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Optical Conductivity From Pair Density WavesAug 03 2016We present a theory of optical conductivity in systems with finite-momentum Cooper pairs. In contrast to the BCS pairing where AC conductivity is purely imaginary in the clean limit, there is nonzero AC absorption across the superconducting gap for finite-momentum ... More

Pair density wave, charge density wave and vortex in high Tc cupratesFeb 08 2018A recent scanning tunneling microscopy (STM) experiment reports the observation of charge density wave (CDW) with period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately period 4a CDW that are ... More

High-performance K-means Implementation based on a Coarse-grained Map-Reduce ArchitectureOct 17 2016The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means algorithm necessary. ... More

High-performance K-means Implementation based on a Simplified Map-Reduce ArchitectureOct 17 2016Nov 22 2016The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means algorithm necessary. ... More

High-performance K-means Implementation based on a Coarse-grained Map-Reduce ArchitectureOct 17 2016Nov 10 2016The k-means algorithm is one of the most common clustering algorithms and widely used in data mining and pattern recognition. The increasing computational requirement of big data applications makes hardware acceleration for the k-means algorithm necessary. ... More

Grünwald version of van der Waerden's theorem for semi-modulesDec 29 2015Jun 17 2016Let $(G,\pmb{+})$ be any given semimodule over a discrete semiring $(R,+,\cdot)$ with a finite coloring, say $G=B_1\cup\dotsm\cup B_q$. By establishing a Regional Multiple Recurrence Theorem for semimodules, we prove that one of the colors $j$ has the ... More

Some criteria for spectral finiteness of a finite subset of the real matrix space $\mathbb{R}^{d\times d}$Jun 11 2012In this paper, we present some checkable criteria for the spectral finiteness of a finite subset of the real $d\times d$ matrix space $\mathbb{R}^{d\times d}$, where $2\le d<\infty$.

Optimal Rate Scheduling via Utility-Maximization for J-User MIMO Markov Fading Wireless Channels with CooperationJun 22 2011We design a dynamic rate scheduling policy of Markov type via the solution (a social optimal Nash equilibrium point) to a utility-maximization problem over a randomly evolving capacity set for a class of generalized processor-sharing queues living in ... More

Product-form solutions for integrated services packet networks and cloud computing systemsSep 03 2013We iteratively derive the product-form solutions of stationary distributions of priority multiclass queueing networks with multi-sever stations. The networks are Markovian with exponential interarrival and service time distributions. These solutions can ... More

An Alternative Method of Extracting $V_{bu}$ from Semi-leptonic B DecayMay 12 1994We propose a new method of extracting $V_{bu}$ from measurements of Semi-leptonic B decay which has much less theoretical uncertainties than conventional methods.

The Salvetti Complex and the Little CubesFeb 05 2006Sep 11 2008We study how the combinatorial structure of the Salvetti complexes of the braid arrangements are related to homotopy theoretic properties of iterated loop spaces. We prove the skeletal filtrations on the Salvetti complexes of the braid arrangements give ... More

Rotation of the cosmic microwave background polarization from weak gravitational lensingNov 14 2013Jan 30 2014When a cosmic microwave background (CMB) photon travels from the surface of last scatter through spacetime metric perturbations, the polarization vector may rotate about its direction of propagation. This gravitational rotation is distinct from, and occurs ... More

Random Walks and Subfractional Brownian MotionMar 21 2013Jan 15 2014In this article, we show a result of approximation in law to subfractional Brownian motion, with $H>\frac{1}{2}$, in the Skorohod topology. The construction of these approximations is based on a sequence of I.I.D random variables

Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zerosNov 20 2015In this paper, we use bifurcation method to investigate the existence and multiplicity of one-sign solutions of the $p$-Laplacian involving a linear/superlinear nonlinearity with zeros. To do this, we first establish a bifurcation theorem from infinity ... More

Grünwald version of van der Waerden's theorem for semi-modulesDec 29 2015Sep 14 2018Let $(G,\pmb{+})$ be any given semimodule over a discrete semiring $(R,+,\cdot)$ with a finite coloring, say $G=B_1\cup\dotsm\cup B_q$. By establishing a Regional Multiple Recurrence Theorem for semimodules, we prove that one of the colors $j$ has the ... More

