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Rotate your Networks: Better Weight Consolidation and Less Catastrophic ForgettingFeb 08 2018In this paper we propose an approach to avoiding catastrophic forgetting in sequential task learning scenarios. Our technique is based on a network reparameterization that approximately diagonalizes the Fisher Information Matrix of the network parameters. ... More

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed ... More

Formula of Volume of Revolution with Integration by Parts and ExtensionSep 04 2016A calculation formula of volume of revolution with integration by parts of definite integral is derived based on monotone function, and extended to a general case that curved trapezoids is determined by continuous, piecewise strictly monotone and differential ... More

A class of cyclic codes whose dual have five zerosFeb 07 2015In this paper, a family of cyclic codes over $\mathbb{F}_{p}$ whose duals have five zeros is presented, where $p$ is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016Nov 10 2016We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed ... More

An Online Approach to Dynamic Channel Access and Transmission SchedulingApr 04 2015Making judicious channel access and transmission scheduling decisions is essential for improving performance as well as energy and spectral efficiency in multichannel wireless systems. This problem has been a subject of extensive study in the past decade, ... More

To Stay Or To Switch: Multiuser Dynamic Channel AccessSep 14 2013In this paper we study opportunistic spectrum access (OSA) policies in a multiuser multichannel random access cognitive radio network, where users perform channel probing and switching in order to obtain better channel condition or higher instantaneous ... More

Higher Toda Mechanics and Spectral CurvesJun 01 2003For each one of the Lie algebras $\mathfrak{gl}_{n}$ and $\widetilde {\mathfrak{gl}}_{n}$, we constructed a family of integrable generalizations of the Toda chains characterized by two integers $m_{+}$ and $m_{-}$. The Lax matrices and the equations of ... More

Group Learning and Opinion Diffusion in a Broadcast NetworkSep 14 2013We analyze the following group learning problem in the context of opinion diffusion: Consider a network with $M$ users, each facing $N$ options. In a discrete time setting, at each time step, each user chooses $K$ out of the $N$ options, and receive randomly ... More

On the arithmetic of the endomorphism ring End($\mathbb{Z}_{p}\times\mathbb{Z}_{p^{m}}$)May 03 2016For a prime $p$, let $E_{p,p^m}=\{\begin{pmatrix}a&b\\p^{m-1}c&d\end{pmatrix}|a,b,c\in\mathbb{Z}_{p},~\mathrm{and}~d\in \mathbb{Z}_{p^{m}}\}$. We first establish a ring isomorphism from $\mathrm{End}(\mathbb{Z}_p\times\mathbb{Z}_p^m)$ onto $E_{p,p^m}$. ... More

A blow-up criterion for the compressible liquid crystals systemNov 19 2010Nov 23 2010In this paper, we establish a blow-up criterion for the compressible liquid crystals equations in terms of the gradient of the velocity only, similar to the Beale-Kato-Majda criterion \cite{majda} for ideal incompressible flows and the criterion obtained ... More

$T$-adic exponential sums of polynomials in one variableNov 03 2009The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the T-adic exponential ... More

The Dynamic Behavior of Quantum Statistical Entropy in 5D Ricci-flat Black String with Thin-layer ApproachNov 05 2008In this paper, the statistical-mechanical entropies of 5D Ricci-flat black string is calculated through the wave modes of the quantum field with improved thin-layer brick-wall method. The modes along the fifth dimension are semi-classically quantized ... More

Matrix-Product Complementary dual CodesApr 13 2016Linear complementary dual codes (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal matrices. Some ... More

Wake Potential in Strong Coupling Plasma from AdS/CFT CorrespondenceFeb 06 2015With the dielectric function computed from AdS/CFT correspondence, we studied the wake potential induced by a fast moving charge in strong coupling plasma, and compared it with the weak coupling wake potential for different particle velocities as $v=0.55c$ ... More

Derivations from the even parts into the odd parts for Lie superalgebras W and SSep 08 2005Let $\mathcal{W}$ and $\mathcal{S}$ denote the even parts of the general Witt superalgebra $W$ and the special superalgebra $S$ over a field of characteristic $ p>3,$ respectively. In this note, using the method of reduction on $\mathbb{Z}$-gradations, ... More

Maximal graded subalgebras of Witt and Special superalgebrasNov 18 2009Mar 08 2010This paper has been withdrawn by the author due to that the main results and approaches are closedly parallel to the ones in Lie algebra case.

