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KLMAT: A Kernel Least Mean Absolute Third AlgorithmMar 11 2016Aug 12 2017In this paper, a kernel least mean absolute third (KLMAT) algorithm is developed for adaptive prediction. Combining the benefits of the kernel method and the least mean absolute third (LMAT) algorithm, the proposed KLMAT algorithm performs robustly against ... More

Two improved normalized subband adaptive filter algorithms with good robustness against impulsive interferencesDec 16 2015Feb 29 2016To improve the robustness of subband adaptive filter (SAF) against impulsive interferences, we propose two modified SAF algorithms with an individual scale function for each subband, which are derived by maximizing correntropy-based cost function and ... More

Mean-Square Performance Analysis of Noise-Robust Normalized Subband Adaptive Filter AlgorithmNov 29 2017Oct 17 2018This paper studies the statistical models of the noise-robust normalized subband adaptive filter (NR-NSAF) algorithm in the mean and mean square deviation senses involving transient-state and steady-state behavior by resorting to the method of the vectorization ... More

An Extended Result on the Optimal Estimation under Minimum Error Entropy CriterionJan 24 2014The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some ... More

Constrained Maximum Correntropy Adaptive FilteringOct 06 2016Dec 14 2016Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained ... More

Bias-Compensated Normalized Maximum Correntropy Criterion Algorithm for System Identification with Noisy InputNov 23 2017This paper proposed a bias-compensated normalized maximum correntropy criterion (BCNMCC) algorithm charactered by its low steady-state misalignment for system identification with noisy input in an impulsive output noise environment. The normalized maximum ... More

Diffusion Maximum Correntropy Criterion Algorithms for Robust Distributed EstimationAug 08 2015Feb 03 2016Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive ... More

Sparsity Aware Normalized Least Mean p-power Algorithms with Correntropy Induced Metric PenaltyMar 03 2015For identifying the non-Gaussian impulsive noise systems, normalized LMP (NLMP) has been proposed to combat impulsive-inducing instability. However, the standard algorithm is without considering the inherent sparse structure distribution of unknown system. ... More

Robust Learning with Kernel Mean p-Power Error LossDec 21 2016Correntropy is a second order statistical measure in kernel space, which has been successfully applied in robust learning and signal processing. In this paper, we define a nonsecond order statistical measure in kernel space, called the kernel mean-p power ... More

Correntropy Maximization via ADMM - Application to Robust Hyperspectral UnmixingFeb 04 2016In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach ... More

Quantized Minimum Error Entropy CriterionOct 11 2017Oct 12 2017Comparing with traditional learning criteria, such as mean square error (MSE), the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in Renyis entropy ... More

Associations among Image Assessments as Cost Functions in Linear Decomposition: MSE, SSIM, and Correlation CoefficientAug 04 2017The traditional methods of image assessment, such as mean squared error (MSE), signal-to-noise ratio (SNR), and Peak signal-to-noise ratio (PSNR), are all based on the absolute error of images. Pearson's inner-product correlation coefficient (PCC) is ... More

Kernel Least Mean Square with Adaptive Kernel SizeJan 23 2014Feb 11 2014Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still ... More

Robustness of Maximum Correntropy Estimation Against Large OutliersMar 23 2017Nov 23 2017The maximum correntropy criterion (MCC) has recently been successfully applied in robust regression, classification and adaptive filtering, where the correntropy is maximized instead of minimizing the well-known mean square error (MSE) to improve the ... More

Generalized Correntropy for Robust Adaptive FilteringApr 12 2015As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied ... More

Variable-mixing parameter quantized kernel robust mixed-norm algorithms for combating impulsive interferenceAug 21 2015Feb 09 2018Although the kernel robust mixed-norm (KRMN) algorithm outperforms the kernel least mean square (KLMS) algorithm in impulsive noise, it still has two major problems as follows: (1) The choice of the mixing parameter in the KRMN is crucial to obtain satisfactory ... More

KLMAT: A Kernel Least Mean Absolute Third AlgorithmMar 11 2016The kernel methods provide an interesting way to improve the performance of nonlinear adaptive filters. In this paper, a kernel least mean absolute third (KLMAT) algorithm is proposed for accelerating the convergence speed of the kernel adaptive filter. ... More

