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RUM: network Representation learning throUgh Multi-level structural information preservationOct 08 2017We have witnessed the discovery of many techniques for network representation learning in recent years, ranging from encoding the context in random walks to embedding the lower order connections, to finding latent space representations with auto-encoders. ... More

Hausdorff operators on the Sobolev spaces $W^{k,1}$Oct 29 2017Mar 07 2018This paper is served as a first contribution regarding the boundedness of Hausdorff operators on function spaces with smoothness. The sharp conditions are established for boundedness of Hausdorff operators on Sobolev spaces $W^{k,1}$. As applications, ... More

Sharp estimates of unimodular Fourier multipliers on Wiener amalgam spacesJul 02 2018Oct 16 2018We study the boundedness on the Wiener amalgam spaces $W^{p,q}_s$ of Fourier multipliers with symbols of the type $e^{i\mu(\xi)}$, for some real-valued functions $\mu(\xi)$ whose prototype is $|\xi|^{\beta}$ with $\beta\in (0,2]$. Under some suitable ... More

Unimodular multipliers on $α$-modulation spaces: A revisit with new method under weaker conditionsMar 16 2019By a new method derived from Nicola--Primo--Tabacco[24], we study the boundedness on $\alpha$-modulation spaces of unimodular multipliers with symbol $e^{i\mu(\xi)}$. Comparing with the previous results, the boundedness result is established for a larger ... More

An improvement on the relatively compactness criteriaApr 06 2019This paper is devoted to the study of the relatively compact sets in Banach function spaces, providing an important improvement of the known results. As an application, we take the final step in establishing a relative compactness criteria for function ... More

Spin torque nano-oscillators based on antiferromagnetic skyrmionsNov 07 2018Skyrmion-based spin torque nano-oscillators are potential next-generation microwave signal generators. However, ferromagnetic skyrmion-based spin torque nano-oscillators cannot reach high oscillation frequencies. In this work, we propose to use the circular ... More

Dynamics of the antiferromagnetic skyrmion induced by a magnetic anisotropy gradientAug 27 2018Oct 09 2018The dynamics of antiferromagnets is a current hot topic in condensed matter physics and spintronics. However, the dynamics of insulating antiferromagnets cannot be excited by an electric current, which is a method usually used to manipulate ferromagnetic ... More

Sharp embedding relations between Local Hardy and $α$-Modulation SpacesSep 17 2016We give the optimal embedding relations between local Hardy space and $\alpha$-modulation spaces, which extend the results for the embedding relations between local Hardy and modulation spaces obtained by Kobayashi, Miyachi and Tomita in [Studia Math. ... More

Hausdorff operators on modulation and Wiener amalgam spacesSep 24 2017We give the sharp conditions for boundedness of Hausdorff operators on certain modulation and Wiener amalgam spaces.

Inclusion relations between Modulation and Triebel-Lizorkin spacesSep 17 2016In this paper, we obtain the sharp conditions of the inclusion relations between modulation spaces $M_{p,q}^s$ and Triebel-Lizorkin spaces $F_{p,r}$ for $p\leq 1$, which greatly improve and extend the results for the embedding relations between local ... More

A stochastic variational approach to the viscous Camassa-Holm and Leray-alpha equationsAug 17 2015May 04 2016We derive the (d-dimensional) periodic incompressible and viscous Camassa-Holm equation as well as the Leray-alpha equations via a stochastic variational principle. We discuss the existence of solution for this equation in the space H1 using the probabilistic ... More

Sharp Weighted Convolution Inequalities and Some ApplicationsFeb 09 2016In this paper, the index groups for which the weighted Young's inequalities hold in both continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are characterized, we also ... More

Full Characterization of embedding relations between alpha modulation spacesJun 04 2016Jul 21 2016In this paper, we consider the embedding relations between any two $\alpha$% -modulation spaces. Based on an observation that the $\alpha$-modulation space with smaller $\alpha$ can be regarded as a corresponding $\alpha$% -modulation space with larger ... More