Upper Beurling Density of Systems formed by Translates of finite Sets of Elements in $L^p(\R^d)$Mar 28 2012In this paper, we prove that if a finite disjoint union of translates $\bigcup_{k=1}^n\{f_k(x-\gamma)\}_{\gamma\in\Gamma_k}$ in $L^p(\R^d)$ $(1<p<\infty)$ is a $p'$-Bessel sequence for some $1<p'<\infty$, then the disjoint union $\Gamma=\bigcup_{k=1}^n\Gamma_k$ ... More

Quantum Manifestation of Elastic Constants in NanostructuresSep 05 2012Generally, there are two distinct effects in modifying the properties of low-dimensional nanostructures: surface effect (SS) due to increased surface-volume ratio and quantum size effect (QSE) due to quantum confinement in reduced dimension. The SS has ... More

Elastic Waves Scattering without Conversion in Metamaterials with Simultaneous Zero Indices for Longitudinal and Transverse wavesMar 08 2015Sep 28 2015We theoretically investigate elastic waves propagating in metamaterials with simultaneous zero indices for both the longitudinal and transverse waves. With scattering objects (here cylinders) present in the metamaterials slabs, while the elastic waves ... More

Twisted exponential sums of polynomials in one variableDec 10 2009The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function ... More

Exploiting Unlabeled Data for Neural Grammatical Error DetectionNov 28 2016Nov 29 2016Identifying and correcting grammatical errors in the text written by non-native writers has received increasing attention in recent years. Although a number of annotated corpora have been established to facilitate data-driven grammatical error detection ... More

Ehrhart polynomials of lattice-face polytopesDec 28 2005There is a simple formula for the Ehrhart polynomial of a cyclic polytope. The purpose of this paper is to show that the same formula holds for a more general class of polytopes, lattice-face polytopes. We develop a way of decomposing any d-dimensional ... More

Posterior Exploration based Sequential Monte Carlo for Global OptimizationSep 29 2015Jul 14 2016We propose a global optimization algorithm based on the Sequential Monte Carlo (SMC) sampling framework. In this framework, the objective function is normalized to be a probabilistic density function (pdf), based on which a sequence of annealed target ... More

Pólya conjecture for the Neumann eigenvaluesNov 08 2014Feb 13 2015For a given bounded domain $\Omega\subset {\Bbb R}^n$ with $C^1$-smooth boundary, we prove the P\'olya conjecture for the Neumann eigenvalues. In other words, we prove that \begin{eqnarray*} \mu_{k+1}\le \frac{(2\pi)^2k^{2/n}}{(\omega_n \cdot \mbox{vol}\, ... More

Uniqueness of scatterer in inverse acoustic obstacle scattering with a single incident plane waveOct 11 2016Oct 17 2016In this paper, we give a simple proof for uniqueness of the scatterer in inverse obstacle scattering problem for acoustic wave with a single incident plane wave. Ramm in \cite{Ram1} showed that the acoustic scattering amplitude $A(\beta, {\alpha}_0, k_0)$, ... More

Model-based Differential Private Data SynthesisJun 26 2016We propose model-based based differential private data synthesis (modips) for releasing individual-level data with strong privacy guarantee. The modips technique is an original framework to integrate differential privacy -- a concept discussed largely ... More

Bridge the gap between network-based inference method and global ranking method in personal recommendationJul 15 2015In this paper, we study the relationship between the network-based inference method and global ranking method in personal recommendation. By some theoretical analysis, we prove that the recommendation result under the global ranking method is the limit ... More

