Results for "Rixin Xu"

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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
Privacy Leakage in Smart Homes and Its Mitigation: IFTTT as a Case StudyFeb 08 2019Feb 14 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
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
Trans-Neptunian Binaries as Evidence for Planetesimal Formation by the Streaming InstabilityJun 26 2019A critical step toward the emergence of planets in a protoplanetary disk consists in accretion of planetesimals, bodies 1-1000 km in size, from smaller disk constituents. This process is poorly understood partly because we lack good observational constraints ... More
Thin Reaction Zones in Highly Turbulent MediumJun 15 2018In a highly turbulent medium characterized by a low Damk\"ohler number Da, reactions are commonly considered to occur in distributed zones broadened by small-scale turbulent eddies. In the present communication, an alternative regime of propagation of ... More
Demographics of Planetesimals Formed by the Streaming InstabilityJun 21 2019The streaming instability (SI) is a mechanism to aerodynamically concentrate solids in protoplanetary disks and facilitate the formation of planetesimals. Recent numerical modeling efforts have demonstrated the increasing complexity of the initial mass ... More
Combinatorial $α$-curvatures and $α$-flows on polyhedral surfaces, IJun 11 2018We introduce combinatorial $\alpha$-curvature for piecewise linear metrics on polyhedral surfaces, which is a generalization of the classical combinatorial curvature on polyhedral surfaces. Then we prove the global rigidity of $\alpha$-curvature with ... 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
A new proof of Bowers-Stephenson conjectureApr 25 2019Inversive distance circle packing on surfaces was introduced by Bowers-Stephenson as a generalization of Thurston's circle packing and conjectured to be rigid. The infinitesimal and global rigidity of circle packing with nonnegative inversive distance ... 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
The minimizers of the $p$-frame potentialJul 25 2019Jul 30 2019For any positive real number $p$, the $p$-frame potential of $N$ unit vectors $X:=\{\mathbf x_1,\ldots,\mathbf x_N\}\subset \mathbb R^d$ is defined as ${\rm FP}_{p,N,d}(X)=\sum_{i\neq j}|\langle \mathbf x_i,\mathbf x_j\rangle |^p$. In this paper, we focus ... 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
The minimizers of the $p$-frame potentialJul 25 2019Aug 01 2019For any positive real number $p$, the $p$-frame potential of $N$ unit vectors $X:=\{\mathbf x_1,\ldots,\mathbf x_N\}\subset \mathbb R^d$ is defined as ${\rm FP}_{p,N,d}(X)=\sum_{i\neq j}|\langle \mathbf x_i,\mathbf x_j\rangle |^p$. In this paper, we focus ... More
Combinatorial Calabi flow with surgery on surfacesJun 06 2018We study the combinatorial Calabi flow for Euclidean and hyperbolic polyhedral metrics on surfaces, which is an analogue of the smooth surface Calabi flow. To handle the singularies along the combinatorial Calabi flow, we do surgery on the flow by flipping. ... 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
A memory mechanism based on two dimensional code of neurosome patternNov 14 2017We have recognized that 2D codes, i.e., a group of strongly connected neurosomes that can be simultaneously excited, are the basic data carriers for memory in a brain. An echoing mechanism between two neighboring layers of neurosomes is assumed to establish ... 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
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
The minimizers of the $p$-frame potentialJul 25 2019Aug 15 2019For any positive real number $p$, the $p$-frame potential of $N$ unit vectors $X:=\{\mathbf x_1,\ldots,\mathbf x_N\}\subset \mathbb R^d$ is defined as ${\rm FP}_{p,N,d}(X)=\sum_{i\neq j}|\langle \mathbf x_i,\mathbf x_j\rangle |^p$. In this paper, we focus ... More
Thurston's sphere packings on 3-dimensional manifolds, IApr 25 2019May 21 2019Thurston's sphere packing on a 3-dimensional manifold is a generalization of Thusrton's circle packing on a surface, allowing adjacent spheres to intersect with non-obtuse angles. In this paper, we prove that the discrete Laplacian for a large class of ... More
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
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.
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
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.
