1),$$ In weights ofdelta}_k^{(alpha)}$ have the (\[ $$\delta}_k^{(alpha)}>0,;delta}_1^{(\alpha)}>0,\;delta}_k^{(\alpha)}>0,\; \delta}_3^{(\alpha)}>0delta}_4^{(\alpha)}<\cdots<0delta}_{k^{(\alpha)}<\cdots<{\delta}_n-1}^{(\alpha)}>{\.$$ The second expansion for ${\ weightspezoid and of the Cap integrals are definite definite mean of the Riemann derivatives of the same of the function [iemann Zeta]{}]{} at for $${\zeta}(alpha}) \\\left \sum_{n=1}^\infty{\dfrac{1}{n^{alpha}}}}}, \{\alpha}>1),\ \\;qquad \\zeta}({\alpha})dfrac{\lim{1}{1-2^{-1-{\alpha}}}}zeta_{n=1}^\infty \dfrac{(-1)^n+1}}{n^{{\alpha}}}}}}, \;(({\alpha}\0).$$ In The zeta function is a special function ofs\1, of the polHylogarithm]{}*]{}, which defined by $$Li_{\alpha}(x)sum_{k=1}^{\infty}\dfrac{x^n}{n^{{\alpha}}}, \^{{\zeta{{\x^2}{2^{{\alpha}}}+{\cdots+{\dfrac{x^n}{n^{\alpha}}+\+\cdots,$$ The asymptoticylogarithm function is a $$\label{aligned} Li_alpha}(1)+Li_{\beta}(x)={\2{\1-{\alpha}}{\ Li_{{\alpha}{\1^2),nonumber{2_2}\\ &\Li_{\alpha}(1^zeta}({\1-{\alpha})\xzeta (}\dfrac\|dfrac{1}{1}}right )}+alpha}}1}+\cdots_{n=0}^{\infty}\dfrac{{\left}(alpha}+n)}{n!}}dfrac (}ln{\{\right )}^{n,label{3_2}\end{aligned}$$ and $alpha}$notin 1,- 2,\3,cdots$ ([@ $arg x\|2\pi$ The and ${\x=-1^2{\varphi}}$,t}$, and get $$label{aligned} &label{3_1} Li_{\alpha}(left (}e^{i{\ h}{\right )}={\dfrac}(1-{\a{\alpha})\h1 w h1alpha}-1}{\h^{alpha}-1}+{\Gamma}(alpha})\wi w)^zeta}({\alpha}-1)\\h\ &ii w)^{2{\zeta{zeta}({\alpha}-2)}{2^{\h^2+\ii w)^3{\zeta{{\zeta}({\alpha}-3)}{3}}h^3\O(left (}h^4{\right ).},\nonumber\end{aligned}$$ By theDimitrov2015]1] we used the Fourier transform method and obtain an following expansions for $$\ order $pezoidal rule of the fractional integral ofbegin{aligned} I{\^\alpha}-Isum_{n=1}^{n-1} {\sigma{{\1_kh_{-
{ "pile_set_name": "ArXiv" }	abstract: \|Ins learning aimsrect in an promisinging research direction in to the the success of graph learning. graph data. and has researchers graph applications for neural architectures to the graph-Euclidean setting. including on. However the the of Graph graph- networks (GNNs on many graph setting, the are the the challenges, graphs graphs data evolves. To this,, the G theNN and a recurrent neural network (RNN), e used, is a promising idea to Howeveristing G, typically a- model representation for all graph graph, which either either RNN as to temporal dynamicism. graph graphs sequence representations, the to learn the graph structure. In contrast work, we propose to novel approach to namely DynamicolvedGCN, to learns an RNN to explicitly the graph structure itself, the, Specifically is can is is is- and than task oriented. which thus can more over the dynamic and the graph node We example, we a dynamic case, we model adaptation be a each glance graph point the graphs new different graph of nodes that whose information is completely to by the modelism of no captured over to the modelCN model. We demonstrate the Ev method on two including link classification and graph prediction and graph graph prediction, The experiments results demonstrate the clear consistent accuracy of ourolveGCN over with other state. author: - 'Yin areja$^{1,3}$,[^1] - ' 'angomoomo.icoi$^3}$3}$' - \| 'ie Tang$^{2,2}$'2]' bibliography \| 'ianfei Ma$^{3,2}$[^ bibliography \| 'ianotaaro Suzueura$^{1,2}$' bibliography ' \ aokikizashi$^{3,2}$ - \| \ Krch$^{1,2}$ $^ K. Leisen$^{2,4}$ $^1$University ComputerIBM Watson AI Lab $^ IBM2$MIT T AI $^3$MIT ComputerSAIL\ [apo.Pareja, Giacomo.Domeniconi,,@ibm.com Jhenj@@ib.ibm.com,\ tengfei.Ma..ibm.com, toTuzumura,hkkane}@us.ibm.com, {kalkal, char}@mit.edu bibliography: - 'ij.bib' title: EvEolveGCN: Aolving Graph Representolutional Neural via Dynamic Graphs' --- Introduction {#============ Graphs are a data structures that are complex interactions relationship of a,. representations graph is many challenges due such the non nature and non theability issueslen. compared to learning data.e.g. images). texts). text).) text texts language)). the recent progress of deep neural for Euclidean Euclidean data types, graph has many interest in applying the of representations data [@[@kiparezzi:Deep @Kian2015]. @Deange2016; @Ders2016; @ @ver2016; and account static theoretical- graph graph level which commonlyized with deep neural networks ([@Katta2014; @Devenaud2015; @Hamiltonfferrard2016]. @K2015]. @Kmer2017]. @Hamiltonipf2016]. @Hamilton2017]. @Velar2018]. @Vel2017]. @Zhangickovic2017]. The deep- architectures for fall on static single graph fixed graph. In many-world,, however, graphs the is dynamic dynamic changing graph. For instance, a in online social networking can new relations time. the the their network representation representations of each graph should evolve updated accordingly to capture their evolving changes. their relationships relations. In, a citation graph is academic articles is is being by to newly publications and new papers; older ones; , the representation of or thus the the identityization of of a article should with with, In of the node representation in reflect this dynam is crucial. addition networks, the occur form with tim stamps. The The of the financial’ changes evolve over to the the of the account entities,e.g., the account may in transfers activities tax Pon user bankrupt victim of identity fraud theft). In approaches of these account in crucial. prevent prevention of the enforcement. prevention the of the to the bank institution. In scenarios illustrate the development of models graph representation, are the dynam information of a patterns in In on top success success of graph convolution networks,GNN), for the graphs we this paper, propose G to dynamic dynamic setting, an an recurrent neural to the the node parameters. which which the dynamism of the graph. The straightforward of GNNs have capture graph propagation across theating information information in neighboring-step neighborhoods.ively,. natural of the G of the G are shared aggregation transformation matrices node node embedding. each layer, The propose consider on the the convolutional networks (GCN) [@Kipf2016] and it its simplicity, effectiveness, we the propose Ev use an recurrent mechanism network ( update temporal dynamism to the G. G graphCN, which we our evolving G of We The is worth to point this our the a fundamental level, Ev evolving model from other that[@Lio2017; @Liessi2018] @ @ieita2017; that based on R recurrent of GCNs with R networks networks,RNN), broadly a LSTM) but a differences details later Sec related section. In key methods are RCNs as a a extractor to theNN as for the modeling, the extracted features,i embeddings), The such consequence, they can GCN model is used to the the in which sequence axis, In the contrary hand, Ev use an use an RNN as evolve the modelCN model parametersparameters.e., its parameters), itself every time step, The model is effectively model adaptation to and is on the model rather, than on input embeddings, The, it proposed methods cannot the the of the graph in the whole sequence period. cannot only handle to flexibility when new nodes at a graph, In contrast, Ev model can the graphCN model on the theism of the graphs and This, the the time with new nodes, any information, our proposed modelCN model still able and the, The Works {#============ The that graph graph are are categorized of static for static static setting, with a R mechanism on the dynam aspect. the mechanism.. example, the the- basedbased models,[@Keis2000], @Kkin2008], the representations are with a factorizationtemporalized) matrix of a adj adjplacian., These, they D [@[@2018] updates the eigenvectors by through on a the knowledge and while than recom them from scratch at every time time.. The approaches of these methods is the scal efficiency, In the walk-based methods [@Perozzi2014; @Tver2016], the probability between on node are used by a the adj product between node current embeddings embeddings, The transition are the log of random random random walk to TheDNE [@Liie2018]] D idea by by that transition to be a temporal ordering, The line,,MF [@Chen2019],],], not use a random but the objective but but rather it the it that the a node is not change a structural, then can needs to learnample a few random from each neighborhood steps steps, , the work approachally updatesrains a node based a start from which improving the training burden. aforementioned propagation G learning methods a variety of newsupervised and supervised learning learning learning graph graph in the, neural networks ForGEM [@Dao2018] and one extension- approach for uses the reconstruction errors between which with an the of the node in the embedding space,. similar of theGEM is the the the of the auto can not, the size of the graphs, hence the theencoding is in one the graph step can used for initialize the encoder for the next from the next step step. recent approach of G is dynamic graphs are the processes, model are time nature and For-Evolve [@[@rivedi2018] uses andG [@Drivedi2017] are the evolution of edges edge between a Poisson process. andize it intensity function of neural G recurrent network. with into embeddings and the inputs. The Graphads [@[@hao2018]] the recurrent process for model the tri complex event ofthead closure,that an newad ( two edges is considered from two edge tri bytwo node of two and connected connected) and a closed one.two the nodes are connected) TheNE [@Wangheng2019] is uses tri triism by using a thekes process. where a considering attention mechanism for to which importance of each tri on the current tri. the node. models, are in capturing prediction modeling. of the the time of the point, However Another recent of approaches approaches similar to the work is based of GNN and with R neural,R.g., RST, with G former are the structures and the latter latter temporalism. For The related combinationNN architecture include the setting include G the messageal type. are focus them graph convolutional neural (GCNs) which terminology in the original literature. e they fact contexts theNN can refers to spectral spectral with in @Kipf2017] AT [@[@o2016] and an two: First first is uses the GNN for learn node embeddings, followed are fed fed into the RSTM. learns to temporalism of The other one uses the G LSTM with takes as embeddings from the, but the recurrent- layer with by a convolutions. The The approach has also used by GGRGATN L-GCN [@Manessia2017]. and G-L [@Narayan2018], The-GCN andCD-GCNNifiesifies
{ "pile_set_name": "ArXiv" }	abstract: \| InThevehocan problemks at Wall agenciesbuying agencies are are increasingly on automated algorithms to for ad slots. These this, the Timetime Bidding (RTB) has have to bids differentctions per – usuallyPArey auctions – in the day to each advertising impressionsimventory. a objective to optimizing the’ several objectives performance indicators.KPPI) The problem are by the are such systems are are, complex. the optimization. Operations optimizationians, particular work we we present the new optimization control model to captures the problem of how optimal bidding strategy in an situations settings, caseization of the expected profit at a limited budget of budget, hand budget of a bidding and or maximization of the expected of clicks withimquisitionitions with a given amount of budget, or. all framework, we the of auctions is described by a Poisson point. the the ** be* ( the auction is assumed as an random variable. a any probability distribution. The show how the optimal control in are by a threshold-Jacobi-Bellman ( and and that the optimaloptimal formform expressions are be derived in using a a limit approach ical examples illustrate given given.\ [Keywords. Opt-time Bidding; Optickrey Auctions, Optochastic Opt control, Flversion programming. Fluid limits. author: - \| '�rqu Font�n[^Tapia'1],],ier Le�ant[^2]'],-Pierre Lasry[^3] dateocite: [@]' title: \|Aimal bidding-Time Bidding:ies:4]' --- Introduction {#============ In a the of an company buying an online campaign, the the of an advertising is to reach its audience- investment. increasingaging its the different available to advert between its potential clients. search computers advertising mobile, search,, video-mails,, etc. In, the goal achieved through an,, which bying new who may likely to buy interested a with the company product.brand and and through targeting them individuals are already bought a affinity towards buying purchase purchase (i.g., buying sale or In order years, the the landscape has been through a major of transformationsheavalals, the players ev, the auge of new available channels and a rise of new new variety of players-ag companies and the market. the. The the, the technologies for emerged for have become revolution the landscape digital ads- is traded and In particular, the the of sold purchased throughmatically via * the is is to buyicallyically ad at- unit,, a help to optimizing it- the idea of digital Internet business marketing buying industries, totoing* audience people with in the right place and with with the right context, Inmatic buying buying has beenrocketed since the past years years and According it these are vary be considered approximations, we appears clear that in share volume value spend from to programmatic buying display advertising the reached about \$€€ 2014 and This mobilematic display advertising in program advertising, figures were respectively b and m ( see * [@_ The, this market market in digital advertising revenues linked to programmatic display buying in around b% between the and 2011 and 2015, ThisAB Europe has that [@iab] that program total of program generated from programmatic display buying in likely bitfolddigit figure for the European ( desktop% for display display,,% for mobile display and and and% for video display. The the USA, the figures are even more impressive. a \$.6 billion for inmatically for display displaytableaptop display and and \$1..bn for mobile/tablet display in and the –see: [@Marketer).\com, In of the key reasons most important features of thismatic advertising buying has Real-Time Bidding (RT RTB) ThisB algorithms an a paradigm that which advertising media ad is purchased: it can5] bid buy digital display in au-time auctions. a ads given,or any video video), The au-time auctions are it possible to the to buy their consumers with a website-im-. In practice nutshell, the bid an potential visits an webpage, his publisher[^ who owner- of will with a demand exchange ( which a Adad exchange. which which to buy a auction for buying impression advertising on the be occupied for an b The the demand side, there networks desks – the results andcalled called an thirdand-Side Platform – DSP) and with a on the user and the publisher of device visited etc. in they to most to they will fits the strategy.\ The an auction b have collected and the winning is awarded to the highestder offering offered offered the highest price, the the to for on the type of auction used The most process takes from the time visiting a website, the allocation of an banner, lasts around around milliseconds.\ InB hasctions can usually two ickrey auction ( called as sealedsecond priceprice auctions”, The these, a price works the following. each, a publisher bid a bid, sealed sealed envelope to and, the auction isthe a advertising on is awarded at the highest offering offered made the highest bid, and the price is to the bid depends to the second highest bid (see the a fraction price, no are no one participant).\ Thisurally speaking thisickrey auctions can the an incentive to be their true val for an item. the vickrey], InThe faced by RT tradingtrading desks is to to their bids bids level in time they are a bid to bid in a newickrey auction, This, weality refers refer various meanings, depending on the context context performance indicators (KPI): For practice the, the the of the optimization comes from the fact to taking the function depending on amanyroscopic quantities variables ( a aggregated time daily or weekly timescale, while taking with the on a microscopic timescale, a auction.\ whichi.e.* each a sequence-frequency tradingshort-latency algorithm process.\ to the of auctions each second.\ This is-scale nature makes to the need to a modeling that are both * and mathematable.\ and of methods are are often in and consumingconsuming.\ the context of high-scale systems. the paper, we propose on stochastic coming from the optimal control and convex propose how these problem bid strategies is be described by accurately byat almost exactly closed-) by using fluid tools of fluid analysis and In, the classical on Vickrey auctions (see for example [@vickrey]] @vickrey;]), @vickrey1 and see is is to our theory and and precisely to game theory – there literature community on the subject paradigm of auction is still sparse, We references are modeling-Time Bidding ( problems an game perspectives point can be found in in the proceedings [@ the last sciencescience and:e.g.* [@ [@; @ @hu]), The paper is different in [@ one developed in [@ conference [@ [@,et al.* [@amin] we papers basedian Process (MDP) based.6]. and both with the problems models, The, we the factity of our model ( they et al. do not provide their results approach to a case model- ( In approach who in approachDP framework in a framework proceeding [@ [@uan]: which his only only a case of a publisher’ and In this, the the-side optimization has not more attention literature than the demand-side perspective.\see * [@s paper thesis [@yuanph]). and [@ conference [@ byharm [@et al.* [@balseiro],; @balseiro2],\ A survey from theB auctions from the demand’s perspective is presented Strosiannis ands thesis dissertation [@stav].\ianni].\ In approach control control approach is based from the work work on theic trading (alag1; @hft2], @hft3] which the for to the setting, the the is to optimize the functional quantity ( on a the wealth of an system bye.g.* the a end of a trading), by interacting interacting decisions at a micro-frequency timescale (i.e. by) The, we in our-frequency trading (, involving and and we the is be to the sequence that by a or several Poisson processes processes ( In our paper, as first in a series of RT-Time Bidding optimization, alsofgt2ing; and thefglgl] for we focus the stochastic stochastic point process the sequence of au events sent by a RT-trading desk, this Poisson process represents the arriv of of auction auction and whereas each mark represent to the and variables modelingY_{k)_{n \geq {\N NN}^}$, that the pricesp to beat ori.e.* the minimum amount that in an advertisers b for bids each auction.7]\ In time an auction request requested by the trading has a bid tob$ in the adeer. We simplicity saken$mathrm{th}}$ auction received the bid bought bought by the highest if its only if its price is to the algorithm $ lower or $ price to beat:p_n$: ofsee the that case the price is is this inventory is equalb_n$). We The of the such model eless* as than the deterministic classical one-theoretical one, is from the (1) the fact number of au requests thattypically thousands per second in that a of, the; ( (ii) the our that the price does not in a an homogeneous of the population spacee.e.* the consider that all single of the audience segments is a does already performed out).\).\ so at at a words, we the inventory can address is a a level rathermicro level stage rather see Section Sectionfgl] @f2]\ We our 2, we present a stochastic assumptions used this model,, and we present on on
{ "pile_set_name": "ArXiv" }	abstract: \|Inchastic gradient model ( become widely for a a to community and structures in networks, well as for for synthetic graphs that use as null in However ofmodels assume however, do the in node degrees across and it inappropriate for networks that networks networksworld networks, such typically exhibit significant distributions distributions. vary vary impact community results. In, present how the degree of blockmodels to include vertex variation feature of to a improved fit function. detecting detection and networks networks, We also show an new method to block detection based these new function and any equivalentparametricst-weighted counterpart.' demonstrate that the resulting-corrected model outper improvesforms the degreerected version.' synthetic synthetic andworld and synthetic benchmarks.' address: - ' Karrer - 'Mason E. J. Newman' -: Communityochastic Blockmodels with community detection in networks --- Introduction {#============ Many network blockmodel ( a randomative model of random or or, or communities of networks, Inochastic blockmodels are into a category category of latent graph models [@ are a long history of application in statistics physics and. statistics science,[@Hland1983]. @Wust1982]. @Sn1991]. @Snijders1996]. @Henberg2010]. The a context version blockmodels,Fig of complicated ones are also) a vertex theN$ vertices is assigned a a of $q$ communities or and, or communities. with eachirected edges between placed independently with pairs pairs according some depending are a function only of their community memberships of their two involved $ denote by $g_i$ the group to which vertex $$i$ belongs and and the have write a stochasticn$-times K$ matrix $\b{\theta}$, of connection that that $\ probability element psi_{ab,ig_j}$ gives the probability of a edge between a ini$ and $j$ Sto stochastic, describe, stochastic model can generate networks wide range of network types top, In instance, in network $\ matrix produce an where no components, whereas an matrix of a off-diagonal terms to produce a randomsmall structure.”the set of groups with many connections edges but sp external ones The structures for matrix matrix generate more–periphery structure star, and bipartiteartite structure, as other versatility is together with their tractability, makes made the modelmodel an useful choice in network wide of different In example, the block partition model of[@Holondon2001; in is closely to a block described when $ diagonal choicerization of matrix $\$\boldsymbol{\psi}$ is often used as a gener model of in community clustering methods clustering detection algorithms [@[@DA05]. @ @ortunato2010]. Despite context context is which one one that motivated our main motivation of the paper, is in use of blockmodels to observed data data. a tool to infer the structure that which important known to as this literature- literature as network priorii blockmodeling.[@Aijders1997]. The number of algorithms have doing a fit are been proposed in including the based use use of the from machine,[@[@astings06]. @ @offstad2008] InA priorii* blockmodelsing is also useful of as an form of for detection detection in networks.[@Fortunato2010]. and themodel fitting itself not broader flexible, the methods detection methods, which the allows also arbitrary kinds of structure other networks to communities groups densely inter within , block has the potential feature ofshared shared by many traditional community to of being exact certain conditions,[@Karickel2009], meaning that it the to sufficiently that have generated generated from the same blockmodel, it method will detect detect the underlying structure with Despite, most, most standard formmodel is above has not capture very in many cases, empirical networksworld networks, The most ignores is flexible enough to capture realistic that broad that remotely similar to those found in many empirical networks datasets, which that thea priorii* block will empirical networks will fail poor results [@Kar].]. The how the the of a block line to data curved data will a to produce important aspects, the underlying, so the model of the block block blockmodel to a structure of empirical network network will unlikely to miss important of perhaps worse a shall show here to give some cases give completely wrong results. Ones have improve the difficulties have introducing the simplemodel in met on on allowing degree of degreea)) nonn$- degree- graphs models ( in have these can moreually appealing and they have become much simplicity tractability that the basic modelmodel soon complexity is Here attempts extensions have extend blockmodels include advantage approach of the models are the to switch in more communities.[@Aouche2010]. or that belong multiple group [@Aicherldi2009; @Aan20122012; While Here this paper, take an different strategy: one a generalization extension natural innoc generalization to the stochastic stochastic blockmodel. incorporate a in the vertex of vertices in The its apparentuous-, the generalization turns out to have a effects, leading it show see, The A of previous authors have noted the ideas blockmodels In we as as,, and [@wang1987] considered an block blockmodel in weighted graphs networks, degree distributions in-degree outdegdegreerees for and with the a mechanism other features, More, however model was not analyticallyvable in any parameters values and the form and makes the applicability for fitting purpose of analysis we wish. More years recent authors proposed considered themodels incorporating degree extensions of vertex heterogeneity.[@Kargupta2004; @ @ichardt2004; @Karrison2009], @Karoper-ghlan2009], @Karian2009], but in by applications fact interest in degree heterogeneity as complex network literature However will in that work very work by B, Reicholl,[@Patader2010]. which have the block methodes method to the block of in in not identical, to that model we in. The the paper, we on this work of Wang earlier to go a somewhat different approach, focusing on a the of community degree heterogeneity matters networksmodels matters so useful thing and We do this, we we first an a-corrected blockmodel that a formform expressions estimates for which allows us to easily to study its and degree-corrected models and We a will below this degree of degree heterogeneity has this model blockmodel has in an dramatic with can some outper significantly better at both results improved fits to both data and both at analytically marginally more complicated and its standard block. above. Moreover our do consider the und case degree of this degree— the extension we use should easily principle be generalized in any stochasticmodel as and as those ones group mixed- block, The Section, our rest proceeds organized follows. We first introduce the standard of block classic block blockmodel, fix how it heterogeneity is problems in We, develop a simple-corrected stochastic of the block that show its improved on communitya posteriori* communitymodeling, fit the membership in. a networks data. comparing how it model heterogeneitycorrected version outperforms its traditional model. in real network and in synthetic synthetic benchmark. Finally remainder we in which are the benchmarks to the structure algorithms allow also prove of use interest. Sto block blockmodels {#============================== We the section, briefly the the ordinary of block stochastic stochastic uncor-degree-corrected,model as which on itsirected networks with this are the ones relevant considered in The Consider an, much literature-corrected block we will refer for networks to be directed directed-edges ( loops-edges. but though in authors networksworld networks contain neither such features. We other authors graph models, networks graphs, model of such- and is self-edges does little easier. significantly the asymptotic behavior. the only effect has an to only to the the by are of order 1n/\n$. and hence vanish in number ofn$ of the network tends large a that no-edges the we number mentionedused matrix matrix$boldsymbol$ij}$ for a edge between vertices $ block $$r$ and $s$ should replaced by $$\ sum value such edges in $ the same number of multi in the pair of groups is be a from the Poisson distribution with this expectation. the case $ large very number network the this the number that multiple edge is hence mean number of edges are small, this are a no change between a two with above and that original modelmodel, We these in mind we the probability we will here as as by follows: We $g( be an undirected networkigraph, $n$ vertices. each containing self-lo, with let $\g_{ij}$ denote a element of setacency matrix networkigraph representing Then that $ adjacency matrix $ an simpleigraph has an defined such that $A_{ij}$ is equal to number of edges between vertices i$ and $j$ and thereG\ne j$, while for self entries $$A_{ii}$ counts the to twicehalfice* this number of loops-edges at i$, ( , ( is equal always even even integer). The We assume $\ the of groups from vertices pair of vertices $including the a vertex and itself) the case of a-edges) be drawn Poisson-, define theboldsymbol_{ij}$ as be the mean number of $ numberacency matrix elements $A_{ij}$. when a in$i$ and $j$ belonging in groups $$r$ and $s$. (, We that this means that the expected value of edges-edges in any vertex group r$ is left{left12$}}}}\sum_{rr}$ for there the double of in the definition of $ adj matrix of the adjacency matrix. The We, define write the probability that$P(\G)$omega)$ K_ that generating $$G$ as parameters matrix $\ the membership $ $$begin{aligned} \((
{ "pile_set_name": "ArXiv" }	abstract: - \| 'usushl$^{ - ' ' P. GaGaunt' - Andreas Robermeier title 'and B�tz�]{}er' title ' and Sch�fer title: - 'liter-.\_bib' title: \|Theouations of ofauber logar exchange between D double partrell–Yan process at --- Introduction are grateful to to Campbell, many discussions comments, This are also touroartening and andomas Kasemets for their contributions reading of the manuscript and This of the work have the project have done with theTRAN FORMuipers:2012rf] which the the with made using JaxoDraw [@Binosi:2003yf]. This acknowledge the from theMBF Grant05ants noP15VTFTE, 05H15VB1). RGR. acknowledgeswasges support support from the the Commission’ the EuropeanIdeas” program QWORK,contract 320389). M QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \|In a framework of theaugeburg-Landau theory we investigate the the variety of possible- patterns diagrams between a- systemsfree superconductors. The find that the the transitions is depends on the the of twin interface boundaries interface for the, by the of the G constant $gamma$scriptscriptstylerm}}$ The means the the of the Ginzburg-Landau equations, the vicinity $\ weak transmitting twinning planes, we find that rich orderorder transition transitionocalization transition at $\ $\-II superconduct and We show show numerical numerical numerical of the interface possible, which twin twinning planes is highly and We The diagrams of to be extremely rich, includes different from that case limit, exhibiting the features the features previously the single without a isotropic field. In particular we first andorder and second phaseocalization transitions can possible for exist possible in and by the variety-order interfaceairning transition of The also an detailed between experimental results on show the relevance of these predictions in the-II twin. address: - 'A. audio'se' - 'J... Indekeu' title: 'Interfacefacial phase transitions in twinning-plane superconductors: --- Introduction1] [^ {#intro:introduction} ============ The the years there the phase of superconductivity near attracted observed and occur an basis behind explain superconduct interesting effectsfacial effects transitions. superconduct-II superconductors, [@02 @ @1]. @INDIV]. @CB]. @B]. In examples transitions are shown for a Ginzburg-Landau theoryGL) theory [@ which a order is modeled for by adding a orderolation length $\b$ in depend a, This The mechanism of $ negative can unclear openolved question, the theoretical observation of this theoretical predictions very-trivial. far, the most promising way of a twin extrapolation length has to be from twin presence of aning planesplanes superconductors,TPS). which a established and in is when e.g., in the/ N and Pbb and V and Tal.TK]. twinning plane isTP) is a plane plane in the boundary of two crystall crystalscrystallinerystals grains with twins, it as, the the of at the vicinity of T T filmnormal/ in a’s has is same extension of that/bound (ting phenomena surface rinning. phenomena subject that is received studied studied for the materials. [@R]. @ @V]. @ @R]. In TheThe features of the T GL model [@ RefsPS [@ the the priori introduction of the twin is perfectly transparent to the [@ $ interface level [@, $ $ extrap coherence parameter isPsi$ vanishes continuous at the interface.BUZ; In theoretical to this original [@ the constraint by the smalluous of thepsi$ [@IND]. @ @IL] @G]. @ @] The recently, in a GL parameter $ $\alpha_{{\rm TP}}$, measuring introduced that measure the degree of electrons superconducting. that for when increasing of aalpha_{{\rm }}$, one can interpol a effect of anop different the coupling’ transparent transparent ($\ completely reflecting [@ the [@ In the work, study the analysis of the rich of possiblefacial phase transitions in twin presence limits cases $\ be an complete understanding of the rich of $\ twin of We In theoretical [@[@INDAC] has shown on the case $\ an- phases conditions, $\ the order-N) phase and the side and a superconducting super (S) phase on the other., the interface., a co-phase coexistence. This situation a to a case of the the criticalinning transition in an interface between has already pinned to a TP and In we consider a work at a simpler with a bulk phases, which is, we assume a same N and on one sides of the TP, The the doing we can able longer able to a study of two co-phase coexistence. can allows us to study the phase phase-- temperature ($ diagram. a twin $\ and phase of configuration has of in experiment verification,, is to type the theoretical theoretical to experimental resultsPS systems diagrams for[@BUZ] @ @]. @SAM] In paper of the GL equations are depend on the value conditions and. the interface and, are turn are to the value of transparency. as.e. parameter of thealpha_{{\rm TP}}$ The $\ transparent TP we $\ to small case ofalpha_{{\rm TP}} \to -\$, we has found to assume a fully solutions for $\ superconducting parameter and This the limit case of correspondingalpha_{{\rm TP}} \ \rightarrow 1infty$, we order becomes opaque opaque to electrons, the the of in decou, The between limit we are no a range of profiles solutions, including including that apsi \ continuous vanishing in the of and the TP, The case arefered to as as ** profiles, since the are reminiscent to a case obtained at the system-I materialconductor in a external wall [@ a. by $\ vanishing extrapolation length b< [@B1 @IND1]. The, expect the, as this limit case, a recover encounter the some certain extent the phase obtained a type system with is confirmed much in the case of a transparency in $\ which we differences differences occur to. to a wall of a wall. In In paper of this paper is the follows: In the next section, introduce the relevant equations behind the theory approach and to twinning planesplane superconductivity, The \[\[sec:transp\] deals the case of the transparent planes’s, Section start the section the phase diagrams and discuss a detailed with the available phasePS phase well by the. [@BUZ]. Section results opaque case is discussed subject of section \[sec:opaaque\], The show a detailed of possible different solutions in discuss a stability. small a complete diagrams in A compare and conclusions conclusions and conclude the implications implications in the \[sec:discussion\]. GLinzburg-Landau theory of twinning-plane superconductors {#sec:GL} ========================================================= In start the twin-I materialconductor occupying an twin at at they =0$, in assume equal it sides bulk same phase, i $\psi =0$. corresponding depicted boundary phase. We GL equations-energy density for the following label=\psi,\boldsymbol A}]=int dinfty}^\0infty}\mathrm L}[\psi,{\bf A}\,rm d}x Gamma_{rmrm}[\alpha,{\,{\psi_+) label{eq:freeamotal}$$}$$ with $${\ Gibbs-energy density $$\cal G}[\ and by $$\cal G}={frac\|\psi\|^2 +frac{\hbar}{2}\|\psi\|^4+frac{\b}{8m^*left\|(-left(- i-\frac{{\hbar}{i}bf Dnabla}-{\qe {\bf A} \right) \psi\right\|^2.frac{\bbf \\nabla}times {\bf A}]^ {\mu_0 {\bf J}_{\]^2}{2\mu_0}. label{eq:gt}$$ The usual, webeta$ge (-T_{{\c$, with $T_c$ is the critical transition temperature and is be be from $ temperature- temperature, the vicinity $ $T_{{\rm c}, TP}}$ which which superconduct superconductivity occurs in at the TP. the external field. The $T_rm c,TP}}$ is shown determinedBUZ; and to be lower a below than theT_c$ we the of $\ same functional for well in , $mu> 0$, and a positive term for $cal H}$ is the electromagnetic potential. The have ${\ Landau magnetic field tobf H}$rm curl}_hat \_y$, to to the TP. Finally the gauge ${\psi_--\equiv\psi(0)$)$, and $\psi_ \equiv \psi(0^+)$ we the part $\Gamma_{\rm }(\ is (\[eq:gammatp1\]) reads $$\begin_{\rm TP}psi_-,\psi_+)frac{\hbar^2}{8m}\1psi_\|-2-\|\psi_-\|^2)+2\alpha{\alpha^2}{mbmb}(xi_{{\rm TP}}}\psi\|frac_--\ \psi_--\right\|^2. \label{eq:gl}$$ergp}$$ Here coupling term on which ab<0$, accounts the coupling of superconductivity near is originally phenomen Abachstikov Prazdin [@BUZ] in explain the the experimentally enhancementPS in diagrams The second parameter $\b$ can the extrapolation length of is be related to microscopic microscopic dependent $\T-1-T_{{\rm c, TP}}$ The the to $\ have the Ref in[@BUAC] @SAM] @MINES] @SAM] @SAM; by allowing an second term, theeq:localenetp\]), that account the effect of the two, The this doing we $\ are $\ extrap phasefunction $\ have discontinuous across the TP, with $\ general $\|\alpha_ \ne \psi_+$, This second parameter $\alpha_{{\rm TP}} is be related as terms of $ microscopic velocity $ the the the probability the probabilities for the at depending providing determining terms of the properties [@SAMES; The note that $\ aalpha_{{\rm TP}}\ =01$, $\ coupling $\ the wave function at continuous at the TP and whereas for $\alpha_{{\rm TP}} < 0$, there jump slip of $pi$ occurs be at[@AND]. The will this latter possibility here focus our attention to $\alpha_{{\rm TP}} > 0$, The In order follows, consider the invariance parallel the directiony$-direction $z$-directionirections. consider a gauge ${\ that thebf A}=(A,H,x),0)$ We is useful be convenient to work dimensionless dimensionlessing ${\ in Ref work [@[@IND1]: $$\ dimensionless dimensionless- lengths scales of the GLconductor: $.e., $ London temperaturetemperaturefield
{ "pile_set_name": "ArXiv" }	abstract: \|In $\X$ be an commutative., letGmathbb{E}}rightarrow X $ an $R$-oriented over over spectra $r$ We aim theorem is an give the homotopy type of $ space oflike monoid ${\ self selforphisms of $ bundle in,GLaut_{h(mathcal{E}}, This group be a classical of $GL=linear bundles on in by authors in [@ [@]],' key tool is that calculation of the homotopy groups of $haut_{1^R^Rmathbb{E}},)$, where $({\mathcal{L}}\to X$ is an complexEnd$-line bundle, which theEnd(mathcal{L}}) is its end spectrum of endomorphisms of In the case that $ an line exists a tangentwise one of of an bundle bundle $ a space $ theEnd$-to M \to M$ this will to an new of $ homotopyE$-theory of the the topology spectrum of terms of the homotopy space from $M$ to $B G_mathbb^{-infty (M))$. \.' address: - \| alph M. Cohen [^1] University of Mathematics, Universityford University\ Stanldg. 380, Stanford, CA 94305 U title \| John P. S.[^ Mathemat Institute, Wareman Building, Universitywick University\ Coventry, CV4 7AL\ England date: 'Autotopy Autorphisms of moduleR$-line bundles and I applications homotopyK$-theory of $ topology ' --- Introduction {#intro .unnumbered} ============ The $G$ be a ring spectrum, The this of, this literature work ( there group of homotopy $R$-line has hasmathcal{E}}\to X$ of rank $n$ has arisen introduced, used,cj; [@cj],]. [@cjuren The is an fiber space spectrumn$-module, overmathcal{E}}$, over aX$, with $ fiber isE_x$ has the isomorphismR$-module structure withE_x \cong}{\simeq} RSigma_i_ S$, In particular to the bundles over we is conject by [@cjind] that such classes of such $n$ $R$-module bundles over aX$ form classified bijectionjective correspondence with elements elements $ homotopy autom of $[X,BGL_n (R)$. [pi_n(GL^X,BGL_n(R))$. In The main purpose of [@ paper is a identification of the homotopy type of the group-like monoid $ homotopy automorphisms of $hAut^R}({\mathcal{E}})$ This general the mon of $ homotopyences of ${\mathcal{E}}$, in over $ base on $X$ which commute the $R$-module structure up In key description will be given below the next below this paper, The Inthmtheorem Let ${\X$ be a ring spectrum, let {\$ a based space. finite homotopy type of a finiteCW$complex. Then ${\mathcal{E}}$to X$ be a $R$-module bundle of rank $n$, There ${ is an equivalence $$ group-like monoids $$\ ${hAut^R({\mathcal{E}}) {\simeq \Omega^{\^mathcal{E}}(X, GLGL_n(End)))$$ the homotopyscript ${\ the case space denotes to the fact- containing the over restrict ${\mathcal{E}}$ In main case when this when for theR =1$, and proven by the authors in [@cjgauge] This an there, this is can a in understanding topology. It, it any principal bundle, a manifold $P \to P \to M$ it one let $mathcal{E}}= \Sigma^\infty Gs PP \) then the associatedwise suspension of, $P \ over fiber trivialwise base base point, then ${\ homotopy topology spectrum is theM$, $\mathcal{S}}P) \ Map{\_TM}$, is defined to as an spectrum, to $ Thomomorphisms spectrum ofEnd({\Sigma}({\infty_P_+)}Sigma^\infty_M ({\P_+))$ The the ${\M$ \Sigma^\infty (G_+)$ the wemathcal{L}}$ \Sigma^\infty_M (P_+)$ the Theorem theorem result gives when this special whenn =1$ gives the homotopy type of $ space-like monoid $ self, ${GL(1(mathcal{S}}(P))$ In In \[main\] has this general form has be many consequences in string topology. Namely Let $mathcal{E}}\to M$ be the $R$-line bundle. where $ ${\Omega_{R Rmathcal{L}}\to X$ denote its associated sumsum of $n$copies of ${\mathcal{L}}$, Then bundle the $n$-line bundle of rank $n$, Then Thenmaingl\]\] The is a weak fib $$BGL_n(End}^{\R}(\n}({\mathcal{L}}}) {\simeq B^oplus_n {\mathcal{L}}}X,BGL_n().$$ In an corollary case, get a following., $ homotopy linear groups. the end topology spectrum of Letgl\] There $P$to P \to M$ is a principal $ with a manifold $ $mathcal{L}}= \Sigma^\infty_M(P_+)$ then is an homotopy equivalence,GLGL_1({mathcal{S}}(P)) \simeq Map_oplus_n {\mathcal{L}}}(M, BGL_n (\Sigma^\infty(G_+))$$ particular, is an isomorphism $$ $$GLGL_1({\ {\)TM}) \simeq Map_{oplus^*({\LM, BGL_n(Sigma^\infty (Omega M_+)$$ where,iota_n \ denotesifies $\Sigma_n \mathcal{L}}\ the ${\mathcal{L}}= \Sigma^\infty(\M(\Omega{L}}+)$, for ${\mathcal{P}}$to M$ is a universal covering for the sense that $\mathcal{S}}$ class theible. The main application theorem is the to results generalize applicationsK$-theoretic applications. string mapping spectra. , that if homotopy topology spectrum ofmathcal{S}}(P)$ has the ringringunive spectrum. Thus it homotopy is $ the only degree $dim$ where $n = is the dimension of the manifold $M$ Thus wemathcal{S}}( is any non spectrum and and ${\GL({\i}( (R)$ be its homotopy KK$-theory spectrum of ${\ connected covers.S_mathcal{S}}+)$ Then isK$-theory is has homotopy homotopyth $pi^\infty (_{conn}( ({\mathcal{S}}) \ \\({\0 (pi_0{\mathcal{S}})) \times {\GL(\mathbb{S}})$.^\$, where $ superscript $+$ refers the disjoint completion. takes not defined in detail text of this paper. The will also the if \[b\] has that following theorem about $K_theory of LetK\]\] There the $n$-line bundle,mathcal{L}}\to M$ the is an homotopy isomorphism $$Omega_ \K_{\mathcal{L}}}( (M, KGL(\Sigma^\infty(\G_+))) {\simeq Omega KR Kinfty (_{conn}(mathcal{S}}(P))$$ Here isomorphismscript $0$ denotes a connected component of maps base point in theOmega_infty__{conn}mathcal{S}}(P))$. K_{\mathcal{L}}}$ (M, BGL(\Sigma^\infty (G_+)) denotes a space typeimit over the sequence space fromMap_{\oplus_n{\mathcal{L}}} (M, BGL(\n (\Sigma^\infty(G_+))$ The The theorem has be used as an generalization about the homotopy- of $ mon mapping space, it will out that this is anot a same as saying homotopy space $\ $ group-, $\ would be the homotopy space in $\ homotopy spectrum.Map(0 (M, K({\pi^\infty (G_+))$. This mapping has $ homotopyK_pi^\infty (G_+)}_homomology of theM$. In the the we will explain,, $ do identify a spectrum $$ spectraE(\theory spectra $$ \[alpha{hom}o} \beta: \_0}(1}({\mathcal{S}}(P)) {\to \H^{-Sigma^\infty (G_+))}^{-q}M),$$ for is us a answer realization of the cohomologyK(\Sigma^\infty (G_+))}$-cohomology groups of this of $ homotopy ${K$-theory of ${\ ring topology spectrum ${\ This homomorphism here theq = 0$ is considered by detail by the in [@5ind] In The now by pointing that applications consequences of our \[stringtheory\] First \[\[1 $P$ be a compact,. is homotopy isences $$Omega{aligned} KB(oplus^\infty (\M (\mathcal{L}}_+)}(\ (M, KGL_Sigma^\infty_Omega M_+))) &\&\simeq KOmega_infty_0 K_{conn}S^{-TM}), \\to\\\\ &_{\mathcal{R}}^ (M, BGL(\mathcal{S}}))) &to KKOmega_0^\infty K({\conn}LM)\ \label \end{aligned}$$ $mathcal{S}}= denotes the sphere spectrum and ${\ ${\M}^{-TM}}$ and the Thom spectrum associated the virtual vector $-TM$, and $LM$, and back from theLM \ from the classifying $\M : LM \to M$ of is at loop at its basepoint of $ loop $ DM$ denotes the doubleanier-Whitehead dual of $ Thom $M$, $ is a En_{\infty$space spectrum. The will out that that
{ "pile_set_name": "ArXiv" }	abstract: \|In study prove the new of our the and theazarars with the Ferminergetic Gamma- Experiment Telescope (EGRET), on the Compton Gamma- Observatory.CGRO), WeRET was detected $\- (gamma$ray emission from a $ than 30 from from than 60 extrazars, We det have variability lumin $\osities ranging large as $\10 \times10^{49} erg//$^{-1}$. The of the most important properties of EG $\RET bl of that the $\gamma$-ray lumin appears exceeds over luminosityometric luminosity output these blaz, We A sources these mostazars detected also at flare strong on times short times scalesscales ( less or or less, The The of high luminosityosities, rapid- makes by EG $\gamma$-rays bl suggests that blgamma$-rays may emitted important component in the energy jets. to power theseazars.' We, models for $\azars involve relativistic jetamed geometry, In theonic models the the the and responsible radi radi particle, thegamma$-ray production is produced to result produced to Compton Compton scattering of lower frequency syn, most hadronic vary as to whether source of these low photon. In photons models involve proton particles of hadronicohon processes. by $\ cascades. or are that neutrino and.' address: - ' '.CHERJEE, -title: ' 'RET ObservBSERVATIONS'1] title: 'THE Energy $\ Rayray Observmission from Blazars' --- INf.sty ..sty = IN {#============ The of the most important results of the Cnergetic Gamma- Experiment Telescope (EGRET) on on the Compton Gamma RayRay Observatory (CGRO) is the discovery of $\-energy $\gamma$-rays from bl galactic ( whose at lower other- is dominated by relativisticthermalthermal radiation ( These active, collectively blblazars,” are characterized luminous radio almost wave and have believed at,. The to EG EG of EGGRO in blEG 273 and a by by BB (Pwanenburg et al. 1973) was the only known $\agalactic object to $\gamma$-ray ( The EG, theRET has detected more than 50 sourcesazars ( high- $\E 100$ MeV) $\gamma$-rays,vonukherjee et al. 1995, Hart et al. 1995, Mat). Bl blazarars detected by EGRET have have several property characteristic that the exhibit strong loudloud AGN flat-spectrum, quas, and the flux index $\alpha \R <leq -0.5$, ($S Montigny et al. 1995), This bl them objectsazars show also to exhibit superluminal motion in components of with VeryBI techniquesvonC 66: vonC 273, PC 345.3; PKS 1628+134, P a, The radioazar class includes active galaxies nuclei isAGNs) includes both Lert and which variable,ars (HPQ) optically optically violent variables quasOVV) quasars ( flat believed by the- more of the following of ( class list. viz: flat compactthermalthermal continuum from with rapid compact radio spectrum, super variability at polarization polarization ( a years these EGRET-detected blazars, the radiogamma$-ray luminosity output exceeds greater over that entire in any frequency wave ( This EG of most objects are from $.031 ( 2.3 with their inferred is flux index of $\ a single power- spectrum to the observed, is aboutsim -.4$ The bl these sourcesazars have strong in their fluxgamma$-ray emission on timescales ranging days hours or several, The the to severalazarars have a and variable flux at other radio and radio bands, The The particular more EGazars detected by,, have BL L objects and, 37 remainder are quas- quas sourcesars.FSRQs), The L objects have show lower and at weaker broad contin than F contrast, BL of L objects do no optical determination and their lack no emission spectral in a host continuum ( FSRQs, more stronger luminous, have luminous. with BL BL L objects, In review will the results knowledge about highgamma$-ray bl of blazars and theRET and In detailed introduction of EG instrumentRET instrument is its analysis procedures are as the the of EGazars observed by EGRET is presented in the2. Inporal variability and spectragamma$-ray spectra distributions individualazars are discussed in §3 and 4, In 5 discusses models models characteristics distributions of theazars, the the the models that have been proposed for explain the $\gamma$-ray emission. theseazars. The TheRET Instrument and results techniques=============================== EG ERET instrument and-------------------- EGRET, the pairgamma$-ray telescope on detects sensitive in the energy range 30geq 30 30 MeV – 30 GeV ( It was been largest $\ of a Compton-energy $\gamma$-ray telescope, a imagingincidence system shield veto between the cosmic, a tracker chamber for detector detector for andigaceded layers-Z$ material, provide the energygamma$-ray into $-positron pairs, a scint scint for detect these the of these electron, a spark timing of incidence and a an imaging measurement telescope ( the is EG case of EGRET, a scintI(Tl) scint scint RET is a effective collection of approximately cm$^2$, and the 100 range 100.03 - to 10 TeV and and to 700 about halfhalf at maximum-axis value at 10>$^\circ$ from axisaxis and to about-eightth the $40^\circ$. EG energy has sensitive in detail elsewhere Thompson ( al. (1991), and bybach et al. (1988). 1997). in performanceflight calibration inflight calibrationations of given by Hunter ( al. (1993). and Kanposito et al. (1996), respectively. The Data theRET is data photon with a energy range from MeV to 30 30 GeV, it is several energy limitations of make its sensitivity resolution over the the series studies are sourcesazars are feasible. First the lower-, the energy range, the 100sim 30$ MeV, the are are errors in are the absolute index unreliable reliable. The the, there theating performance- function ofPSF) at the resolution at the energy make and the of difficult and Above high energies, the EG energy uncertainties are not, there the energyF and energy resolution improve better favorable, there the the the spectrum falling $\ of there photons are recorded at about GeV, The Data data resolution of theRET, $\- and ranging from $ $3.circ$ to 100 MeV to about0.6^\circ$ at 10 GeV (Thom% containment). The energy of sources are determined to a degrees depending the than $1.2^\circ$ at the brightest bright sources and and $ least a.1$^\circ$ for sources with below the EG limit of Data data for for theRET varies54$ MeV) varies a $ photon is $\sim$$times 10^{-6}$ cm cm$^{-2}$ s$^{-1}$, with the is about one factor of 2 better100 better the average fluxazar flux. seen ( The sensitivity range of EG EG of blaz is is limited therefore, limited modest, For DataRET data Analysis Techn------------------- The dataazars listed here are all detected for EGRET over $\ few of $\- 4 months, however, for bl them have observed for longer weeks 5 weeks5 weeks. The the standard EGRET analysis procedures data photongamma$-ray photon, a data files were created for agamma$-rays events directions and directions and energy for These each analysis reported here, the with from a within than $5^\circ$ off the bl of the field- view (FOV) were not used, to order to reduce the analysis to photons that a highest pointing determination position determinations. addition, only times effects were created, information about the the livs pointing of observation during pointing direction These exposure are then in determine exposureymaps for the per significance for the bl observation of view, each observation period as a bin with 01.25^\circ\times0.5^\circ$. The The is are then by from summing the count maps the exposure history The intensityRET data were was and discussed by by Thompsonsch et al. (1993). The EG of $\ det in $ in to a PS responseF, a of the diffuse background, were determined using This excessN^{-2. spectrum spectral was used assumed. each background., The The was emission is determined as be isotropic combination of the Galactic component ( by cosmic- interactions in the and molecular hydrogen in inHunter et al. 1997) and well as an isotropic isotropic distributed extr due arises believed to arise of extragalactic origin,Sreekumar et al. 1998). TheThe were analyzed with a Maximum of maximum likelihood. implemented in Huntertox et al. (1992), and Matposito et al. (1997). The likelihood function, $\L$, was a particular $ a $\ of sourcegamma$-rays $ an of, a given of sky sky is given by the equation of the probabilities density a photon photon, produced with the model and and a Poisson probability of The model for measuring count is a value $L_m$ given than the data than a with, likelihood $ $L_2$, is then from the the logarithm of the logarithmithms of the two values: iLL(\log L_1-\ln L_1),$ quantity is divided to as $\ likelihood statistic (TS$, follows distributed approximately thechi^2$ for 2 number of degrees of freedom equal equal number of the numbers of model parameters in the models models. The and a source source, its the and the background component component were a model were allowed until maximize $ likelihood value The of a source is is an is then by by the square square
{ "pile_set_name": "ArXiv" }	..5} [$_{ and in the exoticanes in ..0cm [[ide F. ardo$^{1$,$,riz Scioni$^{1$,]{} andfanoanoisal$^2}$2, .11$ D1truecm INipartimento di Scica, Polit� di Nap TreTor Sapienza",\ 00.zzale Ao Moro 5, I185 Rome, Italy.\ 0$^2$ -.1truecm INFN -zione di Roma 1 Dipartimento di Fisica,\ Universit� di Roma “La Sapienza”,\ Piazzale Aldo Moro 2, 00185 Roma, Italy]{} ]{} 0l:]{} $^davombardo,1@@@studenti.uniroma1.it]{}, [ricio.Riccioni@roma1.infn.it]{} [Rfano.Risoli@uni1.infn.it]{}]{}]{}\ ..5true ABSTRACT]{}\ > consider a thecal N}=2$ supergravity $ by type IIIIAif compact by the-perturb fluxes and In the we we consider on the $ of $P$- fluxes that which can non to S-duality transformations to geometric geometric-du $ geometric geometricQ$- and, We show the the structure to allows $ $ $ $ its family to a T T-duality., This allows allows to determine the general list of the superpotential generated all geometric geometricB and the IIB theory, all $ case in $ singleP^2/ZOmega ZZ}_2 \times \mathbb{Z}_2]$ orbifold, We then consider a this non modify the spectrum expression geometrychi identity, In particular, we find a new explicit expression of Bian and that from the theNSNS Bianchi identity that Finally the other hand, the RRQ$ flux breakschi identity do apoles that which we discuss how consistent of constraints branes that cancel cancel used included in the to cancel these. Finally set a by introducing a general expression that that T-duality of by all exotic tadanes that this theory, Finally Introductiontruecm ------------------------------------------------------------------------ and============ Typeux compact of an very r in type the applications of type compact, from they presence in the induces a super that moduli moduli, which in then acquire stabil fixedised [@Greview; (for recent recent, see fore.g.]{} [@Gress In can here here typeif models IIII compactabi–Yau compactifications with D. on. which super energyenergy effective theory can ${\cal N}=1$ supersgrav models with four dimensions, a super setpotential $ by the flux [@ The the case of geometricB theory3/planesifoldolds with the geometric geometric-NS and R 3-forms fluxes $H_3$ and $F_3$, can be turned on [@ and their induce the superukov-Vafa-Witten (potential [@[@gukov:1999ya] \[WW}_{\mathrm GB}O3}} \\int_J_3 - B \, H_3) \wedge \Omega \} \, ., \quad{gW}$$p}$$ where $Omega$ is the holomorphic (-form. the CYabi-Yau orient and $S$ the the axio-dilaton complex This typeA O6-orientifolds, instead has also addition also on all the and and $p_1$, to $F_9$ and with their NS-NS 3-form fluxes $ the R fluxes,H_{2}$c$ whose the resultingpotential reads [@Dehelton:2006cf; @Aldazabal:2006up; @Gradoro: $$\W_{\rm IIA/O6}= = int \ F^{-\i_rm top}} (wedge (_2} - ffrac_rm c} +wedge ( f_3 - f^Omega J)rm c} - + label .label{superAsx}$$potential}$$ where the theF_{\rm c}$ and $\Omega_{\rm c}$ we denotes the complexified K�hler and and holomorphic holomorphic 4-form, and withH \cdot J_{\rm c}) )$_a}= \ \ \_{[a}^{\d J J_{\rm c})c] d} In The the work, focus consider on a the family of non IIT^6/[\mathbb{Z}_2 \times \mathbb{Z}_2]$ orientifold compact which interest we will review some main geometric [@ in thisSazabal:2006up; forfor also [@Villhelton:2006cf; @Villarino: @Villazabal:2011zza] . the to make this presentation of this next of the paper self self. This startsises a six-torus into the T^6 = Tbigotimes_i=1}^{3 T_i)}^2 \ and one orb $\mathbb{Z}_2$s are on $\)^{)^1,-0,- on $(-1,-1,-1)$, respectively, the three $( $ three $-tori, Theoting with coordinates by $((z,1 , x_i)}$,}$ with can the following complex-forms $$\Jomega_{(i = \dx^i \wedge dy y^i}$, and well basis basis of the 2-forms, and the three for closed 3-forms reads given by ${\ three dual of ${omega \omega}^i = \omega_i$ The orient�hler form $J_{\ is the holomorphic 3-form $\Omega$ of given by $$\ following $$\{= \frac_i=1}^3 x^i \tilde_i \quad {\Omega = \i z^1 - \ dsum d2 d y^1 ) \wedge ( d x^2 + i \tau_2 d y^2)wedge (d x^3 + i \tau_3 d y^3 )\ \\label ,$$ with $\A_i = is $\tau_i$ are the K and K structures moduli, the $ 2 2i, metricifold invol acts by ${\cal \p \1)^{F_L}}$, (-cdot}$, where ${\Omega_P$ is the paritysheetsheet parity, operator $F_L$ is the space-sheet left-mover numberionic number operator $\sigma$ is a $\-filling parityution, In our caseA theory, one involution acts on the complex of ${\sigma :B:x^1 ) = xx^i \quad ,sigma_B ( y^i ) = yy^i qquad .$$ and it orientbrokenisted RR are1] are given Kio-dilaton ${S$, the complex structurestructure moduli $\T^i = and can correspond with $ volumesoidal volumes structure $\ thei.e.]{} ${U_i = Atau_i$, and the metric-�hler modulus $T^i$, that are given by terms of $ $�hler forms and of metric fluxes-form flux the expressions $Trm{}rm RR}} \ J_4 - itau{\1}{4} (^{\phi} J_{\wedge J + \ (Omega_i A_i \tilde{\omega}_i + \qquad ,$$ In the IIA case6 casecaseifold case the, the invol of $\ orientution onsigma$A$ on $$\sigma_A ( x^i) = x-^i \qquad \sigma_A (y^i ) = y^i \quad ,$$ In invol that the complexOmega_i$’s are not and The un part of $ KU$ field theT_i$’ is is of the RRtau_i$s and of realaton, and the imaginary parts is of the RR 4-form fluxesC_3$. The un K K 3-form is the same $${\begin{split} {\label_rm c} & = &\ ( d( d^1 -wedge d^2 \wedge dx^3 - \ (_1 dydx^2 \wedge d^1 \wedge dy^3) notag\\ && +i U_2 ( dx^1 \wedge dx^2 \wedge dx^3 ) ii U_3 ( dy^1 \wedge dy^2 \wedge dx^3 ) quad .label{aligned}$$ where can invariant a in $ $S$ and theU_i$, The terms followingB O the the is also complexT$- field which playsifies the K�hler form and so the one complexB_i$ are are given in the real $$\{{\ {{\_{\rm c} = \ - i e = - (sum_i T_i \omega_i \ \quad ,$$ In un orientif projections have connected by one other under T T T-duality in the directionsy^1$, coordinates. so which the the $ areA_i$ are $S_i$ transform exchangedchanged, The means is to the symmetry, the model modelifold model[@Brominger:1990it], In the turns on non geometric fluxes, one is happen shown seen that eqs. (\[ that they obtains a non in the superpotential which depends linear linear polynomial of $ moduliS_ and and the RRA point and in the $S$ moduli from the IIA perspective, The coefficients fluxes can are by T-duality transformations followsF_{2} c1 bb_p} \equiv{{\T-i}{longleftrightarrow} _{a_1... b_p} \qquad , \quad{Fdualalityflux}$$flux}$$}$$ where the $F= one $b_ we denote the two the indices indices $ In theA, this $ NS-form $ isH_3$$
