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Construction of Symmetric Complex Tight wavelet Frames from Pseudo Splines via Matrix Extension with SymmetryMar 18 2010Construction of Symmetric Complex Tight wavelet Frames from Pseudo Splines via Matrix Extension with Symmetry.

Matrix Extension with Symmetry and Construction of Biorthogonal MultiwaveletsJun 11 2010Let $(\pP,\wt\pP)$ be a pair of $r \times s$ matrices of Laurent polynomials with symmetry such that $\pP(z) \wt\pP^*(z)=I_\mrow$ for all $z\in \CC \bs \{0\}$ and both $\pP$ and $\wt\pP$ have the same symmetry pattern that is compatible. The biorthogonal ... More

Smooth affine shear tight frames with MRA structureAug 28 2013Finding efficient representations is one of the most challenging and heavily sought problems in mathematics. Representation using shearlets recently receives a lot of attention due to their desirable properties in both theory and applications. Using the ... More

Linear multiscale transforms based on even-reversible subdivision operatorsOct 30 2017Multiscale transforms for real-valued data, based on interpolatory subdivision operators have been studied in recent year. They are easy to define, and can be extended to other types of data, for example to manifold-valued data. In this paper we define ... More

Explicit Bernstein type inequalities for wavelet coefficients in $L_p(R^n)$Aug 28 2017In this paper, we investigate the wavelet coefficients for function spaces $\mathcal{A}_k^p=\{f: \|(i \omega)^k\hat{f}(\omega)\|_p\leq 1\}, k\in N, p\in(1,\infty)$ using an important quantity $C_{k,p}(\psi)$. In particular, Bernstein type inequalities ... More

Matrix Extension with Symmetry and Its Application to Filter BanksJan 07 2010In this paper, we completely solve the matrix extension problem with symmetry and provide a step-by-step algorithm to construct such a desired matrix $\mathsf{P}_e$ from a given matrix $\mathsf{P}$. Furthermore, using a cascade structure, we obtain a ... More

Tight framelets and fast framelet filter bank transforms on manifoldsAug 13 2016Mar 01 2018Tight framelets on a smooth and compact Riemannian manifold $\mathcal{M}$ provide a tool of multiresolution analysis for data from geosciences, astrophysics, medical sciences, etc. This work investigates the construction, characterizations, and applications ... More

Tight framelets and fast framelet transforms on manifoldsAug 13 2016Tight framelets on a smooth and compact Riemannian manifold $\mathcal{M}$ provide a tool of multiresolution analysis for data from geosciences, astrophysics, medical sciences, etc. This work investigates the construction, characterizations, and applications ... More

Digital Shearlet TransformAug 02 2011Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and shearlets. Alongside ... More

Directional Tensor Product Complex Tight Framelets with Low RedundancyDec 17 2014Though high redundancy rate of a tight frame can improve performance in applications, as the dimension increases, it also makes the computational cost skyrocket and the storage of frame coefficients increase exponentially. This seriously restricts the ... More

ShearLab: A Rational Design of a Digital Parabolic Scaling AlgorithmJun 07 2011Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such features is the ... More

Analysis of Inpainting via Clustered Sparsity and Microlocal AnalysisJun 12 2012Nov 28 2012Recently, compressed sensing techniques in combination with both wavelet and directional representation systems have been very effectively applied to the problem of image inpainting. However, a mathematical analysis of these techniques which reveals the ... More

Directional Compactly supported Box Spline Tight Framelets with Simple StructureAug 28 2017To effectively capture singularities in high-dimensional data and functions, multivariate compactly supported tight framelets, having directionality and derived from refinable box splines, are of particular interest in both theory and applications. The ... More

Gabor ShearletsMar 26 2013In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction. As a consequence, ... More

Symmetric Canonical Quincunx Tight Framelets with High Vanishing Moments and SmoothnessJul 27 2015We propose an approach to construct a family of two-dimensional compactly supported real-valued symmetric quincunx tight framelets $\{\phi; \psi_1,\psi_2,\psi_3\}$ in $L_2(R^2)$ with arbitrarily high orders of vanishing moments. Such symmetric quincunx ... More

