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Different Non-extensive Models for heavy-ion collisionsJan 11 2017The transverse momentum ($p_T$) spectra from heavy-ion collisions at intermediate momenta are described by non-extensive statistical models. Assuming a fixed relative variance of the temperature fluctuating event by event or alternatively a fixed mean ... More

A note on the connection between nonextensive entropy and $h$-derivativeMay 19 2019Jul 02 2019In order to study as a whole the major part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the \textit{h}-derivative which generalizes the conventional Newton-Leibniz calculus. This new entropy, $S_{h,h'}$, ... More

A note on the connection between nonextensive entropy and \textit{h}-derivativeMay 19 2019With \textit{h}-derivative which generalizes the conventional Newton-Leibniz calculus, a general two-parameter non-extensive entropy $S_{h,h'}$ is introduced. It is found that $S_{h,h'}$ recovers, as particular cases, several types of non-extensive entropy ... More

Mass hierarchy and energy scaling of the Tsallis--Pareto parameters in hadron productions at RHIC and LHC energiesOct 25 2017The latest, high-accuracy identified hadron spectra measurements in high-energy nuclear collisions led us to the investigation of the strongly interacting particles and collective effects in small systems. Since microscopical processes result in a statistical ... More

Hadron Spectra Parameters within the Non-Extensive ApproachMay 21 2019We investigate how the non-extensive approach works in high-energy physics. Transverse momentum ($p_T$) spectra of several hadrons are fitted by various non-extensive momentum distributions and by the Boltzmann--Gibbs statistics.~It is shown that some ... More

Hadronization within Non-Extensive Approach and the Evolution of the ParametersMay 14 2019We review transverse momentum distributions of various identified charged particles stemming from high energy collisions fitted by various non-extensive distributions as well as by the usual Boltzmann-Gibbs statistics. We investigate the best-fit formula ... More

Realism about the Wave FunctionOct 13 2018Jun 12 2019A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, ... More

Bayesian Mode RegressionAug 02 2012Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all elements in a ... More

Realism about the Wave FunctionOct 13 2018A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, ... More

Time's Arrow in a Quantum Universe: On the Status of Statistical Mechanical ProbabilitiesFeb 12 2019In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate--the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate ... More

Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical EquivalenceJan 23 2019What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition ... More

The Intrinsic Structure of Quantum MechanicsOct 13 2018The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable ... More

Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum StateDec 04 2017Sep 30 2018In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the Past Hypothesis) to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the ... More

PrecoderNet: Hybrid Beamforming for Millimeter Wave Systems Using Deep Reinforcement LearningJul 31 2019Millimeter wave (mmWave) with large-scale antenna arrays is a promising solution to resolve the frequency resource shortage in next generation wireless communication. However, fully digital beamforming structure becomes infeasible due to its prohibitively ... More

deepCR: Cosmic Ray Rejection with Deep LearningJul 22 2019Cosmic ray (CR) identification and removal are critical components of imaging and spectroscopic reduction pipelines involving solid-state detectors. We present deepCR, a deep learning based framework for cosmic ray (CR) identification and subsequent image ... More

A new Bayesian regression model for counts in medicineJan 12 2016Discrete data are collected in many application areas and are often characterised by highly skewed and power-lawlike distributions. An example of this, which is considered in this paper, is the number of visits to a specialist, often taken as a measure ... More

A Simple and Adaptive Dispersion Regression Model for Count DataNov 02 2015Aug 01 2018Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion, which typically ... More

Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable mediaJul 14 2015Jan 07 2016The present paper is devoted to the study of existence, uniqueness and stability of transition fronts of nonlocal dispersal evolution equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space nonincreasing ... More

Transition fronts in nonlocal Fisher-KPP equations in time heterogeneous mediaJul 14 2015Nov 19 2015The present paper is devoted to the study of transition fronts of nonlocal Fisher-KPP equations in time heterogeneous media. We first construct transition fronts with prescribed interface location functions, which are natural generalizations of front ... More

Stability, Uniqueness and Recurrence of Generalized Traveling Waves in Time Heterogeneous Media of Ignition TypeAug 17 2014Apr 21 2015The present paper is devoted to the study of stability, uniqueness and recurrence of generalized traveling waves of reaction-diffusion equations in time heterogeneous media of ignition type, whose existence has been proven by the authors of the present ... More

