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Fourier Domain Rotational Anisotropy Second Harmonic GenerationOct 04 2018We describe a novel scheme of detecting rotational anisotropy second harmonic generation (RA-SHG) signals using a lock-in amplifier referenced to a fast scanning RA-SHG apparatus. The method directly measures the $n^{th}$ harmonics of the scanning frequency ... More

Quantized Photocurrents in the Chiral Multifold Fermion System RhSiFeb 08 2019The rapid pace of discovery of new classes of Weyl semimetals is driving a search for properties that derive from their unique bandstructure topology. One of the most striking of the predicted properties is the quantized circular photogalvanic effect ... More

Fast Reflective Optic-Based Rotational Anisotropy Nonlinear Harmonic Generation SpectrometerOct 31 2018We present a novel Rotational Anisotropy Nonlinear Harmonic Generation (RA-NHG) apparatus based primarily upon reflective optics. The data acquisition scheme used here allows for fast accumulation of RA-NHG traces, mitigating low frequency noise from ... More

Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAsApr 19 2018Apr 20 2018While all media can exhibit first-order conductivity describing current linearly proportional to electric field, $E$, the second-order conductivity, $\sigma^{(2)}$ , relating current to $E^2$, is nonzero only when inversion symmetry is broken. Second ... More

On the integrated squared error of the linear wavelet density estimatorOct 29 2012Linear wavelet density estimators are wavelet projections of the empirical measure based on independent, identically distributed observations. We study here the law of the iterated logarithm (LIL) and a Berry-Esseen type theorem. These results are proved ... More

Survey of Cognitive Radio Techniques in Wireless NetworkApr 29 2011In this report, I surveyed the cognitive radio technique in wireless networks. Researched several kinds of cognitive techniques about their advantages and disadvantages.

A Class of Diffusion Algorithms with Logarithmic Cost over Adaptive Sparse Volterra NetworkJun 28 2016Jun 29 2016In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network. The development of the algorithms is based on the logarithmic cost and l0-norm constraint. To further overcome the ... More

Diffusion leaky LMS algorithm: analysis and implementationFeb 13 2016Jul 30 2016The diffusion least-mean square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such filters may change when they are implemented for suppressing noises from speech ... More

An exact algorithm for the weighed mutually exclusive maximum set cover problemJan 24 2014In this paper, we introduce an exact algorithm with a time complexity of $O^*(1.325^m)$ for the {\sc weighted mutually exclusive maximum set cover} problem, where $m$ is the number of subsets in the problem. This is an NP-hard motivated and abstracted ... More

Diffusion leaky LMS algorithm: analysis and implementationFeb 13 2016Aug 08 2017The diffusion least-mean square (dLMS) algorithms have attracted much attention owing to its robustness for distributed estimation problems. However, the performance of such filters may change when they are implemented for suppressing noises from speech ... More

Subband adaptive filter trained by differential evolution for channel estimationJan 29 2017Mar 17 2017The normalized subband adaptive filter (NSAF) is widely accepted as a preeminent adaptive filtering algorithm because of its efficiency under the colored excitation. However, the convergence rate of NSAF is slow. To address this drawback, in this paper, ... More

An exact algorithm with the time complexity of $O^*(1.299^m)$ for the weighed mutually exclusive set cover problemFeb 23 2013In this paper, we will introduce an exact algorithm with a time complexity of $O^*(1.299^m)$ for the {\sc weighted mutually exclusive set cover} problem, where $m$ is the number of subsets in the problem. This problem has important applications in recognizing ... More

Adaptive beamforming method based on recursive maximum correntropy in impulsive noise with alpha-stable processDec 12 2016Feb 23 2017As a well-established adaptation criterion, the maximum correntropy criterion (MCC) has been receiving increasing attention due to its robust against outliers. In this paper, a new complex recursive maximum correntropy (CRMC) algorithm without any priori ... More

A Class of Diffusion Algorithms with Logarithmic Cost over Adaptive Sparse Volterra NetworkJun 28 2016May 02 2017In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network (SVN). The development of the algorithms is based on the logarithmic cost and l0-norm constraint. Simulations for ... More