Representation of functions on big data associated with directed graphsJul 15 2016Nov 12 2016This paper is an extension of the previous work of Chui, Filbir, and Mhaskar (Appl. Comput. Harm. Anal. 38 (3) 2015:489-509), not only from numeric data to include non-numeric data as in that paper, but also from undirected graphs to directed graphs (called ... More

Representation of functions on big data associated with directed graphsJul 15 2016This paper is an extension of the previous work of Chui, Filbir, and Mhaskar (Appl. Comput. Harm. Anal. 38 (3) 2015:489-509), not only from numeric data to include non-numeric data as in that paper, but also from undirected graphs to directed graphs (called ... More

Haar Transforms for Graph Neural NetworksJul 10 2019Graph Neural Networks (GNNs) have become a topic of intense research recently due to their powerful capability in high-dimensional classification and regression tasks for graph-structured data. However, as GNNs typically define the graph convolution by ... More

Funneled Potential and Flux Landscapes Dictate the Stabilities of both the States and the Flow: Fission Yeast Cell CycleJul 11 2017We have uncovered that the non-equilibrium network dynamics and global properties are determined by two essential features: the potential landscape and the flux landscape. We have found that the funneled potential landscape is crucial for the stability ... More

Optimal and Myopic Information AcquisitionMar 18 2017May 14 2018We consider the problem of optimal dynamic information acquisition from many correlated information sources. Each period, the decision-maker jointly takes an action and allocates a fixed number of observations across the available sources. His payoff ... More

A Spectroscopic Redshift for the Cl0024+16 Multiple Arc System: Implications for the Central Mass DistributionFeb 23 1999We present a spectroscopic redshift of z=1.675 for the well-known multiply lensed system of arcs seen in the z=0.39 cluster Cl0024+16. In contrast to earlier work, we find that the lensed images are accurately reproduced by a projected mass distribution ... More

Log-concavity of a Mixture of Beta DistributionsDec 08 2013We show that a mixture of Beta distributions has log-concave density whenever the mixing weights are themselves log-concave. Some economic and statistical applications are provided in the last section.

The twisted mean square and critical zeros of Dirichlet $L$-functionsFeb 27 2018The asymptotic formula for mean square of the Riemann zeta-function times a Dirichlet polynomial of length $T^\theta$ is proved when $\theta<17/33$ and $\theta<4/7$ for a special form of the coefficient, while for a general Dirichlet $L$-function, it ... More

Product theorem for K-stabilityApr 21 2019We prove a product formula for $\delta$-invariant and as an application, we show that product of K-(semi, poly)stable Fano varieties is also K-(semi, poly)stable.

Smooth Rational Curves on Singular Rational SurfacesApr 07 2016May 17 2017We classify all complex surfaces with quotient singularities that do not contain any smooth rational curves, under the assumption that the canonical divisor of the surface is not pseudo-effective. As a corollary we show that if $X$ is a log del Pezzo ... More

Weak boundedness of Fano threefolds with large Seshadri constants in characteristic $p>5$Nov 08 2017Given $\epsilon>0$, we show that over an algebraically closed field of characteristic $p>5$, the anticanonical volume of a Fano threefold $X$ (with arbitrary singularities) whose anticanonical divisor has Seshadri constant $\epsilon(-K_X,x)>2+\epsilon$ ... More

Disjunctive domination in treesAug 22 2018Aug 29 2018In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the domination number. Given the sheer scale of modern networks, many existing domination type structures are expensive to implement. ... More

Non-zero sum differential games of forward-backward stochastic differential delayed equations under partial information and applicationFeb 16 2017This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient verification theorem ... More

Comparison radius and mean topological dimension: Rokhlin property, comparison of open sets, and subhomogeneous C*-algebrasJun 21 2019Let $(X, \sigma, \Gamma)$ be a free minimal dynamical system, where $X$ is a compact separable Hausdorff space and $\Gamma$ is a discrete group. It is shown that the comparison radius of the crossed product C*-algebra $\mathrm{C}(X) \rtimes _\sigma \Gamma$ ... More

A generalized Goulden-Jackson cluster method and lattice path enumerationAug 12 2015Dec 26 2015The Goulden-Jackson cluster method is a powerful tool for obtaining generating functions for counting words in a free monoid by occurrences of a set of subwords. We introduce a generalization of the cluster method for monoid networks, which generalize ... More

