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Supersymmetric microring laser arraysFeb 08 2019Coherent combination of emission power from an array of coupled semiconductor lasers operating on the same chip is of fundamental and technological importance. In general, the nonlinear competition among the array supermodes can entail incoherence and ... More

Generalized r-matrix structure and algebro-geometric solution for integrable systemsOct 17 2002The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized ... More

Market Liquidity and Convexity of Order Book (Evidence From China)Nov 09 2012Market liquidity plays a vital role in the field of market micro-structure, because it is the vigor of the financial market. This paper uses a variable called convexity to measure the potential liquidity provided by order-book. Based on the high-frequency ... More

Rotational solutions of prescribed period of Hamiltonian systems on $\R^{2n-k}\ts T^k$Mar 13 2015In this paper, we consider Hamiltonian systems on $\R^{2n-k}\ts T^k$. Multiple rotational solutions are obtained.

Outage Effective Capacity of Buffer-Aided Diamond Relay Systems Using HARQ with Incremental RedundancyNov 22 2016In this paper, transmission over buffer-aided diamond relay systems under statistical quality of service (QoS) constraints is studied. The statistical QoS constraints are imposed as limitations on delay violation probabilities. In the absence of channel ... More

Effective Capacity of Buffer-Aided Full-Duplex Relay Systems with Selection RelayingOct 13 2015In this work, the achievable rate of three-node relay systems with selection relaying under statistical delay constraints, imposed on the limitations of the maximum end-to-end delay violation probabilities, is investigated. It is assumed that there are ... More

On the temporal decay of solutions to the two-dimensional nematic liquid crystal flowsSep 30 2014We consider the temporal decay estimates for weak solutions to the two-dimensional nematic liquid crystal flows, and we show that the energy norm of a global weak solution has non-uniform decay \begin{align*} \|u(t)\|_{L^{2}}+\|\nabla d(t)\|_{L^{2}}\rightarrow ... More

Uniqueness for Measure-Valued Equations of Nonlinear Filtering for Stochastic Dynamical Systems with Lévy NoisesJul 25 2017Jan 03 2018In the article, Zakai and Kushner-Stratonovich equations of the nonlinear filtering problem for a non-Gaussian signal-observation system are considered. Moreover, we prove that under some general assumption, the Zakai equation has pathwise uniqueness ... More

New SVD based initialization strategy for Non-negative Matrix FactorizationOct 10 2014There are two problems need to be dealt with for Non-negative Matrix Factorization (NMF): choose a suitable rank of the factorization and provide a good initialization method for NMF algorithms. This paper aims to solve these two problems using Singular ... More

On existence of the incompressible Navier-Stokes equation and the Euler equationJun 15 2017In this paper, we suggest a possible series form solution to the Navier-Stokes equation and the Euler equation. With the initial velocity vector known, a series form solution for the velocity vector and pressure can be calculated. We admit that the convergence ... More

Multiple Rotation Type Solutions for Hamiltonian Systems on $T^\ell\times\mathbb{R}^{2n-\ell}$Mar 21 2010This paper deals with multiplicity of rotation type solutions for Hamiltonian systems on $T^\ell\times \mathbb{R}^{2n-\ell}$. It is proved that, for every spatially periodic Hamiltonian system, i.e., the case $\ell=n$, there exist at least $n+1$ geometrically ... More

Gevrey analyticity of solutions to the 3D nematic liquid crystal flows in critical Besov spaceDec 04 2015We show that the solution to the Cauchy problem of the 3D nematic liquid crystal flows, with initial data belongs to a critical Besov space, belongs to a Gevrey class. More precisely, it is proved that for any $(u_{0},d_{0} - \overline{d}_{0}) \in \dot{B}^{\frac{3}{p}-1}_{p,1} ... More

Effective Filtering for Multiscale Stochastic Dynamical Systems driven by Lévy processesOct 23 2018Nov 07 2018In the paper, we consider multiscale stochastic dynamical systems driven by L\'evy processes. Firstly, it is proved that these systems can be approximated by low-dimensional systems on random invariant manifolds. Secondly, we establish that nonlinear ... More

Negative order MKdV hierarchy and a new integrable Neumann-like systemJan 31 2002The purpose of this paper is to develop the negative order MKdV hierarchy and to present a new related integrable Neumann-like Hamiltonian flow from the view point of inverse recursion operator and constraint method. The whole MKdV hierarchy both positive ... More