Unilateral global interval bifurcation theorem for $p$-Laplacian and its applicationsJul 28 2012In this paper, we establish a unilateral global bifurcation result from interval for a class of $p$-Laplacian problems. By applying the above result, we study the spectrum of a class of half-quasilinear problems. Moreover, we also investigate the existence ... More

Unilateral global bifurcation for fourth-order eigenvalue problems with sign-changing weightJul 31 2012In this paper, we shall establish the unilateral global bifurcation result for a class of fourth-order eigenvalue problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that $(\mu_k^\nu,0)$ is a bifurcation ... More

Almost automorphy of invertible semiflows with compact Hausdorff phase spacesJun 15 2018Let $T\times X\rightarrow X, (t,x)\mapsto tx$ be a minimal semiflow on a compact Hausdorff space $X$ with phase semigroup $T$ such that each $t\in T$ is an invertible map of $X$. An $x\in X$ is called an \textit{a.a. point} of $(T,X)$ if $(t_nx, t_n^{-1}y)\to(y, ... More

Numerical Methods and Analysis via Random Field Based Malliavin Calculus for Backward Stochastic PDEsJun 28 2013We study the adapted solution, numerical methods, and related convergence analysis for a unified backward stochastic partial differential equation (B-SPDE). The equation is vector-valued, whose drift and diffusion coefficients may involve nonlinear and ... More

Equations For Frame Wavelets In $L^2(\R^2)$Sep 17 2015We establish system of equations for single function normalized tight frame wavelets with compact supports associated with $2\times 2$ expansive integral matrices in $L^2(\R^2)$.

Finer filtration for matrix-valued cocycle based on Oseledec's multiplicative ergodic theoremAug 28 2013Apr 08 2014In this paper, we improve the classical multiplicative ergodic theorem.

An extension of Furstenberg's structure theorem for Noetherian modules and multiple recurrence theorems IIMay 27 2016Jun 09 2016Using a recent Furstenberg structure theorem, we obtain a quantitative multiple recurrence theorem relative to any locally compact second countable Noetherian module over a syndetic ring.

Asymptotic Joint Distribution of Extreme Eigenvalues of the Sample Covariance Matrix in the Spiked Population ModelJul 18 2012In this paper, we consider a data matrix $X\in\mathbb{C}^{N\times M}$ where all the columns are i.i.d. samples being $N$ dimensional complex Gaussian of mean zero and covariance $\Sigma\in\mathbb{C}^{N\times N}$. Here the population matrix $\Sigma$ is ... More

Gains in evolutionary dynamics: A unifying approach to dynamic stability of contractive games and ESSMay 13 2018Nov 26 2018In this paper, we investigate gains from strategy revisions in deterministic evolutionary dynamics. To clarify the gain from revision, we propose a framework to reconstruct an evolutionary dynamic from optimal decision with stochastic (possibly restricted) ... More

Distributional stability and deterministic equilibrium selection under heterogeneous evolutionary dynamicsMay 13 2018In the presence of persistent payoff heterogeneity, the evolution of the aggregate strategy hugely depends on the underlying strategy composition under many evolutionary dynamics, while the aggregate dynamic under the standard BRD reduces to a homogenized ... More

Two Whyburn type topological theorems and its applications to Monge-Ampère equationsJun 25 2014In this paper we correct a gap of Whyburn type topological lemma and establish two superior limit theorems. As the applications of our Whyburn type topological theorems, we study the following Monge-Amp\`{e}re equation \begin{eqnarray} \left\{ \begin{array}{lll} ... More

Cellular stratified spacesSep 15 2016The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonz{\'a}lez, and Rudyak with the aim of constructing a cellular model of the configuration space of a sphere. Although the original aim was not achieved ... More

Cellular Stratified Spaces II: Basic ConstructionsNov 21 2011Sep 16 2016This is a sequel to [1106.3772], in which a systematic study of cellular stratified spaces and related concepts was initiated. In this paper, we study important operations on cellular and stellar stratified spaces, including taking subspaces, subdivisions, ... More