An invariance principle for stochastic heat equations with periodic coefficientsMay 13 2015In this paper we investigate the asymptotic behaviors of solution $u(t, \cdot)$ of a stochastic heat equation with a periodic nonlinear term. Such equation appears related to the dynamical sine-Gordon model. We consider the reversible case and extend ... More

A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann EntropyJun 26 2017Jul 11 2017It was recently conjectured by Vivo, Pato, and Oshanin [Phys. Rev. E 93, 052106 (2016)] that for a quantum system of Hilbert dimension $mn$ in a pure state, the variance of the von Neumann entropy of a subsystem of dimension $m\leq n$ is given by \begin{equation*} ... More

On finite-population Bayesian inferences for $2^K$ factorial designs with binary outcomesMar 12 2018Jan 24 2019Inspired by the pioneering work of Rubin (1978), we employ the potential outcomes framework to develop a finite-population Bayesian causal inference framework for randomized controlled $2^K$ factorial designs with binary outcomes, which are common in ... More

GRBS: Standard Model & BeyondJan 03 2001There have been great and rapid progresses in the field of $\gamma$-ray bursts since BeppoSAX and other telescopes discovered their afterglows in 1997. In this talk, the main observational facts of $\gamma$-ray bursts and their afterglows, and the standard ... More

What do $γ$-ray bursts look like?Feb 08 2000There have been great and rapid progresses in the field of $\gamma$-ray bursts (denoted as GRBs) since BeppoSAX and other telescopes discovered their afterglows in 1997. Here, we will first give a brief review on the observational facts of GRBs and direct ... More

Knowware: the third star after Hardware and SoftwareNov 27 2007This book proposes to separate knowledge from software and to make it a commodity that is called knowware. The architecture, representation and function of Knowware are discussed. The principles of knowware engineering and its three life cycle models: ... More

Synthesis of Self-assembled Iron Silicon Oxide Nanowires onto Single-crystalline Si(100)Jul 30 2013Iron silicon oxide nanowire has been synthesized by putting single crystalline Si(100) wafer into ammonium iron sulfate, hydrogen peroxide, and triethylamine solution heated to from 70 to 100 degree in the air. The prepared iron silicon oxide nanowires ... More

On the degenerated Arnold-Givental conjectureJun 01 2008Aug 06 2018We present another view dealing with the Arnold-Givental conjecture on a real symplectic manifold $(M, \omega, \tau)$ with nonempty and compact real part $L={\rm Fix}(\tau)$. For given $\Lambda\in (0, +\infty]$ and $m\in\N\cup\{0\}$ we show the equivalence ... More

Symplectic fixed points and Lagrangian intersections on weighted projective spacesJan 12 2006In this note we observe that Arnold conjecture for the Hamiltonian maps still holds on weighted projective spaces $\CP^n({\bf q})$, and that Arnold conjecture for the Lagrange intersections for $(\CP^n({\bf q}), \RP^n({\bf q}))$ is also true if each weight ... More

Periodic motion of a charge on a manifold in the magnetic fieldsMay 24 1999May 25 2000In this paper we prove the existence of a periodic motion of a charge on a large class of manifolds under the action of the magnetic fields. Our methods also give a class of closed manifolds whose cotangent bundle contain no the closed exact Lagrangian ... More

No-reference Image Denoising Quality AssessmentOct 13 2018A wide variety of image denoising methods are available now. However, the performance of a denoising algorithm often depends on individual input noisy images as well as its parameter setting. In this paper, we present a no-reference image denoising quality ... More

Iterative Reweighted Minimization Methods for $l_p$ Regularized Unconstrained Nonlinear ProgrammingSep 29 2012In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$ minimization ... More

A note on the holomorphic invariants of Tian-ZhuMay 26 2005In this paper, we compute the Tian-Zhu invariant on hypersurfaces of complex projective spaces.