Mixture Diffusion for Asset PricingOct 05 2016Oct 12 2016This paper proposes a general form of mixture diffusion process to model asset price dynamics, using a mixture of infinite number of parametric diffusions. We show that the underlying asset price dynamics of the risk-neutral probability density distributions ... More

Uniqueness of scatterer in inverse acoustic obstacle scattering with a single incident plane waveOct 11 2016Oct 19 2016In this paper, we give a simple proof for uniqueness of the scatterer in inverse obstacle scattering problem for acoustic wave with a single incident plane wave. Ramm in \cite{Ram1} showed that the acoustic scattering amplitude $A(\beta, {\alpha}_0, k_0)$, ... More

Twisted K-homology,Geometric cycles and T-dualityNov 06 2014Nov 14 2014Twisted $K$-homology corresponds to $D$-branes in string theory. In this paper we compare two different models of geometric twisted $K$-homology and get their equivalence. Moreover, we give another description of geometric twisted $K$-homology using bundle ... More

Resolution for Sheaf of Differential Operators on Smooth Free Geometric Quotient of Linear Action of Algebraic GroupSep 13 1996Sep 16 1996We obtain a global resolution for the sheaf of differential operators on smooth geometric quotients of free linear actions of algebraic groups. The terms of our resolution involve symmetric and alternating powers of vector bundles easily constructed geometrically ... More

Necessary Conditions about the Diederich-Fornæss indexOct 20 2016We derive several necessary conditions about the Diederich-Forn\ae ss index. One of the main motivations in the article is to look for a necessary condition for the given bounded pseudoconvex domain $\Omega\subset\mathbb{C}^2$ with smooth boundary such ... More

Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groupsDec 21 2010We propose a relative trace formula approach and state the corresponding fundamental lemma toward the global restriction problem involving Bessel or Fourier-Jacobi periods of unitary groups $\mathrm{U}_n\times\mathrm{U}_m$, extending the work of Jacquet-Rallis ... More

Smooth crossed products induced by minimal unique ergodic diffeomorphisms on odd spheresApr 06 2016For minimal unique ergodic diffeomorphisms $\alpha_n$ of $S^{2n+1} (n>0)$ and $\alpha_m$ of $S^{2m+1}(m>0)$, the $C^*$-crossed product algebra $C(S^{2n+1})\rtimes_{\alpha_n} \mathbb{Z}$ is isomorphic to $C(S^{2m+1})\rtimes_{\alpha_m} \mathbb{Z}$ even ... More

Comptage des multiplicités dans une hypersurfaceJun 30 2016Jul 11 2016In this paper, we give an upper bound of a sum of a function of multiplicity over a reduced projective hypersurface over a finite field.

Stationarity of Stochastic Linear Equations with Additive Noise and Delays in the Unbounded Drift TermsFeb 10 2014This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a consequence, the associated ... More

Heat kernel and moduli spaces IIDec 01 1996Apr 15 1997In this paper we continue our study on the moduli spaces of flat G-bundles, for any semi-simple Lie group G, over a Riemann surface by using heat kernel and Reidemeister torsion. Formulas for intersection numbers on the moduli spaces over a Riemann surface ... More

Lying-Over Theorem on Left Commutative RngsNov 26 2005We introduce the notion of a graded integral element, prove the counterpart of the lying-over theorem on commutative algebra in the context of left commutative rngs, and use the Hu-Liu product to select a class of noncommutative rings.