Constructing non-equilibrium statistical ensemble formalism based on SubdynamicsSep 13 2007In this work, we present a general non-equilibrium ensemble formalism based on the subdynamic equation (SKE). The constructing procedure is to use a similarity transformation between Gibbsian ensemble formalism and the non-equilibrium ensemble formalism. ... More

Space-time derivative estimates of the Kock-Tataru solutions to the nematic liquid crystal system in Besov spacesJun 18 2014In recent paper \cite{DW1} (Y. Du and K. Wang, Space-time regularity of the Kock $\&$ Tataru solutions to the liquid crystal equations, SIAM J. Math. Anal., \textbf{45}(6), 3838--3853.), the authors proved that the global-in-time Koch-Tataru type solution ... More

Multiple Forced rotations for the N-pendulum EquationMar 13 2015In this paper, we consider the planar forced N-pendulum equation. Multiple rotational solutions are obtained.

Convergence of Nonlinear Filtering for Stochastic Dynamical Systems with Lévy NoisesJul 25 2017Sep 06 2018We consider the nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. Firstly, we prove that the dimension for the signal system could be reduced. Secondly, convergence of the corresponding nonlinear ... More

Topological complexity, minimality and systems of order two on torusApr 10 2015Apr 14 2015The dynamical system on T^2 which is a group extension over an irrational rotation on T^1 is investigated. The criterion when the extension is minimal, a system of order 2 and when the maximal equicontinuous factor is the irrational rotation is given. ... More

Condensation and evolution of space-time networkSep 29 2008In this work, we try to propose, in a novel way using the Bose and Fermi quantum network approach, a framework studying condensation and evolution of space time network described by the Loop quantum gravity. Considering quantum network connectivity features ... More

Coal Enterprise Management and Asynchronism of ReturnNov 09 2012For researching the association between coal enterprise management and return in financial market, this paper applies the method of time difference relevance and PageRank method to seek the leader-index of a stock set containing 21 coal enterprises in ... More

Convex Polytopes for the Central Degeneration of the Affine GrassmannianApr 28 2016Aug 30 2016We study the central degeneration (the degeneration that shows up in local models of Shimura varieties and Gaitsgory's central sheaves) of semi-infinite orbits, MV Cycles, and Iwahori orbits in the affine Grassmannian of type A, by considering their moment ... More

Exponential ergodicity for SDEs with jumps and non-Lipschitz coefficientsJul 11 2012In this paper we show irreducibility and the strong Feller property for transition probabilities of stochastic differential equations with jumps and monotone coefficients. Thus, exponential ergodicity and the spectral gap for the corresponding transition ... More

Noncrossing Ordinal ClassificationMay 13 2015Dec 21 2015Ordinal data are often seen in real applications. Regular multicategory classification methods are not designed for this data type and a more proper treatment is needed. We consider a framework of ordinal classification which pools the results from binary ... More

Multi-scale Analysis for Rosseland Equation with Small Periodic Oscillating CoefficientsMay 27 2012Rosseland equation is one of the most popular models of the conduction-radiation coupled heat transfer in the thermal protection system. The well-posedness, the corresponding mathematical theory and the Multi-scale analysis method for the Rosseland-type ... More

An argumentation system for reasoning with conflict-minimal paraconsistent ALCApr 30 2014The semantic web is an open and distributed environment in which it is hard to guarantee consistency of knowledge and information. Under the standard two-valued semantics everything is entailed if knowledge and information is inconsistent. The semantics ... More

N-soliton solutions of an integrable equation studied by QiaoJan 30 2011Feb 28 2011In this paper, we studied N-soliton solutions of an integrable equation.