Gradient estimates of the Yukawa couplingMay 26 2005The paper is related to the classification of special manifolds and projective special manifolds. One of the result of this paper is that, if the Weil-Petersson metric on a projective special manifold is complete, then the Hodge metrc and the Weil-Petersson ... More

A Note on the Analytic Families of Compact Submanifolds of Complex ManifoldsMay 26 2005In this paper, we prove a result related to the deformation of complex submanifolds, modifying a result of Kodaira (Ann. Math, 75(1), 146-162, 1962).

Smooth Optimization Approach for Sparse Covariance SelectionApr 04 2009In this paper we first study a smooth optimization approach for solving a class of nonsmooth strictly concave maximization problems whose objective functions admit smooth convex minimization reformulations. In particular, we apply Nesterov's smooth optimization ... More

On the DDVV Conjecture and the Comass in Calibrated Geometry (II)Aug 21 2007In this paper, we proved P(n,3), which is an important part of the DDVV conjecture. The general case will be treated in the next version of the paper.

On the Rigidity of Horizontal SlicesMay 26 2005In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.

On the Curvature Tensor of the Hodge Metric of Moduli Space of Polarized Calabi-Yau ThreefoldsMay 26 2005Jun 02 2005In this paper, we give an expression and some estimates of the curvature tensor of the Hodge metric over the moduli space of a polarized Calabi-Yau threefold. The symmetricity of the Yukawa coupling is also studied. In the last section of this paper, ... More

On the Lower Order Terms of the Asymptotic Expansion of ZelditchNov 21 1998Jan 31 1999In this paper, we computed the first three coefficients of the asymptotic expansion of Zelditch. We also proved that in general, the $k$-th coefficient is a polynomial of the curvature and its derivative of weight $k$.

The splitting lemmas for nonsmooth functionals on Hilbert spacesFeb 10 2011Nov 07 2012The usual Gromoll-Meyer's generalized Morse lemma near degenerate critical points on Hilbert spaces, so called splitting lemma, is stated for at least $C^2$-smooth functionals. In this paper we establish a splitting theorem and a shifting theorem for ... More

Farrell cohomology of low genus pure mapping class groups with puncturesJul 22 2002In this paper, we calculate the p-torsion of the Farrell cohomology for low genus pure mapping class groups with punctures, where p is an odd prime. Here, `low genus' means g=1,2,3; and `pure mapping class groups with punctures' means the mapping class ... More

Electroweak and Majorana Sector Higgs Bosons and Pseudo-Nambu-Goldstone BosonsMar 14 2016Jun 06 2016We propose a Clifford algebra based model, which treats both gravity and Yang-Mills interactions as gauge fields. There are two sectors of boson fields as electroweak and Majorana bosons. The electroweak boson sector induces fermion masses via spontaneous ... More

Form factor description of the non-collinear Compton scattering tensorJul 10 1997Aug 08 1997We present a parameterization of the non-collinear (virtual) Compton scattering tensor in terms of form factors, in which the Lorentz tensor associated with each form factor possesses manifest electromagnetic gauge invariance. The main finding is that ... More

Symmetry analysis of the hadronic tensor for the semi-inclusive pseudoscalar meson leptoproduction from an unpolarized nucleon targetJun 16 1995Sep 09 1995By examining the symmetry constraints on the semi-inclusive pseudoscalar particle production in unpolarized inelastic lepton-hadron scattering, we present a complete, exact Lorentz decomposition for the corresponding hadronic tensor. As a result, we find ... More

Observability Estimate and State Observation Problems for Stochastic Hyperbolic EquationsMay 03 2013Jun 09 2013In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. ... More

Exact Controllability for Stochastic Schrodinger EquationsApr 26 2013This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the standard duality ... More

Two-Monopole Systems and the Formation of Non-Abelian CloudsJun 29 1998Nov 20 1998We study the energy density of two distinct fundamental monopoles in SU(3) and Sp(4) theories with an arbitrary mass ratio. Several special limits of the general result are checked and verified. Based on the analytic expression of energy density the coefficient ... More

