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Ordinal Constrained Binary Code Learning for Nearest Neighbor SearchNov 19 2016Recent years have witnessed extensive attention in binary code learning, a.k.a. hashing, for nearest neighbor search problems. It has been seen that high-dimensional data points can be quantized into binary codes to give an efficient similarity approximation ... More

Fast and Accurate Neural Word Segmentation for ChineseApr 24 2017Neural models with minimal feature engineering have achieved competitive performance against traditional methods for the task of Chinese word segmentation. However, both training and working procedures of the current neural models are computationally ... More

Towards Optimal Structured CNN Pruning via Generative Adversarial LearningMar 22 2019Structured pruning of filters or neurons has received increased focus for compressing convolutional neural networks. Most existing methods rely on multi-stage optimizations in a layer-wise manner for iteratively pruning and retraining which may not be ... More

A Coarse-to-fine Pyramidal Model for Person Re-identification via Multi-Loss Dynamic TrainingOct 29 2018Oct 30 2018Most existing Re-IDentification (Re-ID) methods are highly dependent on precise bounding boxes that enable images to be aligned with each other. However, due to the inevitable challenging scenarios, current detection models often output inaccurate bounding ... More

Pyramidal Person Re-IDentification via Multi-Loss Dynamic TrainingOct 29 2018May 05 2019Most existing Re-IDentification (Re-ID) methods are highly dependent on precise bounding boxes that enable images to be aligned with each other. However, due to the challenging practical scenarios, current detection models often produce inaccurate bounding ... More

LGM-Net: Learning to Generate Matching Networks for Few-Shot LearningMay 15 2019In this work, we propose a novel meta-learning approach for few-shot classification, which learns transferable prior knowledge across tasks and directly produces network parameters for similar unseen tasks with training samples. Our approach, called LGM-Net, ... More

Scale Invariant Fully Convolutional Network: Detecting Hands EfficientlyJun 11 2019Existing hand detection methods usually follow the pipeline of multiple stages with high computation cost, i.e., feature extraction, region proposal, bounding box regression, and additional layers for rotated region detection. In this paper, we propose ... More

Towards Highly Accurate and Stable Face Alignment for High-Resolution VideosNov 01 2018Nov 22 2018In recent years, heatmap regression based models have shown their effectiveness in face alignment and pose estimation. However, Conventional Heatmap Regression (CHR) is not accurate nor stable when dealing with high-resolution facial videos, since it ... More

Automatic Script Identification in the WildMay 12 2015With the rapid increase of transnational communication and cooperation, people frequently encounter multilingual scenarios in various situations. In this paper, we are concerned with a relatively new problem: script identification at word or line levels ... More

Anti-Confusing: Region-Aware Network for Human Pose EstimationMay 03 2019May 27 2019In this work, we propose a novel framework named Region-Aware Network (RANet), which learns the ability of anti-confusing in case of heavy occlusion, nearby person and symmetric appearance, for human pose estimation. Specifically, the proposed method ... More

Dynamic Neural Network DecouplingJun 04 2019Convolutional neural networks (CNNs) have achieved a superior performance by taking advantages of the complex network architectures and huge numbers of parameters, which however become uninterpretable and challenge their full potential to practical applications. ... More

Exploiting Kernel Sparsity and Entropy for Interpretable CNN CompressionDec 11 2018Apr 01 2019Compressing convolutional neural networks (CNNs) has received ever-increasing research focus. However, most existing CNN compression methods do not interpret their inherent structures to distinguish the implicit redundancy. In this paper, we investigate ... More

Exploiting Kernel Sparsity and Entropy for Interpretable CNN CompressionDec 11 2018Compressing convolutional neural networks (CNNs) has received ever-increasing research focus. However, most existing CNN compression methods do not interpret their inherent structures to distinguish the implicit redundancy. In this paper, we investigate ... More

Anti-Confusing: Region-Aware Network for Human Pose EstimationMay 03 2019In this work, we propose a novel framework named Region-Aware Network (RANet) to achieve anti-confusing, including heavy occlusion, nearby person and symmetric appearance, for human pose estimation. Specifically, our proposed method addresses three key ... More

