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PRIF: A Privacy-Preserving Interest-Based Forwarding Scheme for Social Internet of VehiclesApr 06 2018Recent advances in Socially Aware Networks (SANs) have allowed its use in many domains, out of which social Internet of vehicles (SIOV) is of prime importance. SANs can provide a promising routing and forwarding paradigm for SIOV by using interest-based ... More

Privacy Leakage in Smart Homes and Its Mitigation: IFTTT as a Case StudyFeb 08 2019The combination of smart home platforms and automation apps introduces much convenience to smart home users. However, this also brings the potential for privacy leakage. If a smart home platform is permitted to collect all the events of a user day and ... More

The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. II. The Effect of the Radial Gas Pressure GradientOct 23 2018The streaming instability is a mechanism for concentrating solid particles in protoplanetary disks that can lead to gravitational collapse and planetesimal formation. The energy source that drives this instability is the radial pressure gradient in the ... More

On the Numerical Robustness of the Streaming Instability: Particle Concentration and Gas Dynamics in Protoplanetary DisksMar 09 2018Jun 12 2018The Streaming Instability (SI) is a mechanism to concentrate solids in protoplanetary disks. Nonlinear particle clumping from the SI can trigger gravitational collapse into planetesimals. To better understand the numerical robustness of the SI, we perform ... More

On the global rigidity of sphere packings on 3-dimensional manifoldsNov 27 2016In this paper, we prove the global rigidity of sphere packings on 3-dimensional triangulated manifolds, which was conjectured by Cooper and Rivin in \cite{CR}. This is an analogue of the rigidity part of Andreev-Thurston Theorem in three dimension. We ... More

Remarks on Murre's conjecture on Chow groupsOct 04 2011For certain product varieties, Murre's conjecture on Chow groups is investigated. In particular, it is proved that Murre's conjecture (B) is true for two kinds of four-folds. Precisely, if $C$ is a curve and $X$ is an elliptic modular threefold over $k$ ... More

Discrete Quasi-Einstein Metrics and Combinatorial Curvature Flows in 3-DimensionJan 15 2013May 09 2013We define Discrete Quasi-Einstein metrics (DQE-metrics) as the critical points of discrete total curvature functional on triangulated 3-manifolds. We study DQE-metrics by introducing some combinatorial curvature flows. We prove that these flows produce ... More

On the $\ell_1$-Norm Invariant Convex k-Sparse Decomposition of SignalsMay 26 2013Nov 11 2013Inspired by an interesting idea of Cai and Zhang, we formulate and prove the convex $k$-sparse decomposition of vectors which is invariant with respect to $\ell_1$ norm. This result fits well in discussing compressed sensing problems under RIP, but we ... More

Transverse Dynamics at RHICNov 13 2002Studies of <p_{T}>, transverse momentum spectra and anisotropy flow from nuclear collisions at RHIC indicate early thermalization and strong collective expansion. We propose a systematic study of the anisotropy parameter $v_2$ and the transverse momentum ... More

A combinatorial Yamabe problem on two and three dimensional manifoldsApr 22 2015Jan 13 2016In this paper, we introduce a new combinatorial curvature on two and three dimensional triangulated manifolds, which transforms in the same way as that of the smooth scalar curvature under scaling of the metric and could be used to approximate the Gauss ... More

$α$-curvatures and $α$-flows on low dimensional triangulated manifoldsMay 19 2015In this paper, we introduce two discrete curvature flows, which are called $\alpha$-flows on two and three dimensional triangulated manifolds. For triangulated surface $M$, we introduce a new normalization of combinatorial Ricci flow (first introduced ... More

2-Dimensional Combinatorial Calabi Flow in Hyperbolic Background GeometryJan 28 2013For triangulated surfaces locally embedded in the standard hyperbolic space, we introduce combinatorial Calabi flow as the negative gradient flow of combinatorial Calabi energy. We prove that the flow produces solutions which converge to ZCCP-metric (zero ... More

Evidence for universality in the initial planetesimal mass functionMay 10 2017Sep 13 2017Planetesimals may form from the gravitational collapse of dense particle clumps initiated by the streaming instability. We use simulations of aerodynamically coupled gas-particle mixtures to investigate whether the properties of planetesimals formed in ... More