PRADA Applicability in Industrial PracticeJul 21 2017The proliferation of Android devices brings the fragmentation problem. Selecting and prioritizing major device models are critical for mobile app developers to select testbeds and optimize various issues such as quality-assurance, release planning, revenues, ... More

Morse theory methods for a class of quasi-linear elliptic systems of higher orderSep 07 2017Dec 04 2017We develop the local Morse theory for a class of non-twice continuously differentiable functionals on Hilbert spaces, including a new generalization of the Gromoll-Meyer's splitting theorem and a weaker Marino-Prodi perturbation type result. They are ... More

Parametrizing Program Analysis by Lifting to Cardinal Power DomainsMay 25 2010A parametric analysis is an analysis whose input and output are parametrized with a number of parameters which can be instantiated to abstract properties after analysis is completed. This paper proposes to use Cousot and Cousot's Cardinal power domain ... More

Deriving Abstract Semantics for Forward Analysis of Normal Logic ProgramsNov 06 1998The problem of forward abstract interpretation of {\em normal} logic programs has not been formally addressed in the literature although negation as failure is dealt with through the built-in predicate ! in the way it is implemented in Prolog. This paper ... More

Toward Computation and Memory Efficient Neural Network Acoustic Models with Binary Weights and ActivationsJun 28 2017Jul 04 2017Neural network acoustic models have significantly advanced state of the art speech recognition over the past few years. However, they are usually computationally expensive due to the large number of matrix-vector multiplications and nonlinearity operations. ... More

Semantic Channel and Shannon's Channel Mutually Match for Multi-Label ClassificationMay 02 2018A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. Label learning is to let semantic channels match Shannon's channels and label selection is to let Shannon's channels match ... More

Semantic Information Measure with Two Types of Probability for Falsification and ConfirmationSep 26 2016Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth function (conditional ... More

Magnon band topology in spin-orbital coupled magnets: classification and application to $α$-RuCl$_3$Jul 13 2018Jul 26 2018In spite of flourishing studies on the topology of spin waves, a generic framework to classify and compute magnon band topology in non-collinear magnets is still missing. In this work we provide such a theory framework, by mapping an arbitrary linear ... More

Sequence Training and Adaptation of Highway Deep Neural NetworksJul 07 2016Jul 28 2016Highway deep neural network (HDNN) is a type of depth-gated feedforward neural network, which has shown to be easier to train with more hidden layers and also generalise better compared to conventional plain deep neural networks (DNNs). Previously, we ... More

Constructing a weak subset of a random setFeb 11 2016The tree forcing method given by (Liu 2015) enables the cone avoiding of strong enumeration of a given tree, within a subset or co-subset of an arbitrary given set, provided the given tree does not admit computable strong enumeration. Using this result, ... More

Antifactor of regular bipartite graphsNov 30 2015This problem is NP-complete in general, but for the case when no prescription contains two consecutive gaps, Lov\'asz gave a structural description, and Cornu\'ejols gave a polynomial algorithm. However, results on $H$-factors are known only in some special ... More

Inverse curvature flow in anti-de Sitter-Schwarzschild manifoldSep 30 2016In this paper, we consider the inverse hessian quotient curvature flow with star-shaped initial hypersurface in anti-de Sitter-Schwarzschild manifold. We prove that the solution exists for all time, and the second fundamental form converges to identity ... More

High-frequency limit of the Maxwell-Landau-Lifshitz system in the diffractive optics regimeFeb 16 2012Feb 17 2012We study semilinear Maxwell-Landau-Lifshitz systems in one space dimension. For highly oscillatory and prepared initial data, we construct WKB approximate solutions over long times $O(1/\e)$. The leading terms of the WKB solutions solve cubic Schr\"odinger ... More

On the degenerated Arnold-Givental conjectureJun 01 2008Aug 20 2008This paper has been withdrawn by author due to an error in the proof.