A Simple and Adaptive Dispersion Regression Model for Count DataNov 02 2015Jul 12 2016Regression for count data is widely performed by models such as Poisson, negative Binomial and zero-inflated regression models. A challenge often faced by practitioners is the selection of the right model to take into account dispersion and excessive ... More

Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearityJan 09 2015The present paper is devoted to the investigation of various properties of transition fronts in nonlocal equations in heterogeneous media of ignition type, whose existence has been established by the authors of the present paper in a previous work. It ... More

Generic Image Classification Approaches Excel on Face RecognitionSep 22 2013Sep 30 2013The main finding of this work is that the standard image classification pipeline, which consists of dictionary learning, feature encoding, spatial pyramid pooling and linear classification, outperforms all state-of-the-art face recognition methods on ... More

Regularity of transition fronts in nonlocal dispersal evolution equationsApr 10 2015Nov 12 2015It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In the present paper, ... More

Existence, uniqueness and stability of transition fronts of nonlocal equations in time heterogeneous bistable mediaJul 14 2015Apr 01 2017The present paper is devoted to the study of existence, uniqueness and stability of transition fronts of nonlocal dispersal evolution equations in time heterogeneous media of bistable type under the unbalanced condition. We first study space nonincreasing ... More

Transition fronts in nonlocal equations with time heterogeneous ignition nonlinearityOct 17 2014Jul 09 2015The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with finite speed ... More

Transition Fronts in Time Heterogeneous and Random Media of Ignition TypeJul 28 2014Dec 18 2015The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous media admit ... More

Discrete Weibull generalised additive model: an application to count fertility dataJan 24 2018Fertility plans, measured by the number of planned children, have been found to be affected by education and family background via complex tail dependencies. This challenge was previously met with the use of non-parametric jittering approaches. This paper ... More

Face Identification with Second-Order PoolingJun 26 2014Sep 17 2014Automatic face recognition has received significant performance improvement by developing specialised facial image representations. On the other hand, generic object recognition has rarely been applied to the face recognition. Spatial pyramid pooling ... More

Face Image Classification by Pooling Raw FeaturesJun 26 2014Sep 17 2014We propose a very simple, efficient yet surprisingly effective feature extraction method for face recognition (about 20 lines of Matlab code), which is mainly inspired by spatial pyramid pooling in generic image classification. We show that features formed ... More

Quantum Dilaton Gravity in the Light-cone GaugeSep 18 1992Recently, models of two-dimensional dilaton gravity have been shown to admit classical black-hole solutions that exhibit Hawking radiation at the semi-classical level. These classical and semi-classical analyses have been performed in conformal gauge. ... More

Parametrizing an integer linear program by an integerOct 05 2015Nov 07 2016We consider a family of integer linear programs in which the coefficients of the constraints and objective function are polynomials of an integer parameter $t.$ For $\ell$ in $\mathbb{Z}_+,$ we define $f_\ell(t)$ to be the $\ell^{\text{th}}$ largest value ... More

Elections and statistics: the case of "United Russia", 2009-2012Apr 02 2012The election statistics analysis does not confirm the assumption of correct ballot counting (a survey).

Typical behavior of the harmonic measure in critical Galton-Watson trees with infinite variance offspring distributionMar 03 2016We study the typical behavior of the harmonic measure in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Let $\mu_n$ denote the hitting distribution ... More

Analytic torsion, dynamical zeta functions and orbital integralsFeb 01 2016The purpose of this article is to prove an identity between the analytic torsion and the value at zero of a dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive manifold, which solves ... More

Kolmogorov complexity as a languageFeb 26 2011The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal ... More

Elections and statistics: the case of "United Russia", 2009-2018Apr 02 2012Jun 23 2018The election statistics analysis does not confirm the assumption of correct ballot counting (a survey).