Set-membership versions of improved normalized subband adaptive filter algorithm for highly noisy systemDec 16 2015In order to improve the performances of the recently-presented improved normalized subband adaptive filter (INSAF) algorithm for highly noisy system, this paper proposes a set-membership version of the INSAF algorithm (SM-INSAF) by exploiting the concept ... More

Set-membership improved normalized subband adaptive filter algorithms for acoustic echo cancellationDec 16 2015Jul 27 2017In order to improve the performances of recently-presented improved normalized subband adaptive filter (INSAF) and proportionate INSAF algorithms for highly noisy system, this paper proposes their set-membership versions by exploiting the theory of set-membership ... More

Variable-mixing parameter quantized kernel robust mixed-norm algorithms for combating impulsive interferenceAug 21 2015To overcome the performance degradation in impulsive noise environments, a kernel robust mixed-norm (KRMN) algorithm is presented which no longer requires a Gaussian environment. It incorporates the robust mixed-norm (RMN) algorithm and kernel method ... More

Constrained Maximum Correntropy Adaptive FilteringOct 06 2016Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained ... More

A novel normalized sign algorithm for system identification under impulsive noise interferenceMay 28 2015Dec 08 2015To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm ... More

Robust Adaptive Sparse Channel Estimation in the Presence of Impulsive NoisesFeb 19 2015Broadband wireless channels usually have the sparse nature. Based on the assumption of Gaussian noise model, adaptive filtering algorithms for reconstruction sparse channels were proposed to take advantage of channel sparsity. However, impulsive noises ... More

Granger Causality Analysis Based on Quantized Minimum Error Entropy CriterionAug 07 2018Linear regression model (LRM) based on mean square error (MSE) criterion is widely used in Granger causality analysis (GCA), which is the most commonly used method to detect the causality between a pair of time series. However, when signals are seriously ... More

Maximum Correntropy Criterion with Variable CenterApr 13 2019Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is ... More

Brain Inspired Cognitive Model with Attention for Self-Driving CarsFeb 18 2017Perception-driven approach and end-to-end system are two major vision-based frameworks for self-driving cars. However, it is difficult to introduce attention and historical information of autonomous driving process, which are the essential factors for ... More

Consistency-aware Shading Orders Selective Fusion for Intrinsic Image DecompositionOct 23 2018We address the problem of decomposing a single image into reflectance and shading. The difficulty comes from the fact that the components of image---the surface albedo, the direct illumination, and the ambient illumination---are coupled heavily in observed ... More

A Novel Brain Decoding Method: a Correlation Network Framework for Revealing Brain ConnectionsDec 01 2017Brain decoding is a hot spot in cognitive science, which focuses on reconstructing perceptual images from brain activities. Analyzing the correlations of collected data from human brain activities and representing activity patterns are two problems in ... More

Maximum Correntropy Unscented FilterAug 26 2016The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a ... More

Maximum Correntropy Kalman FilterSep 15 2015Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed ... More

Maximum Correntropy Adaptive Filtering Approach for Robust Compressive Sensing ReconstructionJun 10 2017Robust compressive sensing(CS) reconstruction has become an attractive research topic in recent years. Robust CS aims to reconstruct the sparse signals under non-Gaussian(i.e. heavy tailed) noises where traditional CS reconstruction algorithms may perform ... More

Augmented Space Linear ModelFeb 01 2018Feb 02 2018The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it becomes slower ... More

Robust Matrix Completion via Maximum Correntropy Criterion and Half Quadratic OptimizationMar 14 2019Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In this paper, ... More

Diffusion Adaptation Framework for Compressive Sensing ReconstructionDec 03 2017Jun 22 2018Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively studied. Many reconstruction ... More

Maximum Total Correntropy Diffusion Adaptation over Networks with Noisy LinksFeb 14 2018Distributed estimation over networks draws much attraction in recent years. In many situations, due to imperfect information communication among nodes, the performance of traditional diffusion adaptive algorithms such as the diffusion LMS (DLMS) may degrade. ... More

Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environmentsMar 03 2015Apr 14 2015Sparse adaptive channel estimation problem is one of the most important topics in broadband wireless communications systems due to its simplicity and robustness. So far many sparsity-aware channel estimation algorithms have been developed based on the ... More