Analytical correlation of routing table length index and routing path length index in hierarchical routing modelApr 13 2008In Kleinrock and Kamoun's paper, the inverse relation of routing table length index and routing path length index in hierarchical routing model is illustrated. In this paper we give the analytical correlation of routing table length index and routing ... More

Rationale awareness for quality assurance in iterative human computation processesApr 16 2012Human computation refers to the outsourcing of computation tasks to human workers. It offers a new direction for solving a variety of problems and calls for innovative ways of managing human computation processes. The majority of human computation tasks ... More

The Prasad conjecture for U(2), SO(4) and Sp(4)Mar 28 2019We will give a proof to the Prasad conjecture for $U_2$, $SO_4$ and $Sp_4$ over a quadratic field extension.

The $\hatΓ$-genus and a regularization of an $S^1$-equivariant Euler classApr 17 2008Aug 28 2008We show that a new multiplicative genus, in the sense of Hirzebruch, can be obtained by generalizing a calculation due to Atiyah and Witten. We introduce this as the $\hat{\Gamma}$-genus, compute its value for some examples and highlight some of its interesting ... More

On the passibility of a short-lived free Dirac particleMay 01 1998A time-decaying Dirac equation is suggested. For a free particle with rest mass about 0.5GeV, the live-time is about 10**(-25) second in the rest frame.

The velocity and angular momentum of a free Dirac electronApr 22 1998It is shown that, in Dirac theory, there is a spatial velocity of a free electron which commutes with the Hamiltonian, so it is a conserved quantity of the motion. Furthermore, there is a spatial orbital angular momentum which also commutes with the Hamiltonian ... More

A Study on the Amount of Random Graph GroupiesJan 13 2013In 1980, Ajtai, Komlos and Szemer{\'e}di defined "groupie": Let $G=(V,E)$ be a simple graph, $|V|=n$, $|E|=e$. For a vertex $v\in V$, let $r(v)$ denote the sum of the degrees of the vertices adjacent to $v$. We say $v\in V$ is a {\it groupie}, if $\frac{r(v)}{\deg(v)}\geq\frac{e}{n}.$ ... More

Vortex Dynamics in Type II SuperconductorsFeb 12 2017Apr 05 2017Time dependent Ginzburg-Landau equation is solved for type II superconductors numerically, and the dynamics of entering vortices, geometric defects and pinning effects have been investigated. A superconducting wire with ratchet defects is designed to ... More

On improving Neymanian analysis for $2^K$ factorial designs with binary outcomesMar 12 2018Mar 03 2019$2^K$ factorial designs are widely adopted by statisticians and the broader scientific community. In this short note, under the potential outcomes framework (Neyman, 1923; Rubin, 1974), we adopt the partial identification approach and derive the sharp ... More

Shape Variables for the Doubly-Charmed B DecaysJun 08 1996We propose to use the hadronic shape variables to test the assumption of ``local duality'' in the doubly-charmed B decays, $B\rightarrow X_{c\bar c s}$. We compute these shape variables at leading order in parton model, and discuss how they can be compared ... More

Avoid Internal Loops in Steady State Flux Space SamplingOct 18 2012As a widely used method in metabolic network studies, Monte-Carlo sampling in the steady state flux space is known for its flexibility and convenience of carrying out different purposes, simply by alternating constraints or objective functions, or appending ... More

Introduction to bulk metallic glass composite and its recent applicationsFeb 28 2011Bulk metallic glass (BMG) materials are hot topics in recent years, not to mention BMG matrix composites, which further improve the magnetic and mechanical properties of BMG materials. BMG and BMG matrix materials are fast developing and promising materials ... More

High-speed Video from Asynchronous Camera ArrayJan 17 2019This paper presents a method for capturing high-speed video using an asynchronous camera array. Our method sequentially fires each sensor in a camera array with a small time offset and assembles captured frames into a high-speed video according to the ... More

Sequential Convex Programming Methods for A Class of Structured Nonlinear ProgrammingOct 10 2012Oct 31 2016In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in ... More

Adaptive First-Order Methods for General Sparse Inverse Covariance SelectionApr 04 2009In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [5], we formulate it as an $l_1$-norm penalized maximum likelihood estimation ... More