Rate Region of the Vector Gaussian CEO Problem with the Trace Distortion ConstraintJan 24 2014Feb 20 2014We establish a new extremal inequality, which is further leveraged to give a complete characterization of the rate region of the vector Gaussian CEO problem with the trace distortion constraint. The proof of this extremal inequality hinges on a careful ... More

Multi-component generalization of Camassa-Holm equationOct 01 2013May 10 2015In this paper, we propose a multi-component system of Camassa-Holm equation, denoted by CH($N$,$H$) with 2N components and an arbitrary smooth function $H$. This system is shown to admit Lax pair and infinitely many conservation laws. We particularly ... More

Fourier Coefficients of Theta Functions at Cusps other than InfinitySep 30 2014In this paper we study the Fourier coefficients of theta functions attached to Dirichlet characters at cusps other than infinity. The method is based on expressing them in terms of explicit elements of the adelic Schwartz space and studying the action ... More

Weak Convergence of Equity Derivatives Pricing with Default RiskApr 10 2015This paper presents a discrete--time equity derivatives pricing model with default risk in a no--arbitrage framework. Using the equity--credit reduced form approach where default intensity mainly depends on the firm's equity value, we deduce the Arrow--Debreu ... More

Theoretical Analysis of Nonparametric Filament EstimationOct 24 2015This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density $f$. Points on the filament are considered as local extrema of the density when traversing the support of $f$ along the integral ... More

A regularity criterion for the solution of the nematic liquid crystal flows in terms of $\dot{B}^{-1}_{\infty,\infty}$-normNov 30 2012In this paper, we investigate regularity criterion for the solution of the nematic liquid crystal flows in dimension three and two. We prove the solution $(u,d)$ is smooth up to time $T$ provided that there exists a positive constant $\varepsilon_{0}>0$ ... More

Divergence form nonlinear nonsmooth elliptic equations with locally arbitrary growth conditions and nonlinear maximal regularityMay 11 2012This is a simplification of our prior work on the existence theory for the Rosseland-type equations. Inspired by the Rosseland equation in the conduction-radiation coupled heat transfer, we use the locally arbitrary growth conditions instead of the common ... More

General tree-level amplitudes by factorization limitsOct 19 2014Jun 20 2015To find boundary contributions is a rather difficult problem when applying the BCFW recursion relation. In this paper, we propose an approach to bypass this problem by calculating general tree amplitudes that contain no polynomial using factorization ... More

QCD Pomeron at Linear CollidersDec 21 2000Feb 11 2001Recent developments in theory on the calculation of \gamma^* \gamma^* reaction at high energies, in the aim of detecting the BFKL Pomeron signals, are briefly introduced. The importance of the NLO QCD corrections to the Photon Impact Factor in the game ... More

Vehicle Powertrain Connected Route Optimization for Conventional, Hybrid and Plug-in Electric VehiclesDec 05 2016Most navigation systems use data from satellites to provide drivers with the shortest-distance, shortest-time or highway-preferred paths. However, when the routing decisions are made for advanced vehicles, there are other factors affecting cost, such ... More

A General Theory for Large-Scale Curve Time Series via Functional Stability MeasureDec 18 2018Dec 20 2018Modelling a large bundle of curves arises in a broad spectrum of real applications. However, existing literature relies primarily on the critical assumption of independent curve observations. In this paper, we provide a general theory for large-scale ... More

On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spacesJul 25 2017Jan 03 2018Based on a recent result on characterising the path-independence of the Girsanov transformation for non-Lipschnitz stochastic differential equations (SDEs) with jumps on $R^d$, in this paper, we extend our consideration of characterising the path-indpendent ... More

Strong Approximation of Stochastic Allen-Cahn Equation with White NoiseJan 29 2018Jun 19 2018We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an additive space-time ... More

Negative order KdV equation with both solitons and kink wave solutionsJan 08 2011Apr 13 2011In this paper, we report an interesting integrable equation that has both solitons and kink solutions. The integrable equation we study is $(\frac{-u_{xx}}{u})_{t}=2uu_{x}$, which actually comes from the negative KdV hierarchy and could be transformed ... More

Holographic Equipartition and Gravitational CollapseJan 07 2014It is argued in the literature that gravity is an emergent phenomenon and is a statistical tendency for a gravitational system to attain the maximal entropy state which maintains the holographic principle. In this paper, we show that gravitational collapse ... More

Scheduling in Wireless Networks under Uncertainties: A Greedy Primal-Dual ApproachJan 13 2010Jun 12 2010This paper proposes a dynamic primal-dual type algorithm to solve the optimal scheduling problem in wireless networks subject to uncertain parameters, which are generated by stochastic network processes such as random packet arrivals, channel fading, ... More