Eta Invariant and Conformal CobordismJun 20 2001Jun 21 2001In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an abelian group, the conformal cobordism group, which classifies ... More

Equations For Parseval's Frame Wavelets In $L^2(\R^d)$ With Compact SupportsJul 31 2016Let $d\geq 1$ be a natural number and $A_0$ be a $d\times d$ expansive integral matrix with determinant $\pm 2.$ Then $A_0$ is integrally similar to an integral matrix $A$ with certain additional properties. A finite solution to the system of equations ... More

Spectra of Cantor measuresJan 19 2014Feb 09 2015Let $\mu_{q, b}$ be the Cantor measure associated with the iterated function system $f_i(x)=x/b+i/q, 0\le i\le q-1$, where $2\le q, b/q\in \Z$. In this paper, we consider spectra and maximal orthogonal sets of the Cantor measure $\mu_{q, b}$ and their ... More

A Curvature Flow Unifying Symplectic Curvature Flow And Pluriclosed FlowNov 28 2013Mar 21 2015Streets and Tian introduced pluriclosed flow and symplectic curvature flow in recent years. Here we construct a curvature flow to unify these two flows. We show the short time existence of our flow and exhibit an obstruction to long time existence.

On the E^1-term of the gravity spectral sequenceMar 26 2009The author constructed a spectral sequence strongly converging to h_*(Omega^n Sigma^n X) for any homology theory in [Topology 33 (1994) 631-662]. In this note, we prove that the E^1-term of the spectral sequence is isomorphic to the cobar construction, ... More

Cellular Stratified Spaces I: Face Categories and Classifying SpacesJun 19 2011Sep 16 2016The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonz\'alez, and Rudyak [1009.1851] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it was shown that ... More

Convergence Rates of Finite Difference Stochastic Approximation AlgorithmsJun 30 2015Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes ... More

Collisionless Magnetic Reconnection via Alfven EigenmodesJul 04 2009We propose an analytic approach to the problem of collisionless magnetic reconnection formulated as a process of Alfven eigenmodes' generation and dissipation. Alfven eigenmodes are confined by the current sheet in the same way that quantum mechanical ... More

Characterizations of function spaces on the sphere using framesOct 04 2005In this paper we introduce a polynomial frame on the unit sphere $\sph$ of $\mathbb{R}^d$, for which every distribution has a wavelet-type decomposition. More importantly, we prove that many function spaces on the sphere $\sph$, such as $L^p$, $H^p$ and ... More

Congruences for the number of partitions and bipartitions with distinct even partsApr 22 2014Let $ped(n)$ denote the number of partitions of $n$ wherein even parts are distinct (and odd parts are unrestricted). We show infinite families of congruences for $ped(n)$ modulo $8$. We also examine the behavior of $ped_{-2}(n)$ modulo $8$ in detail ... More

Spectrum of Navier $p$-biharmonic problem with sign-changing weightJul 31 2012Aug 27 2016In this paper, we consider the following eigenvalue problem {{l} (|u"|^{p-2}u")"=\lambda m(x)|u|^{p-2}u, x\in (0,1), u(0)=u(1)=u"(0)=u"(1)=0, where $1<p<+\infty$, $\lambda$ is a real parameter and $m$ is sign-changing weight. We prove there exists a unique ... More

Some Results on the Scattering Theory for Nonlinear Schrödinger Equations in Weighted $L^{2}$ SpaceAug 16 2011We investigate the scattering theory for the nonlinear Schr\"{o}dinger equation $i \partial_{t}u+ \Delta u+\lambda|u|^\alpha u=0$ in $\Sigma=H^{1}(\mathbb{R}^{d})\cap L^{2}(|x|^{2};dx)$. We show that scattering states $u^{\pm}$ exist in $\Sigma$ when ... More

Pointwise convergence of ergodic averages of bounded measurable functions for amenable groupsApr 03 2016Jun 16 2016Given any amenable group $G$ (with a left Haar measure $|\cdot|$ or $dg$), we can select out a \textit{F{\o}lner subnet} $\{F_\theta,\theta\in\Theta\}$ from any left F{\o}lner net in $G$, which is \textit{$L^\infty$-admissible}, namely, for any Borel ... More