Characterization of inclusion relations between wiener amalgam and some classical spacesSep 17 2016Sep 27 2016In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces $B_{p,q}$ and Wiener amalgam spaces $W_{p,q}^s$. We also obtain the optimal inclusion relations between local hardy spaces $h^p$ and Wiener amalgam spaces ... More

Characterization of Some Properties on Weighted Modulation SpacesFeb 09 2016In this paper, some properties on weighted modulation and Wiener amalgam spaces are characterized by the corresponding properties on weighted Lebesgue spaces. As applications, sharp conditions for product inequalities, convolution inequalities and embedding ... More

LAMOST Spectroscopic Survey of the Galactic Anti-centre (LSS-GAC): target selection and the first release of value-added cataloguesDec 20 2014As a major component of the LAMOST Galactic surveys, the LAMOST Spectroscopic Survey of the Galactic Anti-centre (LSS-GAC) aims to survey a significant volume of the Galactic thin/thick discs and halo for a contiguous sky area of over 3,400 deg$^2$ centred ... More

Sharp Weighted Convolution Inequalities and Some ApplicationsFeb 09 2016Sep 06 2017In this paper, the index groups for which the weighted Young's inequalities hold in both continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are characterized, we also ... More

A New Splitting Method for Time-dependent Convection-dominated Diffusion ProblemsFeb 17 2013We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a convection problem ... More

The Navier-Stokes-$α$ equation via forward-backward stochastic differential systemsOct 28 2016In this paper, we use forward-backward stochastic differential systems to study the solution of two and d dimensional ($d\geq 3$) Navier-Stokes-$\alpha$ equation. For the two dimensional Navier-Stokes-$\alpha$ equation with space periodic boundary conditions, ... More

Strong Gravitational Lensing in the Einstein-Proca TheoryJun 29 2015Adopting the strong field limit approach, we investigate the strong gravitational lensing of a spherically symmetric spacetime in the Einstein-Proca theory. With the strong field limit coefficient, three observable quantities are obtained, which are the ... More

A Conditional Variational Framework for Dialog GenerationApr 30 2017Jul 06 2017Deep latent variable models have been shown to facilitate the response generation for open-domain dialog systems. However, these latent variables are highly randomized, leading to uncontrollable generated responses. In this paper, we propose a framework ... More

Object Specific Deep Learning Feature and Its Application to Face DetectionSep 06 2016We present a method for discovering and exploiting object specific deep learning features and use face detection as a case study. Motivated by the observation that certain convolutional channels of a Convolutional Neural Network (CNN) exhibit object specific ... More

Current-Induced Dynamics and Chaos of an Antiferromagnetic BimeronMay 22 2019Magnetic bimeron is a topologically non-trivial spin texture carrying an integer topological charge, which can be regarded as the counterpart of skyrmion in easy-plane magnets. The controllable creation and manipulation of bimerons are crucial for practical ... More

Single-shot realization of nonadiabatic holonomic gates with a superconducting Xmon qutritNov 15 2018Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. The original protocol of nonadiabatic holonomic one-qubit gates has been experimentally demonstrated ... More

A decade of skyrmionics: Writing, deleting, reading and processing magnetic skyrmions toward spintronic applicationsJun 11 2019Jun 12 2019The field of skyrmionics has been actively investigated across a wide range of topics during the last decade. In this topical review, we review and discuss key results and findings in skyrmionics since the first experimental observation of magnetic skyrmions ... More

A decade of skyrmionics: Writing, deleting, reading and processing magnetic skyrmions roward spintronic applicationsJun 11 2019The field of skyrmionics has been actively investigated across a wide range of topics during the last decade. In this topical review, we review and discuss key results and findings in skyrmionics since the first experimental observation of magnetic skyrmions ... More

Comparisons of Some Iterative Algorithms for Biot EquationsAug 29 2017In this paper, we aim at solving the Biot model under stabilized finite element discretizations. To solve the resulting generalized saddle point linear systems, some iterative methods are proposed and compared. In the first method, we apply the GMRES ... More

Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion ModelsDec 13 2012Oct 12 2013In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. ... More

Random Forest for Label RankingAug 27 2016Label ranking aims to learn a mapping from instances to rankings over a finite number of predefined labels. Random forest is a powerful and one of the most successfully general-purpose machine learning algorithms of modern times. In the literature, there ... More