DSFD: Dual Shot Face DetectorOct 24 2018Nov 23 2018Recently, Convolutional Neural Network (CNN) has achieved great success in face detection. However, it remains a challenging problem for the current face detection methods owing to high degree of variability in scale, pose, occlusion, expression, appearance ... More

Aurora Guard: Real-Time Face Anti-Spoofing via Light ReflectionFeb 27 2019In this paper, we propose a light reflection based face anti-spoofing method named Aurora Guard (AG), which is fast, simple yet effective that has already been deployed in real-world systems serving for millions of users. Specifically, our method first ... More

Supervised Online Hashing via Similarity Distribution LearningMay 31 2019Online hashing has attracted extensive research attention when facing streaming data. Most online hashing methods, learning binary codes based on pairwise similarities of training instances, fail to capture the semantic relationship, and suffer from a ... More

DSFD: Dual Shot Face DetectorOct 24 2018Apr 06 2019In this paper, we propose a novel face detection network with three novel contributions that address three key aspects of face detection, including better feature learning, progressive loss design and anchor assign based data augmentation, respectively. ... More

Adversarial Attribute-Image Person Re-identificationDec 05 2017Jul 04 2018While attributes have been widely used for person re-identification (Re-ID) which aims at matching the same person images across disjoint camera views, they are used either as extra features or for performing multi-task learning to assist the image-image ... More

Ultrasmall Au10-12(SG)10-12 Nanomolecules for High Tumor Specificity and Cancer RadiotherapyMay 12 2014Radiosensitizers can increase the local treatment efficacy under a relatively low and safe radiation dose, thereby facilitating tumor eradication and minimizing side effects. Here, we report a new class of radiosensitizers that contain several gold (Au) ... More

Who Will Win Practical Artificial Intelligence? AI Engineerings in ChinaFeb 06 2017Currently, Artificial Intelligence (AI) has won unprecedented attention and is becoming the increasingly popular focus in China. This change can be judged by the impressive record of academic publications, the amount of state-level investment and the ... More

Hierarchical low rank approximation of likelihoods for large spatial datasetsMay 28 2016Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive computational burden. ... More

Enumerating Cayley (di-)graphs on dihedral groupsDec 12 2016Let $p$ be an odd prime, and $D_{2p}=\langle \tau,\sigma\mid \tau^p=\sigma^2=e,\sigma\tau\sigma=\tau^{-1}\rangle$ the dihedral group of order $2p$. In this paper, we provide the number of (connected) Cayley (di-)graphs on $D_{2p}$ up to isomorphism by ... More

An $hp$-version error analysis of the discontinuous Galerkin method for linear elasticityAug 14 2016Dec 24 2017An $hp$-version error analysis is developed for the general DG method in mixed formulation for solving the linear elastic problem. First of all, we give the $hp$-version error estimates of two $L^2$ projection operators. Then incorporated with the techniques ... More

Dark Matter, Mass Scales Sequence, and Superstructure in the Universe (with extension)Sep 18 1999Oct 26 2015There is a category of stable non-baryonic dark matter particles in the universe at the present time: fermions or bosons with mass ~10^(-1) eV. The existence of these do not contradict the dip phenomena of the ultra-high energy primary cosmic ray spectrum ... More

Dark Matter, Quasars, and Superstructures in the UniverseAug 10 2009Feb 02 2016From the observed results of the space distribution of quasars we deduced that neutrino mass is about 10^(-1) eV. The fourth stable elementary paticle (delta particle) with mass about 10^(0) eV can help explain the energy resource mechanism in quasars, ... More

On graphs with three or four distinct normalized Laplacian eigenvaluesNov 16 2016In this paper, we characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues of which one is equal to $1$, determine all connected bipartite graphs with at least one vertex of degree $1$ having exactly four distinct ... More

Automorphism group of the complete alternating group graphMay 21 2016Jun 02 2016Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \emph{complete alternating group graph}, denoted by $CAG_n$, is defined as the Cayley graph ... More

On regular graphs with four distinct eigenvaluesMay 18 2016Sep 17 2016Let $\mathcal{G}(4,2)$ be the set of connected regular graphs with four distinct eigenvalues in which exactly two eigenvalues are simple, $\mathcal{G}(4,2,-1)$ (resp. $\mathcal{G}(4,2,0)$) the set of graphs belonging to $\mathcal{G}(4,2)$ with $-1$ (resp. ... More