Criteria of stabilizability for switching-control systems with solvable linear approximationsJan 10 2012We study the stability and stabilizability of a continuous-time switched control system that consists of the time-invariant $n$-dimensional subsystems \dot{x}=A_ix+B_i(x)u\quad (x\in\mathbb{R}^n, t\in\mathbb{R}_+ \textrm{and} u\in\mathbb{R}^{m_i}),\qquad ... More

Regularity criterion for the 3D Hall-magneto-hydrodynamicsJul 21 2015May 02 2016This paper studies the regularity problem for the 3D incompress- ible resistive viscous Hall-magneto-hydrodynamic (Hall-MHD) system. The Kolmogorov 41 phenomenological theory of turbulence predicts that there exists a critical wavenumber above which the ... More

The Exit Distribution for Smart Kinetic Walk with Symmetric Transition ProbabilityNov 29 2016It has been proved that the distribution of the point where the Smart Kinetic Walk (SKW) exits a domain converges in distribution to harmonic measure on the hexagonal lattice. For other lattices, it is believed that this result still holds, and there ... More

Heterogeneity and aggregation in evolutionary dynamics: a general framework without aggregabilityMay 13 2018We consider general evolutionary dynamics under persistent payoff heterogeneity and study the dynamic relation between the strategy composition over different types and the aggregate strategy distribution of the entire population. It is rigorously proven ... More

The Exit Distribution for Smart Kinetic Walk with Symmetric and Asymmetric Transition ProbabilityNov 29 2016Feb 03 2017It has been proved that the distribution of the point where the Smart Kinetic Walk (SKW) exits a domain converges in distribution to harmonic measure on the hexagonal lattice. For other lattices, it is believed that this result still holds, and there ... More

Uniform positive recursion frequency of any minimal dynamical system on a compact spaceJun 25 2018Using Gottschalk's notion\,---\,weakly locally almost periodic point, we show in this paper that if $f\colon X\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage $\varepsilon$ of $X$, ... More

On the Pin(2)-Equivariant Monopole Floer Homology of Plumbed 3-ManifoldsJul 11 2016Sep 23 2016We compute the Pin(2)-equivariant monopole Floer homology for the class of plumbed 3-manifolds with at most one "bad" vertex (in the sense of Oszv\'ath and Szab\'o). We show that for these manifolds, the Pin(2)-equivariant monopole Floer homology can ... More

Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equationsJul 16 2013Dec 17 2013In this paper we show that if a linear cocycle is robustly periodical stable then it is uniformly stable.

Chaotic dynamics of continuous-time topological semi-flows on Polish spacesJan 09 2015In this paper, we study the chaotic dynamics of a continuous-time topological semi-flow on a Polish space.

A Note on Positive Energy Theorem for Spaces with Asymptotic SUSY CompactificationJun 01 2004We extend the positive mass theorem proved previously by the author to the Lorentzian setting. This includes the original higher dimensional positive energy theorem whose spinor proof was given by Witten in dimension four and by Xiao Zhang in dimension ... More

Eigenvalue, global bifurcation and positive solutions for a class of fully nonlinear problemsMar 23 2014In this paper, we shall study global bifurcation phenomenon for the following Kirchhoff type problem \begin{equation} \left\{ \begin{array}{l} -\left(a+b\int_\Omega \vert \nabla u\vert^2\,dx\right)\Delta u=\lambda u+h(x,u,\lambda)\,\,\text{in}\,\, \Omega,\\ ... More

Mean-variance hedging based on an incomplete market with external risk factors of non-Gaussian OU processesOct 03 2014Aug 26 2015In this paper, we prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semi-explicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck ... More

Stability and Evolution of Color Skyrmions in the Quark-Gluon PlasmaDec 20 2006Feb 01 2007We show the existence of unstable color skyrmions in a class of nonabelian fluid models. Oscillating and expanding solutions are found in the time-dependent case.