Dataset for the First Evaluation on Chinese Machine Reading ComprehensionSep 25 2017Mar 15 2018Machine Reading Comprehension (MRC) has become enormously popular recently and has attracted a lot of attention. However, existing reading comprehension datasets are mostly in English. To add diversity in reading comprehension datasets, in this paper ... More

EKT: Exercise-aware Knowledge Tracing for Student Performance PredictionJun 07 2019For offering proactive services to students in intelligent education, one of the fundamental tasks is predicting their performance (e.g., scores) on future exercises, where it is necessary to track each student's knowledge acquisition during her exercising ... More

University-Industry-Government Relations in China: An emergent national system of innovationsDec 14 2010Since 1992, a new Chinese innovation system has been emerging in terms of university-industry-government relations. In recent years, science parks, incubators, and high-tech development zones have been provided with strong incentives. The commitment of ... More

Image Companding and Inverse Halftoning using Deep Convolutional Neural NetworksJul 01 2017Jul 21 2017In this paper, we introduce deep learning technology to tackle two traditional low-level image processing problems, companding and inverse halftoning. We make two main contributions. First, to the best knowledge of the authors, this is the first work ... More

Random Forest for Label RankingAug 27 2016Jun 16 2018Label ranking aims to learn a mapping from instances to rankings over a finite number of predefined labels. Random forest is a powerful and one of the most successful general-purpose machine learning algorithms of modern times. In this paper, we present ... More

Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion MethodMar 09 2010In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation ... More

Choice number of complete multipartite graphs $K_{3*3,2*(k-5),1*2}$ and $K_{4,3*2,2*(k-6),1*3}$Aug 14 2013A graph $G$ is called \emph{chromatic-choosable} if its choice number is equal to its chromatic number, namely $Ch(G)=\chi(G)$. Ohba has conjectured that every graph $G$ satisfying $|V(G)|\leq 2\chi(G)+1$ is chromatic-choosable. Since each $k$-chromatic ... More

Description of Brownian motion including both kinetic and hydrodynamic effectsDec 02 2017Feb 12 2018It is known that a full description of Brownian motion in the entire course of time should incorporate both kinetic and hydrodynamic effects, but a formula accounts for both effects has been established only in three dimension and only for the limiting ... More

KCAT: A Knowledge-Constraint Typing Annotation ToolJun 13 2019Fine-grained Entity Typing is a tough task which suffers from noise samples extracted from distant supervision. Thousands of manually annotated samples can achieve greater performance than millions of samples generated by the previous distant supervision ... More

On the dispersion management of fluorite whispering-gallery mode resonators for Kerr optical frequency comb generation in the telecom and mid-infrared rangeJan 10 2015Optical whispering gallery mode (WGM) resonators have been very attracting platforms for versatile Kerr frequency comb generations. We report a systematic study on the material dispersion of various optical materials that are capable of supporting quality ... More

The hard-disk fluid revisitedNov 02 2015May 21 2016The hard-disk model plays a role of touchstone for testing and developing the transport theory. By large scale molecular dynamics simulations of this model, three important autocorrelation functions, and as a result the corresponding transport coefficients, ... More

The LAMOST Stellar Parameter Pipeline at Peking University --- LSP3Dec 20 2014We introduce the LAMOST Stellar Parameter Pipeline at Peking University --- LSP3, developed and implemented for the determinations of radial velocity $V_{\rm r}$ and stellar atmospheric parameters (effective temperature $T_{\rm eff}$, surface gravity ... More

Relative Flux Calibration of the LAMOST Spectroscopic Survey of the Galactic Anti-centerDec 20 2014We have developed and implemented an iterative algorithm of flux calibration for the LAMOST Spectroscopic Survey of the Galactic anti-center (LSS-GAC). For a given LSS-GAC plate, the spectra are first processed with a set of nominal spectral response ... More