On graphs with three or four distinct normalized Laplacian eigenvaluesNov 16 2016Mar 27 2017In this paper, we characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues of which one is equal to $1$, determine all connected bipartite graphs with at least one vertex of degree $1$ having exactly four distinct ... More

Gorenstein Syzygy ModulesMar 26 2009Oct 15 2010For any ring $R$ and any positive integer $n$, we prove that a left $R$-module is a Gorenstein $n$-syzygy if and only if it is an $n$-syzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of finitely generated ... More

Dark energy and normalization of cosmological wave function in modified gravitationsMay 05 2017Based on Wheeler-DeWitt equation derived from general relativity, it had been found that only dark energy can lead to a normalizable cosmological wave function. It is shown in the present work that, for dRGT gravity, Eddington-inspired-Born-Infeld gravity ... More

Mechanisms of Electromechanical Coupling in Strain Based Scanning Probe MicroscopyApr 09 2014Electromechanical coupling is ubiquitous in nature and underpins the functionality of materials and systems as diverse as ferroelectric and multiferroic materials, electrochemical devices, and biological systems, and strain-based scanning probe microscopy ... More

Total Variation Depth for Functional DataNov 15 2016There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the total variation ... More

The $hp$-version Error Analysis of A Mixed DG Method for Linear ElasticityAug 14 2016This paper focuses on the $hp$-version error analysis of a mixed discontinuous Galerkin (DG) method for the linear elasticity problem. We first derive some error estimates for two $L^2$ projection operators in terms of the results in [7,13,23]. Using ... More

Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-DisturbanceJan 01 2017This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a representative agent ... More

Large Number, Dark Matter, Dark Energy, and the Superstructures in the Universe (with Extension)Apr 16 2008Sep 12 2016Since there are dark matter particles (neutrino) with mass about 10^(-1)eV in the universe, the superstructures with a scale of 10^(19) solar mass [large number A is about 10^(19)] appeared around the era of the hydrogen recombination. The redshift z ... More

Note on the spectra of a class of graphs derived from set inclusion relationsSep 04 2018Sep 08 2018For any given integers $n$, $k$ and $l$ with $n\geq 1$ and $0\leq k<l\leq n$, we denote by $G(n,k,l)$ the graph whose vertex set consists of all $k$- and $l$-subsets of $[n]=\{1,2,\ldots,n\}$, where two distinct vertices are adjacent if one of them is ... More

The second largest eigenvalues of some Cayley graphs on alternating groupsNov 24 2017Dec 12 2018Let $A_n$ denote the alternating group of degree $n$ with $n\geq 3$. The alternating group graph $AG_n$, extended alternating group graph $EAG_n$ and complete alternating group graph $CAG_n$ are the Cayley graphs $\mathrm{Cay}(A_n,T_1)$, $\mathrm{Cay}(A_n,T_2)$ ... More

A Fast HOG Descriptor Using Lookup Table and Integral ImageMar 18 2017The histogram of oriented gradients (HOG) is a widely used feature descriptor in computer vision for the purpose of object detection. In the paper, a modified HOG descriptor is described, it uses a lookup table and the method of integral image to speed ... More

The Auslander-Type Condition of Triangular Matrix RingsMar 26 2009Let $R$ be a left and right Noetherian ring and $n,k$ any non-negative integers. $R$ is said to satisfy the Auslander-type condition $G_n(k)$ if the right flat dimension of the $(i+1)$-st term in a minimal injective resolution of $R_R$ is at most $i+k$ ... More

Torsionfree Dimension of Modules and Self-Injective Dimension of RingsJun 06 2009Jan 14 2011Let $R$ be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated $R$-modules. For any $n\geq 0$, we prove that $R$ is a Gorenstein ring with self-injective dimension at most $n$ if and only if every ... More

Dark Matter Particles with Low Mass (and FTL)Mar 26 2010Apr 17 2012From the observed results of the space distribution of quasars and the mass scale sequence table, we deduced the existence of superstructure (feeble dark structure) with mass scale of 10^(19) solar mass, as well as the lightest stable fermion with mass ... More