On Extension of Ginzburg-Jiang-Soudry Correspondence to Certain Automorphic Forms on $Sp_{4mn}(\BA)$ and $\wt{Sp}_{4mn \pm 2n}(\BA)$Sep 24 2013Let $F$ be a number field, and $\BA=\BA_F$. In this paper, first, we provide a family of global Arthur parameters confirming all parts of a general conjecture on the relation between the structure of Fourier coefficients and the structure of global Arthur ... More

On quadratic distinction of automorphic sheavesFeb 17 2011We prove a geometric version of a classical result on the characterization of an irreducible cuspidal automorphic representation of $\mathrm{GL}_n(\mathbb{A}_E)$ being the base change of a stable cuspidal packet of the quasi-split unitary group associated ... More

The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifoldsDec 20 2009Jan 31 2011Let $\Omega$ be a bounded domain with $C^2$-smooth boundary in an $n$-dimensional oriented Riemannian manifold. It is well-known that for the bi-harmonic equation $\Delta^2 u=0$ in $\Omega$ with the $0$-Dirichlet boundary condition, there exists an infinite ... More

A Simple Converse Proof and a Unified Capacity Formula for Channels with Input ConstraintsJul 01 2008Given the single-letter capacity formula and the converse proof of a channel without constraints, we provide a simple approach to extend the results for the same channel but with constraints. The resulting capacity formula is the minimum of a Lagrange ... More

The L-functions of twisted Witt extensionsSep 18 2004Nov 25 2005The L-function of a non-degenerate twisted Witt extension is proved to be a polynomial. Its Newton polygon is proved to lie above the Hodge polygon of that extension. And the Newton polygons of the Gauss-Heilbronn sums are explicitly determined, generalizing ... 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

Piecewise Interference and Stability of Branched FlowSep 01 2014The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are largely ignored ... More

Spectral invariants of the Stokes problemOct 16 2014For a given bounded domain $\Omega\subset {\Bbb R}^n$ with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion of the heat trace associated with the Stokes operator as $t\to 0^+$. These coefficients (i.e., heat ... More

Optimal control problems with state constraint governed by Navier-Stokes equationsMay 18 2010This work deals with the existence of optimal solution and the maximum principle for optimal control problem governed by Navier-Stokes equations with state constraint in 3-D. Strong results in 2-D also are given.

A characterization of virtually embedded subsurfaces in 3-manifoldsJun 18 2014Mar 26 2015The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded ... More

Inequality for Variance of Weighted Sum of Correlated Random Variables and WLLNSep 11 2012Dec 17 2014The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive semidefinite matrix ... More

$\mathsf{RT}_2^2$ does not imply $\mathsf{WKL}_0$Feb 11 2016We prove that $\mathsf{RCA}_0+\mathsf{RT}_2^2\not\rightarrow \mathsf{WKL}_0$ by showing that for any set $C$ not of PA-degree and any set $A$, there exists an infinite subset $G$ of $A$ or $\bar{A}$, such that $G\oplus C$ is also not of PA-degree.

Lecture notes on thermodynamics of ideal string gases and its application in cosmologyDec 05 2014In these lecture notes I give a pedagogical introduction to the thermodynamics of ideal string gases. The computation of thermodynamic quantities in the canonical ensemble formalism will be shown in detail with explicit examples. Attention will be given ... More

Holographic renormalization in no-boundary quantum cosmologyDec 04 2014Dec 22 2014Recent results of Hartle-Hawking wave functions on asymptotic dS boundaries show non-normalizability, while the bulk origin is not clear. This paper attempts to addresse this problem by studying (Kerr-)dS_3 cosmology in Einstein gravity deformed by a ... More

Extracting the trustworthiest way to service provider in complex online social networksJun 18 2013In complex online social networks, it is crucial for a service consumer to extract the trustworthiest way to a target service provider from numerous social trust paths between them. The extraction of the trustworthiest way (namely, optimal social trust ... More

Robust Particle Filter by Dynamic Averaging of Multiple Noise ModelsSep 05 2016State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which may result in ... More

The intrinsic line width of the Fe Ka line of AGNAug 26 2016X-ray fluorescent lines are unique features of the reflection spectrum of the cold torus when irradiated by the central AGN. Their intrinsic line widths can be used to probe the line-emitting region. The line widths of the Fe \Ka line measured from the ... More

Recovery of inhomogeneities and buried obstaclesApr 06 2008In this paper we consider the unique determination of inhomogeneities together with possible buried obstacles by scattering measurements. Under the assumption that the buried obstacles have only planar contacts with the inhomogeneities, we prove that ... More