The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. I. The Role of Self-GravityNov 30 2015Mar 31 2016We study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over-densities generated via the streaming instability. To carry out these studies, we implement and test a particle-mesh self-gravity module for ... More

Compressed Sensing Matrices from Fourier MatricesJan 03 2013The class of Fourier matrices is of special importance in compressed sensing (CS). This paper concerns deterministic construction of compressed sensing matrices from Fourier matrices. By using Katz' character sum estimation, we are able to design a deterministic ... More

Discrete schemes for Gaussian curvature and their convergenceApr 07 2008In this paper, several discrete schemes for Gaussian curvature are surveyed. The convergence property of a modified discrete scheme for the Gaussian curvature is considered. Furthermore, a new discrete scheme for Gaussian curvature is resented. We prove ... More

New result on Chern conjecture for minimal hypersurfaces and its applicationMay 24 2016We verify that if $M$ is a compact minimal hypersurface in $\mathbb{S}^{n+1}$ whose squared length of the second fundamental form satisfying $0\leq |A|^2-n\leq\frac{n}{22}$, then $|A|^2\equiv n$ and $M$ is a Clifford torus. Moreover, we prove that if ... More

A Discrete Ricci Flow on Surfaces in Hyperbolic Background GeometryMay 19 2015In this paper, we generalize our results in \cite{GX3} to triangulated surfaces in hyperbolic background geometry, which means that all triangles can be embedded in the standard hyperbolic space. We introduce a new discrete Gaussian curvature by dividing ... More

Inequalities for Euler-Mascheroni constantJul 15 2014The aim of this paper is to establish new inequalities for the Euler-Mascheroni by the continued fraction method.

An Extended Stochastic Model for Quantitative Security Analysis of Networked SystemsMar 28 2016Quantitative security analysis of networked computer systems is one of the decades-long open problems in computer security. Recently, a promising approach was proposed in \cite{XuTDSC11}, which however made some strong assumptions including the exponential ... More

Irregular Riemann-Hilbert correspondence, Alekseev-Meinrenken dynamical r-matrices and Drinfeld twistsJul 25 2015Sep 10 2016In 2004, Enriquez-Etingof-Marshall suggested a new approach to the Ginzburg-Weinstein linearization theorem. This approach is based on solving a system of PDEs for a gauge transformation between the standard classical r-matrix and the Alekseev-Meinrenken ... More

Generalizations of the Sherman-Morrison-Woodbury formula involving the Schur complementJul 06 2016The Moore-Penrose (M-P) inverse of a matrix $M$ that can be decomposed as $M=XNY$ has been established by Castro-Gonz\'{a}lez et al. [1, Theorem 2.2], where $X$ and $Y$ are nonsingular. Some explicit expressions for the M-P inverse of a two-by-two complex ... More

Chaotic polynomial mapsFeb 19 2015This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets, studies the chaotic dynamical behavior and strange attractors, and shows ... More

An alternative proof of the Dirichlet prime number theoremNov 12 2015Dec 10 2015Dirichlet's theorem on arithmetic progressions called as Dirichlet prime number theorem is a classical result in number theory. It states that for any two positive coprime integers $a$ and $d$, there are infinitely many primes of the form $a + nd$, where ... More

On the $l$-adic cohomology of some $p$-adically uniformized Shimura varietiesNov 02 2014Nov 13 2014We determine the Galois representations inside the $l$-adic cohomology of some unitary Shimura varieties at split places where they admit uniformization by finite products of Drinfeld upper half spaces. Our main results confirm Langlands-Kottwitz's description ... More

On the rate of convergence for $(\log_b n)$Sep 26 2016In this paper, we study rate of convergence for the distribution of sequence of logarithms $(\log_bn)$ for integer base $b\ge2.$ It is well-known that the slowly growing sequence $(\log_bn)$ is not uniformly distributed modulo one. Its distributions converge ... More

Circularly uniformizable invariant measures for linear transformationsSep 26 2016In this paper, we prove a threshold result on the existence of a circularly uniformizable invariant probability measure for linear transformations on the line. We show that there exists a constant $c_{\beta}$ depending on the slope $\beta$ of the linear ... More

Multi-Shift de Bruijn SequenceApr 08 2010A (non-circular) de Bruijn sequence w of order n is a word such that every word of length n appears exactly once in w as a factor. In this paper, we generalize the concept to a multi-shift setting: a multi-shift de Bruijn sequence tau(m,n) of shift m ... More

Localization Formulas About Two Killing Vector FieldsApr 13 2013In this article, we will discuss the smooth $(X_{M}+\sqrt{-1}Y_{M})$-invariant forms on $M$ and to establish a localization formulas. As an application, we get a localization formulas for characteristic numbers.