Prognostics Estimations with Dynamic StatesJul 16 2018Sep 23 2018The health state assessment and remaining useful life (RUL) estimation play very important roles in prognostics and health management (PHM), owing to their abilities to reduce the maintenance and improve the safety of machines or equipment. However, they ... More

Kernel Risk-Sensitive Loss: Definition, Properties and Application to Robust Adaptive FilteringAug 01 2016Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian signal processing ... More

Minimum Error Entropy Kalman FilterApr 14 2019To date most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian ... More

Minimum Error Entropy Kalman FilterApr 14 2019Apr 17 2019To date most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian ... More

Gravitational instantons with faster than quadratic curvature decay (III)Mar 28 2016Oct 06 2016This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, ... More

Gravitational instantons with faster than quadratic curvature decay (II)Aug 31 2015Jun 23 2016This is our second paper in a series to study gravitational instantons, i.e. complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models ... More

Angora: Efficient Fuzzing by Principled SearchMar 04 2018Mar 27 2018Fuzzing is a popular technique for finding software bugs. However, the performance of the state-of-the-art fuzzers leaves a lot to be desired. Fuzzers based on symbolic execution produce quality inputs but run slow, while fuzzers based on random mutation ... More

Modeling the Annual Growth Rate of Electricity Consumption of China in the 21st Century: Trends and PredictionOct 21 2017In this paper, the annual growth rate of electricity consumption in China in the first 15 years of the 21st century is modeled using multiple linear regression. Historical data and trends of gross domestic product, fixed assets investment and share of ... More

Characterizations of asymptotic distributions of continuous-time Pólya processesNov 29 2016Sep 02 2018We propose an elementary but effective approach to studying a general class of Poissonized tenable and balanced urns on two colors. We characterize the asymptotic behavior of the process via a partial differential equation that governs the process, coupled ... More

Notes on "Einstein metrics on compact simple Lie groups attached to standard triples"Jan 06 2017In the paper "Einstein metrics on compact simple Lie groups attached to standard triples", the authors introduced the definition of standard triples and proved that every compact simple Lie group $G$ attached to a standard triple $(G,K,H)$ admits a left-invariant ... More

Gravitational instantons with faster than quadratic curvature decay (I)May 07 2015In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known end----ALE, ALF, ALG or ALH. 2.In ALG and ... More

Exact Methods for Multistage Estimation of a Binomial ProportionFeb 13 2013We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, ... More

Embedding of tenable and balanced urn scheme into continuous-time Pólya processNov 29 2016We study poissonized tenable and balanced urns on two colors, say white and blue. In particular, we look at the process obtained by embedding a generalized P\'{o}lya-Eggenberger urn into continuous time. We analyze the number of white and blue balls after ... More

Some sufficient conditions for infinite collisions of simple random walks on a wedge combOct 26 2010In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile $\{f(n), n\in \ZZ\}$. One interesting result is that if $f(n)$ has a growth order as $n\log n$, then two independent ... More

Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficientsAug 30 2017Sep 24 2017Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide a rigourous mathematical theory of two types of nonequilibrium FDTs for inhomogeneous ... More

Delay-Optimal Buffer-Aware Probabilistic Scheduling with Adaptive TransmissionSep 09 2015Cross-layer scheduling is a promising way to improve Quality of Service (QoS) given a power constraint. In this paper, we investigate the system with random data arrival and adaptive transmission. Probabilistic scheduling strategies aware of the buffer ... More

Orthogonal Quantum Group Invariants of LinksJul 09 2010We study the Chern-Simons partition function of orthogonal quantum group invariants, and propose a new orthogonal Labastida-Mari\~{n}o-Ooguri-Vafa conjecture as well as degree conjecture for free energy associated to the orthogonal Chern-Simons partition ... More

On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, IIAug 16 2017By a canonical (resp. terminal) weak $\mathbb{Q}$-Fano $3$-fold we mean a normal projective one with at worst canonical (resp. terminal) singularities on which the anti-canonical divisor is $\mathbb{Q}$-Cartier, nef and big. For a canonical weak $\mathbb{Q}$-Fano ... More