Generalized Pontryagin Maximum Principle in port-Hamiltonian Systems and ApplicationNov 18 2015Dec 31 2015Based on Pontryagin Maximum Principle (PMP), this paper establishes a generalized PMP aiming at control system with with extra input/output terms. The paper details the adaptive target and gives a proof of the generalized theorem. Transformation and application ... More

RSP-Based Analysis for Sparsest and Least $\ell_1$-Norm Solutions to Underdetermined Linear SystemsJul 17 2013Recently, the worse-case analysis, probabilistic analysis and empirical justification have been employed to address the fundamental question: When does $\ell_1$-minimization find the sparsest solution to an underdetermined linear system? In this paper, ... More

An arithmetic transference proof of a relative Szemerédi theoremJul 18 2013Oct 30 2013Recently Conlon, Fox, and the author gave a new proof of a relative Szemer\'edi theorem, which was the main novel ingredient in the proof of the celebrated Green-Tao theorem that the primes contain arbitrarily long arithmetic progressions. Roughly speaking, ... More

Puzzles in charmonium decaysDec 13 2010The open charm effects via intermediate hadron loop transitions seem to play a crucial role in the understanding of several existing "puzzles" in charmonium exclusive decays, such as the $\psi(3770)$ non-$D\bar{D}$ decays, and "$\rho\pi$ puzzle" etc. ... More

χ_{c0,2} decay into light meson pairs and its implication of the scalar meson structuresMay 01 2007Oct 31 2007In light of the recent data from BES collaboration for $\chi_{c0}\to VV$, $PP$ and $SS$, and from CLEO-c for $\eta\eta$, $\eta^\prime\eta^\prime$ and $\eta\eta^\prime$, we present a detailed analysis of the decays of heavy quarkonia into light meson pairs ... More

Study $ω$ and $φ$ photoproduction in the nucleon isotopic channelsFeb 07 2002We present results for the photoproduction of $\omega$ and $\phi$ meson in the nucleon isotopic channles. A recently developed quark model with an effective Lagrangian is employed to account for the non-diffractive {\it s}- and {\it u}-channel processes; ... More

$η^\prime$ photoproduction near thresholdNov 19 2000In this work, the $\eta^\prime$ meson photoproduction near threshold is studied in the quark model framework. A pseudovector effective Lagrangian is introduced for the $\eta^\prime NN$ coupling and the newly published data from the SAPHIR Collaboration ... More

Covariate Balancing Propensity Score by Tailored Loss FunctionsJan 22 2016Apr 17 2016In an observational study, propensity scores are commonly modeled by a generalized linear model (GLM), but the standard maximum likelihood solution may suffer from unsatisfactory covariate balance. This paper proposes to use tailored loss functions---covariate ... More

A coherent study of $χ_{c0,2}\to VV$, $PP$ and $SS$Aug 07 2005Sep 21 2005We investigate the decays of $\chi_{c0,2}$ into vector meson pairs ($VV$), pseudoscalar pairs ($PP$), and scalar pairs ($SS$) in a general factorization scheme. The purpose is to clarify the role played by the OZI-rule violations and SU(3) flavour breakings ... More

Point processes in a metric spaceNov 21 2016As a useful and elegant tool of extreme value theory, the study of point processes on a metric space is important and necessary for the analyses of heavy-tailed functional data. This paper focuses on the definition and properties of such point processes. ... More

Hidden symmetries for thermodynamics and emergence of relativityFeb 02 2010Apr 16 2010Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment ... More

Explanation of Quantum MechanicsSep 10 1999By assuming that the kinetic energy,potential energy,momentum,and some other physical quantities of a particle exist in the field out of the particle,the Schrodinger equation is an equation describing field of a particle,but not the particle itself.