Parameter Optimization of Multi-Agent Formations based on LQR DesignJan 24 2011In this paper we study the optimal formation control of multiple agents whose interaction parameters are adjusted upon a cost function consisting of both the control energy and the geometrical performance. By optimizing the interaction parameters and ... More

Automorphism group of the complete alternating group graphMay 21 2016Aug 26 2017Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \emph{complete alternating group graph}, denoted by $CAG_n$, is defined as the Cayley graph ... More

On plastikstufe, bordered Legendrian open book and overtwisted contact structuresJul 27 2016Aug 03 2016In this paper we prove the presence of an embedded plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that the presence of an embedded bordered Legendrian open book (bLob) also implies overtwistedness. ... More

The properties of sendograph metric on fuzzy number spacesJul 24 2013This paper discusses the variation of sendograph distances under some algebra operations.

Equidistribution and measure rigidity under $\times p,\times q$Nov 17 2014Jun 08 2015We show that equidistribution of irrational orbits on the unit circle implies Furstenberg's conjecture.

The transverse Chern-Ricci flowJun 08 2015We introduce transverse Chern-Ricci flow for transversely Hermitian foliations, which is analogous to the Chern-Ricci flow. We show that when $\mathcal{F}$ is homologically orientable and the basic first Bott-Chern class is zero, starting at any transversely ... More

Sasaki manifolds with positive transverse orthogonal bisectional curvatureJan 07 2013Jan 09 2013In this short note we show the following result: Let $(M^{2n+1},g)$ ($n \geq 2$) be a compact Sasaki manifold with positive transverse orthogonal bisectional curvature. Then $\pi_1(M)$ is finite, and the universal cover of $(M^{2n+1},g)$ is isomorphic ... More

Three-orbifolds with positive scalar curvatureOct 27 2012We prove the following result: Let $(\mathcal{O},g_0)$ be a complete, connected 3-orbifold with uniformly positive scalar curvature, with bounded geometry, and containing no bad 2-suborbifolds. Then there is a finite collection $\mathcal{F}$ of spherical ... More

Ricci flow on open 4-manifolds with positive isotropic curvatureAug 15 2011Aug 30 2011In this note we prove the following result: Let $X$ be a complete, connected 4-manifold with uniformly positive isotropic curvature, with bounded geometry and with no essential incompressible space form. Then $X$ is diffeomorphic to $\mathbb{S}^4$, or ... More

State sampling dependence of the Hopfield network inferenceApr 26 2011Aug 31 2011The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the ... More

The $L^{3/2}$-norm of the scalar curvature under the Ricci flow on a 3-manifoldJan 04 2011Feb 28 2011Assume $M$ is a closed 3-manifold whose universal covering is not $S^3$. We show that the obstruction to extend the Ricci flow is the boundedness $L^{3/2}$-norm of the scalar curvature $R(t)$, i.e, the Ricci flow can be extended over time $T$ if and only ... More

Reconstructing the Hopfield network as an inverse Ising problemSep 10 2009Dec 14 2009We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing technique is adopted. ... More

A countable set derived by fuzzy setOct 19 2015In this paper, it shows that for each fuzzy set $u$ on $\mathbb{R}^m$, the set $D(u)$ is at most countable. Based on this, it modifies the proof of assertion (I) in step 2 of the sufficiency part of Theorem 4.1 in paper: Characterizations of compact sets ... More

A note on Morse's index theorem for Perelman's $\mathcal{L}$-lengthFeb 06 2006This is essentially a note on Section 7 of Perelman's first paper on Ricci flow. We list some basic properties of the index form for Perelman's $ \mathcal{L} $-length, which are analogous to the ones in Riemannian case (with fixed metric), and observe ... More

Log-linear Conway-Maxwell-Poisson models for dispersed countsJun 10 2016Conway-Maxwell-Poisson (COMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to directly model the ... More

Hybrid subconvexity bounds for twisted $L$-functions on $GL(3)$May 31 2016Let $q$ be a large prime, and $\chi$ the quadratic character modulo $q$. Let $\phi$ be a self-dual Hecke--Maass cusp form for $SL(3,\mathbb{Z})$, and $u_j$ a Hecke--Maass cusp form for $\Gamma_0(q)\subseteq SL(2,\mathbb{Z})$ with spectral parameter $t_j$. ... More

