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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

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

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 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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

Fine Residual Carrier Frequency and Sampling Frequency Estimation in Wireless OFDM SystemsNov 08 2012This paper presents a novel algorithm for residual phase estimation in wireless OFDM systems, including the carrier frequency offset (CFO) and the sampling frequency offset (SFO). The subcarriers are partitioned into several regions which exhibit pairwise ... More

Synchronization Clustering based on a Linearized Version of Vicsek modelNov 02 2014This paper presents a kind of effective synchronization clustering method based on a linearized version of Vicsek model. This method can be represented by an Effective Synchronization Clustering algorithm (ESynC), an Improved version of ESynC algorithm ... More

Positive metric entropy arises in some nondegenerate nearly integrable systemsApr 26 2016The celebrated KAM Theory says that if one makes a small perturbation of a non-degenerate completely integrable system, we still see a huge measure of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori are known ... More

Electronic Geometry Textbook: A Geometric Textbook Knowledge Management SystemMay 01 2010Electronic Geometry Textbook is a knowledge management system that manages geometric textbook knowledge to enable users to construct and share dynamic geometry textbooks interactively and efficiently. Based on a knowledge base organizing and storing the ... More

Some recent advances on the RBFJul 26 2002This paper aims to survey our recent work relating to the radial basis function (RBF) and its applications to numerical PDEs. We introduced the kernel RBF involving general pre-wavelets and scale-orthogonal wavelets RBF. A dimension-independent RBF error ... More

Positive time fractional derivativeOct 07 2002In mathematical modeling of the non-squared frequency-dependent diffusions, also known as the anomalous diffusions, it is desirable to have a positive real Fourier transform for the time derivative of arbitrary fractional or odd integer order. The Fourier ... More

A new definition of the fractional LaplacianSep 18 2002It is noted that the standard definition of the fractional Laplacian leads to a hyper-singular convolution integral and is also obscure about how to implement the boundary conditions. This purpose of this note is to introduce a new definition of the fractional ... More

A direct time-domain FEM modeling of broadband frequency-dependent absorption with the presence of matrix fractional power: Model IAug 20 2002The frequency-dependent attenuation of broadband acoustics is often confronted in many different areas. However, the related time domain simulation is rarely found in literature due to enormous technical difficulty. The currently popular relaxation models ... More

An infinite linear hierarchy for the incompressible Navier-Stokes equation and applicationOct 06 2016This paper introduces an infinite linear hierarchy for the homogeneous, incompressible three-dimensional Navier-Stokes equation. The Cauchy problem of the hierarchy with a factorized divergence-free initial datum is shown to be equivalent to that of the ... More

Phrase Based Language Model for Statistical Machine Translation: Empirical StudyJan 21 2015Feb 18 2015Reordering is a challenge to machine translation (MT) systems. In MT, the widely used approach is to apply word based language model (LM) which considers the constituent units of a sentence as words. In speech recognition (SR), some phrase based LM have ... More

Beyond Q-Resolution and Prenex Form: A Proof System for Quantified Constraint SatisfactionMar 02 2014Dec 20 2014We consider the quantified constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quantification, whether or not the sentence is true on ... More

Logistic Models of Fractal Dimension Growth for Spatio-Temporal Dynamics of Urban MorphologyJun 11 2016Urban form and growth can be described with fractal dimension, which is a measurement of space filling of urban evolution. Based on empirical analyses, a discovery is made that the time series of fractal dimension of urban form can be treated as a sigmoid ... More

The Seiberg-Witten theory of homology 3-spheresMar 16 1997Feb 01 2000In this thesis we study the Seiberg-Witten theory of an oriented homology 3-sphere. The goal is to extract topological invariants - the Seiberg-Witten invariants - by counting the solutions to the Seiberg-Witten equations on the manifold. The first question ... More

Counting homotopy classes of mappings via Dijkgraaf-Witten invariantsMay 20 2013Oct 22 2015Suppose $\Gamma$ is a finite group acting freely on $S^{n}$ ($n\geqslant 3$ being odd) and $M$ is any closed oriented $n$-manifold. We show that, given an integer $k$, the set $\deg^{-1}(k)$ of based homotopy classes of mappings with degree $k$ is finite ... More

An allometric scaling relation based on logistic growth of citiesDec 13 2013The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed "exponential allometry", ... More

Phase Transition in (2+1)d Quantum GravityApr 05 1994(2+1) dimensional gravity is equivalent to an exactly soluble non-Abelian Chern-Simons gauge field theory (E Witten 1988). Regarding this as the topological phase of quantum gravity in (2+1)d, we suggest a topological symmetry breaking by introducing ... More

Exotic hadrons at hadron collidersSep 01 2014In this proceeding, an overview of the recent progress of the exotic hadrons studies at hadron colliders is presented, including the experimental measurement results from CMS, LHCb, CDF and D0. The talk covers the physics properties study of X(3872); ... More

On a geometric realization of C$^*$-algebrasSep 09 2015Further to the functional representations of C$^*$-algebras proposed by R. Cirelli, A. Mania and L. Pizzocchero, we consider in this article the uniform K\"ahler bundle (in short, UKB) description of some C$^*$-algebraic subjects. In particular, we obtain ... More

Angular power spectrum of the galactic synchrotron radiationSep 29 2004We calculate the angular power spectrum of the galactic synchrotron radiation induced by the small scale fluctuations of the magnetic field and the cosmic ray electron density. Using the observed interstellar magnetic field spectrum, which is consistent ... More

The Helium abundance problem and non-minimally coupled quintessenceNov 28 2000There is a tension between observed Helium abundance and the prediction of the standard Big Bang Nucleosynthesis. We show that non-minimally quintessence model may help to reduce this tension between theory and observation.