A Lefschetz Hyperplane Theorem for non-Archimedean JacobiansOct 07 2016We establish a Lefschetz hyperplane theorem for the Berkovich analytifications of Jacobians of curves over an algebraically closed non-Archimedean field. Let $J$ be the Jacobian of a curve $X$, and let $W_d \subset J$ be the locus of effective divisor ... More

Frobenius algebras and root systems: the trigonometric caseJan 25 2019We construct Frobenius structures on the $\mathbb{C}^{\times}$-bundle of the complement of a toric arrangement associated with a root system, by making use of a one-parameter family of torsion free and flat connections on it. This gives rise to a trigonometric ... More

Geometric structures on the complement of a toric mirror arrangementAug 30 2018We study geometric structures on the complement of a toric mirror arrangement associated with a root system. Inspired by those special hypergeometric functions found by Heckman-Opdam, as well as the work of Couwenberg-Heckman-Looijenga on geometric structures ... More

On some generalized Rapoport-Zink spacesNov 28 2016Apr 30 2019We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. These such-obtained Rapoport-Zink spaces are called of abelian type. The class of Rapoport-Zink spaces of abelian type is ... More

Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependenceSep 14 2016Mar 21 2017This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or ... More

Test of QCD at large $Q^2$ with exclusive hadronic processesFeb 26 2014My report consists of two parts: (1). Using samples of 102 million $\Upsilon(1S)$ and 158 million $\Upsilon(2S)$ events at Belle, we study 17 exclusive hadronic decays of these two bottomonium resonances to some Vector-Pseudoscalar (VP), Vector-Tensor ... More

A Semi-linear Energy Critical Wave Equation With ApplicationsJan 01 2015In this work we consider a semi-linear energy critical wave equation in ${\mathbb R}^d$ ($3\leq d \leq 5$) \[ \partial_t^2 u - \Delta u = \pm \phi(x) |u|^{4/(d-2)} u, \qquad (x,t)\in {\mathbb R}^d \times {\mathbb R} \] with initial data $(u, \partial_t ... More

Rational curves on Fermat hypersurfacesNov 24 2011Sep 19 2012In this note we study rational curves on degree $p^r+1$ Fermat hypersurface in $\PP^{p^r+1}_k$, where $k$ is an algebraically closed field of characteristic $p$. The key point is that the presence of Frobenius morphism makes the behavior of rational curves ... More

Rod in a train: a mechanical problem of H.Whitney, or Much Ado About NothingJul 02 2019Jul 07 2019In 1941 a mechanical problem about a rod in a moving train (there is a initial position such that rod does not touch the floor while train is moving) was published by R.Courant and H.Robbins in their popular book "What is mathematics?" and attributed ... More

Equation of State for Proto-Neutron StarFeb 26 2012Physics of the Equation of State (EoS) for proto-neutron star (PNS) concerns properties of neutron rich matter at finite temperature over wide range of densities. In this contribution we discuss the structure of PNS inner crust in a relativisitc mean ... More

Scattering of solutions to the defocusing energy sub-critical semi-linear wave equation in 3DDec 02 2015In this paper we consider a semi-linear, energy sub-critical, defocusing wave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional space with $p \in [3,5)$. We prove that if initial data $(u_0, u_1)$ are radial so that $\|\nabla ... More

A renormalization group method by harmonic extensions and the classical dipole gasNov 10 2013Dec 13 2014In this paper we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals related with small perturbations of Gaussian fields. In this new method one integrates Gaussian ... More

On Projectively Related Einstein MetricsOct 19 1999We study the following problem: given an Einstein metric on a manifold, characterize and study all Einstein metrics which are pointwise projective to the given one. By definition, two metrics are said to be pointwise projectively related if they have ... More

Extrapolation for the $L^p$ Dirichlet Problem in Lipschitz domainsJan 02 2018Let $\mathcal{L}$ be a second-order linear elliptic operator with complex coefficients. We show that if the $L^p$ Dirichlet problem for the elliptic system $\mathcal{L}(u)=0$ in a fixed Lipschitz domain $\Omega$ in $\mathbb{R}^d$ is solvable for some ... More

Scattering Theory of Schrödinger Operators with Random Sparse PotentialsMar 11 2014In this paper, we study the scattering theory of a class of continuum Schr\"{o}dinger operators with random sparse potentials. The existence and completeness of wave operators are proven by establishing the uniform boundedness of modified free resolvents ... More