Engaging Audiences in Virtual Museums by Interactively Prompting Guiding QuestionsFeb 10 2019Virtual museums aim to promote access to cultural artifacts. However, they often face the challenge of getting audiences to read and understand a large amount of information in an uncontrolled online environment. Inspired by successful practices in physical ... More

Kalman Filter, Unscented Filter and Particle Flow Filter on Non-linear ModelsMar 22 2018Filters, especially wide range of Kalman Filters have shown their impacts on predicting variables of stochastic models with higher accuracy then traditional statistic methods. Updating mean and covariance each time makes Bayesian inferences more meaningful. ... More

Active Secure Coding Based on Eavesdropper Behavior LearningJul 09 2018The secrecy capacity achieving problem of the wiretap channel against an active eavesdropper with unlimited computational power over is an important foresighted task for secure communication. For active wiretap channel, the effectiveness of cryptography ... More

X-ray Scattering from Random Rough SurfacesApr 12 2017This paper presents a new method to model X-ray scattering on random rough surfaces. It combines the approaches we presented in two previous papers -- \zs\cite{zhao03} \& \pz\cite{zhao15}. An actual rough surface is (incompletely) described by its Power ... More

Performance of a Concurrent Link SDMA MAC under Practical PHY Operating ConditionsJun 01 2010Dec 22 2010Space Division Multiple Access (SDMA) based Medium Access Control (MAC) protocols have been proposed to enable concurrent communications and improve link throughput in Multi-Input Multi-Output (MIMO) Ad Hoc networks. For the most part, the works appearing ... More

Chudnovsky's formula for $1/π$ revisitedJul 20 2018The document contains an outline of a modular proof for Ramanujan-Chudnovsky identity.

Four squares of primes and powers of 2Aug 26 2013By developing the method of Wooley on the quadratic Waring-Goldbach problem, we prove that all sufficiently large even integers can be expressed as a sum of four squares of primes and 46 powers of 2.

Optimal Algorithms for Stochastic Three-Composite Convex-Concave Saddle Point ProblemsMar 05 2019We develop stochastic first-order primal-dual algorithms to solve a class of stochastic three-composite convex-concave saddle point problems, which subsumes many previously studied problems as special cases. To obtain an $\epsilon$-expected duality gap, ... More

Analytic continuation of multiple polylogarithmsFeb 05 2003Feb 14 2003In this paper we shall define the analytic continuation of the multiple polylogarithms by using Chen's theory of iterated path integrals and compute the monodromy of all multiple logarithms explicitly.

q-Multiple Zeta Functions and q-Multiple PolylogarithmsApr 28 2003May 23 2003We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.

Variations of mixed Hodge structures of multiple polylogarithmsFeb 05 2003Feb 14 2003It's well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall {\em explicitly} determine these structures related to multiple logarithms and some other multiple polylogarithms ... More

Witten volume formulas for semi-simple Lie algebrasJan 20 2010In this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in computation of higher-dimensional Dedekind sums. ... More

Supplement to: Goncharov's Relations in Bloch's higher Chow Group CH^3(F,5)Nov 07 2003This is a supplement to the paper "Goncharov's Relations in Bloch's higher Chow Group CH^3(F,5)" submitted as math.AG/0105084. We check the admissiblility of all the cycles appearing in the main article.

A Survey on Theoretical Advances of Community Detection in NetworksAug 26 2018Real-world networks usually have community structure, that is, nodes are grouped into densely connected communities. Community detection is one of the most popular and best-studied research topics in network science and has attracted attention in many ... More

Finiteness of p-Divisible Sets of Multiple Harmonic SumsMar 04 2003Aug 13 2010\medskip\noindent\textbf{R\'esum\'e.} Soit $l$ un entier et $\ors=(s_1, \dots, s_l)$ une s\'equence d'entiers positifs. Dans ce document, nous \'etudierons les propri\'et\'es arithm\'etique de sommes harmoniques multiples $H(\ors; n)$, qui est le $n$-\`eme ... More

Optimal Stochastic Algorithms for Convex-Concave Saddle-Point ProblemsMar 05 2019May 18 2019We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this problem. When ... More

A refined error analysis for fixed-degree polynomial optimization over the simplexDec 20 2013Aug 17 2014We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this paper, we revisit ... More

Sets Characterized by Missing Sums and DifferencesNov 12 2009Aug 08 2010A more sums than differences (MSTD) set is a finite subset S of the integers such |S+S| > |S-S|. We show that the probability that a uniform random subset of {0, 1, ..., n} is an MSTD set approaches some limit rho > 4.28 x 10^{-4}. This improves the previous ... More