The Cartan Model for Equivariant CohomologyAug 12 2016In this article, we will discuss a new operator $d_{C}$ on $W(\mathfrak{g})\otimes\Omega^{*}(M)$ and to construct a new Cartan model for equivariant cohomology. We use the new Cartan model to construct the corresponding BRST model and Weil model, and ... More

$H^\infty$ functional calculus and maximal inequalities for semigroups of contractions on vector-valued $L_p$-spacesFeb 11 2014May 24 2014Let $\{T_t\}_{t>0}$ be a strongly continuous semigroup of positive contractions on $L_p(X,\mu)$ with $1<p<\infty$. Let $E$ be a UMD Banach lattice of measurable functions on another measure space $(\Omega,\nu)$. For $f\in L_p(X; E)$ define $$\mathcal ... More

Fourier series and approximation on hexagonal and triangular domainsFeb 04 2008Several problems on Fourier series and trigonometric approximation on a hexagon and a triangle are studied. The results include Abel and Ces\`aro summability of Fourier series, degree of approximation and best approximation by trigonometric functions, ... More

Triangular dynamical r-matrices and quantizationMay 01 2000Jul 31 2001We provide a general study for triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix always gives rise to a regular Poisson manifold. Using the Fedosov method, we prove that non-degenerate (i.e., the corresponding ... More

Fedosov *-products and quantum momentum mapsAug 03 1996We study various aspects of Fedosov star-products on symplectic manifolds. By introducing the notion of "quantum exponential maps", we give a criterion characterizing Fedosov connections. As a consequence, a geometric realization is obtained for the equivalence ... More

Quantum groupoids and deformation quantizationAug 19 1997Dec 24 1997The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the quantization ... More

Intersection Numbers and the Jacobian ConjectureApr 26 2016Jun 19 2016Moh's claim that Jacobian Conjecture (JC) is true for degree $\le 100$ is well-known. Unfortunately his proof for the case (99, 66) is not complete. For a Jacobian pair $(f, g)$, we obtain two formulas for intersection numbers ${\rm I}(f_\xi, g)$ and ... More

On the convergence of higher-order orthogonality iterationApr 02 2015Jul 04 2015The higher-order orthogonality iteration (HOOI) has been popularly used for finding a best low-multilinear-rank approximation of a tensor. However, its iterate sequence convergence is still an open question. In this paper, we first analyze a greedy HOOI, ... More

Sobolev orthogonal polynomials defined via gradient on the unit ballDec 18 2006An explicit family of polynomials on the unit ball $B^d$ of $\RR^d$ is constructed, so that it is an orthonormal family with respect to the inner product $$ < f,g > = \rho \int_{B^d}\nabla f(x)\cdot \nabla g(x) dx + \CL (fg), $$ where $\rho >0$, $\nabla$ ... More

Variation of the Bergman kernels under deformations of complex structuresJul 22 2013Inspired by Berndtsson's work on the subharmonicity property of the Bergman kernel, we give a local variation formula of the full Bergman kernels associated to deformations of complex manifolds. In compact case, it follows from the reproducing property ... More

Construction of Gel'fand-Dorfman Bialgebras from Classical R-MatricesAug 23 2002Novikov algebras are algebras whose associators are left-symmetric and right multiplication operators are mutually commutative. A Gel'fand-Dorfman bialgebra is a vector space with a Lie algebra structure and a Novikov algebra structure, satisfying a certain ... More

Geometric function theory for certain slice regular functionsNov 30 2016In this paper, we shall study the geometric function theory for slice regular functions of a quaternionic variable. Specially, we give some coefficient estimates for slice regular functions among which a version of the Bieberbach theorem and the Fekete-Szeg\"{o} ... More