An Experimental Study of Distributed Quantile EstimationAug 24 2015Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis. However, quite often, ... More

New Examples and Non-examples of Mori Dream Spaces when Blowing up Toric SurfacesMar 02 2017Jun 19 2017We study the question of whether the blow-ups of toric surfaces of Picard number one at the identity point of the torus are Mori Dream Spaces. For some of these toric surfaces, the question whether the blow-up is a Mori Dream Space is equivalent to countably ... More

Existence of Hopf subalgebras of GK-dimension twoAug 21 2010May 03 2011Let $H$ be a pointed Hopf algebra over an algebraically closed field of characteristic zero. If $H$ is a domain with finite Gelfand-Kirillov dimension greater than or equal to two, then $H$ contains a Hopf subalgebra of Gelfand-Kirillov dimension two. ... More

Counting permutations by runsMay 09 2015Aug 19 2016In his Ph.D. thesis, Ira Gessel proved a reciprocity formula for noncommutative symmetric functions which enables one to count words and permutations with restrictions on the lengths of their increasing runs. We generalize Gessel's theorem to allow for ... More

Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimensionFeb 19 2012Nov 18 2012Let $H$ be a pointed Hopf algebra. We show that under some mild assumptions $H$ and its associated graded Hopf algebra $\gr H$ have the same Gelfand-Kirillov dimension. As an application, we prove that the Gelfand-Kirillov dimension of a connected Hopf ... More

Neural Network Model of Pricing Health Care InsuranceJul 24 2013To pricing health insurance plan, statisticians use mathematical models to predict customers' future health condition. General Addictive Model (GAM) is a wide accepted method for this problem. However, it have several limitations. To solve this problem, ... More

Birational superrigidity is not a locally closed propertyJan 01 2019Feb 28 2019We prove an optimal result on the birational rigidity and K-stability of index $1$ hypersurfaces in $\mathbb{P}^{n+1}$ with ordinary singularities when $n\gg 0$ and also study the birational superrigidity and K-stability of certain weighted complete intersections. ... More

Fano varieties with large Seshadri constants in positive characteristicJul 10 2017We prove that an $n$-dimensional Fano variety (with arbitrary singularities) in positive characteristic is isomorphic to $\mathbb{P}^n$ if the Seshadri constant of he anti-canonical divisor at some smooth point is greater than $n$. We also classify Fano ... More

Eulerian polynomials and descent statisticsOct 23 2016May 11 2017We prove several identities expressing polynomials counting permutations by various descent statistics in terms of Eulerian polynomials, extending results of Stembridge, Petersen, and Br\"and\'en. Additionally, we find $q$-exponential generating functions ... More

A generalized Goulden-Jackson cluster method and lattice path enumerationAug 12 2015Feb 16 2018The Goulden-Jackson cluster method is a powerful tool for obtaining generating functions for counting words in a free monoid by occurrences of a set of subwords. We introduce a generalization of the cluster method for monoid networks, which generalize ... More

Eulerian polynomials and descent statisticsOct 23 2016We prove several identities expressing polynomials counting permutations by various descent statistics in terms of Eulerian polynomials, extending results of Stembridge, Petersen, and Br\"and\'en. Additionally, we find $q$-exponential generating functions ... More

Multivariate mixture model for myocardium segmentation combining multi-source imagesDec 28 2016This paper proposes a method for simultaneous segmentation of multi-source images, using the multivariate mixture model (MvMM) and maximum of log-likelihood (LL) framework. The segmentation is a procedure of texture classification, and the MvMM is used ... More

A New Statistic Feature of the Short-Time Amplitude Spectrum Values for Human's Unvoiced PronunciationSep 23 2016Dec 21 2016In this paper, a new statistic feature of the discrete short-time amplitude spectrum is discovered by experiments for the signals of unvoiced pronunciation. For the random-varying short-time spectrum, this feature reveals the relationship between the ... More

Mean dimension and AH-algebras with diagonal mapsOct 04 2010Feb 01 2014Mean dimension for AH-algebras is introduced. It is shown that if a simple unital AH-algebra with diagonal maps has mean dimension zero, then it has strict comparison on positive elements. In particular, the strict order on projections is determined by ... More