Inflation in the Generalized Inverse Power Law ScenarioNov 02 2013We propose a single field inflationary model by generalizing the inverse power law potential from the intermediate model. We study the implication of our model on the primordial anisotropy of cosmological microwave background radiation. Specifically, ... More

On the Geometry of Classifying Spaces and Horizontal SlicesMay 26 2005In this paper, we study the local properties of the moduli space of a polarized Calabi-Yau manifold. Let $U$ be a neighborhood of the moduli space. Then we know the universal covering space $V$ of $U$ is a smooth manifold. Suppose $D$ is the classifying ... More

A Note on Special Kahler ManifoldsMay 26 2005We proved a conjecture of D. Freed that there are no non-trivial complete special Kaehler manifolds.

Theta correspondence and the Prasad conjecture for SL(2)Feb 06 2018Jun 13 2018We use relations between the base change representations and theta lifts, to give a new proof to the local period problems of SL(2) over a nonarchimedean quadratic field extension E/F. Then we will verify the Prasad conjecture for SL(2). With a similar ... More

A New Proof to the Period Problems of GL(2)Nov 11 2016Dec 18 2016We use the relations between the base change representations, theta lifts and Whittaker model, to give a new proof to the period problems of $GL(2)$ over a quadratic local field extension $E/F.$ And we classify both local and global $D^\times(F)-$distinguished ... More

Uniform bounds of base change conductors and link with the generalized Szpiro conjectureNov 02 2012Mar 11 2014The difference between the Faltings height of an abelian variety $A$ defined over a number field $k$ and its stable height is measured by the so-called base change conductor. In this paper, we give a uniform bound of the base change conductor in terms ... More

Virtual moduli cycles and Gromov-Witten invariants of noncompact symplectic manifoldsJun 17 2003May 03 2006This paper constructs and studies the Gromov-Witten invariants and their properties for noncompact geometrically bounded symplectic manifolds. Two localization formulas for GW-invariants are also proposed and proved. As applications we get solutions of ... More

The Prasad conjectures for U(2), SO(4) and Sp(4)Mar 28 2019Apr 07 2019We will give a proof to the Prasad conjectures for $U_2$, $SO_4$ and $Sp_4$ over a quadratic field extension.

Some applications of theta correspondence to branching lawsApr 05 2019In this paper, we will use the local theta correspondences for the dual pair (Sp(W),O(V)) to investigate some branching law problems.

Equivariant Morse inequalities and applicationsMay 15 2012In this paper, we prove equivariant Morse inequalities via Bismut-Lebeau's analytic localization techniques. As an application, we obtain Morse inequalities on compact manifold with nonempty boundary by applying equivariant Morse inequalities to the doubling ... More

SYZ Mirror Symmetry of Hitchin's Moduli Spaces Near Singular Fibers IAug 18 2012We study hyperkahler metrics and hyperholomorphic connections of Hitchin's moduli spaces after Gaiotto, Moore and Neitzke. Their construction via the twistor technique produces intricate wall crossing behaviors. For certain four dimensional Hitchin's ... More

Backward stochastic Volterra integral equations associated with a Levy process and applicationsJun 30 2011Mar 10 2016In this paper, we study a class of backward stochastic Volterra integral equations driven by Teugels martingales associated with an independent L\'{e}vy process and an independent Brownian motion (BSVIELs). We prove the existence and uniqueness as well ... More

Remark on the kinematics of the one-photon production in electron-proton scatteringMay 26 1997Aug 01 1997I clarify the mistakes in the original version hep-ph/9705427 about the phase space factor for the one-photon production in electron-proton scattering and confirm that the earlier result given by Kroll, Sch\"urmann and Guichon is right.