A new two-component integrable system with peakon solutionsNov 25 2012May 10 2015A new two-component system with cubic nonlinearity and linear dispersion: \begin{eqnarray*} \left\{\begin{array}{l} m_t=bu_{x}+\frac{1}{2}[m(uv-u_xv_x)]_x-\frac{1}{2}m(uv_x-u_xv), \\ n_t=bv_{x}+\frac{1}{2}[ n(uv-u_xv_x)]_x+\frac{1}{2} n(uv_x-u_xv), \\m=u-u_{xx},~~ ... More

Nucleon electromagnetic form factors in a quark-gluon core modelMay 21 2009Nov 23 2009We study the nucleon electromagnetic form factors in a quark-gluon core model framework, which can be viewed as an extension of the Isgur-Karl model of baryons. Using this picture we derive nucleon electromagnetic dipole form factors at low Q^2 and the ... More

A Statistical Approach to Set Classification by Feature Selection with Applications to Classification of Histopathology ImagesFeb 19 2014Set classification problems arise when classification tasks are based on sets of observations as opposed to individual observations. In set classification, a classification rule is trained with $N$ sets of observations, where each set is labeled with ... More

A Beale--Kato--Majda criterion for the 3-D Compressible Nematic Liquid Crystal Flows with VacuumNov 29 2011In this paper, we prove a Beale--Kato--Majda blow-up criterion in terms of the gradient of the velocity only for the strong solution to the 3-D compressible nematic liquid crystal flows with nonnegative initial densities. More precisely, the strong solution ... More

A Uniform Description of the States Recently Observed at B-factoriesSep 26 2007May 17 2008The newly found states Y(4260), Y(4361), Y(4664) and Z$^\pm$(4430) stir broad interest in the study of spectroscopy in a typical charmonium scale. The Y(4260) which was observed earlier has been interpreted as hybrid, molecular state, and baryonium, etc. ... More

The Status of Charmonium Production in Photon-Photon CollisionsNov 30 2001The status of Charmonium production in photon-photon collisions is briefly reviewed. I would like to mention that although the preliminary data were obtained in experiment, the theoretical investigation is not in a compatible status.

A New Approach for Analytic Amplitude CalculationsFeb 16 2003Mar 28 2003We present a method for symbolic calculation of Feynman amplitudes for processes involving both massless and massive fermions. With this approach fermion strings in a specific amplitude can be easily evaluated and expressed as basic Lorentz scalars. The ... More

Double J/ψProduction at Photon CollidersApr 30 2001Jul 11 2001The double J/\psi(DJ) production in direct photon-photon collision is investigated. It is found that the J/\psi production rate in this process is of the same order of magnitude as those of previously discussed ones, which hints the dominant J/\psi inclusive ... More

Persistence Properties and Unique Continuation for a Dispersionless Two-Component Camassa-Holm System with Peakon and Weak Kink SolutionsNov 10 2015In this paper, we study the persistence properties and unique continuation for a dispersionless two-component system with peakon and weak kink solutions. These properties guarantee strong solutions of the two-component system decay at infinity in the ... More

Wong--Zakai Approximations of Stochastic Allen-Cahn EquationOct 26 2017Jun 19 2018We establish a unconditional and optimal strong convergence rate of Wong--Zakai type approximations in Banach space norm for a parabolic stochastic partial differential equation with monotone drift, including the stochastic Allen--Cahn equation, driven ... More

Flexible High-dimensional Classification Machines and Their Asymptotic PropertiesOct 11 2013Classification is an important topic in statistics and machine learning with great potential in many real applications. In this paper, we investigate two popular large margin classification methods, Support Vector Machine (SVM) and Distance Weighted Discrimination ... More

Distance-weighted Support Vector MachineOct 11 2013Oct 08 2015A novel linear classification method that possesses the merits of both the Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is proposed in this article. The proposed Distance-weighted Support Vector Machine method can be viewed ... More

Light tails and the Hermitian dual polar graphsNov 17 2015Juri\'{s}i\v{c} et al. conjectured that if a distance-regular graph $\Gamma$ with diameter $D$ at least three has a light tail, then one of the following holds: 1.$a_1 =0$; 2.$\Gamma$ is an antipodal cover of diameter three; 3.$\Gamma$ is tight; 4.$\Gamma$ ... More

Distance-regular graphs with valency k having smallest eigenvalue at most -k/2Jul 17 2015Jul 22 2015In this paper, we study the non-bipartite distance-regular graphs with valency k and having a smallest eigenvalue at most -k/2.