Fano varieties with large Seshadri constantsJul 07 2017Oct 15 2018We show that the set of Fano varieties (with arbitrary singularities) whose anticanonical divisors have large Seshadri constants satisfies certain weak and birational boundedness. We also classify singular Fano varieties of dimension $n$ whose anticanonical ... More

Irrational Stable Commutator Length in Finitely Presented GroupsSep 29 2007We give examples of finitely presented groups containing elements with irrational (in fact, transcendental) stable commutator length, thus answering in the negative a question of M. Gromov. Our examples come from 1-dimensional dynamics, and are related ... More

Cellular Automata Based Model for Pedestrian DynamicsOct 31 2012Nov 28 2012We construct a two dimensional Cellular Automata based model for the description of pedestrian dynamics. Wide range of complicated pattern formation phenomena in pedestrian dynamics are described in the model, e.g. lane formation, jams in a counterflow ... More

Birational superrigidity and K-stability of Fano complete intersections of index one (with an appendix written jointly with Charlie Stibitz)Feb 23 2018We prove that every smooth Fano complete intersection of index $1$ and codimension $r$ in $\mathbb{P}^{n+r}$ is birationally superrigid and K-stable if $n\ge 10r$. We also propose a generalization of Tian's criterion of K-stability and, as an application, ... More

Comparison radius and mean topological dimension: $\mathbb{Z}^d$-actionsJun 21 2019Consider a minimal free topological dynamical system $(X, T, \mathbb{Z}^d)$. It is shown that the comparison radius of the crossed product C*-algebra $\mathrm{C}(X) \rtimes \mathbb{Z}^d$ is at most the half of the mean topological dimension of $(X, T, ... More

Overabundant Information and Learning TrapsMay 21 2018Jun 19 2018We develop a model of social learning from overabundant information: Short-lived agents sequentially choose from a large set of (flexibly correlated) information sources for prediction of an unknown state. Signal realizations are public. We demonstrate ... More

The $k$-tuple Prime Difference ChampionOct 30 2017Jan 03 2018Let $D_{k}$ be a set with $k$ distinct elements of integers such that $d_{1}<d_{2}<\cdots<d_{k}$. We say $D_{k}^{*}$ is a $k$-tuple prime difference champion ($k$-tuple PDC) for primes $\le x$ if the set $D_{k}^{*}$ is the most probable differences among ... More

On the set of the difference of primesApr 28 2015Sep 09 2015In this work we prove that the set of the difference of primes is a $\Delta_r^*$-set. The work is based on the recent dramatic new developments in the study of bounded gaps between primes, reached by Zhang, Maynard and Tao.

On gaps between zeros of the Riemann zeta functionMar 03 2010Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at least 2.7327 times the average spacing and infinitely often they differ by at most 0.5154 times the average spacing. ... More

Subspace Perspective on Canonical Correlation Analysis: Dimension Reduction and Minimax RatesMay 12 2016Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of ... More

Microphase Equilibrium and Assembly DynamicsJul 10 2017Despite many attempts, ordered equilibrium microphases have yet to be obtained in experimental colloidal suspensions. The recent computation of the equilibrium phase diagram of a microscopic, particle-based microphase former [Zhuang et al., Phys. Rev. ... More

Recent Advances in the Theory and Simulation of Model Colloidal Microphase FormersMay 31 2016This mini-review synthesizes our understanding of the equilibrium behavior of particle models with short-range attractive and long-range repulsive (SALR) interactions. These models, which can form stable periodic microphases, aim to reproduce the essence ... More

Information Propagation in Clustered Multilayer NetworksSep 13 2015In today's world, individuals interact with each other in more complicated patterns than ever. Some individuals engage through online social networks (e.g., Facebook, Twitter), while some communicate only through conventional ways (e.g., face-to-face). ... More

Phase Structure of Nambu-Jona-Lasinio Model at Finite Isospin DensityJan 05 2005Jan 14 2005In the frame of flavor SU(2) Nambu--Jona-Lasinio model with $U_A(1)$ breaking term we found that, the structure of two chiral phase transition lines does not exist at low isospin density in real world, and the critical isospin chemical potential for pion ... More

Phase Diagram of Cold Polarized Fermi Gas in Two DimensionsJan 21 2008Sep 06 2008The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean field theory, the transition from unpolarized superfluid phase to normal phase ... More