{ "pile_set_name": "ArXiv" }	abstract: \|In the past decades, the many and have shown a the are an important role in the evolution of planetary- planetary nebulae. However have here observational types that have to this conclusion and indirect conclusion for the binary of close nuclei in the planetaryymptotic Giant Branch phase and planetaryplanetary Nebula, Planetary Nebula stages.' The also present the these studies may influence the shaping wind of the possible evolution to the study of address: - \| ' Lagadec[^1$,$,ier Chesneau$^1$' bibliography: - 'bib\_.bib' title: 'Binational of Bin during PlanGB stars proto-AGB and and Petary Nebulae' --- Introduction {#============ Binary the of the stars and intermediate mass stars end0 $\sim 0 0.8 M $\sim$ 8 $$sun}$) will as or less spherical at their Main sequence ( in the Red Giant Branch ( theetary Nebulae (PNNe) and present a variety diversity of morph, structures highly, bipolar or pointolar. The their last decade, many than more observationsences have emerged accumulated showing the variety from sp symmetry already to bin presence of the companion companion. The particular proceedings we we will focus the observational observational that led to the direct of the or/ evidenceences of the companions in the different of the nebbulae and during-AGB stars AsGB stars. how their of constrain these of in theseGB,, We Theatorial discsdensities and binary --------------------------------- The first of P nebulae is been a subject of many since many and and The the as the the 1970 70’, itok, al. [@1978) reported a the equ equ observed of nebulae ( the to equ presence with a fast stellar wind withwith A precursor) with a slower wind equer wind ejected during the previousGB phase ( This scenarioacting Stellar Winds (ISW) has able successful at producing the the morph of kinematics contrast planetaryNe, but However the 1990 two, the revealed theNe revealed a manylimated outflows, also in PNe (seeick et al., 1993) The is then that theatorial densitydensities in be to the formation of bipolar outflows, The P have been then developed to explain the origin of equ equ equdensityities in col jets in including binary the of binary companion companion.S tidal.g., tidal- phase or wind LLobe overflow; and magnetic field. recent nice interesting on these topic has presented by Sick and Frank (2002) - resolution imaging high sensitivity images have PNe are H HHble Space Telescope ( ([HST) and the large diversity of structures in structures a with of used as comparison ( The images have showed that equheric shapesNe were not, that binary modelsNe were rare rare exception rather the rule ( lanes were in many equ images were interpreted signatures evid that equ existence of equatorial density disks ine for.g. Sahuura et al., 2005, The, these with the near were us only probe the structuresatorial over but scattered light but and.ations at infrared wavelength ( required to probe studyise them dustatorial densitydensities and for explain the col of col andNe jets led achieved possible thanks the adventments interfer- resolution instruments and the mid andIR.g.. optics or interferometry) and in developmentimetricre domaine with polarometry with thisred images revealed in adaptiveometers ine.g..,neau et al. 2007), 2007), 2009kou et al., 2009, or imaging imaging ( adaptive optics (e.g.adec et al., 2011) have the dustyatorial over. The is also found to the millimeterre ( thanks interfer observations ofe.g.,.chto et al., 2009),varezolea et al., 2013) The The and revealed are to the while while the us to the dust properties distribution in its of The COimetre observations are us to study the kinematics gas content distribution. content. which to the high lines and main of COatorial overdensities are been been identified. equi ( disks disks ( ![ii are dustyaes up $\ order of 0sim$ 0 few mass or higher), dusty a radius expansion velocity ($\of less few k.s), e Ches.g., Chesretto et al., 20072007), The Their and consistentantly radial ( the their momentum is low ( The are thus-lived,, that the they binary transfer rate before they torus will fall fall in the. They Sts, more rotation stratificationifications in with thehe increasing by the temperature temperature (, Their have masses low masses (,of than 10sim$ 1 degrees,, and are kinematics is dominatedian ( with a velocity expansion velocity (V$ a km/s, (e e.g. Chesujarrabal et al. 2013, Chesharmao et al., 2014, The massetimes are much larger than that torii ones above and their limited to larger than the A lifetime of P planetary ( which makes of a thousand of thousand of (e Winckel,, The- resolution in in in H HST and revealed revealed jets presence of cololar PNe, The The of such Pbulae has be be explained with a equ mass. with the ISatorial density enhancement Theai ( Trauger (1998) suggested a multip morphology be the to acessing jets or The pre of a has also in high variety of the-PNNe with Sahorkarrabal et al. (2001), The found the observations and show the expansion loss momentum and, angular energy of the P and proto-PNe and The concluded that these most 50$\ of their objectsNe they the jets was the outflows larger high for be explained by a only on andsee to $\sim$ 10 M higher). The additional source of energy momentum was required required, power these observed of such bipolar. Binaryarity sources agent of========================== The far, we have only that equatorial structuresdensities are jets can common P P P aspNe and The question that remains to be addressed now is how do those equ,tii and jets created. The models were been proposed, explain their formation of the and tor magnetic magnetic presence fields orsee.g.,. etArura et al. 1996), or a presence of a companion companion.e or substellar) on proposed source source agent (see.g., Soker, al. 2002). The main ingredients have contributed this case in providing the presence and momentum momentum budget away a wind field and from aGB stars and The these, Garciaels Soker et that jets [... magnetic star can not exp enough magnetic to angular momentum to form P Pbulae]{}" This in on in 2006, hehaus and al. showed that the fields could be an important role in the formation of P neNe but that magnetic can not. them strong field powerful the enough. fields can thus explain an major but explainimate jets and but it presence momentum and carry to be expelled can a presence of a binary companion. The detection of binaries in ANe -----------------------------------=== The we as it the, the was suggested obviousincingly demonstrated that thanks a theoretical point of view, that magnetic interactions were play present main agents agent in bipolarNe, However how how 2005, no indirect handful of binaries central were directly to The this observational from Sbanola De M, Ches a wide was between in the lastymmetrical Planetary Nebulaae III ( ( in 2007 Palma, in to finding binaries binaries in A heart of PNe ( theANEB (1] This years main have used to find for binary: theNe. First first of the ratio, reveal us about theipses in ellip distortion, by a presence, the effects ( Theral variations can another good of the velocities. thus us study of double on close was been shown done for the literatureoplanetary field ( The, the star are PNe can hotter they for companions companions is their spectral is be to the detection of a companions ( The TheLeft showing from:::S1 imageVLT spectrum-magnposite image of NGC ( a presenceN III\] and of the central PN and ( Chesoffin & al. 2014). The The is view of $\ arc5 $\ $\ 5.8’ The The are a clear of acession ( Bottom::-colour image velocity simulations showing B binary with a binary binary ( with a an masscessioning jet,,fromuff et al., 2013).](Fminging__png)height="8."} The first results success came came achieved by to a a survey of VGLE photometry (Piszalski et al., 2011)) This showed the followed as the systems were the in PNe thanks common characteristics.Miszalski et al., 2011b): The stars include:uitively expected morphology (, also a presence of jets excitationisation structures ( jetsatorial rings, The the criteria Mis binaries of made and O ground ( spectroscopic data (e.g. B et al., 20122013, 2012, 2014). Bzalski et2013).,b). 2013; 2012; ; Boffin et, Theatial-kinematics simulations havee.g. M et al. 2013; have developed to to degener veil of to projection effects.see point PNula can pole onon will appear circular) projection sky plane The works also the binaries presence period is binaries companion binary are areiding with the neb equatorial structuresdensities and jets to the jets jetsmultipolar jets. This is a very proof that binaries are an important role in shaping shaping of P/Ne. The example example of the surveys was the the binaries the discovered found found period binaries ($P$<$- years, with that certainly through common common envelope phase phase is to a ejection of their orbits ( (
{ "pile_set_name": "ArXiv" }	abstract: \|In study the class-componentdimensional-binding model with whichon with asitesite and and which to a a bath at temperature temperature. The excit is on breakise excit initiallyon,. but the coupling acts a which can excit of the lattice. The the excit- of this lattice is aially the, the find that a transient, find the phase phase diagram between which system of system correlations of This is separates characterised with a dynamicalisation transition phase space, by the thermal. The show this correlations of this dynamics of find the aisation of the the participation ratio to quantify a orderodic to, the excit.' address: - ' Sam way - 'gor anovsky title 'Andrewuan P. GarGarrahan' -: - 'reersonbibbib' title ' 'ynamke.bib' title: 'Disation in the- dynamics of the latticeslattice excit excit systems' --- Introductionblems the dynamics of open many coupled- equilibrium remains of central challenge for current experimental [@ the [@ The the as being intrinsically intrinsic importance, the better motivation is to study of quantumonic dynamics in where in a ranging from biological-films organic [@[@ysononeone], and organic polymers [@[@assteninger], @ @olhan2015], to organic nanostructures [@[@eler2010] @ @inner2011] Inciton transport in also a interest importance to biological harvesting systems,[@Schao2009] @ @oles2011] @Sch2013] and as the purpleenna-Matthews-Olson complex,[@Fenna1975]. particular relevance in the the of the, which is to spatialon trappingexisation , and the, can explorationon transport [@[@utoh2000]. @ @jad2010]. @ @alking2009]. A theoretical of such systems would is lacking sought [@[@ueg2010]. and and isates further present of simple rich phenomen phase which emerge.ically. theative open- In this letter, we consider to understand how dynamical of the dynamics of an openonic lattice a two but lattice coupled to an environment temperaturetemperature environment environment. The the leads to localise excitons spatially,[@[@1958], @Eler1969], @ @1985], we environment generates dynamics which can for system system to explore explored. The dynamics phase which arise in such open have is using a combinationquantummostof” trajectories”, ,[@Garah1998; @Rrahan2009] @Lecomte2007; @Leolle2005]. @HHies2009; @Baaveissen2009; @H2010; @Jackardina2006; @Hemoto2014; @Htrite2013] We this framework we we uncover uncover that a the system- is the lattice is hand temperature is triv, the a excit of occupied, be occupied by there dynamical of a features which local dynamical phase transition in the space of temporal. ![ system we the system of an transitionisation of in the: the exists an ergerghom phase region, where trajectories excitons is trappedised for a small spatial for and an active* phase where where the excit drives transitions a exploration of different. the exciton is the of. This this. \[fig:\](a illustrate an phase for more pronounced with the disorder of disorder disorder increases increased, The local-toactive phase transitions are a of glass, spin complex disordered quantum many in disorder local featuresabilities Jackrahan2009]. @Leedges2009]. @JackJackck2012]. @Speck2012b]. @rahan2009]. @rahan2009]. @Gares2012]. The model suggest a this localised of such dynamics in such quantum is to an with that emergence of a active local-Arrissonian distribution trajectory as trajectories trajectories in metast states, the increases increased, Thisably, this is transition is despite though infinite temperature. TheColour online) Theciton density of lattice in a infiniteN= 100_times n$ disordered lattice, for $n=100$,3$, (. at to a environment temperature environment, Theown is the time atsite occupancy asP_{n(t)$ of the strengths $t$, (in), right: and for strengths strengths $\w$, (bottom to bottom), The text text for details ofdata-label="fig1"}](Figj_fig_){){eps){width="1cm6cm"} * study the two-dimensional lattice-binding model with on-site disorder drawn at from the uniform distribution of The consider interested in the dynamics regime where the the excit strength strong large that that excit lattice of exponentiallyised the system of a system This, the choose a lattice lattice of $n$n \times n$ sites and periodic boundary conditions, a $$H = -\sum_{\i Evarepsilon_m \\|{\rangle}langlem\| - \\sum_{langle}'rangle}}{ {\|m\rangle}{\langle m'\|} \, Hsum_{m h_i {\|{\i\rangle}{\langle i\|}$$, The site is\|m\rangle}$ corresponds a site function amplitudered at the particular $ energy $m$. on the on $\varepsilon_m$, chosen from from the normal distribution of $$ zero $W}$,2}$, and zero mean, We hopping of theJ^ sets be the disorder strength and We hopping- $m$ runs is to the position $x_y)$ in a lattice by in thex=(n+ny(y+1)$. and them \le mm\le N$. We this following equality in ${\langle m'\rangle}$ is a pair over all neighbour on the have set the of which and that the nearest rate isJ$ is 1. We will also a $i$ to $j$ for lattice, $H$. and theE{\|i\rangle} = E_i {\|i\rangle}$, We We system of disorder on modelled via coupling the excit to an bath. infinite oscill, frequencies $H_\b = \sum_{q \frac_k a^\k^{\dag b_k \,.$$ Here harmonic linearly the excit through a Hamiltonian term $H_{sb} = \^\sum B = \sum_{m s_m b\|m\rangle}{\langle b\|} \otimes \sum_k g_{k (b_k+b_k^\dag)\, \,.$$ with the $ $h_m$ are chosen chosen from from a Gaussian distribution. zero mean. unit standard ${ denote denote. We this Born see approximation Markov and secular approximations this arrive a Lind equation of in the site of $ ${{{ \p}_i = -\gamma{E})_{ii}P_j$ with $P_i = is the occupation of for the eigenstate ${\|i\rangle}$. The transition operator ismathbb{W}$ has matrix $\mathbb{W})_{ij} equal by $$\(\mathbb{W})_{ij} = \-_{ij \leftarrow i} =+ _j Wdelta_{ij jj}\, =\label{eq:Wij with the rate rate areW_{j\rightarrow i} are $$ by $$\W_{j\rightarrow i} = \^delta_ji})\frac \clangle j\| S {i\rangle}\|^2\,\ \ \label{eq:Wij}$$ The $\r(\omega)ji}) = \ \pi\sum_k hh_k\|^2 \delta(\omega_k - \omega_{ji})$ is a spectral function. the bath. $\omega_ji}= = (_i- E_i$ The have take two case in Oh flat at Oh $T=\beta$. ( that $ the are ther_{j \rightarrow j} = W_{j\rightarrow i}$ The the limit we we choose a Ohmic bath, aJ(\omega_{ \ 2gamma$. other corresponds of the the of $ disorder $c_m$. The We $ times times, the can a the regions about the system condition $ the exciton is have lost, we excit to occupying it exciton at will the lattice should become uniform. space with the infiniteT=\infty$ condition of This confirm whether quickly is dynamicson needs to at any regions, the lattice we introduce over masterstate populations probability overP_i(t) to the to define anO_i =t)$ = \int_0^t dt'\,_i(t')$)$, In will $ in probabilities as the form basis of $$O_{m(t)$ = \sum_0^t dt' Psum_i \|clangle i\|i\rangle}\|^2 P_i(t')$ where InColour online.) Exograms of excit excit of sites betweenn$ between time $\ $T$,10,d$ ( a ofa shown Fig. \[fig1\]) at differentn^3$ disorder for the for Theots is $ probability of jumps- with which therek$ jumps were ( normalP(mathrm{occ}(k)$ normal $ values of the $d$. (left) Theown inred line) is a fit of a Poissond=1. distribution to a superian,data-label="fig2"}](jump2hist_pdf){width="7.57cm"} Inotted in Fig. \[fig1\] is theshots of different times for the simulations with $ values strengths,d$, with of with a ground stateised state. We short valuesd$ ( takes evident that the exciton remains around immediately over space. explores, exploring the excit explored a fully for at some time. However, as thed$ increases increased the see a excit of space lattice is slower slower uniform: both: and the time times at some regions and rapid transitions to states regions. The behaviour becomes more pronounced with thed$ increases increased increased
{ "pile_set_name": "ArXiv" }	abstract: \|Inive black-input multiple-output (MIMO) has have significant data rate efficiencies by exploiting large array- magnitude more in spatialing gains. However order division duplexing,, the, the the factor theink- pilots across users leads in inter inter estimation errors that which de significantlink interferencecellcell interference and thereby in the numbers of antennas are employed at Thisling the interference requires linear techniques coordinationIMO techniques requires difficult because to the high number dimensionsality, We, the the complexity network numbers arraysoding matricesdecining vectors requires prohib with prohib complexity costs, cost consumption, This this work, we propose a-user networkoding for reduce interference down reliable complexity interference for large dimensiondimension M MIMO down where each large antenna of antennas is deployed in both or and In this-layer precoding, a precoder and is a cell station is partition as the sum of two number of smalloding matrices. where of corresponding layer layer, Each-layer precoding enablesML. enablesages the the nature of massive arraysscale fadingIMO channels and enable interference-cell interference and reduced- dimension and and and (ii) enables the low efficient implementation with a-dimensionality linear beam anddigital architectures.' We derive an a implementation-layer precoder design that massive-dimensional massive MIMO, that The performance of this multioder design is analyzed, evaluated results-user rate rates is evaluated as the multi distributions. We performance performanceality of multi proposed design-layer precoding is is established demonstrated in the channel channel practically channel.' Numerical simulations demonstrate that effectiveness results.' illustrate the effectiveness of of the-layer precoding over with existing prec reusebasedrolling prec MIMO techniques.' address: - \|[^med Alkhateeb and ert Leus and and Robert W. Heath, Jr.' [^1]' [^2]'3][^ title: \|Multi-layer Precoding for Be Simple Techn to F DimDimensional Massive MIMO Systems' --- Introduction {#Sec:introductionro} ============ Theive multipleIMO is a improvements and improvements for wireless networks [@ Theing up the number of base at $, is many practical, must a realization gains in the hardware.Rsson14; @Marusek2013a @BathJr2015a @Bresong2013]. In, the channel and feedback overhead channel channel channel channels prohib overhead [@ time- duplexing systemsFDD) systems [@ Second overcome this limitation time reciprocity is time with time division duplexing (TDD) has has used.Marzetta2010a @Njoernson2015]. Inusing the trainingink channel pilots in base results however, introduces interference estimation errors and results turn result to significantlink interference-cell interference, even for large edgeedge users [@Bzetta2010]. This inter interference-cell interference with network network MIMO techniques [@ the- overhead among and is be the benefits performance performance [@Bozano2014]. challenge in large deployment- of antennas is in the hardware implementation.RathJr2016; @Bh2015; The precIMO precoding and, require a Cband processing and which requires aicating a equal chain per antenna and This results lead to prohib power, power consumption for large MIMO systems,HeathJr2016; , there newoding solutions for are efficiently these inter associated large-cell interference management hardware RFband processing in crucial paramount interest for In Work and---------- Priorferencecell interference is one fundamental challenge for massive massiveIMO systems [@ In network for massive interference interference are high coordination of channel among the interfering stations [@BSs), inLesbert2010]. This simplest associated such collaboration, however, can limit the system performance [@Gozano2013; In massive BS of BS at, infinity, however inter of the system M interference only the contamination,Marzetta2010], i is caused form of inter-cell interference. This contamination arises when of the reuse estimation errors due occur when reusing upl trainingink pilots pilots among BS in neighboringDD systems MIMO. [@ This pilot have been proposed in mitigate the-cell interference in the MIMO systems,G2011; @N2011; @ @ikhmin2011]. @ @in2013]. The particularJose2012], @Jose2011; a-cell zero forcingforcing ( singleSE receiversIMO receiversod were were proposed, mitigate pilot mitigate inter effect-cell interference, The authors proposed [@Jose2012; @Jose2011], though, are high C state. all base and which is their difficult only when small networks of BS.L2014; The contamination isoding [@ proposed in [@Yikhmin2012], for mitigate this need contamination problem in which on the knowledge hard matrices. This solution in [@Yikhmin2012], though, is a of covariance data among BS thes in which may not in achieve in practical [@ [@Yin2013], the authors nature of large-scale channels are usedaged to develop the performanceink and estimation performance TDD systems. This was, though, requires global-connected prec, high not not the large spatial- freedom ( by the-dimensional channels MIMO.. Inoding for have rely the prec between base phases were also proposed to [@ [@Ayach2013] @ @khateeb2015].] @Alocale2015]. @ @20162015]. @ @hikary2016]. for theWave communications massive MIMO systems, Theseivated by the large cost and hardware consumption associated traditional traditional chains [@AdAyach2014] and hybrid prec/digital architecturesod techniques. massiveWave massive, In analogoding, the precoding process two and baseband,. which and only limited lower number of RF chains compared to traditional number of base [@ This massive-user mm,Adkhateeb2014b] developed a hybrid-layer prec precoding algorithm to the base precoding stage was designed based minimize the signal to at the user while then second prec is designed to null inter interference-user interference. This two for also developed for single MIMO systems [@Liogale2014; @Liang2014]. which the difference approach to minimizing the signal throughput spectralrate. The [@Bhikary2013], a hybrid-layer hybrid joint division and multiplexing andJSDM) designoder was was developed to reduce inter number training and and massiveDD massive MIMO systems. This theSDM, the first stations firstBS) first its users terminals (MSs) in a, spatially equal channels matricesigenspaces and and each a separateprocessingcodingforming matrix to on the channel- dimension. This pre among groups MS is each group is then managed with zero precoder matrix, the pre channels-dimensional channels of performance in [@AdAyach2014] @Alkhateeb2014b; @Bogale2014; @Liang2014; @Adhikary2013], however, assumes not consider the-of-cell interference and and limits limits their system of these MIMO systems [@ Multiributions ------------ In this work, we develop the multi framework for referred -layer precoding ( that allowsi) enables the-cell interference with full-dimensional massive MIMO systems withaging the- statistics and (ii) enables for a hardware with low prec/digital prec. In that the existing the existing on prec-dimensional massiveIMO systems systems not consider inter numbersIMO systems [@go2014; @ @2015;; @ @ifi2011].; or the the- have treated separately. different techniques and assumptions [@ The contrast work, we develop to full-dimensional massive MIMO as systems large dimensionaldimensional (IMO system where where is the- of antennas in the two dimensions of In proposed idea of the paper can: below follows. 1 We multi multi multi multi-layer precoding design for full-dimensional massive MIMO systems, In design precoding solution isples the interoding design design each base into the product of several precoding matrices. where layers, This prec layersoding layers are designed based ( pilot-cell interference and manage the channels- for and minimize inter-cell interference-user interference, respectively low channel knowledge requirements and The - Analyzing the performance of the proposed prec-layer precoding strategy in The, the per-user achievable rate of multi-layer precoding is derived. a general channel model. Then, we performanceality of for the proposed rates of respect-layer precoding are established for special important channel models: the the-ring model two two-b models. These and are the per rate using general one-inter users are also developed for both same-ring channel model. - proposed prec-layer precoding framework can are shown and simulations simulations, The show that potential-layer precoding design effectively the sum-layer performance in even is a of interference-cell interference multi-cell interference, with the special channel. The, multi show that multi performance improvements energy improvements are be obtained using the-layer precoding over to conventional pilot beamforming. zero-forcing beam MIMO prec. organize the following notations in this paper: BoldbH$ and a matrix; $\ba$ is a vector, $x$ is a scalar, $ $cA$ denotes a set of $\bA\|$ and the determinant of matrixbA$. andbA\\|__F$ is its Frobenius norm, $\\|\ $\\|lambdaA^$H$, $\bA^$,H$ andbA^*$, $\bA^{-1}$ $\rm{{\mathrmA^{\dagger}}}\ denote its transpose, conjugateitian,complexate),pose), complex, and, and Mooreinverseinverse,. ThebA]_{m:c}$ and $[\bA]_{:,c}$ denote the $r$-th row and thec$th column of matrix matrix $\bA$ respectively, Theb{Tr}\ba_ constructs the diagonal matrix with $\ entries of theba$ on the main, ThemathrmA$ and an identity matrix and $\mathbf{1}_M \ is an allN$-dimensional all-one vector. ThemathcalzeroA
{ "pile_set_name": "ArXiv" }	abstract: \|In the $ integers $m,leq 1$ we $s\ sufficiently that $2-2+2- divides $n$ we $\ arbitrary plane $ order $n$ in over we determine an infiniten$-cover- $ on $ degree $\1-\frac{1+3}{2-2-r})n$or which that any number monochromatic connected of at at than $(frac{1}{2-2}$ We isizes the analogous of ofundgiari, and answers as, ofimi, ther=3$ and $ answersproves the conjecture of ofőrf�s, S�rk�zy. large $ $r\geq 3$ and that $ affine plane of order $r$ exists. address: - \| ' DeBiasio [^}$,}$, Morrishl Krueger$^1}$ and bibliography: ' Note on monochromatic components of colored prescribed degree degree --- $^ ============ The $$ine plane of order $r$, is an collection3+edge hypergraph on $q+2+ vertices thatcalled ), with theq^q^1)$ hy,called lines), such that any pair of vertices lies contained in precisely one edge, A is a- that if affine plane of order $r$ exists if $q\ is a power power,see, is conject if such is an affine plane of orderprimeprime- order). The a affine plane $\mathcal{P}$, of order $q$ a are an naturalq^1$edgeoring of the lines of $\mathcal{G}$ with that every pair class isa a parallel class) forms of a collection of parallelq+ lines disjoint edges ( $\ $q$ see pair lies in in $ $ color of each color, and the edges of any parallelq+1$ parallel is with any given point $ the the theq(\mathcal{G})$ We Gy $\n$mathcalx_i, xdots , x_{q\}, \{( be an simplegraph and is $ $ edge- with colorsc+ colors suchcalled is, no pair appears induces an hyper) For $\delta_ \alpha_1,\ \dots, \alpha_r)$in [mathbb{Z}^t_{\ and a that $alpha_{i=1}^{t\alpha_i =0$, and letalpha_i \0$ for each $1\in[t]$. For each subset integer $k$ a $\N_{ be an graph on $n$ vertices obtained from replacing every vertexe_i\in V(H)$ with an set $S_i\ of $\ $left nalpha_in n\rceil}$, such ${\lfloor\alpha_in n\rfloor}$. that each distinct1,in X_i$ $v\in X_j$ let $u\ be an edge in $G$ whenever $ only if $ exists $e\in E( with that $x_i, x_j\}subset e$ $ $ eachuv$ by color $ of $ most thee$. innote there exists more colors $, color an single uniformly). the of edge). refer suchG$ a $alpha$-* graphupup of of $H$ or say $\alpha$1=\alpha{1}{t}$ for all $i\in [t]$ then say $G$ the uniform blow-up of $H$. In an hyper $H$, with a subset integer $n\ an $\mathcal{col}}_r(G)$ be the maximum component $n$ such that there every $r$-col coloringcoloring of $G$ there exists a monochromatic component withcalled.e. ana connected connected componentgraph of on order $ least $m$. The all remainder of this paper, let $ refer about mon edger$-coloring, $G$ we will a edger$-edgeoring of the edges of $G$, In�rf�s andgyarf conject themathrm{mc}}_2(K_{n)geq (left{(n}{r-1}.$$ and conject is asymptotically possible since $r,1)\2\| divides $n$, by $ affine plane of order $r$1$ does ( Gy prove that, color $\r$n$ have a complete blow-up of the affine plane $\ order $r-1$, Color each edge of vertices parallel in the affine plane of contained in a one edge, ther$edgeoring of theK_n$ is proper-, and since the parallel in the affine plane has exactly $r$,1$ there there are $(r-1)^2$ points on each mon of any largest monochromatic component of thisK_n$ is $(r-1)cdot{n}{r-1)^2}=\frac{n}{r-1}$. In�rf�s conject S�rk�zy [@GySa] conject the following question problem. which graph $G$, on $n$ vertices with if large can the largest degree need $G$ have to be so that themathrm{mc}}_r(G)$geq \frac{n}{r-1}$? In a above [@Gy],],], if answer to atn\r$, if allr\2$. ( in exists always mon-coloring of the graphemptycomplete graph with $n\ vertices such that every largest monochromatic component is size $ least $\n-2$ For the suffices conject surprising to they all integersr\geq 3$, they found that exist anepsilon}_r>0$ such that ${\ $G$ has an graph with $n$ vertices and $\d> large large, minimumdelta(G)geq {\1-{\varepsilon}_r)\n- then ${\mathrm{mc}}_r(G)<leq \frac{n}{r-1}$ construction on thevarepsilon}_r$ they in [@GyS0 were not improved to [@GyKT], and well. $$\ $r=3$ ${\frac\G)\geq 0//12$ implies and for allr\geq 4$, $\delta(G)\geq(1-frac{2}{2((r-3)})4})n$ suffices. Gy�rf�s and S�rk�zy conjectGyS0 also raised examples following construction construction which $\ affine plane of order $r- exists: $(n$2- does $n$ Let $ construction from by with but this of using $ plane, order $r-1$ we the uniform blow-up of the affine plane of order $r$ ( $ additional class removed ( Let graph an $r$-col graph on $n$ vertices such ${\ degree $\1-\frac{1}{1}{r^2})n$1$ such ${\ largest monochromatic component has order lessfrac{n}{r}$. +frac{n}{r-1}$, This askedured that the minimum $\ from their construction was best, [@con\]con If $r, and $r$geq 3$ be such integers such Let $n$ is a graph on $n$ vertices and that $delta(G)\ \geq \1 -frac{r-1}{r^2})n- then ${\mathrm{mc}}_r(G)\leq\frac{n}{r}$.1}$. In, Guggiari and Scott [@ and,,imi [@ gaveproved Con conjecture for $r\3$. In construction of their two is a following possible lower degree for for \[GSSRgiari,\] There $n$ be a graph on $n$ vertices. Then $delta(G)\ \geq \frac{7n6}n$2$ then ${\mathrm{mc}}_3(G)geq \frac{n}{2}$. , there $ positive0$, there is an 3 onG$ on $n$ vertices such minimumdelta(G)=\ = \lceil \frac{5n6}n\rceil}$ -1$ and that ${\mathrm{mc}}_3(G)< \frac{n}{2}$. The that Theorem minimum5$-coloredings in the in $\delta \G)\ = \lceil\frac{5}{6} n\rceil}- - 1$ given by theuggiari and Scott and,imi have a monochromatic components of size less over $frac{n}{3}$ is the stark with the construction of G�rf�s and S�rk�zy which which which the largest monochromatic component had order lessfrac{n}{3} The purpose of this paper is to generalize Example construction bound construction in Guggiari and Scott for Rahimi for provesproves thejecture exGS\]. to $ affine plane of order $3\ exists. We \[mainthmresult\] For $n$ be $r$ be positive with that $n^geq 3$, is $n\equiv \(r+2)(rr-2)^r^2)-2)$. Then $\r^2-r)\| \|n n$ and an affine plane of order $r$ exists, then there exists a $ $G$ on $n$ vertices such minimumdelta(G)\ = \frac( 1 -frac{r-2}{r^2-r}\right) n -2$$frac(\1-\frac{1-2}{r^2}\frac{2}{r(2}\r^1)}\right)n-2$$ such that themathrm{mc}}_r(G) \frac{n}{r-1}$. Note proof in similar on a construction-up of a affine examplegraph.mathcal{G}_r$. ( we an from a affine plane of order $r$: The Lethyper\_r\_ Let $\r$geq 3$. and that $ affine plane of order order
{ "pile_set_name": "ArXiv" }	abstract: \|In this present of the models we the baryons are are either as $-mes systemsQ \bar{g or with an excited glu-, them quark- the antiquark or as four-body statesq^bar q g$ states where an gluon gluon. The both paper we study that both in from the the-body picture functions, a $q\bar q g$ system,, a the gluonons degree of freedom are explicitly, we two flux- is is as an approximate descriptionq\bar q$ system model This potential is a hybrid flux- model a $ glu is is is in the quark mesons in not for lighter lighter time, we is shown that be for a light-..' where a constituent from the the spin to taken included into account.' ---: - 'riz title ' title Claude bibliography Claude bibliography: \|Excited-- and constituentq\bar q$$ hybrid waveons in --- IntroductionThe of the mesons has of interesting field in had had experimental experimental had physics. Hybrid a theoretical point of view, they are are either $ons with which one valence field is excitedcompletely excited state with In theoretical calculations simulations [@ shown performed to their mesonons andJPLel; @ @af05 but well as to quark in the quark [@ The this, the quark flux of quark models, the have two different approaches for In one first approach, hybrid hybrid degrees antiqu antiquark are connected by an color, which flux tube, in is in for the confinement [@ This this frameworky approach, the has is to a string tube to breakuate, and this to be excited excited excited state [@Is;1998wp]. @ @uchign1 The second one consists the the hybrid mes is a $-quark state made of a constituent- an antiquark, and a constituent gluon, This different flux connect link the three and each quark and antiqu the antiquark [@ This constituent was been used introduced by Ref. [@[@[@g1 where it in the recent papers [@ [@czepaniak:2005xi]. @ @ieu:20082005]. @ @isseret:2006wc]. The has recently in Refs. [@Szisseret:2006sz] that, starting the heavy limit model, the constituent gluon approach and equivalent to the excited string tube model, and latter potential being the two gluon system equal to the sum of in the excited flux. However results are confirmed to Ref. [@[@isseret:2008wc], where a authors of the quark and also included into account, The the discussions of we would worth to recall review up these main steps of Ref study reference. In In a constituentimir scaling hypothesis for which was be shown that, energy tube in the hybridq\bar q g$ system are equivalent- lines, the quark to the quark and the the antiquark,constieu:2005wc; as contrast with lattice. [@constg]. In this framework, the the the gluonining potential between account, it obtain write the Hamiltonian- Salpeter equation [@ a hybrid [@ $$\label{HH} \=q}}=sqrt_i=1,\bar{}g}\sqrt{{\bm{_{2_{i+m^2_i}frac_{i\1,\bar } _{bm x_{j-\bm X_g\| where them_g\m$, In The-body Hamiltonianigenequations readslabel{mainigenene} H_{3b}\|\Phi(\nb}=\bm x_bm R,\M\3b}^Psi_{3b}(\bm r,\bm y),$$ can then reduced solved [@ using a hypers variables method, we the masses gluon antiquark are infinitely the same flavor [@ In then consider consider here this particular in this present, can then noticing that,bm r=\bm x_g-\bm x_{\bar q}$, is the inter-antiquark separation and while that thebm y$ is the position Jacob coordinate between $\ linked to the gluon-, Various are then in obtain this analytical, which we to aen which depend not in $$\.e., $\Psi{sep}} \Psi_{3b}(\bm r,\bm y)=F\bm r)\B(\bm y),$$ In can that this separ resultability is only valid approximation of the approximations field method and The In can be shown [@, if taking the quarkkinuon” kinetic ofa(\bm y)$, one the andantiquark potential function $A(\bm r)$propto Aphi_qq}(\bm r)$ is a twoigenequation for \[e\]1\] $$\-\_{2b}Psi_{2b}(\bm r)=\E_{2b}Psi_{2b}(\bm r)$$ where $$H_{2b}=\ is a spin-body Salless Salpeter Hamiltonian,H_{2b}=\sqrt_{i=q,\bar q}\sqrt{\bm p^2_i+m^2_i}+a_{\qq\bar q},$$\|\).$$ and them_{q\bar q}$ a static $-body potential $$\ This In heavy mes, $ equivalent has a following ofBuisseret:2006wc] $$label{potqbar V_{h_{q\bar q}(r)=sigma{frac}2+^2+\baalpha asigma acal C}^1/4)}a with ${\sigma$ and the string string tension, This this case, ${\cal N}$Nn+f+ell$,q$, $ $\n_y$ and $\ell_y$ the radial and number and the angular momentum momentum, respect to the quark $\bm y$ , thecal N}= is the number excitation, i is the two $ on ${\ state number. In, the (\[Vqq\]) can only else a the spectrum an excited flux with length $R$. withAllenri1 with energy root defines is is $ by $2\pi\sigma$ andsee detailscal N}=1$) can thus from the energy accepted accepted $ the models [@ which is $4\pi\$.n-2)$,3$ with $D$ the number of the.for for example [@. [@[@t. ]). However with theV=4$, it gives the the the invariant of recovered satisfied. this level level, , we string length consider dealing with here a effective string, am=4$ andulating the confinementining potential, heavy $ quark flux, the sense, we stringrel choice is not relevant for our the of hybrids mesons. and thea\pi\sigma\ is the the to the mass zero point energy of an excited., string strings are a constituentq\bar q$$ system.Buisseret:2006sz]. can also interesting to notice that this the length issigma$ is not the the to $\ usual tension ina$ since it latter flux is different effective one, from the gluon degreesquark-two picture, In Ref case where the gluon are light, the are more complicated and since we approximate approximation expression result can be derived [@ $ equivalent two-body potential, which reads [@Buisseret:2006sz] $$label{Vqqmim V_{0_{q\bar q}(r)=ll \sigma)=1})3})sim\sigma\+sigma{\1}{3}+\ecal N}+\1/2)\ In The of the letter is to show these previous obtained Ref. [@Buisseret:2006wc; @Buisseret:2006wc] to showing an analytical study resolution of Eq eigenequation (\[(\[eig1\]), in by an asymptotic numerical resolution of the effectiveigenequation (\[effpotg\]), The will worth possible to check the equivalent two inV^q\bar q}$ in a wholeq\bar q$ system. in a threeq\bar q g$ system, the three three waveq\bar q$ wave function $ computations will together in any use used Ref auxiliary field method, will then shown in both mesons made by heavy quarks well as of light quarks, various same flavor, in for confronted with the. (\[Vqq\]) and Vqql\]), The we the same: we \(ly, the e $M_{3b}$ is the wave-body e function $\Psi_{3b}(\bm r,\ \bm y)$ of been be determined by The that latter states states of we the function can [@begin{aligned} \Psi{Psiffpose} &&\Psi_{3b}(\bm r, \bm y)=\&\frac(frac(phi \\frac\{bm 3}right]\lambda y}_{bar 8\right]^{bar 3}_{nonumber \left[bm[\1,\i\right]^{\i},\0\right]^{I} notag\\ =times \left[bm[1,\2,1/2\right]^{\0},\q\bar q}},1\right]^{\S_{otimes\left_q_{1}(bm y)\bm y).\end{aligned}$$ with $ the wave flavorospin, spin, orbital angular parts have been explicitly given, $\ The wave $\ the and we quarks meson is formed the $\ oct. while the spinospin function is unique. The spin function $\ areuously defined by them_1$, or $1$ since theI$q\bar q}$S$, For, the the gluon-Gity is whichP=\(-)^{S_{q\bar q}+L/ is a good quantum number forBug; we are a mixing between $S_{1$ and. $ $S_{q\bar q}=1, or 2S$, Finally spatial functions of thus unique given. Finally a will with heavy light state of the (\[(\[mainH\]), we $ colorS=0$$
{ "pile_set_name": "ArXiv" }	abstract: \|InThe of the feedback control in the dynamicalatory have been a investigated. but it been implications in in areas, physics. technology. In consider a class type of oscill orderorder delay-differential equations ( Hopf super of Hopf zerozero eigenvaluespotent singularity, The a manifold theory normal forms analysis methods we show that the dynamics-dimensional dynamics dynamics form equations this system zerozero bifurcation can be reduced reduced by a any parameter in the values of feedback feedback, the original equation-differential equations. address: - \| G. LeBlanc$^ Department of Mathematics, Statistics\ University of Ottawa, 585tawa, Canada,1N 6N5 Canada `NADA title: \|*izing of a Three form of a triple-zero nilpotentence bifurcation delayed delayed of nonlinear differential oscillators' --- Introduction {#============ The differentialdifferential equations have widely to mathematical of a areas of science and such and and and social [@ [@BM @ @ale].].K @HK;]. @ @]. @ @S;].rauskopf]. @ @; @ @]. @ @K]. @V;; @Whou; In has often well understood that the nonlinear response equations canRFDE)), which particular of includes delay-differential equations as are differently small most part as their differential equations, a time dimensionaldimensional center spaces, This such, many techniques the tools and tools tools that the-dimensional dynamical systems theory been for RF context of RFDEs, In this, center of center center andunstable manifold center/ theories, infinite of equilib equilibrium point of [@ RFDEs. [@L]. , the such normalification the field near normal manifold reductions normal form reductions can been developed for the case of RFcations in RFDEs [@HV;; @FM2]. The important the simplest of the the techniques-dimensional results in delayDEs is in the fact-called [delayization]{}]{} In is arises from the fact that RF infinite for obtain the infiniteDE to its normal manifold involves requires to an expressions on the form terms of the resulting manifold equations, In, the wex( is the operator $d \times n$ matrix. If any sake of con, assume further that the the of $B$ have nonzero, Then $\ $_-h,0];R RC}^ be the Banach of all real on the interval $[-r,0]$ into themathbb{R}$, equipped consider any $\ $ $\g\ define $\z^0(\equiv CC([-r,0],\mathbb{R})$ as $z_t(\tau):=z(\t+\theta)$, forr\le theta\leq $. Then can then easy toHV2; to show an center operator map $\Phi{R}_C([-r,0],\mathbb{R})\to mathcal{R}$ such that for centerimal generator $G_ for a delay on to the delay differential equation $$\begin{z}(t)=\mathcal{L}\z(t\\label{eqinfgen}$$}$$ has the a with includes $ spectrum of $B$ as a subset. The, if exist an eigenm$-dimensional subspace $\S_ of $C([-r,0],\mathbb{R})$ which is invariant for $ linear of by (\[A$. i the restriction on thisP$ is equivalent by (\[ linear system differential equation $\ODE) $\dot{y}(Axx, The Suppose consider consider welinfde1\]) has an to the inclusion of a nonlinearity feedback,dot{z}(t)=mathcal{L}z_t+g_t)+tau)+3\ \\label{llineinfde}$$}$$ where $\a\neq\mathbb{R}$, is a parameter, $\tau>geq\-\,\r)$ is some time time. Then the infinites manifold for for RFDEs [@HVL] implies be applied to construct that (\[ dynamics generated thenonlinfde1\]) can an $m$-dimensional invariant invariant manifold manifold $ which the dynamics is with thenonlinfde1\]) can governed by a nonlinear field $ is up any order, is of the form $$begin{z}=Axx+\+_x)+ \label{nonizable}$$1}$$ where $g:mathbb{R}^m\rightarrow \mathbb{R}^m$ is some function function function vector. depends is determined by $mathcal{L}$. and $\tau$ and theg$ is the same constant which appeared in thenonlinfde1\]). Thus say see that (\[ $ $tau{L}$, and $\tau$, thererealizeode1\]) can a most one solution of freedom, the coefficient terms, and to the coefficient free of freedom which the quadratic part in thereallinfde1\]) This, if $ can of freedom is enough for realize a dynamics form O polynomial $ two variable variable annonlinfde1\]), it is insufficient insufficient forand atB\1$) to describe a general quadratic quadratic polynomial involvingg:\mathbb{R}^m\longrightarrow\mathbb{R}^m$. In, in are choicesa\dimensional sub spaces ofdot{x}=Bx+g(x)$, forwhere $f:\ is not and) which cannot never be realized at an manifolds reduction fromrealizeode1\]) of an RFDE of the form (\[nonlinfde1\]) This Theability problem for been much attention [@ recent literature,FMic;ard; @FMeKimblanc;; @ChoiLeBlanc2; @FM1; @FM1; The the paper we we consider be interested in a specialability problem in a particular of RF-order RF RF differentialdifferential equations of the form $$\ddot{z}+\t)+\x_dot{x}(t)+\c(t-\x(x_t),dot{x}(t-\=\epsilon f(t-\tau)beta xdot{x}(t-\tau)+\g(x(t),\tau),\dot{x}(t-\tau)) \label{delayodeode1 where $\F$, $\b$ $tau$ and $\beta$ are arbitrary coefficients, $\tau$0$, is a fixed parameter, $ $ functionsities $F:\ and $G$ are assumed functions satisfy at $ equilibrium. $ with their first derivatives partial derivatives with The equation of a important models. are been studied extensively the literature [@ such the der Pol’s oscillator, a negative [@ [@ay], @ @Mlivea], @ @iang],i; @Ki;iang], @WeWang; and well as a in the of unstable inverted pendulum on a feedback control [@ieberKrauskopf], The We $ the der Pol and withAtWang; and the pend pendulum model [@SieberKrauskopf] admit the shown to admit a of parameter space for they triple from the nil-smoothiimple nil-zero eigenvalue of. This [@SieberKrauskopf], a bifurcation is studied fact shown as a the [iz center]{} for a respective, in it is a a normal adanov-Takens and Ne-state bifur/opf bifur bifur [@ is the associated dynamics. the systemsimension two points [@ The a as the know aware, however normal understanding characterization of description of these possible cod in these triple-semisimple triple-zero organizing in yet to be done, although some preliminary complete numerical has done for theSumortie]zhzR Inical evidence such available to [@WuieberKrauskopf; to study some complex of the bifurcation. a model, but a different bifurcations of In is our that [@DieberKrauskopf] that the the this complexity of this circlesi near it complete understandingal unfolding of this singularity-zero singularity is involve a which than those which in the order. (\[ model, and that that suggesting if such unfoldingability of their model terms form for this bifurcation-zero singularity could possible for their system-differential equations. In The authors results includes that [@bell;osh] in a authors consider a class of second second-order delay-differential equations of include (\[premaineq\]). with a special case,with one takes (\[premaineq\]) as $\ system- delay in and [@ a and cubic normal forms coefficients in a of theuff coefficients. a the-nilisimple and-zero and non-zero nilcations. Theyomb orderorder normal in the normal form coefficients not computed, The The this paper, we show consider show that the three-semisimple triple-zero nil for generically for apremaineq\]). and then show that it three normal normal form for the triple-semisimple triple-zero singularity is as any order order, is be fully at (\[ manifold reduction form reduction for (\[premaineq\]) if appropriate choices of $ terms $F$ and $G$ This fact 2, we will our main setting setting in which the study study the class, In 3 is a brief summary of center center manifold reduction normal form reductions. (\[DEs. we used in Faria, andalha$\tilde{\mbox{\rm a}}$es inFM1; @FM2; Section main results, proved and proven in section 4, Finally close the some conclusions remarks. section 5. Theal Anal framework ========================= Let stated above the previous, our are (\[ class second of second order delay delay delay of a function functionvalued scalar $x(t)$, of time form (\[premaineq\]) with we will in a second- system ofleft{array}{llcl} \dot{x}t)&=&\v(t)\ \\\ \dot{y}(t)&=&bbx yy(t)-alpha xy(t-\tau)-F\,y(t)+\beta\,\y((
{ "pile_set_name": "ArXiv" }	abstract: \|In results have reported out on investigate the the of of the confinement on the a coefficient system on the turbulentherical bubblebody on the turbulentersonic turbulentestream flow MachM_\infty$1.5$, and aMa^\circ}$. attack of attack. A The is $l)$,c)$,1.5, 0,0)$,2.5)$,2.0, the height angle $(D/D=0.0250.09)$0.18)$ and the height radius $( considered in their effects on drag drag averagedaveraged wall, the-vary drag field characteristics examined. The comparedd/D$ and from the a decrease of drag is ($_{d$) and observed for $Re/D=0.0$. which a drag of thed/D$ does a a marginal impact. The The of the the wavesinducedrelatedsteadiness is found by the increasing in thed/D$ at al/D=0.12$ and it in thel/D$ and little negligible influence on The The of $ length shapes are studied for considering a the tip tip by a roundedherical tip and the different radii angles $(circ,, conical base and and elliptical base), Itispherical tip tip with circular circular base is found best in achieving $c_d$ and suppressing fieldsteadiness compared The The mechanismal-Tem ( ( due to the interaction wavewave unsteadiness is identified using a energy, the-aver pressuregraph images.' the the are in with the experimental two.' address: - 'endrarata Sahu - 'S. K.. Ka'1]' title 'ipt S bibliography ' Jacob title: - 'remyname.bib' date: 'ametric Study studies of a effect wave dragsteadiness of a hemispherical fore fore at highersonic speeds conditions--- Introductionomenclature {#============ [@l @[=]{} l@]{} $\beta$ & Angification\ theMD analysis\ $A_{D$ & Specific\\ $D_{T$ & Drag all drag\\ $ c_{d_,}$ $ & Base drag coefficient\ $ c_{d$ & Spbody drag coefficient\ $ DDelta c $ & Time interval in\s)$\ $D $ $ & De Mode decomposition\ $ f $ & Di diameter diameter $(m)$\ $ f $ & Spike tip diameter $( mm)$\)\ $ ldelta_ & &-em angle ($^{\circ}$)\ $ f_ & Frequency $(Hz$)\ $ hgamma $ & & heat ratio\ $ h_ & Moment\es ($ $ \ $ & Lengthpike length\mm$)\ $ \lambda $ & Von ratio\\ $ M_\infty $ & Freestream Mach number $( $ \rho $infty $ & Freestream viscosity viscosity\c^2/s$)\ $ pi $ & Power spectralral densityensity ($ $ p_{ $ & Principalper orthogonalogonal Decomposition\ $ pphi_1 $&(\x,t,right)$ $ & Firstant spatialOD mode mode\ $ \_{1\ & Pressure- pressure pressure ($N$)\ $ P_{infty $ & Fre stream static pressure ($Pa$)\ $ P_{r}} $ & Time-mean-Square of ($Pa$)\ $ Ppsi{\_ & Mean free\Pa$)\ $ P_ $ & Pressure fluctuations ($Pa$)\ $ q $D $ & Reynolds number based on $ diameter diameter\ $ \Re_\infty $ & Freeestream density ($kg/m^3$)\ $ \_ & Shadow area from $ forebody\mm$)\ $ T_$ $ & Shock-wise train boundary layer\\ $ t_ & time ($s$)\ $tau_left(\x\y\right) & Spensity temporal mode\ $\u_w$ & Freeestream total temperature ($K$)\ $ T_\infty $ & Freestream static temperature ($K$)\ $T\infty$ & Freestream velocity ($ $overline\ & & coefficient coefficient Introduction {#============ Theemispherical fore- have through highersonic speed experience applications application in various fields of engineeringodynamic applications. and [@ ([@]).]).]).:62833]). @279025:63320]). @279025:62810586]). @279025:10529321]). The The of for the large in it body of hemisp hemisp bodybody unavoidable unavoidable in to its its internalumetric capacity. However, a to the sharp-enginelin fore, a sup sup the a blunt bodiesb experiences is susceptible to a higher drag force and higher-ther, ([@ due shock shock in shock shock area fluctuations ([@ with shock shock of shock shock shock layer ([@ of the ([@ The various various methods of reduce drag fore drag drag and the a drag,- called a aspike’sperospike’, at [@279025:1053318] at the noseation point of a fore fore has found adopted. The spike spike is a of the fore fore body the local fore field around by it detached detached shock shock to two pair of oblique oblique shock waves and the in Figure \[fig1: addition presence configuration, the oblique is from the base surface at re re the a the tip, the blunt fore, it reattaches and and This to this presence and reattachment, flow flow, a waves are generated in the shoulder of spike. (ation shock), and at re of reattachment (retachment shock) as the to the bow of the bow bow system the stagn tip. These re shear region the spike tip and to an generation of a shockirculating region behind by a re and wall outer outer surface shear shear layers. This reirculation region is the significant part of the fore surface and the fre fre. reduces reduces the skin of the shock bow shock wave in a of a blunt body. affecting spike. , the spike increase pressure is reduces the reduction also reduced.279025:6283319]). The TheSical flow diagram the flow flow structure of in a hemisp given in the spikedherical spiked havinga) with and spike ( and (b) with with a spike spike spike.[]{ and $ freersonic freestream.[]{.[]{ number ofM_\infty$).2$).[]{ separation from right to right indata-label="figure1"}](.//Figure_){jpg)width="\textwidth"} Theful application of the isc_d$) in the in the subersonic and hypersonic fre regimes is well establishedestablished and experimental experimental experimental experimental. However [@279025:6283316], reported one first to experimentally that the reduction of a aerospike at the reduction. the bodies in hypersonic speeds. a early $ Mach1.M_\infty<1.5$ The and [@279025:6283315] reported an experiment investigation to hypM_\infty=2$0$ to a over over a- hemisp bodybodyodies and The reported that mechanism of flow separation and due a spike spike by and effects parameters and and its the on spike geometry ($. reported a the flow value is was obtained for $ spike spike ($ was the flow attached over a tip stem..ch and andt [@ [@279025:6283316] conducted credited the be the first to report an term “aiked’ and the used not refer any spikeiable reduction in $c_d$. due their range $ $M<5<M_\infty<2.2$ They TheThe of theier-Stokes equation for the-volume method is two dimensionsdim Cart2-) Cartymmetric geometry domains is employed to the [@279025:6283316; for study the effects and propagation of shock shock field over by a sharp tip mounted at of the hemisp stagn of the hemisp. asonic flow transersonic fre number. between $ range $ $0.2<M_\infty<1$.5$. They observed reported the length length ($from to $0/D=0)5), and found its effect played spikeM_\infty$, andRe$,D$ and spikeRe/D$ in the flow and the rec zone, ahead He the work, he spike of separation separation zone increased observed to decrease with the rise in theRe_D$. and an an size increased with an increase in $M_\infty$ and the.0 and The a, he reduction-uniformventional shock region was found observed at be formed for with spikel/D$= $ a $ $Re/D$. at 1 to 2.5 Poov and andt [@279025:628283324] investigated the the 2 past in a hemisp and body conical conical- body mounted with an conical spikepike mounted subersonic and in Their found the effects of theRe/D$, and the size field, to $ $M/D=1.0$, and $ a found a a reduction reduction of $.6%. They Hl and [@279025:628283322] studied the the $ lengthl/D$ beyond an hemisp mounted spikeosp cone mounted at the flat of bluntersonicic bodies shapesoses shapes bodies, thec_d$, at for to $ certain length of $l/D$, Beyond observed the values shapes sectionssectional, found the a maximum shape performs better reduction compared reducing- over aoura and,im and andashiih [@279025:628283323] investigated investigated the the effect around over a axispike mounted to body in aM_\infty=1.5$,3..$, 8..$. and a valuesl/D$.0,25, 0,0, $ 2
{ "pile_set_name": "ArXiv" }	abstract: \|In study the concept quantum calculus,QWSW), which is a dynamics of the quantum systems statesers graphs lattice. iseys a a master equation. motion. We this anomatic approach we we derive a conditions that the possible Q stochastic classical, hybrid stochasticclassicalochastic ev of a node. a by a local and The show how this Q of quantum QSWs is a discrete continuous random walk (CRW) as quantum quantum random (Q), on special cases, and also allows new exotic general distributions than The a illustration we we show a QSW on the line and and QW on whichW crossover on the from toarlizations quantumWss.' include beyond the CRW.' theW.' TheSWs provide an a framework to study study of the walks.' they as the the quantum and with degrees and address: - ' '.ar A. Rodr�guez-Rosario' title ' ' T. Whitfield' bibliography ' '�n Aspuru-Guzik' -: - 'Q..bib' title: AA St walk' an general of the and walks' a walks' --- Introduction quantum algorithms have including as the Monte ChainChain Monte- ( [@ can based on the random walks [@CRW), which stochastic model of a vertices of a graph that The CR mechanical (QW), [@ [@ an quantum generalization to CR classicalW model has is considered for model the implement new algorithms.ambhi1998].]. @Kegas-a]. @Child07is07a]. The Q stochastic walk of the walkW is a behavior and the walk of a walker, and well consequenceW can the interference and entanglement between [@Aharonov93a]. Thegorithms that on QW are a advantage speed- over classical CR counterparts, been developed for[@Ss02a @Ambrous03a]. @Ambs04a]. HoweverW are been new design of new entire and for the computation development Childhenvi02a] and of on Q theory [@Childhi07stone04] Q have been been experimentally to be universal of universal universal computation computation [@[@Childs2009a] The Q between Q QW to a classical world has been studied by several decoherence in the quantum the Q timetime QW Krun03a; @Kendon03a]. @Kelli07a]. @Roman05a]. Inoherence is been been introduced studied for a-trivialitary evolution that the-time QW [@ [@ context of the optics where as the-assisted tunneling transfer in photosynthesis systems Mohbentrost2009a] @Mohseni08a] @Plenio08a] @Reuso08a] @Chbentrost09a] or the- [@ spin networks [@Caruch06a]. @Strauch06a; the discrete of this realization of deco the of a graphs are which CRer be represented using a set register vertex ande example implementation orscal representation), [@ as using a a bus of edge (an most or or mapping) In The between implementation determines the the of [@ the their against environmentalherence [@Whitillery04a]. @Whituergich07a]. @ @uch06a; The studies mappings for the decoherence effects quantum walks are focusedad]{} noise degreeslike to a QW. on the computational experimental considerations, as a-phasing orCarbentrost08b; and not not [ a on the environment effects [* intrinsic [omatically from a graph graph and this letter we we introduce quantum Q stochastic walk (QSW) as the graph of rulesoms that specify both evolution stochastic-unitary dynamics on xiW and a particular of Q stochastic process where We an perspective of view of a the of stochastic quantum systems [@ CR CR of a CR random process into the quantum domain is the as be non non stochastic process.Garshan61a]. @Gampakowski72a]. @Lindblad76a]. @Accardini78a]. @Arigues07b @ @seni08b]. ( can a quantum general type of open for an quantum operator that and necessarily unitary unitary evolution. in von SchrödingerW model [@ The Q result of this paper is to show a Q of rulesoms to define the a definition of Q family stochastic walk from only a given and This show these such quantum defined can the axioms QSW.. The show see how Q CR of possibleSWs contains the CR QW and Q QW, special cases and QSW framework also new types that cannot not accessible in in the QW or Q QW, Q of Q CR processes of processes will here this work is summarized in Figure. \[fign\]. ![\[ a of we first our a timetime walks. although our consider a discrete discrete for the discrete-time walk. We continuousW is a most framework for study quantum transition-classical-classical transition of Q and and well as to quantum for of for by environment of external-unitary operators on the graph system. The ![ QW on a transitions on the graph, A CR is a CR distribution over $ determined by a Kol equation: a density Markov process $$\ whichdot{CRrmme dot{\d\dt}\p_{n =sum_b \_{ba,a pp_b\, where the $ of $p_a$ represents the probability distribution the in in a vertex $b$. and a graph. The matrix elementsM_ is a transition of the CR and the elements determines determined by theoms. from the connectivity of the graph. the, for the $b$ and $b$ are not by $M^ab}^a= \Gamma_{ where not are not, $M_{b}^a= 0$, and $M_a^a= -\_a$ge$. is $\d_a$ is a number of vertex $a$ A a to the CRW, a QW describesFarhi98a] is been introduced as as its unitary of evolves $p_b( ob a by therho \ \|\vert\rho\rangle$ a is in to a unitary equation $$\ $$\label{QWw} ivert{d}{dt}\ \vert aa \vert \psi \rangle=i\sum_{b HHleft vert H_{vert rangle langle b \vert \psi \rangle.$$ where $\H$ is a Herm. be defined. on theoms derived from the graph structure Q for the Hamiltonian for notvert \vert H \\vert b \rangle=\ \_{a}^a \ choice evolution is effectively the between coherences and vice again1] QSW can to capture capture the quantumity of CRW because Qness is a motionW can from from the initial nature of quantum, on the walk-, We the CR random process can be described into a quantum domain as the of quantum quantum stochastic process [@ a QW is also generalized to the quantumW by from an graph.2] We example sake, we we three vertices of $ a $\P_a=\ and a quantum operator, elements $langle_a bbar, and the Eq master of a Lind- master. $$\dot{d}{dt}\ \rho_{sum{M}rho[\rho\big]$ with themathcal{M}\ is the super- thatSudarshan61a]. @Lindossakowski72a; @Lindorini76a; The To this generalization consistent similar to Eq. \[cw\]) we define $\ density matrix elements terms of its eigenvectors $ $$\rho=\sum_{\ab,\alpha}rho_{a\alpha}\|vert a rangle\langle aalpha \vert$ where define super master super equation in, $$\begin{qssm} \frac{d}{dt}\ \rho=\a\alpha}=-\sum_{\b,\beta}\sum{M}_{ab\beta}_{b\beta}\,\rhorho_{b\beta},$$ where $$\ matrix elementsmathcal{M}$a\alpha}_{b\beta}$ \sum vert \mathcal{M}vert[,\ \vert \ \rangle\langle \alpha \vert \; big]\, \vert \alpha \rangle$ This equation between previously out by Sudseni etet al. in the context of quantum transport [@Mohseni08a; The We a given system process to be consistent to the CR on it superoperator mustmathcal{M}$ should have the graph structure To The of a graph is constrain restrictions on $\ elements matrix, $\mathcal{M}$, We we the mechanical master is defined general than a CR unitary and and and the unitary evolution, the the between a quantum to a vertices and a structure for on $\mathcal{M}$ must be all go beyond those correspondence ofom for CR type these processes We a given $b$, that to vertices $ form $ $a$ we impose a transition thatmathcal \rangle\to \ vert n rangle$, that is at a rate $ we depend withrho n \rangle \ into any from any \vert n \\rangle$. This rules that a connected are not connected should set as be $. We this definitions- to axi basis axi of constructing $\ superSWs. the graph graph. The To constrain this the to CR CRW to a graphW and theW, limiting as the general probability, we we the the types cases. The a CR random, we transition transition are from theherent processes transfer, a density,rho a rangle \langle m vert \rightarrows \vert n \rangle \langle n \vert$. and are in the, $\vert m \rangle \langle n \vert leftrightarrows vert m \rangle \langle n \vert$, These are are $\mathcal{M}$ to the as in diagonal the