On the anti-canonical geometry of $\mathbb{Q}$-Fano 3-foldsAug 27 2014Feb 02 2015For a $\mathbb{Q}$-Fano 3-fold $X$ on which $K_X$ is a canonical divisor, we investigate the geometry induced from the linear system $|-mK_X|$ in this paper and prove that the anti-$m$-canonical map $\varphi_{-m}$ is birational onto its image for all ... More

Minimum K_2,3-saturated GraphsDec 19 2010Nov 11 2012A graph is K_{2,3}-saturated if it has no subgraph isomorphic to K_{2,3}, but does contain a K_{2,3} after the addition of any new edge. We prove that the minimum number of edges in a K_{2,3}-saturated graph on n >= 5 vertices is sat(n, K_{2,3}) = 2n ... More

Spin and hyperelliptic structures of log twisted differentialsOct 17 2016Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian ... More

On the Imbedding Problem for Three-state Time Homogeneous Markov Chains with Coinciding Negative EigenvaluesSep 11 2010For an indecomposable $3\times 3$ stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means ... More

Faster Deterministic Algorithms for Packing, Matching and $t$-Dominating Set ProblemsJun 15 2013In this paper, we devise three deterministic algorithms for solving the $m$-set $k$-packing, $m$-dimensional $k$-matching, and $t$-dominating set problems in time $O^*(5.44^{mk})$, $O^*(5.44^{(m-1)k})$ and $O^*(5.44^{t})$, respectively. Although recently ... More

Exact Sample Size Methods for Estimating Parameters of Discrete DistributionsNov 08 2012Nov 19 2012In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal property assumptions, ... More

Principal boundary of moduli spaces of abelian and quadratic differentialsNov 05 2016The seminal work of Eskin-Masur-Zorich described the principal boundary of moduli spaces of abelian differentials that parameterizes flat surfaces with a prescribed generic configuration of short parallel saddle connections. In this paper we describe ... More

Gröbner-Shirshov bases for metabelian Lie algebrasJun 13 2011In this paper, we establish the Gr\"{o}bner-Shirshov bases theory for metabelian Lie algebras. As applications, we find the Gr\"{o}bner-Shirshov bases for partial commutative metabelian Lie algebras related to circuits, trees and some cubes.

The Noether inequality for algebraic threefolds (With an Appendix by János Kollár)Mar 15 2018Jul 19 2018We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq ... More

CrowdFusion: A Crowdsourced Approach on Data Fusion RefinementFeb 02 2017Data fusion has played an important role in data mining because high-quality data is required in a lot of applications. As on-line data may be out-of-date and errors in the data may propagate with copying and referring between sources, it is hard to achieve ... More

Adaptivity vs PostselectionJun 13 2016We study the following problem: with the power of postselection (classically or quantumly), what is your ability to answer adaptive queries to certain languages? More specifically, for what kind of computational classes $\mathcal{C}$, we have $\mathsf{P}^{\mathcal{C}}$ ... More

Bounded Rationality, Strategy Simplification, and EquilibriumFeb 24 2010Jun 26 2011It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with minimization ... More

On the fundamental domain of affine Springer fibersMar 19 2013Mar 11 2014For $G$ a connected reductive group, $\gamma\in \kg(F)$ semisimple regular integral, we introduce a fundamental domain $F_{\gamma}$ for the affine Springer fibers $\xx_{\gamma}$. There is a beautiful way to reduce the purity conjecture of $\xx_{\gamma}$ ... More

Product Formula, Independence and Asymptotic Moment-Independence for Complex Multiple Wiener-Ito IntegralsDec 05 2014We present the product formula for complex multiple Wiener-Ito integrals. As applications, we show the Ustunel-Zakai independent criterion, the Nourdin-Rosinski asymptotic moment-independent criterion and joint convergence criterion for complex multiple ... More

A Geometric Method to Obtain the Generation Probability of a SentenceJun 04 2014"How to generate a sentence" is the most critical and difficult problem in all the natural language processing technologies. In this paper, we present a new approach to explain the generation process of a sentence from the perspective of mathematics. ... More