On Certain Computations of Pisot NumbersFeb 26 2012This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number $\alpha$ such that $\Q[\alpha] = \F$ given a real Galois extension $\F$ of $\Q$ by its integral basis. This algorithm ... More

Effects of chiral imbalance and magnetic field on pion superfluidity and color superconductivityMay 20 2015Jan 21 2016The effects of chiral imbalance and external magnetic field on pion superfluidity and color superconductivity are investigated in extended Nambu--Jona-Lasinio models. We take Schwinger approach to treat the interaction between charged pion condensate ... More

A positivity-preserving scheme for the simulation of streamer discharges in non-attaching and attaching gasesJun 04 2013Assumed having axial symmetry, the streamer discharge is often described by a fluid model in cylindrical coordinate system, which consists of convection dominated (diffusion) equations with source terms, coupled with a Poisson's equation. Without additional ... More

Meson Mixing in Pion SuperfluidDec 23 2006Aug 29 2007We investigate meson mixing and meson coupling constants in pion superfluid in the framework of two flavor NJL model at finite isospin density. The mixing strength develops fast with increasing isospin chemical potential, and the coupling constants in ... More

A Non-Intrusive and Context-Based Vulnerability Scoring Framework for Cloud ServicesNov 22 2016Dec 07 2016Understanding the severity of vulnerabilities within cloud services is particularly important for today service administrators.Although many systems, e.g., CVSS, have been built to evaluate and score the severity of vulnerabilities for administrators, ... More

Small-Network Approximations for Geometrically Frustrated Ising SystemsJul 14 2011The study of frustrated spin systems often requires time-consuming numerical simulations. As the simplest approach, the classical Ising model is often used to investigate the thermodynamic behavior of such systems. Exploiting the small correlation lengths ... More

Active Faraday optical frequency standardsJul 13 2014We propose the mechanism of active Faraday optical clock, and experimentally demonstrate active Faraday optical frequency standards based on 852 nm narrow bandwidth Faraday atomic filter by the method of velocity-selective optical pumping of cesium vapor. ... More

Neobility at SemEval-2017 Task 1: An Attention-based Sentence Similarity ModelMar 16 2017This paper describes a neural-network model which performed competitively (top 6) at the SemEval 2017 cross-lingual Semantic Textual Similarity (STS) task. Our system employs an attention-based recurrent neural network model that optimizes the sentence ... More

Semitotal domination in treesMar 28 2018Sep 20 2018In this paper, we study a parameter that is squeezed between arguably the two important domination parameters, namely the domination number, $\gamma(G)$, and the total domination number, $\gamma_t(G)$. A set $S$ of vertices in $G$ is a semitotal dominating ... More

Multi-Stage Complex Contagions in Random Multiplex NetworksJul 02 2018Jul 03 2018Complex contagion models have been developed to understand a wide range of social phenomena such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a riot. Most existing ... More

Robust stability for fractional-order systems with structured and unstructured uncertaintiesJun 07 2011Dec 17 2012The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust stability is given; ... More

Stable Sarma State in Two-band Fermi SystemsMay 30 2008Jan 24 2009We investigate fermionic superconductivity with mismatched Fermi surfaces in a general two-band system. The exchange interaction between the two bands changes significantly the stability structure of the pairing states. The Sarma state with two gapless ... More

Relativistic BCS-BEC Crossover at Zero TemperatureMar 05 2007Apr 18 2007We investigate the BCS-BEC crossover at zero temperature in the frame of a relativistic model. The universality of the BCS-BEC crossover for non-relativistic systems breaks down in relativistic case and the crossover can be induced by changing the density. ... More

Breached Pairing Superfluidity at Finite Temperature and DensityJul 22 2003A general analysis on Fermion pairing at finite temperature and density between different species with mismatched Fermi surfaces is presented. Very different from the temperature effect of BCS phase, the recently found breached pairing phase resulted ... More

Multi-path segmentation networkNov 27 2018Dec 15 2018We present a new type of convolutional network for semantic segmentation here. We tested it on several benchmark datasets, including PASCAL VOC, PASCAL Context and Cityscapes. It achieved superior performance compared to state-of-the-art segmentation ... More