Complex versus real orthogonal polynomials of two variablesJul 30 2013Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal ... More

Orthogonal expansions for generalized Gegenbauer weight function on the unit ballFeb 09 2015Orthogonal polynomials and expansions are studied for the weight function $h_\kappa^2(x) \|x\|^{2\nu} (1-\|x\|^2)^{\mu-1/2}$ on the unit ball of $\mathbb{R}^d$, where $h_\kappa$ is a reflection invariant function, and for related weight function on the ... More

Studies of the Vector-Meson Mass Generation Scheme by Chiral Anomalies in two-Dimensional non-Abelian Gauge TheoriesJan 13 1999Higher order effects of the two-dimensional non-Abelian gauge theories, in which the vector-meson mass is generated by chiral anomalies, will be studied. The $\beta$ function and the topological nature of the non-linear $\sigma$ model in the action and ... More

On the intersections of rational curves with cubic plane curvesNov 08 1995Jul 12 1996Let C be a smooth cubic curve in the complex projective plane. We show that for every positive integer k, there are only finite number of rational curves of degree k each intersects the cubic C at exactly one point. The number of such rational curves ... More

Three circles theorems for harmonic functionsJan 09 2016We proved two Three Circles Theorems for harmonic functions on manifolds in integral sense. As one application, on manifold with nonnegative Ricci curvature, whose tangent cone at infinity is the unique metric cone with unique conic measure, we showed ... More

Competing orders in PZN-xPT and PMN-xPT relaxor ferroelectricsJul 16 2009Neutron and x-ray scattering studies on relaxor ferroelectric systems Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$ (PZN), Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$ (PMN), and their solid solutions with PbTiO$_3$ (PT) have shown that inhomogeneities and disorder play important roles ... More

Mass Differences within Isotopic Multiplets in a SUSY Electro-weak TheoryJan 13 1999Based on the idea that electromagnetism is responsible for the mass differences within isotopic multiplets, and possibly also for the whole mass of the electron, a supersymmetric gauge theoretical model based on the group $SU(2)_{L} \times SU(2)_{R} \times ... More

On the Power of Centralization in Distributed ProcessingMar 22 2012In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner (e.g., to serve ... More

Reflected backward SDEs with two barriers under monotonicity and general increasing conditionsMay 08 2007In this paper, we prove the existence and uniqueness result of the reflected BSDE with two continuous barriers under monotonicity and general increasing condition on $y$, with Lipschitz condition on $z$.

Automatic tracking of protein vesiclesJun 05 2015With the advance of fluorescence imaging technologies, recently cell biologists are able to record the movement of protein vesicles within a living cell. Automatic tracking of the movements of these vesicles become key for qualitative analysis of dynamics ... More

Carleman and Observability Estimates for Stochastic Wave EquationsMar 20 2007Based on a fundamental identity for stochastic hyperbolic-like operators, we derive in this paper a global Carleman estimate (with singular weight function) for stochastic wave equations. This leads to an observability estimate for stochastic wave equations ... More

Towards Shockingly Easy Structured Classification: A Search-based Probabilistic Online Learning FrameworkMar 29 2015There are two major approaches for structured classification. One is the probabilistic gradient-based methods such as conditional random fields (CRF), which has high accuracy but with drawbacks: slow training, and no support of search-based optimization ... More

Growth Index after the Planck ResultsJun 12 2013Oct 19 2013The growth index $\gamma_L$ was proposed to investigate the possible deviation from the standard $\Lambda$CDM model and Einstein's gravity theory in a dynamical perspective. Recently, thanks to the measurement of the cosmic growth rate via the redshift-space ... More

The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin LiquidsMar 06 2008Jun 10 2009We study the instabilities caused by four fermion interactions on algebraic spin liquids. Renormalization group (RG) is used for three types of previously proposed spin liquids on the square lattice: the staggered flux state of SU(2) spin system, the ... More

Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft GravitonsSep 22 2006A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The ... More

Maximum likelihood type estimation for discretely observed CIR model with small $α$-stable noisesMay 04 2016Oct 07 2016A maximum likelihood type estimation of the drift and volatility coefficient parameters in the CIR type model driven by $\alpha$-stable noises is studied when the dispersion parameter $\varepsilon\to0$ and the discrete observations frequency $n\to\infty$ ... More