Optimistic versus Pessimistic--Optimal Judgemental Bias with Reference PointOct 10 2013This paper develops a model of reference-dependent assessment of subjective beliefs in which loss-averse people optimally choose the expectation as the reference point to balance the current felicity from the optimistic anticipation and the future disappointment ... More

The spatial meaning of Pareto's scaling exponent of city-size distributionSep 19 2013The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the fractal dimension. ... More

Scalar field quasinormal frequencies of Reissner-Nordström black hole surrounded by quintessenceMay 27 2016Jun 03 2016We evaluate the quasinormal modes of massless scalar field around Reissner-Nordstr$\ddot{\text{o}}$m black hole surrounded by a static and spherically symmetric quintessence by using the continued fraction method. The appropriate Frobenius series for ... More

Localization Formulas About Two Killing Vector FieldsApr 13 2013In this article, we will discuss the smooth $(X_{M}+\sqrt{-1}Y_{M})$-invariant forms on $M$ and to establish a localization formulas. As an application, we get a localization formulas for characteristic numbers.

Sequential change-point detection based on nearest neighborsApr 12 2016We propose a new framework for the detection of change points in online, sequential data analysis. The approach utilizes nearest neighbor information and can be applied to multivariate or object data sequences. Different stopping rules are explored, and ... More

The Cartan Model for Equivariant CohomologyAug 12 2016In this article, we will discuss a new operator $d_{C}$ on $W(\mathfrak{g})\otimes\Omega^{*}(M)$ and to construct a new Cartan model for equivariant cohomology. We use the new Cartan model to construct the corresponding BRST model and Weil model, and ... More

On bootstrap approximations for high-dimensional U-statistics and random quadratic formsSep 30 2016This paper establishes a unified theory of bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when $d$ is large. Specifically, we show that the empirical bootstrap with the ... More

Normalizing and Classifying Shape Indexes of Cities by Ideas from FractalsAug 31 2016A standard scientific study comprises two processes: one is to describe a thing, and the other is to understand how the thing works. In order to understand the principle of urban growth, a number of shape indexes are proposed to describe the size and ... More

Universal Logarithmic Scrambling in Many Body LocalizationAug 09 2016Aug 28 2016Out of time ordered correlator (OTOC) is recently introduced as a powerful diagnose for quantum chaos. To go beyond, here we present an analytical solution of OTOC for a non-chaotic many body localized (MBL) system, showing distinct feature from quantum ... More

Equivalent Relation between Normalized Spatial Entropy and Fractal DimensionAug 06 2016Sep 25 2016Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy to fractal dimension is ... More

Non-divergence Parabolic Equations of Second Order with Critical Drift in Lebesgue SpacesNov 04 2015Feb 02 2016We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift \[-u_{t}+Lu=-u_{t}+\sum_{ij}a_{ij}D_{ij}u+\sum b_{i}D_{i}u=0\,(\geq0,\,\leq0)\] in some domain $Q\subset \mathbb{R}^{n+1}$. We prove growth ... More

Wave equations with moving potentialsOct 30 2016In this paper, we study the endpoint reversed Strichartz estimates along general time-like trajectories for wave equations in $\mathbb{R}^{3}$. We also discuss some applications of the reversed Strichartz estimates and the structure of wave operators ... More

von Neumann-Landau equation for wave functions, wave-particle duality and collapses of wave functionsMar 22 2007Sep 29 2007It is shown that von Neumann-Landau equation for wave functions can present a mathematical formalism of motion of quantum mechanics. The wave functions of von Neumann-Landau equation for a single particle are `bipartite', in which the associated Schr\"{o}dinger's ... More

Variants of Bell inequalitiesNov 13 2006A family of Bell-type inequalities is present, which are constructed directly from the "standard" Bell inequalities involving two dichotomic observables per site. It is shown that the inequalities are violated by all the generalized Greenberger-Horne-Zeilinger ... More

Deeply Virtual Compton Scattering and Skewed Parton DistributionAug 02 2000An overview of the current status of and possible future theoretical, phenomenological and experimental studies of DVCS and SPD's is presented.