Generalized Fixed-Point Algebras and Square-Integrable Representations of Twisted C*-Dynamical SystemsApr 07 2015This paper shows that Ralf Meyer's theory of square-integrable group representations of C*-dynamical systems can be generalized quite naturally to the case of twisted C*-dynamical systems. An outcome of this is a generalized fixed-point algebra that is ... More

Statistical mechanics of unsupervised feature learning in a restricted Boltzmann machine with binary synapsesDec 06 2016Revealing hidden features in unlabeled data is called unsupervised feature learning, which plays an important role in pretraining a deep neural network. Here we provide a statistical mechanics analysis of the unsupervised learning in a restricted Boltzmann ... More

$L^{2}$ harmonic forms on complete special holonomy manifoldsJan 13 2018In this article,we consider $L^{2}$ harmonic forms on a complete noncompact Riemannian manifold $X$ with a parallel form $\omega$.The main result is that if $(X,\omega)$ is a complete $G_{2}$- (or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- (or $Spin(7)$-) ... More

A Gauge field Induced by the Global Gauge Invariance of Action IntegralSep 16 2007Sep 27 2007As a general rule, it is considered that the global gauge invariance of an action integral does not cause the occurrence of gauge field. However, in this paper we demonstrate that when the so-called localized assumption is excluded, the gauge field will ... More

Disoriented Chiral CondensateJan 25 1995The current theoretical understanding of disoriented chiral condensate is briefly reviewed. I discuss the basic idea, the formation mechanism and experimental signatures of DCC in high energy collisions.

Explicit Barenblatt Profiles for Fractional Porous Medium EquationsDec 02 2013Mar 29 2014Several one-parameter families of explicit self-similar solutions are constructed for the porous medium equations with fractional operators. The corresponding self-similar profiles, also called \emph{Barenblatt profiles}, have the same forms as those ... More

The sharp drop in the flux striking the accretion diskJun 10 2004In this paper,We present a simple relativistic approach to analyze the flux striking the disk which is possibly from a source up the Black hole.The X-ray source is locate above an accretion disc orbiting around the black hole,this assumption is invoked ... More

Rational points on elliptic K3 surfaces of quadratic twist typeJun 20 2018Dec 21 2018We propose a double covering method to study the density of rational points and density of fibres of prescribed rank on quadratic twist type elliptic surfaces $f(t)y^2=g(x)$, where $f,g$ are cubic or quartic polynomials (without repeated roots). We apply ... More

Approximation diophantienne et distribution locale sur une surface torique IIMay 10 2018We study the local distribution of rational points of bounded height on a toric surface, on which cuspidal rational curves and nodal rational curves all give the best approximates outside a Zariski closed subset. By deleting a thin set, we prove that ... More

On Learning to ProveApr 24 2019In this paper, we consider the problem of learning a (first-order) theorem prover where we use a representation of beliefs in mathematical claims instead of a proof system to search for proofs. The inspiration for doing so comes from the practices of ... More

Asymptotic behaviour of instantons on Cylinder ManifoldsJan 22 2018Sep 16 2018In this article, we study the instanton equation on the cylinder over a closed manifold $X$ admits non-zero smooth $3$-form $P$ and $4$-from $Q$. Our results are (i) if $X$ is a \textbf{good} manifold, i.e., $P,Q$ satisfying $d\ast_{X}P=d\ast_{X}Q=0$, ... More

Discrete maximum principle and a Delaunay-type mesh condition for linear finite element approximations of two-dimensional anisotropic diffusion problemsAug 03 2010The finite element solution of two-dimensional anisotropic diffusion problems is considered. A Delaunay-type mesh condition is developed for linear finite element approximations to satisfy a discrete maximum principle. The condition is shown to be weaker ... More

An $L^{2}$-isolation theorem for Yang-Mills fields on Kähler surfacesNov 16 2016We prove an $L^{2}$ energy gap result for Yang-Mills connections on principal $G$-bundles over compact K\"{a}hler surfaces with positive scalar curvature. We prove related results for compact simply-connected Calabi-Yau $2$-folds.