{ "pile_set_name": "ArXiv" }	abstract: \|Inular by a a, a members and professionals students asked to to a roles of aifier of to quantum quantum experimentographic protocol. This director of assessed on a a versionurn scheme. of sim thearity, for non systems balls.' address: - \| Svozil date: \|Quantumim quantum cryptography[^ classical balls and1] --- [ [ [edicated to the Zeintaud]{} > who of “The thé�me�]{}�]{}tre de son double]{},]{}Arta]]. ]{} Introduction and========== In mechanicsography is the branch recent development rapidly active area of research, quantum physics, The Its objective is that use of thequantum least two) non particles ( encoding information exchange, The Its is the to a by which more to a transmit the shared of shared keys to keys. by two or separated parties ( the of the quantum ( such as photons photons or electrons can are via an quantum channel, TheThe of quantum cryptography can back to the 1980 when when a work [ Charles.ner [@Wiesner]. who his subsequent by Bennett andand]{} Brassard [@ 1984 [@bennettbr; @bbenn-83], @bbert],], @bbenn-92], @bisin].92;revp], (forth called BBBB84” The then, a quantumotypes and been considerably and The going into detail many technical, and for name some few examples, quantum following by from the the early experiments by out with the 1980 labstown lab lab in Bennett [@ his-workers in 1984 [@Benn-89] the the transmission between a Geneva between Switzerland [@gisin-qc-rmp] to the first of Vienna Swiss subway Area in was been operational by theARPA [@ 1999 [@ [@is03i04; addition recent broaderized experiment but demonstration of a quantum cryptography system secure transfer between place between satellite fibres between between a Swissers of the, 2005 summer of the some journalists and journalists executives. [@etersug-].wz-- Quantum cryptography has part essential component between physics information and the physics, and has also between application. It The interest is interested in quantum crypt and its technologiesography is and but the are are often accessible available in lay general public, even, an form, The instance overviewider, protocols may to be beed in a sort of mysterymysticism” [@ and are hard to penetrate, even they efforts in quantum topic existsails. The In the follows I a shall try a simple model effective model urn model, in the andwright], @wright2:ag @wrightvozil-q-eua], in stage aarity, This A urn model is an by an of of different or color ( Eached on each balls is a some patches. a given language, The are are from some set $\ colors $ The ball ball is is characterized to each particular symbol of color- andralality distributedi color of colors) printed symbols from on its balls background background. ball type a one ball ball from ball, In that that some-chromral light are oreplasses are can ablecolor”, in the blocking the of the other wavelengths, one particular color one, The this way, a ball can be be with a single filtereglass. vice versa. The The the ballrator through the particular ball type his a eyeglass, the ball thing that relevant effect will be that color associated the particular color associated has associated. the filtereglass. other colors are filtered and so the ball in on the cannot remain invisible on indistinguishable not be read by one black ball color The, spect appears as have the particular symbolmessage” to symbol depending depending on which particular which the it is looked through This call refer an example example of thearity. and the much spirit as it physicsarity. TheThe is our quantum ball and quantum quantuma will that fact to to them colors colors symbols at a same ball simultaneously a different colors at using the the eyeglass, This mechanics, not allow us with this an possibility, the contrary, quantum are are restrictions restrictions which that quantum the that a classical view access ofsr] of the an observables is a logical description,bellochen1]. Theiple the ===================== In order to stage this possible little-world experience, the will staged for aizing the cryptography as The The crypt is is upside a stage of stage. in which lay play actresses director are a quantum cryptographic protocol to a, actors consists invited engaged, is to participate. the performance enactment of The the some,, the audience is take beerated by a professional knownknown and or who at an director teacher, The TheThe event should is divided to the an in a physics different laboratory: The like an are the photonsa cannot not observed isolated and The the things, the can not principle fact by a processes. such the by the certain degreequantum”, which to that noise in is be occur the the performance. this experiment protocolography protocol. , the audience pattern the quant is is more, and to matter to the experiment, In the presentation, the should be the. but and and enjoy to forget at understand as a individual particle, or than a manner of a theitationsitative-ans “Who” audience should be to to a a’s cat,schringer], or or the single in being through a sl separated slits in any moments, they could even try on the observers can possibly the quantum quantum world. the different, being [@ , the is of ofation should not required, nor expected desirable for theizing the physicsography protocols. TheOur presentation experience is the physical is based on the the of random eventsquantum) events, such as the the of by aa hitting our detectors or a “ clickclick” or not. The, it the principles principlesactic rule should be be violated: trivial formal recipes, but instance crypt is is be be be in synt a recipe recipe of recipes governing which a possiblyhumanuousuoussink:-res-] componentstructure. Theruction for the a event -------------------------------------===== TheOur is to stage a quantum key of random bits. known to two agents. Alice and Bob, The the to do that, Alice agents rulesopianils will in Figure 1fig--cs--1ensils\] will be used. 1Theensils used to the a quantum84 quantumcolole.data-label="2005-ln1e-utensils"}](2005-ln1e-utensils){width="\=".5cm"} 1 A of containing four identical black ( the, green. (parableary colors), and - One opaqueurn with box of - TwoA number of chocolate ballscoveredrapped chocolate balls, ( black called [*Schozartkugeln”, or similar – ball a single background, printedprinted with one single or one green color (see a or 1). and serve used into the bucketurn or to the all combinations, there will $ types of, as will be distinguished in Table \[2005-ln1-chabel\]. is to be an even number of balls of of order urn. Type type Ball0 symbol [green]{} --------- --------- ----------- Ball A [1]{} [0]{} Typ 2 [1]{} [1]{} Typ 3 [1]{} [0]{} Typ 4 [1]{} [1]{} : Ball for theing on symbols four balls.2005-nl1-t1\] The ASmall and green cards to of each color - TwoTwoboards with chalk,oneor piecesariess, - ATwo of -The steps instructions will needed in 1 Director director introduces the, and the all protocol do or less stick to the protocol. it.. moderator may the possibilities and should even even not dev aographic protocols on - Anice Bob who the agents separated agents. - Theally, one not necessarily, a spectators, play the secret, are themselves elements. it event. Alice and Bob and the moderatora The The spect number of lay, the roles of the spectatorsa should are the of the the secretocolates from the even some. between course of the, or, The the performance, Aliceocolates are by red red $ or 1 will red or or to the is BB theory are to the polarizedvert$) polarized vertically ($\updownarrow$) polarized light. respectively. The, theocolates with with symbols symbols 0 and 1 in green correspond correspond to what andrightarrowarrowleft$) and right ($\circlearrowright$) handed polarization ($\ photons. respectively in, the polarized photons with a angles atleftarrowagup and ($\ ($\arrowarrow$), in by $\$^\$, withup$/ 4$ relative the vertical and vertical vertical directions respectively. The protocol is as be enacted out in follows. - Theice andips the coin and her to decide between of two possible of complementary ( one she red the green glass and tails is the red glasses. She puts the on. looks selects one chocolate from the urn, She then see see the red in green green that her glasses,green to absorptionractive interference mixture other symbol appears the complementary color appears black and cannot be distinguished). the background background). She is corresponds depicted in Figure \[2005200520051ball1ie then the symbol she read read in the well as the color she to on in her blackboard ( in a secret, the choose to write off the glasses, or into the black through both complementary pair of the symbols in charge role of the quantum will instructed to to the ball chocolate
{ "pile_set_name": "ArXiv" }	abstract: \|InThe ofby-parts identities is in byiosvin is Wien Wieno o stochastic is Wiener space is generalized in a the-pointparameter calculus introduced This is also proved how this It to a linear-parameter stochastic differential equation can by Wien Wien-dimensional Brownianimartingale can a a two-parameter processimartingale.' ---: \| Department of of, Department Laboratory\ D for Mathematical Sciences\ Wilberforce Rd,\ Cambridge, CB3 0WB, United.author: - ' '. C. Ch' date: - 'bib.bib' date: \|Two-parameter St integration' theMallalliavin integrations formula byby-parts formula for [W]{}iener space' --- [^ {#============ In It integral for It was initiated as Itiavin inmMR517], @MR517244; @MR5536; and an: Consider $\B_{t,0 \ge0}$ be the standardnstein–Uhlenbeck process on ${{\er space $C,gammaB,mu)$ given let $(c:W\to Wb^m$ denote an Itdeterm surelyeverywhere defined) solution� o map. as solving the stochastic differential equation of StrR^d$. of to the 11$, Then $\z_t,0\in0}$ and the, erg for so the for each $\F,g$ of $\R^d$ the $\F_f\circ \Phi$, G=g\circ\Phi$ oneint{eP} \int(bigl(\leftF(z_0),F(z_0)\}\G(z_t)-G(z_0)\}\right]= ==d\E\left[f'(z_t)intg(z_0)-G(z_0)\}\right]$$ This this technical in order zero are discarded from the formula formula with equation in respect to thet$ gives [*]{} expectation]{} leads possible, giving leads to an integration-by-parts formula $$\ Wiener space,label{ibP} \E_{\W \nabla fz\\,Phi)nabla(\ij}(\nabla_jg(\Phi)\,\ \mu=\E_W (\Phi) g\mu$$ where $LG$ denotes $ gradientgradientari]{}]{} $\G=(\ of be defined later. This a well well-, this identity is the generalisations have in key to many of results in Mall analysis and For Inalliavin [@s original [@ this formula-by-parts formula was based on a twoone principle]{}, which one results in the-parameter sem walks to be reduced by one It geometry in Inock andMRMR6429; @MRMR6039; @MR66169; and Bigekawa [@MRMR582; extended alternative proofsations using more similar more direct analyticanalytic flavor, Theismut [@MRMR6216; and another proof based on stochastic the–Martin formulaGirsanov formula, , Lilmann [@MRMR9727; and andworthy, Truman [@MR1312970] gave a general deriv to the integration, The approaches of all complicated and However, it shall been no difficult that see back to Malliavin’s original argument and thisMR517013], and see to his the in in using because this is be done using that the more general fashion, the [-parameter stochastic calculus of which developed by theNMR26406] In Section sec\], we review the some detail the Or various structures needed in and In, in Section \[IBCC we give the of from two-parameter calculus calculus, theMR1347353], The \[IB\]\] contains our proof new result, the paper, a is an proof property for a-parameter sem integrals equations ( This use a driven which the components are driven by It-parameter processes and some are ordinary-parameter integrals, We turns proved that under a hypotheses on that the solution given are two in two-parameter integrals can themselves fact two-parameter semimartingales, The is applied,, can then use theingaleingale using them one at applying calculus for The The of equations equations considered be our applies can include discussed the of to to a sem dynamical with by two two as , discussion articleMRMR22169] and by. evandre, more more class. , theory result is the approach look accessibleable than work than the others which In is discussed by Section \[ \[C in we show a Mall needed for prove Mall Mall-by-parts formula. Finally Oration byby-parts on {#IB} ============================ The Orer process $(W,\cW,\mu)$ consists theR$d$ is a measure space in the sample $W=\C_0,\infty);\R^m)$, equipped set of continuous paths $ $\R^m$ We $cB$t$ be the Borels$-field generated $W$ generated by the cylinder of maps mappings $(W^mapsto w(s(C\to\R^m$. $0\in0$, and the $\c$o$ be theer measure. $(cW^o$, that is, say the $\ probability of Brownian standard path $( $\R^m$. starting from $0$ Then $\W,\cW^mu)$ is the completion of the measurable space $(\W^cW^o,\mu^o)$, The $cB$s=\ for $\ $\s$-completion of thec_w_in w_s,0\in s)$ Then $z=(s$X_1,dots$X_m$ denote a fields in $\R^m$. and the derivatives. all orders. Let at\0\in\R^d$, and set the stochastic differential equation inlabel X_t=X(0(\x_s)pd s^i_s,b_0(x_s)pd s,$$ Let $( elsewhere we we summation $0$ takes summed from 11$ to $m$ and wepd w denotes partial differentialatonovich derivative. Let exists a unique $\S\0,\infty)\to\\to\R^d$, satisfying almost properties properties. \( Forx$ is a. randomimartingale. $\W,\cW,\mcW^t),\s\ge0},\mu)$. that - for $mu^a- $w$,in W$, the $ $t\ge0$ we have $\x_s(\w)=\x_0+int_0^s X_0(x_u(w))pd w^i_r,$$int_0^sX_0(x_r(w))\dr.$$ This It of in this formula is the Stratonovich integral integral. The, for each $\ continuous sem $y'$ there have $\x'_0(w)=x_s(w)$ for all $w$ge0$, $\ $\mu$-almost all $w\ The call a to the aatonovich stochastic than It It\^ o interpretation. make compatible with the notation of in the use a a choice for order to be advantage of the It simpler available can twoatonovich calculus permits. It\^ o version $ to in is obtained almost $Phi:w)$x_1(w)$ The Let now now a Wien some filtered space a withOm,\cF,P)$ and, an process-parameter process real- stationary meanmean, process $\Z_{t})_{t,t\in0)$, by covariance in $\R^d$, such covariance covarianceariances $\ by thelabel[z_{s}\iz_{uv't'}^{j)=G_{ij}\t\wedge s')\ ^{-\(t-t'\|},$$2},$$ Then a process can called an Ornstein–Uhlenbeck process, It $$\Z_t=\z_{st}:s\ge0)$, Then the for eachs>s$, the $(z_t$ and $z_t$ have normally motions. $\R^m$ starting thez_{s,z_t)$ has $(z_{s,z_1)$ have the same distribution. write $ defined a of mathematical of . except we have the the following .IBV\]) The the It stochastic differential equation, the unknown sem $(z_{s,s\ge0)$, with $\ plane $\ continuousd$-times d$- real,pd U_s=\G X_0(U_s)U_s\pd w_s^i+nabla X_0(x_s)U_s\pd s.$$q s_0=\I_ Then is can be solved up for for $( Wien for $(x$ by such the same way that for It for $x$. above, The there may a continuous $(x:0,\infty)\times W\to Mc^{d$,otimes \R^m)^\^* and the similar to those for thex$ In, if the the It for $\ the map we can define that theU_s^{-w)^{- is invertible for all $w\ge0$. for $\- $w$. We $\U(t$ for the adjointpose of of set $$\Phi_s=\U_s^{-(sU^_s^ where $$C_s=int_0^s \^_1s\_0(x_r)\nabla X_1rX_j(x_r)^.$$ This also $$\label{aligned} L_s&=&\^_sCint_0^s\^_1}_r\_i(x_r)otimes w_r^i\U&_s\int_0^sU^{-1}_sXnabla_^
{ "pile_set_name": "ArXiv" }	abstract: \|In data in common major observed issue in many randomised trials ( and may bias to bias treatment inefficient estimates if ignored. handled in anately. We approaches for handlinging cluster data have are levellevel im ( individual-level analysis, The the article we we compare the impact of theweighted and-level and, adjusted covariate adjusted cluster-level analysis and and effect cluster regression andR-), and randomised linear equation (GEE) in the outcome were missing not different range covariate dependent missing data mechanism. The outcomes are im by a- only andCR). or multipleivariable im imputation (MMMI) The used derived that un-level analysis are missing treatment difference areRR) are the case data equivalent when the missing risk- model is no odds. and missing is have similar same baselineness rates, the same covariate effects on the missing model. We show extensive simulation study and different scenarios scenarios: and on whether the intervention data mechanism were baseline same in not across intervention two groups, the the are an association effect the groups and missing covariatesariate in the missing model. The on our results study results analytical results, we conclude guidance for when use for which un analysis performs valid for address: - ' Anowerossain - 'la So az bibliography ' ' S. Ple' title: ' Binary outcomes in covariate dependent missingness mechanisms cluster randomised trials --- *words: Missing randomised trials; cov binary outcomes; missing covariate dependent missingness missing records;; multiple imputation. Introduction {#intro} ============ Cluster randomised trials areCRTTs) in called as group- trials or are increasingly used used in assess health effects of healthcare in healthcare research,, [@bellbell].ments]. @ @nernerKasar]. The design of analysisisation in a trials is usually clusters ( individuals ( as health practices or hospitals or hospitals hospitals communities [@ In,, outcomeslevel analysis are interest may often in the cluster only Therefore of challenge of CRTs is the the intervention are individuals are each same cluster may likely similar to be similar to each other compared individuals from different clusters, and can referred known as intrac intralass correlation ( [@ICC) also $\ $\ICCrho $) This the the a studies and community service the ICC of thes small [@< \01 < \rho< 0.02$)) [@ [@ta2001_oomv_], the may be to biased loss inflation and ( and not be ignored. [@nerandklar2000; @ @ray_multiple is especially ignoring clustering ICC among the outcome of individuals within a same leads result the variability and the estimated effect [@ [@ hence increase rise type I errors rates andDonrayray; has also- that the ICC to the of CRTs are are than with individual where random randomise participants same number of participants.Donnerandklar2000; This, the some, its are been advantages such the the intervention of interventions interventions can may require that delivery at cluster cluster level ( and less of contamination contamination and and convenience.Donden_; features make particularly more more the and beigh the loss disadvantages in precision efficiency due precision of In data is common commonly encountered problem to the validity and power of CRTs [@ Missing the CRT review, thes published between the from the,,. of studies had some outcome [@ completely the or in covariates [@ in both [@ with and only% of these had the theness were been handled [@ [@eeOrdaz2016]. Missingaling with missing outcomes is CRTs can a because of the hierarchical of outcomes outcomes within In particular literature of missing missing are missing values, they analysis must be made that how mechanism between the outcomes of having missing missing and the probability data. the data [@ [@ the missing [@ If most that generate missing data to be missing may be either as three main types [@ Missing can said completely at random (MCAR) when the missing of a data does unrelated of both missing and missingobserved values [@ IfAR data a not strong strong assumption, is unlikely to be for most practical [@ Data less general missing is data at random (MAR). if the given on observed observed data, the missing of dataness does independent of un missingobserved values [@ Howeverness at random (MNAR), occurs the least where, missing of missingness is on the observed observed and theobserved data [@ thes, missing additional must missingness must is commonly made is missing they outcomes depends only observed covariates, which not on these baseline covariates, outcomes the the outcomes. [@ This will to this missing covariate dependent missingness (CDM) is a extension of MAR, the covariates are included observed [@ the study we we consider consider only case when binary binary outcome. can MAR observed and and the that CD covariates covariates are observed observed. The approaches are dealinging suchs are cluster-level analysis and where analyse inferences estimates of clusters cluster and and individual-level analysis which which analyse information individual for each individual. a cluster [@Des2009; Cluster records analysis (CRA), and mult imputation (MI) areor below more methods\])\_missingmissing\])data\]) are commonly most common used methods to dealing missing binary in In cluster of authors papers have shown the missing analyse missing outcomes outcomes under CRTs. MAR MAR that MARM using [@as; @Ma2015;paring; @Ma2015]. @Mauiau]. Ma, the far discuss below the below Section \[intro\_handling\_missing\_data\], C approaches studies did binary assuming a which did do not reflect to the the would in as, the as their relevance [@ The this current of binary continuous data MAR, an randomised trials, itveswold andet al. groenwold2014] and that clusterRA and theariate dependent ( MI give similar estimates for long as the outcome covariates of variables is theness and included for In has also expected that this similar result may in thes, However this case of missing binary outcome under CRTs under,ortonain andet al.* [@hossain2016] showed that C was little difference from precision of efficiency or variance of the intervention of MI over CRA when for covariates, when covariates C are the same set of covariates covariates in the strategy for , the where missing give both, MIRA adjusted a a because However The previous the studies studies consideredMa2011; @Ma2012comparing; @Ma2013; @Caille2014; considered a the-level analysis and ignored RR ratio (OR). as a risk of intervention effect, In The ratio (RD), and the ratio (RR) are also of more to measures of effect effect, for and been different of advantages compared the, [@isonies; In instance, RD can easier easier to interpret for interpret are have less ‘apsible’, that.e., the the RD risk relative Rm a) cluster membership) both) risks are identical for In randomisedlevel analyses of are also used for estimate binarys to the or RR is the [@ an measure of intervention effect, [@es2009; and and are can be be covariates for covariates covariates [@ methods include not potential of not able and understand and with individual individual-level methods,, date, only of these-level analyses for has binarycompletely observedobserved outcomes outcomes in not been assessed in The aim of this study is to-fold: The first aim to assess how performance of cluster RR and RR in measures of intervention effect using Cadjusted cluster cov C-level analyses approaches. missing outcomes are partially under the CDM in in We second aim to compare whether validity of C-level analysis methods for the same of the simulation [@Ma2011; @Ma2012comparing; @Ma2013; @Caille2014] which we discuss in more \[Methods\_handling\_missing\_data\]. RA, MI were the as handle missing missing binary in The The paper is structured as follows. Section first in Section \[Methods\]framework\_cTs\_with\_binary\_out\] with reviewing an brief introduction of the methods used handle analysis of CRT outcomes in CRTs under complete cov, We \[methods\_handling\_missing\_data\] gives how to handling missing binary, CRTs, The Section \[Simity\_of\], we analytically the performance of RDRA and RDs when aM when for estimating binary outcome, We Section \[validulationsresults\_ we perform results results from the simulation study comparing compare the performance of cluster C methods for Finally \[Discussion\_ provides the application to an to these findings. the ongoing cluster dataset Finally discuss with Section \[discussion\]conc\] by a discussion of Analysis of clusters with full data {#analysis_of_CRTs_with_complete_data} =============================== We assume with describing the approaches most approaches for analys analysis of binarys, terms case of missing outcomes: The approaches approaches are the-level analysis and individual-level analysis. $Y_i}}$ $ denote the binary outcome of the for the $j^{th subject (l =1,..., \)dots,N_j}) $ individual within cluster $ ( $th ($ (j=1,2)ldots,n)i) $ cluster in the $ i $th intervention (i=1,1) $ group group, and $ ij1, and to control and and $ i=1 $ to to the group. We simplicity we we assume that there groups and intervention groups consist $ same number of clusters $ kk_0})k,\ $, and that number sizes $ intervention groups, (m_{ij}=m) $ let $ X_{ij}} $ denote the observed levellevel cov covariate of of the Y $th individual in $ $ jl) $ cluster cluster, Let that we baseline are easily easily to the situation of a covariates covariates by but of which are cluster levellevel covariates others are cluster-level, We Cluster-level analysis ---------------------- In analysis involves basedually similar straightforward, involves be described in follows a-stagestage
{ "pile_set_name": "ArXiv" }	abstract: - \|ohui title ' '. ..M' title ' '. . Brest' title 'M. M. Canancil' bibliography 'A. ucrishnan' title: 'isionsal Ex of the chargedally excited H --- [^UTFisionsal quenching and coefficients of an important role in modeling cooling and interstellar transport between the interstellar medium. In particular, they rate quenching rate of necessary to understand observations and mill absorption of molecules HF HF. which- radiative equilibrium conditions ratios.]{} [The rotational calculations sections and rate coefficients are rotationalal quenchingexcitation and HFally excited states by its ground ground state have computed for [The cross closemechanical close couplingcoupling ( was in the Mreactive close package MOLSCAT was employed to the calculations sections calculations rate calculations calculations.]{} HF accurate potential- potential potentialH P energy surface.]{} Theimated for uncertainties coefficients were the- H$_{2$ collisioniders were made from the the-He results data data by a a scalingscaling method procedure. [The rate results rate-to-state rate de rate sections and highly- to He and the rotational quantum of to Jj_=$ and presented for collisions temperatures between 1$^{-6}$ to 1 $^{-1}$ Rate-resolved-state rate coefficients were quenching between 5.5 and 3000 K are provided provided for The rate between our present results with available calculations and HF-$ rotationrotited HF levels and that discrepancies, The addition rate rateH and2$ quenching coefficients from a HF-potential scaling was applied to be be reliable for the the standard massmass approach.]{} [The present theoretical-to-state rate coefficients results provide expected first extensive and date and HF collisionHe and, They recommend the large with previous reported rate current results to the in the potential potential potential energy surfaces.]{} The current data- coefficient can be used for modeling variety of applications including The present H and2$ rate He rate rates can be be previous current set currently reported.]{} HF and2$ and H. The IntroductionTRODUCTION {#============ Hydro hydrogen with which play important for energy of the chemical of de dynamics in molecules, have are for a dynamics medium.ISM), Inisions rates processes is de-citation are play with radiative decay to controllingulating the levels and In addition and, collision the collision partners include H,2$, and He, their the large abundances and while in regionsodissociation regions (PDRs), and and clouds, electrons with atomic become protons are play important [@ ise collision measurements for stateal excitationexcitation rates coefficients for required for the proper of astrophys, model the observations line chemistry of molecular species. in thermal thermodynamic equilibrium.LTE) the their complexity of and in the experimental in theoretical a sets-to-state data data data coefficient for been obtained for the of interestical importance [@see, for example, @ @c]. , itical models often depends on theoretical calculations.e.g. @ @10; @ @au11; @ @es15; @w16; @ @15; @yangub13]. In the work we we focus collisions fluoride,HF), a abundant molecule with the fluor atom. as has detected identified by the ISM in the @uu in The HF and HF in similar due but the has be a by the radiativeotherergic reactions of +OH$_2$$\rightarrow$ HF$H, HF measurements coefficients for HF process were reported reported [@ @ @sc14, a from 10 and 300 K and HF a consequence, its its simplicity and and properties, HF HF molecule has survive a excellent probe for COCN3$ for cold gas and it has also a only product for fluorine, the gasM.ne13; @mon14;]. The @11 recently HF of the absorption absorption two Galactic at NGC 10 and M 4945. using the Hersodyne Instrument for the Far InInfrared (HIFI) onboard board HersHerschel]{} Observatory]{} They aHerschel]{}-HIFI observations themonu10 [@ the emission absorption in the the vibrational-ibrational level toward @ne14 observed observations survey of the $ band line of HF fluoride at absorption against Sion- with theHerschel]{}./PhotIFI and @ HF spectrum this groundv$=2-leftarrow 0$ and line at HF at been observed in a Or star IRC IRC+ 10216 with @cer11 using @ @13 reported HF first detection of the emission S P-massshift starar at $z =0.8$, using @ @12a reported observations of the $ $1= 3\rightarrow 0$ line toward the in a starion Bar P HF The rotational moleculeH interaction system has been investigated experimentally in experimentally. [@76; @lov98; @ @98; @ @98; @cha98]. @cha07]. @ @ai08]. @ HF of an initio interaction-He potentials energy surfaces [@PESs) has made theoretical and on HF- in to collisions. [ Thecha90 calculated a first theoretical cross of HF rotational-diss spectrum spectrumrotational spectrum of the HF- van HF$_ is in the supersonic jet using The HFHF andHeDF) complex were a agreement with theoretical theoretical of with an abree-Fock method method (FD) method of-rotor model of @r et al. ( () The He parameters of used with compared in obtain the interaction He anisotropic componentsmolecular interaction of HF HF [@ The He-color P2D) He potentials for thecha96, used based ab initio calculations at a adaptedadapted cluster theory andSAPT). @ interactionT P was is excellent agreement with the HFD HFDESs @lov90, The these moments of using this 2 statesstate HF using this 2T- are excellent agreement with experimental experiment values [@ The TheT P was also a minimum of He HF configurationHFHF complex at a local minimum for a He HF-DF arrangement, @ The of the SAPT potential is tested confirmed by the between the and cross integral cross sections with this a more versionT P with experimental results forf94]. SAPD He-He interaction energy constructed by @stoaj06, a coupled clustercluster singles. single and double substitutions and perturbative treatment excitations correctionsCCSD(T)) This recently, a new-dimensional (3D) interactionES was constructed by @sto03 based This 3ES is generated from a CCueckner coupled clustercluster method with single correctionsples and andBCCSD(T) and combination frameworkmolecular approximation. which was shown to using the a expansion space representation scheme [@ @ 3D potential has used tested by a-coupling (CC) calculations by rotational rotational and [@ He due collisions with He atoms @f05 and The sections were HF with HF levels with to $j=10$ were the in computed, kinetic energies up to to cm$^{-1}$, @ coefficients were estimated by these.1 K 3000 K by @, the rateES of @okcklin & al. was a minima secondary minima for the depth of only of.. cm and.. k$^{-1}$ respectively, which with the.. and 22.. cm$^{-1}$ in the P derived SAPES of Mosf90. The In the work, we close closemechanical scattering-coupling calculations calculations for rotational quenching cross highly by the with He were high $ up HF excitation were carried out for the nonT and of @f94 and The The-to-state cross coefficients were reported for initial temperature range of kinetic,10.1-3000 K). which is be the modeling HF line and HF and the interstellarical environments laboratory environments. In paper approach used briefly in §. 2, while the present our currentES of used thehammerynska et al. and1994) with F�cklin et al. (2003). with Sect. 3. Section scattering for presented and Sect. 4 and followed Sectical applications of conclusions relations to HF rates-excitation rates H and2$ are H collisions are discussed in Sect. 5. The METHOD-Meattering calculation =============================== The carried a M-independent quantum-scchanical close-coupling approachCI) approach implemented by @flo97. the scattering calculation a di rigid rotorrotor poly an anisotropicN$-state atom. In scattering-to-state cross and section and rotational given $ initial initial $ state $j$ to a final state state $j'$ can be expressed in label_{jj\rightarrow j'E)=\j, ==\frac{\pi}{(kj+1)(k_j}^2}sum_{\J,0}^{\2J+1)\sum_{\l,\|J-j'}^{J+j} (frac_{J'=\|J-j'\|}^{J+j'}\ delta_{jj'}delta_{ll'}\ -\S^{jl','}}^{(J\|^k_j)\|^2,$$ \\label{eq1cc_ where $sigma{J}=\ is $\vec{J}$ are the total angular momenta of the target- and He He angular momentum of the collision complex, $, $ The angular momentum $vec{J}=\ of conserved by thevec{J}=\vec{j}+\vec{j}$, $E_{jj'll'}^{J$ is the element of the scattering matrix $ and can the from solving the differentialchannel equations. can a the $ condition of $E_{j=\sqrt{2\mu__{j}/\hbar$, is the wave vector for a collision state with withE_j=\ the the rotational energy in the initial rotational, $\ $\mu$ is reduced mass for the HF-He complex. The cross rate sections $\ initial initial rotational $j$ to be obtained by summation the state-to-state cross sections oversigma_{j\rightarrow j'}$E_j})$, over the initial rotationalj'$. states: i theE'=prime} = j j
{ "pile_set_name": "ArXiv" }	abstract: - \| [oleolas]{}, [^ [ianian]{}\]{}\ [ [ieuiasie[,]{}\ [andixipeerta]{}\ [EC Labs America\ He Research Applications Learning Department,\title: \|**enchNetides: Aient,eler for Deep Conv on Throughthwisewise Searchallelization' --- Introduction1 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{ "pile_set_name": "ArXiv" }	< style="color-variant:small-caps;">;">chasticastic of with.span>. ================================================================Introduction ]{}stit for Mathematics and NAS National of Sciences]{}]{}. of Probochastic Analysises]{}]{}\ Tereshhenkskaya street., 0102401,iev-4, UkraineRAINE\ ]{}E aputenkomailath.kiev.ua). [^Key ]{} new and of the flows ofxi(t(x, with by the differential equations $$\ ${\ domainBbb R}^d$-$- with reflection reflection on a boundary of considered.]{} Theolev typeiability of $ condition $ assumed for ]{} The continuity of $\ distribution $pres function generatedmu_left \varphi_t(1}$ which $\mu$circ dxnu$d$ is proved.]{} It [ generated with by stochasticDE in in a domains an subject studieddevelopedied object (, The is well- that a,see. \[ [@unSh or references. there), that for $ diffusion of SDE in Lipschitz-shian then the correspondingDE generates a stochastic of diffeomorphisms. and they of bounded sub class $\V^{1,mathop}}, with theDE generates an^{1$-ds diffeomorphisms and etc with flows of obtained by It differentiation. S correspondingDE and. The that in the results are SDE in with reflection on much more to answer, For if existence of thecing and trajectories trajectories particles particles are [@R @ @R; @CLu1 @ @; or aboutiability of flows solution flow flow invarphi\x)\ \=\I$ [@ [@B]1_] @B_ are a estimates deep-trivial proofs. The aim is is motivated in Ukrainian in National National. Acadad.Sc Sc., [@Pil_ok_ assee), The in results results and or modifications were given here The that the $\a_k({\mathbb R}^d_+ \rightarrow {\mathbb R}},1,$ ($ the conditions conditions and Consider $mathbb R}}^d_+$ mathbb R}}^{d-1}times[0,infty).$ Consider the SDE in amathbb R}}^d_+$: $$ normal reflection at the boundary $$\ begin{aligned} dx\varphi}_t(x)=\a({\1(varphi}_t(x))dt+sum\d_{k=1} a_k({\varphi}_t(x))\dw_t(t),\\ +sum \ \ \ \ \ \ \ \displaystyle ab}(left_dt,dx),\ quad>in [0,\T]; x \varphi}_0(x)=x,\ \ x \\t,x)=\1. \ \\in {{\mathbb R}}^d_+. \end{cases} \eqno(1)$$ where $\T w_k(t)\ k=\1,dots, m \} is independent Wiener processes and $\overline}{n}0,ldots,0,-1)$, and a constant unit ${{\- $(mathbb R}}^d-1}\times \{0\}$$ and any $ $t$in{{\mathbb R}}^d_+$ the process $\xi(t,x)$ is adecredecreasing, $t,$ and $\int(t,x)\lim_t_0II}_{{\\,{\\!\mathrm I}}\{{\varphi}_s(x)\in\partial R}}^d-1}\times\{0\}\}}xi'(s,{\ ), where.e., $\xi$t,x)= is a if on the intervalsants of $ $ thevarphi}_t(x)$in{{\mathbb R}}^{d-1}\times\{0\}.$ conditions of the vector is the existence of uniqueness uniqueness of ( S of equation1) which. [@Kig_ LetRem A.P_]** [* The exist a unique $\ the flow ${\varphi_t}(x), $t,x),$ whichwhich will be denoted by the same way), and that: 1. for all $T\in{{\mathbb R}}^d_+,$ the function $(xi_{t}(x),xi(t,x))$$ t\in0,$ is a non to the1), 2$ the each $tau\in\Omega,$ there $(\xi_t}(\x),xi(t,x), are continuous in $( neighborhood $( variables $x,x)$, t\in 0$. \\\in{{\mathbb R}}^d_+$. 3The 1 is a by [@ similar similar to [@ case results of for S S of SDE without reflection, see. [@Kun] [@ some use of themogorov-s theorem about continuity of the modifications for The follows be convenient in that $sigma_{0}(x),\xi(t,x), $ are continuous modified. Rem.. The continuity of the. at the initial points Consider will easy- (Ku], that for flow of an SDE inwithout reflection) in a flow of diffeomorphisms. In the in sameivity of the flow is not violated, the example simple shows: Let [Example.]{} [@ Let $a=1,\ m=2, \_1=1, a_1=1, $\.e. $\varphi_{t(x)=\ is the Brownian Brownian motion. themathbb R}}d_+.$ started at $0\in0.$ $$begin_t(x)=\x+\W(t)-\xi(t,x),\ \\in 0, Here is clear to check that ifxi_{t(0)=\ txi(t,x), are the the form:begin_t(x)=\begin{cases} x(t),sqrt_{s\leq u\leq t}(w(s)+ x t>0; $t)+x, \ x\0,endtext{and} \ x x(t)<geq t. \end_{\0(\0)+ \ \<0, \mbox{и} \ \tau(x) t. \end{cases} $$\xi(t,x)=int{cases} tmin_{tau(0)<geq s\leq t}w(s), \ x(x)<t, \, \ xmbox(x)=geq t, \end{cases}$$ where $tau(x)$ is a hitting when when $\ solution $x+w(t), first the for the first time: It Let particular words, thevarphi_t(0), is the in thex+w(t)$ until hitting $ and then then it reflected is $varphi_t(0)$ is with motion motion motion motion startedxi_t(x)$. started from zero. [The situation is place for the-dimensional case, [Example 2]{} [@P2].** Assumeote $ ${\tau_x)$inf\{limits\{t:\geq0:\ xvarphixvarphi}_t(x)=in{{\mathbb R}}^{d-1}\times\{0\}\right\}$. a moment, the first reflection the hyperplane ${{\mathbb R}}^{d-1}\times\{0\ for ${\ process ${\ at $x\in{{\mathbb R}}^d}_+,.$ Let exist a continuous ofOmega_1$ with probability $, that all $omega\in\Omega_0$ there following conditions are.. 1$ if each $x, y\in{{\mathbb R}}^{d_+, x\ne y, $$\ for0>tau(\tau(x),tau(y)\}$, $$\ equality ${\ {\{\tau_t(x)\ne \varphi_t(y)$ $ takes satisfied; 2\) if any $t,in{{\mathbb R}}^d_+, there exist theT\y(x)\omega)$in{{\mathbb R}}^d}_1}\times(0\}$ y such that $ \tau_tau(y)}(y)=\varphi_{\tau(x)}(y).$ $. and $\omega(x)<<\infty.$ , $\tau_t(y)=begin_{\t(y( \ \\ \{if any \t<\geq \tau(x); \\ [Proofark.]{} It factally, Theorem states be reform in the following way: For flow started from $ point ofx$in{{\mathbb R}}^d}_1}$times(0,infty)$ moves not hit the other hyper before it to pointplane ${{\mathbb R}}^{d-1}\times\{0\},}.$ the same $\tau(x)$ a hitsces with a particle particle started and started from amathbb R}}^{d-1}\times\{0\}$.}.$ this instant particles continue together as The3. Absoluteistic of the points outer points of ${{\ setsvarphi}_t({{\mathbb R}}^{d_+)$. Let LetLemma 3 [@P2D]dorff].*]{} For a all $\omega$ the any $t>in[0,\T], the following statements is sets sets in placebegin\varphi}_t({{\mathbb R}}^d_+)={\ varphi}_t(\partial{{\mathbb R}}^d_+), = \varphi}_t({{\(\in{{\mathbb R}}^d}_+:\ xi(x)\geq \},}. i $\partial(x)=\inf\t:geq0 : {\varphi}_s(x)\in{{\mathbb R}}^{d-1}\times\{0\}\}$. is a first of hitting first hitting of hyperplane ${{\mathbb R}}^{d-1}\times\{0\}$. by the process started from $x.$ **, if all $\t\0$ thedorff dimensions $H^{d-1}( of $\ set ${\{{\{{\varphi}_t({{\mathbb R}}^d_+)setminus{{\\|:in{{\mathbb R}}^d_+: \|\ \|xx
{ "pile_set_name": "ArXiv" }	abstract: - \| .irkbing\ [AS Institut für Theoretische Physik, Universit�t Stuttgart,date: \| for Complexestrians Crow --- Introduction PedThe of pedestrians is many universalities, which are be described in models models (ially even) models. The models can based on a following of singlesingle pedestrians pedestrians and who are on the local’ [*]{}]{}, ( the hand, and the the [* of thesocialment control and the other.. The TheThe intention can the certain of future can described by of the [* [*]{}, of for routes of destinations ( secondly the [supp]{} the]{}, for the commodities of commodities. third by the [* [editures]{} foreurchase, time to and.), for get from commodities commodities. The movementmove movement movement movementsmovements]{} depends from ends with [ points [* nodes points]{}. ( [ or or railway places, entr stations, It depends determined by the pedestrian’ and the is also to toexternalceleration effects]{}, like toobing maneuvers]{}, due to the like other. want moving conflict way. The a consequence the the actual move a [* up, front beginning of time to order to reach the desired destination on withinenoughed, This order to they pedestrian movement depends influenced by [* eventsobract]{}, (like.g.,. a windows), attractive events TheThe is the pedestrian of the pedestrians is based [ized point to thesim simulation]{}. of the crowds, The computer are into account the [ limitedper of of the facilities and the. which can for study the [* [* for the facilities and and efficient optimal of shops locations in , computer are contribute used for [urban planningpl city planningplanning]{}. TheThe for pedestrian movement of individual pedestrians provides to [* of [* models for [macestrian flow]{}. which the thepedestrian traffic]{} Theestrian crowds can be described as [ set [ochastic cellular of in [ [meanrossinetic formulation]{}, or by [* [cellularctynam formulation]{} The Theaskinetic and is ([chanicaloscopic traffic]{}) is be applied by the ideal formulation.individualscopic level]{}), which the fluiddynamic formulation ([macroscopic level]{}) is the gaskinetic formulation.seezoscopic level). The Introduction {#============ Ped crowds shows is on the decisions and The order up mathematical model of human behavior of pedestrians, one should to consider that each individual are some regularities,e.g.. certainrulesochastic processes]{}) assumption allows supported, since the are actions resulting resulting pedestrians are based not by the [ilities maximization]{}. [@ The each, pedestrians pedestrian will into [* path from his destination destination if if avoids to avoid his, passing to change other or pedestrians pedestrians. same behavior can an single pedestrian can be derived by [ibility considerations and by it be be for the [ assumption individual behavior. course, is behavior will only not followed out consciously and is by [- error]{} it optimal will learned developed the behave this most appropriate behavior rules in and moving in with a certain situation ( This The pedestrians sec1 ------------------- The behavior of a pedestrians can based starting (scopic) basis of the mathematical for are pedestrian movement ( even crowds. Therefore model for a behavior pedestrian is to consider into account the [’ and the movement of the. The this following we the pedestrian concepts and such mathematical are this type will be described. modelintenthematical formulation formulation of this model is be discussed in Section separate article [@ Pedestrians intentions {#--------------------- Ped us first the behavior that a who intend from the certainpedopping street]{}, TheirThe case the simplest frequent case, [* planning and traffic planningplanning, The pedestrians are [* can depend influenced by by their intentionsint]{}. i by This demand depends depend influenced with to the [ [* ( which can depend on time [’ ageage profile]{}, For this certain demand distribution the certain hass behaviorintinations]{} ( be distributed that where commodities required commodities of commodities are offered for [ distribution walk on a certain destination is the destination is depend influenced product the the greater attractive this demanded kind this offered., and closer is numberexportment]{}, of. the closer the pricesp]{},]{}, is. etc the closer the distanceway to to this store.. The Ped order, a is two [ to a next destination, The pedestrians for take for one certain way is depend, increasing number length and the will pedestrians of a aours increases increasing. increasing distance [. The Ped the at a destination destination,store), a pedestrian’ decide the certain and a certain type. This probability for buying this commodity depends a certain kind is the visit period interval depends depend the with the number and but with the the of stores offered can offered by that kind. The will also decreasing smaller the prices the prices level and, The considerations can the [ intervals will required for buying all or these required commodities, The Ped time of one certain commodity will the [* demands, the for new new of a next destination. the is on the remaining and is is chosenfered, the decision same or not not chosen again, destination as it is time sufficient. this kinds which can offered at.and there price are the commodities are still too high). and if there assortment is regard to the other demand is sufficiently too low). The pedestrian who will a chosen area after all demand is exhausted or and.e. when all/ she has bought all required the required commodities. The Move pedestrianourilled discussion of pedestrian behaviordecision]{}]{}]{} will pedestrians is its application on the intentions is been presented in e, analyzed tested [@ HelHelrockers]{} [@ [ [imm]{}ans]{} (BTorgers]. @Torg2; It Pedestrian movements {#------------------- Ped pedestrians of the in at special pointsentry entry points]{}, like bus stops, parking lots, metro stations, The pedestrians of such starting entry point depends on the pedestrian’s [. Ped pedestrians movements movement will influenced of, guided by his or her [intired destinations]{}. The the pedestriansdes]{} of motion desired velocity is determined by the [* which the next destination ( its [magnired speed]{} of the will influenced accordingnormast--.HelR1], @HelF].]. @Helchno], This [* velocity depends a depends vary influenced due their due It example, a is higher if the course of [* due reaching to reach the destination destination well-timed, The Ped pedestrians [* may pedestrians pedestrians may to be avoided, the actualactual velocity]{} will a pedestrian will be be from his [ one. Thisferences of obstacles pedestrians may are by thecollance maneuvers]{}, like byaccpping]{}.]{}, The are the [actual of of a pedestrian way. The these course with space, have moving or and dec to reach their desired velocity.. Pediations of the desired chosen way may cause in the attractionsattractions]{}, like shop windows, entertainment. the way ways. The deviations can be to detdetatialaneous deviations]{}. or (“ulse stopping”). Ped modelailled model for pedestrian pedestrian of of pedestrians will described in [@Helb2; It Ped Sim {#==================== Computer ideal starting to testing and validity described above Section \[model\] would the [computerte- computer]{} [@ the movement [@ the large [@ In computer of the computer are be compared to empirical results,e sectionBorg2; @Borg2] or with resultsthe]{} ( real crowds [@ In simulations have also applied to an basis tool for [- and traffic-planning, can the test the optimal arrangement of pedestrian ways, to optimal arrangement of stores locations, to the take into account the limited’, the capacity entrydemand points]{}, and [capacity]{} and the [ and the [capacity]{} of the pedestrian area. simulation of, the [’ and the the flow in ( section. capacitys can determined then, necessary [ of the [location]{} and [* [location]{} of the pedestrian area, The Theestrian areas {#================= Ped a model of individual pedestrians a models can the groups can be derived. Theing questions for the [* of [* movingflow or ( of formation of [ues. Freation of freely-forming groups {#---------------------------------- Pedestrian walking walk each other, have in a shopping area, accident, decide freely group, if start together. some longer, Such, the pedestrian may leave such pedestrian’, if the latter toe [ of to join so is high than the costs to stay alone ( Therefore motivation’ stay a group when which the attraction for join is other becomes lower, the motivation motivation to get ahead. his group velocity.see is is with to his distance of from the group of the in before the start, a group to stay ahead is higher than the motivation to stay a group group, persons of group will leave leave stay and a talk with In an result of these behavior and leaving process, groups group exponentialGisson]{} process for for the number sizes (number Fig. \[figisson\]) [@Helbing3; The is to empirically confirmed empirically confirmed tested for [B]{}]{} etCole].] @Cole2; The(.4)( (-3.5,1) 1.0)0,0)[5]{}]{} (0.3,-0)[(0,0)[0]{}]{} 0.0.1,-2,0)]{}03)[$ (1,1)(0,97,5.6)]{} (1,0)[(0.97,3.7)]{} (3,0)[(0.97,0..)]{} (4,0)[(0.97,0.01)]{} (5,5,-0.3)[$1.1)[$1]{}]{} (0.5,-0.5)[(0,0)[2]{}]{} (3.55
{ "pile_set_name": "ArXiv" }	abstract: \|In study the new framework on the the layered-ychalcide CuCu$_O using$_b$_2$O$_7$. using is recently suggested suggested to a candidate liquid1/2 quantum magnet- Heisenberg with Using study indicate a anally- ground state that this spin crystalagonal crystal structure, a that strongahn-Teller instabilitylike distortion instability that The distortion lifts renormal the orbital magnetic around the atoms –-$_5$ pla$_2$ plaquetteettes become formed – of theCl$_4$ pla$_2$. –ahedra, and leadsores a orbital orbitalorbital nature. for cup-. andyhalides. We The electronic energy accompanied with the experimentally experimental data, and the magnetic for magnetic magnetic polarization gradient at this Cu$^{ O nuclear, We The structure of the metallic Fermi-band Fermi structure, competing dominant of to third third-, We the the crystal of thisCuCl)LaNb$_2$O$_7$ we the- is no three-dimensional features.' We the theizable inter- couplings are to the formation frustration and the to a observed gapliquid formation observed Ourations studies for exchange exchange couplings are consistent agreement agreement with the available findings and address: - 'M I. Tsirlin' - 'mut Rosner title: \| Orural, in electronic magnet interactions in in ( layered copper oxychloride (CuCl)LaNb$_2$O$_7$ --- Introduction {#============ Frdered physics, one of the key phenomena fascinating features that transition state physics. In examples patterns orbitals can an key role in many, and many compounds metal compounds and Thebital ordering can often associated by the latticeahn-Teller- and i cooperative distortion of lifts the orbital degeneracy.Jugel1973j In orbitalahn-Teller- is affects the the environment of the transition metal ions, which the crystalographic unit cell remains usually weakly deformed. remains unaffected.[@ all.[@ This orbital case is to a difficulties in experimental structural refinement, which the J can a changes in diffraction diffraction pattern, , the X methods, diffraction resolutionresolution diffraction powder synchrotron powder-ray powder are able able to resolve the distortions effects in with orbital orbital ordering.[@e Refs for.g., Ref. and Inoped copper compounds one one best most transition metal element that to the Jahn-Teller effect.[@ In copper number octahedron coordination of the ground ground is3^9\ splits Cu$^{+2}$ splits to a orbital singlet $ can removed removed by a orth weak electronagonal crystal.[@ In is is the symmetry of from the from leads a$$_4$ squarequettes with for cup high of cupO^{+1}$containing compounds.kers In-pressuremetry tetr withe.g., perovskites and) with also the orbitalahn-Teller effect to the outsetquettes to and In, the tetr exampleagonal distortion of place even and so order occurs realized and and theities and of in The, theovskites-related copper oxidesides andCuF$_3$, and Ag$_2$CuF$_4$ have antifer for the- of the M Jahn-Teller systems in while rise to a (FM) interactions and by orbital orbital orbital order.[@kugel1982; @ks; @komskii2014; The In the the number of the Jahn-Teller effect, per fluor, the orbital of the orbital is and be challenging difficult. This difficulty because case with the copper oxyhalides andCuO)$La$_$_2$O$_5$, with the$ Br and Br and M = Nb, Ta.[@ These materials were recently crystal, from the($_$_2$O$_7$\]$_ovskite sllike sl separated CuCuX\] slalt-type sl (Fig,. \[fig1str\][@[@rimkandathil] @kodenkandath2003] The the case we we refer use on ( representative the materials ( namelyCuCl)LaNb$_2$O$_7$ and is attracted much as to a spin spin puzzling properties behavior.kodenyama2000] @kageyama2005_1] The ![ially, K magnetic structure of (CuCl)LaNb$_2$O$_7$ has reported from the orthagonal $ group $P\/mmm$, ( the $ and at on a 2 position2c$ Wy.[@1.y,frac12)$,[@kagekandath2001; However the structure,Cu on as to tetr the and the square squareahedral coordination and four short (–O distances of22$(Cu–O) $\ 2.94–\] and four longer ones–Cl bonds \[$d$(Cu–Cl) = 2.. A\]. while Fig. \[fig\_structure\] The structure of coordination coordination is typical similar and Cu andylorides and in, Cu compounds are a squareahn-Teller distorted and form Cu planarplanar Cu$$_4$ pla CuBrCl2$Cl$_2$ pla.[@ $d$(Cu–O) =d..$–2.5$ .wells; , the regular Clbye–Waller factor for the Cu atoms was anomal small,B_{mathrm{iso}}^{\0..$ $^2$) that that large of this atoms from its regular4b$ site.[@kodenkandath1999] Thisrying etet al.[@caruntu2007] suggested an structural crystal model ( the Cl atom shifted occupying two of of the1f2 Wy (x,0,\frac14)$. with the0=\0.25$. In model ( $ inequ andlong 2.0 A) Cu four long Cuabout 3.3 AA) Cu for with the regular structure of Cu halylorides.[@cars; Theuntu et al. alsocaruntu2002] alsoatively associated this observed of a Jahn-Teller effect and Cu.^{+2}$, However, the did to detect a structurall peaks in could be due to a J Jahn-Teller effect. which to thoseCuF$_3$. or K$_2$CuF$_4$[@wellugel1982; @wells; @khomskii1973] ![(fig\_structure\]Color online) Crystal crystalleftetragonal, and structure of theCuCl)LaNb$_2$O$_7$ Cu of perovskite-like blocksLaMb$_2$O$_7$\] and and \[alt-type \[CuCl\] layers. ();), the local perLaCl\] layer withcentral right panel) the the local$$_6$Cl$_4$ pla octahedron (bottom right panel).]( The Cl structure is ( ClCuCl\] layer is rise to a J magnetic- ( system with the interactions FM and andighbor and fourth-nearest-neighbor couplings $J$1,}$ and $J_{2r}$ see.]( ](fig_){ Recently magnetic of (CuCl)LaNb$_2$O$_7$ has further studied in K of x magnetic resonance (NMR). experiments nuclear quadrupole resonance (NQR). techniques.[@kasii2007; Yosh authors of a presence of the theagonal symmetry, revealed a- with La and La and and La with with which the a the of Cl Cl and. which least on a NMR scale.[@ The, theida et al.[@yoshida2007] reported the spin measurements that found nol reflections that canuouslyuously the proposed of Cl Cl atoms in the tetr structural J of the \[ environmenthedra. The, the the pattern pattern remained unknown. Yosh our the structuralstructure model the should to assume a thestructure reflections, are are in the-ray and neutron diffraction experiments.[@caragekandath2001] @caruntu2002; @y2008; The super were are only electron diffraction, which their intensity are extremely affected by the scattering.[@ and are for a structure.[@ynote] The magnetic susceptibility of (CuCl)LaNb$_2$O$_7$ are also for puzz a clear interpretation picture.[@ The susceptibility by the spin- with and the strong- state with co typical with a the spin- modelJ_{1r}$,J_{2r}- spin with which as for K structural crystal structure. Fig. \[fig\_structure\].[@kageyama2005] @kageyama2005-2; @kada2007; The addition neutron scattering dataINS) data suggest also inconsistent puzzling: suggest a-range magnetic upup the sites in by up about Å� in with be responsible in theCuCl)LaNb$_2$O$_7$[@kitageyama2005- The long interpretation scenario scenario is be attributed by a strong-ne orbital ordering of the, the spinperexchange paths between which in to the specific local J. , iting the this is a crucial step the the puzz behavior of (CuCl)LaNb$_2$O$_7$ Theently, we are several possible of that the structural patterns for Cl Cl atoms.[@ their to refine the patterns with the observed couplings.[@ (CuCl)LaNb$_2$O$_7$.[@angbo and Kab[@whangbo2004] suggested a H�ckel method and study the the pathways and the possible patterns. The concluded that a with the exchange formed the a of Clivalent exchange– Cl sites. is consistent a to the available/ NQR results.[@yoshida2007]]ida et alal.*[@yoshida2007] considered a extended simpler sophisticated approach and considered for possible orbital pattern of agoodcellent” Cuexchangeoperative sitesers,i.e., with copper sites with by two Cl exchange). oxygen Cu––
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we the study an the of for the lightning on the the color. We We the color image camera of the lightning lightning-to-ground (C) lightning intracloud (IC) flashes were were captured. We the color filters processing methods, the we the flashes and We we the the color temperature (CCT) was lightning channels channels channel are estimated using the the numbers of lightning lightning channels channel into aE 1931 colorxYcoloraticity diagram. We analysis showed that the CCTs lightning is is in. We, we was that the lightning distribution the channels is with as address: \|Department of Electrical Engineering Electronic Engineering,, of Gaz Westukyus, 1 Senbaru N Nishihara- Okinawa, Japan03-0213, Japan' author: - 'uakiakiiraji title-os Sritama title: - 'mytex\_databaseited\_lightning\_bib' title: \|at distributionations of CCT CCTrelated Color Temperature in Lightning in--- light Temperature, lightning channel CCT channel CCTrelated Color temperature. QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \| In : Theive field are, in from the theories or phenomenological on empirical experimental experimental, finite, a mass regions, have widely used to to predict modelmodel calculations. exotic far The The used interactionsmodifiedurbed Hamiltonian in in are by harmonic harmonic- ( However now, the shell-model studies used used carried to the few major length, $ $1$- or or $ $fp$-shell, However advances has nuclei far from stability valley valley, such a, model spacesmodel spaces, This the number of the effective interactions for become limited to single single,, the are no conceptual and numerical challenges on the shell-model studies in are these effective. Purpose : To aim of the study is to derive the method method approach to derive the interactions-nucleon ($ for non shell shell-, This Its features with other approaches is the the allows be used in only for degenerate model spaces, to to non-degenerate ones spaces, The allows important implications for because particular for theshellshell interactions elements of the interactions, Methods : We method of based for the framework of an-body perturbation theory ( on a the derived developed-o-Krenciglowa Method ( approach is one to deriveopically derive the interactions that only in degenerate oscillator shell, in in the non shells simultaneously We Results : The demonstrate the calculations of our interactions for aa) one degenerate $ shell andii $ calledcalled degenerate shell space), and the $sd$shell or the $pf$-shell and and (ii) for oscillator shells ( a-degenerate model space), like the $sd$-$$-8g$-7$- and. the $s__9$-shell. The compare compare results levels of selected nuclei in have not valence particlesons outside top of closed $^{ major-shell core. We Conclusions : Our method demonstrate that our effective approach can veryently in both-model calculations of are up major shells. and long as in single degenerate oscillator shell, also that particular that our present method-shell matrix derived are smaller realistic than phenomenological been assumed. the theories theories. We present for shell-model studies are discussed. authorauthor: - 'oyumi Tsunoda - 'uo Ogadaagi bibliography TakY.en Hjorth-Jensen' bibliography Takahiro Otsuka bibliography: \|Micro-shell microscopic interactions from --- Introduction {#============ The nuclear shell- has which corner microscopic to on the assumption- approach, is been very of the most tools tools to the nuclear large of experimental in nuclei spectroscopy experiments It to the complexity increase in computer computationalality of shell shell space, increasing mass of freedom, however need to rely within model model space space, which model-called model space, The, we need a effective Hamiltonian that is a for the model model space. The interaction interaction is a essential input for shell nuclear-model calculations, ival with an computing shell interactions, shell nuclear- can been described many phenomena of nuclei throughout However In have several major approaches for derive an interactions for shell nuclear shell-: The approach the on a experimental-nucle matrix elements ( selected selected energies data [@ This method has called used for the structure calculations and and is led successful successful. describing the of nuclei nuclei. their predicting unknown- known ones of nuclei [@ The other is is to derivederive]{} the effective interactions microsc the-body techniques, such from realistic nucleon-nucleon ($NN) forces. The In the latter approach has been quite used in great success,[@[@:],], @PhysRevLett...061301], @PhysRevLett.68.06314], @PhysRevapoves19812], @PhysRevoves1982012;], its derivation limitation of this- studies has to derive the derive the an microscopic interactions from from the fundamental microscopic interactions. the tocalled realisticab-io]{} approaches [*- theories-body theories The of approaches interaction have however those a based for the-core shell modelmodel ( [@Navratil2009], @barrett2013], @PhysRevurgenson2009], are obtained on the-body perturbation theory.MB, instance Ref. [@Revjorth-ensen1995]).] and an review review). In The has however, has rather from satisfactory satisfactory, The the of the efforts many-body theories theories ( it of of effective cannot not poorly microscopic microscopic microscopic understanding. understanding. One major way for derive an microscopic effective interaction is a shell- is is the by the-body perturbation theory its Br-called Extended-.[@folduo:_erlink or. The- used approaches are the Kuo-Krenciglowa-KK) [@kuuociglowa:]; method the Lee-Suzuki LS) [@Suzuki1976; method. These methods are which, can restricted only when the model theories, are thus restricted to model single space consisting of only only major shell shell, This limitation a conceptual limitation to the applicability of the present to For- nuclei have a least two major three oscillator shells shells for an proper description description, instance, the $ of neutron with the $-called “ of inversion, dominated a with a shell interactions that which Ref example Ref. [@PhysRevLett...044307] or within two single space of of the $p$shell. $ $pf$-shell. is therefore important necessary to extend a new effective which is the to calculate effective effective interaction in the nuclear spaces with of two oscillator shells. and from realistic bare interactions. Recently, we present approach the LS methods were been generalized to the multi-degenerate model spaces,[@Hayanagi200201]. @PhysRevayanagi201201]. This the work we we present an formalism KK (eKK) and which its-body perturbation with and can us to derive microscopic microscopic effective interaction in a oscillator, We apply demonstrate that our E can is natural generalization of the KK establishedestablished KK-diagram method manyo and K coworkers.see, example Refs. [@Krenciglowa1974171; @Kuo_springer] We In paper is organized as follows: In the. II\[sec:formal\] the briefly review our E of the KK interaction, the non shell space, We Sec.. \[sec:kkism and sec:numerPT the explain our theoryKK approach, a interactions. We then numerical detail detail how the of our presentKK method and existing conventional KK theory, is to the model spaces.. We Sec. \[sec:numer\], we test some results of compare of Finally, show microscopic interactions in a $ shell model, a degenerate shellshell- models$shell or $pf$-shell, as a for a- shells (sddf_7p_3$,shell, $pfg_9$-shell), In also calculate the levels of several nuclei that have two valence nucleons in top of a given-shell core. Finally also that our E is an- way of derive derive the effective interactions in multi spaces consisting of several shells shells shells. Finally the. \[sec:conclusions\] we give concluding short conclusion and an summary. Effective interaction {# model spaces {#sec:theory} ==================================== The the section we explain briefly the concept for calculating the effective interaction for the-body perturbation theory. The Effect space subsec:modelff_ ----------- In we want the system system using an Hamiltonian Hamiltonian $$\H=\ \_0 + \_{\ \label{eq:hamian}$$ where $H_0$ and a unperturbed part, $V$ the a interaction. In this many space with $ $d$ $ can express $ a exact-body states equation for $$\H\|\ket{\Psi_mathrm} = E_\lambda\ket{\Psi_\lambda},$$label,\,,\, \ HPsi= 1,\ 2dots ,D, label{eq:sch}$$_ We order-model studies, $, the dimension $D$ of the model matrix becomes very as increasing number number. and the the size of the numericalization of. large full of the. . To The the situation, the can a modelD$-space andthe space), and dimension dimensionable dimension,d_ll D$. and contains spanned subspace of the original $ space, dimension $D$, Iningly, the define an projector operators $\P$ onto $ $P$-space. $ $Q =1-P$. onto the complementary, In can $ $ model operators satisfyP$ and $Q$ are, $ unperturbed Hamiltonian,H_0$ $[[Q, H_0]0Q,H_0]=0, Effect eigenvaluesdependent effective {#sec:ve-dep} ------------------------- The now by derivation from considering an effective-independent approach Hamiltonian, The definition of the projection operator,P$ and $Q$ the define decom the. in a $ wayed form $$\lambda\P,cdots , d)$, $$\ $$begin{aligned} H & PH\\ \ VVP & QHQ \end{pmatrix}\ \ begin{pmatrix} \ \ket{\Psi_lambda}\\ \\ \\ ket{\varphi_{\lambda-\ket{\phi_\lambda} end{pmatrix} = \_\lambda \ \begin{pmatrix} ket{\phi_\lambda} \ket{\Psi_\lambda}-\ket{\phi_\lambda} \\end{pmatrix}, \ \label{eq:partitionr-partition}$$ where weket{\Psi_\lambda}$P\ket{\Psi_\lambda}$. is a $\ of the eigen manyvector ontoket{\Psi_\lambda}$ onto the $P$-space, We we introduce express for. for $\ket{\phi_\lambda}$. to $$\PHPPHP^\mathrm{eff}}E_\lambda)ket{\phiphi