Energy Dependence of Moments of Net-Proton, Net-Kaon, and Net-Charge Multiplicity Distributions at STARNov 22 2016One of the main goals of the RHIC Beam Energy Scan (BES) program is to study the QCD phase structure, which includes the search for the QCD critical point, over a wide range of chemical potential. Theoretical calculations predict that fluctuations of ... More

A Simple Technique for the Converse of Finite Blocklength Multiple Access ChannelsMay 08 2013May 13 2013A converse for the Discrete Memoryless Multiple Access Channel is given. The result in [13] is refined, and the third order term is obtained. Moreover, our proof is much simpler than [13]. With little modification, the region can be further improved.

Homological dimensions and strongly idempotent idealsMar 06 2013Let A be an Artin algebra and e an idempotent in A. It is an interesting topic to compare the homological dimension of the algebras A,A/AeA and eAe. For example, in [2], the relation among the global dimension of these algebras is discussed under the ... More

Spectra for Gelfand pairs associated with the free two step nilpotent lie groupAug 19 2016Let $F(n)$ be a connected and simply connected free 2-step nilpotent lie group and $K$ be a compact subgroup of Aut($F(n)$). We say that $(K,F(n))$ is a Gelfand pair when the set of integrable $K$-invariant functions on $F(n)$ forms an abelian algebra ... More

Conifold Transitions for Complete Intersection Calabi-Yau 3-folds in Products of Projective SpacesFeb 06 2012We prove that a generic complete intersection Calabi-Yau 3-fold defined by sections of ample line bundles on a product of projective spaces admits a conifold transition to a connected sum of S^{3} \times S^{3}. In this manner, we obtain complex structures ... More

Generalizations of Quantum DiscordDec 03 2010Jun 01 2011The original definition of quantum discord of bipartite states was defined over projective measurements, in this paper we discuss some generalizations of it. These generalizations are defined over general measurements, rank-one general measurements or ... More

Geometric global quantum discordMay 02 2012May 07 2012Geometric quantum discord, proposed by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010) 190502], is an important measure for bipartite correlations. In this paper, we generalize it to multipartite states, we call the generalized version geometric ... More

Oblique discordJun 01 2015Discord and entanglement characterize two kinds of quantum correlations, and discord captures more correlation than entanglement in the sense that even separable states may have nonzero discord. In this paper, we propose a new kind of quantum correlation ... More

Global classical solutions to the compressible Euler-Maxwell equationsSep 26 2011In this paper, we consider the compressible Euler-Maxwell equations arising in semiconductor physics, which take the form of Euler equations for the conservation laws of mass density and current density for electrons, coupled to Maxwell's equations for ... More

Three Dimensional Z2 Topological Phases enriched by Time-Reversal SymmetryJul 30 2013Feb 20 2016We study three dimensional $Z_2$ topological phases enriched by $Z_2^T$ time-reversal symmetry with bosonic bulk excitations. Some of these phases can be constructed by simply coupling the three dimensional symmetry protected topological phases with $Z_2 ... More

On examples of intermediate subfactors from conformal field theoryNov 02 2012Motivated by our subfactor generalization of Wall's conjecture, in this paper we determine all intermediate subfactors for conformal subnets corresponding to four infinite series of conformal inclusions, and as a consequence we verify that these series ... More

Algebraic Conformal Field Theories IIMar 16 1999Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal coset of type ... More

Some computations in the cyclic permutations of completely rational netsNov 27 2005In this paper we calculate certain chiral quantities from the cyclic permutation orbifold of a general completely rational net. We determine the fusion of a fundamental soliton, and by suitably modified arguments of A. Coste , T. Gannon and especially ... More

Conventional description of Unconventional Coulomb-Crystal phase transitions in three-dimensional classical O(N) spin-iceNov 16 2009Nov 25 2009We study the phase transition between the high temperature Coulomb phase and the low temperature staggered crystal phase in three dimensional classical O(N) spin-ice model. Compared with the previously proposed CP(1) formalism on the Coulomb-crystal transition ... More