On the sharpness of Tian's criterion for K-stabilityMar 12 2019Tian's criterion for K-stability states that a Fano variety of dimension $n$ whose alpha invariant is greater than $\frac{n}{n+1}$ is K-stable. We show that this criterion is sharp by constructing singular Fano varieties with alpha invariants $\frac{n}{n+1}$ ... More

Large scale geometry of commutator subgroupsJul 29 2008Oct 27 2008Let G be a finitely presented group, and G' its commutator subgroup. Let C be the Cayley graph of G' with all commutators in G as generators. Then C is large scale simply connected. Furthermore, if G is a torsion-free nonelementary word-hyperbolic group, ... More

Stable W-lengthAug 12 2010Mar 28 2011We study stable W-length in groups, especially for W equal to the n-fold commutator gamma_n:=[x_1,[x_2, . . . [x_{n-1},x_n]] . . . ]. We prove that in any perfect group, for any n at least 2 and any element g, the stable commutator length of g is at least ... More

Lifting KK-elements, asymptotical unitary equivalence and classification of simple C*-algebrasFeb 11 2008Mar 10 2008Let $A$ and $C$ be two unital simple C*-algebas with tracial rank zero. Suppose that $C$ is amenable and satisfies the Universal Coefficient Theorem. Denote by ${{KK}}_e(C,A)^{++}$ the set of those $\kappa$ for which $\kappa(K_0(C)_+\setminus\{0\})\subset ... More

Noise Contrastive Estimation and Negative Sampling for Conditional Models: Consistency and Statistical EfficiencySep 06 2018Noise Contrastive Estimation (NCE) is a powerful parameter estimation method for log-linear models, which avoids calculation of the partition function or its derivatives at each training step, a computationally demanding step in many cases. It is closely ... More

Photoproduction of Pentaquark $Θ^+$ and Chiral Symmetry Restoration in Hot and Dense MediumMay 24 2005Jan 12 2006The photoproduction rate of pentaquark $\Theta^+$ is calculated in a hot and dense medium. At high temperature and density, due to the restoration of chiral symmetry, photoproduction energy threshold is increased. Above the thresold the production cross ... More

$λ$-factorials of $n$Jul 08 2010Recently, by the Riordan's identity related to tree enumerations, \begin{eqnarray*} \sum_{k=0}^{n}\binom{n}{k}(k+1)!(n+1)^{n-k} &=& (n+1)^{n+1}, \end{eqnarray*} Sun and Xu derived another analogous one, \begin{eqnarray*} \sum_{k=0}^{n}\binom{n}{k}D_{k+1}(n+1)^{n-k} ... More

Quark Potential in a Quark-Meson PlasmaMar 05 2008We investigate quark potential by considering meson exchanges in the two flavor Nambu--Jona-Lasinio model at finite temperature and density. There are two kinds of oscillations in the chiral restoration phase, one is the Friedel oscillation due to the ... More

Supervised Learning Enhanced by an Entangled Sensor NetworkJan 28 2019Various existing quantum supervised learning (SL) schemes rely on quantum random access memories to store quantum-encoded data given a priori in a classical description. The data acquisition process, however, has not been accounted for, while it sets ... More

Equilibrium phase behavior of the square-well linear microphase-forming modelMar 02 2016May 11 2016We have recently developed a simulation approach to calculate the equilibrium phase diagram of particle-based microphase formers. Here, this approach is used to calculate the phase behavior of the square-well linear model for different strengths and ranges ... More

Meson Scattering in a Pion SuperfluidFeb 16 2012Oct 23 2012Instead of the fermion-fermion scattering which identifies the BCS-BEC crossover in cold atom systems, boson-boson scattering is measurable and characterizes the BCS-BEC crossover at quark level. We study $\pi$-$\pi$ scattering in a pion superfluid described ... More

Recover Feasible Solutions for SOCP Relaxation of Optimal Power Flow Problems in Mesh NetworksAug 22 2017Oct 23 2017Convex relaxation methods have been studied and used extensively to obtain an optimal solution to the optimal power flow (OPF) problem. Meanwhile, convex relaxed power flow equations are also prerequisites for efficiently solving a wide range of problems ... More