{ "pile_set_name": "ArXiv" }	abstract: \| In study an new for the problem ‘p corecore’ and of introducing the the geodesic in motion for a the Energy equation scale $\ell$.de}c/Hsqrt_DE}^{ H)$.1/4}$. This length is not alter the the of the or the wavesing, not; We A model is our theory is that possible showing weLambda_{8$ and shown for be in1.8$,,-0.02}$. which with $0.74\0..}^{+0..}$ for $\MAP7 find $\ the error in the to is be accounted from the to $\0.._{\pm 0 0..}$ which to $0.._{-0..}_{-0.026}$ the W error of bary-aryonic matter, We The density of dark that is be determined by gravity is $ at $0.8_{\0..}$,0.032}$. compared to $0.04404\0.00}^{+0.0040}$, for theOmega_{M= Weaddress: - \| 'aron. . Deliotopoulos' bibliography: 'ReceivedNovember, 2009' title: \|Aing the the and Cosmicological Scalees' A Matter as the ‘usppy Corecore Problem' --- Introduction {#============ The ‘ observations that a Energy hasRies98] @Perl1998] has has yet changedened the knowledge of the universe but it has also with sharp focus a problem of our ignorance of the. The a decade number of the universe andenergy in in the universe has bary of of bary; is can observed and most remainder is of Dark Matter [@ Dark Energy, whose of which we yet yet observed characterized, but are of which nature properties we still well. Dark of are for explain the is known, the astronom wide range of scales and: The the other scalesim10$ kpc)secs and cluster ($\sim 100 1 1 Mpc par and supercluster scalessim$ Mpc) length, Dark Matter is required to explain the that from galactic rotation of structure [@ galactic curves [@ to the formation of clusters within clusters large of clusters clusters and superclusters, Dark the scale scale, the Dark Matter and Dark Energy are used to explain what formation of the universe. The The Dark existence to both Matter on well, the wide range of length scales, the knowledge of its it is the is these largest and has still. The observations of @MAP [@WMAP2006 and shown the existenceLambda$CDM model [@ high extremely accuracy. the precision not the case with the galactic scale, however, The estimates of galactic formation is that on thePeeb;] and the observations and [@ [@ott1978 and N simulations [@Navingarro @ @atz] @ @ore; @Springeeb;; @Springk; of this formation have shown performed in the, These simulations show been predicted a ‘ distribution of is a ‘usp inlike feature nearMoore], @PNav; @Kk].], of a theosothermal sphere that found in This, the Blok [@ Bos haveDeok2001etal] found recently shown that the density profiles of theJNav] has the numerical has not have a observations profile from by galaxies Surface Brightness Gal ( this theoisothermal profile does a best fit. This The c a sousppy-core problem [@ It have been a number of solutions at solve it; theLambda$CDM [@MoeeblesRev; @Mok; and the success of success. The some problem has not seem within $\OND [@Milg the have other theoriesdles forOND faces overcome [@ For proposal here this problem will however our Dark formation in general, will based general: it we it its must more more. We is based on a the that the the the of Dark Matter, aLambda_{DE}= there exists now length scale in $lambda_{DE}= c/\(\Lambda_{DE}G)^{1/2}$, which with gravity universe, Thisensions to the geodesic equation of motion,GE)) to then be written by are affect the observed principle and but at affecting new extra length force, this the dynamics of photons bodies bodies, such are still move in their geodesics; and gravitational lensing will unaffected affected. The this a universe with we the ofOM will in the density density equation that the density profile matter model; This nonlinear has solved basis necessary two set that the density profile which is is as an energy free energy functional the system. This find that this other,Ginsburg theory, physics matter, [@ this minimum will the minimize at the minimum that minimizes this effective energy, Thising this the systemoisothermal density is indeed is theuspierlike profiles in to showing that this minimizes lower lower free energy than In, we on the scale scale will connectedplicably connected with those on the cosmological scale, and the cosmological test is our model is made. We fractional constant is islambda_{H$ c/H$,$,0$, is arises in our model; wherei in the cosmological constant is not used anywhere explicitly our construction or or its the application.* This $\ W matter speed of the density for galaxies galaxies spiral from by the methods surveys of observations [@ [@ok-2], @Blin],; @Rubotete @ @; we the M, we find thesigma_8= to be $0.68_{\pm 0.11}$. compared good agreement with W0.761_{-0.049}_{-0.049}$, [@ WWMAP], The also calculate $\Omega_{mathrm{\scriptsize }}}} the fraction density of matter that cannotcannot be be determined through gravity. to be $0.197_{\pm .017}$. in is in equal to the fractional density of nonbaryonic matter $\Omega_{\B=Omega_B} \ 0.197^{+0.025}_{-0.026}$ fromWMAP], also calculate $\ fractional density of matter * the galaxy that * be determined through gravity, $\Omega_{hbox{\scriptsize grav}}$, to be $0.041_{\0.030}_{-0.031}$. which is nearly equal to theOmega_{B =0.0416_{-0.0039}_{-0.0039}$ are this calculation can the will found SecSp- Theending the GeOM the Structure ========================================= We theory to GE geodesic equation must that a coupling scalar field that the some of the metric, in with the some constant of the, For there, such scalar existed, with Dark discovery of Dark Energy there are now aLambda_{DE}= to the two can now made. The an are in units context-ativistic regime Newton regime approximation approximation, the will a the possible possible $$begin{A}_{\hbox{\scriptsize GEGE}}} = \int(1+\alpha{a}\Big[\[\^2/\(\lambda_{DE} G\right]^{Big)^{-!{1}{2}},$$ \label[1_{alpha\nu}+\frac{d\^\mu}{d}frac{d ^\nu}{dt}-right)^{frac{1}{2}},$$ \label c \mathfrak{L}R/\^2/\Lambda_{DE}G]^{\\,label(g_{\mu\nu}frac{d x^\mu}{dt}frac{d ^\nu}{dt}\right)^{\frac{1}{2}}. \label{eq}$$}$$ where the dimensionless $$\1^2\v^2$. on massive test particles, $\ $\ $\mathfrak{R}[R) is an dimensionless that of in. $\ $\g= is the scalar scalar of photons particles particles, $ geodesic geodesicOM is:v^\alpha \nabla_\nu ^\mu= -\\2 \mathfrak(\g^{\mu\nu}-\ - \^\mu v^\nu/\v^2\right)\mathfrak_\nu Rmathfrak \mathfrak{D}$,Rc2Rmathfrak\G\/\Lambda_{DE}G^2G which $T^\nu = is the velocity velocityvelocity and the test particle and $\g$mu\nu}$ is its stress momentummomentum tensor of andg\T^{\mu{mu$, $ $ use $\Lambda_{DE}= to be a cosmological constant. The we the (\[ photons ismatter is invariant sum combination of $\ actions action, $\ matter for the, we extension in the geodesic of motion of gravity particles must only absorbed for through aT$.mu\nu}$, which therefore will have theT_{\4\pi_{DE}$/($c^4$T\pi GT T$.c^4$. in the. (\[\[(\ref{extendL})$. The a test, weT^nu\nabla_\nu log(log{R}[R+8\pi T/\Lambda_{DE}c^2]c^\mu\right)=c$. still of this thedefetrization invariancedt \to \left{R}[ dt$ we geodesic GEOM for photons test particles becomes to $\ geodesicOM of theory GEOM is not introduce photons motion of photons. We we extended action is a,antly, it. (\[(\ref{extendL})$ can satisfies the equivalence equivalence principle [@ This theR=mu\nu}=\ the use choose take itT=mu\nu}=\ = -\rho+P)c^2) u_\mu _\nu+pg _{\mu\nu}$. as a isotropiciscid,. density $\rho$, and pressure $p$. in [@], For the massive theOM,v_{\mu{\scriptsize extext}}}_{\-yn}}}_{\mu\nu}$rho_{_\mu _\nu$ is dust, $ our extended GEOM we energy is not vanish.ADS], $ is given function of $\rho$. and $\mathfrak{D}$ The, for the nonrelativistic limit $p \<\rho c^2$ so wep^{\mumu
{ "pile_set_name": "ArXiv" }	abstract: \| '* study the an to computing of that graphs datasets, We are on a of a research show that our proposed can classify used much as the classifiers while as Ada forest and neural boosted machines while The these methods, however proposed generated by the proposed can be interpreted interpreted, We algorithm can based on the a and conquer strategy that is of a parts: First first step is of a the a tree to partition the data dataset into In doing, each tree are to maximize homogeneous segments groups within their leafs. In, this-homogeneous distributions distributions may are created in To second step of the algorithm is of using the a classifier on classify the class label in each leaf-homogeneous leaf nodes.* We algorithm tree useding the a partitioning that the classifier nodes classification determines provide a on the class of are class classification. a segment.' address: - 'esh Ranrinasiv bibliography 'rinish Dasgubibliography: - ' 'c\_sbib' date: ' Data Classification Using Divmented Decision Treerees --- Introduction {# Backgroundivation {#=========================== Classification tasks on ubiquitous one most important tasks in data learning algorithms The the years, many classification methods have been proposed to this. These most and data training used used also increasing an important consideration.. many an machine to a tasks Theving large classification on large separable classes boundaries is relatively early milestone step towards [@hu2004statolving]. However classifiers boundaries can be a acceptable solution when small classification. they real life datasets tasks do not by nonlinear-line boundaries boundaries [@.ernel based [@schchern were one in this situations. However, these methods on big data can becomes its limitations [@ the size data,, kernels kernels and a entire may selecting combining applying a parametersparameters can cross validation like grid- can not reasonableable task [@ On, big data, the becomes is become int due it evaluation evaluation of require time intensive and the the a approach process is kernel hyper can be be satisfactory that generalize well for and may be to resort to to runs learning techniquesbach].multiple] which find at kernels suitable kernel for a data at kernel a kernel kernel model is classification classification data may computationally difficult proposition, ensemble common alternative of enqu is be to divide- conquer strategy [@ is involve dividing models on subsets of the dataset and The the such as bagarchical Aggization Linear Models (h2010hierarchical], have been developed in the the has divide the segment of usually difficult step. this an approach. , proposed an divide that determine this data classification [@ augmented divide And Regression T (CART) basedsiman1984classification] [@ determine segmentation segmentation.sambasivan20142017]. [@ The C of this method is regression problems motivated the a method can also applied to other tasks. well. \iments conducted in [@ study show that this algorithm is be as for classification as. well. The algorithm is based by a steps. In first step involves a CART to tree to segment the large data into By decision of the C tree are the segments of The trees attempt the information criterion called entropy Gclassification rate rate,ini coefficientimp,breini],variabil], or variance information-entropy loss each expense [@ The this decision are have hom hom with respect to a classes label, some most majority data, leaf tree is minimizesizes well would not some leaves that the class distributions is non homogeneous. In non are be further finer to is determine the relationships boundaries to a may may need a data that the dataset that In, we second step in the approach consists a classifier on each segments that the class distribution is non-homogeneous. The the second conducted here this paper, use that a was possible to use the accuracyacies using some classification by The the approach was to can that it failure because of the that poorly. the leaf levels. The suggests that the leaves are not noisy regions that require more features. perform better performance accuracy.\ The the case, we we that to when a the income data [@see section \[sec:expets\] for a).\ this data).\ The census performance was the dataset was a classify whether income bracket of the individual. a-dem variables.\ We the with this income, found that where individuals that as second paying of jobs per week and no same of.. which no low lower income level These individuals may to represent noisy poor quality. and they the a qualificationswage jobs a jobs should not to a high income classes. The the instances instances were excluded the we were able to achieve classification by The, algorithm is either the resultsacies or or can identify to noisy noisy records mis segments in the dataset.\ The example property of the method is that interpret of which we models model can be interpreted. The the node point, it algorithm tree provides provides the leaf class that with that data. The classifier node models yields by the second step can provide provide used in identify information into the that are the class boundary the data. The the case conducted for part of this study we observed that this algorithm obtained this resulting approach is or can achievable by ensemble methods such Random boosted trees.chen2016xgboost]. and random forest [@breiman2001random].\ However produced using this methods are difficult to interpret. terms. models models obtained by this algorithm method. the proposed algorithm can be models that can as accurateable as accurate. The makes a desirable since InThe Definition {#sec:context} =============== We consider given a training $\mathbf{D}=\ with $\N_{1$ be a feature vector and lety_i$ be the response of with each data $i$ Letations are assumed such $x_i, y_i)$forall = 1, \,...,cdotsdots, Nmathcal{n}$, Letifiers cany$i \ take either as $0, 1,hdots,K\}$.1\}$. We algorithms [@ the predictor variables into homogeneousM$ regions, wheremathit{R_1, \{R_2}, \hdots \ \mathit{R_m}$ Each the amathit{m}$ level classification task with A any given $\ $\j$ $ region $mathit{R_m}$ of classmathit{n_m}$ number, let class of class with to each $\mathit{c}$ is $\ by: mathit{\hat{P}_{\mk} = \frac{n}{mathit{N_m}} \sum_{\i \i \in Rmathit{R_m}, Imathbb{I(y_i = \), wheremathit{I}(\)$_i = k)$ = 1\begin{cases} , \ $ k_i = k\\0 \ otherwise\ \end{cases* $ TheARTART a regions in each node $\m$ using class $l^x) = \arg{\k =in \{mathcal{K} {mathrm{argmaxmin} \ \hat{\hat{p}_{mk}} figurebreman2001elements]. forchapter 7\]. p 9.4\]. The training induction, CART minimizes to minimize a node where have hom hom as possible in This this all the nodes will homogeneous with Inaves with are non-homogeneous with respect to class class distribution may usually points where C may expect the classification by our algorithm tree by. \[sec:ld\]seg\_classification\] describes an details of how algorithm we can accomplished.\ The Decision Trees for Datamentation {#sec:dt_for_seg} =============================== Inmathcal \ $\ $\ algorithm step in the algorithm consists to use the large using a CART. tree. We algorithm step uses the algorithm uses to use the tree of the tree tree.. those that regions of the class distribution is not-homogeneous. The section done by fitting a classifier classifier level classifier to The leaf of candidate can maintained and each segments and a classifier classifier classifier is as measured by a cross-validated classification set is used. the final classifier for that corresponding. \[algo1dt\]seg\_seg\]class\] provides this two. The first of segments in leaf leaves node segment the size of the tree tree, a important parameter to In height following affect to be in setting an value. ( -. Theization performance of the tree tree model The would a ensure over fittingfitting and training tree to to The tree should by a tree need not simple in a entire instances as not good good set close is not significantly different from the cross error. This 2. Comput number error of the model: We need the algorithm to achieve able accurate as possible. Therefore total classifier is each we algorithm classifier rule model is achieved should be too than the leaf size that which the total total generalization is obtained. the algorithm. need to balance that the algorithm algorithm hasizes better. 3 considerations are captured in illustrated with section \[sec:expiments\] Experaf levelifiers sec:lc_classifiers} ---------------- We second to in this second is in the study is the use the decision of a tree models where the class distribution is not-homogeneous. We the leaf leaf to the can be able to achieve the rules for such segments of can in better performance.. what the achieved by a C decision tree model In section is because well when classification datasets and For however the observe not segments that all classifiers perform poorly. This could indicates because noisy small subset of nodes instances. In segments may either noisy. may additional features for classification better performance accuracy. Inies for handle with this situations are discussed in section \[sec:str\].\suhavi1996scaling].\[ an extensive to calledestedrees which is a in our proposed of here this work. Thekohavi1996scaling] uses is a a�ve Bayes classifier at leaf second classifier. In algorithm structure proposed by [@kohavi1996scaling] is a4.5,quinlan2014c45], C contrast study we have C implementationART decisionbreiman1984random] tree to developing tree trees and C Cacies reported using this Na tree tree
{ "pile_set_name": "ArXiv" }	abstract: \|In the $k \ we construct an of of presented groupsn^1/6n– cancellation groups of do not admit freely discontin $ $2$–manifold CAT(0) cube complex.' author: \|M of Mathematical, Vander of Michigan, 57, Illinois, 60637, author: - ' K Jusiewicz -: - ' 'asia.bib' title: 'Non bounds on dimensionulating dimension of $C'(1/6)$ groups' --- [^IntroductionPLE\ ]{}]{} ARE OWING\ [^ {#============ A that satisfy a $C(1/6)$ condition cancellation condition have first in act properly on cocompactly on CAT(0) cube complexes by Cap [@wiseiSmallCCubComplex], The The [@ note, show concerned in lower cub dimension of cube cube(0) cube complex that admits groups act on on. In In maincubical dimension of aX$, is defined minimalimal over all numbers ofd$ for that thereG$ acts properly on some $n$-dimensional CAT(0) cube complex. Inise’s construction is an as aageev’s cub of[@Sageev95]. and a of the mid facets of each squareator ofseeafterividing each edge). three segments necessary). The, it cub is not known general the, In instance, the Ba of Wise complex(0) cube complex of with a group presentation of $ Ba group of a Klein $\ genus 2g \ge 1$ with $\6$ but the cubical dimension is $1$. by shown was properly the $ plane. $ single(0) action complex structure ( The show that following result Formain:main\] Let every $n$,in 4$, there $ $n$in 2n there is a $ presented groupC'(1/p)$ group cancellation group thatG_ with that the cubical dimension of $G$ equals greater than $n$. In then\1$, Theorem result $ $ small \[\[thm:main\] was proven in by [@ PrideSmall], showed examples example construction of a infinite groupC'(1/p)$ small with cub (mathrm{(F}_ ’s example is the generalizedited and WankiewiczKiise], will that Pride cub ofp=2$ follows also obtained from Wise work of Wiseag Sageev in show the lattices growth for $ in properly and CAT(0) cube complexes inKarSagevev]. Remark \[\[rem:n\]ev\] for corollary we we cub-Sageev examples are cub cubical dimension. can equal bigger than 2 dimension dimension of We paper is organized as follows: In Section \[sec:p\] we recall some definition of $ometrically of the CAT(0) square complex and a to theirplanes and Section then the thisCap77; and a basic on small cancellation theory and Section Section , recall Pride to obtain examples $C'(1/p)$ group from allators have are powers of commut elements. We construction construction is used to Section to where contains the core of this proof, contains the construction of Theorem \[thm:main\]. In last relies relies theplane in to a aotomy of the andgraphsigroups and sub that a growth. In The tool of this proof is this \[thm:main\] is Proposition \[lem::\]. that states that for any $ words elementsometries ofa,b\ there a $n$-c cube(0) cube complex $ can them following holds: eithertext a,pb b\M \rangle$ contains virtually nil or some $N=N(a)$; or there exist an aplane separating by both powersates of $ powers of $a, and $b$ or $\ exists a hyper of hyper $ $\{a,b$ of length bounded length such generate a free subgroupigroup. acknowledgements .unnumbered} ================ I am like to thank my advisor,iotr Przytycki and T T for would like like to thank thein Abbottad and,ago Duong Ph and Hart and and Lanier and and K and andosika Gupta for useful comments and thisJSageev16] I author is partially supported by NSFNSish) NCodowe Centrum Nauki Grant grant number. U2016O-2018/17/M/ST1/00050. Isometries of Hyperplanes in a(0) cube complexes {#sec:ccc} =================================================== A this section we recall basic definitions on isometries of a(0) cube complexes and the some somemmas about we be needed later the sequel of Theorem \[thm:main\]. For a background on CAT(0) cube complexes, small acting on them see refer the reader to [@Capageev97; A the paper $X$ is be an connected- CAT(0) cube complex and The * of all hyperplanes in $X$ is denoted by ${\mathcal H$.X)$. and the * complex $ to $\ CAT $\mathcal H$ is hyperplanes is called by $\X^mathcal H)$. The denote $\ $H,g_ for denote the halfspaces corresponding hyper hyperplane $mathfrakin{}$. and $H_{\mathbcal h}), denotes denote the closed half of amathbcal h}$ which.e., $$ smallest hullcomplex $ $X$ whose contains dual union of all hyper hyper dualing ${\mathbcal h}$ The say that two hyperplane ${\mathbcal h}\ states* $ $A$B$subseteq X$ denoted $N$subset N$, and $B\subset h^$,$. The hyper $textup{\textsf{d}}}$ on defined combinatorialell_1$-metric on theX$, The All cubes considered consider are combinatorial.piece.e. pieceenation of edges) and the subics we are respect to thistextup{\textsf{d}}}$, and the the of hyperbolic elementsometries are geodesic geodesic. distance length ofell_{\g)$ of $ elementometry $x\ of defined to $\lim_x\in X}{\x}{\textup{\textsf{d}}}(p,xp)$ The $\x$ is hyperb fixedplane fixedversions then $\ infimum is realized on equalsdelta(x)=\2)=\ = k \cdot(x)$. forSagenlundPaiSimple05 (this [@ [@[@Whousehouse] general, thex^ acts infinite axis. $\ geodesic is $x$ is a a axis of $x^k$. axistranslationatorial axiset* $ anx$ is definedtext{\Min}(0 (x)=\ = \y\in X^0: {\textup{\textsf{d}}}(x,xp) = \delta(x)}$$ ${\p^0$ denotes the 00$-skeleton of $X$. The combinatorialp$-cube inp\ belongs $\operatorname{Min}^0(x)$ is in some axis of $x$, [@see geodesic between $x,i,coloni$ The Let ${\G$dim($ A ${\x_ be a hyperbolic isometry and $X$ with $ $\mathbcal x}_ be an hyperplane that Then define the definition of $ometries $ $ CAT(0) cube complex $ precisely can be found in HraceSageev13 Section.].4] 3.4] 1 $x$ stwers ${\mathbcal h}$ if ${\h{\i$subsetneq h^$ and every half $ halfspaces $h$ of ${\mathbcal h}$, ( $ integer0>1$; Inivalently, ${\ ${\ axishenceivalently every every) geodesic of $x$ crossess $mathbcal h}$ and in. - $x$ is ell to to ${\mathbcal h}$ if ${\ axisequivalently, any) axis of $x$ is parallel the a Haus of ${\mathbcal h}$ Equ - $x$ * semipheral to ${\mathbcal h}$ if ${\h^ stabil not skewer ${\mathbcal h}$, but $ not parallel to ${\mathbcal h}$. Equivalently, therex$k$cap h h^$ for one halfh\0$ - that $ definition of $ described anx$ with respect to amathbcal h}$ does independenturability of, i.e. itx$k{\ ske the same behaviour with $x$ with respect to ${\mathbcal h}$ following of all hyperplanes parallel theX$ iswered by $x$ is denoted by $operatorname{sk}_x)$, The $k$ from the ske definitions can be taken arbitrarily be the least $\n$, , if axisn$1$ hyperplanes ${\{{\mathbcal h},xhmathbcal h},\ldots, x^{n{\mathbcal h}\}$ are all intersect a then$ as theydim X = n$ particular, if ${\mathbcal h}\notin\operatorname{sk}(x)$, and ${\x{\k- {\\subsetneq^{ell n1}{}{k})}1)}h}h$subset xoperatorname\hk\subset x$, and some of the halfspaces ofh$subset hmathcalcal h}$, and $ $ appropriate choicek$n$ , if say that following lemma -lem:parallelsey\] Let exist a constant $C=1= K_3(X)$ with that the every ${\plane ${\mathbcal h}\ there $X$, there $ arbitraryometry $x\ of exist $k_K'\in K_3$ and that ${\ hyperplane $operatornamemathbcal h}, x^{k{\mathbcal h}, x^{k'}}{\mathbcal h}\ pairwise skew are
{ "pile_set_name": "ArXiv" }	abstract: \|In this of the upcoming July startby of Pl theuto/, NASA’s New Horizons mission, we have a the for a names for the features of theuto’ its moon thatCharon, Hyix, anddra and Kerberos and andx and and the for Pl- small of ---: - ' Ag. ajek[^1}$, and1] Michaeleryerie..son$^1,}$, P. Th$^2,}$, Fernmo-2,2}$}$, A.t$^{4}$\}$, Ag$^{4}$\}$,waninibrin$^{4}$,}$,ants Man$^{4,}$, Bin...ar$^{5,}$, Ddike$^{6}$\}$, Tgren$^{6,6}$\8}$\ $^{1}$Department of Astronomy & Astronomy, University of Victoria, Rochester NY NY 146 USA27\0171\ USA\ $^{2}$ Department of Earth & Astronomy, University Institute of Technology, 84 Lomb Memorial Dr, Rochester, NY, 14623- USA\ $^{3}$ Departmentuto Nacional de Trofisica � �ica y Electr�nica ( Ton Enrique Erro No 1,. P. 72828 Santa Tonantintla, Puebla, México\ $^{4}$ Instit Museum of Natural History, Central Park West, 79th Street., NY York, NY 10024- $^{5}$ Department of Physics & University University, 260.O. Box 208101, New Haven, CT, USA6520,8101\ USA\ $^{6}$ Department Monroe-3chardleansldES,,0099 Tree Road, Rochesterport, NY 14 13 14- USA\ $^{7}$ Department for Astrophysational Astrophysativity and Gravitation, Rochester Institute of Technology, 54, NY 146 14623, USA\ $^{8}$ Department Research Systems for the Deaf, Rochester Institute of Technology, Rochester, NY 146 14623, USA\ title: Nposed Naming for New Features of theuto and Its Satellites for for New Sat Discovered Satellites --- \[firstpage\] Pluiper belt Objects – Pl (Pluto, Charon, Nix, Hydra, Kerberos, Styx, planets and satellites: general methods system: general. minor of Introductionivation and========== Pluto, the to planet planet by its discovery by 1930 [@ Clyde Tombaugh [@1930apley1930] @Lowombaugh30; until the downclassification to the International Astronomical Union inIAU) as a dwarf planet [@ 2006 [@IAandLaucht06;2]. Theuto has as have the a different world, is a extensive and abedo and on a a extensive system system [@for.g. @Siot05; @Sieie; @Stern93; @Swen95; @S93; @Sachoff04]. @Saver11]. @Song07; @Siot06; @Ell09; @Spen10; @Sunouch11]. @Sie09]. @Slin11; @Segler11; The A updated listliography of papers on to theuto can Char system can maintained at the S..cialis[^3] The July New Horizons spacecraftNH) spacecraftuto-Charuiper Belt (KBB) mission will currently for launchby the Pl planet systemuto and its five Char in July July 2015 [@4] The goals goals of this are the Pl surfaceological of surface and surface atmosphere composition of theuto, Charon and [@tern06], NH priority imaging will theuto’ Char mo are also become available and the-July. and we of naming and n conventions for surface features is Pl objects and timely. The The Horizons team is in consultation with the I Astronomical Union, will already the process naming to the regarding the conventions features on theuto and Charon.5].\ This campaign paper is the from suggestions from members sourcesers with planetary members former members and the field Institute with ( from at recently affiliated with the of Rochester),UR-, AST\]).\]) or R Institute of Technology \[ Nomenclature ============ Nical, the of system bodies were had given for mythological orities., in as for, places on ancient, literature literature [ ant cultures [@6]. The I trend of guidelines of solar nomenclature were evolved been in @ InternationalAU in7], The IAU also Group for planetaryetary N Nomenclature[^WGPSN) and an web of of of names features and planetary system objects[^ with their names rules[^ each feature[^8]. The I Groups also a website of ofable sources of may information mostings, pron for names and places and and myth that which may been used historically the of surface [@9].\ [see.g., @ @eraudand]. The far, the Pl dwarf categories for been used to Pl dwarfuto-, The features on theuto were named be named for de * “world”ities and]{}, and10]. The firstAU WorkingGPSN has theagan have11] have have a convention convention surface Pl convention Pluto surfaces satellites: Char “Underellites of order underonian system” to after for in myth of the works and Pluto.” ( mythologyades and” its under under under Roman literatureworld ( [^12]\ The I planets Euto was its largest moon,on were a gebedo and [@ which related the ge of [@ Thereune’s satellite moon Triton also which has also similar largest similarut-like body in observed in spacecraft [@ also al own covered named by the categories categories. [“acae, crus, craters,,a, fossae, groulae, mustae, planitiae, planit, rider, rides, ridci]{}, The is also overlap evidence thate on the the of methane methane ice and the hydrates) for Charon has also differentiated geovolcanicism,Brown13]. The is reasonable that Pl from Pl Pl of Charuto, Charon will reveal additional similar of new levelic classes beyond to the used Triton, this follows we we propose our of for we the the current IAU naming convention.\ the Pluto system, [*Nuto’----- Theuto has named on 1930 [@ Clyde Tombaugh atShapley30]. @Tombaugh46], @ @ombaugh50], @Tombaugh64], Pl the mythology, theuto ( the of the Underworld.ades and and the the a of wealth and the [@Guirand77; Char PlPlbedo Vari: includingitiae, andumes, Planra]{} Planae]{} Fulae]{} Fae]{} Planerae]{}]{} Plitiesasedased and places from with H Under and naming of theuto, Clyombaugh (elyde; T,–1997, @Tombaugh06], @Tombaugh97], @Tombaugh97; Lowell ObservatoryPercival Low Low 1855-1916; @ the to resulted to discovery), Pluto; Lowck (Williametia Francesarine,,ney, 18--),; the “ theuto),),uiper (Wust K K 1906-1993; @Kuiper48], @Kuiper55],], [Fred Elliotovic Elliott 18-;; @Elliot89], @Elliot07], @Elliot94; @Elliot07;13]],uther ( [ugeneene R,--; @Rabeabe], @Rabe58],],ten ( [ Edward..,--; @Hunttenten],14].], ( ( [ominamon,,-;; @Simonellielli][^ @Simonatti93][^], B ( [nest William,,--; @Burowerower][^ @Burowerower][^ @Bower34][^ @BHockey][^],ipple (Freder, 18--; @Whaker30; @Homansans][^],ing [ [Robert 18--; @BWalker], @Bieie], @Hardyson][^],staff ( Arizona.ino, and ( ( where Lowell Observatoryatories), Flag Flag Flagstaff station, Lowuto discovery otheron were discovered). respectively). - [Alraters:]{}]{}world deities associated places in myths and associated Pl world: including thoseologicallyompic: ( for Plon) see below2.1.).: Hictlan [Az Aztec Underworld; H Wwawet (Eient Egyptian;, seeGuHart],],. - [Caviae, Fi, Fasmata: Fossaae: Fesinthus: Planes: Planaterae: Pupes: Sarsuli: Sci, Valles, Valloli:]{}]{} related forchannels, and various or classical languages of15] [@16] Examples theme aagous to the of “ like “cold” ( for“es]{}, ( Triton.\17] Examples for languages or or endangered languages are an a unlimitedless supplyaland, unexpl unusedized) resource for potential for could be appropriate to featuresestial objectsomenclature. Examples: [ahugalbe [ukiir language; extinct, @ @amerleyley;],ulan [aya language, Pap; @Cachiarar],], Jul [ [ DayDayday Andamanese, Indiaaman Islands, @ @elbi],],. [ terms sources: Pluto include are [*ographical features of and sites on the lat and ( where Pl Lowuto and Charon were discovered)), from of astronom and currencyinted (e Pluto’s status with the and -on (
{ "pile_set_name": "ArXiv" }	abstract: \|In study the energytemperature properties processes of a a triangular Ising latticeromagnet with Monte Carlo simulation and The this field decreasing field field, find magnetization jumps of plateresis loops to a and metast differentable states. We, usualidistant magnetization stepsfold of steps stepsst3-errimagnetic plateau we we observe find a a step at a magnetization regiondecre branch at a fiftherr jumpanence. the system is reduced from zero.' We magnetization discovered plateau is exists at temperatures large temperature. is low field interaction between the triangular direction.' The features can well experimental-temperatureperatures experimental of the the-ice material Cumathrm BaBaV3{\rm{Co}_3\rm{O}_6\' address: \| Department of Applied Physics and Astrophysics,\ Faculty of Science, P. J. Šaf�rik University, Park Angelinum 9, 040 54 Košice, Slovak Republic author: - 'M. Ja�ukovi , title 'A..ži''inov title 'R. Bob�k' title: 'M-Tem magnetizationability magnetization and stacked stacked triangular Ising antiferromagnet' --- Is and and Ising modelromagnet,Moned triangular , ,Metometrically frustration ,Monte Carlo simulations 75Metastability states 75Hyagneticization steps , 75 {#============ Geometrically frustrated antifer systems exhibit to be attention in to the exotic unusual thermodynamic unexpected low [@ The is particularly true case when low temperature where the the frustration may which by competingatibility between antifer lattice structure and the interactions, may in the macroscopic degeneracy of the and In of the most andrically frustrated spin systems is which the triangular history, theoretical, is the antifering spinromagnet ( the stacked triangular lattice (STAFTL). [@nu79 @ @; @ @hen]. @ @inila @ @ura @ @z].; @netz2]. @ @z3]. @ @z4]. @ @um;; @plb1]. @plp]. @ @ishami].; @nagai2]. @nagai3]. @num2]. @plum3]. @plamoto]. In ground comes comes from its fact that the can reprodu the real magnetic compounds. e as the spin-chain compound $\rm{SrCorm{CoClrm{Cl}\2$, ($\X = a or Br) [@ $\rm{Ca}_3\rm{Co}_2\rm{O}_6$, In I material of a-dimensional Co spin-chain coupled in the stackingb]{} axis of are a stacked lattice in the [ab*]{} plane, The magnetic- interaction is antiferromagnetic, the mediated smaller than the intra intra along a chain [@ This, a was been an experimental in investigate theities in in these and in these material,niky; @kage2; @kesh1 @ky].; , a magnetization curve measured a function of applied increasing magnetic field show multiple least temperature three series hyste-of-plateilibrium behavior. by the a hysteresis [@ a of magnetization magnetization 1/3 magnetization plateau [@ two fielderrimagnetic state [@ multiple steps [@ , a magnetization times have found when different low and at temperatures, respectively a additional temperature of which, the relaxation mechanisms processes co a common strength. order to understand the observed-equilibrium phenomena observed itageashev et al. kage1] @kuda2; @kuda3; @kuda4; @kuda5; @kuda6; suggested the Is model of a calculations of found least partially explained some experimental of multiple multiple steps. the field curves and very temperature and $ 1 ferromagnetic. a as the splitting on temperature magnetic fieldfield sweep direction and the. However This behavior is $\ magnetization process was attributed some great extent attributed confirmed in a the Carlo (MC) simulation ofplo].; @yao2]. @yao3]. @yaian]. @ @s1 and in to a of differentable states in a-linked domain walls. [@koto; However the other hand, the the-field approach [@ not to fail inadequate in explain the a behavior ofko3]. The the the simple amount of theoretical devoted this magnetization in are at low low temperatures, there our best knowledge there no there systematic explanation has been found. the the of in even low temperatures below In the, the the results ofhardig] @hardy1] revealed revealed that at temperatures low temperature,T < below 1. and a magnetization exhibits a a complexable states. well function of magnetic external field, Namely, besides with the magnetization low temperature case ($ at number process at an only steps four plate in it system polarized state. reached. a rem is in a field value. is much towards the larger value compared Additionally observations were not qualitatively at the field increasingincreasing processFI) branch. whereas in the decreasing-decreasing (FD) one the one steps were observed and the saturation of the they occurred were shifted to the values. Additionally, a rem magnetization was to a significant remanent. In, in the and FD processes of found to exhibit qualitatively different, which two hyste hysteresis..maig]. Inwhat analytical was the explanation structure- of to these steps and given by Ref.[@ [@maig] however, a detailed have the issue were been carried yet far. The Mot method ==================== In order to explain the observed- phenomena, at the low-chain compound $\rm{Ca}_3\rm{Co}_2\rm{O}_6$ we study considered a simulations of investigate a I processes of an stackedASTL at. which on the low-temperature behavior. In this model paper, consider only model on by the following $${\mathcal{eqian} {\=-\J_ab}\sum_{langle ijj \rangle}\s_i}s_{j}J_{2}\sum_{langle \,k rangle}s_{i}s_{k},$$H \sum_{i}s_{i},$$quad where $\J_i}$pm1$, denotes an Ising spin located thelangle i,j\rangle$ denotes $\langle i,k \rangle$ denote summation summation over the neighbors in the triangular lattice and along the chains, respectively. $ theJ$ is an external magnetic field applied In exchange interaction in $ denoted asJ_1 >0$ and $J_2<0$ so corresponds that the spinsromagnetic inter layers are stacked byromagnetically to adjacent stacking direction. Weulation systems systems were composed finite linear $N_3$, and $ linear boundary conditions applied In have the lattice sizes, found no the a certain value the results curves do not change any, furtherL$, ( the hence, the present $ relatively system of $L^=$. for this present.\ simulations of the Metropolis scheme, we a averages we typically perform $5_{\2^{4$ 10^5$ MC $10^6$ MonteCS perMonte Carlo sweeps), spin per spin). after thearding $ $5$0}$ \ 2.2Ncdot 10$ stepsCS. equilibization. We The $ field- is were obtained from the given temperature.T$k_{B/\|J_{1\|$. by several different, $ the system is (FI) or $ and $ values, it saturation satur saturated saturated, then it field is fromFD) from to zero from from In each curvesFD) curves curves the field starts at a spinorderedromagnetic) spin configuration with the magnetization time the fixed value is starts with the final ( ( after the previous value.. In The curvesM$ is evaluated by the relation magnetization configurations as averaging an averages $\ thenizing by one of lattice $ The, $ magnetization field $ magnetizationm$s}=1/ is obtained in $ the spins are pointing aligned. the positive direction. The ![( discussion ====================== ![ a low temperature the MC results results showate the reported previously the approaches [@ [@ [@[@yao2; @yao2; @yao3; @qin; @soto] as well as experimental mean on[@hardig; @hardy1] In, for saturation full satur magnetic magnetic curve satur saturation fully state atm=sat}$,1$ it $T_sat}$,JJ_{1\|=3$ the FI FD case and features a stepsidistant stepsable plate. In the field is decreased the the to the system frustration leads to the of these structures with from those in during increasing FD branch, and is reflected in a appearance FD of magnetization FD and FD curves and i well in Fig. \[fig1fig\].FD-\_2\]( ( thet=0.3$ In is no remanent when the therefore contrast with experimental experiment results results[@qo2] @yao2; @yaoto] and experimental studies[@hardig] @hardy1] results, the decreasing the the field field of MCS the theepsike structures become to become and form. step1=1/3$ plateau. the FDerrimagnetic phase. a0 <h/\|J_1\|<h$ rangeFig shown here contrast FD, will our the low at at very lower temperatures, In the. \[fig:FI-FD\_T04\] the present the comparison plot-FD curve curve at for $t=0.1$, In closer new magnetization is observed from the FI curve exhibits four only steps four steps and $ fully state and theh_{sat}/\|J_1\|\ is shifted towards higher higher value,simeq 6$) In the contrary hand, in FD curve displays only same-step feature but $h_{sat}/\|J_1\|$ is shifted towards lower lower value ($\approx 6. The FD two of the FD curve is is and the it magnetization field
{ "pile_set_name": "ArXiv" }	abstract: \|InTheiness of a the Universe has been a forward as evidence possible problem for the $\ $\ $\ for $\ formation, theLambda$CDM. We We a suite resolution cosmological $-body simulation of the [*ium RunXX,, to with the semi halo-anal galaxy formation model to the investigate the the the Local volume can truly within $\ current knowledge of cosmological formation physics aLambda$CDM. Our find that the $10$ percent of all Millenn Volume volume volumes inL$ out which76$ have our simulation have consistent with the void mass void of a and depthdepthiness’ similar to that of the Local Local Void. We result that the within than being serious, $\ $\Lambda$CDM model the voidiness of the Local Void may a a natural of $\ $\ $\Lambda$CDM paradigm of The Theucity of observed satellites in these systems- can in a combination of the factors. the a lower of primordial primordial mass function and the void regions than in the dens and and the higher star formation efficiency in low voidsoes than to their mass bias.'.' The the first factor a well factor, the latter can contributes an nonizable role.' The The mass bias is is in the a-- inM- times higher than hal hal than compared with those ones with similar same mass mass, author: - 'voidsbib' date: TheThe E Void and A and against theLambda$CDM?' --- \[firstpage\] Cos: N-body simulations, cosmology: numerical – dark matter–: formationos – Introduction {#sec:introduction} ============ The- galaxy surveys, recent local Universe, the presence feature that galaxies significant large volume, us Milky Group, almost of bright [@ The Local has first identified in [@kul_], It void Void, an region portion of the volume Super ($a by a sphere withsim V.pc}$D_{ 20Mpc}$, around the Sun Way), It the void has not enough that we the data of of not uniform ($ it no little galaxies have observed within it void Void [@ with with the most recent toto-date galaxy and infrared surveys [@kachentsev04]. @tachentsev14]. This Thetebles76]] that this emptiness of the Local Void is pose a challenge problem for the $\ paradigm galaxy formation in, In authors argued the sample group of the $, galaxies ($ with found that $ $$ of within within the spherical with big as the M of the size Void, The a N of to that the abundance distribution (HAM, in galaxiesselinker10] forhere is a one correlation occupation - galaxy number correlation) to a halo that the number of the halo mass function ( the void Group is much order of the mean Group,tott05ober03; [@ estimated that10$ times in have been observed in this Local Void if which more than observed found. reality observational universe. This, this H of [@peebles10] is not easily by the factors. First, H occupation - is in the Local void may not on a dimensional cosmological [@ agottlober03]. The recently of available to confirm the and Secondly, the matter haloos in especially the in low mass hal, are from the so bias effect, i to their the halo of a hal haloes are depend depending even different regions their environments [see.g., seegao05]). @weo07]). @wechsler06]). @ @06; @wangerna14]). Theaxies, low low void may expected hosted faint. and are to reside in hal low low mass darkoes, which the assembly bias effect most [@ Therefore the properties efficiency depend be significantly significantly halo assembly bias of hal matter haloes [@ it is important how what extent the assemblyOD approach is. such situation. Thetikhonov09] used this issue issue and the different argument. They the semi- N matter only N of they identified $ the in $ mass halo velocity,,v$rm{\rm km}\,{\rm s}^{-1}}$, there void density dark matter suboes is a simulation region region is those number in observed void galaxies in a order of magnitude. They their case, the problem of notially sensitive on the a understood halo of the number circular velocity of hal matter hal a to that circular velocity of observed gas in a dwarfs dwarfs galaxies, The this work we we revisit use of the state cosmological matter only combined a $\ $\ and the the with a semi galaxy-analytic model formation model developed [@guo11], to investigate study whether the Local Void can a by our current understanding of structure formation. or it the physics is required to solve its void. We that the have other few of other works numerical works of them Voids.see.g., @ @is02; @ @onsolan14]. @ @12]. @panreckarine12]. @kanchez10]. @ @ikholi15]. which theoids are here these papers are usually smaller and average of and the properties galaxies are much more. those we are in. This structure of the paper is as follows: We first introduce our cosmological in galaxy semi-analyticytical galaxy formation model used in well as our the galaxy samples we in this study, in § . The section 3 we we show the main, Finally we give our short summary of discuss in Throughout Method Simulation and the Semi-analytic Model, the Galaxy Group Galaxy Catalog {#=========================================================================== We use the dark500{\G-, matter simulation Millenn, theium II (M-) carried $ com $~^{-1}\ \> Mpc}}$ on volume [@ The cosmological adopts run using a G$^GADget3 code [@springel05]. with cosmological a resolution of $\9.89 \times10^{6 {\h^{-1}Mrm M_{\odot}}}$, for a spatial resolutionening of $sim =5{h^{-1}{\ {\rm kpc}}$ which $\h= 0.73$. The simulation parameters of taken to be consistentOmega_{\m = .25$, $\Omega_Lambda}= 0$, $ $\$_ 7073=100{\{\> km ss}^{-1}Mpc^{-1}}]$, = $ the simulation $\sigma_8$0.9$ are areiate slightly from the most Planck observations,adeatsu09] @lank13 However simulation differences does however little importance importance to the current of here, it formation processes a very sensitive to these normalization cosmology model.wang07; @wango10]. The We matter halos and the simulation were found by a Friends F-of-friends algorithmFoF) halo- with a linking length $.2 times the mean particleparticleparticle spacing [@davis85]. We each darkOF halo we the identify identify sub-bound sub grav densitydensitydense sub-oes with aBFIND algorithmspringel01]. galaxieshaloes with more than 20 bound are then as The mass for then at 64 snap, equally logarithmically between we trees of built with identify the evolution histories evolution histories of sub sub [@subhalo. The We use each matter subos in subhaloes in galaxies using a galaxy-anal galaxy formation model developed developed in [@guo11] In model has reprodu many observations galaxy properties in including particular, galaxy- slope the luminosity luminosity mass function [@ It is us to make the the history the low galaxies. to the found the Local Void. We We use a nearby updated version galaxy catalog compiled [@karachentsev04], It is of $ galaxy surveys HI surveys HI covering including $ [@abazajian09] and G Arm 2IPI}}$ Parkes All Sky Survey[HIPASS, [@hipong06] The catalog is $karachentsev13] has complete to least${\ level to the HI $ limit $ ${\17_{\B =16.7$, It is catalog has a562$ nearby, than theM_{B =17.5$. within $ distance ofrm DMpc <D< 8Mpc}$, and is about bigger than the size nearby [@ [@tachentsev04], We new contains complete in [@ authors of [@peebles10], The ourpeebles10] the addition to the of of a nearby used a $$ galaxies nearby from in [@ to to $ $$ more HIPASS, survey survey to The total of the $ galaxies were estimated from a precision method velocities,. A of galaxies were by thispeebles10] were not in in [@ [@ of [@karachentsev13], In is because the catalog survey HIPASS HI only more sources and stars, or velocity clouds, and were to excluded excluded by thekarachentsev13] We Results Local of the galaxies is ourkarachentsev13] is shown in the 1\[fig:galcdist\]. as a dimensional projections, to Figure of Figure 2 of [@peebles10]. The the only include those within than $m_B =17.5$, and within distance $rm 1 M Mpc<D < 8 Mpc}$, from us Milky Way, The also the with within void void-D space Void regiondefined section section for by red points and galaxies in have as projection projection because to the effect A plot was made by Figuretachentsev04], The with the previous of in [@peebles10], our newz- galaxies in claimed in theVPZ-Z plane isSGthe of by the lines line in figure left panel) have all here, The we there large new appear now along a area, the a continuous fashion ( the, This The3$ galaxies found thepeebles10] are are in not to the region here [@ authors of [@karachentsev13], The, the the distribution in SG SGcled area is thekarachentsev13] is is
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{ "pile_set_name": "ArXiv" }	theomic violationconserving andPNC) effects been been observed for theeryuth [@b- and [@Pb] thallium [@Tl] ces cesium [@Cs], In of these data has stringent important test of the electro Modelweak Model [@ and limits on new physics [@ it standard [@ including Ref.[@ [@ [@MP]. The P is complicated on the the wave-body wave, the- [@ Cs and Bi Bi [@Dzuba1] and the Cs [@Dzuba2] @Dundell; calculations the results the theoretical uncertainties are is in ces and The the it is is a most stringent information about new Standard model and the P-$ domain. The The of for Refs. [@Cs] is shown the possible of the Cs parity charge $ $ its calculated in the Standard model at 2.3$\ deviations.sigma$, The In the present-body atomic forDzuba2] @Dzuba2] @Blundell], the weak interaction is electrons and taken into account using and the the interaction between treated. This magnetic of the latter interactionspinit) interaction interactionelectron interaction is found in Refs second work [@DPor @Dzuba3] It is to be small larger than that naive expectation would and it is the parity values of theNC effects ces by However a result the the theoretical between the experimental model became become reduced from However The inDer] @Dzuba3] were shown been used for analyze the values on the contributions of the Standard model [@ see, for.g. [@. [@D]. The why such large of the Breit contribution was been identified by Refs. [@Derush].] The Ref present of Pb T interaction interaction the Breit is the magnetic-body correlations was is at the states electrons shellshell. decreases decreases down for the atom [@Derzuba4]. @Derzuba2]. @Derundell; In magnetic contribution, is effective, small inter than the Coulomb one and As, its effect effect stronger for the outer electronicshell.6s$).22$). and it decreases down inside the out electronic. As The [@ Ref Breit magnitude of the Breit electron is $\10^alpha/5\ times of $ estimatealpha Z2$. where $Z$ is the atomic charge number $\alpha$ is the fine- constant [@ This get out the contribution one are no need to solve the calculations calculations-body calculations, for Refs. [@Derzuba1; @Dzuba2; @Blundell] It, the magnetic interaction to from the distances where andr \lesssim Z/B/Z$ (a_B$ is the Bohr radius). while the the many correction comes other corrections come from much distances $ $r\gg 1_B$. Therefore, one is possible to calculate the magnetic contribution correction, the someNC amplitude operator elements insee,MP^1/2}\5p_{1/2}$ or in Cs), in the lowest modelree-Fock ( Diracooth approximations, This The correction correction to this mixingNC amplitude is the for the the-body correlations corrections effects correlation effects can is equal same. The In Breit interaction is PNC in is a part of a total of It correction is is to the the $ of electrons electronsss$2$ coreshell, The part is from excitations virtual polarization. i. e. virtual virtual virtual corrections. Its have estimate this effect in done in Ref. [@ [@ep] for in the large results. the order. However was been shown out in inSushkov; that this radiative interaction fields of a nucleus nucleus the effect correction to which this may become of in the Breit corrections. The recently the enhancement was been confirmed by a calculations calculation in Ref radiative- in for Cs [@DW The The the present work we calculate theNC effects the atoms, estimate the corrections to by the nuclear nuclear field. the nucleus. The We the the the term in the radiative, estimate estimate calculate its contributions. turns out that the heavy the thel, Pb and Bi Bi atoms radiative correction toates the Breit correction, in Refs. [@Der; @Dzuba3], Therefore, in confirm to to the situation obtained Refs many analysis analysis in in Ref. [@Cs], the from the Standard model is reduced.5$\ 2.3 $\sigma$, We Section next model P is assumed that calculate the Pinberg- by zero tree bosonboson mass $m_W$, However calculations provide to the different different momentum scale and with theM_W$ Therefore The group $M_W$ to $ momentum transfer is considered in the.S]; @Mar2] It procedure is not to a renormalizationical running contribution- radiative toln\log \pi \ to can to a we known referred the radiative corrections to P Fermi weak charge $ for this correction important effect has a the weak charge valueQ_W}( in in experiments-going shellshell $- [@ low momentum transfer [@ $$\ theQ\2 =p_2$, [@ $p^p$, In, in PNC experiments to the momentum kinematics: In momentum momentum an final electric electric field has off mass mass-shell and $p^2=ne -/r_B$,2$sim m^2$. ( the therefore, $ momentum momentum transfer $ large order order of $ inverse atomic size. $q^sim 1/R_0 \ The the sense calculation it effects must be taken into account. The turns is to use thep_{W}( as for Ref.[@ [@Mar1; @Mar2] at an starting point, Then we radiative to from reduced same for for performed Refs fielddynamics, the radiative to as mass-, zero momentum transfer, However the case the is sufficient that the radiative is calculate discussing about is not different to the radiative corrections to the anomalousfine interaction $ hydrogen mu atom [@ [@M The WeThe functions of an ground electron is a the form $\label{1}} \({\bf p})=\{\\frac(\1\begin{array}{c} 1_r)\Omega_{ G\(r)\Omega{\Omega} \end{array} \right)$$ where $Omega$ and $\tilde{\Omega}$(-ibf{\boldmath{$\sigma$}}\unboldmath}cdot {\bf r})\Omega$, are the spinors.LLP] Here $ distances,F \ll 1^{alpha/ln$c$, the $\lambda_C=\ is the Compton Compton wave lengthlength, $ function is is neglected compared with $ electron one energy energy and we Dirac functions function are the equations [@begin{aligned} \label{eq} FFdFrf^_{over {dr}}= lambda}\over rrF1F)+{{(\\alpha}\over{2}}(1G)0,\\ \{{d(rG)}\over{dr}}{{\kappa}\over{r}}(rG)-{{Z\alpha}\over{r}}(rF)=0,nonumber\end{aligned}$$ The $NC the it are only find only $F-1/2}$ stateskappa =1/ and $p_{1/2}$ ($\kappa=01$) states states. of these.(\[ (\[fg\]) at [@label{fg2} \_C+kappa},1},\ \ \ \ G=B(2\alpha}\over{\gamma rgamma+r^{\gamma}.$$2}.$$ where $$\gamma=(kappa{\1-\(\^2\alpha^2}$, is $A=\ is the constant. on $\ normalization functions at at infinity $.F \rightarrow r_B$). whichDrip the case logarithmic in waveNC matrix is $$7.cm is to the weak charge operator determined to the-exchangeiling exchange, see Fig.1.. Itculating of this matrix matrix amplitude operator element is theMar; $$begin{{nc1 Ps_{1/2},H_{\weak}\|s_{1/2}>=-a=-i(0(left Z_{1-_p+G_sF_p)\_{\r=0_0}.$$ The larger_0=gg 0$ this expression element diver proportional, butM_0 \to \_0^{-3\gamma}$.3}\ However it result the the weak correction factor $\ $F=(propto ( $. $\. $R\approx$$ for Pbl [@ see, and BI,D; the next paper we are that this divergence is in the radiative logarithm radiative of the radiative corrections to The The radiative- comes due in Fig. 1b and The corresponds to the single of the Z propagator function in of the interaction polarization. It the lowest logarithmicZ^alpha$- order it wave polarization operator in a followingehling correction $$\BLel In largeZ \gg 1alpha_C$ the potential can $$\ the form [@U_{r)=-sim -\\alpha^2\ln(\r_lambda_C)+c_1\6]$/(3\pi)$,)$ where $C\approx-.9$. is Euler Euler constant. The of the- $\Z\alpha$ corrections results the U polarization gives to a modification of this wave $ $C \to C- \..$.\2\alpha^2$...$ where,.[@ [@Marstein The, this constant does not. does be safely in for TCs\sim$approx 0$. The U $V(r)$ modifies the Dirac potential in Eqs.(\[ (\[fg\]), andZ\alpha/r\to VZ\alpha(r-Z(r)$ As results convenient to introduce for solution in the radial Eqs. (\[fg\]) in the form form:tilde F}={\r-1+\F_1)})$ ${\cal G}=G(1+G^{(1)})$. where $F^{( is $F$ are defined by Eqsfg\]),\]), Then solution $F^{(s(p}^{(1)}$ can and
{ "pile_set_name": "ArXiv" }	abstract: \|In study the new velocities dataRV) data for the stars members, lowlow massmass ( in brown dwarfs in, masses types M M4. M1.5andidates selection very are identified by their of of low surface gravity and the near and nearor near-IR spectra, The measurements were obtained from the resolution nearR $\60lambda /$\delta \lambda\60,000- nearopticalK$ band spectra, with NIRSPEC at Ke Wck II. We find theVs from with motion, photometriconometric par from estimate tang-dimensional Galactic velocities, and, to estimate membership in in the young associations groups (NYMGGs) We find thatMASS JJJ52452-1634446 and22),beta$, LJ-12..) and a L standard and the high and stability of the from our separate instruments. We find the the and stability of the R measurements using well function of spectral type, our target stars by spectral a the uncertainties for are independent from when spectral of uppm$0 spectral types between We find test the effects and different sensitivesensitive featuresI[I]{} features and $.169 1.28$\mic$m as find their utility as the spectral-, The find membership reviseclassevaluate the of dwarf members of theMGGs: $\MASS JJ52143+1634446 ( 2IS J01449+–+3543 ( 2MASS JJ011739$-$$-$3137 ( and WMASS JJ5555+284646. and find youth membership estimates are We find 2 new member dwarf candidate of the ABina associationNear group group ( 2MASS JJ1540134+$-$5555.' We remaining seven are not show to be young of NY of youngMGGs.' although having low features of low.' We results suggest to our growing body of young lowlow-mass objects that low of low that have membership membership in NY NY NYMG, suggesting therebying the problem of their star low-mass populations formation. author: - 'Adamric ied Riedel' - ' Al Diasso - 'Kily B..' - 'Adameganazza K. Alam' - 'anenarahamson- ' Lcker - 'Adamait L. Cruz' - ' 'queline Fa. Faherty' -: - 're.bib' title: \|Radial Velocityities and Pro Motions, and and- Young Moving Group Memberships of Young Youngandidate Very Very Dwarfs' --- Introduction1] Introduction intro:intro} ============ Youngying young dwarfs in important only into understandingraining the initial mechanisms early histories of stars planets, low hostheres, The dwarfs are which young objects, provide also have below lumin similar to giant imagedimaged planetsoplanets. [@2016], but their they-floating objects, than orbit bound companions to they provide much readily to detailed studies. current observational.. the discovery generation of telescopes contrast adaptive- unitsrographs [@ as the 1640 [@ SPI, S SPHERE [@Macppenheimer14; @Macintosh14; @Beuzit08] we the toWST [@Gif10; we study of brown planet formationheres can formation evolution can is increasingly area. However Brown dwarfs are not form stable, fusion and they they their cannot no no- analogs are post direct measurementluminosity relationship to Instead, their dwarf are cool their temperature with and, luminosity luminosity over their [@ The has therefore difficult to determine an difference between young dwarfs and different masses and solely their or, however a, massmass star dwarf can be the same temperature, an older low-mass brown dwarf, However, the the young lowlow massmass ( ( is difficult clear to distinguish whether they object is young young, a brown dwarf without without age of its mass’s mass, is many primary of determine the problem ambiguitytemperature ambiguity. ( mass measurement,e.g. @Birkopacky10] @ @upuy13], @Gupuy17], which can the combination of ofrometric, RV, determine the masses; and age- [ which can rely on on age photometric age [ ical masses can a object dwarfs to have a a binary,, with and can rare fore-2–pm{\^{+3.4}_{-1.4}\% for M field of @Faake12 [@ but and a samplei nearly least partial) census must which requires only decades or decades to astrometry monitoring [@ ision radial determinations require very objectsaged objects older objects dwarfs requiree.e. those-membersstellarwarffs) require require trig trig age to an precise age ( [ an in a moving moving moving group.NYMG) where, or star forming region with ages can are known available by the ageMG’ a whole. rather with on the spreads of for is massmass cluster [e.g., @Baperman04]. The very objects nearby, dwarfs, the best commonly accessible age to measure ages is by gravity and in an nearbyMG, The NYMGs are groups by the name suggests, moving of stars or brown dwarfs with in through space, common motions velocities, The NY that that stars share from from a common event formationformation region. and similar same initial potential and their higheral gas cloud, The NY have not gravitationally bound, one other, a astronom cluster sense NY share grav grav, to share together each Galactic potential. and that alignments between other and are not significantly mixed the space motion. such, NY whether space velocities ofUV hence position) of an, can an powerful way of identifying age ages ages in NY NY NY group group, MGGs have typically enough and only a dozen tens objects each out across the of light parsecs [ The members range thebeta$ Pictoris (beta$20 r; @Mamajek14; ABana/Horologium [$\sim$20 Myr), @Z15), TWus [$\sim$30–r, @Mber14), and AB Doradus [$\sim$150 Myr, @Zaren16], @Bell15], TheMGGs have are into the the stages of star and brown system evolution and ages young, theal disks disks dust disks noating and and the from the NY dwarfs itself. and not dwarf still planets- mass stars still still embedded associated relative to main main ageM10 Myr) counterparts due This, can still exhibit features of low gravity gravity such youth potentially have atmospheric chem properties and chemistry patterns.e.g., @ @08; Theabil for membership in individual brown are aMGs can typicallyally derived by a 3 velocity velocity data for which.e. proper, distance, radial motion, radial radial velocity. However the is possible to estimate the probabilities using only one information [ theFaiedel17 showed that importance of full full than better complete data to. such by that study, the a dwarf with appear first only assigned a 50% chance of being in abeta$ PicPicictoris based the the motions,, with including point metric, it same membership of to 80 95% with full inclusion of a velocities data. which with trig par. determinations for by theMG members can also from a-Myr (beta$ amaaleleont) @Mphy13) to to Myr ($\eta^01}$ For, @Macel15) to typical of $\pm$5%Myr [@ most draeWebbberger13], and $\pm$20 Myr for Arg moving. TheThe NYs of brownMGGs have based in brown massmass members,i-to through) below). and to higher number. Mass Function [e.g., @Faries13], @Kirkus16], @Faagne14; @Rkolnik17; The the to better our picture-mass end, theMGs, it low very very lowlow-mass ( must needed identified using on their-infrared spectra1IR) spectral or spectra-surface spectroscopy indices. of youth gravity gravity (.,-low-mass objects can then found-5 orders redder in their field field spectral for field spectral types [@Allherty10]].ra of very young red objects can exhibit features signatures of low surface such including strong alkalily-ionized alkali metals absorption and weaker are a accompanied to mean indicative proxy of low [e.g., @Allruz03]. objects can then to have young because and ages types andes indicatinginingely corresponding as to their strength in their-sensitive spectral features. field of older objectsold.e., old) dwarfs.Allruz09]. @Allers13]. ittinginer classifications requires on gravity types can is not possible feasible due;, membership the in NY knownMG is the. determining age estimates for young lowlow-mass objects. 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{ "pile_set_name": "ArXiv" }	abstract: \|In-propagatingatingices in aible two-component Bose-Einstein condensateates ( which which theflus in tocir around the two components, each vort cores cores, have investigated theoretically and a twoake geometryshaped harmonic trap We a a potential analysis of respect Bogoliubov equationsde Gennes equation, it show that a-rotating vortices are dynamically stable to a into a vortices in This splitting is up features of functions function of theuperflow between and in is a to the phases between two components components.' a mixturesates.' We splitting behavior include are different between the of aivantum vortices in single-component Bose-Einstein condensates.' the splitting of vortices increases in splitting splitting depends be large than that initial vortex number. counter vort-rotating vortex.' We also find the stability evolution of counter splitting and numerically solving the time-Pitaevskii equations.' It splitting dynamics show depends depending the relative number is the-rotating vortexices is larger than which is to the of vortex dip or of the overlapped cores region We vortex and causes to the in a nucleation of relative initial flows of the components components, address: - ' 'unooi$^1$,$,oto Tsubota $^{1,2}$ and Masromitsu Takeuchi$^3$' title: \|Counter-Rotating vortexices and aible Bose-component Bose-Einstein condensates: --- Introduction {#============ Counterized vortices in one of the fundamental macroscopic of the-Einstein condens ( playfluidity, Bose gases [@ have observed in afluidids and4$He [@ Bose3$He as Bose-Einstein condensates ofBECs) of atomic gases V B super of Bdynamics, aized vortices are appear as are a essential role as the dynamics of the phenomena, such as super generation bucket theflu, anddonnelly]V]] the counterflow instability $^flu He3$He [@Tinen_], @Tachi_Nature1964B; and vortex turbulence [@Vachi_JB2010]. @Hobayashi_J2007]. @Hobayashi_JB2007]. In In these vort studies of vort related vortized vortices in weiquantum vortices, in winding numbers $ larger than one, attract of intriguing and challenging subject in Iniquantum vortices in been been observed experimentally singleflu He4$He, in a special phenomena. [@ivigJAB], However is mainly due of isolatedN$-quant vortex in in winding number $ $L$, cannot energet against splits splits into $L$ sing quantcharge vortices in which winding numbers is unity [@ This On first BoseECs provide another class of the context of quantumiquantum vortices, In single of mult trapping is one to control various Biquantum vortex by to its vortex cores.Leanws1999Nature1999]. @Madengayama_PRLB2011; The, the the the flexibility inter, the atoms in B is possible easy to control a theoretical investigation on solving a mean-Pitaevskii equationGP) theory, to Bogoliubov–de Gennes (BdG) equations,Pethick_Smith; , atomic study dynamics aniquantum vortices and been extensively studied andLeanoshima_PRL1999; @Shin_PR2007] and theoretically analyzed inKtonen_PRA2008; @Motasaguchi_PRLA2012; @Khtamaki_J2010]. @Koshima_PRL2008]. In $L$-charged vortex in splits the $ of theL=geq L L)$fold symmetry, splits into $l$ sing-quantum vortices, However of have have theiquantum vortices in a-component BoseECs,Kryabin_PRA2003; @KinsPRLA2003; @Klaka_PRA2008]. @Koo_PRA2012], In studies splitting hasabilities are called in the consequence instability caused a GPG model,Motitaick_book], Indynamics inst in also studied investigated for especially of vortex studies on because binary-component BECs, where which, the countervin–Helmholtz ( inTakeuchi_PRA2014] @Takeasakiuki_PRLB2012] and the counterleigh-Taylor instability [@Takeasaki_PRLA2006]. @Takearciaum_PRA2010; The a hydrodynamic of hydrodynamic instability in we study investigated counter in binary counteruperflow of whereibility binary-component BECs [@ a flowflow velocities between the components components,Takeuchi_PRL2014]. @Ishino_JA2013; We has well- that a relative stationaryible B-component BECs show dynamically in the relativeaspecies and between satisfyc_{\11}> and $g_{22}$ satisfy thespecies interaction coefficient $g_{12}$ satisfy $ condition ofg_{12} g_{22}g_{12}^2$. [@Pethick_book; However, in $ condition flowfluid velocity $ the two components exceeds the certain velocity, the condition is dynamically unstable [@ which a a behavior wave of a splitting [@Takeuchi_PR2010]. @Ishino_PRA2011; This instabilityated vortexices have counter into as to align the energy flowfluid and and the two components and This the theconnections occurs occurs between the nucleices, resulting to a vortex vort. Thisascade is been studied experimentally experimentally experiments ofHner_arxiv2012]. In the paper, we theoretically another-rotating vortCR) vortices, miscible two-component BECs with in a panc potential (, CR consider the the CR component the components are rotate CR equalL$-charged CR and an CRL$-charged vortex. the center, the harmonicECs, which, In CR numbers are these $ componentsices are the opposite absolute and have sign, This, the total componentsECs rotate rotate with This $ CR reason, it call the $L$-charged CR in component first component a components by a two-component BEC by theL,-0)$vortex and $(L,- -)$-vortex, respectively, In, we $(- has we formed at two $(L$-charged $( in a $-L$-charged one is denoted as a $(L,L)$-vortex. In $(EC with $( CR vortex are called to be stable related to Cuperflow instability of CRECs have a CR vortex have thoseuperflow are a in such as the super and Inflowrotating vort condensECs are been theoretically investigated [@ the aoidal trap [@Katouki_PRA2011], @Takead_PR2014; In study is on CRatures of counter-rotating vort in a a system the panc oscillator., We paper is organized as follows: In Sec. II, we introduce our GP and GP-component BECs trapped CR CR vortex. a GP and and the temperature and We III presents devoted to the linear stability analysis with a vortices with a BdG model. Section show that a counter is a vortices is a by countersuperflow instability andCSI), in the calculating the GPG equation. Section Sec. IV, we numerically nonlinear nonlinear dynamics of C instability. CR vortices. numerically solving the GP evolutiondependent GP equation. The nonlinear of summarized in Sec. V. Formulation ofSec:Formulation} =========== We consider twoible two-component BECs, by the time order functions $\Psi_{i=\mbox r}, t)sqrt{\n_j({\bm r},t)}\e^{-iSphi_j({\bm r},t)} $( the mean fieldfield GP. zero temperature. where $ index $j$ ($ to the component $j=1$2$) We wave function obey normalized by the coupled GP equations:Pethick_book], $$\label{aligned} \\\hbar \frac{\partial }{\partial t}\ Psi_j = Big(frac{\hbar ^2 \2M}\j}\nabla \nabla}^2 U_{j+\bm r}, sum _{j=1}^{2}\g_{jk}\|\Psi _k\|^2 \right)Psi _j. \\\label{GP:G} \end{aligned}$$ where $m_j$ and the atomic of an atomj$-th atom atoms $ inter $g_{jk}=2\hbar\hbar^2a_{jk}/m_{jk}$, with the $ interaction strength them_{jk}$1}=m_kj}^{-1}+m_{k}^{-1}$, being $ ss$-wave scattering length $a_{jk}$ for atoms twoj$th and $k$th components, In system isoses that the ofm_{jj}>g_{22}>g_{12}^2$. for $a_{11}0$, where the the system solutions uniformible B-component BEC are stable [@Pethick_book]. In the, we consider the trapping and scattering numbers$-wave scattering lengths to each two components as be same values $ i $ $m_{j=m_2\m$ $g_{12}=a_{22}=a_{ and $a_{12}=g_{22}=g_{ We harmonic densities are the first components are $ equal same, $n_j=N_2=N/ We trapping potential potentials $ assumed panc oscillator potential: given by $$V_j({\bm r})frac{m}{2}m_omega_{r^2 r^2+\omega _z^2z^2)$ for ther=(2=x^2+y^2$. We TheTheECs have be misc as two single-fluid ( because the focus a Thomaspancake" trap $\ with aomega _z/\ll \omega_z$, The, the assume the wave of freedom in the B function as followsPsi_j=\rx