Strong laws of large numbers for capacitiesJun 03 2010In this paper, with the notion of independent identically distributed random variables under sub-linear expectations initiated by Peng, we derive three kinds of strong laws of large numbers for capacities. Moreover, these theorems are natural and fairly ... More

Machine Translation Model based on Non-parallel Corpus and Semi-supervised Transductive LearningMay 22 2014Although the parallel corpus has an irreplaceable role in machine translation, its scale and coverage is still beyond the actual needs. Non-parallel corpus resources on the web have an inestimable potential value in machine translation and other natural ... More

Sub-Gaussian heat kernel estimates and quasi Riesz transforms for $1\leq p\leq 2$Jan 10 2014On a complete non-compact Riemannian manifold $M$, we prove that a so-called quasi Riesz transform is always $L^p$ bounded for $1<p\leq 2$. If $M$ satisfies the doubling volume property and the sub-Gaussian heat kernel estimate, we prove that the quasi ... More

Electron and phonon correlations in systems of one-dimensional electrons coupled to phononsJun 02 2008Aug 16 2008Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2k_F$-wave components of the electron ... More

Hsiao-Code Check Matrices and Recursively Balanced MatricesMar 08 2008The key step of generating the well-known Hsiao code is to construct a {0,1}-check-matrix in which each column contains the same odd-number of 1's and each row contains the same number of 1's or differs at most by one for the number of 1's. We also require ... More

The curvature of spectral energy distribution of blazarsMay 06 2014The SED of blazars show significant curvature. In this paper, we study the curvature properties for a large sample of Fermi/LAT bright blazars based on quasi-simultaneous SED. Both SEDs of synchrotron and inverse Compton (IC) components are fitted by ... More

GKM theory, characteristic classes and the equivariant cohomology ring of real GrassmannianSep 20 2016Oct 07 2016We use GKM theory to understand equivariant cohomology of real Grassmannian and oriented Grassmannian, then relate this to the Borel description which says the ring generators are equivariant Pontryagin classes, Euler classes in even dimension, and one ... More

On The Hardness of Approximate and Exact (Bichromatic) Maximum Inner ProductFeb 07 2018In this paper we study the (Bichromatic) Maximum Inner Product Problem (Max-IP), in which we are given sets $A$ and $B$ of vectors, and the goal is to find $a \in A$ and $b \in B$ maximizing inner product $a \cdot b$. Max-IP is very basic and serves as ... More

Time-space fabric underlying anomalous diffusionMay 08 2005This study unveils the time-space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time-space fabric on physical behaviors and accordingly derive fractional quantum ... More

The Value of Interaction in Data IntelligenceDec 14 2018In human computer interaction (HCI), it is common to evaluate the value of HCI designs, techniques, devices, and systems in terms of their benefit to users. It is less common to discuss the benefit of HCI to computers. Every HCI task allows a computer ... More

Discretized sum-product for large setsJan 27 2019Let $A\subset [1, 2]$ be a $(\delta, \sigma)$-set with measure $|A|=\delta^{1-\sigma}$ in the sense of Katz and Tao. For $\sigma\in (1/2, 1)$ we show that $$ |A+A|+|AA|\gtrapprox \delta^{-c}|A|, $$ for $c=\frac{(1-\sigma)(2\sigma-1)}{6\sigma+4}$. This ... More

Computing twisted Alexander polynomials for Montesinos linksSep 10 2017Oct 25 2018In recent years, twisted Alexander polynomial has been playing an important role in low-dimensional topology. For a class of links, namely Montesinos links, we present an efficient method to compute the twisted Alexander polynomial associated to any linear ... More

Einstein-Weyl structures on almost cosymplectic manifoldsJan 17 2018Nov 22 2018In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(\kappa,\mu)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl structures. ... More

A Concise Proof of Discrete Jordan Curve TheoremNov 17 2014Nov 26 2014This paper gives a concise proof of the Jordan curve theorem on discrete surfaces. We also embed the discrete surface in the 2D plane to prove the original version of the Jordan curve theorem. This paper is a simple version of L. Chen, Note on the discrete ... More

Secure Communication over Interference Channel: To Jam or Not to Jam?Oct 30 2018We consider a secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap ... More

Convergence of Krasulina SchemeAug 28 2018Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. Consider the points $X_1, X_2,..., X_n$ are vectors drawn i.i.d. from a distribution with mean zero and covariance $\Sigma$, ... More