Cosmological magnetic fields: generation during inflation and evolutionSep 23 2003This paper concerns the generation and evolution of the cosmological (large-scale $\sim Mpc$) magnetic fields in an inflationary universe. The universe during inflation is represented by de Sitter space-time. We started with the Maxwell equations in spatially ... More

Regularity problem for the nematic LCD system with Q-tensor in $\mathbb R^3$Aug 26 2016We study the regularity problem of a nematic liquid crystal model with local configuration represented by Q-tensor in three dimensions. It was an open question whether the classical Prodi-Serrin condition implies regularity for this model. Applying a ... More

Regularity criterion and energy conservation for the supercritical Quasi-Geostrophic equationMay 09 2015Jul 12 2016This paper studies the regularity and energy conservation problems for the 2D supercritical quasi-geostrophic (SQG) equation. We apply an approach of splitting the dissipation wavenumber to obtain a new regularity condition which is weaker than all the ... More

Existence of regular solutions to the full Liquid Crystal SystemSep 02 2013We study the general Ericksen-Leslie system with non-constant density, which describes the flow of nematic liquid crystal. In particular the model investigated here is associated with Parodi's relation. We prove that: in two dimension, the solutions are ... More

A positive solution to a conjecture of A. Katok for diffeomorphism caseJun 10 2008In this paper, using Pesin theory and Liao theory, we give a positive solution to a conjecture of A. Katok.

On $\mathrm{C}^1$-class local diffeomorphisms whose periodic points are nonuniformly expandingJun 11 2012Using a sifting-shadowing combination, we prove in this paper that an arbitrary $\mathrm{C}^1$-class local diffeomorphism $f$ of a closed manifold $M^n$ is uniformly expanding on the closure $\mathrm{Cl}_{M^n}(\mathrm{Per}(f))$ of its periodic point set ... More

Time-preserving structural stability of hyperbolic differential dynamics with noncompact phase spacesMay 17 2008In this paper, we study the structural stability of hyperbolic differential systems on Euclidean spaces using Liao theory.

The Grothendieck Construction and Gradings for Enriched CategoriesJul 01 2009The Grothendieck construction is a process to form a single category from a diagram of small categories. In this paper, we extend the definition of the Grothendieck construction to diagrams of small categories enriched over a symmetric monoidal category ... More

On chaotic minimal center of attraction of a Lagrange stable motion for topological semi flowsJul 02 2015Jul 09 2015In this paper, we study the chaotic dynamics of a minimal center of attraction of a Lagrange stable motion for semi flows.

Antiferromagnetic order and spin dynamics in iron-based superconductorsMar 08 2015Jun 18 2015High-transition temperature (high-$T_c$) superconductivity in the iron pnictides/chalcogenides emerges from the suppression of the static antiferromagnetic order in their parent compounds, similar to copper oxides superconductors. This raises a fundamental ... More

Intensity Distribution and Luminosity Function of the Swift Gamma-Ray BurstsDec 24 2008Apr 23 2009Using the sample of long Gamma-ray bursts (GRBs) detected by Swift-BAT before June 2007, we measure the cumulative distribution of the peak photon fluxes (log N - log P) of the Swift bursts. Compared with the BATSE sample, we find that the two distributions ... More

A Positive Mass Theorem for Spaces with Asymptotic SUSY CompactificationAug 26 2003We prove a positive mass theorem for spaces which asymptotically approach a flat Euclidean space times a Calabi-Yau manifold (or any special honolomy manifold except the quaternionic K\"ahler). This is motivated by the very recent work of Hertog-Horowitz-Maeda. ... More

A criterion of simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matricesNov 09 2011In this paper, we consider the simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices.