Distributed Throughput-optimal Scheduling in Ad Hoc Wireless NetworksFeb 07 2011In this paper, we propose a distributed throughput-optimal ad hoc wireless network scheduling algorithm, which is motivated by the celebrated simplex algorithm for solving linear programming (LP) problems. The scheduler stores a sparse set of basic schedules, ... More

Mass-Dependent Baryon Acoustic Oscillation Signal and Halo BiasFeb 07 2013Apr 11 2013We characterize the baryon acoustic oscillations (BAO) feature in halo two-point statistics using N-body simulations. We find that nonlinear damping of the BAO signal is less severe for halos in the mass range we investigate than for dark matter. The ... More

Stationary Measures for Stochastic Differential Equations with JumpsSep 04 2012Feb 17 2014In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two special cases, ... More

Extrema of locally stationary Gaussian fields on growing manifoldsOct 23 2015We consider a class of non-homogeneous, continuous, centered Gaussian random fields $\{X_h(t), t \in {\cal M}_h;\,0 < h \le 1\}$ where ${\cal M}_h$ denotes a rescaled smooth manifold, i.e. ${\cal M}_h = \frac{1}{h} {\cal M},$ and study the limit behavior ... More

One Explanation for the Exotic State Y(4260)Oct 18 2005Jun 21 2006In this Letter we interpret the Y(4260), a state recently discovered by the BaBar Collaboration that has a mass within the range of conventional charmonium states, as having a molecular-state structure. In our scheme this molecular-like state is not constructed ... More

J/psi Pair Production at the TevatronJun 10 2002Jun 17 2002The double J/psi production in p\bar{p} collision is revisited. It is found that the J/\psi pair production rate at leading order with p_T > 4 GeV in conventional scheme is larger than the rate derived from color-octet mechanism by a factor of five. As ... More

Univalent harmonic mappings with integer or half-integer coefficientsJul 12 2012Let ${\mathcal S}$ denote the set of all univalent analytic functions $f(z)=z+\sum_{n=2}^{\infty}a_n z^n$ on the unit disk $|z|<1$. In 1946 B. Friedman found that the set $\mathcal S$ of those functions which have integer coefficients consists of only ... More

A new characterization of the dual polar graphsNov 16 2017Nov 17 2017In this paper we give a new characterization of the dual polar graphs, extending the work of Brouwer and Wilbrink on regular near polygons. Also as a consequence of our characterization we confirm a conjecture of the authors on non-bipartite distance-regular ... More

Linear algebraic analogues of the graph isomorphism problem and the Erdős-Rényi modelAug 15 2017Oct 01 2017A classical difficult isomorphism testing problem is to test isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. It is known that this problem can be reduced to solving the alternating matrix space isometry problem ... More

Mean Li-Yorke chaos along some good sequencesJul 19 2017If a topological dynamical system $(X,T)$ has positive topological entropy, then it is multivariant mean Li-Yorke chaotic along a sequence $\{a_k\}_{k=1}^\infty$ of positive integers which is "good" for pointwise ergodic convergence with a mild condition; ... More

Fredholm Groupoids and Layer Potentials on Conical DomainsJul 14 2018We show that layer potential groupoids for conical domains constructed in an earlier paper (Carvalho-Qiao, Central European J. Math., 2013) are Fredholm groupoids, which enables us to deal with many analysis problems on singular spaces in a unified treatment. ... More

Greedy Maximal Scheduling in Wireless NetworksJul 27 2010In this paper we consider greedy scheduling algorithms in wireless networks, i.e., the schedules are computed by adding links greedily based on some priority vector. Two special cases are considered: 1) Longest Queue First (LQF) scheduling, where the ... More

Scheduling in Multi-hop Wireless Networks with PrioritiesJan 19 2009In this paper we consider prioritized maximal scheduling in multi-hop wireless networks, where the scheduler chooses a maximal independent set greedily according to a sequence specified by certain priorities. We show that if the probability distributions ... More