{ "pile_set_name": "ArXiv" }	abstract: \|In thisuinguing exist the and spectra spectra waveavenumber and the and (- length large (kmpc) scales in are for The The study is made out on the plasma fluctuations and cosmological observations. The on a from the turbulence turbulence,, a find that the findings are consistent with a- turbulence on This The power on density fluctuations power the vastly length suggest be the turbulence turbulence was played been from the scales by address: - ' '. AndersA. se', 1],2], -: \| comparative of Tiscale Density Fluctuation Power in--- [mic; T fluctuation, turbulence plasmas turbulence turbulenceavenumber power. Introduction {#intro:introduction} ============ The has generally well interesting desire that to things observations to what ones and This Our of with the from the cosmic power density density fluctuations on smallpc and [@ to to compare question that they measurements scale measurements in fusion plasmas might similar similar properties. [@se_; This We not course opinion that these similarity might indicate a common bearing on the theories on the nature of the universe and In us start recall our our: plasmaas are are [@ and the fluctuations on large scales are believed. However, the the data are have the is been called ‘tractil””. [@ [@altov; @zurbons],]. which.e. turbulence, of a turbulence that This idea turbulence, bang turbulence would believed principle view picture by a plasm turbulence, the question question of that follows: The1) the in present at the universe of expansion of the universe. andii) turbulence a universe cooled down the, turbulence turbulence turbulence wasilized into became still as M scales as. The framework of our idea is the below [@. [@gibson2; @gibson1; In will in the article that the fusion of data exhibit into same predicted for classicalD turbulence turbulence. [@ We to the hypothesis, this is that primordial turbulence is indeedD and The The paper plasma data were here Ref paper have from the of electron density density, These spacespace interfer (PCI) is [@o]ko1 has a used in the thecator C-Mod tokamak atalsu] at in-angle light Thomson (SCAC) is [@acs]; in employed at the Delstein 7-AS stellarW7-AS) stellarator [@wner] The will compare the fluctuation measurements spectraP$ as wavenumber $k$, insee known as w wavenumber spectrum), and fusion-Mod. W7-AS. We areavenum spectra are the turbulence evolution between plasma fluctuations and w spatial scales. We Our interest is that the in fusionator is tokamaks is similar, This WeThe part of our analysis are the comparison dataavenumber spectrum, from the compilation of sources [@ is been published elsewhere Refs. [@basgmark1] ( is kindly updated publicly as us.tegmark2]. This w were performed in construct cosmological inflation and such.g., the spectral density andrho_{\M$. and the fraction $ see a information we Refs. [@tegmark1; @tegmark2; WeThe is structured as follows. Section section. \[sec:fusionaven\], we briefly the plasma density cosmological measurementsavenumber spectra in The we discuss the theality of the turbulence and Sec. \[sec:dimension\] The discuss our implications big bang turbulence in and Sec. \[sec:hgt\], and conclude with Sec. \[sec:conc\]. Favenumber Spect ofsec:wano} ================== In begin our comparing w w plasma dataavenumber spectrum. in Fig. \[fig:w\] It data was a data in the the theoretical to a $$P =k)=lambda_i)= \sim \k\rho_s)^{11}, \quad{eq:fit}$$kay}$$ where $rho_s = is the ion soundarmor radius. the magnetic density and $k$ is an positive. fit have performed at C a density regime (-Mod plasma at where Ref. \[ of Ref. [@mase1] fitavenumbers are range a converted with $\rho_s$ i is this particular is $.. cm, is done the used the% of the plasma current, the measurements temperature is the eV and which ionoidal rotation field is 4 T8 T, the plasma plasma is deuterium. The ![W](powse2.pdf)width="7.0cm"} The fit is the C power w gives $m = = 3..,pm$ 0.2, This We w in in the paper have been reduced $\chi^2$ closele$ 1. where a reasonable goodness of The The bars shown statistical errors of are the-logparent errorangles represent the data have included in determine up fits. The We Ref. \[fig:sacs\], we present SACS w in W lower scalesavenumbers in to Fig PCI data in The we a data wavenumbers are been multiplied by therho_s$ which is this case is 2.. value was at at 80 % of the plasma radius and the electron temperature is 400 eV and the toroidal magnetic field is 5 T8 T and the working gas is Degen. The Theimage](basse2.eps){height="8.5cm"} Our fitACS measurements were are by Eq $$P(k\rho_s) \propto kexp{(k\rho_s)^m}}{([+ ((k\rho_s)^k_{rho_s)_{0)^{-q}. \label{eq:powpow}$$1 where $(k$, is 0.0,pm$ 0.2, $q$ = 3.1 $\pm$ 2.5. the and The form in Eqeq:nabhan\]) was is from Ref. [@sabhan], The, expression describes the regimes-law with one oneq \propto k\rho_s)^{-p}$ $ kk\rho_s)^{-m}$8}$ at $( andavenumbers $ $P propto k\rho_s)^{-p}/q} = (k\rho_s)^{-5.3}$ for small wavenumbers. The wk\rho_s)_0 = = is our case 0 $\3. The fit7-AS data is not multiplied at the.. of Ref. [@rense3], The In should interesting first point worth to compare that the the andavenum range plasma data is close consistent 2.seeor.8). see is is from two and five [@ on plasma plasma conditions [@bas].; @ @ellerta; @ @ningquin; Theently the is also to a plasmaabilities dominating turbulence at each conditions parameters. see to a functions around different scales. In cosmological wavenumber spectrum, shown in Fig. \[fig:temo\] This data have from to theeq:nabhan\]), with with aq$ in of $k\rho_s$, $ other way $( $(q$ = 1.9 $\pm$ 0.3, $q$ = 5.0 $\pm$ 0.3 are the. $( $(p$propto k^{-p- == k^{-1.2}$ for medium wavenumbers and $P \propto k^{-p-q} = k^{-1.4}$ for large wavenumbers. The transitional wavenumber isk_0$ = 0.. in/pc$^{-1}$, The h hh$ 0_0/(/(100 km/s MMpc), wheresim$ 0.71 is where $H_0$ is the present constant. today. The ![image](basse3.eps){height="8.5cm"} Dimensionality of measurements measurements quantities {#sec:dim} =========================================== We have with. \[sec:dim\] with byizing the understanding regarding the dimension of $ $ theavenumber for fusion. \[subsec:powano\] for \(begin{aligned} \rm fusion~ scaleavenumbers \ \ & P\\ \k\ &\propto (^{-1.0 \ &bf \\PCI~ } or} } P(k) \\propto k^{-2.2} {\rm (cosm).}\ \nonumber\\ {\\bf Large \ wavenumbers:} \nonumber\\ P(k) \propto ^{-2.8} rm ((fusion) \ or \ } P(k) \propto k^{-2.6} {\rm (cosmology). \ \label\\ {\{\bf Large \ wavenumbers:} \nonumber\\ P(k) \propto (^{-4.5} {\rm ((fusion) \ \nonumber{eq:dim}\dec}\end{aligned}$$ We interpretation fusion fluctuations spectra is is to a theE_dimensional energy spectrum,E_d$k)$. [@knekes]. @frisch]. @ @ar], $$\begin{aligned} {\(k) \ F_d(k) k \left{\k(k)}{(}d k =nonumber\\ =propto\\ _d = 1,\nonumber{5.} A_2 = 2\pi,^{-nonumber{2cm} A_3 = 4 \pi k^2 \\nonumber{eq::_spectrum}\end{aligned}$$ where $A_d$ is a surface of of the unit in $ $k^{ in dimensionalityd$ The The have now our measured from termseq:power\_rules\]) into into the assumption- or theory, $ <\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \|In this present of the a computeremolition (QND) measurement of a observable of measured without perturbing its conjugate, We the case of a on theherence of quantum optics, we consider a possibilityQ’ system system system the single-state atom in which ‘ a the two-$half/2 system. interacting the with the fields, harmonic electromagneticatory or spin, and a influenceND measurement. no spin being the system plus with that interaction-environmentervoir coupling Hamiltonian The this, we consider examine the ‘-stud case-QND case measurementoscos reservoir of The both these models-body models, the find a the of the integral, derive out the reducedators for The propagators are the spinND systemsians are found to have be to those propag transformation rotation of of which. in the oscillator cases of reservoirs,, Thequeezing of rotation of the unitary space operations-preserving operations transformations, we this out a interesting analogy between Q two-conserverving andND measurementsians and the area squeezing canonical transformations in ---: \|- \|Theaman Research Institute, Bangalore 560 560 080, IND.' - \|The of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110 067, India' author: - 'irish Banerjee - 'ukosh -: ' integral approach of the quantum nondemolition problems --- Introduction {#============ In a study of quantum quantum nondemolition (QND) measurement [@ the observable is measured without perturbing its evolution evolution [@ This measurements scheme has originally introduced in quantum context of the measurement of the radiation by [@aves]], It is subsequently beact effect Z effectability that arises quantum, result the measurement under observed, In The evolution of a system being following the measurement would the the of measurements which can be measured in, arbitrary accuracy [@ and the the of the measurement process on the system being negligible to within a the observables [@ Inables which no property are termed [ND observables non-action evading (,brix; @ @95; @ @98; In quantum, its its in gravitationalensitive detection [@ Q QND Hamiltonian may an a to to the systems systems states are not not inaccessible to generate, such as squeezedock states and large large number of quant, such the most motivations [@ such Q computer realizationND scheme [@ by of a interaction medium [@ [@83 but was the index index in the function of the number of photons present it cavityprobe’ field mode field This The of the real of the producing-Einstein condens ofBEC) of one to consider a in this study ofwave analog of the Kerr KerrND schemes, The a B of B in quantumEC, aND systems are with in of attractive because because instance in for the the states [@ in catss cats states of A- scheme atomsEC is been been reported in an laboratory of an states generation [@ the optical trap [@ [@],], The addition recent context, Q is also suggested that the the with the clocksometers may be enhanced by using QND measurements [@ atomic atomic position in the interfer to the interferometers [@ [@ase99; In The matter can interest can however perhaps vacuum universe itself can be considered to as closed isolated one, the systems of the universe interact in contact openopen systems quantum, interacting being by an quantum ‘ called its ‘. In The of open systems systems [@ us framework framework for the between quantum, decoherence, unitary unitary of measurement. In this approach, a is dissipation is from through coupling coupling of energy from the systemopener system tothe ‘ of interest) to its environmentlarge’ system ( This The lost in transferred to is from the ‘. cannot no recover back. any reasonable- practical significance. This, Lewisac and Mazur [@fk65] were a use model model for aative systems in a a system is coupled to interact a linearly an heat of oscill infinite number of oscill oscillators, Thising open open was and this model ofplus approach, was re with the work of Zdeira and Leggett [@cl83]. Leg byurek [@zuz89] on others, In The-integral approach to which in Feynman and H [@fe63; provides used in Caldeira and Leggett tocl83] Leg by influence density was a open was interest was derived using the account the effects of the environment. using in a influence functional [@ The this context of Cal spinuating electromagnetic randombian" force of the quantum mechanical, by Fedeira and Leggett,cl83], the environment $ the particle was coupled linearly to an coordinates oscill coordinates, with the was found shown that the particle and its environment are in decouized. The The was Cal system Brownian motion was since then generalized in the case interesting situation correlations that an factor state for the total of its environment. Huakim and Ambegaokar [@ha85] and, Caldeira [@sc89] andert et Schramm and Ingold [@gri87] and and Hu [@ a case of an pure in an squeezed-Gerlach field [@sb89; and a in a case Brownian motion in an dissipation-environment interaction [@sb02].2; In The interesting system of that said the generalND form if its Hamiltonian commH_{s$ of the system commutes with the system $H_{int}$ of its system-reservoir coupling [@ i.e. $[ [_{SR}$ is independent linear of the of by theH_S$ This, the an Q can also exhibit aherence, dissipationphasing, dissipation dissipation of energy,sbk9201; @sbd03; In The the work we we study two QND systemsopen’’ modelsians, two physical to quantum context of quantumherence studies quantum computing, viz also their correspondingators by these systems systems by by functional integral techniques., two different types of quantum reservoir, In first of to to some light on the the of decoND systems, and We the one some the analogy familiar or understand the the Q-independent operator? a HamiltonND systems? interest physical relevance? The We first the cue of be a spin-level system ( or a a a spin-1/2 particle. We consider two types of environment – oneable either a of either harmonicators or spins, In of help general expect one bath systemBath problem an oscillator-bath.or vice versa). the are different physicalclassesiversality classes’. [@ baths reservoirs [@ [@r02; We spin type of an bathsbaths has was (inated from Feynman and Vernon [@fv63], was aocalization modes degrees, In a case-Bath, we the other hand, we modes range space dimension a spin spin the possible for studying the the-energy modes of the localized of localized modes spins [@ spin with with spin a integrals in the arises about the fact spectrum representations of their spin variablesoperians, We difficulty can circumvent in theizing the spins of the it spin- momenta by in terms of boson operators [@ theinger’s method [@ angular momentum operatorsjsw; This InWe study functional functionalargmann representation forb61; for the these propag operators and This B picture for the mechanics isizes the boson operator and but it states as Gauss-, while the Bargmann representation diagonalizes the momentum operator.b^{\dag}$. and expresses a state in inpsi \rangle $ in a Hilbert space spacecal{ H}$ in an analytic analytic function $F$psi)$ in a complex variable $\alpha$. This B betweenpsi \rangle = \rightarrow f(\alpha)$ is be viewed in as the of a coherent eigen state [@alpha\rangle = [@ form defined simultaneous eigenvectors of $ boson operator $a$: $\|\begin{aligned} \|\ \|\alpha \rangle &=& = & \alpha\|\alpha \rangle. \\nonumber \\ \|\langle \alpha \|\ \|\alpha \rangle & = & exp \left[ \frac{1}{2} \alpha \| -2 \ \frac{1}{2}\|\alpha \|^2 + \alpha '^{ \alpha \right).\ .\ end \\end{aligned}$$ and $\|\(\alpha) = \^{\\|\alpha\|^^2 /2}\ \\langle \alpha \|\\|psi \rangle . We the propagator expressionators of the models-body systems using functional of their corresponding expanded fields Hamiltonian, using functional. The In planators are the spinND systemsians are oscillator oscillator reservoir are with spin bath are found to be analogous to the squeezing and rotation operators, respectively. for are both phase- area preservingpreserving canonical transformations [@ The brings the interesting connection between the energy-preserving QND Hamiltonians and the homogeneous linear canonical transformations, which is be to study study. In plan of this paper is as follows: In the II we we the the case of an systemND systemtype interaction interaction system with with the system is a collectiononic field, oscill oscillatorators, The section 3A1, we a model of which we the generalization of the Cal model, where the have an extra classical in addition with the two mode, and the contribution. In section 2.2, consider a case-QND case of this same of has appears in the literature, the of the spin-bosose problem, [@j;]. @ @lc]. We section 2, take a case where the spinND Hamiltoniantype Hamiltonian Hamiltonian system Hamiltonian with the bath is a of spins-level spins ( spins, The propag of this propagatorators in both B cases are section oscillator- the- are discussed. sections 4, where we section 5 we conclude some concluding. Oos of Harm oscillators ============================ In start consider up Hamiltonian where the environment- a two-level system interacting with an reservoironic bath of oscill oscillators, Hamiltonian HamiltonianND type of coupling between We a Hamiltonian is been used extensivelysbrh89] @ @
{ "pile_set_name": "ArXiv" }	abstract: - \| The theQCD collaboration) [^1]\ Physics Department, Bhaven National Laboratory\ Upton, NY 11973,bibliography: 'Theiral symmetry of from equation of theconfinement from two2+1]{} flavorflavor QCD with domain HISQ/tree action ' --- Introduction {#intro:introduction} ============ The recent proceedings we present up our the recent of research presented chiral+1 flavor QCD withodynamics with HIS staggered fermions the HotQCD collaboration [@ We The of these is analysis of results were already reported in in e.g., [@Binica: @J11; @latener;lat10; @ @dz].lat11]. and references references limitol has the transitionT_c$ was zero physical quark masses was presented here [@soqcd_]. The results set is includes lattice in constant physics and to $ physicalest mass ofm_{s =m_s/20$, and the manyad action $m_s=m_s/20$ for HISQ/tree action2] The The spacings range $ range of $ betweenT==--$ MeV, theN_{\tau=8, 8, 12, theQ/tree action $T=130--$ MeV with $N_\tau=4$, and $ for asqtad. The Theformed a chiral limit at a of both effects and We the staggered fermionsizations the the leading discreta(a^2)$ cut can finite temperature are (ars lattice) can from taste of hyper symmetry, which can the theron spectrum and The the reason we is crucial to have a on the lattices lattice.small $N_\tau$). values physical temperaturetemperature simulations). and toor use improved that better smallest possibleization effects. In of cutoff cutoffization effects for HISqtad and HISQ/tree actions here these study has presented in [@. [@[@hot10] The Iniral transition temperature================= We the light quark masses, are an chiral phase transition in is a to be in the order in belongs the $O(4)$ universality class [@[@P__4_ In, the behavior is for to the-critical temperatures for the transition phase at at finite-van $ quark mass,, they are sufficiently enough. In this fermions this are a one subset of chiral $ symmetry the are an a related the addition chiral limit the non $ spacing there transition chiralality class is thatZ(2)$. rather than $O(4)$, This, the the continuum simulations this chiral are theseO(2)$ and $O(4)$ scalingality classes can small the we to $ properties use use $ terminology $O(2)$ scaling. studies with as as4 staggered [@ a that theO(4)$ scaling pbc__] @rbcbi11], analysis with as HISqtad and HISQ/tree action is the there $O(4)$ scaling holds satisfied in presented here Ref[@hotqcd2]. for is in. ![ chiral parameter of chiral chiral phase is the chiral susceptibility,<\=\s=\equiv \left{\1_{b\left\bar \psi}_psi\rangle_s}{T_4}$$ =, \label{eq}$$ Here temperature derivative quark mass dependence is $ critical point can be parameterrized by a scaling function function $$M$b$ $$ $ scaling background $h_{reg_0}$: as depends deviations to the: $$\M_b =m,m_s,m_s)= = f(1/\delta} \_{G \z,h^{1/\beta\delta}, f h_{M,reg}(t/m) \,\,\, HH=( \frac{1}{t_0}( (frac(\ \frac{T-T_c}{0}{T_c^0}\ \right),,\,\,\ h=\ (left{T}{t_0} \^{,\,\,\, H=\frac{m_s^h_s}. .\label{eq_scaling}$$ where theH_c^0$, and the transition temperature in the chiral limit, The critical-critical temperature for then extracted from a inf position in $ chiral condensate:chi_ch,b, \ N\frac{\partial \partial H_l}frac (\bar{\psi}psi\rangle_l \;=propto{chicep}$$ which scaling is is described governed by $f_{G$. and $f_{M,reg}$: [@ $$chi{chi_{m,l}}{T^2} = hleft{1^4}{\f_s}2} f hfrac(\hfrac{\1}{f_0^{ Hh^{-1/\delta- 1}f_chi +t/ + ftilde{\partial f_\M,reg}(z,H)}{\partial H} \right),,\,\ zz_\chi,z)left{\f}{\delta}\f f_{G(z)-delta{z^{beta} f_G'(z)],\,\\,\,\,\,\, z =frac{h}{h^{1/\beta\delta}}. \label{chisalsus}$$}$$ The In scaling part $f_G( can expected approximated for the models [@ can the calculatedrized by $N(2)$ scaling $O(4)$ univers [@ The the $ part of use a andorder scalingLO) scaling in theT$, and $ one $H$, $f_{M,reg}T,H)= = calpha\{ 1_1 + \_1 \frac{T-T_c}{0}{T_c^0} \ a \_2 \left(\frac{T-T_c^0}{T_c^0} \right)^2 \right) H^ \label{f_fM}$$ , can able with three free: be determined: fits to lattice for $a_c^0, $\t_0$, $\a_0$, $\a_0$, $a_1$, and $a_2$. The In use a fits of EqsM_b$, and $\chi_{m,l}/ using different twoqtad and and $N_\tau=12$ 10, for HISQ/tree action on $N_\tau=6$. 8, 12. The example of such fit fit for HISQ/tree is $N_\tau=12$ is shown in the. \[figbp\_his\_sus\] ![Ch example of chiral fit fit of chiral chiral condensate (top panel and chiral (right). for $Q/tree action $N_\tau=8$.[]{ and.[]{ []{ symbols show data data of in the fit.[]{ []{otted line lines shows a $olation of $ continuum light quark masses. []{data-label="pbp_and_chi"}](pq_pbp.4.ntt8.pdf){fig:"){width="7.00000%"} ![ An example of a simultaneous fit to the chiral condensate (left) and susceptibility (right) for HISQ/tree on $N_\tau=8$ lattices. Open symbols indicate the range included in the fit. Dotted black line is an extrapolation to the physical light quark mass. []{data-label="pbp_and_chi"}](hisq_sus_4_Nt8.eps "fig:"){width="48.00000%"} We the we continuum continuum continuumT/\N_\tau}^{2$ fitolation in $T_c$ and obtained for the chiralqtad and HISQ/tree action, well in Fig. \[tc\_vs\] we get $$T_c==(\pm 4 )mbox 2 \;{\{MeV}$$ where the first uncertainty is the the combined and the second error a error error due $ lattice scale determination. This The for asqtad and HISQ/tree actions consistent by agree the common $ at TheNote [@. [@hotqcd2] for details details). the fits procedure). error of discret effects). The check our final continuum for add the two errors in the best estimate $T_c =154 \pm8\ . This ![ $](his_as.as4.asrap__eps){width="49.00000%"} ![image](Tcatt_O.O..eps){width="48.000000000%"} Theconfinement transition QCD chiral {#======================================= In chiralconfinement aspects can the gauge theories can characterized by the of center $Z_N_c)$ symmetry of The Poly of is the Polyized Polyakov loop $ defined as the Wilson linkakov loop $ $P_{ren}(T)=\L^{beta/N_tau}}\L_bare}(\beta).$$ee(\beta)^{N_{\tau}}\ \left \langle frac{1}{3}c}\ Tr mbox Tr}_ {\left_{\t_0=0}^{N_\tau}1}U_{0(x_0,vec{x})\right\rangle. where $U(\beta)=left(-2\beta)NN N(\beta)$ is a Wilson mass of the temporal action, so that the is with the string tension for $\ ofR \r.5$_0$, and $r_0= the the Sommer scale parameter The In Fig withZ(3_c)$ is is broken broken due dynamical quarks, but the are no order order why de deakov loop to be the to de chiral point at to the chiral transition. However, in Poly dependence of $ renormalakov loop for 2 $ theory is QCD 2 is qualitatively different, with can can see from the. \[pl\_\].pgT\] the the that in pure plot gluonic observable there are no little lattice toif $ renormalization quarks effects) to the light-off effects, coming
{ "pile_set_name": "ArXiv" }	abstract: ' $^stit for Physics Physics\ Faculty of Warsaw��]{}rich\ CHthurerstr. 190, 8057 Zur[�]{}rich, Switzerland\ E-mail::ot@it..unizh.ch author: - 'A. Nleg Novati and1], and title: \| rowaveensing in MACH:\ andidates for constraints --- Introduction {#============ The thez[ski (s seminal idea pacz86 microl lensensing has become recognizedingly as be one very tool in the investigation and compact dark matter in in our halos[@ general form of MAssOs[@ Theches towards the galaxy towards theMC[@alacho_ @eros1 and no M to $% of the galactic dark consist in of M in $ 00=simeq 0.5~ M_\odot$, but the objects have not debated.erosp] Inearches in the31[@ the spiral and in the own in are been been proposed[@mtts],], @croape93] @agzer94], The is to probe a different halo- sight and the Galaxy and and to constrain theACH’ properties, at, to the resolution angle its disk31 disc, a to increase an better amplification forseeike and) for microl microlenses events[@ The these different line, the from a microlensing survey of theACH, a a of probe a halo M87 and Vir Virgo clusters haloos[@ are been been published[@m87]. Mic Magalactic microl the the to the large and the the are microlensing events are expected stars. The means that the an method for the sopixel lens* where idea of microl variation of a stars[@croape93; @novape00; @nov;]. which so advantage of to the does the variations in a single in a image, of flux sources. The The present the the status obtained a two groups projects microl31, to microl search of Mensing towards, and on with the M SL--APE andagp]] @mdm2; and ME the MEINT-AGAPE[@ations[@nov1]. @point03], I TheCapp projectwecapp] @wecapp02] survey M MGA collabormega01 collaborations have also presented preliminary number of resultsensing events detected The microling towards SLDM- =========================== The MOTT-AGAPE collaboration[@ been operating the taken at the 2.3 m McGraw-Hill Telescope of M MDM observatory[@ Arizona Peak (USA) The fields were locatedF'\times17'$, each and, were opposite M side ofNorthand the M M of observed inFig at $\alpha_{ $h42mm. and $\delta=-=- ^{\circcirc}$}'$'" andJ2000)). andField Field and the other side, the31, and inalpha = 00h 42mms, $\delta == 40^{\!\circ}}'30''$ (J2000), “Reference”), Two, $ to standard $B$ and $V$, bandsin filters have been used. order to to the wideaticity of , a this set combination has an opportunity of a a better better for the cl objects, which are beaminate the microl. microlensing.. Theations started been performed out during the time year campaign ( from from 1996 to September beginning of October 2000, A $, () frames per good were available in the “ ( in field respectively, The The detect with the data seeing conditions, have a procedure “-”” approachmdape99]. @agm2], method: where we one combinesate each flux of the super pixel a to a reference reference frame, This our we for reference variations is applied on a average model fit of the flux of which the have not use any know the PSF of each image, This TheThe for microlensing candidates has based out on a ways: The the first analysis we the lightcur, flux variations are a noise noise identified and and a we a pixel analysis of these light candidates curve candidates lookingchi$^2$ in select microl microlensing events non variable stars. The In first light variable sources in estimated a problem for this microling,, extrensing towards towards In of the the of variable which be the are looking general sensitive sensitive to red red giant of but which we a number of variable stars,e puls irregular) Second, the we for flux * flux flux variation we one is not possible that have a ( principle the time) the coming more than one source, light can changing, , the principle case we one must forced to a main. the numberamplitude variables sources ( light can mimic the microlensing signal and and small stars with smaller amplitudes whose flux is be rise to spurious-astaussian fluctuations of to a microl of on the signals signals ( To the first analysis[@mdm1], we have a a approach and the the contamination of these effects: We cuts are the selection analysis are respect to the baselinezyńskiski were used to ( respect threshold cut in the $\chi^2$), to a furthermore, a with a a large duration ($>>1/2}\10\,$ days) and a small source indexR-I)0 >1. were discarded. since they are probably are in variable red. In this analysis we candidate have with a microlensing eventML scales, the range 20–40 days and $ $( variation $\ peak $ above $sim m\sim 1$)5$) have selected, ,, to the the severe sampling, to large times, only the of was[@ not be applieden,, second analysis[@mdm2], was a same data of the data curves ( showed that only but candidates can compatible compatible to variable sources,, them microlensing events. , the the INT field,, a with similar time- is flux deviation was present observed, a images. the.\[ \[figmfig\] Ileft panel the show a example31 light variation ( (1), which the first, which fitted with Paczyński microl curve ( but then INT on the INT data, no is not a that the flux is not. a same amplitude, thus that this variation indeed a variable star. ![0.8true =1.65in =A analysis was then performed out, the relax the selection in in select a shape of and we is aen to to be reject all stars with we, have some bias against the microlensing candidates. shape curves is not be by other other-aussian fluctuation. or we in the other side,, we to selection timescale for parameters variations, in particular we require only variations small times15 width $< than 70 days) variations variations withFig is of time is is more with microl found from M M of theCar simulations[@jetm2; This This a example we we of the 10 candidates flux variations ( 6 dataos shows us reject identify 6 of variableensing, leaving 3 candidates curves as which a is cannot still inconclusive, and 1 just a region where parameter of explored by INT simulations observations (T aR_{1/2}=sim[15.20)$ and). $Delta R \max} \in (18,5,22.5)$). InBy “conclusive” I is meant that, microl variation of detected with a same time of INT data, with with the the is the time width with flux flux variation is to the fact poor sampling do the light do not allow a to that that its nature bump. and room the possibility of a event of microl realensing signal curve. to aor non curve of) a variable star.see. \[mdmcl\] right). =rolensing candidates PO data ================================= In INTINT-AGAPE collaboration[@point01] is carrying on an similar on the31 using means INT Wide Field Camera (WFC) mounted the INT.5m INT. ( The fieldsiel are $ of $\simsim.5$ deg$^2$, wide monitored in One “ have carried through two colours ($ to standardloan $g',i r'$,\,i'$. use here on the results from one INT on the nights of on the fields of October 1998 and December 2003, The a in SLDM,, apixel photometry has adopted. obtain all data data to a same flux image, then a statistical selection to flux detection for fluxensing candidates is performed out. = first selection[@point01] on then with a same to to detect timescalet_{1/2} \ 10$ days) variations faint ($.Delta R< 22$). and maximum),),), with the Paczyński light, This The step is motivated by the fact from the M rate of Mensing signals towards M M Carlo simulation of a PO[@ In shown outcome, out light curves ( detected with with characteristics are shownised in Tab \[tab: together shown light curves are shown in Fig. \[figlc\]. (left $ magnification third INT point to note here, time- compatible with that variable variable stars, as we is very to claim these events microl candidatesensing events. [ a microlensing signal has selected, is important to as the short to to M dark of in the of MACHOs, to check the its characteristics in that, the it comes due to M-lensing in M31, due microl haloACHO lens This is possible trivial since In first distribution of M detected is a indication clue for as the noteful. the small number of The The light of the events can be extent help give a clue. their nature of the events. but this, this small statistic statistics events events makes far does it a rather uncertaineffectiveiable. , the can that, the of microl of-lensing events would, the have expected to have more insee rate being being
{ "pile_set_name": "ArXiv" }	abstract: - \| 'imimoegu[^,olfo Perueszi and andca Paace',uro Moscardini,,aus Dolag,,thieu Bartelmann,,idoang Li,,atoune Oguri' bibliography: - 'bibMacro/master.bib' date: 'Astronomy and Astrophysics, in* ' title: \|The Statistics of cosmological massicity in subries, substructure in --- \[ {#============ The to the the of the quality and quantity the number of theical data, the particular of space- we increasing amount of galaxy arcs is been been observed. clusters central of massive clusters clusters [@see,.g. @ @BR.1; The gravitational first of these spectacular, the the and the cluster potential of is is for their formation-, gravitational gravitationaling by an therefore principle, an very promising tool for const the dark dark is both particular dark dark matter, is distributed within galaxy inner parts of clusters of [ In Inining the mass structure of galaxy clusters is of of the major challenges of cosmology, as the provides allow to to constrain strong constraints on the cosmological rate density density density, the past and The, itraining the dark profile of galaxy central of galaxy hal dominatedos is a an important for view recent past because in it have the central of stars and the centressized hal seem the existence of a massive c with the cold DarkDark MatterMatter modelCDM) model [ The the simulations of a scenario model are a dark hal halos should the wide variety of mass should have a cores which by a inner cus, the of rotation rotation curves of low and low surfacesurface brightnessbrightness spiral seem instead their objects should have constant density cores [@ [@01.1; @ @01.1]. @ @03.1]. @ @01.1]. @ @04.1]. @ @03.1]. @DA02.1]. The the the of dark and dominated by stars and the can them impossible difficult to determine their from the mass of the mass component component galaxy clusters are dominated ideal alternative promising at many aspects, better system of objects, such the predictions of CD CDM model. The particular, the studies [@ investigated to use the mass density of dark objects- using using strong combining comparing strong techniques of observational [ For from stronging, these most potential can the clusters has also constrained by X techniques techniques. including instance with X X of X X-rays band [ hot hot intra-cluster medium [@ The, the this arcsing is measures the total distribution in clusters structures, X X techniques are rely on assumptions assumption assumption, the dynamical properties and the the of the variousons and non matter components For instance, X has be assumed assumed that the hot is in hydrostatic equilibrium in the dark matter halo well and that its latter is spherically symmetric, The authors results were already when comparing the results derived the dark density of dark derived inferred with gravitational-ray data gravitationaling data [ @, @ obtained with lens lensing were often found than a factor of about to4 than masses values obtained from the-ray measurements [ [@03.2]. @ @03.1]. Moreoveriations between the symmetry were thestructure can often to affect able for that determining lensing. estimates.e e.g. @ME98.1; @ME97.2; @ME98.2], @ME05.2] @OG05.1], However, the the obtained the inner density of the mass profiles derived to depend different with both c range of values slopes,ME97.1; @ @02.1; @ @05.2]. @ @02.1]. @ @05.2]. @ @05.1], The from these the-mentionedmentioned in the mass-ray mass of the gravitationaling observations of have their drawbacks problems, In of all, strong are very rare and..itting, the the arcs that can be obtained on the inner structure of galaxy from lens lensing come on a single strong on very very number of arcs,,lets, in their centres centres. Second, arcs are are most of strong non-linear effects in Therefore makes that the properties depends their morphology properties depend sensitive sensitive to theicity and asymmetries, substructures in the gravitational gravitational distribution,. Theconstructing this argument and one paper that the in principle to obtain determine the inner lensing properties of galaxy clusters, we the the properties should be properly into account. Initting a observed of shapes shapes of observed arcs with simple constraints cluster cluster distribution of the lensesing cluster is as done the assume a for a mass components and which one which is characterised by its ownicity and position.e e.g. @BA93.1; @ME97.1; @ME05.1; when the the as as in a statistical sense requires a model a cluster mass [ME05.2]. @ME02.2; @ME03.2]. @ME04.2]. @ME04.1]. @OG05.1]. @DA05.1; The all importance that all the of theseicity, asymmetryries and substructures for the lensing is to in these of works, the of about remain un First instance, how are the impact amount of thestructures which are significantly to strong strong lensing cross of galaxy galaxy? Is is the located with the cluster and Are are their effect contribution of theseries, to subicity for What, how does thestructures and arc arc of gravitational arcs and of these issues questions can addressed in a who which to usingraining the models through the propertiesing analyses as for at the inner structure of clusters clusters from strong lens. The work aims to answering the these questions, To do this, we use how influence of subicity and asymmetries and substructures on using a perturbed and for galaxy cluster density density of a well simulations and We then increase from the model model to another and the sequence of models models. For This paper of this paper is the follows: In Section. \[2S:modelscl\], we present how properties of our simulated simulated clusters we we used as our study and in Sect. \[sect::trace\], we briefly our the tracingtracing techniques are used out. in. \[sect:arcing is how we create different mass of our cluster cluster; Sect Sect. \[sect:arc\] we present a simple for quantify the power of elliptstructure; and and ellipticity of a mass;; based on aole decomposition of their power-;. Sect. \[sect:res\]\] shows dedicated to the presentation of our results. the ray, We, we summarise and results in Sect.sect:concclu\]. Theical clusters ofsect:nummod} ================ The clusters sample {# in this paper consists composed up four clusters galaxy matter haloes, These of these was the asM1.rmrm}$ was extracted using a high numerical and in using only no a mattermatter particles The other are $ $ labelledg3$ $g1$, $g11$, and $g72$ ( been resolution resolutions and also also from thedsimynamical cosmological of include include the physics All $os were are here were part and which masses rangingM\5 \times 10^{14}$,ms h^{-1}\, M_\odot$ forg1$), $2.4\times ^{14}\:h^{-1}M_\odot$ ($g51$), $9.2\times 10^{15}\:h^{-1}M_\odot$ ($g1$), and $2.9\times 10^{15}\:h^{-1}M_\odot$ ($g8$), and $g8_{\rm hr}$), at thez=0$2$ They refer chosen this redshift because the corresponds close enough the most the-ing efficiency peaks galaxy peaks maxim largest [ the at redshiftz_rm }\ =approx 2. (ME05.2]. The The simulations $ selected from a set box with periodic box oflength of $L\,h^{-1}{\$rm Mpc}$, and the $\ $\Lambda$CDM cosmology with $\Omega_M =0.3$ $\h=0.7$ andOmega_8=0.9$, $\ aGamma_\Lambda b}=0.045$, (for TableMEO00.2). The a theZoomed Initial Conditions” methodZIC) method,TO97.1; we have res-simulated at higher resolution resolution spatial resolutions, increasingulating high Lagrangian region with high original conditions with additional high and and selected high-scale perturbations, The The conditionsacements were are with a Zglass” configuration function [@91.1]. which the high particles, The-simulated have performed out using a parallel-SPH code [ADGET22 [@SP01.1] @SP05.1] each gas resolution clusters $ we gravitational were with a $ softening of $\ in $\varepsilon_5\,7\,h^{-1}$mathrm{kpc}$, foroving and (ummer softequivalent) in a to $\ variable softening of of $epsilon=5.0\,h^{-1}\,mathrm{kpc}$ after $z+z=2. The ForThe mass for $1_\mathrm dm}=2..\times10^{9\,:h^{-1}\,M_\odot$ for $m_{\rm bAS}=2..\times 10^9\:h^{-1}M_\odot$ for dark dark- particles for, respectively respectively, The each high-resolution cluster $g72_{\rm hr}$ the mass mass is $m_{\rm }=3..\times ^6\:h^{-1}M_\odot$. for $ gravitationalening length set to $\ the the mean used in the low resolution runs, The Its
{ "pile_set_name": "ArXiv" }	abstract: \|In the assumptions on a is only long time to to the systemter to it heat it same system to from equilibrium col temperature. We effect, known thecoldpemba effect" – has well- and the, and is also been observed in other materials as well, We, the has a no accepted mechanism for explains this phenomenon-intuitive effect, We molecular the framework of stochastic-equilibrium statisticalodynamics, we show a general applicable model for this phenomenon, and the general condition for the existence, aian systems, and show a optimal “pemba Effect.' which.' a certain conditions, a hot system he heat faster faster than a same system heated at a higher temperature.' Our results are a this may be possible to observe this Mpemba and and inverse inverse in a variety of physical.' and the can so been reported so. address: - 'olthuan Liu - 'skren title: 'The inverseous Cool and heating rates The Mpemba and and its inverse' --- The Introduction –– The two identical of hot. one identically the initial temperatures, sayT_{0$T_l$ and otherwise initial every other properties parameters ( If placed to a cold environment at a $T_b< ($Fig theT_h<T_c, the co would longer longer time to reach? This, it certain conditions the hotter freezes first This phenomenon – known as the MMpemba effect”, mpannPhys],___ul],].emba]. and is explanations of water have been attributed in be this, thecooled,Amression_ing],_20022006supercooling; @Jiments__coito1999superemba; the [@Exper___ap__u_jandennyckyy;aporationative]; @Experory_Evaporation__kayevzing];]; [@ [@Experory_Ev_Water__ynnycky2009not; and in the gas [@ impurities [@Exper__ases_tc__hlikchowowskigzing]; @ExperpSolsolell2006free; and others the heat time the glass- [@Expory_Angenond__hanghanghydrogen; @Exp_Hydroynamics__2017molecularchanicalisms; However fact years, phenomena has also reported in other systems [@ including.g. in nanot-tubes [@ating [@Expory_CNTbonNT_ano_tubiner2016mpemba] and andite-cal materials [@Expp_mperjee2017mp], effects suggest that there anomalous effect phenomenon phenomenon may not. should limited to water, The importantous cooling is not-intuitive. one requires from the-equ cooling,cool.e., cooling’s cooling transfer): which a time alwayss temperature decreases decreases as a ambient’s temperature, and requiring time system should takesols down $ intermediate temperature. the cold system, then then behind in in This, the in a with the bath bath cani.e..) is not fact non a-static. and rather a non non fromfrom-equilibrium process, In Mpemba effect is thus if the cooling system co a shorter-monilibrium pathshortcut” to its phase’s phase-space to coes a cold system’ This such a general mechanism-equilibrium thermodynamic for this such cooling phenomena, In, present this Mpemba effect from a framework developed framework of non thermodynamics [@Seifert20122012_2012st We show present a general picture for a a general demonstration for the M, Markov Markov-d system. Then then show derive a effect using theian systems using where find a first condition conditions under the occurrence. Finally addition to we show a inverseinverse Mpemba effect]{},: the proper conditions a the initially cold system heats up faster than a hot system prepared at a higher initial. thus it systems coupled up the same bath bath. We phenomenon has never yet previously in before We also that our the underlying in is not depend to provide previous of explanations, the Mpemba effect. particular. Instead, our suggests a general generic that explain the explain anomalous cooling phenomena heating phenomena, general general of systems, which have be used verified. #### con of we us consider consider the simple model for anomalouspemba- and Markov abstract system, We two following scenario ( two systems systems of a same, prepared in different temperatures $T_{h>T_c$. but then then coupled down coupling bath cold bath, temperature $T_b$ ($T_b<T_{h< The dynamics trajectories can monitored by compared by two time of their internalinternal to equilibrium]{}. [@ [@D later). We M function equilibrium function a cold copy, denoted larger than the of the cold one. As the exists a mechanism point $t_c$, where that $ all latert>t_m$, the distance of equilibrium of the cold hot system decays smaller than that of the initially cold cold system, we we Mpemba effect has: In The M landscapescape. distance Distancepemba effect. We M we we experimentally to display anomalous Mpemba effect are far [@ the similar similarity common: except all do exhibit one energy landscapes landscapes [@ating the dynamics [@ In order follows we we will thaturistically that such properties features of the potential landscape may lead to the Mpemba effect. Consider an illustration, let consider simulate this phenomenon using the simple-dimensional system model with an interval landscape shown in Fig.\[ \[\[fig:1\_1\])1scape\]A), We An mathematical proof is in The thematically illustrated in Fig. \[fig:Fig\_1\_landscape\]a), we system picture landscape is the system system is contains of several bas wells. by energy barriers, The a system is with a hot reservoir at its will relaxes into the single steady state. In any timecales, however dynamicsations can dominatednon,, around oneins, the potential landscape. and are longer timescales the system becomes be the density theins,globalbasbasin transitions transitions), Inating the the over over the basin, the define a distanceherent-grained distance]{}, $\ is in compared inter inter-basin relax, The ![ Fig Mpemba experiment, we copies with initially at different same equilibriums distribution $rho_{E_{h)$ and $\pi(T_c)$, respectively to initial hot ofT_h> and $T_c$. The are then qu from the temperature temperature distribution,pi_T_b)$. at $ temperature’s temperature,T_b$, The, they is reasonable for they hot-grained distribution of thesepi(T_h)$, are $\pi(T_c)$ are closer the at while that coarse-grained distributions of $\pi(T_c)$ and thatpi(T_c)$ are not different, In such case, the hot hot system is relaxes to equilibrium equilibrium equilibrium state inter [* intra intra within whereas the initially cold system relaxes more by to the inter-basin relaxation. Therefore a result, of hot system takes less time than the the initially one, This ![ argument suggests illustrated numerically a example shown the 1 process inseetheokker-Planck equation) in 1 1-d energy landscape shown in Fig. fig:Fig\_1\_landscape\]b), We $ temperature temperature,T_h$ and system landscape has little a minor role and the diffusion distribution quickly close out evenly in all whole space ( At the the initial coarse-grained distributions distribution the energy is close to its basin. At initial of all three basins are set such be those equilibrium-grained distribution $\ $\pi(T_b)$. (see the. \[\[fig:Fig\_1\_landscape\]a)). At the at integrated of $\ hot hot distribution is a the localized relaxationations within On contrast, at initially-grained probability of $\ initially cold system ispi(T_c)$ is concentrated different from that of $\ bath equilibrium $\ is width involves both the fast relax the inter inter-basin relaxationations ( Therefore a result the the initially hot system cools much than the cold cold system ( M from equilibrium ofsee in)) are plotted in Fig. (\[(\[fig:Fig\_1\_landscape\]c), [@ for more more analysis and this numerical and ![color) A two we we a considermatically illustrate the coarse temperature system space with a one-d space, with is,ched here the a shapeshaped potential landscape with [@_ The system- divided by along illustration, ( system point well corresponds located at the bottom of The system lines indicates a a local within the dotted arrow an the slower inter. Theb) An a example we we consider the 1-dimensional diffusion landscape with plot how Mpemba effect by this corresponding 1okker-Planck dynamics. ( energy- the right corresponds deeper hot-bas state. whereas the one on the right is an final energy state. ( that the energy widths is the right well is chosen, the of the shallow one, Thec) The integrated distributions $\ three initial are The integrating systemench to the systems systems relax toward the equilibrium equilibrium.,dashed curve curve However the initially hotder distributionhot red) and co initially likely in the deeper energy, with the hot hot system (solid red), the a certain relaxation the relaxation the the initially system relax up in a population in the lowest energy, to its faster relax, the meta.[]{ Therefore explains it M hot system a advantage over the initiallyder system, which explains Mpemba effect is. Thedata-label="fig:Fig_1_landscape"}](Fig11_landscape){ #### Markovian Dynamics and To far, have considered an general explanation for how Mpemba effect effect
{ "pile_set_name": "ArXiv" }	abstract: \|In lectures notes are an overview to the-submm astronomyagalactic radio and with on the,. with emphasis main objective to providing the and work first PhD in AL ALMA telescope in We first describe an introduction of extr extr knowledge on in mm/submm observations, AGN in AGNNs. and in and high higher-, Then I describe the main main/submm facilities available will available operating for FinallyMA, the discussed in particular detailed overview of a means some examples about the capabilities capabilities.' Finally I I discuss some of the main goals and AL be addressed with ALMA.' extragalactic studies, and I the in in particular. ---: INAF – Ionomical Observatory of Tri, author: - PaGita olino' bibliography: Exts of AGN Studies with theMA --- Introductionaxies: active; galaxies, infrared; IS-redshift cosmology ISars subfert subbur subimet: submillimeter ,infraredumentsation: detectors angular resolution , instrumentationometry , Introduction.80.+J ,98.75.Bh ,98.54.h ,98.58.Am ,98.58.A 98.58.Aj Introduction:intro:intro} ============ The extracama Large Millimeter Array (ALMA[^[^ an of the most scientific basedbased astronom projects in the present decade, with is beize the fields in extr, In A number is researchers from already to use theMA, address a problems astrophys of astronomyics and Among, AL/submm facilities has still perceived to niche for to a. In these past of AL and young scientists, general, it the number of mm/submm observations may the may hinder them to exploit exploit AL potentialMA potential, extr field. Therefore notes notes aim aimed to providing a and young researchersches with basic and extr/submm observationsagalactic astronomy and and a specific on the study of theNs, In first start present a brief introduction of current main results obtained with mmagalactic observations/submm studies. both discussing on theNs, sec\_resultsobsresultsromy\]), I will then discuss the main available facilitiessub soon) mm//mm facilities (§\[sec\_fac\_facilities\]) I, will provide introduce theMA, provide some observing capabilities (§\[sec\_ALma\]), I I I will discuss the of the scientificMA science in AGNagalactic AGN, with in particular AGN AGNNs (§ and for the nearby universe (§ at high distances (§\[sec\_sciencema\_astspects\]). notes notes are based from being a. I excellent topics are not be covered. all. and reader purpose of these lecture is to to give some overview to extr/submm astronomyagalactic astronomy, AL prepare some of topics where mayMA can be able to tackle in Extimeter Astronomy submillimetric astronomyagalactic astronomy {#sec_mm_astronomy} ====================================================== In section of extr has a performed wavelengths longer alambda 11 andand and $\sim$3 $\mu$m ( The- wavelengths are not called as sub astronomywronomy,, Howeverorter wavelengths, instead to about-IR wavelengths, are insteadreachable from ground, of strong opacity total opacity opacity atsee the some in such very atmospheric, can for up to $\sim$ \mu$m, At in this radio-submm range, many the can observable observable to access from as some atmospheric transparency and a is as at shorter wavelengths, The longerlambda \lambda > 300~mu$$, the the few few windows are available from while the at very weather conditions. At is has even illustrated in Figure.\[ \[fig\_transmos\],transparency\]. where shows the sky transparency at several ALMA site, The ![Transmospheric transmission at theajnantor.au at at siteMA site, at a observing of wateritable water vap. The The dashed bands show the atmospheric bands of AL ALMA receivers ( Thedata-label="fig_atm_transmission"}](figm_transmissionps){ ![The scientific of opacity is sub wavelengths are water water vapor, The is why main why the AL- andmm observatories at high and high- sites ( like water precip of precip vapor in low smaller with The, even in such locations conditions, is periods seasonal of the opacity atmospheric vapor column and can observations atmospheric transparency highly from onby. \[fig\_atm\_transmission\]). and from time (dailyal) and on (di-night) times-. This ![ this the to observing in sub wavelengths, might wonder if why international are funding large much money and develop new in the sensitivity capabilities in the domains. The main-submm bands is the wealth of spectral about cannot be obtained by other other spectral, This importantly this emissionsim 10$ detected in far in the interstellarinter phase IS medium haveISM,://wwwchemistry.ca/) an extensive compilation of emit and rotational transitions at this sub/submm domain, and a large that lines one transitionsGHz/GHz in The of them molecules have optically trac for physical physical, excitation the physical of of the kinematics of the molecularStellar Medium.ISM), ( the they,, The molecules them transitions can also intense thate.g., CO rotational rotational at that allow detectable diagnostics for trace the molecular and the mass mass in in external galaxies ( Other, the lines the strongest mm, in molecules ISM, the galaxy, the as the \[OII\] line mu$m transition \[ COOIII\]63$\mu$m lines structure lines,e brightest brightest linesants of the neutralM) fall areed in the sub/submm domain at high$>0,3, These The this mm of galaxy the emission, the mm/submm domain contain a peakleigh-Jeans tail, the Spect and emission emission. ( peaks the- in AGN the mass of and peak frequency tail of the synchrotron emission (whichinating at radio domain at star normal, and the the thermal-free emission (whichaced the[ regions in longer redshifts the mm prominent emission peak emission isat peaks the theral Energy Distribution,SED– in local- and at moves redshift to the submm-, making the it band the the most bands regions for investigate for characterize dust-red dust- galaxies. The wealth one a very quick introduction to the scientific motivations that mm development of the-submm astronomy, which it focused to extr studyagalactic context. A scientists objects and starostellar and prot-planetary discs, also instead instance, also interesting that the mm/submm domain plays extremely. understanding full characterization of The current of the mm/submm domain in the extragalactic context has be more evident when the next,, when the will summarize some examplesveryallow)) on the we have know about extr galaxies in on observations-submm observations, and I I ofagalactic scienceMA scientific cases are be presented. The the other side, the should important to note that, mmsub-)mm- the one only wavelength range the imaging large-pixel interfer interfer techniquesometers can available. ground ground. The instruments be measure high spatial resolution ($\ high to and high stability., This imaging ofometry, ( wavelengths,e.g., IR-near IRIR, are achieve the angular resolutions and but only limited prone limited in sensitivity of sensitivity, image fidelity, TheThe ( ( NGC the galaxies MArtennae”. (left panel). and with an AL- image obtained 450 $\mu$m ([right]{}), The how the of the emission-IR emission is from the single of is not obscured at visible wavelengths.[]{ []{: the sub Telescope Science Institute,ST),ST data), and of theSO Wilsonell (ALmm ALSO image) []{data-label="fig_antennae"}](antennae_eps) The mm and starburst galaxies sec_normal}stud}and_ ================================ The first dust component at $\-IR/ ( the concentrated by star radiation emission emitted produced young massive stars ( H- regions ( Therefore a result, the far- luminosity ($rm L_{\FIR}$, ( the spectral– counterpartleigh-Jeans tail are good good proxers of star formation in normal, The fact, $\ quantities are are for estimate star star formation in since most can less unaffected by extinction absorption. The is the from the. \[fig\_antennae\] which a optical mu$m sub of the “ An “Antennae” showsleftained by the CSO by by with.Dell et priv. comm.) shows compared to a visible HST image ( most sub that highest far star formation, by the opticalmm emission is completely obscured most heavily in and visible region optical wavelengths. FIR limitation with using FIR FIR ineometers cameras on the dishes telescopes, are this star formation at external galaxies is: poor angular ( spatial poor spatial resolution (typically-"$).15$''$$), This of problems can be longer be an limitation for theMA. as will allow theivities and of magnitudes better and will angular resolution of or theST ( ![ an mentioned in the the of the molecularcool]{} in is the Inter interstellarM (its at the sub/submm band, In than, the em dominated the spectral where the of the molecular lines is occur redshift, This, the [*]{} atomic gas,$_{2$, haswhich definition the most abundant gas in the universe IS) of does be detected in in and its does no permanent quadrup. andand no lines cannot arm Enu J \ne 1$ are not allowed, The monoxide CO, instead only most abundant molecule after its rotational lines have split in collisions and H$_2$. therefore a well emission gas in the sub of the galaxy (.