A Global Uniqueness for Formally Determined Inverse Electromagnetic Obstacle ScatteringJan 17 2008It is proved that a general polyhedral perfect conducting obstacle in $\mathbb{R}^3$, possibly consisting of finitely many solid polyhedra, is uniquely determined by the far-field pattern corresponding to a single incident wave. This improves earlier ... More

Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone OperatorsNov 02 2010In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators. In particular, ... More

Generalized Canonical Correlation Analysis and Its Application to Blind Source Separation Based on a Dual-Linear Predictor StructureMar 09 2014Blind source separation (BSS) is one of the most important and established research topics in signal processing and many algorithms have been proposed based on different statistical properties of the source signals. For second-order statistics (SOS) based ... More

Channel Equalization and Beamforming for Quaternion-Valued Wireless Communication SystemsMay 31 2015Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms for channel ... More

Noise-Sustained Convective Instability in a Magnetized Taylor-Couette FlowAug 19 2008Oct 13 2008The helical magnetorotational instability of the magnetized Taylor-Couette flow is studied numerically in a finite cylinder. A distant upstream insulating boundary is shown to stabilize the convective instability entirely while reducing the growth rate ... More

Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette FlowDec 15 2007Apr 26 2008In this paper we present axisymmetric nonlinear simulations of magnetized Ekman and Stewartson layers in a magnetized Taylor-Couette flow with a centrifugally stable angular-momemtum profile and with a magnetic Reynolds number below the threshold of magnetorotational ... More

A Short Note on Infinite Union/Intersection of Omega Regular LanguagesMar 17 2016We in this paper show that omega regular languages are not closed under infinite union and intersection. As an attempt, we propose to add step variables and quantifiers to temporal logics to enhance the expressiveness of the underlying logic. We also ... More

Sieve Method and Landau ProblemSep 25 1999We solve Landau's four unattackable problems, including Goldbach Conjecture and Twin Prime Conjecture through sieve method.

Recent Results on Light Hadrons from the BESIII ExperimentSep 01 2015The BESIII experiment has collected world's largest direct $e^+e^-$ colliding beam data at the $J/\psi$, $\psi'$, $\psi$(3770) and at and around the $Y$(4260). These data have enabled the study of hadrons at unprecedented precisions. We present results ... More

An Extension to Gaussian Semigroup and Some ApplicationsNov 21 2006We look at the semigroup generated by a system of heat equations. Applications to testing normality and option pricing are addressed.

Residues and duality on semi-local two-dimensional adelesMay 06 2015Oct 28 2015In this note, we establish a duality result under the residue paring between certain two-dimensional adelic spaces, which are associated to a closed point on an arithmetic surface.

q-conjugacy classes in loop groupsNov 23 2010We classify twisted conjugacy classes in loop groups, restricted to classical groups. The main tool we used is the so-called D_q module, an object which is related to vector bundles over elliptic curves.

A Simple Discussion on Wave Functional in Free QEDNov 18 2005Jun 18 2009This paper has been withdrawn by the author due to some mistakes

Estimates for Forward-backward Asymmetry in $B\rightarrow K^*(892)\; l^+ l^-$Jan 12 1995Jan 12 1995Forward-backward charge asymmetry in rare dilepton $B$-decays is formulated with the assumption of an on-shell b-quark. We find the asymmetry is expressed in terms of two spatially transverse helicity amplitudes, which are determined by combining the ... More

Slope filtrations in familiesSep 01 2008Jan 01 2012This paper concerns arithmetic families of $\varphi$-modules over reduced affinoid spaces. For such a family, we first prove that the slope polygons is lower semicontinuous around any rigid point. If the slope polygons are locally constant around a rigid ... More

Cohomology and Duality for (phi,Gamma)-modules over the Robba ringNov 27 2007Sep 03 2008Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated etale (phi,Gamma)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, ... More