Eta Invariants for Even Dimensional ManifoldsOct 13 2011In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to $K^1$ representatives on even dimensional manifolds, ... More

A Gel'fand-type spectral radius formula and stability of linear constrained switching systemsJul 01 2011Using ergodic theory, in this paper we present a Gel'fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup $\bS^+$ restricted to a subset that need ... More

The finite-step realizability of the joint spectral radius of a pair of $d\times d$ matrices one of which being rank-oneJun 05 2011We study the finite-step realizability of the joint/generalized spectral radius of a pair of real $d\times d$ matrices, one of which has rank 1. Then we prove that there always exists a finite-length word for which there holds the spectral finiteness ... More

Lower order tensors in non-Kähler geometry and non-Kähler geometric flowMar 21 2015May 31 2016In recent years, Streets and Tian introduced a series of curvature flows to study non-K\"{a}hler geometry. In this paper, we study how to construct second order curvature flows in a uniform way, under some natural assumptions which holds in Streets and ... More

Gluon Radiation of an Expanding Color Skyrmion in the Quark-Gluon PlasmaApr 02 2007The density of states and energy spectrum of the gluon radiation are calculated for the color current of an expanding hydrodynamic skyrmion in the quark gluon plasma with a semiclassical method. Results are compared with those in literatures.

Ill-posedness of the incompressible magneto-hydrodynamics system in $\dot{B}_{\infty,\infty}^{-1}$Nov 16 2012Jul 25 2014We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed in the largest scaling invariant space $\dot{B}_{\infty,\infty}^{-1}$. The construction method of initial data used in this paper is different from ... More

Dynamics of Bohr almost periodic motions of topological abelian semigroupsJun 09 2016We study the topological and ergodic dynamics of Bohr almost periodic motions of a topological abelian semigroup acting continuously on a compact metric space.

A New Class of Backward Stochastic Partial Differential Equations with Jumps and ApplicationsMay 04 2011We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion coefficients. ... More

Heavy traffic limit theorems for a queue with Poisson ON/OFF long-range dependent sources and general service time distributionMay 06 2011In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service times) can be generally ... More

Commutative-like Encryption: A New Characterization of ElGamalNov 16 2010Commutative encryption is a useful but rather strict notion in cryptography. In this paper, we deny a loose variation of commutative encryption-commutative-like encryption and give an example: the generalization of ElGamal scheme. The application of the ... More

Viewing the Welch bound inequality from the kernel trick viewpointMar 24 2014Apr 02 2014This brief note views to the Welch bound inequality using the idea of the kernel trick from the machine learning research area. From this angle, some novel insights of the inequality are obtained.

Neutrino in Astrophysics and CosmologySep 23 2003At first we introduce the Neutrino in the standard Model, then the Dirac and Majorana Masses. After introducing the See-Saw Mechanism, we discuss the neutrino oscillations and the neutrino in astrophysics and cosmology. We finish this paper with a brief ... More

Criterion for quasi-anosovian diffeomorphisms of closed manifoldsApr 08 2014Quasi-Anosov diffeomorphism is a kind of important dynamical system due to R. Mane 1970s. In this paper, we present a criterion for such dynamics using ergodic theory.

Quantified separably injective spacesFeb 10 2014Apr 28 2016Let $X$, $Y$ be two Banach spaces. Let $\varepsilon\geq 0$. A mapping $f: X\rightarrow Y$ is said to be a standard $\varepsilon-$ isometry if $f(0)=0$ and $|\|f(x)-f(y)\|-\|x-y\||\leq \varepsilon$. In this paper we first show that if $Y^*$ has the point ... More

Asymptotic Joint Distribution of Extreme Sample Eigenvalues and Eigenvectors in the Spiked Population ModelApr 22 2013May 03 2013In this paper, we consider a data matrix $X_N\in\mathbb{R}^{N\times p}$ where all the rows are i.i.d. samples in $\mathbb{R}^p$ of mean zero and covariance matrix $\Sigma\in\mathbb{R}^{p\times p}$. Here the population matrix $\Sigma$ is of finite rank ... More

Approximation to multifractional Riemann-Liouville Brownian sheetDec 08 2012Dec 25 2012In this paper, we first introduce multifrational Riemann-Liouville Brownian sheets. Then, we show a result of approximation in law of the multifractional Riemann-Liouville Brownian sheet. The construction of these approximations is based on a sequence ... More

Convergence in law to operator fractional Brownian motionsDec 31 2011In this paper, we provide two approximations in law of operator fractional Brownian motions. One is constructed by Poisson processes, and the other generalizes a result of Taqqu (1975).