On minimal 3-folds of general type with maximal pluricanonical section indexApr 17 2016Let $X$ be a minimal 3-fold of general type. The pluricanonical section index $\delta(X)$ is defined to be the minimal integer $m$ so that $P_{m}(X)\geq 2$. According to Chen-Chen, one has either $1\leq \delta(X)\leq 15$ or $\delta(X)=18$. This note aims ... More

Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noiseMar 30 2016Partially motivated by the recent papers of Conus, Joseph and Khoshnevisan [Ann. Probab. 41 (2013) 2225-2260] and Conus et al. [Probab. Theory Related Fields 156 (2013) 483-533], this work is concerned with the precise spatial asymptotic behavior for ... More

Error analysis of staggered finite difference finite volume schemes on unstructured meshesJun 03 2016This work combines the consistency in lower-order differential operators with external approximations of functional spaces to obtain error estimates for finite difference finite volume schemes on unstructured non-uniform meshes. This combined approach ... More

Social Networks and the Choices People MakeFeb 13 2014May 02 2014Social marketing is becoming increasingly important in contemporary business. Central to social marketing is quantifying how consumers choose between alternatives and how they influence each other. This work considers a new but simple multinomial choice ... More

A New Model of Urban Population Density Indicating Latent Fractal StructureSep 25 2016Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal cities, we ... More

Optimal time-dependent lower bound on density for classical solutions of 1-D compressible Euler equationsAug 18 2015Sep 16 2015For the compressible Euler equations, even when the initial data are uniformly away from vacuum, solution can approach vacuum in infinite time. Achieving sharp lower bounds of density is crucial in the study of Euler equations. In this paper, for the ... More

Magnetic monopole condensation in pyrochlore ice quantum spin liquid: application to Pr2Ir2O7 and Yb2Ti2O7Feb 06 2016May 09 2016Pyrochlore iridates and pyrochlore ices are two families of materials where novel quantum phenomena are intertwined with strong spin-orbit coupling, substantial electron correlation and geometrical frustration. Motivated by the puzzling experiments on ... More

Poincare polynomials of hyperquot schemesMar 14 2000Hyperquot schemes are generalizations of Grothendieck's Quot scheme to partial flags. Using a Bialynicki-Birula decomposition, we obtain combinatorial data for the Betti numbers, and collect this information into the form of rational generating functions ... More

Fractal Analysis Based on Hierarchical Scaling in Complex SystemsNov 22 2016A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and spatial network ... More

Truncated affine grassmannians and truncated affine Springer fibers for $\mathrm{GL}_{3}$Jan 09 2014We state a conjecture on how to construct affine pavings for cohomologically pure projective algebraic varieties, which admit an action of torus such that the fixed points and $1$-dimensional orbits are finite. Experiments on the affine grassmannian for ... More

On the fundamental domain of affine Springer fibersMar 19 2013Oct 14 2016For $G$ 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

The $ξ$-stability on the affine grassmannianFeb 05 2012Sep 17 2015We introduce a notion of $\xi$-stability on the affine grassmannian $\xx$ for the classical groups, this is the local version of the $\xi$-stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the ... More

Quantum Finance: The Finite Dimensional CaseDec 26 2001Jul 04 2002In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the ... More

Wigner-Yanase skew information as tests for quantum entanglementDec 13 2004Feb 20 2010A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems ... More

On the microscopic spacetime convexity principle for fully nonlinear parabolic equations I: Spacetime convex solutionsMar 20 2014May 23 2014Spacetime convexity is a basic geometric property of the solutions of parabolic equations. In this paper, we study microscopic convexity properties of spacetime convex solutions of fully nonlinear parabolic partial differential equations and give a new ... More

Matroids: A Macaulay2 packageNov 14 2015We give an overview of the Macaulay2 package Matroids, which contains functionality to create and compute with matroids. Examples highlighting the use of all major functions in the package are provided, along with explanations of some of the algorithms. ... More

On birational boundedness of Fano fibrationsSep 29 2015We investigate birational boundedness of Fano varieties and Fano fibrations. We establish an inductive step towards birational boundedness of Fano fibrations via conjectures related to boundedness of Fano varieties and Fano fibrations. As corollaries, ... More

Boundedness of anti-canonical volumes of singular log Fano threefoldsNov 25 2014Sep 22 2015We prove Weak Borisov--Alexeev--Borisov Conjecture in dimension three which states that the anti-canonical volume of an $\epsilon$-klt log Fano pair of dimension three is bounded from above.

Bounding the volumes of singular weak log del Pezzo surfacesMay 28 2013We give an optimal upper bound for the anti-canonical volume of an $\epsilon$-lc weak log del Pezzo surface. Moreover, we consider the relation between the bound of the volume and the Picard number of the minimal resolution of the surface. Furthermore ... More

A Digital-Discrete Method For Smooth-Continuous Data ReconstructionOct 16 2010A systematic digital-discrete method for obtaining continuous functions with smoothness to a certain order (C^(n)) from sample data is designed. This method is based on gradually varied functions and the classical finite difference method. This new method ... More

Length of separable states and symmetrical informationally complete (SIC) POVMFeb 04 2013This short note reviews the notion and fundamental properties of SIC-POVM and its connection with the length of separable states. We also review the t-design.

Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free RepresentationsApr 08 2010We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated to Poisson algebras and a quasi-derivation found by Xu. These algebras ... More