Radial prescribing scalar curvature on $RP^n$Mar 11 2015The study of radial prescribing scalar curvature of X.Xu and P.C.Yang [2] in 1993 showed a nonexistence result on $S^2$. Later in 1995, W.Chen and C.Li [2] generalized the nonexistence result to higher dimensions. G.Bianchi and E.Egnell [1] suggested ... More

Estimation of the spectral measure of multivariate regularly varying distributionsSep 21 2010In the paper, the estimator for the spectral measure of multivariate stable distributions introduced by Davydov and co-workers are extended to the regularly varying distributions. The sampling method is modified to optimize the rate of convergence of ... More

Gaussian integrability of distance function under the Lyapunov conditionSep 30 2014Feb 15 2015In this note we give a direct proof of the Gaussian integrability of distance function as $\mu e^{\delta d^2(x,x_0)} < \infty$ for some $\delta>0$ provided the Lyapunov condition holds for symmetric diffusion Markov operators, which answers a question ... More

Finding binary active galactic nuclei candidates by the centroid shift in imaging surveys II. Testing the method with SDSS J233635.75-010733.7Jul 04 2016In Liu (2015), we propose selecting binary active galactic nuclei (AGNs) candidates using the centroid shift of the images, which is induced by the non-synchronous variations of the two nuclei. In this paper, a known binary AGN (SDSS J233635.75-010733.7) ... More

Origin of coda waves: earthquake source resonanceAug 20 2015Sep 14 2016Seismic coda in local earthquake exhibits characteristics of uniform spatial distribution energy, selective frequency, and slow temporal decay oscillation. It is usually assumed to be the incoherent waves scattered from random heterogeneity in the earth's ... More

Hearts of cotorsion pairs are functor categories over coheartsApr 21 2015Jan 18 2016We study hearts of cotorsion pairs in triangulated and exact categories.We give a sufficient and necessary condition when the hearts have enough projectives. We also show in such condition they are equivalent to functor categories over cohearts of the ... More

On the critical one-component velocity regularity criteria to 3-D incompressible MHD systemSep 18 2015Let $(u,b)$ be a smooth enough solution of 3-D incompressible MHD system. We prove that if $(u,b)$ blows up at a finite time $T^*$, then for any $p\in]4,\infty[$, there holds $\int_0^{T^*}\bigl(\|u^3(t')\|^p_{\dH^{\frac 12+\frac 2p}}+\|b(t')\|^p_{\dH^{\frac ... More

Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only 1-electron interactionsNov 22 2016We introduce the isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian (with only 1-electron interactions). This suggests that all methods developed for the former can be employed for the latter, and vice versa. ... More

A Class of Ring-like ObjectsNov 26 2004Nov 26 2004We introduce the notions of one-sided dirings, 3-irreducible left modules, 3-primitive left dirings, 3-semi-primitive left dirings, 3-primitive ideals and 3-radicals. The main results consists of two parts. The first part establishes two external characterizations ... More

Transformation DigroupsSep 16 2004We introduce the notion of a transformation digroup and prove that every digroup is isomorphic to a transformation digroup.

How to Expand the Zariski TopologyJun 23 2005Jun 24 2005We introduce the notion of a Hu-Liu prime ideal in the context of left commutative rngs, and establish the contravariant functor from the category of left commutative rngs into the category of topological spaces.

Yang-Baxter relation planar algebrasJul 22 2015Apr 04 2016We give a new type of Schur-Weyl duality for the representations of a family of quantum subgroups and their centralizer algebra. We define and classify singly-generated, Yang-Baxter relation planar algebras. We present the skein theoretic construction ... More

Higher integrality conditions, volumes and Ehrhart polynomialsNov 11 2009A polytope is integral if all of its vertices are lattice points. The constant term of the Ehrhart polynomial of an integral polytope is known to be 1. In previous work, we showed that the coefficients of the Ehrhart polynomial of a lattice-face polytope ... More