An alternative proof of the Dirichlet prime number theoremNov 12 2015Nov 14 2016Dirichlet's theorem on arithmetic progressions called as Dirichlet prime number theorem is a classical result in number theory. In this article we give an alternative proof of it based on a previous result of us. Also we get an estimation of the prime ... More

Uniformly Area Expanding Flows in SpacetimesAug 16 2015The central object of study of this thesis is inverse mean curvature vector flow of two-dimensional surfaces in four-dimensional spacetimes. Being a system of forward-backward parabolic PDEs, inverse mean curvature vector flow equation lacks a general ... More

Unbounded Sobolev trajectories and modified scattering theory for a wave guide nonlinear Schrödinger equationJun 24 2015Jun 25 2015We consider the following wave guide nonlinear Schr\"odinger equation, \begin{equation} (i\partial \_t+\partial \_{xx}-\vert D\_y\vert )U=\vert U\vert ^2U\ \tag{WS} \end{equation} on the spatial cylinder $\mathbb{R} \_x\times \mathbb{T} \_y$. We establish ... More

Blocked regular fractional factorial designs with minimum aberrationFeb 23 2007This paper considers the construction of minimum aberration (MA) blocked factorial designs. Based on coding theory, the concept of minimum moment aberration due to Xu [Statist. Sinica 13 (2003) 691--708] for unblocked designs is extended to blocked designs. ... More

An Efficient Implementation of Belief Function PropagationMar 20 2013The local computation technique (Shafer et al. 1987, Shafer and Shenoy 1988, Shenoy and Shafer 1986) is used for propagating belief functions in so called a Markov Tree. In this paper, we describe an efficient implementation of belief function propagation ... More

A closed formula for the asymptotic expansion of the Bergman kernelMar 15 2011Aug 11 2012We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants. The ... More

Markov Chain Approximations to Singular Stable-like ProcessesOct 10 2012We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these chains to ... More

$p$-adic families of automorphic forms over some unitary Shimura varietiesMay 29 2014Jun 11 2015We construct some $n$-dimensional eigenvarieties for finite slope overconvergent eigenforms over some unitary Shimura varieties with signature $(1,n-1)\times(0,n)\times\cdots\times(0,n)$ by adapting Andreatta-Iovita-Pilloni's method. We also show that ... More

An invariance principle for stochastic heat equations with periodic coefficientsMay 13 2015In this paper we investigate the asymptotic behaviors of solution $u(t, \cdot)$ of a stochastic heat equation with a periodic nonlinear term. Such equation appears related to the dynamical sine-Gordon model. We consider the reversible case and extend ... More

Stable-Range Approach to Short Wave and Khokhlov-Zabolotskaya EquationsNov 23 2008Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a diffraction sound ... More

Regularization to orthogonal-polynomials fitting with application to magnetization dataMar 11 2016An obstacle encountered in applying orthogonal-polynomials fitting is how to select out the proper fitting expression. By adding a Laplace term to the error expression and introducing the concept of overfitting degree, a regularization and corresponding ... More

On the cuspidal support of discrete series for $p$-adic quasisplit $Sp(N)$ and $SO(N)$Apr 30 2015Jan 04 2016Zelevinsky's classification theory of discrete series of $p$-adic general linear groups has been well known. M{\oe}glin and Tadic gave the same kind of theory for $p$-adic classical groups, which is more complicated due to the occurrence of nontrivial ... More

Incompleteness of pressure metric on Teichmüller space of a bordered surfaceAug 13 2016We prove that the pressure metric on the Teichm\"uller space of a bordered surface is incomplete and its partial completion can be given by the moduli space of metric graphs for a fat graph associated to the same bordered surface equipped with pressure ... More

Multivariate Splines and PolytopesJun 06 2008Oct 16 2010In this paper, we use multivariate splines to investigate the volume of polytopes. We first present an explicit formula for the multivariate truncated power, which can be considered as a dual version of the famous Brion's formula for the volume of polytopes. ... More

Towards Optimal One Pass Large Scale Learning with Averaged Stochastic Gradient DescentJul 13 2011Dec 22 2011For large scale learning problems, it is desirable if we can obtain the optimal model parameters by going through the data in only one pass. Polyak and Juditsky (1992) showed that asymptotically the test performance of the simple average of the parameters ... More