Mapping of dissipative particle dynamics in fluctuating hydrodynamics simulationsJan 15 2008Dissipative particle dynamics (DPD) is a novel particle method for mesoscale modeling of complex fluids. DPD particles are often thought to represent packets of real atoms, and the physical scale probed in DPD models are determined by the mapping of DPD ... More

Parton distribution of nucleon and nuclear EMC effect in a statistical modelJan 16 2016We study the parton distribution of nucleon and nuclear EMC effect in a statistical model. We find when we choose the parameters appropriately, the predictions given by pure statistical laws can fit the experimental data well in most range of $x$, this ... More

Representations of Rota-Baxter algebras and regular singular decompositionsMar 18 2016There is a Rota-Baxter algebra structure on the field $A=\mathbf{k}((t))$ with $ P$ being the projection map $A=\mathbf{k}[[t]]\oplus t^{-1}\mathbf{k}[t^{-1}]$ onto $ \mathbf{k}[[ t]]$. We study the representation theory and regular-singular decompositions ... More

Annular gap model for multi-wavelength pulsed emission from young and millisecond pulsarsOct 22 2012The multi-wavelength pulsed emission from young pulsars and millisecond pulsars can be well modeled with the single-pole 3-dimension annular gap and core gap model. To distinguish our single magnetic pole model from two-pole models (e.g. outer gap model ... More

An integrable (2+1)-dimensional Camassa-Holm hierarchy with peakon solutionsJul 28 2014Jul 31 2014In this letter, we propose a (2+1)-dimensional generalized Camassa-Holm (2dgCH) hierarchy with both quadratic and cubic nonlinearity. The Lax representation and peakon solutions for the 2dgCH system are derived.

Structural Phase Transitions and Vertical Mode Spectra in 2D Finite Plasma CrystalsJun 30 2008A numerical simulation utilizing a box_tree code is used to investigate the structure and vertical mode spectrum of finite two-dimensional (2D) plasma crystals. The overall structural symmetry of the system is examined for various Debye lengths and a ... More

Topological equivalence for discontinuous random dynamical systems and applicationsOct 02 2012After defining non-Gaussian L\'evy processes for two-sided time, stochastic differential equations with such L\'evy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological ... More

Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and ApplicationsApr 23 2012Feb 17 2014Motivated by studying stochastic systems with non-Gaussian L\'evy noise, spectral properties for linear discontinuous cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem is proved ... More

Dynamical evolutin of quintessence dark energy in collapsing dark matter halosJun 18 2009In this paper, we analyze the dynamical evolution of quintessence dark energy induced by the collapse of dark matter halos. Different from other previous studies, we develop a numerical strategy which allows us to calculate the dark energy evolution for ... More

Charm-sea Contribution to High-p_T ψProduction at the Fermilab TevatronFeb 25 2002Mar 26 2003The direct production of $J/\psi(\psi')$ at large transverse momentum, $p_T \gg M_{J/\psi}$, at the Fermilab Tevatron is revisited. It is found that the sea-quark initiated processes dominate in the high-$p_T$ region within the framework of color-singlet ... More

Learning Confidence Sets using Support Vector MachinesSep 28 2018The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of the two classes, ... More

Divergence form nonlinear nonsmooth parabolic equations with locally arbitrary growth conditions and nonlinear maximal regularityMay 15 2012This is a generalization of our prior work on the compact fixed point theory for the elliptic Rosseland-type equations. We obtain the maximum principle without the technical Steklov techniques. Inspired by the Rosseland equation in the conduction-radiation ... More

Sparse Fisher's Linear Discriminant Analysis for Partially Labeled DataSep 17 2015Classification is an important tool with many useful applications. Among the many classification methods, Fisher's Linear Discriminant Analysis (LDA) is a traditional model-based approach which makes use of the covariance information. However, in the ... More

Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spacesAug 09 2015Aug 16 2015In \cite{GW12} (Y. Guo, Y. Wang, Decay of dissipative equations and negative Sobolev spaces, Commun. Partial Differ. Equ. 37 (2012) 2165--2208), Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions ... More

DeepWriter: A Multi-Stream Deep CNN for Text-independent Writer IdentificationJun 21 2016Aug 03 2016Text-independent writer identification is challenging due to the huge variation of written contents and the ambiguous written styles of different writers. This paper proposes DeepWriter, a deep multi-stream CNN to learn deep powerful representation for ... More