Existence, Uniqueness and Anisotropic-Decay-Caused Lifshitz Tails of the Integrated Density of Surface States for Random Surface ModelsSep 23 2012The current paper is devoted to the study of existence, uniqueness and Lifshitz tails of the integrated density of surface states (IDSS) for Schr\"{o}dinger operators with alloy type random surface potentials. We prove the existence and uniqueness of ... More

Funk Metrics and R-Flat SpraysSep 05 2001The well-known Funk metric F(x,y) is projectively flat with constant flag curvature K=-1/4 and the Hilbert metric H(x,y):=(F(x,y)+F(x,-y))/2 is projectively flat with constant curvature K=-1. These metrics are the special solutions to Hilbert's Fourth ... More

A stochastic-variational model for soft Mumford-Shah segmentationOct 23 2005In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte-Carlo or other stochastic algorithms. ... More

Typical behavior of the harmonic measure in critical Galton-Watson trees with infinite variance offspring distributionMar 03 2016Feb 25 2017We study the typical behavior of the harmonic measure in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Let $\mu_n$ denote the hitting distribution ... More

Lectures on Periodic Homogenization of Elliptic SystemsOct 30 2017In recent years considerable advances have been made in quantitative homogenization of partial differential equations in the periodic and non-periodic settings. This monograph surveys the theory of quantitative homogenization for second-order linear elliptic ... More

A Differential Topological View of Challenges in Learning with Feedforward Neural NetworksNov 26 2018Among many unsolved puzzles in theories of Deep Neural Networks (DNNs), there are three most fundamental challenges that highly demand solutions, namely, expressibility, optimisability, and generalisability. Although there have been significant progresses ... More

Conic Kähler-Einstein metrics along simple normal crossing divisors on Fano manifoldsMar 21 2016We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also establish a curvature ... More

Recent $J/ψ$ Results from BESIINov 17 2004The studies on the multi-quark candidates, light scalar mesons and excited baryon states at BES are presented, based on $5.8 \times 10^7$ $J/\psi$ data collected with BESII detector. The measurements of some $J/\psi$ and $\eta_c$ decays are presented ... More

J/psi Radiative DecaysSep 16 2002The previous results of J/psi radiative decays from MARKIII, DM2, Crystal Ball and BESI are briefly reviewed in this talk. The main part of this talk focuses on presenting the recent results from BESII 58 million J/psi data, including the Partial Wave ... More

On some generalized Rapoport-Zink spacesNov 28 2016We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. These such-obtained Rapoport-Zink spaces are called of abelian type. The class of Rapoport-Zink spaces of abelian type is ... More

On some generalized Rapoport-Zink spacesNov 28 2016Dec 07 2017We enlarge the class of Rapoport-Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. These such-obtained Rapoport-Zink spaces are called of abelian type. The class of Rapoport-Zink spaces of abelian type is ... More

The parametric Frobenius problem and parametric exclusionOct 05 2015Nov 07 2016The Frobenius number of relatively prime positive integers $a_1, \ldots, a_n$ is the largest integer that is not a nononegative integer combination of the $a_i.$ Given positive integers $a_1, \ldots, a_n$ with $n \ge 2,$ the set of multiples of $\gcd(a_1, ... More

A uniformness conjecture of the Kolakoski sequence, graph connectivity, and correlationsMar 01 2017Apr 24 2017The Kolakoski sequence is the unique infinite sequence with values in $\{1,2\}$ and first term $1$ which equals the sequence of run-lengths of itself, we call this $K(1,2).$ We define $K(m,n)$ similarly. A well-known conjecture is that the limiting density ... More

Axiomatic approach to the theory of algorithms and relativized computabilityNov 15 2018It is well known that many theorems in recursion theory can be "relativized". This means that they remain true if partial recursive functions are replaced by functions that are partial recursive relative to some fixed oracle set. Uspensky formulates three ... More

Are random axioms useful?Sep 26 2011Oct 16 2011The famous G\"odel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being added as axioms, ... More

Weak embedding theorem and a proof of cycle double cover of bridgeless graphsDec 11 2017In this article, we give a positive answer to the cycle double cover conjecture. Ones who are mainly interesting in the proof of the conjecture can only read Sections 2 and 4.