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
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
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
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
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
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 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
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
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
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
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
Economical and efficient network super points detection based on GPUMar 30 2018Network super point is a kind of special host which plays an important role in network management and security. For a core network, detecting super points in real time is a burden task because it requires plenty computing resources to keep up with the ... More
Distance-based Protein Folding Powered by Deep LearningNov 08 2018Nov 12 2018Contact-assisted protein folding has made very good progress, but two challenges remain. One is accurate contact prediction for proteins lack of many sequence homologs and the other is that time-consuming folding simulation is often needed to predict ... More
Special solutions to a fourth-order nonlinear parabolic equation in non-divergence formAug 28 2018Feb 02 2019In this paper we study a crystal surface model first proposed by H.~Al Hajj Shehadeh, R.V.~Kohn, and J.~Weare (2011 Physica D, 240,1771-1784). By seeking a solution of a particular function form, we are led to a boundary value problem for a fourth-order ... More
On the perturbation of an $L^2$-orthogonal projectionSep 01 2018The $L^2$-orthogonal projection is an important mathematical tool in scientific computing and numerical analysis, which has been widely applied in many fields such as linear least squares problems, eigenvalue problems, ill-posed problems, and randomized ... More
Restriction of $p$-modular representations of $U(2, 1)$ to a Borel subgroupFeb 06 2019Feb 12 2019Let $G$ be the unramified unitary group $U(2, 1)(E/F)$ defined over a non-archimedean local field $F$ of odd residue characteristic $p$, and $B$ be the standard Borel subgroup of $G$. We prove in this note that the restriction of any supersingular representation ... 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
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
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
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
Minimal surfaces in AdS C-metricAug 04 2017Jun 06 2018We shed some light on the field theory interpretation of C-metric by investigating the minimal surfaces which are homologous to the given boundary regions. The accelerating black holes change the asymptotic structure of the space-time. We focus on the ... 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
Search for Ultra-High Energy WIMPs by detecting neutrino signatures from the earth coreJan 21 2018Jan 24 2018I study the possibility of probing Ultra-High Energy (UHE from now on) dark matter particles (>10$^8$ GeV) due to the decay of superheavy dark matter via detection of UHE neutrino signatures from the earth core. The UHE WIMP event rates are estimated ... More
Interleaved lattice-based maximin distance designsJul 06 2018We propose a new method to construct maximin distance designs with arbitrary number of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more dimensions. Applicable ... More
How many real solutions of a random equation (I)Jun 21 2019Jun 25 2019In this paper, we discuss how to calculate the expectation of the number of real zeros of a equation with a random continuous parameter variable in a interval. First, we present some proprieties of this expectation. Then we discuss a special case that ... 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
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
On the Tractability of Public Persuasion with No ExternalitiesJun 18 2019Jul 09 2019Persuasion studies how a principal can influence agents' decisions via strategic information revelation --- often described as a signaling scheme --- in order to yield the most desirable equilibrium outcome. Recently, there has been a large body of algorithmic ... More
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
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
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
Nonarchimedean components of non-endoscopic automorphic representations for quasisplit $Sp(N)$ and $O(N)$Mar 22 2019Arthur classified the discrete automorphic representations of symplectic and orthogonal groups over a number field by that of the general linear groups. In this classification, those that are not from endoscopic lifting correspond to pairs $(\phi, b)$, ... 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
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
A combinatorial solution to Mœglin's parametrization of Arthur packets for p-adic quasisplit $Sp(N)$ and $O(N)$Mar 24 2016Jan 20 2019We develop a general procedure to study the combinatorial structure of Arthur packets for $p$-adic quasisplit $Sp(N)$ and $O(N)$ following the works of M{\oe}glin. This allows us to answer many delicate questions concerning the Arthur packets of these ... 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
Stokes phenomenon and Yang-Baxter equationsAug 23 2018We describe the monodromy of dynamical Knizhnik-Zamolodchikov equations via Stokes phenomenon. It defines a family of braid groups representations by certain Stokes matrices. In particular, these Stokes matrices satisfy the Yang-Baxter equation.
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
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
An equation about sum of primes with digital sum constraintsMay 23 2017We know that any prime number of form $4s+1$ can be written as a sum of two perfect square numbers. As a consequence of Goldbach's weak conjecture, any number great than $10$ can be represented as a sum of four primes. We are motivated to consider an ... 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
Geodesic orbit Finsler space with $K\geq0$ and the (FP) conditionJul 13 2019In this paper, we study the interaction between the geodesic orbit (g.o.~in short) property and certain flag curvature conditions. A Finsler manifold is called g.o.~if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the ... More
READ: a three-communicating-stage distributed super points detections algorithmJul 18 2019A super point is a host that interacts with a far larger number of counterparts in the network over a period of time. Super point detection plays an important role in network research and application. With the increase of network scale, distributed super ... 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
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
On the pro-$p$-Iwahori invariants of supersingular representations of unramified $U(2, 1)$Mar 25 2018Jun 08 2018Let $G$ be the unramified unitary group $U(2, 1)(E/F)$ over a non-archimedean local field $F$ of odd residue characteristic $p$. In this paper, for any supersingular representation of $G$ that contains the Steinberg weight, we prove its pro-$p$-Iwahori ... 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
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
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
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
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.