$L^{2}$ harmonic forms on complete special holonomy manifoldsJan 13 2018Feb 13 2019In this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a nonzero parallel form $\omega$. The main result is that if $(X,\omega)$ is a complete $G_{2}$- ( or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- ... More

Unique Continuation through Hyperplane for Higher Order Parabolic and Shrödinger EquationsJul 26 2017Jun 01 2018We consider higher order parabolic operator $\partial_t+(-\Delta_x)^m$ and higher order Schr\"{o}dinger operator $i^{-1}\partial_t+(-\Delta_x)^m$ in $X=\{(t,x)\in\mathbb{R}^{1+n};~|t|<A,|x_n|<B\}$ where $m$ is any positive integer. Under certain lower ... More

Regularity and uniqueness for a class of solutions to the hydrodynamic flow of nematic liquid crystalsMay 26 2014In this paper, we establish an $\epsilon$-regularity criterion for any weak solution $(u,d)$ to the nematic liquid crystal flow (1.1) such that $(u,\nabla d)\in L^p_tL^q_x$ for some $p\ge 2$ and $q\ge n$ satisfying the condition (1.2). As consequences, ... More

High-redshift Mini-haloes from Modulated PreheatingFeb 26 2019May 09 2019Intermittent type of primordial non-Gaussian fluctuations from modulated preheating can produce an overabundance of $\sim 10^8M_\odot$ mini-haloes at high redshift $z\gtrsim 20$. This may have a significant impact on the formation of high-redshift supermassive ... More

Mean-parametrized Conway-Maxwell-Poisson regression models for dispersed countsJun 10 2016Feb 14 2017Conway-Maxwell-Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to directly model the ... More

On generalized estimating equations for vector regressionMar 01 2016Nov 24 2016Generalized estimating equations (GEE; Liang & Zeger 1986) for general vector regression settings are examined. When the response vectors are of mixed type (e.g. continuous-binary response pairs), the GEE approach is a semiparametric alternative to full-likelihood ... More

Quantum variance for Eisenstein SeriesNov 07 2018In this paper, we prove an asymptotic formula for the quantum variance for Eisenstein series on $\mathrm{PSL}_2(\mathbb{Z})\backslash \mathbb{H}$. The resulting quadratic form is compared with the classical variance and the quantum variance for cusp forms. ... More

Sup-norm and nodal domains of dihedral Maass formsJul 16 2018Feb 25 2019In this paper, we improve the sup-norm bound and the lower bound of the number of nodal domains for dihedral Maass forms, which are a distinguished sequence of Laplacian eigenfunctions on an arithmetic hyperbolic surface. More specifically, let $\phi$ ... More

Native point defects in CaS: A focus on doping limit for persistent luminescenceJul 22 2015We studied native point defects in CaS by DFT+ Hubbard U method. The effect of the localization of the d orbitals of Ca pseudopotential has been included. The Hubbard U corrected d-orbital for Ca sites are playing a role assisting the charge transfer ... More

Ising Spins on Randomly Multi-Branched Husimi Square Lattice: Thermodynamics and Phase Transition in Cross-dimensional RangeFeb 21 2015Jun 13 2016An inhomogeneous random recursive lattice was constructed from the multi-branched Husimi square lattice. The number of repeating units connected on one vertex was randomly set to be 2 or 3 with a quenched ratio $P_2$ or $P_3$ with $P_2+P_3=1$. The model ... More

A Triangular Array of the Counts of Natural Numbers with the Same Number of Prime Factors (Dimensions) Within 2n SpaceJan 07 2014By defining the dimension of natural numbers as the number of prime factors, all natural numbers smaller than 2^(n+1) (n is a natural number) can be classified by their dimensions, and the count of numbers of each dimension gives a dimensions distribution ... More

Gamow Vectors in a Periodically Perturbed Quantum SystemApr 26 2009We analyze the behavior of the wave function $\psi(x,t)$ for one dimensional time-dependent Hamiltonian $H=-\partial_x^2\pm2\delta(x)(1+2r\cos\omega t)$ where $\psi(x,0)$ is compactly supported. We show that $\psi(x,t)$ has a Borel summable expansion ... More

Color Superconductivity at Moderate Baryon DensitySep 14 2004Nov 04 2004This article focuses on the two-flavor color superconducting phase at moderate baryon density. In order to simultaneously investigate the chiral phase transition and the color superconducting phase transition, the Nambu-Gorkov formalism is extended to ... More

Mean ergodic theorem for amenable discrete quantum groups and a Wiener type theorem for compact metrizable groupsJun 08 2015Mar 11 2016We prove a mean ergodic theorem for amenable discrete quantum groups. As an application, we prove a Wiener type theorem for continuous measures on compact metrizable groups.