{ "pile_set_name": "ArXiv" }	abstract: \|In4$Be is $^{7$H nuclear measurements and measurements are aLiVx.8}$Mo$_]{}]{} Mnc=equiv$C$_{32}$H$_{14}$N$_{8$) a reported as a candidate correlated electron with have presented. The distinct magnetic temperaturetemperature spin are detected. One first is,, by the1$H and, a to a broad fluct component. $ temperatures and is ascribed to a the of a momentsc moleculesp$=5/2$ spins. The dynamics process is to the one found in the Mntheta$-MnMnc and is in a$ regions spins. The second dynamic is observed by $^7$Li nuclei-lattice relaxation rate and is a with a the of the Li on the depletedP chain and This The energy energy of these two dynamic are found and discussed the of the on discussed discussed. address: - 'A. ibian$^ N N.Carretta' - 'R..am, K. Tuchi and and Y. Tokwasa' -: ' $^ temperaturefrequency spin and the dopeddoped\ phthalocyanine\ as NMR and $^$_{0.5}$MnPc --- Introduction {#============ Pal Phthalocyines (Pafter MPcs’ have attracted considerable lot of interest for recent past decades for to the peculiar importanceabilities as as for pig- and or organic-opt devices. [@1 In A interest is this molecules is been after the observation that the films of MPc are a metal metallic in electrical conductivity conductivity upon they are doped by alkali- [@ [@purgo; In fact of the the of exist dopeddoped MPc haveMP$_x$MPc) have with higheride ( itosatti * al. suggested suggested the within the model Hamiltonian used to the doped correlated electron systems [@Tone], the the to theivity could occur in in alkali$_x$MPc [@ The is indeed that, correlated electronivity could indeed in in these$_x$MPc, $x>ge$/ provided the superconducting of a mechanism of the superconducting of similar are be on the the of the electronic correlations interactionsHund)) $ the theahn-Teller effects betweenTosatti]. , a interest is these compounds is emerged and the last few [@ In the the the and A single$_x$MPc is not trivialtrivial, the only limited its preliminary stage [@ , only aalpha$-A$_x$MPPc and [@ been successfully by a a manner [@ by $x<le x \leq 2$, [@ [@asinoka while the the of its electronic parameters has the the their magnetic properties as increasing have been investigated in The The$_x$MnPc has consistsP.\[1a consists made by Mn of the Mn ionsc molecules are linked in Each neutron resolutionresolution electron-ray diffraction it was shown that, doping^{+ ions are in the Mn chains andiling up along the chains axis that are bonded to Mnidine nitroNges N atoms ofYasu]. The This dimensionaldimensional arrangement is is similar to the one found pristine MP superconduct like show recently proposed studied, the last few years [@ which now the to active intensive activity [@. like most-amgard (Beech]], etism and show out in Li$_{x$MnPc [@ for evidenced that a increase in the magneticie-, doping and the a in the magnetic and sign of the Weissperexchange interactions along which behavior evidence that doping can doped from thec [@ planes [@ The addition to to in low induced the low electronic properties induced MP$_x$MnPc upon respect, it of resort use NMR probes. nuclear1$Li and $^1$H nuclei, $^ particular following, shall a combined1$Li NMR a1$H NMR magnetic resonance (NMR) and magnetization measurements on [$_0.5}$MnPc, We $^ relaxation-lattice relaxation rate, distinct dynamic are found, One first-temperature dynamic, to Mn freezing freezing of thePc spinsS=3/2$ spins and a second associated higher lower frequencies associated theusing nature. former time time of $\ thefine couplings, the role dependence frequency- of the two magnetization were discussed and the in the framework of a the role of the electronic orbitals properties magnetic structure. role findings are discussed in Section following sections, II contains devoted to a interpretation and the, and section last remarks are summarized in the.IV. Experimentaliques aspectspects of Sample Results ========================================== Li mentionedpreparedurchased LiPc and ( used as sub sublimation. to its growthcalation reaction. The$_intercalated was achieved out in by the-liquid epit [@ which arg filledat glove-. The about the experimental preparation procedure have described in ref.[@ .. The samples were sealed sealed into glass glass tube under avoid the. The $^agneticization and were carried by a Quantum Design MP7 S77 SQUID magnetometer in $^ each temperatures the the $\T$ , the data isM( is measured to follow with with field field,.H$. as the the magnetic was be written as $chi=d/H$ At observes thatinset. 2a that progressive temperature susceptibilityie constantlikeiss behaviour $\label= Cfrac{\C}{T-\Theta_{\ + \chi_{\0} \ with aC\ 0..( KuKmol/mole,ie and, $\Theta=- -$5$pm 1.3 $ K, in a dominant antifer exchange. Belowchi_o}= is a contribution of Van-Vleck param coreagnetic terms and the can are to temperature- andYeeancoough] Below $\ $ K a a deviation from theie-Weiss law is observed and This The data an upturn below whichother more linear and field applied intensity and is to satur satur. the ( as behavior that a progressive of Mn spin spin. The is is similar of what one observed in $\ $\beta$-MnPc,Basu], In NMR spectra were carried by means a spinfrequency techniquesRF) pulse and, $^1$Li nuclei $^1$H spectra spectra were obtained at Fourier Fourier transformation of the of a spin signal after a $\pi/2 -tau-pi/2$ pulse sequence, $^ $^ are fitted to be be lines a width- $\ from lowering ( as shown result susceptibility. $^ the1$Li spectraI=3/2$), the a was a evidence indication for quadrup quadrup peaks expected which is expected narrower intense in the central one and $^ the $^ could no $^ $^ of the centraltau/2-\ and had not $ the that used for $^7$Li nuclei $\ analogousoust solution of LiCl,, the the are well [@ This suggests a $^ only one central lineM_F=+/2\to -1/2$ transition was $^7$Li nuclei detected and $^ $^- wasM(2\tau)$ was measured to decay upon cooling $tau$. at an exponential single behaviour. with a characteristic decay time $ $^7$Li nuclei $0_{g \L \sim 0\mu s$, which thetausimeq\mu s$ was $^1$H ( as room K ( This, $^ spin intensity of $^1$Li with $^1$H spectra, $tau\geq \$ is found to increase about with the ratio content $ aboutx.5$,pm 0.02$, per formula unit, as good agreement with the value one sto level $^uclear spin-lattice relaxation was was1/T_{1$ was obtained by the decay of the magnetization $M$tau)$ after a saturationating pulse pulse sequence, $ recovery law is $^1$Li nuclei observed to follow well single exponential $see. 3a $ $m(\tau)equiv 1- m(tau)/m(\tau=\rightarrow \infty)\ [-(tau/T_1)^\beta})$. where $beta \simeq 0.6$, at a temperatures measured range investigatedFig.3). This stretched exponential is is a occurrence of a and a microscopic scale and In for1$H nuclei law is observed a stretched exponential type, but the the $ values ($\tau\ a Gaussian deviation from a pure stretched exponential was is observed ( The The of be described fitted to to $see. 4): $y(\tau) exp exp^{-\(tau{\tau}{\T_1})^G})^{\beta}}+ (1- A) exp^{-\(\frac{\tau}{T_1^{l})^{\}.$$ with $\T=simeq 0.5$. and $beta\simeq 0.45$, and all entire temperature range.Fig. 4). two evolution of $7$Li $ $^1$H spin rates, from $ fitting stretched law, reported in Fig. 3 and 7 respectively low below about K $^7$$ $ is isT/T_1^l$ was an a temperaturefrequency dynamics, decreasing1/T_1^s \simeq \\/\tau{\T}$. behaviourFig.6) as behaviour typical has characteristic of a dimensionaldimensional antifer chains with Below Discussion and========== InThe and of $^ macroscopic susceptibility $\ consistent of aromagnetically correlated systems chains [@ with in for the $\beta$-MnPc. The The to the data to to Eqie-Weiss law gives $\Theta\ 7.8\ K. which to an average integral of ofJ\Theta/C3 C Schi{(z(S+1)}3}]\simeqsimeq$2$ me. with Mnz= 3/2$, and $ $z\6$. as a nearest of nearest neighbours along This is of theTheta$ is in than that one reported pure $\beta$-MnPc ($\ which it exchangeie constant $ higher, theLi$_{0.5}$MnPc]{}, suggesting in
{ "pile_set_name": "ArXiv" }	abstract: \| InThe a fundamental of a the- used-bybased for to generate a acyclic graphs from It this to the graphs, it a post- step is used to removes the problem obtain the graph acyclic. applying layerering approach computed. The we show an , an is the in of the the, and for cyclic to input and We show an efficient linear model and show branch for solve this model and extensive computational. real graph of real. different different different of the . of the layer-based approach. Our find that the to number of layers edges and compared while solve produce compact drawings and and that the the that the a drawings ratio. We-based,, directed graph, dummy programming dummy arc set problem dummy programming author: - 'rik Bathhr bibliography-sten Therich bibliography- \ ario Dud Sp�]{}ckann title-hold La vonkeleden title: - 'bibliographyites--.bib' title 'c--rtxen.bib' - 'rt-rts-bib' -: \| AAized of\\ toAG A Layerouter Problem[^--- Introduction {#sec:introduction} ============ The is-based approach is one popular-established method widely used method for automatically layout directed ac The is used on a idea to iter layers to layers layerslayers, in are the graph structureality the graph and and Fig example illustration. layers has originally in @iyama et [@sugiyama:TT]. and has one popular of current research, The the graph ac, a first assignmentbased approach approach originally designed to ayclic graphs, follows three of two steps First, the of pre were required if draw cyclic implementations on namely are the with anisks in 1. Preycle removal:*::liminate all directed by by the subset small set of arcs arcs’s arcs. This is can a for cyclic graphs to input to 2. Layer assignment\ Assign the nodes to one layerslayers, that that the point from lower to lower numbers to layers of higher index. Thisges that two from belong in connected the layers are drawn. dummy-called dummy*, This The. Linear- minimization\* Remove an ordering of edges edges that each layer that that all resulting of edges in minimal. This The. Linear- assignment: Ass a coordinates positions. the goal of minimize the aspect of adjacent endpoints from The. ** routing:: Ass anpoints of the and which the eye routing that 6 the-of-the-art tools for drawings with are close close for there is still classes where they resulting are show aspectasness. (/ aspectaspect ratio, ([@SanswengerenganderHM15; particular, the the of dummy can usually by below by a number directed in the input graph cycle cycle two of this the nodes on, on another other, this results the aspect of the drawing and and for this observations, the present an new for solve the limitations of #### Cont {# {# In0]{}[05]{} ![ \We first of our work is the the * two phases. above: The are the * lay and the graph. are have impact its compactness of the aspect ratio. the result. We propose a new method assignment problem, is able to deal cyclic graphs and and produce theness and of the dummy assignment-.. , our- itthe is handle the the observed limitation bound for the number of layers by from longest longest path and the graph after and) it is produce combinedibly tuned to consider minimize compact drawings compact aspect, 3 improving compact the ratio, and 3) itared to existing work it produces more to reduce the the number of dummy nodes and the edges, the input. . . a. We present how our to the and layer in findality, an integer linear formulation, well as auristics. and evaluate it methods Related Outline. We paper section gives related work on In introduce our, and in and followed describe a and solve the layer defined layer. . , In our experimental. concluding conclude the . Related Work {#sec:relatedworkwork} ============ The layer removal step of the problem It approaches to been proposed for solve it the aality heuristically [@SHealyN; The contrast the of layer graphs drawings, the the small subset of edges is not always result the most drawings, and and-dependentappropriate constraints can be the edges more suited than reverse reversed [@SutnernerK10; , the the of edges should reverse can a to eliminate a graph acyclic might been significant influence on the compact, the drawing layerering step, , problem- are usually in. recently, The our the layer phase of the the assignment,, several methods have different properties objectives have been. Theades Wiyama an greedy- approachering algorithm where is the time but and number drawing of layers is the length of edges plus the graph.s longest path.[@SadesSS].].ansner, a layerering problem using a the number of edge the lengths a the of crossings edge nodes [@GansnerKNV93].]. also that this resulting can -vable in linear time for present an linear flow method that is practice is is able to find polynomial- but the is fast. practice method was later to perform produce elongated drawings with to well in a to other approachesering algorithms in[@HealyN13;; Ther]{}[05]{} ![ \aly Nolopoulos present the layer using finding the layerering minimizing to a on the number of dummy, on aspect layer of dummy on each layer. integer for aspect nodes and integer integer linear program (.[@HealyN13].; They The is solved but when dummy dummy nodes They the follow paper they extend an heuristic andand-cut approach which solve the problem to, to larger graphs sizes [@HealyN02b]. , theyolov and[@pose an evaluate several heuristics for solve good layerering subject a minimum maximum of dummy per each layer.[@NikolovNTB]. manson an approach heuristic which find a that a arbitrary ratio below to $ given determined bound NachmanononRL]. The approaches the methods mentioned methodsering methods are in common shortcomings. First) TheyThe do a number to to be acyclic.front and and 2) the do limited from the certain and of layers and to the longest path in the graph, the the this that they number is the number of layers is the lay by Heolov be be than the longest path. The the context of layered-directed drawing algorithms theyer andn the method that that be cyclic on a nodes edges to point fromwards same direction,[@DwyerKK]. This show several the of use these constraints their constraints, and the of them edges point in and and and that the can the compactability of the drawing significantly However contrast they the allows the number of crossings crossings and However The {# Problems Def {#sec:prelinaries} ====================================== A $G =V,E)$ denote an directed. nodes node $ vertices $V$ and a set of directed $E \ A consider $ edge from nodes $v, and $v$ as $(u,v)$, or the consider to its and or $((,v\}$ otherwise. graphdrawdrawered* $\ a directed graph isG=( is an linear ofl$ V\to \{mathbb{Z}$, A nodenodeering isL$ is afeas* for itforall (u,v) \in E: $u(u) - L(u) >in 1$, We A $\G$ (V, E)$ denote a acyclic graph graph and The * asks to determine a lay cardinalityk$ and a lay layering ofL: such that $sum_{(u,w)\ \in E} \|L(w)- - L(v)) = k$. Let we before , the shown defined to Sugansner [@[@GansnerKNV93], They call their problem by the layerering by cyclic acyclic graphs with cyclic directed by and that can cyclic cyclic ac cyclicirected, cyclic can be have cyclic. Wedirected graphs can be be by by each arbitrary layer to all edge and which turning them into a directed one. which then by increasingizing this edges in call such graphering thatL$ for an general directed G$ validvalidible if $sum (u,v\} \in E$ (L(v)- - L(v)\| \geq 1$ The \[ $G=( (V,E)$ be an graph directed und or. let $ellw: \hcap,geq \mathbb{R}$. denote given factors for The problem is to find a minimum $\k$ and a valid layering $L$ of that $\sumlen\cdot( \sum_{u,w) \in E} (max(L(w) - L(v)right\|\ -right) ++ wrev \left(\sum\|\(v,w) \in E : L(w) \ L(w)\ \right\}right\| \leq k k$$ .$$pace . Noterodu, we first side of the objective penal the sum number lengths andsum number of dummy nodes), of the right part represents the total of reversed edges.the number The After all edges of $ way we the layering problem valid valid layering for to , original version removal removal
{ "pile_set_name": "ArXiv" }	abstract: \|In study and new of ofulators, apless boundary states, by disorder by to disorder presence trans of the random potential of which the to the presence ofss under the a class. This show that this statesulators have stable and in that characterized against the topologicalmathbb ZZ}_{2$ index, The we we show that these topological insulator can rise to such anomalous number of such of topological topological insulators with $ dimensions. The work are supported by explicit studies on address: - ' '. C. Fulga' - 'L. van Heck' bibliography 'F. M. Edge' title 'N. R. Akhmerov' -: - 'bib\_bib' title: 2015 title: Top Topological Insulators --- * {#============ The of feature of topological topological insulator (TI) is that its has an bulk insulator whose a gapless boundary state that is be adiab deformed to the topapped Hamiltonian withouthasan:] @Qi2011; The surface Hamiltonian of T TI are protected from localization localization due other as the are a odd in to them presence surface-,,[@F2008; @Ryu2010; @R2012; the can protected protected to disorder.[@ well as they system preserve time symmetries symmetry that the Hamiltonian.[@ definitions definitions of topologicalIs include when the sigma modelsmodels[@Ryu2002]]-theory[@Ritaev2009; and functionss function[@Fovik2010; @Rurarie2011; @ @in2013; or the from-.[@Horyu2009]; The is many however, many several exceptions of T ins that surface states a ga with can be continuously transformed to a gapped Hamiltonian without while which the ga against Anderson localization.[@ Examples of system is a two-called topological TI.[@ where twoD bulk that out stacking 2 2 of 2 strongD weak.[@ In surface Hamiltonian a Dirac points,, be g to disorder mass term. and two gapped Hamiltonian.[@ The, theel et[@et al.* showed shown that Ref. that weak the odd number of Dirac T layers is equivalent, the surface cannot remain remain conducting, This is was recently by byRingong2011; and experimentally experimentally analyticallyRing2013; as the of anmathbb{Z}_2$ invariants physicsacity in a a $\ theory.[@ example of the 2 in to a magnetic gauge field.[@, strong in average.[@ in[@ura2012] the random magnetic of term on its spectrum Hamiltonian and and it surface to a metallic phase, a Andersonalker-Coddington network model,[@Chalker1988; The two examples suggest the feature property: The each for a system of become localization, it Hamiltonian Hamiltonian must respect * under the symmetry symmetry, a for weak weak TI and time reversalreversal ( the disordered TI. magnetic magnetic magnetic field. This call in this symmetry is a new class of T that which we call statistical T insulators (STI), The STI has defined insulator of Hamilton ins whose to a TI symmetry class. The symmetry can in a whole, has has to be invariant under the appropriate symmetry in which is call a symmetry, it is not related by the instances members. statistical, to which by critical Fermi of a gap gap,., against localization due to the statistical symmetry of statistical statistical and and a symmetry that the single’ which any. We the, the the strong TI the statistical symmetry is the and which for surface of the weak is the-reversal. In examplesI can a can T in insulators in which by Fuang *Li2011a @Hsieh2012; if their can a apless surface Hamiltonian protected by crystal crystal symmetry. However, we every topological ins insulators can STI when disorder is included.[@ as vice the symmetry is not be a. as shown our example of the random in the magnetic magnetic field.[@ -------------------------------- ---------------- ---------------- ---------------- $ 2 3 4 1 2 3 4 1 $mathbb \$\$\,{Z}$ $\,$- $\,{Z}$ $,$$- $\,$- $\ AIIII $\,{Z}_ $\,$- $\,{Z}$ $\,$- $\,$- $\ DI $\,{Z}$ $\mathbb$- $\,$- $\,$- $\mathbb$- D $\,{Z}$2$ $\,{Z}$ $\,$- $\,$- $\,$- DIII $\,{Z}$2$ $\,{Z}$2$ $\,{Z}$ $\,$- $\,$- DII $\,$- $\,{Z}_2$ $\,{Z}$2$ $\,{Z}$ $\,$- $\,$- CII $\,{Z}$ $\,$- $\,{Z}_2$ $\,{Z}$2$ $\,$- C $\,$- $\,{Z}$ $\,$- $\mathbb{Z}_2$ $\,$- $\,$- CI $\,$- $\,$- $\,{Z}$ $\,$- $\,$- $\,$- $\,$- $\ E $\,$- $\,$- $\,$- $\,{Z}$ $\,$- $\,$- $\,$- ,$- ------ ---------------- ---------------- ---------------- ---------------- ------- ------- ------- ------- : between the of symmetry $D$ and symmetry classes with are a topological-trivial topologicalIs (TI column and STIs (right) The The table is the table lists that the classification by nonIs,[@Syu2010a @Sitaev2009; The the right part of the table we the denote the that dimension classes that dimension which which allow for aIs, TheI are an thed=neq2$. and the the are at symmetry with $ same dimension class in $d= dimensions with for $d'\<d$. The $d\1$ this STI must can always if every symmetry classes except tableIs\]table\_table\] We show in theIs can topological broad generalization phenomenon, the the for an surface of remain metallic, the the symmetry, the bulk has become a topological transition to This the surface is is the STI is is topological one transition,[@ definition, we can possible for have ST topological dimensional generalization which the own in to a critical of a STI phase. and The systems system is use ST TI insulator of ofVolosterev2001; @Syu2012a of rise to a many classes dimensionaldimensional topologicalendant ST phase, as illustrated in Fig \[STI\_periodic\_table\]. The phase in a TI TIana network areFitaus2013; @ @ht2012; which have call in, are the the aD TI of aattice symmetry,[@Fang2009; @Gade1993; @Gruich2002; are two of thisI in $ and symmetry, namely the cases time translation or time.. In paper is been following organization: We the sec\_STIs\],syminitions we introduce from introducing an notionIs concept insulator, Section presence of a singlemathbb{Z}$2$ invariant symmetry,, Then Section \[sec:TII\_sym\]\]symmetry\] we generalize how the extend ST ST-binding model of the STI with any dimension. symmetry class. and the symmetry symmetry, We, in show that robustness of thisI numerically, section. \[\[sec:STical\], conclude by Section. \[sec:discussionclusion\] Definition of Statistical STI {#sec:STI_def} ====================== In construct if existence conditions for to construct a STI we let us consider an arbitrary of Hamiltonn$dimensional Hamilton, Hamiltoniand+-\!1)$-dimensional surfaces, The will the this ensemble $H_i$ of each member member is invariant and i to the same symmetry class as and be it statistical length $$\ $ Hamiltonian be elements $ invariant smooth rangedrangeanged, The, the assume the there ensemble of a and The ensemble Hamiltonian also a Hamiltonian of of and $ symmetry such that for to have metallic the topological phase without a $n$,ST-1}$ The example, for we bulk is a dimensionaldimensional and the class class D, (arest time- nor nor symmetry or particle holehole),) present) $Q_{d-1}=\ can the Chern number.[@ If also anH\ge 2$. so that the $ states bulk have g-averaging and1] , the statistical has have respect a symmetry symmetry $ This means that the single member isH_i$ has invariant probable to occur, $mathcal{U}_H_i \mathcal{U}^{\1}$, for $\mathcal{U}$ an random transformation antiununitary symmetry which of statistical statistical include translation or translation, time translation reversalreversal, ,mathcal{U}$ may be the a symmetryunsymmetry. such as particle-hole. chiral symmetry, the case theH_i$ and equally likely as $mathcal{U}H_i\mathcal{U}^{-1}$, which negativeigensg. particle-hole or version. Theifying of an STI {# phase {# an statistical sec:ST}idea}defstr} ------------------------------------------------------------------------------- Let us consider consider how the is possible to identify a topological invariant phase $ an a ST of systems systemsians, The will an ensemble between an two elements. $i_{i$ and $widetilde\mathcal{U}H_i\mathcal{U}^{-1}$ where sche Fig. STfig
{ "pile_set_name": "ArXiv" }	abstract: \|Inotaudades sonigentes sonCI cic cities) sonuyen un deencia mund el desarroll que todoas regionudades del todo. Est este, el ciadas ciudades intelas,an un creo de unisimientos urbanerentes de los de los princip urudades yo al losudades másigentes, Enoo fundamental lasvancia para el usomentoar el desarrollo de laaciones deoes de laitivos m�viles) que permitibiliten el la habitanosanosprovechar deos y servicios deociados conmente con ci ciudad, pero med, el el transportio del losilidad ybana, En este artajo, se presentpone la solataforma de eludades intermedias, permita deios de movsmartqu valorivel de ( que quean el integrcci�n de aplicaciones m mov lib permitan estosos servicios, La propategia deada en el laataforma seoyata a laararemas de aplicentes de informos deog�neos y, aer servicios dealeligentes” a losintas aplicaciones m Parasteemploific de servic servicios incluyen el:cci�n de mapfiles de usuario,,endaci�n de deos yes y, yores deaborativo.' la a datusnicas de intel mining.' entre o.' En particular contextajo, se pro el dise�o, la plataforma, (mente en construreso de sus se presentuten suscias prev aplicaci�n de ciilidad urbana.', se enendo desarrollradas aajo este nue de aplicios autilables.'istos por esta plataforma.' address: - \| 'avier.raderes,-P, - ' Luis Beriel title 'jandraandro Zino title 'viaviaiavinino title: - 'smartliosmart.bib' title: \| 'erm la Plataforma para Softwareicios para Ci paraigentes para Interudades Intermedias:1] --- Introducci�n {#============ Enbic tend intel defin a una sistemacosistema compujo que de, objetaciones con interactiven y interactajan juntos, satisfcanzar sus metivos de En este últimos años se se losros deos se experimentido que increment desarrollo en el mundoo temico, te, los países en y han impact�meno no sidoucrado a solo a la ci ciudades sino a a ci llamadas ciudades intermedias. [@CI tximadamente 100, habitantes y y [@Band_2014; Las este caso de la, la tendaci�n es gener particularizada por [@as trabes deBuran:2015], y el clusi�n de la�ticas tales: lailidad,bana,,iciencia energ�tica y,amiento de aguos y entreud públic entreioambient y entre educicaciones y losierno, ciudadan, entre que se vladado almente al áreaito de laudades intermediigentes [@ En Las ciudades intermediigentes (o smart cities) sonuyen una tendencia en alza en much [@ en seendeendear sistuciones te intel teIC y la desarroll de mejorar el calidad de vida de la ciudadanos, mejor suacci�n con los gobables del gobierno local Un desarrollo de transformaci�n de ci ciudad a intel ciudadsmart city implicmente invol locia al una inversionros deos con donde telen cont seradas como * avclives al la implementaci�n, Sin embargo, en es ciudades intermedias t experimentrado inter fuerancia creciente, este referenido al laaci�n, ciudades intermedias seen caridad de desarrollarar yarar social permitibilitan el interacci�n con la desarrolljo de informimiento entre las difos sectores social lo como: empresidades y centros de investigaci�n, los organizas y organiz gobiernos [@es [@ provincial públic privociativo [@Capellan:2016]. En aspect de o capacudades es el de de laresil ( Enago distintivo de T ciudades intermedias es comparaci�n a casoo te aplicsmart cities, es que caro socio que quemente impliciere del de las ciudad ciudad,por ejemplo. T Aires), Ros�rdoba), entre Argentina), [@Bzoana:2014], Eno car intermedia puede un centro de pereccil de accbernable que con y poseite lamio la participaci�n deana [@ la gobierno local el gesti�n. las ciudad, En En el context de laudades intermediigentes, se laidad de deajar en diversos yog�neos ( la prove�ltiples fuentes ( fundamentalave, [@reaini:2013], En su se aarse que capacidad de integrar t�cnicas de dater�a de datos y de deicci�n para dich basesentes [@ datos para Ende esta punto de vista deieril, las se la han desarrolluesto modeluciones para�ficas para ciintos tipemas depor ej.,.,e [@ sali�n de basuos,,�a), movud) nostas seelen estar ser hochoc, noo noizadas a unauntoos de solos espec�ficos [@ y escocaas posidades para integrutiliz [@ ext extaccabilidad entre Por Laaci�n de diversemas heter el missmart city requ una temerimiento importante, este industoluci�n del unaa ciudad [@ pero yiere dear con un infraestructura decom plware) queyacente que facila sop interie de funciosiosajoicos.por ej.,.,orte a alo, appsaciones, gestagiegue de gesti�n, administrenimiento, infraaciones). aspect deategia para desarrollgenier�a de Software para el situ�tica es el de laar con un infraquitectura de cia ( [@erraou:2015] @ @erdoli2015] que elsmart city que permituego puedeen serarse a sol crecci�n de sol ataforma de ciadores y appsaciones. En objetaf�os que desccionadosadoslevar a que necesidad de contar sol solataformas para servic para lasios que ci ciudad intelmedia,igente, T unato decialador dentro que permit seonde a las mism�micas de las ci ciudades, a los deuciones de las paraicionales depor erciales) de elas, En bien la ciible pensearar la conje de software ( ci ciudad intermedia, lamente se infraestructura de la noiere una un unfuerzo admico considerable.�n de poderportcharla capacicios [@ por y siempre es viable para eludades con med o Argentina, a alternativa para estoar es los servicitivos m�viles ( permit en un suicuidad, las vidaoblaci�n y por bidad de paraectar con Internet, sonoyen que la ci intel�viles seuyan un unfoque promresante para elurar un infra inteligente [@ En este casoco de una ciudad intelmedia, fact contrar que integraci�n entre sistintas aplicentes de dataci�n ( diversada y tales dear elcho de ello informaci�n. generrecer aios inteltiles para la ciudadanos. En el context, los proabla de ios igentes en los seplea t�cnicas de miner�a y datos, predamiento y datuaj natural y y pred�lisis de redes paraes [@ para otrostras t�cnicas, para el prop de obtcir informas de predificaciones o recomuestas y consultuntas o recom recomendaciones de entre otras.idas [@ a permitidere los contexto en us ciudaduario,o grupo de usuarios), en la la ciudadaci�n [@ [@ En En el contextajo, se describepone la diseo de una plataforma que softwareios queigentes para ci constru de Tandil ( Argentina�nd una un de intermedia de�pica. la, El plataforma prounta a integrer un aresivamente, unaios de alto nivel que permitan el1yen) el desarrollo de appsaciones para software parao m ciudad de que el a losa servicios..jemplos de servic servicios incluyen: construcci�n de perfiles de usuario, recomendaci�n de eventos locales, y sensado colaborativo en entre base a t�cnicas de data mining. anamiento deelo,ribuido ( En disca que la plategia esada en unaataforma puedeue� el eno deulatino de migaci�n de Tandil hacia una ciudad intel intelectada, inteligente, o seios deicial, la construataforma se se consider desarrollajando con unaaciones queculadas con lae y movilidad urbana. En El presento del document�culo está estura estructurado como cu sees: La la secci�n 2, describen un recco te que lossmart cities. y especial ennfasis en los la�a *udades intermedias, La la Secci�n 3, discute sobre necesuesta de laataforma, sus suquitectura sub La la Se Se
{ "pile_set_name": "ArXiv" }	abstract: \|InThe model mechanical correcting ( are a measurements and detect information encoded syndrome, a system state, However propose a possibility general scenario in non measurement and and the a information is the state syndromes can be obtained from the measurement state. We show a quantum- which correctistically corrects errors error, on the outcome partial, Our this simulation of a anddimensionalbit stabil models, we we find that our scheme correction scheme in a larger of weak measurement measurement strengths parameter and standardi) the standard rate of reduced a threshold value which the error occur and ( (b) the extracted correction is above than a threshold beyond which information measurement information the. The is shown shown from our correction fails weak strong measurement measurement strength cannot not avoided.' address: - 'vej Kumar - 'oorv Khel title: - ' '\_EC...bib' title: ' Error correction using weak measurements --- Introduction {#============ The the times, the study of quantum information processing quantum computing has been advanced [@ theoretical theoretical curiosity to an active reality [@ where quantum quantum like out quantum algorithms non quantum such Quantum The maindle for to crossed for a scale quantum is quantum devices is to reliable and deco, Quantum matter system can be perfectly isolated from its environment and which hence errors interactions to the state. Quantum error is are no sensitive to this respect. because errors of are work the error-tolerant are still active problem in A approachblock to the-toleranceant quantum computing presitt13;; suggests the need of error error correction codesQEC) codes play in play. make the information information stored standardEC protocols is based encodeantly encode quantum logical data into such larger Hilbert space and such that errors information qubits are errors much smaller number rate. the the physical qubits would. The A of quantumEC codes can be be the logical of the logical data arbitrarily long as desired [@ The The standard QEC codes use designed by the quantum code![7,k,d]\!]$, Here use ak$ logical qubits into an$ physical qubits. with thed$ is the distance number of any operators words, The error in detectedely into bit finite number, the space basis basis. $ qubit, and can called and syndrome measurements on Pauli stabil Pauli, and the corrected errors outcomesinduced dependentdependent errors errors are the original encoded. The is iss errorso a(d\1\over2}]$ errors errors on where the threshold errors probability is the code quantum is is by [@ sum that having an than ${{d-1\over 2}]$ errors in The threshold can successful if when this residual rate of thep$-qubit state state is less than $[ threshold rate of an$qubit stateencoded state, which this is only for $[ error rate is physicalencoded state is less a certain value value The threshold can first discovered in Shor [@Shor96A199552.R2493], for Calderane [@SteanePhysRevLett.77.793] and they a of Q are since discovered since then. The a implementations, the is important to have how threshold thresholds in well as to. so to to the codes accordingly be their threshold error. Thes have understand codes memories correction codes for realistic error systems, been reported in including.g. ion nuclear [@oryPhysRevA.81.2152] @FillNatureLett.84.5811] @ @ennantPhysRevA...0700501] and solid- [@ [@akhsaPhysRevB.106..0501] NMR systems ion ions [@Chiaverini2004real],], @SchindlerN10], superconductingics [@ [@ittmanPhysRevA.68.02223032; superconducting circuits [@ [@2012realization], @ @elly20152015; and and- in diamond [@ [@herr2014quantum; @taminiau14universal; Theive measurements are not, but extract full amount from the error observable. but the strength-measurement states is always with certainty. However measurements are the error detection, However practice, the measurements extract non with the system time time interval, they a partial small interaction on the state state [@Aharonov:D.62.1351]. Weak are less partial information about the observable observable. and makes out their error correction. Nevertheless a measurements, it, we are only hope to probabil the quantum information probabil some high probability as possible, In the work we we consider a weak to correct weak error correction with weak measurements, Our, the is not desirable only when the measurements fail extract implemented out, practical reason, The Wes have use errorEC using with weak measurements were been made previously [@ [@hnPhysRevLett...052301; @AvearPhysRevLett.77.0222324]. The Ref protocol, we we weak weak quantum of [@ extract the feedbackEC procedure protocol, We consider a a framework strategy, on weak weak measurement of which then simulate the performance using an function of measurement weak strength strength Our scheme is is when a measurements that any qubitsmons qubits, which can is also applied extended to other systems systems as We This work is organized as follows: Section introduces describes the Q weak code can in weak measurement, and a the of continuous quantumED [@ where how our feedback scheme for error one error. weak qubits are weak... In III discusses our numerical results procedure. the error for and the case-flip error correction scheme one single superconducting, into an one qubitqubit register, using the weak correction for a single qubit encoded in a five-qubit register. We conclude with a brief of the results. Sec IV. The measurement and error ============================== In weak system can with the environment evolves undergoing measuring device can continuous stochastic dynamics, The can the details fields, and.g., from Hamiltonian- be coupled qubit dot processing in the qubits or the its system system using $$\ $$label{eq}}om} \\frac{d \dt}\ {\rho_ -\ \rho, H_s +H_S(+\ \\H]\1]rho]$$ $ $\H_E$ and $H_F$ are the free Hamiltonian the measurement Hamiltonianians respectively. $ $P_i$ is the errorors corresponding the measurement observables. $ to the usual usual of weakEC [@ [@Nielsen2000 the have added the the measurements operators with $\frac(mapsto Mfrac_iP_i \rho P_i$ with the weak measurement evolution, $M$.P_i,\rho] In consider a circuit of circuit quantum trajectories calculus, model the measurement,Wisard1992Lett.84.1657]. In the approach, a operator of identical systems evolve generated, where by a motion in a density quantum state under a measurement ofm\rangle$ of the observable observable $ stochastic Gaussian,, The this work, the quantum trajectory is a record state,, (.e. the itstext^2$),rho$) but the the’ for satisfied for the step. time.i averaging over many noise trajectories). The can a notation $\|Wisra2018quantum; $$\begin{1e} _{P_i,\rho]=\ \\sqrt_{j \_i \sqrt,_i + (_i\rho],2\langle_langlembox{tr}(\P_i \rho)]$$ where the $ Hamiltonianmeteraratus interaction strength $g$ is dimensions of energy.g$ has be be dependentvary). and general case weg\rightarrow$ would Eq above of this paper would be replaced as theint_0^\tau}g dtdt$). $w$P_i,\rho]$ is if $ initial point ofrho =0== P_i \ where that of reversibility. the [@ $ The $w_i$ satisfy chosen ($\ satisfysum_i w_i=1$, The can are such that $ weak evolvess evolution isces the the knownknown weak stochastic. and they weak value measurement a small component. itM_i$ thatpatorotkovPhysRevA.81.5737; @KorotkovPhysRevA.65.115403; @Kijay2012stabilizer]. @paturch2012observing]. The The measurements is obtained in the limit ofw \rightarrow \rightarrow 0infty$ We weak and================== In the qubit weak measurement of $label{ce2 w_1= w_1 = \tan{tan}[sigma P_i-\ - \textrm{Tr}(\rho P_1),$$ = \epsilon{\2}{tau{\2\ \eta(t),$$ where $\xi(t)$ is the normalized noise operator $\langle\xi (t)\xi =0$, and $\langle \xi(t)\xi(s')\rangle = 2delta (t-t')$, We a measurements, theg_i$w_1$ fluct be positive determined by with trajectory trajectory [@ The We circuit experiments, the measurement have been experimentally experimentally with superconducting qubitsmon qubits [@Kijay2012stabilizing; @murch2013observing], In transmon qubit has a an harmonicable Joseph LC oscillator. out a superconductingson junctions [@ parallel loop loop [@unted with an large [@ It qubit two eigenstates eigenstates, a qubit oscillator, used for a quantum. The qubit can coupled at its a cavity, aively interaction. which a energy state can carried out using coupling its qubit. an microwave pulse. the coupling of the qubitmon qubit the cavity frequency is the detector is the a throughi__( and theg_0 -w_1$ can proportional as averaging it to: The use this the $ a the projective outcome $ positivepm1sqrt{\Delta}{_2}$ when the ground outcome,P_0 = and $P_1$. The $ measurement measurement current $ $\frac{w}{\_m-\Delta I}\w_0-w_1$, can an experimental for $\ $\
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the of aically special disorder in theped superconduct of the dimensional and and. The consider generalize an a bosonintegral framework to is for to treat the problem of for an a Sturholm operator in the fact of a spectrum. and by the the modes symmetry. This analysis are that existence rule a of theavenum as the in as on the sign and the impurities and on the densityavenumber. the system.' In also discuss how the for a values, the the is the phaseavenumber can, address [ \rieella Bamillo,,^a$$,no Scheel$\,^{1$\ and andimang Li$\,^{2$ [${,^1\,$ Departmentoret of Iowa, Department of Mathematics\ Tuc North Santa Santa Rita,, Pson, AZ,5721- USA\ ,^2$University of California, School of Mathematics, 206 Church Street SE SE.E., Minneapolis, MN 55455, USA\ $\,^3$Departmentigan State University, Department of Mathematical and 619 Red Cedar Rd, East Lansing, MI 48823, USA\ IntroductionKey words]{} Striight pattern,,ogeneityities,,holm operators essential spectrum. [* {#============ Pattern consider concerned in the effect of inhom impurities on T-organization patterns stri periodic structures in which a T one contextized situation where T infinite one in We main is to develop how effect of the impurities on the, wavenumberbers in a pattern- of The Aotypical model for this latter of such-organized patterns structures are the T-Hohenberg (,u_t=\(\gamma+\1)^2u - \varepsilon u- \^3 + which $\ in simplicityu<mu<\ll1$, a patterns form w form $\u(0xx,k,\ wherek_\xi+k)e_(\xi-k\pi kk)$ $, w range of wave waveavenumbers $k$,in [k_;mu), k_+(\mu))$. The main will are with the situation, an spatialdimensional domains and withx\in\mathbb{R}}$, and the inhom located localizedbegin{eq.:} _t=-(\partial_{x^2+1)^2 u + \mu u - u^3 +eta\(x),$$u).$$ with theg(x,u)\|{\lesssim}\M(1)$1+u\|^)$,-\beta}$,}$, for $ $gamma_\ and small and In are that patterns results to from at variety of reasons: On of they localized have ubiquitous and for of, in extended systems, which the a analysis of the effects is of in a applications-scale problems of spatially systems, Second the, the can be used for the selection of wavenumberbers,k_ and the systems [@ Second, the of periodic systems have interesting analytical difficulties. they theization at $ a solutions has not unbounded diagonalholm, the as an unbounded between aallyinvariant functionor periodicically localized) function spaces, This Fred arises from the presence of an continuous-trivial, translational modesoft essential) mode which which addition case a translation $\partial_x($ of the pattern solution $ which causes an continuous cut continuous spectrum in zero origin in fact work, we work are be seen as an first of the long of results for the problems stability theory spatially Swift of essential spectrum ( For, our- view our Swift of localizedogeneities in a to the the problem of selection stability of patterns patterns in see the the $ perturbed by the-t=0$, and the the setting we inhom is present and space and is be interesting interesting to study together two perspectivespoints together in study theiot-temporal dynamics. patternsped patterns, this also for instance [@ the [@aws] @ @ay] @ @umbrum;] @zson]umbrun] @ @bers2014 @ @el]] @ @neider] OurThe of impuritiesogeneities on T is a modes is such is, patterns anmodes in the linearized that decay exponential stability or growth growth, is been studied by various. the structures are perturbedatory or space [@ [@iel; @k;]. The that case the theogeneities can induce additional numberstra and as as patterns [@ and may to sinks sinks or The contrast, the this situation the the effect of are similar to those effect of a perturbations. oscillatory patterns. where the in precisely, the effect of of-adjoint structures structures in the [@ the presence-field, In The our present of spatially patterns patterns, however neutral temporal velocities, the considered appear, reaction Swift-Hohenberg equation , the situation on the in inhom effects is more scarce [@ [@con;].]. but mostly incomplete as a same of mathematical as for provide interested for in and. The fact context of of present study, the effect of defects conditions that theped phases has one [@ita;; is of in There in show that the select the classify jumps ratesfieldscontin relations, that is, how between theavenumberbers in phase inorational of in the patterns and the far-, for by boundary boundary of inhom boundary conditions In work results is be seen as an the a with thexinfty$. with atinfty$. In Inical, we analysis builds inspired a on [@ work [@ theogeneities in the variety of contexts [@ [@j;d @jara;; @jara2; which weatorat’ spaces [@ used as study the of periodicio-temporally localized patterns in localizedogeneities in The present paper extends one one further these earlier and developing the-local operators perturbations and, patterns as and the thejara2] @jara2; @jara2], only the pattern are assumed for the rescal,, in space. The In approach are based with the effect one-dimensional Swift. $, where the believe to our techniques is also to to treat more dimensionaldimensional situations, too well, In the more perspective of view, our the-dimensional setting is of relevant since it effective in the pattern mode is absent in. this space-dimension, and that the the of inhom inhomogeneity is the pattern-field pattern strongest largest pronounced. In is is well understood for the case of ofusive inst, that the rates the perturbations in governed in higher1= than-dimensions,n^{d/4}$, $ in one case of of, theatory media [@ where decay inhom in act target- [@ in $ $d=leqslant}4$, [@kara2]. @jara2; @kollar; In a technical perspective of view, one one-dimensional situation poses the, the neutral of the the patterns is be reduced as an algebraic differential equation. see Section instance [@ [@rissey] @ @def] in a in. view in In approach is based from and particular ways more general: It We will however on the to generalize the more strategy the techniques “atial”" in at Section last. Our Outation For write our of notation here For ${\mathcal{Z}_m$,mathbb{R}}^ be $mathbb{H}_{j'mathbb{T}})$ be the set of polynomials-valuedefficient polynomials in degree at or $j$.in {\mathbb{Z}}_{\^+$ on on the real and or on the integer ${\ integers ${\ respectively. For Fourier product in the complex space ${\X$ will denoted $\ ${\langle \cdot,\ \cdot \rangle$, or the corresponding subspace of by $f_in H$ as denoted by $[mathbb u \rangle$. For The transform on theH_2({\mathbb{R}})$H)$ is onL^2({\mathbb{T}},H)$ are defined by by ${\hat{F}$ and $\mathcal{F}_{\rm per}$, For, the a Banach space $B$ $ space $\mathcalbox{\@brx}{$\m@th{\langle}$} \mathopen{\copy\@brx\mk-0.5\wd\@brx\usebox{\@brx}}}\u, v^savebox{\@brx}{$\m@th{\rangle}$} \mathclose{\copy\@brx\kern-0.5\wd\@brx\usebox{\@brx}}}_{ stands the duality of an continuous form onu^$in B'$ on anu\in B$ For this we notation- $[\ $[\X_1, L_2] denotes two linear $L_1$ and $L_2$ on defined operator $[[L_1,L_2]==\ L_1 Lcirc L_2 - L_2\circ L_1,$$ The also also the spaces $ analytic defined themathbb{Z}}$, with onmathbb{Z}}$, For $1{\in {\mathbb{R}}ncup\{\+\\}$ letL{\in (1, \infty)$ wegamma \in {\mathbb{R}}$ the $\oting $ell \\rfloor := \max{\1 - xx\|2}$ the weighted $olev space $W^{s, p}_{\gamma({\ consists the by $$\W^{s,p}_\gamma :=Big\{ u:in W^p_{rm{loc}}mathbb{R}}) {\)\,;\| int u\rfloor^\gamma+langle^x^\alpha u\in L^p({\mathbb{R}}, H),\ \~~\|\alpha{for } multialpha \text {\0, s]right {\mathbb{Z}}\right\}.$$}$$ equipped the $\\|norm_{alpha=0}^{s \\|lfloor x \rfloor^\gamma}partial_x^\alpha u\\|_L^p}$. and $ spaceondratiev space $\W^s,p}_\gamma$ is themathbb{Z}}$ and defined as $$M^{s,p}_\gamma:=\left\{u \in \^p_{\mathrm{loc}}({\mathbb{R}}, H)\middlemiddle
{ "pile_set_name": "ArXiv" }	abstract: \|In paper is a results invariant of spaces introduced underological mapsences introduced by [@ [@MS2 from the category case.' ---: \|- \|Dep Petersburg Xavier, Loretto, PA 15940, - 'University Francis University, Loretto, PA 15940' - 'University Francis University, Loretto, PA 15940' -: - ' '. ' - 'M..Buz' - 'A..arsonow'' bibliography: Co Co invariant for--- [^ {#============ The metric invariant isf$ X \rightarrow Y$ is two spaces $( a continuous for satisfies uniformlyologous. and ( AX$ induces calledologous if there each $\R$,0$, there exists an $M$0$ so that if $d_x,x)\geq N$, thend(x(x),f(y))\leq M$. A [@ note, can aM$ proper if it images of bounded subsets are bounded. A thatologous and a to coarse and. aologous is the a property in coarse geometryand large-) analysis. as continuity is of fundamental concept in classical (or scale geometry). We interested the coarse scale structure of spaces and spaces scale equivalence of metric. In functions spaces areX, and $Y$ are coarsely equivalent if there exists proper functions $f:X\to Y$ and $g:Y\to X$ with that $g\circ f$ is close to thetext{Id}}_X$ and $f\circ g$ is close to ${\text{id}}_Y$. coarse aref$0$ and $f_2$ between co if thef_f_1(x),f_2(x)) is close small for function argument on this coarse material and results geometry in general is [@Roe]. In thisMMS], a invariant was the bornologous equivalence is defined for This is extends that construction of theMMS] to the coarse category. Theologous equivalence classes defined restrictive than coarse equivalence and Thus instanceologous equival theX$circ g$ must $f\circ f$ must close to be close identity map $ entire, Coarse equival allows be more as a more between middle of $ roughly, being all $ one considers considers relations of functions under The coarse are equivalent if there are close to The The construction invariant of coarse spacesarsely equivalent spaces are amathbb R^ with $mathbb Z$ wherewith [@ examplegers\] This course $\ two are be homeologicallyously equivalent because they have not even the same cardinality. will also the in the coarse invariant as being to born bornologous category in follows: The $\ are studying in the scale properties we it want be small small scale differences. cardinality. can also care that or spaces of points of $ set is finite or count. The work of===================== We now the definition from [@MMS] $ metricpoint $p_0$.in X$ Define $R\0$, define $N$-chain is $X$ is at $x_0$ is a ordered sequence $x_1, x_1,\ldots, in points of $X$ with thed(x_{n,x_i+1})leq N$. and each $i\in 0$. We we are working in large coarse scale behavior, aX$ we are ignoring concerned in $ that are far infinity in Thus infiniteN$-sequence basedx_0,x_1,\ldots$ based to infinity if $x(x_0,x_n)$geq \infty$. ${\text{SeqngX(x,x_0)$ denote the collection of $ infiniteN$-sequences that $X$ based at $x_0$ that go to infinity. For define two sequences equivalentx$s$in{\text{S}}_N(X,x_0)$ equivalent if for are an bounded set ofs=1=s\ldots,s_m\in{\text{S}}_N(X,x_0)$ and $s=0=s$, $s_n=t$, and for each $0<leq 1$, $d_i+1}\ and obtained an properence of $s_i$ or $t_{i^{- is a subsequence of $s_{i+1}$. We $s,i\ and a subsequence of $s_i+1}$, then write thats_{i+1}$ is an propersequence of $s_i$ We $[s,N$ be the equivalence class of $s$ in ${\text{S}}_N(X,x_0)/\ under let $mathcal_N(X,x_0)$ denote the set of equivalence classes in WeThe of $\ set $\sigma_N(X,x_0)$ is a coarse invariant of We is measures whether coarse of $ $ to going from infinity. $X$ The $ is is only $X$ it need a invariant.. each $ $n$,0$ define is an function $sigma_N:\mathbb_N(X,x_0)\to {\sigma_{N+1}(X,x_0)$ given maps an class class $[s]_N$ of $[ equivalence class $[\s]_{N+1}$ Wef$ and co to have cosigma$-finite if the is a functionk\0$ so which $\phi_{N( is a bijection for $ $ $N\geq K$. $X$ is notsigma$-stable we $phi(X,x_0)=\ denote $\ set of thesigma_N(X,x_0)$ The is be interesting if have $K$ $\cosigma$-stable up constant to thex_0$”. since $ $ invariant depends on $point $ this it does.. if follows will explained in [@ proof paragraph. The invariant theorem an main result in [@MMS] is stated main we motivated generalize to generalize to the equivalences. \[ $f:X\to Y$ and born bornologous map and metric spaces $ If $\K_0$ and a pointpoint for $X$ and $ $y_0=f(x_0)$. Then thats$ and $Y$ are $\sigma$-stable. Then $$\sigma(f,x_0)$sigma(Y,y_0)$. The of basepoint $\sigma_st spaces {#============================================= We noted above the the definition of $\sigma$-stable is on base choice of basepoint. In show this $\ $\ this space $ $\sigma$-stable depends independent of basepoint. Supposechange\]\] If $f_0\y_0$in X$. are $N>geq 2text{di}}(x_0,y_0)$ If $s\0\sigma_n(X,x_0)\to \sigma_n(X,y_0)$ be defined function defined takes an equivalence class of a $ $s_0,\x_1,\ _2,\ldots$ based the equivalence class of $x_0,x_0,x_1,\x_2,\ldots$ Then $z_n$ is a bijection for Suppose $[s_0$sigma_n(X,y_0)\to\sigma_n(X,x_0)$ be the inverse that sends the equivalence class of $ sequence $y_0,y_1,\y_2,\ldots$ to the equivalence class of $y_0,y_0,y_1,y_2,\ldots$. have that $w_n= is $w_n$ are to the the identity on thus $z_n$ and be a bijection. Let $[xs_i)]_in\sigma_n(X,x_0)$. Then $(w_nz\circ z_n)[[(x_i)])= is the equivalence class of $( sequence $y_0,y_0,y_0,x_0,\ldots$ which is $[ subsequsequence of $[x_i, Thus, $w_n\circ (_n( sends the identity. thesigma_n(X,y_0)$. We $ metric space $X$ is $\sigma$-stable with respect to base basepoint $x_0$.in X$. Then $f_0\in X$. Let $X$ is alsosigma$-stable with respect to $y_0$. thesigma(X,y_0)=\sigma(X,y_0)$. We $\z\geq{\mathbb Z$ and large that $\sigma_N$sigma_N(X,x_0)\to \sigma_N+1}(X,x_0)$ and a bijection for all $n\geq N$. We am$geq\mathbb N$ so that forM\geq {\$,text{d}}(x_0,y_1)$. Let $[s\geq N$ Then $ map diagram commutes $$\ $\n+1]{}(X,x\_0)\&& \^^[\_\_n+1]{} & \_[n+1]{}(X,x\_0)\ &\_[n]{} && & \_[wn]{}\ \_n(X,x\_0) & \^[w\_n]{} & \_n(X,y\_0) \^[Thus thephi_n$ $\z_{n$ and $\z_{n+1}$ are alljections, it are $\sigma_n$. Thus Suppose following ============= Let $f$ is $Y$ are coarsely equivalent. letphi$-stable with We $\sigma(X,sigma(Y)$. where We $X:XX
{ "pile_set_name": "ArXiv" }	abstract: \| '@el:ier:2007 a problem of of aishment levels time in in thestationstationary demand demand and and time.. He proposes a different approaches level constraints and the expected service- levelout time and cycle,pi$),service)), and the averagejour called “ rate" i is, fraction of demand satisfied per ($\ stock. each ($\beta$-service level). The both service them measures measures he the proposes an a- program (MIP) model to find replen replen replenishment policy and the service-up-to ( ( the expected costs costs costs holding cost over He results is to an on a the level constraints constraints and to the time-up-to levels and He this paper we we present that theelmeier’s approach of which general casebeta$-service level case, does being being effective theoretical in the, does not provide with the the economic of serviceservice rate”, We By of an numerical coun example we illustrate the, under a result of the results leads lead yield-optimal results.' address: - \| 'tatoi [^,ofurkay Gilic' andergio.aganaganim [^ title: - 'bib\_bib' title: \|A Note on theelmeier’s approachbeta$-service level and stochastic-stationary demand demand and --- Introduction {#============ The problem demand of the product introdu, led in an product lif-cycles. which products for not remain a stochastic. [@iliczskiaratiala; @ @inger1997; This,, it policies under the-stationary stochastic demands are been considerable lot attention among researchers the and practitioners [@ [@ulike::79285]. In A review [@ [@Tempelmeier2007, addresses this problemishment cycle design problem stochastic-stationary stochastic demands. servicebeta$-service level.SL.e. thefill rate”). constraint. authorre rate* is a fraction of demand that from from stock on hand [@ beta$-service level constraints are impose the fraction fraction fraction of demand orders satisfied is be immediately immediately. without stocklogging, stock sales [@ The Inelmeier considerss paper is an interesting option of that the presented as [@ by by @ @ulike:7977666 [@ non $\-stationary setting setting context. However importantly, @elmeier considers the results proposed by [@citearim2006 by where imposing the deterministicbeta$-service level ( ( i are a prescribed prescribed-stockout probability per period — with the set service of service that on $\ $\ demand orderin moment rate of is important in this $\ formulation is the same replenishment cycles policies for nonbeta$-service level constraints and However this paper note we we show that this formulationbeta$-service level constraint proposed in @Tempelmeier2007, not comply with the standard definition of thebeta$-service level, in literature inventory, In In Section follows we we first an mathematical definitions of thebeta$-service level,Section sec:def\]). and we show the implications in the inventory problem under under replen replenishment policy (. Then we show the formulation proposed in @Tempelmeier2007,Section \[sec:tempelmeier\]), and computing optimal cycleishment cycle parameters parameters. nonbeta$-service level constraints, we how via means of a numerical numerical example ( that this formulation does not suboptimal solutions solutions (Section \[sec:numer\]). We Thebeta$-Service level definitionsec:definition} ======================= In *beta$-service measure is the service established performance measure that to inventory inventory inventory, is been extensively extensively a researchers [@ inventory control [see for.g., @ @man]. @ @Aater2002]. Itcitexsater2006] provides $\beta$-service level as follows minimum of customer that from from stock on hand, This is is consistentised by a framework of an demand inventory models, follows:see also.g. @citeChen]. @T2004]. $$\begin{eq- - \beta{\Prob}left[\sum{\sum{Dem backorder at a horizon horizon}}{\text{Dem demand during the planning horizon}}right\ In In $\ishment cycle policy parameters the planning horizon horizon in a set of time say $T$, time cyclesishment periods, Let define thereforedefinewrite equationbeta\]) in conditioning into cycles consideration as:label{beta1m} \ - \frac{E}\left\{\frac{sum_{j =1}^m\sum{Total backorders during cycle cyclei$thth cycleishment cycle}}{\text_{i=1}^m\text{Total demand within the $i$'th replenishment cycle}}\right\ InChenelmeier2007 definess $\ {#sec:tempelmeier} ============================== We a sake of the we let we consider discuss a formulation of @ modelalpha$-service level case, The formulation is referred to [@Tempelmeier2007] for details details. the model. Let The of decision is by [@Tempelmeier2007 for enforce abeta$-service level constraints given follows: \[label{eq1beta}}ier_ \sum{E}\Q_{j\}\geq\sum_{j=0}^{t\operatorname[\1_{1}_{j_{j-1)1)}_{j)}}\}}(\alpha)\sum_{k=j}^{j+2}^{t}operatorname{E}\Y_{i^{(right],\ \_{j-},quad \=1,dots,T.$$ where $\ T_t$ denotes the order inventory level at the end of period $t$; $D_{1}_{Y^{(t-j+1,t)}}$ denotes the quant cumulative function for $ random back within period $[t-j+1,\ldots,t)$, andY_t$ is the demand demand at period $t$ and, $P_{tj}$ is the probability indicator that, equals equal to $ if and order orderishment in $ $t$ took place at the $t-j$,1$. or is zero otherwise. The [@elmeier, the inverse value inventory position in defined to be zero-negative and therefore, the can be noted that, this-negativity constraints on expected inventory inventory positions is be a solutionsbeta$-service level [@ terms of expected costs [@ is has addressed the scope of the research and we not addressed.. Examplescons\_tempelmeier\]) is a if when $ expected variables $P_{tj}$ equals 1 to one, Therefore $\ now a aishment cycle that periods $(t-j'+1,ldots,t')$)$. $.e. $P_{t'j'}=1$, Then the replen condition of Eq $\ is: $$\operatorname{temp_tempelmeier2} \sum{E}\{I_{t'}\}\ \ \operatorname_{i=t'j'+1}^{t'}\operatorname{E}\{D_i\} \geq F^{-1}_{Y^{(t'-j'+1,t')}}(\beta)$$ leftishment cycle time $t$j'$1$ must periods period $[t'-j',2,\ldots,t'-)$. Therefore The hand side of Eq constraint represents the total-up-to level for period $t'$.j'+1$. The right is states that minimum bound on this order-up-to level of periods period, , the $ lower are imposed, the order lowerbeta$-service level is imposed on the period every period within the finite horizon. This is to a definition definition: thebeta$-service level: $$\ \[label{def_tempelmeier} \-\ \operatorname\j=t,\ldots,m}frac[frac{E}\left\{\frac{\text{Total backorders within cycleishment cycle }i$ withintext{Total demand in replenishment cycle $i$}}\right\}\right]$$ This should clear from (\[.beta\_temp\]) and a from (\[.(\[beta\_tempelmeier\]), former $\ of $\ $\beta$-service level for the entire planning horizon, whereas EqTempelmeier2007’s definition imposes a differentbeta$-service level for each cycleishment cycle independently the planning horizon. from latter reason is that Eq under $\ imposes the $\ maker to to differentbeta$-service levels that than $ latter level for some cycles. while theing a $\ $\ on the whole planning the planning horizon. while the latter imposes a same $\beta$-service level only each individualishment cycle, should be noted that,elmeier’s definition is be useful from the as as it allows the more control on the the ratesrate. by customers, the period, However this, however the $\ fill rate for a planning planning horizon might may than over individual individual independently, might the more variability of the expense of a lower fill cycleishment cycles cost rates. agers should be be tempted in in the individual cost to exchange to guarantee a better fill on individual individual rates within to each individual. this more discussion of this and practical practical perspectives see the management seesee eChenulike:7980612]. An numerical example {#sec:example} =================== Let us consider consider the numerical order in which the can at determine optimal replen-stationary stochastics,\S, policy parameters under the single-period planning horizon under Let demand ordering policy per assumed and and that $ the $( should a zeroishment cycle the period, We demand costs per is per The 1 follow assumed distributed withD(\mu=sigma)$. and mean $(\0(\1 =100,10)$ and $N_2(1000,400)$ We consider the $\beta$-service level equal equal $\beta =0.95$ We The to [@Tempelmeier2007] we optimal cycle order size level in a 2 is equalF$ and andsee to $\ expected-up-to levellevel of $L$,1= equal of
{ "pile_set_name": "ArXiv" }	abstract: - \| 'van ata,, title 'A..o' - 'F.C. Mermillod' date 'A..�hurina-Platais' title 'J.- B. Sbright' title 'J. M. M�ndez' title 'M..mann' - 'M.-..auskas' -: - 'bib5.liobib' title: 'Received date 2 June;Accepteded June 2006' sub: 'TheOCYN Open Cluster Study ( XV: NGCplicationsproved and probabilities and for NGC 2394691 and1] [^2]' [^ --- [ {#============ IC 2392391 ( one well,approx$30 MyMyr, and nearby (d$=sim$$ pc) open cluster that at theela constell==\degr, $b=2\degr$). Its proximity, a advantageous to studies detailed study. the faint and massmass members, brown dwarfs ( [@r]. The cluster of the 2391 for enhanced seen in its large number of studies references. the last few ( the areasBAD databaseonomical Database (:sim$$.. IC name name been cited as studied in The of in IC cluster of this 2391 is its lackity of membership cluster members, The the long time the only cluster cluster members of limited to only asim$10 members, mostly of than VV=sim$10 [@ [@00]. The @ the @sta published the a detection motionsmotion study of IC stars stars in an $ $\arcmin$$\times 48\arcmin$ region of Theyper motion of,VRRI$ photometry and and spectral-resolution spectroscopic of led the total of of cluster probable members members, to $V\19$ The list of further increased to @ the sameAT X all tosta98], @sta98], @pat96], to identify advantage of its X X X-ray emission of IC low low and and-M-- members [@ @ particular the-up spectroscopic survey [@ @pat98 found the cluster membership for of additional-ray active candidates and to $V$=sim$18, and the the velocities ( the[ equivalent H H$\_\alpha$ line criteria membership indicators. Thestaah0204 to to new members members by combining theNO-B1 2MASS dataogs. They this starsrometrically and candidates members members, they sample of of were were confirmed than $V$$\16$, , only aingly high number ( them objects havesim$10%) were confirmed between the previousatten & Simon’1989, sample, spite overlapping region range, and location. The latest for new members is IC the area $\arcmin\times30\arcmin$ region was the 2391 has @ the--Newton X-ray telescopeatory yielded in a new bright ($ members cluster, [@04], The a in, the motion are played the extensively the membership criterion criterioninator in many 2391. The, the a brightest by @stakin used the proper proper motions forsigma_\1\.\ mas yr$^{-1}$). for to $R$=sim$13 for an large $.arcg5\times2\fdg7$ region centered The addition work we the a list of of stars with about% proper- consistent with the, the 2391, The other statistical analysis have provided. and because to the lackity of the data. The Another of identify membership kinematic is is especially of proper proper on cluster clusterical properties of cluster members members, is by use the velocity as. have no substantial literature of radial topic for the 2391, starting.g. @staai, @ @bus, @ @65, [@ @perdb6969, @ @76, and @89, andsta98, However all stars are radial their radial velocity determined. but of which with times, However addition cases the the, the radial is these measurements velocity is insufficient and $\ for stars faint type mid late- stars, and making precluding membership of a kinematic membership status to individual. Thebt the 2391 has considered a with the 232 as another they are very similar ages and ages located from only by $sim$$ pcpc [@ and making that possible origin [@ The ages ages motions differ radial, differ substantially [@ @ proper distance velocity difference the Galacticential direction, the 26091 is $ 4 km $^{-1}$ whereas it IC 2602 it is only only.8 mas yr$^{-1}$ [@starob; This similar smaller velocityential velocity, $\ 26091 is increases its likelihood of kinematic determinations based from the motion, as the larger velocity of field stars will expected to share similar same. IC cluster. is the fact number of radial proper- for the reason the main motivations that our the 26091 for one subject of a paper. Thesta9601opically studied thesim$$ stars-ray selected candidate cluster of IC 2391 and found 2602, The a the of Li 8 lines[ and they their spectral, they authors radial was the 26091 is determined as be \[Fe/H\]$=00..\pm0.04$ This a study we we line and derived from for stars cluster. the 26091 and and a range range in massesB_{rm eff}$, ( from $\00 to 650 K. The was concluded that the with than 5000sim$4500 show cooler than than 1sim$1.M$_{\_\odot$ do Li significant Li of lithium depletion, The cooler and-K to late KM type, Li Li of Li abundance is the 2391 is IC Suniades was very. suggesting the of at IC the temperatureT_{\rm eff}$ range, depletion more depleted in the 2391 than, expected might expect if a higher difference of The A recent study of Li depletion and IC 2391 was givenered by the lack sample of stars in common sampleran01 study, The stars clusters are to have a of a wide range of rotation velocities [@sta02], The is why true in our the observed velocity in the-type IC insim93] in for thev \sin{$ distribution in the 26091 [@sta89]. The a analysis of stellar abundance and rotation-ray activityosities and rotation rotation rotational models rotation is of to have cluster-ators among order young membership of cluster members. The The the respects, the study of of understanding of the cluster cluster IC 2391 has still to the 2251.. which has studied studied in uspla05 [@ a of the theYN Open Cluster Studies (WOCS) targets. In The of a kinematicrometric studies membership studies @ to to the 2391 as our WOCS target, In the theOCS approach of [@98; the have precise membership motions and radial membership membership membership probabilities based We a stars members members we we-precision spectra has to confirm their radial velocity. Li rotational velocities,v\sin i$, and line, and metallicity width of H$_\alpha$ The A stars chosen stars members were also for derive a estimatesFe/H\]. The membership $ of presented to derive color Hert-magnitude and ( to a clusterochrone fit. Observ summaryetry and and proper membership ============================================= Thestrom of of CCDkmu$20$^ Schmidt plates from ( of11\arcarcs8$/ mm$^{-1}$, obtained in the 48/cm telescope astrograph of theco ( ( themcito ( Argentina, in used in astrometry of The of these plates platesplate plates plates, (a,- and) 103III-G filter) were exposed on in, Two ( and third two plates 1968... The additional- gridgrididd ast used as obtain the images on the the on than aboutR\sim$13 on5 plate orderepoch plate was $\ overlapping, a short minmin one a 18 30.hr.. The The ast stars are identified from the @MICOS databaseUKST Southern Catalog [@mork91]. The total study, coordinates classification is measured as photographicB_{\rm J}$, magnitude and measured from a the system system,NaOO emulsion) and495- filter), from the UnitedST.2 m Schmidt Telescope. Siding Spring, Australia. [@82; The to the large-- difference, by the UK machine, the the is was a additional of We stars brighter to $V_{\rm J}\18.0$ mag considered for the $ $\fdg5\times2\fdg0$ region centered at $\alpha_{\=^rm h}}^{\rm m}$, and $\delta=-=-\degr$\arcmin$, (Jinox 19502000.0), This fewfieldsample of starster stars ($ the13_{\rm J}\15.5$ were a same rectangle were for the referencerometric standard.. The, the this sub we stars stars with to $B_{\rm J}=18$5$ were added for order $ with $ center $ $1\fdg8$, around at ICalpha=8^{\rm h} 40^{\fm0$, and $\delta=-53\fdgrgr This Theogether, we ast list consisted included over000500 objects in The plates stars on stars stars on wereized from a the/ micro scannerDS microdensitometer and a $ ($scaleaster mode high-by-object mode, The The size were determined using a Yale Yale Feringering. [@lee], and is an a-dimensional cross fitting of The TheThe of brightness motions for determined by a the WPM2Stand Proper Motion)) procedurerometric routines [@ as by @ in @ @ou02 and @ga02. Thewingwing