Equivariant eta forms and equivariant differential $K$-theoryOct 07 2016In this paper, we construct an analytic model of equivariant differential $K$-theory for closed manifolds with almost free action, which is a ring valued functor with the usual properties of a differential extensions of a cohomology theory, using the ... More

On a Qualitative Difference between the Dynamics of Particle Production in Soft and Hard Processes of High Energy CollisionsDec 10 1998The qualitative difference between the anomalous scaling properties of hadronic final states in soft and hard processes of high energy collisions is studied in some detail. It is pointed out that the experimental data of e^+e^- collisions at $E_{cm}=$91.2 ... More

A time-work uncertainty relation in quantum systemsAug 02 2016In quantum systems, a plausible definition of work is based on two energy measurement scheme. Considering that energy change of quantum system obeys a time-energy uncertainty relation, it shall be interesting to see whether such type of work as well obeys ... More

Py-oopsi: the python implementation of the fast-oopsi algorithmMay 06 2014Fast-oopsi was developed by Joshua Vogelstein in 2009, which is now widely used to extract neuron spike activities from calcium fluorescence signals. Here, we propose detailed implementation of the fast-oopsi algorithm in python programming language. ... More

The Pointwise Estimates of Solutions for Semilinear Dissipative Wave EquationApr 02 2008Jan 06 2010In this paper we focus on the global-in-time existence and the pointwise estimates of solutions to the initial value problem for the semilinear dissipative wave equation in multi-dimensions. By using the method of Green function combined with the energy ... More

Optimizing ETL Dataflow Using Shared Caching and Parallelization MethodsSep 05 2014Extract-Transform-Load (ETL) handles large amount of data and manages workload through dataflows. ETL dataflows are widely regarded as complex and expensive operations in terms of time and system resources. In order to minimize the time and the resources ... More

Two-level Data Staging ETL for Transaction DataSep 05 2014Sep 13 2014In data warehousing, Extract-Transform-Load (ETL) extracts the data from data sources into a central data warehouse regularly for the support of business decision-makings. The data from transaction processing systems are featured with the high frequent ... More

Noninformative Bounding in Differential Privacy and Its Impact on Statistical Properties of Sanitized Results in Truncated and Boundary-Inflated-Truncated Laplace MechanismsJul 28 2016Protection of individual privacy is a common concern when releasing and sharing data and information. Differential privacy (DP) formalizes privacy in mathematical terms without making assumptions about the background knowledge of data intruders and thus ... More

Composed inclusions of $A_3$ and $A_4$ subfactorsAug 26 2013In this article, we classify all standard invariants that can arise from a composed inclusion of an $A_3$ with an $A_4$ subfactor. More precisely, if $\mathcal{N}\subset \mathcal{P}$ is the $A_3$ subfactor and $\mathcal{P}\subset\mathcal{M}$ is the $A_4$ ... More

Combinatorial bases for multilinear parts of free algebras with double compatible bracketsAug 26 2008Let X be an ordered alphabet. Lie_2(n) (and P_2(n) respectively) are the multilinear parts of the free Lie algebra (and the free Poisson algebra respectively) on X with a pair of compatible Lie brackets. In this paper, we prove the dimension formulas ... More

An Efficient Implementation for WalkSATOct 25 2015Dec 04 2015Stochastic local search (SLS) algorithms have exhibited great effectiveness in finding models of random instances of the Boolean satisfiability problem (SAT). As one of the most widely known and used SLS algorithm, WalkSAT plays a key role in the evolutions ... More

How to detect super-massive binary black holes at parsec scalesOct 09 2014Jan 05 2015It is difficult to find or identifying the binary black holes in parsec scales, since the dual AGN may be merged quickly. It is required to explore more possibilities to identifying binary black holes in parsec scales, we give some discussions, especially ... More

Quantum walks in the density operator pictureJun 08 2015A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal state is described ... More

Kasami type codes of higher relative dimensionJun 07 2015Jun 10 2015Some new Kasami type codes of higher relative dimension is introduced. Their weight distribution is determined.