Partial Reduction and Delaunay/Deprit VariablesJan 23 2014Jul 12 2014Based on a concept link between the partial reduction procedure of the reduction of the rotational symmetry of the N-body problem with the symplectic cross-section theorem of Guillemin-Sternberg, we present alternative proofs of the symplecticity of Delaunay ... More

Dipole-Dipole Correlations for the sine-Gordon ModelAug 16 2011We consider the dipole-dipole correlations for the two-dimensional Coulomb gas/sine-Gordon model for $\beta> 8\pi$ by a renormalization group method. First we re-establish the renormalization group analysis for the partition function using finite range ... More

All-optical Nanoscale Control of Photon Correlations: Dressed States Assisted Quantum Interference EffectsFeb 04 2018Apr 06 2018We propose an all-optical scheme to control the photon statistics using hybrid quantum plasmonic system. With the aid of dressed states assisted quantum interference effects, it is shown that the photon correlations of a signal field can be continuously ... More

Well-posedness and Gevrey Analyticity of the Generalized Keller-Segel System in Critical Besov SpacesAug 01 2015Aug 18 2015In this paper, we study the Cauchy problem for the generalized Keller-Segel system with the cell diffusion being ruled by fractional diffusion: \begin{equation*} \begin{cases} \partial_{t}u+\Lambda^{\alpha}u-\nabla\cdot(u\nabla \psi)=0\quad &\mbox{in}\ ... More

On the number of limit cycles in quadratic perturbations of quadratic codimension four centersNov 10 2010This paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of quadratic codimension-four centers $Q_4$. Gavrilov and Iliev set an upper bound of {\it eight} for the number of limit cycles produced from the period annulus ... More

Large Sieve Inequalities with Quadratic AmplitudesDec 13 2005Mar 26 2006In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish non-trivial bounds.

A Monte Carlo simulation study on the wetting behavior of water on graphite surfaceSep 20 2012This paper is an expanded edition of the rapid communication published several years ago by the author (Phys. Rev. B, v76, 041402(R), 2007) on the simulation of wetting transition of water on graphite, aiming to provide more details on the methodology, ... More

Measurement of Vcb and Charmless Hadronic B decays at CLEOJan 10 2001The recent results on the measurement of Vcb and charmless hadronic B decays from CLEO are presented.

Advances in Basis Light-front QuantizationNov 28 2014Jul 07 2015Basis Light-front Quantization has been developed as a first-principles nonperturbative approach to quantum field theory. In this article we report our recent progress on the applications to the single electron and the positronium system in QED. We focus ... More

A Deformation of Commutative Polynomial Algebras in Even Numbers of VariablesJul 23 2009Jan 18 2010We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right ... More

Generalizations of the Image Conjecture and the Mathieu ConjectureFeb 02 2009Oct 23 2009We first propose a generalization of the image conjecture [Z3] for the commuting differential operators related with classical orthogonal polynomials. We then show that the non-trivial case of this generalized image conjecture is equivalent to a variation ... More

Jacobson's lemma via Groebner-Shirshov basesFeb 21 2017Let $R$ be a ring with identity $1$. Jacobson's lemma states that for any $a,b\in R$, if $1-ab$ is invertible then so is $1-ba$. Jacobson's lemma has suitable analogues for several types of generalized inverses, e.g., Drazin inverse, generalized Drazin ... More

Gorenstein homological invariant properties under Frobenius extensionsDec 25 2017Dec 07 2018We prove that for a Frobenius extension, a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective. For a separable Frobenius extension between Artin algebras, we obtain ... More

Geometric realizations of Lusztig's symmetries on the whole quantum groupsApr 01 2017In this paper, we shall study the structure of the Grothendieck group of the category consisting of Lusztig's perverse sheaves and give a decomposition theorem of it. By using this decomposition theorem and the geometric realizations of Lusztig's symmetries ... More

Prediction of System Evolution by Learning MachineMay 10 2019The orthodox approach for understanding a dynamical system is to establish its equation of motion, by which one can unveil its dynamical behavior at a given system parameter set, and reveal how the dynamic behavior evolves as the system parameters change. ... More

Side Window FilteringMay 17 2019Local windows are routinely used in computer vision and almost without exception the center of the window is aligned with the pixels being processed. We show that this conventional wisdom is not universally applicable. When a pixel is on an edge, placing ... More

Existence and Stability of Coexistence States for a Nonlocal Evolution SystemMay 20 2011Mar 05 2012In this paper, we study a nonlocal evolution system. We apply abstract results from the bifurcation theory to obtain the existence of coexistence states. Their stability are investigated as well.