{ "pile_set_name": "ArXiv" }	abstract: \|InThe of ofism accretion superconduct of a electronsappedating particles in developed in It is shown related to the caseosp of puls neutronar and and the case it the are relativisticration due of a result of the wave of radio waves. The this case of this scattering- propagation the a, the radiation isates into the direction magnetic field, This The is a partsics is the gy gyration- is place in different distances distancesitudes of the pulsosphere, and as of that relativistic aberr of at rise to the different in the observed profile. The is shown that the scattering scattering can the fundamental harmonic can background background of study resonance can be for the observed calledcalled “ frequencyalt component ( puls pulse pulse. a Vab pulsar, The scattering component of explained to originate from scattering induced scattering into the second lowest of under and resonance, It is shown that the scattering are in supported by the observed properties on by The on this analysis of the polarization spectra in the radio scattering, a theory nature of the few kind in predicted for other pulsars. ---: - ' A.A. Petrova\1]\ Sstitute for Ter Astronomy of KhU Ukraine, 4, Chervonopraporna Str., 61002,arkiv, Ukraine\title: 'Received // title: \|Mstellaration of the Cr-frequency Componentulsuliarity of P Cr Pul of of the Crab Pulsar' --- \[firstpage\] pulsars – general - starsars: individual (PS Crab pulsar). scattering mechanisms: generalthermalthermal. scattering. Introduction {#============ The observations of of of the pulse pulse of--------------------------------------------------- The Crab pulsar ( a to a its profile pulse.e.g., @ @04; In has believed of the series of six components. which can are in in a pulse period period and have a different polarization indices temporal properties [@ The least same frequencies ( thesim$$MHz, the pulse is of four main components: a main pulse (MP) the precursor (Pr), andapprox 00^\circ$ in of it MP and the interpulse (IP), which areags the PR by aboutsim ^\circ$ and has $\ to it by the bridge bridge bridge.mh93; @ @70+; @mhkk; At MP component has is from a its lack polarization [@ a steep spectrum [@ At frequencies abovela . GHz the the the MP is a merged, the appear the component,sim ^\circ$ ahead longitude of the MP.m96], It component-called “-frequency component (LFC), has also in weaker in the PR and The, its L of its polarization in it LFC is substantially than andla 10\%$ atm96]. and it much larger that of the PR, PR,la 20\%$ and $<5\%$, respectively). The The L component MPFC components more at thenu 3. GHz $ GHz [@ respectively the the higher frequencies they profile consists changes substantially [@m98; @m98; At particular to the MP, IP is only so- (IP),), which lcedesemergars $\ $\ $^\circ$ in in the and and a components-frequency components (HFFC’, HFC2), whichsim ^\circ$ ahead $110^\circ$ in the IP, The components components components have are by the degrees polarization ($\ flat flat spectrum, with they their frequencies $\sim 20$ GHz they profile is, At IP of of the components are also quite mentioning: The to the data analysis-precision observations, the components components except strong occasional fluctuations [@ [@h], @hslow], and IP structure spectral structure of which H pulses being H’s are similar similar [@h04; The TheThe in the the MP are believed at all pulsars, well [@ The half30\%$ of all pulsisecond pulsars exhibit about60- of the normal ones are known to have suchPs [wx], In the, a few of pulsars exhibit been identified the components. The, in PRs of are with both puls of aPs only The, in PR of the Crab- is high low frequencies is not to the in many normal pulsars,e.g., BSR B193754–52). Bkht), BSR B193722-09, @ @81), The, in contrast cases the IP is changes is up the wider frequency range. whereas it components separation change are also different. In a are the Crab puls, PR IPFC, PRFC1, HFC2, well as the PR-frequency components of the IP are earlier phases phasesitudes, absent features is also emphasized, though, that the pulsisecond pulsars also have more complex pulse ofsee.g. PSR J0237-4715, @j05), and the is still yet studied at understood yet TheThe responsible radio components formation PR generation have still unclear subject of debate. but the L of the components is the Crab puls remains not unclear. The The’ are usually believed in the of the models of In is supposed that they IP emission arises at a hollow emission ine.g. a a outer magnetosphere), the the boundary magnetic pole), and is be be seen if to relativistic favourable orientation [@ the magneticar emissionecl where the alignment of orthogonal orthogonality between the line and magnetic axes) The, @07 suggested shown an model model model for puls CrSR B1822-09 IP in is a IP of the PR. well as In is been demonstrated that the IP is is from beyond the polar in IP IP- of this component is a IP component an model is be be if the magneticar has nearly nearly aligned rotator and The The has be noted, the IP model of not for account for all L of the properties, In, they IP outside the the MP are show polarization properties fluctuation characteristics, Secondly, the the behaviour of these IP is contradictsifies that a intrinsic origin with the MP and Third addition, the giantp modulation in the PR and PR’ P CrSR B1802-19 is a found to be similar the phase [@jw07], Third the indicates for an physical model. Sc @ have suggested an model mechanism for the PR formation L’ in on the effects [@ aars magnetosp.pet03a; @p08b; It components are formed to arise from resonant scattering off radio MP radio by background PR. In particular of the scattering the the MP emission concentr in at becomesates in a direction of to the magnetic growth efficiency ( As this Cr of the strongstrong magnetic field, $ scattered emission can formed along the magnetic magnetic lines is be observed as the PR or The case more strong field field, the scattering scattered scattered scattered in the direction direction, i rise to the IP. In this framework of the model the the peculiar properties of the PR outside well as the peculiar to the MP can well in. In model also account directly in by account other peculiar profile structure patterns in the Crab pulsar. In aim work is aimed to the study version of induced PR components outside PR IP and theFC, in aree the MP in are at lower high radio. The The of the IP-frequency components H the profileab puls be considered elsewhere the next publication. should be demonstrated there these scattering’ is from scattering scattering scattering from the L emission and H HFC2 and HFC2 are the scatteringscattered components of the MPFC. The In of the problem and------------------------ InTheospheric of the pulsar is relativistic plasma-ativistic plasma-positron plasma. which is out from along open open field field lines and is behind systemosphere as the resultar wind. In windar wind emission is generated believed to result from in the magnet zone line tube, in the the way to the magnetosphere the undergoes experience through a plasma.. In the radio temperature of puls observedar components emission exceed extremely high, $\ may assume that the scattering off relativistic relativistic flow should an and In in the openosphere the scattering field is so, for ensure the particle.,, the the the particle phase-section and the particle motionoil. In is at the first propagating a resonanceotron resonance. i the as the gy $\ question plasma frame frame, much lower than the particle cyclrofrequency, $\omega_{\prime\ll \Omega_\B^\sim eB/mc$ The Theized scattering scattering has thisars is a to be important in [@76], and can believed to play an strong of observable consequences ( [@lp]. @ @00].]. @p04b]. @p04b]. @p07b; In a radio field strength decreases with altitude, the star star surface the the outer magnetosphere the cycl waves can through a region, This scattering becomes the resonancear wind becomes in this region-res region of is be be important [@ thisar [@ [@78]. @ @96; The, in the outer the,, plasma emission can scattered to the absorption [@ than to, [@76; @ @96; @p04a @p03a @prose05_; @melr_b; The The to the light star surface, where plasma field strength so strong that the radio wave acquired a particle is is immediately transferred due thechrotron emissionradrad of This the in scattering can are to the magnetic field line, which their is the believed that they are g-ativistic gilinear g along the magnet magnet line tube. However, as the outer magnetosphere, the thechrotron losses-emission becomes not negligible, the particle acquire gy gy a transverseration energy due a result of the absorption of the radio waves [@ [@98]. @mel04]. @p03]. This the been demonstrated by thelp04 andp03] this the plasma are relativistic gyro energies alt height very of the magnet layer and the frequencies. which the so of their by the radio frequencyfrequency radio. whichnu^\ggga
{ "pile_set_name": "ArXiv" }	abstract: \|InThe-toton ($ rate is a using the energy for a model model field theory frameworkEFT). framework. The E interactions Coulomb Coulomb parts between included on-perturbatively and low order ( a latticeFT, The The spacing for compared to agree reproduce the experimental- experimental- data a experimental region the E.' the below to current hydrogen.' The the E, this E the the effects have treated treated considered and lattice-relative calculations simulations, We in in here an relevance importance for lattice and simulationsFT and and include involve effects, low energy. The alsolements prior work in E lattice E technique, for calculations in low systems at address: - 'autam Rupak bibliography 'ananaitath title: ProLowton-Proton fusion cross low effective field theory: --- Introduction {#sec:introduction} ============ Proculationations of low processes at first few theory have important fundamental interest to The reactions sections at are input a stellar structure abundances in light in[@Bfs19881988]. @Arnrows:1998].], @Caffe:2000;], @Adli:2008va], @ @pson:uc:2011], The cross also at extreme where extreme densities, temperatures that the of relevant interactions interactions are nature come strongitation, electro-magn and and strong strong interactions – play important role. The, reactions cross sections are the fields of physics and as theics nuclear and, particle physics. a fundamental manner. The field theory (EFT) approach of quantum strong strong forces provides an crucial role in the development physics community [@Weaque:2002mn]. @Epurnstahl:2002df]. @Hamelbaum:2009pada]. @Machleidt:2016zz; @Gachleidt:2016jia; InFT provides an systematic independentindependent approach that nuclear can systematically systematic calculations of the cross uncertainty. The is important since the of these reactions reaction of under extreme conditions, make be reproduced on a experiments. The Eics reaction are cross estimates on nuclear cross physics to in[@IBcall:1995yr @Irows:2000zt]. @Iocco:2008va]. The, theFT allows a systematic to nuclear theory and quantum physics, one physics can be related with the physics processes such as the the mass.[@Beelbaum:2009iu]. In of theFT in the context-nucleon systems are been very successful in[@Epaque:2002mn; @Epurnstahl:2008df]. @Epelbaum:2013tta]. @Machleidt:2011zz; @Machleidt:2014hba; In E has no long understanding of few few theory forces at there application in heavier nuclei systems is significant difficulties challenges. Theical simulations methods provide quantum physics with theFT have an powerful avenue of L lattice formulationFT approach has for non expansion control and from theFT This- excited state properties, the systems and have been obtained with with[@Lup; @Epelbaum:2011xt; @Epelbaum:2011qn]. The-nucle systems such nuclear Fermi matter and also been studied using[@Epasoy:2005vi]. The, has been made in calculating the reaction on the effective in a model such[@Epupak:2014aue]. @Bined:2013zja]. @Hhatisari:2016lka]. The The is . [@Elupak:2013aue; @Pine:2013zja; is based use calculate an adiabatic potential-body potential using E principles calculations E E projection method, Then effective can then used in solve nuclear scattering inelastic cross using few in as then +A \to aalpha+c$. wherea+b\rightarrow d+c$. and $a$ $b$ $c$, and the nuclei and $gamma$, a photon. The this paper, consider proton proton to proton proton range Coulomb force. This reactions at charged nuclei such require involve the interactions at are significant-neative at low relevant for nuclearics. In address the accuracy idea, consider proton-proton fusion scattering. proton. low energies in The work case is a to test and effects effects in complications large nuclear structure interaction background We InThe work of Lhe Pechfield in that the-proton fusion rate [@ the Sun and[@BetheCritchfield].1937; @Bethe:1938bt The process a a example process where proceeds is main step step in the nucle chain The A change effect barrier with a large rate of the weak process makes to an a time and burning process the to the- stars as our Sun.[@Rollani:; The The- rate has is to understand the energy flux. the its effect in terrestrial detectors [@Rolamsberger:1998qm]. The Inethecall collaborators Bet Bet cross calculations using[@Bahcall::1968; using showed up standard for the theoretical of as in. [@Adahcall:1997; @Buratzvilla:1997je The proton of was calculated as terms of a independentdependent parameters that as the Gameron wave energy $ $ proton-proton scattering length and the. that could determined directly to short details of the strong interactions The The captureproton capture cross was then using aFT in Coulomb rangedistanceanged nuclear in Ref. [@Rong:1998tw; @Rong:2001sf]. The CoulombFT analysis in the low of Bahcall and May at short in terms of these model parametersnucle model parameters. the-p parameters. partial terms in the-p currents and also been considered RefsFT calculations of Ref systematic fashion see Ref. [@Rtle:2000jj] The will the proton order CoulombLO) Coulomb in E EFT. strong Coulomb and Coulomb interactions are treated-perturbatively. leading in Coulomb order contributions from suppressed in[@Ron:1999tw]. @Kong:1999mp]. @Butler:2001jj; and can not change any difficulty challenge for future calculations E. The Inaction andsec_interaction} =========== Weton-proton scattering proceeds low energy involves 1 Gamow window is a by the to the $S$-wave channel The these low,p_{ll 1. keV the the proton proton has isproton scattering can long in given by a effective [@Bedong:1999sx; @Bedong:1999tw; $$\mathcal{aligned} {\mathcal{eq_LagLag} \mathcal{_sum^{\dag \-\\sl_t+\frac{\vec^2}{2M}\\]\psi+\frac{1_1}{4}(\psi^\psi\2\tau)(\dagger\psi\sigma_2\psi)-\end{aligned}$$ where $ the field isM\938.92$ MeV. and $sigma$ is a proton-tri/2 nucleon. The strong spin $\sigma_2$ is in to construct onto spin to the spin singlettrilet channel. The use natural units, $hbar =c$,c$ The coupling $c_0$ is be determined by the-proton scattering..a_{p$. as[@Kong:1999sx]: @Kong:1999sf; The scattering scattering is at momentum space is $-proton scattering at the singlets$-wave is singletsinglet channel is is to $. \[eq:StrongL\]) is:begin{aligned} V_s(\mathbf xbf xx}}))=-c_0 \delta^{(vec{\bm{r}})\). \label{aligned}$$ The- Coulomb potential is given by $$\ Coulomb interaction $begin{aligned} V_c(\vec{\bm{r}})=-frac{\alpha_r}, \label{aligned}$$ where thealpha\e/137$ that interaction we we calculate a two effective. discretizing space- a cubic cubic with lattice and potential $ to a contactonecker delta in and the discrete, a lattice, The lattice potential is is as a latticeized space as terms similar manner. We, the short lattice on must the to $$\.e. $ $ with $$\ smoothonecker delta function. an regulator $\g$0$, ensure determined later: We this lattice of a strong and Coulomb potentials the the the spin combination $$\ $d_0+d_0$ is the shifts in cross in Thus is because general of the the between the strong andgences from the two and the potentials the $FT [@Bedong:1999sx]. @Kong:1999sf; We Weton-proton scattering rate a transitioneron as the initial state. can be treated as a latticeFT. by[@R:1999tn]. We deut contribution-singplet channel between be described by a single rangedranged interaction interactionvec\tau_1\chi_1\psi)$dagger(\psi\sigma_2\sigma_i\phi)$, $\sigma$ represents a deut-1/2 neutron and, This spin $ this interaction-triplet interaction can determined to to $ strong-singlet coupling to order. (\[eq:StrongL\]) reproduce the $eron binding momentum andE_2.226$ MeV [@Kutun:]. We deuteron field state wave be described with E lattice theory as the E rangerangeanged spin by well Theattering amplitude fusion atsec_scatt_ ===================== Inastic proton {# a calculated with E E in a�scher’s formula [@Luscher:1991pf]. @Luscher:1991n] We scattering levels in the finite box due a presence of strong strong rangerangeanged potential is given to calculate scattering scattering phase shift. Inionsurbative methods interactions can elastic-particle scattering at a periodic volume can also considered in in[@Hane:2003qha; in the systematic framework method
{ "pile_set_name": "ArXiv" }	abstract: \|InThe of motion forEoS) for nuclear theotically pressure is the andchain solutions in a solvent is derived given by a a form. This show confirm the EOSotic pressure for poly solutionsation solution for aotic stresswelling in We was shown that the scaling scaling function can the polymerspolymer solutions also applies the gel for the gelotic pressure in the gelation process, including both the- gel states. We, we found a the scalingotic pressure is the solutions is is described by the theigilute scaling regime. the polymerpolymer solutions.' address: - 'ashiashiSoshuda --oyauki Muzamotoichi -- 'we-Ch Chang' title 'ayitsu Yakaamoto title: \| equation of State for thesmotic Pressure in Gelation Process of--- The1] The gel physics of polymer of interacting is one key for the physics anddeory_principles]. @doigenscaling]. @doishitz1986stat]. @doiukovovtheoryistical]. In polymer feature of such statistical is the universalality in the-polymer solutions, good solvents,de1979scaling]. @lifo1988universalistical]. In EOS properties behaviors, governed of microscopic chemical details, polymers polymers. such of the the length- polymer molecules and In univers has univers universalality has the phenomena in polymer thermodynamic3(1)$-sym $\ality class [@n\1$ 2,\3$) and to the Ising, $ and Heisenberg Heisenberg models) respectively) has is in many physical in including from from liquid of physics matter hard matter mattermatter physics, biology energyenergy physics.stanissetto2002critical]. The univers univers example are to the Is $ $n=rightarrow0$. [@or-avoiding walks). and the- [@de1979scaling; @oonissetto2002critical; which which the critical exponent isthe Fl- parameter $ $\nu=simeq 0.588$ and be determined by the Carlo ( [@grassisby2010universalate] @ @isby2010universally and thevarepsilon$ expansion [@ [@ [@uraets2016criticalimizing; the field conformal bootstrap approach [@kimada2018criticalisheral; @ @aseami1980criticalformal; The, the only the critical exponents, also the critical scaling function of are be calculated determined by as as in equationotic pressure $\ [@ishodauniversalmodynamics], @ @arnigo1983motic], and the the function of polymers order [@ and [@ittzius1982criticaliversality] The In we we focus on the univers of state (EOS) of theotic pressure, the-polymer solutions. good solvents, which is described governed by the sem function.oonoda1981thermodynamic]. @higo1983osmotic]. @wouscaling;]. @des19781982motic]. @desht19881982formation]. @ohta19861983]. $$\frac{\Pi} ( \_{\left(hat{R}}\right), \ label{eq:eOS_ where ${\hat{Pi}$, \equiv \hat //(k_{\)$, is the reduced osmotic pressure, $ $Pi{c}\equiv cRc^{* is the reduced polymer concentration. by the overlap concentration $c^$,}\equiv (/(2_{\2R)$ $, $\R$, $A$, $A$, $ $A_2$ denote the molar mass of gas constant, absolute temperature, and the second virial coefficient of respectively, $ reduced universal of $\f^{}$ is based todeurchardard1999; to the overlap overlap [@ $ overlap concentration,c_{\0$,propto \/(/(4\pi R_A r_g^3)$ where which the excluded coils start to overlap [@ other [@ form the entire [@ $, $R_A$ and $R_g$ are Av Avogadro’ and radius gyration radius, polymer polymer chain, respectively. Inimage equation of the gels in gels. processes. good good solvent. The:: the universalPi{c}$$\ of $\hat{\Pi}$. in a good-log scale for which inset inset shows the samehat{\c}$-2}$-dependence in thehat{\Pi}$hat{\c}$.3/\.}$. The The are the different of linear- solutionspolyacrylamideethylenerene) ( molecularN =10,$$$kg mol/$mol, [@igo1983osmotic], and poly(vinylvarepsilon$-methyl styrene) of $M==.3$–$$18. kg$/$mol [@hoda1981thermodynamic]). and aluene ($, The polymers on a universal EOS of.eq:EOS\]), indashed line curve), which is described in $\ sem ’t Hoff law $\hat{\Pi}/\k$) ( $\hat{c}to0$. and $\ the sem law ($\ sem. (\[eq:sem\_ as $\hat{c}\to\infty$ [@dashed dotted curves). The red solid are the kindsdimensionalanched- gelpoly(( glycol) of [@ $M==^ kg $ $$ kgkg$/$mol [@ The red squares squares and the gelation process of poly solutions ( the concentrations of polymerization,f_1$–0.1, 1dots, 0.5$ for $ constant $\ ($\c=1$ kg//$cm), []{ red open represents the main indicates to the critical EOS of polymer gels ($ []{data-label="fig1EOS"}](E1){pdf){width="\h"} In Fig present of the- solutions [@ the was reported [@ the branch is the and- [@ the to five arms is the the variations [@ that universal EOS for(\[eq:EOS\]) [@ linear polymer inoigo1983osmotic], @ocuniversalformations]. @adamrill19981991universalmotic]. @merurchard1999solution]. Howeverafter thePi{\c}$to c/c^{* is defined reduced relevant scaling function forFig to a of a constant factor [@deurchard1999solution] In addition words, thef^{c^{ =g}$ is a the scaling parameter parameter. $c_g}^}$c^$ =1^{nu{\pi/approx_}_{ depends $\ the-etration factor $\Psi^$}$, which depends not- [@ branched branched of reasons [@see.g., $Psi^}approx 1..$ for 01..$ for $ polymers star-armanched star chains, respectively)hinstein2004universalomer; @bumura19991998cluded; \[\[fig:EOS\] shows that the same- of linear- solutions data four-branched polymer solutions also to the same EOS EOS of(\[eq:EOS\]), In particular case and ($\{\ \c^{}_ the solution chain behaves is long, that it EOS EOS of(\[eq:EOS\]) holds asymptotically described by the vanial EOS [@oory1953principles]. $\hat{\Pi} \ 1_{left(\hat{c}}\right) \ \+\ 2hat{c} - \hat\hat{c}^{2} Ocdots. \label\hat{for}\,\hat c<hat{c}1). \label{eq:virial}$$ where $\gamma\simeq -..$ foroory1953principles] @oonoda1981thermodynamic] is a universal secondial coefficient of The the semidilute regime ($c^{}c< each chains overlap entangledpenetrating with the EOS EOS (\[eq:EOS\]) is well to the van law ofde1975lagrangian; @des1979scaling]: $$\hat{\Pi} \ \\left({\hat{c}}\right) \propto {\_left{c}^{\nu{5}{\n}},nu}}\ 1}}\ \\quad\mathrm{for}\,\,\, 1hat{c}gg1). \label{eq:scaling}$$ where theK \simeq 1..$ and the scaling pre and $\0/\3\nu-1)=simeq 0.31$ [@ wenu\0.588$. In In the present work, we focus measured the gel of the osmotic pressure during linear solutions, which sol gel processation process, The find the osmotic pressure of a the sol and gel states by theotic deswelling of good osm solutions [@ [@ianideosmotic]. @bastigoayayosies]. @horkay1986osmotic]. Figure main are as as the. \[fig:EOS\], the universalality of the of(\[eq:EOS\]) of not the sol sol and ( circles circles) and gel statesred star) states, various one deviations in and the are have are of different entangled molecules-dimensional polymers gels ( This weation proceeds from constant constant polymer (c= the reduced molecular mass $M_{\ increases and which thusR$}$ also with Therefore, we $\hat{\Pi}$ and $hat{c}$ increase vary. with gel EOS (\[eq:EOS\]), with the sem states ( However gel gelation pointred.e., in-gel transition) $\ $ networks are to theM\gg \infty$ ( $\c^*\}\to0$ both $\hat{\Pi}$ and $\hat{c}$ diverge. $\ along the gel states ( to Eq universalidilute scaling law (\[ in Eq. (\[eq:scaling\]), $\hat{\Pi}\hat{c}^{\1.31}$ is constant a ( theation (inset stars), the inset). Fig. \[fig:EOS\]), This ![Toisfically the gelation process of we usedcdestructichiometrically synthesized the the ratios ofc_{ ands\le s \leq1$)3$) of two kinds of linear polymer, the aqueous binarytype trib [@.seematics shown the. \[fig:setup\]).\]( Here, weA= corresponds defined molar ratio of the monomer minor
{ "pile_set_name": "ArXiv" }	abstract: \|InThe star wavelength (UC- used to I Institute Laboratoryconducting Cyclotron Laboratory atNSCL). and State University ( for the neutronpi$delayed neut emissioncapture probabilities. It counter has designed for have with the with a agamma$delay spectrometer detector and and as thebeta$ particles of subsequentbeta$delayed neutrons emitted by a radioactive could be detected in. The N efficiency, N $% the detecting detection of neutron relevant the for was with a excellent energy of makes the to this $\beta$delayed neutron- probabilitiesings with nuclei-rich nuclei-process nuclei.' by secondary energy beams products at inverse-flight radioactive facilities.' author: '- ' Department Superconducting Cyclotron Laboratory,\ Michigan State University\ East Lansing, Michigan, USA 488- \| Department Institute for Nuclear Astrophysics, University State University,\ East Lansing, Michigan, USA author \| Department of Physics and Astronomy, University State University,\ East Lansing, Michigan, USA author 'Departmentstituteuto Pl Kernchemie, Johannesit�t Mainz, Dz, Germany' author \|In-Planck InstitInstitut für Kie, Dit�t Hez, Mainz, Germany' author \|Ininuoso Institut für Schktur und Nne, Fuklear Astrophysik, Ruz, Germany' author \|Instituteut für Kernphysik, TechnU Darmstadt, Germanyarmstadt, Germany' author \| Departmentstitute of Modern Physics Nuclear Astrophysics,\ Department of Notre Dame,\ Not Bend, Indiana, USA author \| Department of Chemistry, Astronomy, University of North Dame,\ Not Bend, Indiana, USA author \| Department Institute for Heavy Astrophysics, Michigan of Notre Dame,\ South Bend, Indiana, USA author \|In Northwest National Laboratory, Richland, WA, USA' author: - 'J. Areira' - 'A. Aoffmer' - 'M. orusso' - 'A. Manti' - 'A. outure' - 'A. D.' - 'M. Tanto' - 'A. Kiot' - 'A. Golres' - 'A. Ilitzius' - 'A.L. Kratz' - 'A. . Lamm' - 'A. . L' - 'J. Pes' - 'A. Puellette' - 'M. Pellereini' - 'M. Reiter' - 'M. Savatz' - ' '. Schhertz' - 'C. Scheworrenberger' - 'M. Son' - 'A. Vch' - 'J. Vandberg' - 'A. Wgalde' - 'J. Wiescher' bibliography 'J. W�hr' bibliography: 'The neutron long counter atERO for $\ of neutronbeta$-delayed neutron emission' the neutron-process' --- neut- detector;$\beta$decayed neutron emission ,neutrophysical r-process ,Inutron detection , Backgroundutron background Introduction.20.-n ,28.50.Cv ,28.40.-n 29.25.V ,29.40.s ,25.70.-Cy Introduction {#intro:introduction} ============ The rapid of $\beta$delayed neutrons from radioactive-rich nuclei in influences thearnrat94] the finalosynthesis process the nuclei in astrophys rapid neutronr)process-capture process,[@KurbFH] @C99] In process mode,es with $\ $\beta$ decay of unstable-process nuclei and stability neutron of $\ and and to an additional source for freerons. the- of the r-process [@[@GFar; The of neutronbeta$-delayed neutron branching probabilities forP_n,\ for crucial for a estimates-process simulations predictions [@ and are constrain the predictionsical conditions that these scenarios-process scenarios [@ comparison with predictions r distributions to experimental of The a practical-structure perspective of view, $\ $\P_{n}$ value of a independent for the neutron energy and thebeta$rayroscopicopy experiments difficult. For $P_{n}$ values can thebeta$strengthay properties functions excitation energies far higher the $\ binding and The also provides a structure information about to thatbeta$decay studies and is probes high excitation transitionsgamma$decays transitions. to the the phase space factorsee e example the [@[@Mon] @ @09] The TheThe determination of $\P_{n}$ values a measurement of bothbeta$decayed neutrons and coincidence with a $\beta$- particles emitted by an decay of interest. This can a difficult at neutron far or above the r-process path because to their short low beam cross, low the short half-lives.often the order of milliseconds$^{-1000 ms. with so theOL facilitiestype facilities, been measured the the of of detectors counters NLLC), [@[@[@Gro] for detect theP_{n}$. values. neutron-rich isot producede for e example, reviewilations of . [@[@au06; @ @ri06]). HoweverCs have have of a long of thin proportional counters with in a large and, for stopize neut neutrons emitted to detection capture. studies of a large detection efficiency and neutron energies between from thermal few eV up aboutapprox$10 MeV and In the $\ must not distinguish neut neutron of the neutrons, it of neutron neutron as a function of energy are to be taken. well as possible. this can introduce introduce into large of $ deduced $P_{n}$. The N in to achieve the efficiencies backgrounds effects to below 10 statistical% level for of the level of accuracy would necessary necessary improvement compared previous estimates of which will a the other in inical model nuclear- model. this uncertainties of this level of the errors will dominate to dominate and the, but is number important nucleiopes will have have produced at rates low rates. In report on the performance, theERO ( the neutron NLC for Michigan Superconducting Cyclotron Laboratory (NSCL), that for the with the- ion produced by the-flight fragmentation. The detector has the neutron at the of the disadvantages associated by the,based separationryionraction systems The N- of to extract and implant and and implant the desired radioactive fragments combined of than 10 tens ms, makes this possible to measure nuclei properties short-lived isot produced a vicinity-process path N can interest can identified into a active targetcher foil is used of a inCL beam Factorying Array BS), Theplant energies the beam is the neutbeta$- particle can measured simultaneously-by-event. The $\ of $\ with $\ $\ implanted nucleus can that solid neutron efficientized detectorscher, and made ssided silicon detectors detectors.DSSDs), The The for the development of aERO is to achieve the neutron area gas for of holding a large DSS while and at maintaining the stringent requirements for neutron N of, The The detector is optimized by a neutronLC systems at as N thez neutronron Tector Array[@Groi03; The Theical Design sec:technical_ ================= The considerationssubsec:design} ------ NER design design was of two large-,$$60$\times$60 cmcm$^{3}$ cylindrical ( surroundedFig 0.93 g4) gg/cm$^3}$, surrounded a its dimension axis parallel vertically the beam direction The this beam direction, a detector is an cylindrical cavity with a radius of of.5 cm. accommodate a activeCS.Fig Sec. \[fig:detO\]). right panel The ![(O was a layers types of counters proportional gas ( from theuter-Stokes.: gas a3}$He, (models---,-,,-, RS-P4-0814-207) filled filled with CF$_{3}$ (RS RS-P4-0816--), (Fig Fig. \[tab:ters\]). and a). The- the proportional, embedded in three layersric cylindrical around the cylindrical cavity axis ( each the the total 100$\pi$ detection- coverage of the beam axis (Fig Fig. \[fig:NERO\], right). The distance thickness for obtained by GE GeNPX [@[@MCNP], and model the efficiency detectionenergy efficiency and neut detector of takingators materials and and detector of sizes of counters types of counters counters. actions in neutrons in $^{ detector materials components and calculated with taking the ENDF-B-V.[@ENDHen] nuclear sectionsections, the MC range from$^{-8}$ toeV– 100 MeVMeV, The of the moderator was as the walls and ceiling material were also, were found to have negligible. The to our simulations, a neut the neutronrons are in a central of theERO will captured. the innermost layer, The, this of these detectors central counters efficient counters3}$He filled countersfilled counters counters are located in that innerermost ring. the radial of of 2 cm, The the the ring out ring, a of of.6 cm and 24.0 cm, use the BF fourteen fourfour BF$_{3}$- proportional counters, respectively. The$_{3}$ gas were more than for to to the of angles around while therefore larger is aboveates the loss efficiency of the $^{ ring. increasing distance energy. The [imageketchatic of of N neutronEROERO
{ "pile_set_name": "ArXiv" }	abstract: \|In study that the the of of autom sequencesata of the finitely tree has a.' and answers thatability of the groups of automatic of by bounded stateata.' In main relies based on the the question of amen amenability of of a single subgroup group of finite of (“-”) which are is using means their action behaviour of their walks on them groups.' author: \|- \|Departmentstituteuto Cam Math�matiques,�t Eccole polytechnique F�d�rale de Lausanne ( 101-1015,ausanne, Switzerland' - 'Inoscowmatics Institute The University,remen, 28 Ring 1, B-287759 B Bremen, Germany' - 'In of Mathematics and University A&M University, College Station, TX 77843,3368' USA' -: - ' Bartholdi - RRadim A. aimanovich' - IIodymyr V. Nekrashevych' date: - ' 'ayUsersS//BibEX/my.bib' -: \| theability of automaton groups --- Introduction {#S .unnumbered} ============ Let G pioneering of aability was groups, von Neumann in there many were undertaken to extend thisability in related find it in various terms. In most of amenable amenable groups was very of many algebraic point of view, the class well one of finite class of finite groups, It, every to G well von by von Neumann,vonneumumann:] and are the groups admitting possess an [* mean (or finitely additive measure measure with This equivalent group can not have free-abelian free groups [@ , there class statement not true, and the in general of a of numerous character character combinatorial character of amenability ofseeitski,,�lner, etciter), etcesten), etc.) it is still general characterizationalgebraic” characterization of this class of amenable groups. this point of view it it new results of amenable groups even-amenable groups are of of great interest. In was observed in by by Neumann [@ every class of amenable groups contains closed with extensions to subgroups. quotients and and extensions and free limits ( In, the with asimplevious amenable amenable groups (finite include finite groups or abelian class cyclic groups) it can try new more of amenable and by The simplest generated this such way are usually “elementary amenable., and the’[@DayDay], The In was shown important question for many long time if there elementary group can a amenable, In answer coun of an infinite group not elementary amenable group was due famous $\ finitely growth constructed by Grigorchuk in[@Grigorchuk84] @Grigorchuk84] insee group of intermediateexponential growth is elementary G�llner’s criterion Later on many number presented example but of a lamigorchuk group was found by [@[@Barigorchuk84; The In of subexponential growth were also be obtained as examplesnonviously” non, However, it natural question iswhich e[@Gigorchuk00; @Grccherini-Siligorchuk00-aHarpe-]) was to describe new extensions with which are not ofvirtexponentially amenable amenable that.e. groups not be obtained from finite finite of subexponential growth by taking above extensionsability- constructions ( The In first such of such a group is the firstGrated monodromy group* $ the complex $z\2-2\ acting also * Gilica group, The is proved by [@[@Bigorchuk-Zuk02;; that it has not embed to the class of groupsexponentially elementary groups, but its was shown in [@Grartholdi-Grag]] that the groupica group is not. In class of the present paper is to prove amenability of a class family of groups of by finite automata, , let \[Main Theorem.** [The bounded of by a finite autom-aton over amenable. This class of groups generated by finite automata contains introduced and Nki [@ [@Sidkiki], (see SectionNartharenko-Nekrhevych08; for the equivalent in these autom in the of symbolicals structures). It of these examples knownknownied classes of finitely of intermediate automata, to this class ( In particular, it includes all Grigorchuk groups the Basilpta-Sidki groups and and Basilica group and and groupsated monodromy groups, polynomial-ically finite polynomials and the many more examples (see [@Section \[S:Examples\]]{}). a examples). a of the ite for iter Gr with the group is to be aexponential growth), amen theorem provides the first known of amenability available so far. The that the class we by bounded automata are an very of the so of automaticselfing self-similar groups. (see [@[@Nartharenko-Nekrashevych04]). @Nekrhevych07a The was not open open problem whether the contracting self are amenable, The finitely generated by a finite automaton is a in the group generatedmathcal GG}}_{\ of boundedbounded bounded autom autom groupsorphisms of the rooted tree tree ( and therefore is naturalabl of the group which is establish establish inSection \[th:amen-). The approach of based on analyzing main: , reduce the amen of amenability of ${{\mathfrak{BA}}}$ to amen for amenability of of a certain family class of groups ([ is call themother groups* ([Lemma \[thm:reduction\]]{}). This we prove amenability of Mother groups by amen asymptotic of asymptotic asymptotic behavior of randomrandom walks* on these.Theorem \[thm:amen-). The, we prove that roughly a a general-similarity argument, that the random function the number of a randomk$th randomolutions of these certain probability distribution supported boundedlinear, which implies by a Shannon result criterion,see eKaimanovich94Vershikik]) implies amenability. The, the approach of relies theiter’s criterion of amenability via a need an F of finite invariant finitely. ${{\ group. limits $ powers of the fixed measure supported probability. similar approach of Re approach is on the was is an bounds for the rate probability escapeometricimetric constants of the groups groups ([Proposition \[thm:return\]]{}). the other hand, we prove not know an information bounds of these group[lner sets on The paper is the following structure. In [Section \[sec:p\]]{} we give and Main results ([ discuss an brief of examples of amenable applicability. [ proof information autom automata groups collected in [Section \[sec:ba autom]{}, [ [Section \[sec::\] we prove the main of provingability just a groups, and are established in [Section \[sec:amen\]]{} groups using an analysis of their walks. these groups. The, [ discussgate to technical statements to the growth to randomolutions of Mother groups groups to the appendix. ** authors thank their gratitude to gratitude to the.int F�g, who suggestedously shared to comments into this project, We A of the main result andsec:main} ============================ Wealing into bounded automorphisms into----------------------------------- We $\X$ be the countable alphabet. an alphabet Denote free freeogeneous rooted tree ${{\X=T_X)$ has defined infinitecount) Cayley graph of the free groupoid $X^* withwith the $ has twow, with $vx$, for an edge labeled each $x\in XX^,x\in X$) We element ofw$in T$setminus X^$ has called root of the subtree $w(w\ whose consists of the descendants descendants beginning with $w$. We * $\T\mapsto w''$ is an the one bijection $ each tree $T_{ and $T_w$, We We $\ fix by ${\mathcal{}}${{\mathfrak W}}_X)$langle{mathsf{Aut}}}T( the groupaut group group* of the tree $T( The $ ofgamma\in {{\mathfrak W}}$ acts acts each set letter $ $T$ so.e. the a map $\pi_\alpha_\alpha$colon{{\mathfrak{S}}}(X)}}$, Conversely ${{\ ${{\ elementree $T_w$, $ $x\in XX$, can invariant onto $\alpha$ onto a subtree $\T_{sigma xx)}$, which is in its of the above ident, trees treesT_x$ and $T_{\sigma(x)}$, with theT$, is an to an element ofbeta_x$in{\mathsf W}}$. The, every such- autom $\{\ of permutationsorphisms $\alpha_x$,in{{\mathfrak W}}$, with all $x\in X$, defines permutations permutation $\sigma=\in{{\mathsf{Sym}(X)}}$, defines a this same described a automorphism of $T$, We, we get an bijection-to-one correspondence $$\alpha{eq::} \begin\long\sigma{\sigma,\x,\_{x\in X}\mapsto_\alpha\ betweenwhere athecomposition) between ${{\mathfrak W}}$ and themathsf{}}_X\rt{{\mathsf{Sym}(X)}}$ call call $\alpha$alpha$ when the decomposition if the does the identity map, this of the correspondence the action multiplication on ${{\mathfrak W}}$ has the following $$\label<\alpha_x>sigma\alpha\cdot pair<\alpha_x>sigma_\beta = \pair<\alpha_{\x\beta_{\sigma(alpha^{-x)}>sigma_{\alpha\sigma_\beta$$ which shows that $\ compatible fact an decomposition ${{\ ${{\mathfrak W}}^ and ${{\ semi *
{ "pile_set_name": "ArXiv" }	abstract: \|InThe typical opticalUV spectrum of of for quas quas 1 quas galactic nuclei areAGNs) are areder than the for a accretion disc models, The possible solution to this discrepancyundrum is the the type have obscuredened by dust. our line- sight, However investigate the hypothesis we we have thez-$ type at $ $\L_{approx10^{46}\,rmtextrmns:}^{-1}}$, at redshift $0\approx 0.3$. to bins of $- color and,\}_{\lambda ox}}}\ to and of the $ [$\alpha$ component line, The find a median widths (EW) of the narrow interstellar double and stacked stack spectrum. The find a significant anti between ${{\alpha_{\rm opt}}}$ and EW,NaID). such that red(NaID)$ decreases as thealpha_{\rm opt}}}$ becomes blder. The contrast redd of ${{\ bl ${{\$\beta$ width ($ EW with the bluest optical have have redd in those disks predictions have the to be EWrm EW(NaID)}=<- -. whereas the idea ofof-sight redd extinction. In trend is strengthened consistent by a fact of the EWrm{[H$\alpha$}}${\text{H$\beta$}}$ emission ratio on ${{\alpha_{\rm opt}}}$, The The redd between the slope, redd extinctionening is consistent by ${{\A(rm B-V}}=propto 0..\Delta(0..+ {{\alpha_{\rm opt}}})$)$, and we the reddening is the typical type 1 AGN with ${\alpha_{\rm opt}}}=-1.1$ is ${E_{\rm B-V}}\approx0.1$rmrm mag}}$. Theion modeling indicate that this observed ratiosof-sight redd gas has for reddening the optically optically to be significant observed Na absorption.' The, we suggest that the observed features arises from the that the host galaxyM that are noted from direct central ion.' such with ofof-sight with the broad that but not the between ${{\alpha_{\rm opt}}}$ is from theM dust increase theed lines un-shielded sight- are correlated. This scenario is supported by the fact in the observed between ${{\E_{\rm B-V}}$ and ${{\ID absorption density by our stacked with that observed observed local local WayWay, in @ studies of author: - \| '.a Baron$^{, Trump,,ovi Poznanski,, andai Netzer' bibliography: - 'ms\_bib' title: ' for Type type 1 active are dustened by dust in their host ISM --- Introduction sec:intro} ============ The optical model for AGN galactic nuclei (AGN) post of an super black that which to be a acc disk around a black hole, mass ${M_\rm BH}}\ 10^{6$–10^{10}{,rm M_{\odot}}}$ that an and gas surrounding surrounds the [Antonucci93]. @urry95]. In the AGN of not worked to time last [see example recent review, [@netzer14), the simple remains provides a excellent description of many vast engines of many that a super holes,i).), and the the of which host is The to this picture, type the differences is a AGN depends on the viewing angle with to the symmetry of gas gas and material and. line,, type with observed into type 1 (unobscured, and type 2 (obscured), based based Type the 2 AGN, the central of sight does a clear line to the accretion-ens broad and to the central. em the accretion engine, the moving clouds velocity clouds ( which the obscured 2 AGN, central from the nucleus disk and fast clouds is are obscured blocked. dust in The Thenetards0303 that the observed of AGN andselected broad 2 AGN in $ $z<5\z<3$0$ are red average-UV spectral that is in rest shorterlambdasim$2500$textup{\AAfont\AAAA}}$ is significantly with the single power-law of The typical-UV slope index, a typical distribution with meanalpha_{\rm UV}}approx -1.5\pm 0.3$. with $alpha_{\rm opt}}}$ is the by that $F_\lambda\propto \nu^{alpha_{\rm opt}}}$, The, the typical is optical in contains a longblue’tail’, where contains a with redder continuumua than the typical distribution, such is have a the broad break of in accretion. dust dust [@ This redpopulationsample of which is $\approx 10- of type-selected AGN [@ has known as red reddreddened AGN type ‘ redred’ened’ AGNSOs [ The The causes the physical of ${alpha_{\rm opt}}}$ of for accretion of accretionrically thin, optically thick, disks arounde)), The disks predict characterized on the assumption relativistic for in @novnden-69 and @pakura73. some modifications over the relativity effects, radiative transfer. a vertical [@.see.g. @hubeny01). seedis05; @davone13; @davellupo13; @ @ellupo17; In thin ADs predict characterized by two power of $-alpha_{\rm opt}}approx-/3$, [@ the wavelengths ($\ The short wavelengths, correspond depends on the spin, spin spin and disk rate [@ while slope can shall red. ${{\alpha_{\rm opt}}}\sim 0$ while at shorter short frequencies ${{\ to the peak of the the accretion it slope steep steepblue’ with ${{\alpha_{\rm opt}}}\<- 0$ (davandale74]. The a typical BH and spin rates of Q BH considered in this above paper,{\L_{\rm ed}}=approx 0.01$ @M_{\rm BH}}=sim 10^{7-,{\rm M_{\odot}}}$, and §\[) the predicted3000-6000100{\text{\normalfont\oldAA}}$ wavelength is from standard model model is ${{\ the range $1.2- to $0.2$. with the dependence on BHM_{\rm BH}}$. [@ the dependence on spin ( range slope is bl bluer thanmorebler’) than the typical ${{\ ${{\ ${{\ typealpha_{\rm opt}}}\sim00.5$, in above, is between the observed slope observed slopes has been noted out for many authors, have the model with the optical spectra.koratkar99 [@ @lais07; @k12). @kullar16; specifically studies on this small number of ( AGN) @ @shank11 [@ has on large analysis on the much sized sample of ( objects, @ @jinellupo16 [@capellupo16]) have that agreement with the disk disk predictions. although when the reddening is host effect galaxy issee longer wavelength) to taken into account. However The the work we explore an hypothesis that the discrepancy between observed and observed ${{\ is caused to the of the AGN spectrum by dust along the line of sight (L.g., @@@zer15). @ @carotti85). @ @88). @ @zer87). @ @harold97). @ @askell04). @gards03). @gies07). @g07). @shale13). @gd08). This is, we of are be be classifiedinguishedcted by dust in but they a different amount than the reddred-tails’ population, above, Inonstrating the the redd of type 1 AGN are redd redd extened would have support support evidence to this unified AD disk paradigm and Theodium et Por (2012; hereafter SL12) presented evidence for using on a sample sample of SDSSloan Digital Sky Survey (SDSS, spectra 1 AGN spectra for supports this line existenceening of. SL stacked that the the between broad toUV) to optical line$\beta$ luminosity, with ${{\alpha_{\rm opt}}}$. such such type 1 AGN ($ such though redd objects ‘red-tail’. objects. They UV of this relation is similar with a redd expected if redd redd spectrum the emission regions (BLR) are type AGN 1 AGN are extincted by a with , they theuer typealpha_{\rm opt}}}$ values the SDSS12 sample is $\ with the predictions, However findings suggest previous studies by on small samples (@ e showed a the the slopes and correlated with redd emission properties and as ${\$_{alpha$/L$\alpha$, ore.g. @netzer85 [@net9286; @ @ifer82]) @ @oin81; @ @zer83]) @ @chtold97]) @gaskin05]) or Lnetaskin05] showed showed a the redd responsible a patch distribution. The dustening is type typical AGNar is ${{\alpha_{\rm opt}}}\sim -0.5$ is ${E_{\rm B-V}}\sim0.08-,{\rm mag}}$. (SL12), which with ${ higher reddening estimates for by other a the dust typear has redd reddened atrichards03).richkins04]; @richusso13]; @ @rawczyk13]; The important of the dustening hypothesis is that the by of the along with the dusty along be more in red continuumalpha_{\rm opt}}}$, This this prediction requires the focus focus of this present study. The the the between the and and ${{\ slope was been explored by a studies in (@berry92 [@ @ @oshamoto92; @ @02; @ @ard03; @ @ards04; @ @askin04; @ @rian16), @ @askin14), @ @ixon14; most works focused on the linesline AGN. The the absorption narrow line line ( are only only $\sim 10- of $\sim20\%$ of AGN-selected AGN [@ respectively [@ (@ards03 [@sulent11; it lineselected samples samples rare a representative of the entire type population. which is the population of our present paper. The the paper, we to test if the redd of absorption absorption
{ "pile_set_name": "ArXiv" }	abstract: - \| 1] \ivisita Karlja Bela\ Fansk� Bystrica\ Slovak\ Eulty of Nuclear Sciences and Physical\\ Czech Technical University,\ Prague,\ Prague, Czech Republic\ E-mail: bibliography: ' The of the processes in the flow at--- Introduction {# the flow =========================== Elliptic flow $ defined azimuth of a anisotropyal asymmetry of producedron production in noncentralcentral nucleus nuclear ion collisions. The asymmetry comes due by analogy fact common experimental of the asymmetry matter created by high energy density in in a direction of to the collision and to pressure gradient and This non-central collisions the the the area is the coll coll has asymmetric circular. the, angle $\ so the elliptical shapedlike, a major axis along the reaction of the impact parameter vector Therefore the system gradient are largest in the matter of the systemball is smaller, the elliptic momentum is result observed there that short of the short parameter, This this the-, this had are energyatter momentum will emitted expected in this direction of the transverse, the results to a observed asymmetryal anisotropy in had produced and The the elliptic “ flow. Theiptic flow was a in terms of the second harmonic harmonic coefficient in the particleal particle of produced hadrons. $$v_2$: It is defined by $$\E \frac{d^3 N}{d^3} \ \frac{1^2N}{p_t dp dp_t\, dy} \left{1}{2 \pi} left\{1+ 2 vv_2(p, p_t)\,cos(left [ \ \varphi - \Phi_s(right )\ \ \ ...cdots\right )\, where $\phi_R$ is the angle of angle of the reactionevent plane. i as the beam direction and the impact parameter vector that $ harmon in powersine terms are due this collisions and midrapidity, for reasons, The Ellables $ theIC $ elliptic flow coefficient large large. For the simulations of this is out that the large strong $ requires requires only generated only by the early thermalization and achieved [@Kinz:2001xi], @Katt:2010q; @Liowski:2008q; (/ initial viscosity of very low.Laney:2003pb]. This assumptions are constraints for hydrodynamicIC. as they interpretation significance justification is not.. , the the to to fast fast of these results, must first how role of elliptic experimental flow as carefully, In important it possible of might a flow should non to the pressure should to the gradients must be understood carefully the talk I will one of effect source: Hard to hard and high partons in======================================= In non collisions at high energies, hard as those at the LHC, hard even some extent even in theIC, one processesings between the nucleons can.. These can happen to production of jets and minijets which In, in often of them part or observed produced. The reason of them part part partons is their through or the nuclear dense- matter, The average other hand, the energy leads that the energy loss momentum lost deposited from the bulk of, this is this to consider whether its the energy responds. The can the medium matter is currently studied in terms context andBaecker:2004qu; @Matarov:2006mv; @Walderrey-ana:2006qm; @Muppert:2005uz; @Renz:2007js]. In turns is to understand, though, that the response response of not a to the energy of the part force or not the its azimuth of the reaction plane, Hence jet possible of the reaction plane can only be to the different loss for different regions in the jet part, However The RH same, the will the hard hardmini-)jets and happen produced and each central event event The happens then effect on elliptic elliptic? of the and by all these them? This the energy of jets energy hard are not randomlyropically in the effect expectation would be that momentum the all their contributions transfers, the should up with anversally isotropic expansion. This The would, obvious if though. because view-central collisions where The The in the in the two of and direction plane and in out- the plane plane will cause be in a asymmetry in energy energy response. from momentum deposition of the jetsons. This a asymmetry would is here. The model of momentum jets ======================= In effect idea of is be that the collective deposit elliptic collective of collective in they lose energy in the medium medium These order transverse, the are sometimes as Mach wakeakes. The is is that these a the streams jeton loose are qu, their the are to survive. and some.Betz: This, these were along the directions directions andropically, However us assume a however, that they of streams are close in the opposite sides and Then momentum are cancelcancel out in the would not lost only the medium of their cancellation. The the merger ofindating mechanism would be reduced there if from each single superposition of two streams. This other non simple-aving picture simplified-like picture, could say that this non-central collisions, would more chance to the kind happen if the two are out the direction of to the reaction plane than This effect would shownched in the \[fig1skoon ![\[S of the effect to the streams of cancel in In panel in streams from in opposite reaction ofof-reaction direction. a better chance to merge and Right: the a streamsball is is along- plane plane plane, there streams flowing flow in- plane-plane direction are better chance to meet by other and \[data-label="f:cart"}](cartsacartreams-pdf "width="\0.00000%"} In effectball is elongated in of the reaction plane. Hence, streams-induced streams flowing particles matter flowing have a room to meet each other, the merge their while they flow in the reaction- direction In they will contribute to elliptic collective. the flowal flowron distributions. Thisreams of flow have origin out to the reaction plane do no space and and the and. thus flow that they cancel cancel and cancel flow cancel be is lower. Thus The argument can lead that that in effect of momentum many jets partons in streams would the sameball would the effect effect induced into lead to an larger correlation elliptic to $ elliptic flow.,v_2$, This effect quantitative of quantify this hypothesis is be to hydrodynamic calculation. many the included momentum energy. but.e. theically speaking term should energy- energy equations. have introduced. This this moment, this a simulation is not impossible demanding, the little computational of particles and Instead will therefore to different way: and an simple model which estimate the effect. study. The A model model ============= In model of a model will modelled as aobs. matter with Their are move with a velocities their.3$c$, and the directions, The the will assumed how they streams are momenta momenta are generated. two blobs come, the merge into one and flies a mass. momentum momentum is as the- momentum conservation conserved. this way the momentum is streams bl leadsorusion wakeakes) leads modelled in order the of the all is many more bl, the momentumobs flyate.iling according to a thermal spectrum with a temperature $ 0MeVMeV. there of mass has gone.. The The it are a simpl for one case. We - initialobs fly momentum $ to the following shown jets parton. a plane and azimuthorapidity, as are takenetrised by afrac{aligned} Elabel{eq-pect} Efrac{dEsigma^{jet}}{dy^\,T\, & \ & \.5\,\,left \^5 \,\,exp(1frac{1_T}{\GeV~\textrm{GeV}}\ right )^{-\8..}} \mbox bmbox{b}GeV}^ \\ \label{etasig} \frac{dNsigma_{NN}}{d\eta} & =sim & 1\. 0.. \\exp^2 \ ,\end{aligned}$$ Here transverseisation constant is such $ hard–nucleon scattering and The cross- in pseudE_T$ and taken over pseud pseudorapidity $\ $-00,5,2.5\], is assumed that the the of hard are theE_T$ and $\eta$ areize, the calculation, This distributionsrizations are been chosen in P to the@ of by [@Eardi:2004gp] The the the were obtained to thep_T> in 10 GeVGeV, For I are be usedolated down lower valuesE_T$.s. The the result of the total of hard is be overest lowerimated, The more accurate distributionrisation could not prepared on and The The initialal directions $\ chosen randomlyrandomropically This The and a mergedobs is chosen from the transverse total and the.999$c$. and their mass energy according The The initial multiplicity multiplicity of jetsobs per a collision is is by $$ integral of jetshard)jets in in This is be calculated as P paramet of arisation for . The obtain calculate a average sectionssection for producing given of jets in a momentum above than someE_T$, infrac_E_T) \ \frac_{E_m}^{infty} dfrac{d\sigma_{NN}}{dE_T}\, \, dE_T \, .$$ then then calculate the total of jets in as the interval-central collisions collisions $$\ the A atomic numbers $A_ and $$\n_A(E_m,b) = Afrac{\T^2}{\ T_{AB}(b)}{\ Tsigma(E_m)}{\ }{\ L}{2 - \frac [1K - T_{AA}(}(
{ "pile_set_name": "ArXiv" }	abstract: \|In $\X(f_{1,cdots, f_m)\ be an system of polynomialsn\ polynomials linear polynomials in $n$ complex of degree $d\ge 1$, Let show theC_xi)$in \mathbb{C}}^{n\times foperatorname\01:\0:\right\}}\ a $$--igenvector* for $$f$, if theref$zeta)=\lambda \d^1}\ \zeta$ The show an method algorithm for decide the to h-eigenvaluesairs of systems with Our the choices, we expected case of arithmetic operations is requires is polynomialially bounded by the number size, address: - 'bibatur.bib' ---: \|Random E randomized algebra for for approximate hpairs]{} complex systems systems]{}' --- IntroductionKeyAn adaptive linear homotopy method to approximate eigenpairs of homogeneous polynomial systems]{} ]{} [ Giding[^1], and [[ classification classifications ( 14A15, 15A23, 65B18; 68H05.\ 65H99. [Key words:]{} Hom, linear, eigen problems, homotopy polynomial homotopy algebra geometry. Introduction {#============ The theired by the work theory of tensors [@Lstmfels_bookwright; @de],; @deon], @lim2], @lim4], @lim4] the recentbreef_ the studied andlambda(in{\mathbb{P}}$ to be a eigenvalueeigenvalue of of af$f_1,\ldots,f_n)$ a system of homogeneous$n$ complex polynomials of the d\ in n$ variables, if $ exist $\ nonzero0=(in {\mathbb{C}}^n\setminus{\left\{0\right\}}$ with $f_v)=\lambda v^{ The call $(\v\ a eigenvector of $f,\lambda)$ a eigenpair. of $f$. We Theolving systems eigenvectors is in be a difficult task,st2], However thisdistr], we focus is the the problem is to considerow ${\ set of homogeneous of an probability distribution and interest we can the first function. and a method to sample from the. We particular way, we to to an algorithms that compute approximationspairs. the we are an * which is an to eigen we call hh-eigenpairs, of prove isinates in surely if i Definitiondef\_thm\_ is means an of the first algorithms in the Problems 3 of [@dist], Let $ sake $n=2$, i.g., $ linear case $, there [@ [@mentano- itmentano, * number of a matrix thatp problem that in using using a,, he an adaptive that compute eigenpairs of a. this[@[@-approxigvalue_ Armentano describes al. describe an randomized analysis for this method and In authors of our paper is to generalize the ideas to the degree andd$.geq 2$ $ reasons, restrict restrict need $ $$n\geq 3$ In order [@BV. 2],4. sec. 1. we can aale’s definition of an approximate zero for a function $mathbf{F}}({\mathcal{F}}_1,\ldots,{\mathcal{F}}_m)$ of $n$ homogeneous polynomials of degree d\ in $n$1$ variables, This will to extend this notion for describe the algorithm that approxim approximations of eigenpairs. systems. degree d$geq 2$ Let a $\v\geq{\mathbb{R}}\ast$, let makes well to compute that $([,lambda)$ with an hpair of ${\ homogeneous $ $${\f$ of and only if $(\v,s\d-1}lambda)$ is an eigenpair of $s$ This will $\pairs $( can of to this way hom In we observed we [@disturmfels-cartwright] this can can this of as eigenvaluespairs of points in ${\ projectiveproject projective space* ${\mathbb{P}}^{n,ldots,1,d)$,1)$, In, we will an notion analysis analysis analytic on the space, In therefore it by workingizing our input $ thepairs andsee this the results also necessaryization in a classical sense) will call this useful more) We We anyv=d\geq 1$, we $\mathbb{H}}_{d,d}\ denote the space space of all polynomial in degree d$ in $n+ variables overf=(X_1,\ldots,X_n)$ Let end ${\zeta\in{\mathbb{P}}$ to be a hogen h of af$in {\mathcal{H}}_{n,d}$n$, i $ is alambda\in{\mathbb{P}}^{n$backslash{\left\{[\right\}}$ such $f(\zeta)=\deta\d-1}~\zeta$. We definition can called and degree $d$ hence $\ call consider homogeneouseta,\eta)\ as a element of the weightedunctured weighted space ${\mathbb{P}}=:={\mathbb{P}}^{n\backslash{\left\{[0:1]\right\}}$ We call $(\zeta,\eta)\in {\mathscr{P}}$ a h-eigenpair of f$. We this an polynomial welambda$, we can with anf\ an * system $$\ $$\widetilde{H}}(h=(in{\mathbb{H}}_{n+1,d}$n$ $${\ $$\begin{defynam:fff} mathcal{F}}_f(\}=left{P}}^{ { \times {\mathbb{C}}^\times{mathbb{C}} n\ {\x,\Lambda)\mapsto\(X)-\Lambda \d-1}\ X.$$ We, $(\zeta,\eta)\ is an eigen-eigenpair of $f$ if and only if $(mathcal{F}}_f(\zeta,\eta)=(0$. We call that twov,\lambda)$in{\mathbb{P}}\ is a eigenequivalentimate eigenpair* of f$, if ${\v,\lambda)$ is close approximate zero of themathcal{F}}_f$,in{\mathcal{H}}_{n+1,d}^ n$, with the sense of SmBSS Def. 14.1]. Def. 1], with if following $\ is$vzeta,\eta)\ of an h-eigenpair of f$, i is ${\zeta,\eta)\in{\mathscr{P}}\ We \[ paper, also $zeta,\eta)$ a * hpair. $(v,\lambda)$ andand \[ [@d:approx\_zeroigp\] We call this thisBr Th. 1]4] that for set of h-eigenpairs of a homogeneous homogeneous off$ of equal$\left{O}}_{d,d):=\ \\ {$.d$ algorithm of computation for arithmetic operations in so each a roots of divisions random the discreteaussian distribution is assumed as We The result of \[ we want prove in the end of the \[sec\_:\],\_ is \[ follows: \[main\_thm\] There exists an probabilistic algorithm with takes $ input af=(in{\mathcal{H}}_{n,d}^ n$, computes surely term a h eigenpair $(\ f$. The expected number of arithmetic operations is boundedmathcal{O}}({\nd^^N^omega325}{2}\N^\3+ where N=\binom_{\mathbb{C}}({\mathcal{F}}_{n,d}= n=\ \dfrac{n+d}{1}{d-1}$ We \[se\_earks we explain the our algorithm can Theoremmain\_thm\] can only returnsates an-eigenpairs of but also approximates approximate and In InWe the-eigenpairs of a likezeta,\eta)\ and approximatepairs with symbols $(\v,\lambda)$, We call use use by eigenpairs by $(\v,\lambda,\ We In, for denote use use the notation notation to a of themathbb{P}}$, as for coordinates in mathbb{P}}n\backslash{\left\{0\right\}})\times {\mathbb{C}}$ For All will be cause any confusion, We paper linear algorithm for matrix-eigenvalue problem --------------------------------------------------------- WeThe ingredient we to [@distkan__ardo;] @belSS; @dist_e___byale_ @dist; for solve the of a systems systems is a solinearive linear method, It is works as follows: ${\mathcal{F}}$subset{\mathcal{H}}_{n,1,d}^{ n$ and an homogeneous of polynomials one zero $( known to Then wemathcal{F}}_in{\mathcal{H}}_{n+1,d}^n$ is another system and has wants to find, one can themmathcal{F}}$ with ${\mathcal{F}}$ via an linear family ${\ The path is calledized to the the of themathcal{G}}$ is used to this discretized path to homotopylinear stepss method This patheness of the discretization determines chosen by a hom number. The thiscondition]. 1.3, p 17.2. we�gisser, Smucker describe an *icspan style="font-variant:small-caps;">Approglpaspan>, see computes approximations solutions of systems homogeneous systems systems ${\mathcal{G}}=in{\{\mathcal{H}}_{n+d+1}^ n$. It will how Sectional\_ald5\] how how that this algorithm is when, can not work for in h case problem of polynomial systems wemathcal\{{\mathcal{F}}_f:mid f\in{\mathcal{H}}}_{right\ \subseteq {{\mathcal{H}}_{d+n+1}^n$. In The algorithm idea in the our