Strange Quark stars: Observations & SpeculationsDec 24 2008Mar 12 2009Two kinds of difficulties have challenged the physics community for many years: (1) knowing nature's building blocks (particle physics) and (2) understanding interacting many-body systems (many-body physics). Both of them exist in the research of quark ... More

Astro-quark matter: a challenge facing astroparticle physicsFeb 05 2008Quark matter both in terrestrial experiment and in astrophysics is briefly reviewed. Astrophysical quark matter could appear in the early Universe, in compact stars, and as cosmic rays. Emphasis is put on quark star as the nature of pulsars. Possible ... More

Looking for Lorentz Violation in Short-Range GravityOct 28 2016General violations of Lorentz symmetry can be described by the Standard-Model Extension (SME) framework. The SME predicts modifications to existing physics and can be tested in high-precision experiments. By looking for small deviations from Newton gravity, ... More

Pulsars: Macro-nuclei with 3-flavour symmetryMar 23 2015A pulsar-like compact star is the rump left behind after a supernova where normal baryonic matter is intensely compressed by gravity, but the real state of such compressed baryonic matter is still not well understood because of the non-perturbative nature ... More

Possible evidence that pulsars are quark starsSep 10 2007Sep 18 2007It is a pity that the real state of matter in pulsar-like stars is still not determined confidently because of the uncertainty about cold matter at supranuclear density, even 40 years after the discovery of pulsar. Nuclear matter (related to neutron stars) ... More

AXPs/SGRs: Magnetars or Quark-stars?Nov 20 2006May 19 2007The magnetar model and a solid quark star model for anomalous X-ray pulsars/soft gamma-ray repeaters (AXPs/SGRs) are discussed. Different manifestations of pulsar-like stars are speculated to be due to both their nature (e.g., mass and strain) and their ... More

Circularly invariant uniformizable probability measures for linear transformationsSep 26 2016Jun 07 2017In this paper, we prove a threshold result on the existence of a circularly invariant uniformizable probability measure (CIUPM) for linear transformations with non-zero slope on the line. We show that there is a threshold constant $c$ depending only on ... More

Moving-Frame Approach to Nonlinear Internal Waves in OceansJun 17 2013In this article, we introduce a moving-frame approach to the geophysical equation of two-dimensional uniformly stratified rotational fluid in oceans and find a family of exact solutions containing ten arbitrary parameter functions.

Learning Nonlinear State Space Models with Hamiltonian Sequential Monte Carlo SamplerJan 03 2019State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors. However, SSM is ... More

Backward Doubly Stochastic Equations with Jumps and Comparison TheoremsJan 17 2016Apr 11 2017In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under some weak ... More

Necessary and sufficient condition for the comparison theorem of multidimensional anticipated backward stochastic differential equationsOct 22 2009Mar 03 2011Anticipated backward stochastic differential equations, studied the first time in 2007, are equations of the following type: {tabular}{rlll} $-dY_t$ &=& $f(t, Y_t, Z_t, Y_{t+\delta(t)}, Z_{t+\zeta(t)})dt-Z_tdB_t, $ & $ t\in[0, T];$ $Y_t$ &=& $\xi_t, $ ... More

Uniqueness and propagation of chaos for the Boltzmann equation with moderately soft potentialsMay 30 2016We prove a strong/weak stability estimate for the 3D homogeneous Boltzmann equation with moderately soft potentials ($\gamma\in(-1,0)$) using the Wasserstein distance with quadratic cost. This in particular implies the uniqueness in the class of all weak ... More

PoPPy: A Point Process Toolbox Based on PyTorchOct 23 2018Oct 25 2018PoPPy is a Point Process toolbox based on PyTorch, which achieves flexible designing and efficient learning of point process models. It can be used for interpretable sequential data modeling and analysis, e.g., Granger causality analysis of multi-variate ... More

Projective Oscillator Representations of sl(n+1) and sp(2m+2)Mar 28 2014The n-dimensional projective group gives rise to a one-parameter family of inhomogeneous first-order differential operator representations of sl(n+1). By partially swapping differential operators and multiplication operators, we obtain more general differential ... More