A Clustering Based Approach for Realistic and Efficient Data-Driven Crowd SimulationJun 15 2015Oct 29 2015In this paper, we present a data-driven approach to generate realistic steering behaviors for virtual crowds in crowd simulation. We take advantage of both rule-based models and data-driven models by applying the interaction patterns discovered from crowd ... More

Extremal regular graphs: independent sets and graph homomorphismsOct 28 2016This survey concerns regular graphs that are extremal with respect to the number of independent sets, and more generally, graph homomorphisms. The main motivating problem is the following: in the family of $d$-regular graphs, which graph $G$ maximize/minimize ... More

A Spectral Analysis of Subspace Enchanced PreconditionersApr 07 2013It is well-known that the convergence of Krylov subspace methods to solve linear system depends on the spectrum of the coefficient matrix, moreover, it is widely accepted that for both symmetric and unsymmetric systems Krylov subspace methods will converge ... More

A Study on Perturbation Analysis of Spectral PreconditionersOct 10 2011Dec 10 2011It is well-known that the convergence of Krylov subspace methods to solve linear system depends on the spectrum of the coefficient matrix, moreover, it is widely accepted that for both symmetric and unsymmetric systems Krylov subspace methods will converge ... More

Remarks on PBW bases of Ringel-Hall algebras of cyclic quiversAug 22 2016In this paper, we give a recursive formula for the interesting PBW basis $E_{A}$ of composition subalgebras of Ringel-Hall algebras $\fkH_\vartri(n)$ of cyclic quivers after \cite{DengDuXiao2007generic}, and another construction of canonical bases of ... More

Ballistic Motion in One-Dimensional Quasi-Periodic Discrete Schrödinger EquationJul 31 2015Feb 10 2016For the solution $q(t)=(q_n(t))_{n\in\mathbb Z}$ to one-dimensional discrete Schr\"odinger equation $${\rm i}\dot{q}_n=-(q_{n+1}+q_{n-1})+ V(\theta+n\omega) q_n, \quad n\in\mathbb Z,$$ with $\omega\in\mathbb R^d$ Diophantine, and $V$ a small real-analytic ... More

Note on a class of anisotropic Einstein metricsJun 24 2011A class of anisotropic Einstein metrics is presented. These metrics are axial symmetric and contains an anisotropy parameter $\alpha$, which is identified as the amplitude of the proper acceleration of the origin, thus explaining the ellipsoid shape of ... More

Duality for relative logarithmic de Rham-Witt sheaves on semistable schemes over $\mathbb{F}_q[[t]]$Nov 26 2016We study duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes $X$ over a local ring $\mathbb{F}_q[[t]]$, where $\mathbb{F}_q$ is a finite field. As an application, we obtain a new filtration on the maximal abelian ... More

Topological circuits of inductors and capacitorsOct 09 2018Dec 11 2018Alternating current (ac) circuits can have electromagnetic edge modes protected by symmetries, analogous to topological band insulators or semimetals. How to make such a topological circuit? This paper illustrates a particular design idea by analyzing ... More

Numerical Implementation of Gauge-Fixed Fourier AccelerationDec 14 2018In hybrid Monte Carlo evolution, by imposing a physical gauge condition, simple Fourier acceleration can be used to generate conjugate momenta and potentially reduce critical slowing down. This modified gauge evolution algorithm does not change the gauge-independent ... More

Irregular Channel Polarization and Its Applications to Static Adversarial Wiretap ChannelDec 01 2018The problem of achieving the secrecy capacity of static adversarial wiretap channel with discrete memoryless channels is studied in this paper. To construct the explicit secure coding scheme, an irregular channel polarization operation is proposed which ... More