Functional Renormalization for Chiral and U_A(1) Symmetries at Finite TemperatureSep 04 2012We investigated the chiral symmetry and U_A(1) anomaly at finite temperature by applying the functional renormalization group to the SU(3) linear sigma model. Expanding the local potential around the classical fields, we derived the flow equations for ... More

On the Betti Numbers of Shifted Complexes of Stable Simplicial ComplexesNov 20 2004Let $\Delta$ be a stable simplicial complex on $n$ vertexes. Over an arbitrary base field $K$, the symmetric algebraic shifted complex $\Delta^s$ of $\Delta$ is defined. It is proved that the Betti numbers of the Stanley-Reisner ideals in the polynomial ... More

Asymptotic unitary equivalence in $C^*$-algebrasJun 28 2012Aug 11 2013Let $C=C(X)$ be the unital $C^*$-algebra of all continuous functions on a finite CW complex $X$ and let $A$ be a unital simple $C^*$-algebra with tracial rank at most one. We show that two unital monomorphisms $\phi, \psi: C\to A$ are asymptotically unitarily ... More

Equilibration of quantum chaotic systemsAug 07 2013Dec 02 2013Quantum ergordic theorem for a large class of quantum systems was proved by von Neumann [Z. Phys. {\bf 57}, 30 (1929)] and again by Reimann [Phys. Rev. Lett. {\bf 101}, 190403 (2008)] in a more practical and well-defined form. However, it is not clear ... More

Equal-Time Hierarchies for Quantum Transport TheoryOct 22 1996We investigate in the equal-time formalism the derivation and truncation of infinite hierarchies of equations of motion for the energy moments of the covariant Wigner function. From these hierarchies we then extract kinetic equations for the physical ... More

Impulse response of a generalized fractional second order filterJun 07 2011Dec 17 2012The impulse response of a generalized fractional second order filter of the form ${{({{s}^{2\alpha}}+a{{s}^{\alpha}}+b)}^{-\gamma}}$ is derived, where $0<\alpha \le 1$, $0<\gamma <2$. The asymptotic properties of the impulse responses are obtained for ... More

Characterization of projective spaces by Seshadri constantsJul 19 2016Jul 11 2017We prove that an $n$-dimensional complex projective variety is isomorphic to $\mathbb{P}^n$ if the Seshadri constant of the anti-canonical divisor at some smooth point is greater than $n$. We also classify complex projective varieties with Seshadri constants ... More

Multi-scale deep neural networks for real image super-resolutionApr 24 2019Single image super-resolution (SR) is extremely difficult if the upscaling factors of image pairs are unknown and different from each other, which is common in real image SR. To tackle the difficulty, we develop two multi-scale deep neural networks (MsDNN) ... More

A tracially AF algebra which is not $\mathcal Z$-absorbingFeb 08 2019Feb 28 2019We show that there is a simple separable unital (non-nuclear) tracially AF algebra $A$ which does not absorb the Jiang-Su algebra $\mathcal Z$ tensorially, i.e. $A \ncong A\otimes\mathcal Z$.

Analytic Solution of Strongly Coupling Schroedinger EquationsDec 24 2002May 18 2003A recently developed expansion method for analytically solving the ground states of strongly coupling Schr\"odinger equations by Friedberg, Lee and Zhao is extended to excited states and applied to the pedagogically important problems of power-law central ... More

Critical Zeeman Splitting of Fermi Superfluidity at Infinite Scattering LengthMar 28 2008Aug 15 2009We determine the critical Zeeman energy splitting for Fermi superfluidity at infinite s-wave scattering length according to the Monte Carlo and experimental results of the equations of state. Based on the universality hypothesis, we show that there exist ... More

Chiral Phase Transition beyond Mean Field ApproximationSep 14 2007Based on the analogy between the Nambu--Jona-Lasinio model of chiral symmetry breaking and the BCS theory of superconductivity, we investigate the effect of $\bar q q$ pair fluctuations on the chiral phase transition. We include uncondensed $\bar q q$ ... More

Random Distances Associated with HexagonsJun 11 2011In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent hexagons sharing a ... More

Random Distances Associated with RhombusesJun 07 2011Parallelograms are one of the basic building blocks in two-dimensional tiling. They have important applications in a wide variety of science and engineering fields, such as wireless communication networks, urban transportation, operations research, etc. ... More