Tensor-Tensor Product ToolboxJun 17 2018Jun 20 2018The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor spectral norm, ... More

Subjective Information Measure and Rate Fidelity TheoryMay 24 2007Using fish-covering model, this paper intuitively explains how to extend Hartley's information formula to the generalized information formula step by step for measuring subjective information: metrical information (such as conveyed by thermometers), sensory ... More

A Polymorphic Groundness Analysis of Logic ProgramsOct 31 1998A polymorphic analysis is an analysis whose input and output contain parameters which serve as placeholders for information that is unknown before analysis but provided after analysis. In this paper, we present a polymorphic groundness analysis that infers ... More

From Bayesian Inference to Logical Bayesian Inference: A New Mathematical Frame for Semantic Communication and Machine LearningSep 03 2018Bayesian Inference (BI) uses the Bayes' posterior whereas Logical Bayesian Inference (LBI) uses the truth function or membership function as the inference tool. LBI was proposed because BI was not compatible with the classical Bayes' prediction and didn't ... More

Asynchronous Physical-layer Network CodingMay 16 2011Jun 05 2011A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as ... More

Comment: Bayesian Checking of the Second Level of Hierarchical Models: Cross-Validated Posterior Predictive Checks Using Discrepancy MeasuresFeb 06 2008Comment: Bayesian Checking of the Second Level of Hierarchical Models [arXiv:0802.0743]

Sampling with Walsh TransformsFeb 22 2015Jul 26 2015With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources as well. Under ... More

Uniform estimates for Stokes equations in domains with small holes and applications in homogenization problemsOct 06 2015Oct 24 2016We consider the Dirichlet problem for the Stokes equations in a domain with a shrinking hole in $\mathbb{R}^d$. An almost complete description concerning the uniform $W^{1,p}$ estimates as the size of the hole goes to zero is shown : for any $d'<p<d$, ... More

Practical Tera-scale Walsh-Hadamard TransformJun 28 2016In the mid-second decade of new millennium, the development of IT has reached unprecedented new heights. As one derivative of Moore's law, the operating system evolves from the initial 16 bits, 32 bits, to the ultimate 64 bits. Most modern computing platforms ... More

Small Generalized Breathers with Exponentially Small Tails for Klein-Gordon EquationsJul 24 2013We consider a class of nonlinear Klein-Gordon equation $u_{tt}=u_{xx}-u+f(u)$ and show that generically there exist small breathers with exponentially small tails.

Compressible Euler equation with damping on Torus in arbitrary dimensionsSep 19 2013Oct 19 2014We study the exponential stability of constant steady state of isentropic compressible Euler equation with damping on $\mathbb T^n$. The local existence of solutions is based on semigroup theory and some commutator estimates. We propose a new method instead ... More

A central limit theorem for stochastic heat equations in random environmentNov 05 2015In this paper, we investigate the asymptotic behaviors of solution to a 1-dimensional stochastic heat equation with random non-linear terms which is generated by a stationary, ergodic random field. We prove the central limit theorem in L^1 sense with ... More

On the asymptotic linearity of reduction numberAug 20 2016Sep 17 2016Let $R$ be a standard graded Noetherian algebra over an infinite field $K$ and $M$ a finitely generated $\mathbb{Z}$-graded $R$-module. Then for any graded ideal $I\subseteq R_+$ of $R$, we show that there exist integers $e_1\geq e_2$ such that $r(I^nM)=\rho_I(M)n+e_1$ ... More

Food Image Recognition by Using Convolutional Neural Networks (CNNs)Dec 03 2016Food image recognition is one of the promising applications of visual object recognition in computer vision. In this study, a small-scale dataset consisting of 5822 images of ten categories and a five-layer CNN was constructed to recognize these images. ... More

A New Proof to the Period Problems of GL(2)Nov 11 2016We use the relations between the base change representations, theta lifts and Whittaker model, to give a new proof to the period problems of $GL(2)$ over a quadratic local field extension $E/F.$ And we classify both local and global $D^\times(F)-$distinguished ... More

Evolutionary system, global attractor, trajectory attractor and applications to the nonautonomous reaction-diffusion systemsFeb 17 2015Jul 19 2015In [Adv. Math., 267(2014), 277-306], Cheskidov and Lu develop a new framework of the evolutionary system that deals directly with the notion of a uniform global attractor due to Haraux, and by which a trajectory attractor is able to be defined for the ... More