An Introduction to MMPDElabApr 11 2019This article presents an introduction to MMPDElab, a package written in MATLAB for adaptive mesh movement and adaptive moving mesh P1 finite element solution of second-order partial different equations having continuous solutions.

Moments for multi-dimensional Mandelbrot's cascadesMay 12 2014We consider the distributional equation $\textbf{Z}\stackrel{d}{=}\sum_{k=1}^N\textbf{A}_k\textbf{Z}(k) $, where $N$ is a random variable taking value in $\mathbb N_0=\{0,1,\cdots\}$, $\textbf{A}_1,\textbf{A}_2,\cdots$ are $p\times p$ non-negative random ... More

On Twisted Virasoro Operators and Number TheorySep 04 2009Jan 02 2010We explore some axioms of divergent series and their relations with conformal field theory. As a consequence we obtain another way of calculating $L(0,\chi)$ and $L(-1,\chi)$ for $\chi$ being a Dirichlet character. We hope this discussion is also of interest ... More

Generalizing Lieb's Concavity Theorem via Operator InterpolationApr 05 2019We introduce the notion of $k$-trace and use interpolation of operators to prove the joint concavity of the function $(A,B)\mapsto\text{Tr}_k\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big]^\frac{1}{k}$, which generalizes Lieb's concavity ... More

On $U$-Dominant DimensionSep 10 2004Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. We show that the $U$-dominant dimensions of $_{\Lambda}U$ and $U_{\Gamma}$ are identical. As applications to the results obtained, we ... More

On S-duality and Gauss reciprocity lawOct 08 2009Jan 02 2010We review the interpretation of Tate's thesis by a sort of conformal field theory on a number field in \cite{1}. Based on this and the existence of a hypothetical 3-dimensional gauge theory, we give a physical interpretation of the Gauss quadratic reciprocity ... More

The Weil-Petersson Geometry On the Thick Part of the Moduli Space of Riemann SurfacesMar 03 2006May 03 2006On the thick part of the moduli space of Riemann surfaces, where there is a positive lower bound of the systole of the surface, we show that all Weil-Petersson Riemannian curvatures are bounded, independent of the genus of the surface.

Asymptotics of the Gaussian Curvatures of the Canonical Metric on the SurfaceApr 26 2006We study the canonical metric on a compact Riemann surface of genus at least two. While it is known that the canonical metric is of nonpositive curvature, we show that its Gaussian curvatures are not bounded away from zero nor negative infinity when the ... More

Asymptotic flatness of the Weil-Petersson metric on Teichmuller spaceDec 22 2003The sectional curvature of the Weil-Petersson metric on Teichmuller space is known to be negative. We show that this Weil-Petersson sectional curvature is not pinched from above by any negative constants, i.e., there is no negative upper bound.

Compositions with restricted partsDec 28 2018Jan 14 2019Euler showed that the number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts. This theorem was generalized by Glaisher and further by Franklin. Recently, Beck made three conjectures on partitions with restricted ... More

Cross-Layer Optimization for Power-Efficient and Robust Digital Circuits and SystemsDec 11 2017With the increasing digital services demand, performance and power-efficiency become vital requirements for digital circuits and systems. However, the enabling CMOS technology scaling has been facing significant challenges of device uncertainties, such ... More

A uniform generalization of some combinatorial Hopf algebrasJun 09 2015Dec 05 2015We generalize the Hopf algebras of free quasisymmetric functions, quasisymmetric functions, noncommutative symmetric functions, and symmetric functions to certain representations of the category of all finite Coxeter systems and its dual category. We ... More

McShane-type identities for quasifuchsian representations of nonorientable surfacesFeb 08 2018We adapt Bers' double uniformization for nonorientable surfaces and show that the space $\mathcal{QF}(N)$ of quasifuchsian representations for a nonorientable surface $N$ is the Teichm\"uller space $\mathcal{T}(dN)$ of an orientable double of $N$. We ... More