$L^p(Ω)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous DriftApr 09 2014We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$-difference of SDEs using the norm of the difference of coefficients, where the discontinuous ... More

Continuous dependence for $H^{2}$ critical nonlinear Schrödinger equations in high dimensionsMar 31 2012The global existence of solutions in $H^{2}$ is well known for $H^{2}$ critical nonlinear Schr\"{o}dinger equations with small initial data in high dimensions $d\geq8$. However, even though the solution is constructed by a fixed-point technique, continuous ... More

Maximum principle and one-sign solutions for the elliptic $p$-LaplacianJul 28 2012In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.

Eigenvalue, bifurcation, existence and nonexistence of solutions for Monge-Ampère equationsJul 27 2012In this paper we study the following eigenvalue boundary value problem for Monge-Amp\`{e}re equations: {equation} \{{array}{l} \det(D^2u)=\lambda^N f(-u)\,\, \text{in}\,\, \Omega, u=0,\,\text{on}\,\, \partial \Omega. {array}. {equation} We establish the ... More

Unified Systems of FB-SPDEs/FB-SDEs with Jumps/Skew Reflections and Stochastic Differential GamesJun 15 2015Sep 14 2015We study four systems and their interactions. First, we formulate a unified system of coupled forward-backward stochastic partial differential equations (FB-SPDEs) with Levy jumps, whose drift, diffusion, and jump coefficients may involve partial differential ... More

Asymptotics of orthogonal polynomials and the Painlevé transcendentsAug 16 2016Sep 14 2016In this survey, we review asymptotic results of some orthogonal polynomials which are relate to the Painlev\'e transcendents. They are obtained by applying Deift-Zhou's nonlinear steepest descent method for Riemann-Hilbert problems. In the last part of ... More

On the Homology of Configuration Spaces Associated to Centers of MassApr 01 2010The aim of this paper is to make sample computations with the Salvetti complex of the "center of mass" arrangement introduced in [arXiv:math/0611732] by Cohen and Kamiyama. We compute the homology of the Salvetti complex of these arrangements with coefficients ... More

Discriminative Embeddings of Latent Variable Models for Structured DataMar 17 2016Sep 26 2016Kernel classifiers and regressors designed for structured data, such as sequences, trees and graphs, have significantly advanced a number of interdisciplinary areas such as computational biology and drug design. Typically, kernels are designed beforehand ... More

The formulas of coefficients of sum and product of p-adic integers with applications to Witt vectorsJul 06 2010The explicit formulas of operations, in particular addition and multiplication, of $p $-adic integers are presented. As applications of the results, at first the explicit formulas of operations of Witt vectors with coefficients in $\mathbb{F}_{2}$ are ... More

Numerical modeling of a high power terahertz source at ShanghaiJul 28 2011On the basis of an energy-recovery linac, a terahertz (THz) source with kilowatts average power is proposed in Shanghai, which will serve as an effective tool in material and biological sciences. In this paper, the physical design of two free electron ... More

The Intersection R-Torsion for Finite ConeOct 22 2014Oct 23 2014We prove a formula for the intersection R-torsion of a finite cone and use it to introduce a family of spectral invariants which is closely related to Cheeger's half torsion.

Real embeddings and the Atiyah-Patodi-Singer index theorem for Dirac operatorsMar 25 1999We present the details of our embedding proof of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary.

Technical Report: Observability of a Linear System under Sparsity ConstraintsApr 13 2012Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain sufficient ... More

Weighted Superimposed Codes and Constrained Integer Compressed SensingJun 16 2008We introduce a new family of codes, termed weighted superimposed codes (WSCs). This family generalizes the class of Euclidean superimposed codes (ESCs), used in multiuser identification systems. WSCs allow for discriminating all bounded, integer-valued ... More

A Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spacesApr 09 2013In this paper we prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, our result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a smaller ball ... More

Hybrid Precoding for Physical Layer MulticastingNov 20 2015This work investigates the problem of downlink transmit precoding for physical layer multicasting with a limited number of radio-frequency (RF) chains. To tackle the RF hardware constraint, we consider a hybrid precoder that is partitioned into a high-dimensional ... More