Learning Low-shot facial representations via 2D warpingDec 13 2017Feb 05 2018In this work, we mainly study the influence of the 2D warping module for one-shot face recognition.

Perfectoid Shimura varieties of abelian typeJul 07 2015Sep 12 2016We prove that Shimura varieties of abelian type with infinite level at $p$ are perfectoid. As a corollary, the moduli spaces of polarized K3 surfaces with infinite level at $p$ are also perfectoid.

On stochastic stability of non-uniformly expanding interval mapsJul 13 2011Dec 17 2012We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic stability.

Prym-Tjurin Constructions on Cubic HypersurfacesNov 28 2011Oct 22 2013In this paper, we give a Prym-Tjurin construction for the cohomology and the Chow groups for a cubic hypersurface. On the space of lines meeting a given rational curve, there is the incidence correspondence. This correspondence induces an action on both ... More

Developments and Obstacles in Chinese eBook MarketJul 17 2012The purpose of this study was to provide insights into the eBook market in China through case studies on eBook companies and a survey research with individual eBook users. The information from three companies, Beijing Superstar Electric Company, Beijing ... More

I-method for Defocusing, Energy-Subcritical Non-linear Wave EquationMay 21 2012In this paper the author considers the global existence and well-posedness of the non-linear wave equation $\partial_t^2 u - \Delta u = -|u|^{p-1} u$ in 3-dimensional space, assuming that the initial data is in the space $(\dot{H}^s \cap \dot{H}^{s_p}) ... More

Towards Semantic Big Graph Analytics for Cross-Domain Knowledge DiscoveryFeb 20 2019In recent years, the size of big linked data has grown rapidly and this number is still rising. Big linked data and knowledge bases come from different domains such as life sciences, publications, media, social web, and so on. However, with the rapid ... More

Towards a Mathematical Understanding of the Difficulty in Learning with Feedforward Neural NetworksNov 17 2016Nov 21 2017Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training algorithms do not ... More

A Complete Equation of State for Astrophysical SimulationsDec 19 2015We construct a complete equation of state (EOS) covering a wide range of temperature, proton fraction, and baryon density for the use of astrophysical simulations. We employ the relativistic mean-field (RMF) theory to describe nuclear interactions and ... More

Motives of Noncommutative ToriMar 09 2014In this article, we propose a way of seeing the noncommutative tori in the category of noncommutative motives. As an algebra, the noncommutative torus is lack the smoothness property required to define a noncomutative motive. Thus, instead of working ... More

The Coleman-Weinberg Mechanism and First Order Phase TransitionsMar 26 1993Aug 06 1993Revised and reduced the size of the text. Removed figure 2 in previous text. So, old figure 3 and 4 become new figure 2 and 3, respectively. Added figure 4 for first order phase transition observation in the strong coupling region. Postscript files for ... More

Weil-Petersson Teichmüller spaceApr 11 2013Oct 30 2017The paper presents some recent results on the Weil-Petersson geometry theory of the universal Teichm\"uller space, a topic which is important in Teichm\"uller theory and has wide applications to various areas such as mathematical physics, differential ... More

Birational Chow-Künneth decompositionsJun 15 2016We study the notion of a birational Chow-K\"unneth decomposition, which is essentially a decomposition of the integral birational motive of a variety. The existence of a birational Chow-K\"unneth decomposition is stably birationally invariant and this ... More

A manual proof of the Four-colour TheoremOct 30 2017Jul 06 2018In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

Cobordism invariants of the moduli space of stable pairsSep 16 2014May 29 2016For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by integrals of the Chern ... More

An analogue of Szego's limit theorem in free probability theoryJun 06 2007Aug 07 2007In the paper, we discuss orthogonal polynomials in free probability theory. Especially, we prove an analogue of of Szego's limit theorem in free probability theory.