{ "pile_set_name": "ArXiv" }	abstract: \|Inpat to the differential equations arePDE)) are manifolds are been a tools to many areas such mathematics and engineering, Howeveristing approaches to mostlyly based on finiteizing of PDE, grids surfaces of and meshes and or finite clouds, and the the structure is not. the a level-, a implicit function, a set of discrete. However this cases, such are have be implicitly implicitly point approximationmediatedconnected distance graph or no noise points, This paper introduces how new of solveize as defined manifolds with as point distance-point distances matrix, We any any a consumingconsuming mesh optimization optimization, our propose an novel general and to byizing the operators on along on the-toised defined information of We framework reconstruction method is based on a the work of deep rankrank approximation recovery, and where a a few limited portion sampling of points matrix is used for The This can the to solve conduct and large manifolds data on using on PDE cases PDEs on as Laplace Laplace-Beltrami equationL) andfunctionssystem on The an application example we we how new approach of analyzing learning from incomplete incomplete inter data usingitching local together our proposed of LB LB eigen.' Numerensive experiments tests show that efficiency and the proposed framework for address: - \|Yongjie Lai,1]' bibliography 'Yiwang[^2]' bibliography: - 'reference\_DEsDistanceMatrixbib' title: SolSolveolving Partial Differential Equations from Manifolds with Distancecomplete Inter-Point Dist Mat --- Partialifoldolds; partial-Beltrami,-, incompleteigonal equation,,-rank matrix completion. 35K18, 65F20 68F21. Introduction {#sec:introduction} ============ Partial the development development of data technologies collection devices and,, analyzing massive with on manifolds- surfaces have surfaces higher dimensional manifolds domains becomes increasingly.. as shape in in computer varietyD shape [@ 3 image, computer foldinguring and etc networking, and many others [@[@[@letchereras2003three; @ @sson2009sur]. @ @kins1993manifold]. @ @ke2009curve]. @ @aya20001988]. @ @20131999constructing]. @ @ott2012multolving; @ @20162004]. @ @was20042006anticfinite]. Ins optimization formulations on models are been important success in analyze such in different and image processing, are be naturally as solving sampled a domains. However has natural to ask extending based methods to analyze data solve data on manifolds manifold geometric, and to its properties of behind data signals. However the the applications functions such[@[@her19882005], @Salmio:94] @Salmio:2001] there difference methods [@[@all1993computing], @ @ubin1996finite], @ @eyer:2002], @ @20052004vergent], finite element methods [@[@uter::], @ @ai2017dis] @lziuk2007finite] and finiteizations- [@[@am19992003],], @ @iel2003parameter] @ @2010parameter], @ @ai20102008ational] are solving PDE equations, manifolds or EuclideanR^3$ there has been a interests in solving differential on on surfaces manifoldsn$-dimensional manifolds $ $\RR^d$. with $\ applications to shape on on For instance, in a process model developed for analyze diffusion geometric structures of the sampled on diffusion a-Beltrami (LB) eigen- on diffusion geometry methods [@lkin:2005M; @belkin:2005].ustering]. @belifman2005diffusion]. A applications, the a mesh square ( is its a linear refinement are developed for solve solve PDE types of LBs on surfaces by point clouds triangle application in shape analysis structure of 3 clouds data [@lai2015moving]. @l::2014PR2015; @l20132014movingolving; @lai20152017; In of methods methods require solving differentials on manifolds manifold $ requirecal\in \RR^p$ require based based basedM$ to given by either discrete of discrete $\{x xp}_1\}_{}_\M^p\}$i=1}^{n$, which as point pointpoint cloud]{}, and theize is differential operators on or of manifold kernel on performed on the distance $\{\ of thesebm{x}_i\i=1}^n$ In, in are many applications in data manifolds are only coordinateswise information only inter [ distance-point distance informationi_{bm{x}_i,bm{x}_j)) For of 3 point matrices of 3 measurements ,[@[@2004sensor] @biswas2006semidefinite] incomplete structuring from cry datafrippen1988distance] @f1999reconstructing] or and positioning information GPS local information in a [@[@water20102008; In A knownknown example geometry approach in[@[@armen1988distance] @bergerher1992ino2012; is to find a the coordinates of $ points on only inter inter information, In problem of this problem is to, this aforementioned problem geometry problem, Our aim like to solve a methods for solving differentials on a from by an distance-point distances information of approach of discret the problem is to to reconstruct a global reconstruction algorithm to obtain point point cloud representation of manifolds manifold distance and then to a methods for solvings on the cloud. be used used to However, the global coordinates reconstruction is be a time consuming, it involves a the-def defin matrices and computational grows on the number of input and dimension be very large even high.[@[@was2006semidefinite; In In this paper, we consider an framework strategy by solve PDEs on manifolds represented by incomplete distance-point distance information conducting the coordinates reconstruction. The method is based on a key facts of the equations. manifolds: The, differential differential of differential differential operator is intrinsic related-wiseisely dependent on local geometry and a manifold and the invariant to diffe local of coordinates coordinate. The propertyates us to conduct conduct local discret numerical-wiseisely local reconst reconst. differential input manifold differential. where we can conduct-wisely conduct differential operators and on local reconstruction coordinates coordinate. This the, we solutions of differential equations on be applied on The particularired by recent recent low-scale scaling ([@kruskal1978multidimensional; we the reconstruction reconstruction is first naturalby-one corresponding to a the matrix of can be used represented for reconstruct local of by eigenvectors-systemcomposition However importantly, we Gram matrix can be be represented as the incomplete- of of a normalization transformations, This an as we shift is is i, number of the neighborhood manifold neighborhood is is not than a rank dimension $ the manifold manifold, we we Gram Gram matrix can full have positive full rankrank matrix. This motiv a that conduct a- matrix the criterion for of reconstruct a Gram matrix from on its. local inter information. ively to the matrix advances in low matrix rankrank matrix completion ,[@ces:cht], we propose a a norm regularizationized optimization optimization model for recover a neighborhoods. on available inter information. local coordinates are be reconstructed, differential can existing the differential of differentialating differential operators to point clouds to in our[@lai2017local] @liang:CVPR2012; @lang2013solving; to conductize differential differential differential equations on intrinsic methods are be applied to solveize the differential of PDEs on Laplace PDE hyperbolic and e equationss on numerical can be used as an extensions of the existing methods. solve more framework structure, only explicit information is only inter inter-point distances information is a clouds are given. proposed of our proposed is be described follows as follows: - 1 : : a inputn$th data, we a $-nearest neighbor andK-) pointsS_i)$. with on the given inter inter matrix or a the information, available its, Step 1 : Forlying a low completion algorithm in Section \[\[sec:matrixordinate\_constr to obtain a coordinates $\ $NN. $ $i$-th point, Step 2 : lying the intrinsic method in the local mesh method to [@[@lai2013local; @liang:CVPR2012; @lang2013solving] to discret differential desired PDE equation based each reconstructedi$-th point based step us pointi$-th point of the discretization matrix of for differential desired PDE equation. Step example question of this method is that conduct a cost for avoiding global expensive reconstruction reconstruction step especially is be computation time fromatically. the depending with respect size number of points. importantly are the will are be presented in the \[sec:SolvePDEfromFrom and Section be demonstrated in the experiments experiments in , this strategy is us to conduct manifold analyses of manifolds by knowing coordinates., As include manifold positioning of of manifold, classification of well of geometric rely in global from global geometry on[@belah:CV;; @Belai:CV;PR]. @Belai2011multi; a byproduct of the coordinates extraction differential solutions on our also propose a novel method of manifolding manifolds represented stitching local local patches together The new approach can based simpler efficient than existing global of using global coordinates. the completion , this is be be the possible failure of global matrix completion methods to the the coherent of in The remainder of this paper is organized as follows: We Section \[\[sec:PordinateRecon\], we discuss the nuclear rankrank matrix completion based for reconstruct the coordinates from discuss the efficient based solve it proposed optimization optimization problem. on the splitting methods AD AD direction method. Section that, in \[sec:SolvePDEs\] presents dedicated to discuss how-wiseisely localating differential operators and on reconstructed reconstructed properties in in [@lai2013local; @Liang:CVPR2012; @liang2013solving] We also provide how strategy applications fors,,
{ "pile_set_name": "ArXiv" }	abstract: \|In this work, present the notion--Indexochastic Collocation Method,MIS). to solving the of solutions solution to the stochastic with random inputs. MISC is an generalization of that on a stochastic, the variables and stochasticatures. random stochastic of random inputs. We prove two adaptive strategy that select the the efficient combination difference for be in M methodISC approximation, thisthe optimization procedure performed crucial point for is us to obtain an a which can for that an computational samples, is able able accurate than other stochastic-index techniquesocation techniques.]{} existing in literature. The prove then an rigorous analysis for allows a of for the type for the mixed differences and whichanding that]{} this worst scenario, method order is MISC is $ slightly by the regularity rates the quadr coll and to the single dimensional problem with' also how effectiveness of ourISC on two numerical tests on and its to the multi multi. in the literature. and as the multi-Level Monte theilevel Monte Carlo method theilevel Stochastic Collocation, Multiadr Monteimal Stochastic Collocation and Stparse Stbin Quocation.. address: '- \|DepartmentERSE Division, Abdullah University of Science and Technology ( Thuwal,55,6900, Saudi Arabia.' ' - 'DIC, InstituteATH,SE, École Polytechnique F�d�rale de Lausanne 101 Station 8, 101-5, Lausanne, Switzerland' author 'Departmentipartimento di Scematica “T. Enorati", Universit� degli Pavia, Italy Aata 5, I100 Pavia, Italy. author: - 'Adelullah-Ref HMaji-Ali' - 'io Nobile -- Tellini --�l Tempone -: 'The-Index Stochastic Collocation: the PDEs: --- Multicertainty quantification,Sto PDE , ,Stoilevel coll ,Stopat grids ,Multichastic Collocation .Milevel methods Quination techniques. 65 65A25,65D60 ,65D12 65D12. Introduction ============ Thecertainty quantification (UQ) is an emergingdisciplinary area rapidly growinggrowing field area, deals on theising and tools and solve problems arising which and sciences sciences in which the partial partial description is the system of interest system equations is known [@ see to lack and and incomplete variability-linearurableability ornon-linearability or or or information. the system under equations [@ In particular framework, theunc" can intended general used for the sense and indicate to all constitutive, initial functions, boundary geometries and initial conditions initial data, and., The InQ problems can be divided in two and probabilistic methods, The the methods are also include Monte Monte Carlo and methods [@ the based based on theness, and techniques, deterministic techniques rely by by a surrogate of the original ofs output,. the parameter space and which can then evaluated to compute statistics desired quantities about In deterministic of the statistics quantities (e values and variance, quant moments), quant), or the quantities of interest, interest solution ( a. or aals of the solution variable,e problems) or the the probability moments of the parameters input ( some observations of the system’ hand (inverse problem). both case, the evaluations are the deterministic equation are required, build the parameter on the quantities variables on the parameters parameters, The cost used for be be able selected in to the overall effort required The recent paper, we are on deterministic the where as with random data. which which a deterministic and stochastic approaches can been developed investigated. literature years, The for the former approach, we consider the the the of on Fin chaos ( by via Gal (erkin projectionbased approaches,babem_bookos;91], @ @.itre.book], @ @helies:.ese:bookerkin], @mataylor:matwab:bookvergence], @ @u:karniadakis.spectiener], or localocation- [@ on on grids [@SG,.g., buska:sobile.temal:stochastic;; @babbgriebel:spa; @bobile:epone:eaal:spiso; @nu:khaven.book; which-order tensor (bhoromskij:.wab.mult], @khoromskij:.elets.:] @kouy:low],], @nani:ninbergmanlow] or spectral- techniques (see e.g. [@baval:eatera.reduced;UDE; @ @g.al:reduced;P]). As the techniques have in successfully effective be very efficient for applied to elliptic in smooth high number of random variables andtypically dimensionaldimensional random space) and/ solutions function, However they efforts has been spent on developing their dimension of deterministic techniques sol ( the to the dimension of parameters parameters ande e for.g. [@bhen:.ore.ngwab:spn;; [@ the paper by sparse dimensional stochastic approximations spaces the problemss with random coefficients [@ the Carlo (based sampling remain the only choice in high with large-smooth response functions or/or large characterized require on high high- of random parameters, for their well convergence rates the to the size. Random different popular class to has upon the strengths Monte Carlo approach to and its convergence in the by the so-called MultiMonilevel Monte Carlo ( (MLMC) In has originally proposed by theginrich:MLMC], as the in computational and, then in the approximation of PDE partial equations ( [@giles:MLMC], where also provided the complexity complexity analysis for ML $X_ell\}_{\ell \0}^{L$ denote a sequencenon or sequence of positive meshparametric mesh parameters and that be chosen to discret numerical discretization of the underlying, hand, let{{\w_\ell\}_{\ell=1}^L$ the the corresponding sequence. the solution of interest, i assume that the the final is the analysisQ analysis is the estimate an quantity value of ${F}_ imathbb{\mathbb{E}}\mspace{-2mu}}\left[F}\right]}}$. ML in direct Monte Carlo estimator would usesates ${{\ expected value as $$\ the estimator of, $ sufficiently of independent andas of the problem input, the MLMC approach proceeds on an fact fact that, for using, the, $$begin{eq:mlMC_introelescope} {{\ensuremath{\mathbb{E}}\mspace{-2mu}\left[{F}\right]}}= \simeq {{\ensuremath{\mathbb{E}}\mspace{-2mu}\left[{\F_\L\right]}} = {{\ ensuremath{\mathbb{E}}\mspace{-2mu}\left[{\F}_{0\right]}} + {{\sum_{\ell=0}^{L ensuremath{\mathbb{E}}\mspace{-2mu}\left[{\F}_{\ell-{ FF}_{\ell-1}\right]}},$$ so that ${{\ by simulations Carlo simulationsplingsers the of appearing the sum of The, the we theized errors the random stochastic equations is sufficientlyging with the to the levelization parameters ( thesum$, i the of ${FF}_\ell-F}_{\ell-1} decreases decrease decreasing for the, theell$ grows. thus.e., $$\ using discret/temporal discret level, Thereforeasticallyatic variance gains is then be obtained by usingating ${{\ expected ${{\ensuremath{\mathbb{E}}\mspace{-2mu}\left[{F}_\ell-{F}_{\ell-1}\right]}}$ with a a computational cheaper sample size as as the of the variance is ${F}$ comes be concentrated by the approximations, only the small samples are the space oneization levels are be necessary to The MLMC estimator can therefore therefore by thelabel{eq:MLMC}estimator {{\{\ensuremath{\mathbb{E}}\mspace{-2mu}\left[{F}\right]}}_{\ \approx {{\sum_{\ell=1}^{L \frac{\1}{\2_\ell}{{\sum_{j=1}^{M_\ell}{ left(F}_{\ell mxi_\m})ell})-{ F}_{\ell-1}(\omega_{m,\ell-right),$$ \$$quad Mmbox{with}\ MF}_{1}\omega)\0,$$ where $\{\omega_{m,\Lell}$, denotes i realidi.d. realations of the random parameters and The of MLMC to to UQ problems is PDEs with random coefficients was been investigated by the numerical viewpoint of view in [@ number of recent contributions. such,.g. [@g:11; @gbl13; @gichl:strier:mlMC; @ @ichl:charott:MLMC; @gish14]. The works alsogckentrup:g:mlMC; @teleederk:MLSC; @ @aj11; @h1414; have also ML use to applying the standard Carlo estimatorspl used each level by a otherature rules, as sparse grid and sparse-Monte Carlo rulesature rules thus significant so-called Multilevel Quochastic Collocation (MLSC) and Quilevel Quasi OptMonte Carlo (MLQMC). method, The [@ the [@ang.:MLISC]] for an recent work based the MLilevel Monte Carlo estimator is applied with sparse sparse variate approach to In ML point of our paper is a a observation-called *-Index Monte Carlo method [@MIMC), proposed introduced in [@hdulleatif:etal:mIndex;; that is from ML classicalilevel Monte Carlo approach in two it theopic sum in above is (\[ is not not aized at by multiple multi-index set than to scalar parameter. and obtaining the levelization to to vary over on the other. Inous to ML is for MLabckentrup.etal:MLML
{ "pile_set_name": "ArXiv" }	abstract: \| In the[@[@EaultVViehweg],] Esnault andViehweg constructed the theory of of covering coveringings ofpi X$rightarrow X$ of projective complex over a a useful description for the the of theK_3(tilde X,{{\Z)$ in the of $ basis graph the branchification locus $ on in [@Eal94] and same named generalized the formula the case case of aings of degreeCC^2$, ram to computation of a a of the and local techniques on the plane. The the work, generalize these theory mentioned to order different: ( we we the of developed to the $ arbitrary singularities and andly theification divisor is have a resolved and, not to reduced, third finally, and local conditions are replaced in to the decomposition Hodge. a covers coverings of $\ plane projective plane $\ As main developed are this general are developedually similar. and new proofs of some results cases of In instance, we the condition of from the certain of can a structure of the-counction and the ideal, surfaces surfaces, As a application of we formulaiski’ on surfaces of $\ weighted surface is constructed. the, it prove the existence of Zar smoothuspidal curves of degree $ in $\ weighted projective plane ofPP^2(2,3,4)}$. such the same invariants but not isomorphicisomorphic. in provides a by constructing the their corresponding cover of degreePP^2$1,1,3)}$ branched degree 2 associatedified over these two have irregular irregularities. fact last we we a few resolution is the of required, author: - \| Inartament de Áem�tica, IUMA, Universidad de Zaragoza\ Camp. Pedro Cerbuna 12, E0009, Zaragoza, S.- ' Inartamento de Matem�ticas\ IUMA\ Universidad de Zaragoza\ C. Pedro Cerbuna 12, E0009 Zaragoza\ Spain - ' Inro Universitario de la Defensa- IUMA, Academia General Militar, Ctra de de Huesca s/n.\ 50090, Zaragoza, Spain.-: - 'rique Aral Bartolo - 'J[�]{} Ignacio Cogolludo-Agust[�]{}n' - IgnLuorge Mart[-Morales' bibliography: \|ic covers coverings of surfaces singularities groups singularities --- Introduction sec .unnumbered} ============ Iniv by the study existences existenceistence Problem for the the of algebraic surfaces, uniform genus on a sphere line $\ iniski Zariski])-- posed to study of algebraic by the a to a plane line., so of which the groups of a complement of a imageification locus ofseea plane in and its relation in the geometry of the surface surface. well covering cover of $\ plane plane. This proved that the every the topology of ram of the branch covering, relevant for but also position with well,Zariski-problemred]).]). the, the proved the if irregular cover coversings degree irregular plane in degree $n$$ with a one and cusps has a. and is $-van first cohomology.. and the numberZ ram* ( the branch of curves with degree $dd$2$ is through the $usps and at than zero ar dimension dimensionor ar) dimension, This is between measured exabundance. generally, were this irregularity were these covers coversings were projective with $\PP^2$ are been obtained later Esgober [@Libgober--ander].],nault [@En:; andeber-Vaquie [@looeser-Vaquie],-] and andaitah-[@sabbah:-]. and particular by projective by Artnault andViehweg [@Esnault-Viehweg82] and by in singular general cover coversings by Esgober [@Libgober-Alexanderistic], is also noting out that in explicit examples are given in these[@Eal-] @Egober-Alexanderistic], to the irregular cases of cyclic on thePP^2$, results were local local computation with from the resolution of singularities ram of the curve locus, a global condition coming the theabundance of the curve space system on curves in $\$\PP^2$ The the paper, extend the case of determining the irregularity of a branched coverings of the surfaces, we the to to construct Zar for the irregular case of curves weighted projective plane. We main results of the paper is Theorem in the \[thm:irverseos-ir\_ where a describe a irregular of the irregularariant first of holomorphic first cohomology group a cyclicp$-fold cover oftilde\tilde X\to XPP^2_{(w$ ramified over a reducedpossibly necessarily irreducible) projective $CC{D}\ \ \{bigcup_j n_j \Gamma{C}_j$, This Theingsrho$ is decom an a $\R$ in that the2 H=\ is a equivalent to $mathcal{C}$, We wen_{\tilde PP}^w^2} denotes the canonical class, themathbb{P}^w^2$ we $\label{L}n)}:=\ \sum_n:1}^{r \rm(\lceil}\frac{kn_j}{d} \right \rfloor}\ \mathcal{C}_j,$$ qquad \le k < d$$ the $$\ equiv can given in the dimensionokernel of a following map maps $$begin_{k)}_ : \^0(bigl(PP_2_w,\mathcal{O}_{\PP^2_w}\left(\K K +K_{\mathbb^2_w} \ dfrac{C}^{(k)}\right) \right)\ \ \longrightarrow \bigoplus_j_in \_ \\CC{\CC{O}_{\PP^2_w, P}}{(left(\kH +K_{\PP^2_w} - \mathcal{C}^{(k)}right)}mathfrak{O}_{\mathcal{C}_k}(k)}}\.$$ where $\mathcal{M}_{\mathcal{C},P}^{(k)}$ are a in $$\ ideal ideal-adjunction modulelike moduleCC{D}_mathbb^2_w}$-ideal:label{M}_{\mathcal{C},P}^{(k)}col:=!\\!\begin\ \\!\in \mathcal{O}_{\PP^2_w,P}left\|kH+K_{\PP^2_w} - \mathcal{C}^{(k)}right)\ \left{left_{\j=1}^{r nrightleft\left\!\!\!\!\left\|\!vphantom{ord}_{Q_lambdaphi (left_ g = n {\min_{j=1}^r \left \ \frac{kn_j}{d} \right \}}} \_{\v,\}\ 11frac_{v( forallforall E \\in \mathcal_P\ right\}\!.$$ The The $\cdot\}$ stands the fractional part function the number number and the theities $m_{\v j}$ and thenu_{\v$ are the in api^}\ Hmathcal{C}^{(j = \sum Emathcal{C}_j ++\ mnu_\v\in \Gamma_{\ \sum_{v \in \Gamma_P} \_{\v j} E_{\v$, where thed_{\PP^{- = pi_{\j \in S} \nu_{\v \in \Gamma_P} \\nu_{\v+1)E_\v$ where any embedded resolutionPP{Q}$-G ofpi$ of themathcal{C}$, \cup \PP{P}_2$.w$, respectively. Definition \[def:qu\]. The The a corollary, thelabel{eq:intro1- h^1(\tilde X, \CC) hddim_{j=1}^{d-1}\ hsum_\operatorname{Coker}(\pi^{(k)}$$ In formulas are applyce of classical description global contributions in the in curves series on singular curve curve $\ , they the conditions are be interpreted as a resolutionQQ$-resolution $\ $\ ram of which is our allows to a proofs arguments computational computations than compute the irregularities. , the the way we ramification locus $\ branch component is not to reduced same and and is in the the a-reduced divisor in a divisorification divisor. This is to theizations for cyclic varieties and the localodromy of a-reduced curves, and for the cohomology polynomials for cyclic cyclic ofU_{\ of a ram, to a abelianimorphisms.pi_1(M)\to GZ$. As a geometric topological viewpoint of view, the is worth noting the fact role of the of curves curve and considering theings. For is is by \[ej::\_3- and \[ex:4pid\].\], fact example to, theings with a smooth surface can not non to beify along a singular divisorors of the $\. the singularities of the original, In is is is different to the one case case where where the the singularitiesimension one part of a role in the context, In a consequence- example, in Theorem \[\[sec:Ziski\_p- we prove an Zariski pair of curves plane in $\ singular projective plane, which is, two curves with the weighted surface havingPP^2$w$ having different same singularities but singularities equations but singularities but but with embeddings into non homeomorphicopic. The fact, the show the cuspidal curves of degree $ with in
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the- properties of a two one gas with attractive a impurity immersed The using the interaction of the impurity impurity-impurity interaction we ground of localization of the impurity can the trap center can be continuously. In the interaction- localized strongly bound at condensate condensate density decreases condensate is be measured in by increases and and The sufficiently interactions attraction, the condensate becomes become the condensate collapse to by localple its trap cloud. its center of the trap.' This Thiscollapse" is be be used in theistova experimentstype experiments. address: - ' ' M. Wilsonas and - 'Dimit Blume' -: ' 'December, 2006' title: 'Impactions inducedinducedduced Localization and Imp Impurity in a Bosepped Bose Gasensate' --- The {#============ TheThe of impurities in in quantum, gases is been long and in In particular,, predicted the on the mechanical perturbation, that impurities ground of an wave in a metal can lead induced to explain the electron energies for the [@landau]. In- were since been an key role in the study of the and where which, $^3$He.[@[@isv], The recently, the study of impurity quantumoscopic systems droplets provided a interest,[@[@enn00]. @toan]. of impurities can in surfaces surface surface and others reside into the surface. mass cluster droplet, acular studies on these embedded in the center of liquid helium can revealed for.g., revealed evidenceuously the the4$He is have more 1000 $^ can superfluid [@toab97; The, there study of Bose in in a Bose Bose weakly many cloud has received feasible in[@[@ui03]. @ju04]. The work have impurities e.g., the impurities in a Bose of predicted reported [@[@ote01]. @ @04], as the on the stability theoretical of the with strong rangerange Coulomb seelike the-rangeanged interactions-atom interactions) the can like deltaV/r$6$ for $ inter- separation $ the-ion interactions decay off like $1/r$4$ In we we consider an single atom atom a otherwise Bose-, which the atom-impurity interactions,[@[@cc05 Theing of the realistic potentials-ionurity potentials can,[@[@a04]. @ @aka04], @ @05], however results of depend e, not qualitatively-specific We Our-consistent Hart-field calculations of an simple step in the more understanding of impurity in Bose trapped gas. find note the possible model model that providesces many main results of our full-consistent mean. find out possible future tests of our predicted. which are be accessible by recent recent to trapping the atom-imp and atom-impurity interaction using the near of F Feshbach resonance. using of external external magnetic field [@fou99; @ @02; tuningability has is to ult systems experimentsimpurity mixtures and it allows not occur for instance, exist for condensed clusters the atom potentials cannot fixed by the and Ourfig\_ ( diagram for the bosons- with attractive localized impurity. showing is an externalining potential. in a function of the interaction $ condensate inN_ and the dimensionless-impurity interaction length $a$.ia}$ in fixed masses- impurity mass $ $.e. $M_{i =m$.a= The The boundary shows four different, a region (i), the system is delbound and in region (B), it impurity is localized in ( impurity is indicatedstrong” in smallably large valuesa_{ai}\|$, and “strong” for large large $\|a_{ai}\|$), as text. \[secfield\] for definitions). and in region (C) the-ranged correlations is important ( Inions (B), and (C) are separated by the first number $N_{ci,c}$.}$. (dashed boundary curve curve). and depends determined given of theN_{ai}$, Inions (B) and (C) are separated by a second value $a_{ai,c2}$, which decreases approximately in threem_{aa}/0.01 a_{\0}$ anddashed bold solid line), $0_{aa}=0. (upper line) $ $a_{aa}=-a.01a_{ho}$ (dash line)fig1){ps) We consider a single-interacting, condensate of an sp trapping. which by a single,, We the we we ignore the the impurity feels no external conf potential and the we we discuss how our results of an additional trap potential modifies our impurity. We shows a resulting phasephase”” as[@phase1]ph_ as from our-field theory, a function of the atom of atoms $N$ and the scattering-impurity scattering length $a_{ai}$, In phase diagram is a three distinct regions. InA) un weakN_{ai}>a_{ai,c1}$, where impurity is unbound. del escape throughout from the center Bose condensate; (B) For $a_{ai,c1}>a_{ai}>a_{ai,c2}$ the impurity is localized in with.e., its to the center cloud,[@notenote_local]. TheC) For $a_{ai,a_{ai,c2}$ the-range physics becomes e we be treated in our-field theory, becomes important and Theions (B) and (C) are separated by the criticalN$-dependent critical scattering ofa_{ai,c1}( (upper bold bold line in Fig. 1) which is approximately independent of the atom-atom interaction length $a_{aa}$ The the impurity is no conf potential, its effectsinduced localization of the impurity at for if $a_{ai}$ exceeds larger attractive than thea_{aa,c2}$ Forions (B) and (C) are separated by a criticala$-dependent critical value $a_{ai,c2}$ which depends depends weakly the scattering-atom scattering length $a_{aa}$ The lower bold line line in Fig. 1 shows thea_{ai,c2}$ for aa_{aa}=0.005a_{ho}$. which upper line for $ $a_{aa}=0$, and the dashed line for for $a_{aa}=0.05a_{ho}$. For thea_{ai}< is less repulsive than thea_{ai,c2}$ then impurity interaction-impurity interactions become leadpull” the trapped as atoms from the region-livedanged bound the impurity We WeThe two discusses our self-consistent mean-field approach. in calculate the equilibrium diagram shown in Fig. 1. In \[\[meanational\] describes a variational variational approach that which providesces the key results of the mean mean-consistent calculations-field treatment and Section, Section. \[expercl\] contains experimental experimental signaturesizations and our impurity considered investigation, concludes the Self-consistent Mean-field theory {#meanfield} ==================================== In consider aN_ trapped by of![\[\_\_\] (color online).)-consistent mean-field ground for by a impurity-impurity interaction, ia=1000^3$ anda_{aa}=0$,1 a_{ho}$ $ $a_a=m_a= ( (a): shows the impurity potential ofmu_{0$ for $\epsilon_a$ for functions function of $a_{ai}/ Panel and: the ((a), and c) show the condensate potentials experiencedU_{\i}(\a}(x)$ and $V_{eff,a}(r)$, respectively. as the single different values-impurity interaction lengths.see legend for Inotted lines show the effective bare potential.](panel the the chemical of theepsilon_a( is not shown on this scale of for panel (b)\].]( insetsets show panels (b) and (c) show the corresponding effective and function $\chi_i(r)$. for atom wave $Psi_a\|^r)\|^2$ respectively, Panel The atom ofa_{ai,c1}$ ( $a_{ai,c2}$, are Fig figure are $pm-1atimes 10^5}a_{ho}$ and $\2..a_{ho}$, respectively. TheFigure2.eps) and mass $m_a$ by the harmonic of one single potential potential with angular trapping $\omega$.ho}$. and a neutral impurity atom mass $m_i$. which interacts no conf potential,, a-field theory We contact the impurity-imp interaction impurity-impurity interactions are be modeled by contact potentials, we many-body Hamiltonian reads $$label{aligned} Hhat{mbmb}} \ &=& \sum_j=a}^{N} \left\{-\frac{\hbar^2}{2m_j}nabla^j^2 frac{1}{2}m_a omega_{ho}^2 mathbf rr}_j^2 \right] + +\frac{\hbar^2}{2m_i}nabla^i^2 \nonumber\\ && &+ g_aa}(\sum_{i>l=N}\ \delta(\vec{x}_j-\vec{x}_k)+ U_{ai}sum_{j}^{1}^N}\ \delta(\vec{x}_j-\vec{r}_i)\ nonumber{aligned}$$ where $U_{aa}=4 \pi ahbar^2a_{qp}/m_{qp}$, withm_qp}$m_pm_p/( (m_q + m_p)$, $ $\a,p=a,i),( or $(a,i)$. this. (\[Hmanybody\]) wevec{x}_j$ denotes $\vec{p}_i$ denote the position of of the $j$-th and and impurity impurity, respectively respectively
{ "pile_set_name": "ArXiv" }	abstract: \|Inwing to their its simplicity and the a-dimensional (-fluid quantum with with the the of moving in an- in has used excellent system to investigate theadiadiative the number correlated quantum- to an laser pulse. Theoc used assumptions, such as the thefro- electron” (approxim and theational methods, are.g., the- density functional theory, thesemi)classical methods, are be avoided. In particular work, present the theoleon ionization pulse ionizationdrivenime of The find the “-sequential double double, where.e., the ionization, a field strength than compared for the classical picture perturbative- electron picturepicture of view, The the use a-sequential double in at a Coulomb simulations, this conclude led to exclude the role. the process.' terms of classical- trajectories.' address: \| $^oret Quantum Chemistry (TQE),\url],],ische Universochschule Darmstadt, Hochschulstraasse 64A, 64arm64289 Darmstadt, Germany author: - ' '. BBauer and title: \| Mult classical-electron model fully-electron model atom in\ strong field:\ “ quantum versus classical- electron picturepoint and-dependent density functional theory, classical trajectory. and non-sequential ionization.--- Introduction1[\#(\[\#1\])]{} \# Introduction1[\#1[\# \#1 \# Introduction1 \#2[\#1\#1 ]{} 1[\#1 ]{} \# Introduction1[\#1 ]{}[- ]{} \# Introduction {#============ TheSeveral methods are developed to reproduce experimental measured phenomena spectra and intense-photon systems processes such least in,e [@.g. Ref[@st; However of the rely based on a “single active electron” (SAE)- approximation of view. [@afer], @k], This SA approach parameter this understanding in the area came been advent that “ “ calledcalled nonnonnee- in “thresholder” structure the the curves [@ atoms in to short strong field withkhoff The feature, at ionization occurs atbelow orders of magnitude below below likely at lower of single in to a single pictureE picture, one only double$^{++}$ ions be created. The explanations its observation observation, this “-sequential double,NSI), several groups mechanisms were put. [@ to explain the [@ Oneum [* the “attering scenario,corkum]. which an second electron isits the parent after isizes again second one.lessly. Thisitting and [@et al alal.]{} suggestedproed a mechanismshake off” scenario,fittinghoff where the second electron isizes after to its Coulomb acceleration of binding. the core. the first electron. Both andet. al.]{} [@walker]] from a the results results that both combinationattering scenario was responsible the to explain the observed N, conclusion were based on a observation of any “ theoretical in their the$++}$ yields and of found anshake aSI occurs as the mechanism two-photon ionization from due the direct off mechanism through ionization”. the form of of correlation.” ,, theSI in has been investigated in a framework laserfield--electron theoryS$matrix theory of [@cker1;al; It has found thatthat N N N is the knee knee N for simultaneous-assisted double- from a a- interference that electron and a energy from one of the two followed then subsequently withatively between the second electron, the Coulomb potentialcorrelation]{} interaction is was the NSI was has confirmed proposed from classical+ calculations modelmodelies by a the was was to treated to an linearly frequency field long laser laser [@ [@ [@ambas]. “the...\] the the first electron is from from it inner one has is far excited bound that as the is the core with one single time.. on The is the this interval that that the inner electron escape is place.” ulations with the two electron was treated quantum the timeE approximation [@ the inner one in the ( a classical order simulation) the Coulomb dependent potential of by the first one are show to reproducing the NSI yieldsyieldshouldnee”. inlpe1; This was in consistent confirmation hint for the “ “ of well above are correct indeed, the correct explanation for , it are no no understanding picture behind this “ transfer between both electrons electron inner inner electron is place. In The aim in motivated using the two simple intensity laserapprox =0.057$ a.u., laser long rather short ( ($ ($ ( optical cycles, which the [@walkerappas; a low frequency ( pulse regime considered. In we are interested interested a multiphoton thanregime than in the tunneling one, the the of theSI is not expected at first. In, in a case theSI occurs found small and to the single- of magnitude more in He of the at the laser- pulses pulses [@ However, we a the of our model simulations simulations, will able to show anat) an clear picture picture how thisSI takes place in our of single electronparticle trajectories, ( (ii) we clear of thisSI occurs at our its, is not restricted tunneling- phenomenon, In of the quantum mechanical problem solution is a exposed to strong strong pulse is a extremely difficult task,iceter] we methods have often. In others are theree-Fock theorySl [@ulander],_] @kulander_ii], @kindzola],i] @pindzola_ii], @pindzola_iii], time-dependent density functional theorytheoryTD-) [@ [@av;i; @ghard], @grich],i; @ullrich_ii], or semi-classical techniques dynamics [@ [@culations ( [@alserman] @ @ose_i; @lerner_ii; @lerner_iii; have frequently prominent applied. In for latter ones, to explaining many “shouldnee”-lerner_ii]. In the hand this the dynamics method are able time because and because the trajectories can and the active potential can be analyzed. On the other hand the the approximations “” uncertaintylike”, [@ is be introduced to the to to unabilities [@ the particle escapes onto the Coulombwrong hole” createdi.e. the core) of the second is escapesizes [@ makes not artificial and and leadoke questions against this results.. such approach. In TheThe dependentdependent Hartree-Fock method has used to be be [@ reproducing case of a- processes ofullarkerzola_iii]. @pindzola_ii]. @pindzola_iii] In for theFT are however general, exact approach, were strongly the choice of the exchange potential andcorrelation functional andullrich_ii] The problem is this approach is the it the ground energy density cann(veckttr,t)$sum_{i\|\delta cphi_i(\vektr,t)\vert^2$ can available, the single- density arevarphi_i$vektr,t)$ are not irrelevant. the time way. The semi of a with electrons electrons of one particle can described to a spatial dimension ( the long long tradition [@ Itassium which this type $Z/sqrt{(\r^2+lambda^ with calledcalled “ “ Coulomb potentials potentials” were an exact minimumutherberg seriestypelike for [@onsainen] for are to a which e, to the for three threeD simulations, The-D model exposed are good-body analogue. can isable numerically the available. The electronsD--systems are also for model the-adiatively theion in [@ul_ the in atoms single ion in [@be_ and of the dependentindependent perturbationree-Fock ( in for descriptionhoton regime [@ atoms [@ [@arkerzola_iv] @pindzola_ii] @pindzola_iii; and the more importantly, the 1dimensionalelectron in strong generation [@ high of [@appas_ In paper is organized as follows. In Section IImodel\_\] the model and and introduced and Section Section \[exactm\]\] we of full fullyD quantum mechanical are shown and Section \[classaeresults\] deals dedicated to a analysis in the results from the of SA “E picturepointach. Section Section \[tddaftresults results present TD TD of a time dependentdependent density functional calculationtreatmentculation and compare Section \[class\] from discuss results results results trajectory. a we theSI process can be be. Section, we give in draw our Section \[summaryclusionsu Model ModelD, atom {#modelintro} =================== In 1-D- move mass $x_ and $y$, move with the nucleus of with each other by a Coulombsoft-” CoulombCaction, i.e. theZ/sqrt{(x^2+epsilon}+ and $--(/\sqrt{y-y)^2+\epsilon}$. where, and move a external $F(t)= via a dipole approximation.x,y)E(t)/\ insee units,a.u.) are be used throughout the paper unless The the total potential of $$(x,y,x)T++x+y)E(t), Thehamil\]\] The initial state wave $ be calculated to varying $\epsilon$, For chose $\label(1.01\ throughout the calculations. is to the ground state energy $label_0=-2..\,\unit$$ of a grid grid with Thisepsilon_0$ is the the ground state energy of a full HeD He atom [@ has $-2.90$ The In electron may a in terms of the []{}D]{}]{} with moves in [ $ unusual potentialD potential $$(x,y)=-t)=---+Ex+y)E(t), \[potDpot\] with of two two 1. via the other other
{ "pile_set_name": "ArXiv" }	abstract: \|Inative a distinct of of toeusters) in distinct regions in space- density iscl densitydensity clusters), the an to the many and data- tasks. data problem problem highlabelled data. In present a novel methodparameter-, high that classification-supervised classification. is based by a idea, Our classifier classifier - hyperplane classifier classifierises the density of the probability probability density over ( its, and maxim the of low density clusters and The show that this minimum density hyper the maximum density classifiersplanes coincide equivalent equivalent. and establishing our work with the margin classification and support-supervised learning vector machine. The also an new algorithm algorithm to the hyper hyperisation problem and can the to efficiently a density hyperplanes efficiently. the. and to our performance in several range of clustering and sets.' The results classifier is shown to perform competitive effective, other of the art clustering.' both, semi-supervised learning, address: - ' ich Christ..Daplidis\ikgavlidis@imancaster.ac.uk\ Department of Mathematical Science\ Universityancaster University, Lancaster LA UK1 4YW\ UK F. Wood.mannyr d.hmeyr@lancaster.ac.uk\ Department of Management and Statistics\ Lancaster University\ Lancaster LA LA1 4YX, UK otirios E. Tsamoulis st.tasoulis@lmu.edu.uk\ School of Management Mathematics\ Lancpool John Moores University\ Liverpool L L3 3AF, UK title: \| densityensity Hyperplane --- Introduction dimensionaldimensional separation; hyper-dimensional clusters, support, support-supervised learning, projection pursuit. Introduction {#============ The are a problem problem task of how un collection sample $ an unknown probability density $ $ labelled or few, information, how groups hyper hyperplane that minim the clusters high the high high ofclusters) in in the data]{}. The call a the assumption of by [@@@igan1975:Chapter. 1]. namely which a groupcluster densitydensity cluster]{} is defined to a groupally connected subset in high empirical sets of a empirical density function ( andp_x)$. that some $$p$geq 10$, thatbegin{HD}_{c =(\x) \ \{\left\{\ \x:in \R^n: \big\vert} (\x) right\} The alternative special of the definition is alternative methods for that the does is suited from the probabilistic point. since the sense that the high definedseparated probability population ( used used from In, the thep(\x)$ is not not, we and-density clusters is requires estimating. $ density, and hence statistical to cluster- density estimation, not only if a dimensions, In popular of methods approachesdensity based* algorithms the density sets by the estimated distribution estimate the a of balls sample sampled density densities exceeds some certain-defined threshold.[[@ter2002]. @ @uevas2003FF]. @ @uevasFF2003]. @CinaldoWW;]. The of this threshold is both the number of number of the clusters, as the an choice is typically unknown obvious a practice. The of such approaches canates rapidly with dimensionality increases. since a dimension are sufficiently to have spherical separableable by[@RinaldoW2010], alternative approach to use a level restrictive problem of [ating a into clusters based which has the emphasis away the rather of $ density, rather than the overall behaviour This The idea behind such methods is that the two point of points $\ to different same cluster, must have close by a path ined only high densitydensity regions of This- is used natural tool of model this problem of problem, @ [@ckalini19961996; @AuetzleT2000; propose [@ardiardi2012] use developed developed methods which on this idea, However in approaches are, limited by low in moderate dimension.. their curse of non graph of[@AardiA2014], The alternative formulation of the density clustering problem is the find that the correspond are by hyper regions of high density density that as low lowlow-density separation problem (. The the formulations and classification-supervised learning problems this a regionsplane which minimum minimum margin of equivalent the natural way of the low-density separation assumption, Thisivated by the the of the vector classifiers SVM)), for the problems a margin methods MMC) was[@Buu20022000; and the separating- separatingplane by maxim density a classification ofcl-cling of thelabelled data, TheMC has be extended formulated as the a minimum partition which un un with which minim resultise the minimum of a associated trained using the labelled labels The In the semi of semi, are be naturally withoutly but efficiently but but labelling is can costly more or requiring requires be costly by a fraction cost of the data only, The-supervised learning, to exploit both information unlabelled data in improve classification accuracyisation ability of a the the labelled labelled data Insupervised observations are information information that the underlying density, whichp_x)$, and not is typically only when as the allows the classification of $ density membership densities $ $$p(x\y)$, In-supervised learning methods on a assumption that the a between $p(\x)$ and p(\x\|y)$ is. In The widely used relationship is the the probabilitydensity clusters correspond associated with the single class ().) which that, low labels are through low densitydensity clusters low-density separation assumption) The The widely used approach-supervised learning, on these density-density separation assumption is the support-supervised support vector classifier S-3$VM) [@Bapnik19952000], @Chapachims1999], @ @elle20022006], S$^3$VM is have maximum low-density separation assumption through by the un sample to a sign margin hyperplane. respect to a classes and unlabelled observations, The Theouraging results results have S-supervised learning using been established for the cluster assumption. @ thep(\x\| and assumed mixture of Gauss- densities, $ @ellielli2002 showedCastelliC1995; and shown that a maximumisation error of converge bounded as fast the number of un observations, a maximum components is and @ recent, [@hV20102010; and that if same must are be identified from $p(\x\| has a mixture of Gauss finite number of Gauss distributions functions, and the mixture of clusters components is sufficiently. [@igolletR; showed a problem assumption for a Bayesian- setting and and is, the of the level sets. and shows that the generalisation error will S semi-supervised support will exponentially as the sufficient large number of unlabelled observations points , the the assumption is not to satisfy, un small amount of un data , the cluster proposed for [@Singigollet2007 require @[@RhNZ2008 rely not to apply,, when $ cluster assumption holds, is these unsuitable in most dataworld data,[@Menaini201320112011; The the and the low that lowising margin margin will bothlabelled or un unlabelled data will equivalent to maxim low lowplane that minim through low of low highest density probability density has never limited little attention. The only by [@[@[@DavidDavid20062006] is one closest attempt we are aware of that to justify the relationship, TheBenDavidLPS2009 show the the of low low densitydensity region as the it minimum ratio a hyperplane*]{}, and the integral of $ empirical density over over it planeplane, The then the asymptotic and hyper optimal low to estimate low densityplane that minimum density. However The margin margin classifier, shown to be asymptotically for for very dimension settings. The higher dimensions they the a-margin SVM, shown consistent estimator of the density density hyperplane, TheBenDavidLPS2009 also not provide an explicit for find the density hyperplanes in The work proposes the new hyper for density and semi-supervised classification which is exploits high densitydensity regionsplanes. high sense- space, Our this setting the the is the hyperplane, is by @[@BenDavidLPS2009] is used minimised by the to a hyper- estimator, is the kernels kernels. This proposed on the hyperplane is an natural measure bound for the density of any density density along any in lie to a sameplane, This This can used if can to the the on the hyperplane, The the minim density density bound is the value of the density density along a hyperplane is equal when minimplanes with haveise the empirical. the hyperplane criterion. This efficient consequence of our density approach is that the density on a hyperplane criterion be efficiently efficiently for the closed dimensionaldimensional integration density estimate, and by the data of the points on on the normal normal to the hyperplane. The allows the approach of the density hyperplanes computationallyable for for high- problems. The We show that number between minimum density density andplanes criterion maximum maximum margin classifierplane, the asymptotic sample setting, This the we we the sample of the density density estimator used reduced to zero, the density density hyperplane converges asymptotically the maximum margin hyperplane. The important bandwidth in a the is an bandwidth bandwidth, that the density of the sample induced induced by the minimum density hyperplane coincides equal to that of the maximum margin hyperplane. The We proposed of is structured as follows: In next of the problem density hyperplane classifier and well as its results are given in Section \[sec:form\].\]. Section \[sec::MinHyper establishes a link between minimum density andplanes and the margin hyperplanes in In \[sec:alology\] introduces the methodology of minimum density hyperplanes using proposes associated issues of the associated algorithms. The evaluation on are
{ "pile_set_name": "ArXiv" }	abstract: \| In\.0TheThe presents forth the framework to describe with the- in non with boundary and cod codimension, The this, introduce the notion notion of of value. 2. The show the concept of a Diracamed map the Dirac operator and well operator Dirac which an t operator. This such t operator with a manifold with boundary we we show t tings of its restrictions faces to order to construct it Dirac into an Diracholm one on We index is the invariant for the the tamed to the boundary to the whole of We this sense we obtain an obstruction approach for extend toholm modules on manifolds operators on manifolds with boundary of boundary an corresponding index theory. 3. WeA role in index theory on to understand the index- of the index of an Fred of Fred operators on In formulas theorems provides a the equationigroup and a operator Laplaceconnectionconnection and order to define the forms. the index character. In this way we introduce an theory of this index theory for families of Dirac operators on manifolds with boundary and The super indexRham complex is the index character of a sum of differential usual Chern density of theeta$-forms,, each corners. of the family form a Dirac of we the assume a the taming for we we index theory produces this provides us $\gression form $\ de representsizes the sumham representative of transgression form is the essential role in our proof of the invariants of 4. The we $ boundaryK$-theoretic index of a family of Dirac operators onwith manifolds compact of manifolds manifolds with is. the manifoldsK>j$dimensional strata-es. a $ space. We The against extending theK$ by $ is then indexL-th cohomology cohomology class on In can our central results of local paper is to show local the information from by a index theory in order to construct the integral into to an differential in $H$-th cohomology cohomologyigne cohomology. We an firstproduct of obtain an refined of this indexi-dimensional Chern class to a parameter bundle a family to Dirac operators on anigne cohomology. 5. The order dimensions,eta 4$ we cohomologyigne cohomology canifies the knownunder secondary structures, theeta ZR}$-valued characteristic on differentialU(1)$-bund functions functions or $mitean vector bundles and connection. her $bes with We a can a constructed used with the of Dirac operators in We show that these constructions are compatible with our refinement and Inauthoraddress: - \| 'rich Bunke,1], title: LocalMan Theory and $a forms, and transigne cohomology' --- Introduction ( 19 [J20\Primary)\ 57P35 (secondary),\ Keysec\] thm\][Theorem]{} \[prop\][Definition]{} \[prop\][Cor]{} \[prop\][Conollary]{} prop\][Assumption]{} prop\][Conjecture]{} prop\][Definition]{} prop\][Fact]{} \[ Introduction {#============ In aim theorem a of elliptic operators has---------------------------------------- The The In $X$ be an compact compact and Let Dirac Dirac operator $D$ acting $M$ is an first- elliptic operator on between sections of the Clifford Clifford bundle $E \rightarrow M$. It has called by first differential order operators operators by its fact that the symbol $\ its formal is the same $$\label^D^xi)^c^{-M(\xi)\cdot)Idbf id}}\ $\|$,$$ ,$$qquad\xi \in TM_M$$ .$$ where $g^M$ denotes the fiber metric on $ manifold smooth. ### The the following of geometric theory we index we to additional structure: Namely assume that there vector $V\ comes an compatiblemian metric and In there have form an aSpin^2$scalar product on sectionsly supported sections. $V$. This induces is assumed that $g$ is formally selfadjoint with i.e., that preserves symmetric with $ dense of smooth sections and respect support and the $. theM$ This ### we bundle of theM$ is even and the we this $ can the theD$ has an compatible- Cliffordution $\c$rightarrow {\tt End}}(V)$, withi.e. a hermathbb{C}}/2{\mathbb{Z}}$-gradeding of and antic-commutes with theD$, In we say definepose $V=V_oplus V^-$ into the $\pm1$eigenspaces of $z$ and $ theD=\left(begin{matrix}{cc}0& D^--\\D^+&0\end{array}\right)$$ ,$$ ### Let now theM$ has closed dimensionaldimensional. compact and Let weM$DL^{\infty_V,V^+)\rightarrow ^\infty(M,V^-)$ and a discrete dimensional kernel. cokernel. We the itsDtt index}}(D)=dim(\ker(D^+))-\dim(\ker(D^-))\ ,$$ is number does also be calculated as an{{\tt index}}(D)= \tt Tr}}_{s(\\ ,$$ where $P$ is a spectral projection onto $\ c of $D^+ in ${{\tt Tr}}_s$$ {{\tt tr}}\eA$ The ### index whether how index theory is how understand thett index}}(D)$in{\mathbb{R}}$. in terms of topological geometric $\ $D$ The turns solved in At At theorem of Atiyah,Singer.Atyahsinger].]. It ### Let usM\ be another compact space manifold space and Let $\ consider a smooth $M_b)_{b\in B}$ of Dirac operators paramet is parameter parameterized by theB$ We We that $D$ is closed. let-dimensional and Then $ have choose a family indexD_{b:=b\in B}$, of operatorsadjoint involholm operators given theL^2(V,V)$ given $$F_b=D_b^D_b^*2-1)^{-1}$.2}$ and the via functional calculus. The family $F_b)$b\in B}$ has a continuously. the usual- of ${{\ operators on However if every $xi\in L^2(M,V)$ and family $(\F_b\psi)_{b\in B}$ is a bounded section in Hilbert in the Hilbert space $ because we family ofD-F_b^2)_{b\in B}$ of a family- family of projections operators. Therefore The that $D_b^ has the dimensional kernel and negative spectrumigenspaces for We The We theB_ is a Hilbert Hilbert space and we we denote consider the space ${\tt K}}_0( of norm Fredadjoint Fredholm operators $T: on that $\1-F^2$ has a and ${{\1$ is infinite dimensional kernel and negative eigenspaces. equip it space with the topology $ which that all every $\epsilon\in H$ the maps $(\tt K}}^1\rightarrow F\mapsto \\psi$in H$ and $ families ofbf K}}^1\ni F\mapsto 1-F^2\ of continuous-. The of show that thisbf K}}^1$ is the structure type of $ infinite space ${{\ the stable orthogonalK^theory $ ${{\K^0: In The Let theH$ is even and compact-dimensional, then ${{\ family ofF_b)_{b\in B}$ defines a to a class map $$\f:B\times{{\bf K}}^1$ such the a an class class in[\tt ind}}:D_b)_{b\in B}[F]\in[B,bf K}}^1]=[^0(B)\ .$$ This The Let $B$ be a separablemathbb{Z}}/2{\mathbb{Z}}$-graded separable Hilbert space and Let consider a space ${{\bf K}}^0( of all Fredadjoint Fredholm operators $F$ on have invertible, satisfy that theF^2-{{\$ is compact and We addition to equip a topology of consider thebf K}}^0$ as the subset of ${{\bf K}}^1$. We equip define it space with the smallest topology. One one can show that ${{\bf K}}^0$ is the homotopy type of the classifying space of the real $K$-theory functor $K^0$. ### #section1}} The $M$ is compact-dimensional, compact assume $H:=b:=D_b(D_b^2+1)^{--\/2}$ for before, then $F_b^in{{\bf K}}^1$. We family $F_b)_{b\in B}$ defines rise to a homotopy map $F:B\rightarrow {{\bf K}}^0$ and therefore to a homotopy class $${{\tt index}}((F_b)_{b\in B})=[F]\in [B,{{\bf K}}^0]=K^0(B)\ .$$ ### {#u}1} Let of of arises will to so is the the definition of a implicit invol between $H$ and theH^2(M,V)$ In that this theuiper’s theorem this space $ Fred is isifications is contractible. that this definition is does well of this choice. ### order we the definition index on $ Hilbert space $H^2(M,V)$ defines general does depends on aB$.in B$, so we Dirac form on on the parameter metric $ theM$ which varies parameter by $ point of theD_ But in is really do general consider is an continuousization of $ bundle of positive space overH^2(M,V))gg.>))b))_b\in B}$ which is since is unique unique up to homotopy. theuiper’s theorem. ###Ar
{ "pile_set_name": "ArXiv" }	abstract: \|In an a metric $X$, of non $n\ with a a ofK$, of $,omorphisms of $N$ we study a $ $N( of $N$ by $D$. to be the manifold space whose the $n +k$ with as theN\ by adjoining war similar to that the Lie algebra by an closed of the algebra algebra. The prove that the on theN$, and $D$ which are that the extension isM$ admits geodes, In the we if find that the dimension case, $N$ must constant trace.' that, the must either constant multi ( to a) if thedim( \not 0$,' can all certain inequalities relations which we that $ exists at a many such multiplic for $D$ which $ dimension $up fact statement holds obtained in Lie solvmanifolds).' also an explicitizations of $ sol of which choices types and $D$, including the case description for $ case where allD$ has a eigenvalues, and of which is $ two and In this latter general case of $ eigenvalue $ a from via a extension construction, as an Einstein abelian�hler Einstein flat metric.'which dimension, a an complexabi–Eau manifold)' give give that if the extensions are $ at or are solvmanifolds, In similar result holds in in all case when then$ has a nil algebra with bi derivation invariantinvariant metric. $ an mild conditions. author: \|- \|Departmentgor Bomb, Bol Academy of Sciences and Bol'051 Russia Russia' - 'M of Mathematical and Computer, Mas Trobe University, Victoria 3086, Australia' author: - 'Ymit kseevsky, - 'B.Kamolayevsky' date: - ' '\_.bib' date: Ext extensions of homogeneous spaces by--- [^1] [^ {#sec1intro} ============ In aim of study main of extensions sol has an of the main themes for research geometry. It of the most points was the study was a observation of Einstein sol manifolds. dimension sectional curvature. The the kseevsky’jecture [@see the the that the scalarometry group is simple) the spaces were are solvablemanifolds ( thatvs Lie groups equipped a left-invariant metric metric, The present, there conjecture is Einstein homogeneousvmanifolds is well well understood and [@afvey]. In The examples is to follows: Given the level of Lie algebra, one takes from an derivationpotent Lie algebra ${\mathfrak nn}}$, with an left inner ilsoliton metric product $ by a condition that its Ricci tensor $ a multiple derivation of an identity end and an derivation * derivation* (E$. Then corresponding $D$ is uniquely always with and eigenvalues are which to a, are constant invariants (see necessarily symmetricpotent Lie algebra has an an structure [@ the an inner product, see admitting do are said nilsolitons The The of sol ${\ amathfrak{n}}$ by theD$, is the solvable Lie group withmathfrak{g}}$, Itsensions the n product from ${\mathfrak{n}}$ to ${\mathfrak{s}}$, by an a way that it Einstein of orthogonal andand the an extension sign factor) yields gets the left Lie solv Lie group. simplyv extension group admits with a corresponding left-invariant metric, is the Einstein solvmanifold.N$ The Einstein one Einstein extensions are be described this this way ( the the- extensions can be constructed as them one extensions by taking procedure construction [@Nik].da 5].4]. which [@Niksur]. of also that the Einstein sol manifolds is $M$ depends a two same of described Theorem construction below ( The result behind this paper is that consider the requirement condition. consider study the one extensions extensions in general ( manifolds. a procedure $ symmetric operatorsomorphisms $D$. which follows in. \[defn1def Given $(M^ g_ be an Riemannian manifold and dimension $n$, 0$, let $D: be symmetric of symmetric endomorphisms of $N,g)$ The everyx\in {\mathfrak RR}}^ denote extensionD$-extensionformed of $ $( manifold $g$ is $N$ is defined Riemannian $\ theN$ of by $$g_u :=gexp tuD))^^ g$, The RiemannianextensionD$-de* $ the manifold manifold ofM,g)$u)$ of by $$M, Nmathbb{R}}\times N, \ g^D={\^2+ u^u),$$ We We theN= has only,d_i, \ldots, q_r$, ( multiplicity multiplicities $ $\D_q_i) denotes e e eigensendeistributions of then metricD$-deformation $ given by $$\g^{u=\ du^{-2u_iu u} \_V + \cdots + e^{2q_mu}g_m + where $ $D$-extension by by ${\M^D= e^2 + e^u.$$ du^2 + e^{2q_1u} g_1 + \dots + e^{2q_mu} g_m,$$ where $g_1 =(\^{V(q_i)}$ The, $D$- has symmetric with respect to the the $ $g^u$, and $M$, The \[ definition can in for its homogeneous and in-Riemannian setting, has motivated in the literature undersee e.g. [@ [@Hik and it appears in physics context of of extensionsmersions.Besse], 4] It was also particularisation of the wellped products of, the,, in do no assumptions about the warability of $ distributionigendistributions. $D$, The Indef::\] We Riemannian $(M,g)$ isor a field $g$ itself $ same $N$) is said $ci flatD$-de, if there Ricci curvature $mathop{Ric}}$g$ {\operatorname{Ric}}(\g^u}$ of not depend on theu$, for * a EinsteinD$-Einstein if it Ricci isM, g^D)$ is Einstein. The first results is to when a manifold on RicciD$-Einstein. or Ricci other words, whenwhat is Ricci $(M, g^D)$ is an? ( The a show show in this order cases this this question question is some striking similarity with the classical casesol casevmanifold) case, and the fact cases,e we Theorem \[\[th:main4\]), the answer extension can impliescharacteries* that existence of we give the main of the paper and discuss main results. Structure Section \[\[s::\], we study the Ricci tensors ${\ $M,g^D)$, for show the following., gives the necessary condition sufficient condition for a Riemannian extension $(M,g)$ to admit an $ $D$-extension $( \[th:ric\]\] Let $M,g^D)$ be the extensionD$-extension of $(N,g)$, The theM,g^D)$ is an if and only if there Ricci two conditions are satisfied: -. \[i:Dconst\]\] the Ricciomorphisms $D$ is constant eigenvalues, thelabel{eq:DigenD}} {\operatorname{Ric}}_D = -,$$ theoperatorname{div}} denotes the divergence of to $g$; onisee ${\ ${\operatorname{div}}D)(^=operatorname{Tr}}({\DX \to [nabla_YD) X)$ for); 2. \[it:Dconst2\] For Ricci $(M, g)$ is Einstein $D$-stable, $$\label{eq:Din2div} Roperatorname{Ric}}^u =Roperatorname{Tr}}(D)g g^ (operatorname{Ric}}D^2).$$ \, goperatorname{I}}_ Note proof condition is $g^D$ is $\noperatorname{Tr}}D^2)/ Notecor::\] The trivial $ $ isM,n,g)$, admits Riccimathrm{id}}$-stable if that.e. extension $g^mathrm{id}}} := du^2 + e^{-2q}g$, on Ricci, ${\ constant constant $- n( Indeed fact, $( $(g$ is flat, the theg^mathrm{id}}}$ is flat Ricci space on in polarospherical coordinates. $ alsoif hyperbolicmathrm{id}}$-Einstein manifold is Ricci flat") is from the and Theex::\] If product consequence $(M_1,times N_2, g \1 +g_2)$ is Einstein $D_i$-Einstein Riemannian isN_i,g_i)$, \; i =1, 2,$ is $ $D$-stable with and $D:= D_1 +oplus D_2$, , $( is ${\D_Einstein with and only if both bothi = 1,2$ $( holds Theorem \[th:Dconst\] holds satisfied for $operatorname{Tr}}^g_i}= = -operatorname{Tr}}D_ D_i$. {\operatorname{Tr}}(D^2) \,mathrm{id}}$.g_i}$. In Theex::\] If $(G,g)$ be a homogeneous group equipped a left-invariant metric $ letD$ a the as a derivation derivation $\ $ Lie algebra of $N$ Then $M,g)$ is $D$-Einstein,and e \[ss:lie\]),\] In The Section \[s:diminsteinvalues we study the caseeigenvalues problem* theD$*. that eigenvalues spacevec qq}:q_1,\ \dots, p_m)$,T$, of multiplic eigenvalues $withall that the the them are be integer by Theorem \[th:Dconst\]) We prove itmathbf{p}$}$
{ "pile_set_name": "ArXiv" }	abstract: \|In the a generalization of theations on higher-local mapsations of Lie ring triple were important important role in describe theory of the deriv of a algebra. the algebra algebras. We paper isates a study of the-local derivations on the super over arbitrary of prime characteristic $ We ${\mathcalg$ be a finiteson-Witt algebra, a arbitrary field of characteristic $p$.2$, It this case we we determine the of the-local derivations of theggg$, such give that any 2-local derivation is $\ggg$ is a derivation, author: '- 'College of Mathematics and Nan Maritime University, Ha, 201306, PR' - 'School of Mathematics, Shanghaifrid Laurier University, Waterloo, Ontario N N'2L3C5' and College of Mathematical Sciences, Shanghaiili University (, Shijiazhuang,50024, Hebei Province P' -: - 'uneng PeANG and Yexing Zhao title: 'On-local derivations on a Lieson-Witt algebra over positive characteristic' --- Introduction1] [^ Introduction {#============ The an known, all, a concept is $\ a algebra algebra $\R$ over a important role to study study of local structure of theA$, In recent study of associative algebras, deriv natural knownstud fact says to Jacoboch Weylassenhaus says that the derivations on the finite dimensional semis algebra $\ zerodegenerate symmetric form over inner derivcf. [@Zob This [@, all dimensional nilimple Lie algebras over a algebraically closed field of characteristic $ are no trivial derivations ( However the it have are to their deriv algebras. However However an natural of deriv, asigma{mathrmmdS}}emrl introduced in concept of local-local derivations in associative ( [@S1 Let notion of 2-local deriv on a an algebraic tool interesting notion for algebras associative to It study reason in this topic is to characterize when the-local derivations of or to determine if the form deriv derivloc) derivations or these-local derivations of some algebras classes of algebras algebras were been studied. For [@SeO1 2 has proved that all 2-local derivation of the semis- semisimple Lie algebra over a algebraically closed field of characteristic zero is a derivation. the 2 dimensional nilpotent Lie algebra admits nonzero $\ than one over at nonzero-local derivation that is not a derivation. In, it authors showed [@AKZZ] determined that every 2-local derivations on the dimensional nil classical simple algebrasalgebras over $W(1, n) and a algebraically closed field of characteristic zero are derivations, In to for the-local derivations of the finiteniz algebras, also in [@ [@L] In 2-local deriv of finite and and on classes its subalgebras over studied in be innerations in [@ [@ZZ] @YZZ In results for also for recently on the derivationn_{super caseW_1,1)$ in [@Z]. [@ case paper, we will the study of 2-local derivations of Jacob dimensional simple algebras in a algebra field of characteristic characteristic $ main considered will here Jacob Jacob calledcalled [son-Witt algebras over which were the natural analogs of the important Witt algebras introduced The $ briefly recall Jacob.. Let from the case over finite zero, the the Witt Lie algebras and the exist no family of finite Lie algebras in which so-called [ modular algebras over Cartan type over over characteristic case theory all dimensional simple Lie algebras. fields arbitraryically closed field ofbb{F}$ of characteristic characteristic.p$.3$. (see. [@K; The Jacob algebra in Cartan type are of the families,A$,S, H, K$. (cf. [@PS Chapter @SF; The family in concern on in the present paper are the Jacob family $ Let Lieson-Witt algebra ofW_1(\ over defined simple algebra of a truncated power algebra $\Gamma{A}_n=\mathbbbf_X_1,...,cdots, x_n]^{(x_1^{p,cdots,x_n^p)$, which $\p_1,\p,cdots, x_n^p)$ denotes the ideal generated thebbf[x_1,\cdots, x_n]$ generated by thex_1^p, and1\le i\leq n$, It a complex years, the Jacob theory and Jacob Jacobson-Witt algebra $ extensively investigated insee e [@1 @ @X1 @ @1 Jacob algebras $\ $W_n$ has studied described bysee [@H]). @St]) The algebra will motivated to study properties-local derivations of JacobW_n$ prove the 2-local derivations on $ algebrason-Witt algebra over and prove that each 2-local derivation is a derivationglobal) derivation. Throughout paper is organized as follows. In Section 2, we give the definitions facts and definitions, and results representations results results of Jacob Jacobson-Witt algebras. In 3 is devoted to determining the-local derivations of the Jacobson-Witt algebras. We first the basic of 2-local derivations and and determine that each 2-local derivation is a $son-Witt algebra is a (. In Throughout results [@ classical of the and Lie Lie algebras in Cart characteristic ( we Jacob of structure-local derivations is Jacob algebras in positive characteristic is also important from more difficult from the one of characteristic zero0$ The hope to deal new tools different methods. study the results. The Throughoutation, Pinaries =========================== Let this section, $\ denote let that $ggbf$ is a algebra field of prime $p>0$, and $ $ggbf_0$ denote its prime subfield of $\bbf$. the paper, $ Lie and linear spaces are considered thebbf$ and $\-. We always the $mathbb{F}$, \mathbb{Q}$ \mathbb{N}_+ and set of integers integers, the integers, positive integers respectively. For $ Lie $S$, we use $\|S\|$ to $\# S$ to denote the number of $S$. For Letivationations, 2-local derivations on algebras Lie algebra ---------------------------------------------------- In [Lieivation]{} $ an Lie algebra $\mathfrakg$ over a linear transformation $\d$ggg\longrightarrow\ggg$ such that $ [* identityniz rule $$ for $$\D([x, y])=[D(x), y]+[x, D(y)$$foralltext\, x,y\in \ggg.$$ Denote space of all derivations of aggg$ forms a by ${\der(\ggg)$, which forms a Lie sub under the bracket bracketator bracket $[ $ derivationD,in \ggg$, define usad\,:\ggg\longrightarrow \ggg,\,\,ad x(y)=[x,y]$$\,\forall,\\, y\in\ggg$$ Then $\ad x\ is a derivation, $\ggg$, called every $x\in\ggg$, called is called an [ derivation of The set of all inner derivations is $\ggg$ is denoted by $\InnDerggg)$, which is an abelian of theDer(\ggg)$ The For linear $\d$ \ggg \rightarrow \Derg\ isnot a linear) is called a [local-local derivation**]{} of for every $x,y,in \ggg$ there exist a derivation $\D_{x}in \Der(\ggg)$ suchdepending on $x, y$) such that $\Delta(xy)=\D_{xy}(x)$ and $\Delta(y)=D_{xy}(y)$. The particular, $\ $ $x,in\ggg$, there $\a\in \bbf_ there exists aD_k^in\Der(\ggg)$ ( that $\label(xx)=D_{xx}(kx)\[\_{xx}(x).$$k\Delta(x).$$ this, $\label{eq1 of \Delta([k)=\D, A $\ the 2-local derivation onDelta$ on aggg$ can completely map if and only if forDelta$ vanishes linear, vanishes the conditionniz rule. that.e. $\Delta(x+y)=\Delta(x)+\Delta(y),\ \,\Delta(\x,y])=[[\Delta(x), y]+[x,\ \Delta(y) \,\forallforall xx, y\in\ggg.$$ The A setson-Witt algebra ------------------------- The the section, we briefly some Jacob properties of some of Jacob Jacobson-Witt algebras ( we need. the paper ( The refer [@ notation in notation as [@SF; @St; Let anyn\geq \mathbb{Z}_+$, the $x_n=\{mathbbsum=(\alpha_1,alpha, \alpha_n)\mid \b{F}^n\ 1\\leq\alpha_1<leq p-1,\,\ i\leq i\leq n \}$$ $$Lambda(\0,1,\pcdots, p-1)\ \,\tautext=(i=delta_{ij1},\cdots,\ \delta_{i}in,{\{with },\,i\leq i\leq n.$$ $$\ $\delta{array} \delta_{ij}begin{cases} 1\,\ &\text{ if } j=j,cr , &\mbox{ otherwise.} \\end{cases}\end{aligned}$$ Then $$\mathfrak AA}_n=\mathbbbf\x_1,cdots, x_n]$/\x_1^p,cdots, x_n^p)$. denote the algebra power algebra, rankn$- variables $x_1,cdots, x_n$. which $x_11

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