Study of the Fracturing Behavior of Thermoset Polymer Nanocomposites via Cohesive Zone ModelingJul 21 2018Sep 03 2018This work proposes an investigation of the fracturing behavior of polymer nanocomposites. Towards this end, the study leverages the analysis of a large bulk of fracture tests from the literature with the goal of critically investigating the effects of ... More

On rank-critical matrix spacesFeb 28 2017Mar 01 2017A matrix space of size $m\times n$ is a linear subspace of the linear space of $m\times n$ matrices over a field $\mathbb{F}$. The rank of a matrix space is defined as the maximal rank over matrices in this space. A matrix space $\mathcal{A}$ is called ... More

A Theory of Selective PredictionFeb 12 2019We consider a model of selective prediction, where the prediction algorithm is given a data sequence in an online fashion and asked to predict a pre-specified statistic of the upcoming data points. The algorithm is allowed to choose when to make the prediction ... More

Error Assessment in Modeling with Fractal Brownian MotionsOct 29 2013To model a given time series $F(t)$ with fractal Brownian motions (fBms), it is necessary to have appropriate error assessment for related quantities. Usually the fractal dimension $D$ is derived from the Hurst exponent $H$ via the relation $D=2-H$, and ... More

On Negative Order KdV EquationsJul 31 2011Aug 25 2011In this paper, based on the regular KdV system, we study negative order KdV (NKdV) equations about their Hamiltonian structures, Lax pairs, infinitely many conservation laws, and explicit multi-soliton and multi-kink wave solutions thorough bilinear B\"{a}cklund ... More

Notes on Entropic Interpretation of GravityFeb 20 2014Some essential conceptual aspects that will fill some logical gaps of the frame to interpret the gravity as an entropic force was investigated, we focus on some crucial issues that didn't emphasized in Verlinde's original paper[arXiv:1001.0785]. This ... More

Maximal Scheduling in Wireless Networks with PrioritiesDec 02 2011We consider a general class of low complexity distributed scheduling algorithms in wireless networks, maximal scheduling with priorities, where a maximal set of transmitting links in each time slot are selected according to certain pre-specified static ... More

Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noiseJan 04 2012Feb 17 2014The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e., differential equations ... More

Concerning the searches for Higgs bosonsJun 30 2010Dec 29 2012The great successes achieved by the Standard Model(SM) lead us to believe the existence of the Higgs particle. On the other hand, there are many evidences indicate that some unknown dark matter particle must exist in our universe. To identify the Higgs ... More

Simulation studies of dark energy clustering induced by the formation of dark matter halosDec 19 2011In this paper, we present a simulation method within the two-component spherical collapse model to investigate dark energy perturbations associated with the formation of dark matter halos. The realistic mass accretion history of a dark matter halo taking ... More

Analyticity, Gevrey regularity and unique continuation for an integrable multi-component peakon system with an arbitrary polynomial functionNov 10 2015In this paper, we study the Cauchy problem for an integrable multi-component (2N-component) peakon system which is involved in an arbitrary polynomial function. Based on a generalized Ovsyannikov type theorem, we first prove the existence and uniqueness ... More

Global existence and propagation speed for a generalized Camassa-Holm model with both dissipation and dispersionNov 10 2015In this paper, we study a generalized Camassa-Holm (gCH) model with both dissipation and dispersion, which has (N + 1)-order nonlinearities and includes the following three integrable equations: the Camassa-Holm, the Degasperis-Procesi, and the Novikov ... More

Significance Analysis of High-Dimensional, Low-Sample Size Partially Labeled DataSep 21 2015Classification and clustering are both important topics in statistical learning. A natural question herein is whether predefined classes are really different from one another, or whether clusters are really there. Specifically, we may be interested in ... More

Algorithms based on *-algebras, and their applications to isomorphism of polynomials with one secret, group isomorphism, and polynomial identity testingAug 11 2017Feb 06 2019We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an invertible ... More

Sparse multivariate polynomial interpolation in the basis of Schubert polynomialsApr 15 2015Sep 29 2016Schubert polynomials were discovered by A. Lascoux and M. Sch\"utzenberger in the study of cohomology rings of flag manifolds in 1980's. These polynomials generalize Schur polynomials, and form a linear basis of multivariate polynomials. In 2003, Lenart ... More