Embedding Dimensions of Finite von Neumann AlgebrasApr 06 2006We introduce "embedding dimensions" of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II$_1$ factor. These embedding dimensions are von Neumann algebra ... More

On Voiculescu's Semicircular MatricesAug 17 2005Oct 03 2005Assume $\N$ is a von Neumann algebra of type II$_1$ with a tracial state $\tau_{\N}$, and $\M$ is the von Neumann algebra of the $n\times n$ matrices over $\N$ with the canonical tracial state $\tau_{\M}$. Let $\mathcal D_n$ be the subalgebra of $\M$ ... More

Maximal Injective Subalgebras of Tensor Products of Free Groups FactorsAug 16 2005Aug 25 2005In this article, we proved the following results. Let $L(F(n_i))$ be the free group factor on $n_i$ generators and $\lambda (g_{i})$ be one of standard generators of $L(F(n_i))$ for $1\le i\le N$. Let $\A_i$ be the abelian von Neumann subalgebra of $L(F(n_i))$ ... More

Necessary and Sufficient Conditions for the Solvability of the $L^p$ Dirichlet Problem On Lipschitz DomainsSep 26 2005We study the homogeneous elliptic systems of order $2\ell$ with real constant coefficients on Lipschitz domains in $R^n$, $n\ge 4$. For any fixed $p>2$, we show that a reverse H\"older condition with exponent $p$ is necessary and sufficient for the solvability ... More

Location of the Path Supremum for Self-similar Processes with Stationary IncrementsApr 15 2016May 21 2016In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. To this end, a point process is constructed and its relation to the distribution of the location ... More

Typical behavior of the harmonic measure in critical Galton-Watson treesFeb 19 2015Mar 03 2016We study the typical behavior of the harmonic measure of balls in large critical Galton-Watson trees whose offspring distribution has finite variance. The harmonic measure considered here refers to the hitting distribution of height $n$ by simple random ... More

Traveling Wave Profiles for a Follow-the-Leader Model for Traffic Flow with Rough Road ConditionNov 06 2017Feb 05 2018We study a Follow-the-Leader (FtL) ODE model for traffic flow with rough road condition, and analyze stationary traveling wave profiles where the solutions of the FtL model trace along, near the jump in the road condition. We derive a discontinuous delay ... More

$C^{2,α}$-estimate for conical Kähler-Ricci flowDec 08 2014We establish a parabolic version of Tian's $C^{2,\alpha}$-estimate for conical complex Monge-Ampere equations, which includes conical K\"ahler-Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical K\"ahler-Ricci ... More

Parametrizing an integer linear program by an integerOct 05 2015Nov 01 2015We consider a family of integer linear programs in which the coefficients of the constraints and objective function are polynomials of an integer parameter $t.$ For $\ell$ in $\mathbb{Z}_+,$ we define $f_\ell(t)$ to be the $\ell^{\text{th}}$ largest value ... More

Revealing the missing heritability via cross-validated genome-wide association studiesJul 30 2013Aug 07 2013Presented here is a simple method for cross-validated genome-wide association studies (cvGWAS). Focusing on phenotype prediction, the method is able to reveal a significant amount of missing heritability by properly selecting a small number of loci with ... More

Pentaquark Search and Other Multiquark Candidates at BESOct 29 2004Results are presented on $\psi(2S)$ and $J/\psi$ hadronic decays to $K^0_SpK^-\bar n$ and $K^0_S\bar p K^+n$ final states from data samples of 14 million $\psi(2S)$ and 58 million $J/\psi$ events accumulated at the BES II detector. No $\Theta(1540)$ signal, ... More

Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependenceSep 14 2016This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or ... More

Tamely ramified geometric Langlands correspondence in positive characteristicOct 30 2018We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for $GL_n(k)$. Let $k$ be an algebraically closed field of characteristic $p> n$. Let $X$ be a smooth projective curve over $k$ with marked points, ... More

Stochastic quantization of an Abelian gauge theoryJan 14 2018We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. This also yields convergence of some gauge invariant ... More

Algorithmic Information Theory and Foundations of ProbabilityJun 24 2009The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.

Rod in a train: a mechanical problem of H.Whitney, or Much Ado About Nothing (In Russian)Jul 02 2019In 1941 a mechanical problem about a rod in a moving train (there is a initial position such that rod does not touch the floor while train is moving) was published by R.Courant and H.Robbins in their popular book "What is mathematics?" and attributed ... More