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The noncommutative Waring problemMar 14 2019This paper poses and treats a noncommutative version of the classical Waring problem for polynomials. That is, for a homogeneous \nc \ polynomial $p$, we find a condition equivalent to $p$ being expressible as sums of powers of homogeneous \nc \ polynomials. ... More

Characterization of Type Ia Supernova Light Curves Using Principal Component Analysis of Sparse Functional DataFeb 16 2018With growing data from ongoing and future supernova surveys it is possible to empirically quantify the shapes of SNIa light curves in more detail, and to quantitatively relate the shape parameters with the intrinsic properties of SNIa. Building such relationship ... More

CSI-Net: Unified Human Body Characterization and Pose RecognitionOct 07 2018Jan 22 2019We build CSI-Net, a unified Deep Neural Network~(DNN), to learn the representation of WiFi signals. Using CSI-Net, we jointly solved two body characterization problems: biometrics estimation (including body fat, muscle, water, and bone rates) and person ... More

Ligand-field helical luminescence in a 2D ferromagnetic insulatorOct 16 2017Bulk chromium triiodide (CrI$_3$) has long been known as a layered van der Waals ferromagnet. However, its monolayer form was only recently isolated and confirmed to be a truly two-dimensional (2D) ferromagnet, providing a new platform for investigating ... More

Interlayer coupling and gate-tunable excitons in transition metal dichalcogenide heterostructuresDec 13 2017Bilayer van der Waals (vdW) heterostructures such as MoS2/WS2 and MoSe2/WSe2 have attracted much attention recently, particularly because of their type II band alignments and the formation of interlayer exciton as the lowest-energy excitonic state. In ... More

Rotation Invariance Neural NetworkJun 17 2017Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol ... More

Large Magellanic Cloud Near-Infrared Synoptic Survey. V. Period-Luminosity Relations of MirasAug 16 2017We study the near-infrared properties of 690 Mira candidates in the central region of the Large Magellanic Cloud, based on time-series observations at JHKs. We use densely-sampled I-band observations from the OGLE project to generate template light curves ... More

Fermionic formula for double Kostka polynomialsFeb 29 2016The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\Bla,\Bmu}(t),$ ... More

The M33 Synoptic Stellar Survey. II. Mira VariablesMar 03 2017Mar 24 2017We present the discovery of 1847 Mira candidates in the Local Group galaxy M33 using a novel semi-parametric periodogram technique coupled with a Random Forest classifier. The algorithms were applied to ~2.4x10^5 I-band light curves previously obtained ... More

Period estimation for sparsely-sampled quasi-periodic light curves applied to MirasSep 21 2016Sep 23 2016We develop a non-linear semi-parametric Gaussian process model to estimate periods of Miras with sparsely-sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum ... More

Period estimation for sparsely-sampled quasi-periodic light curves applied to MirasSep 21 2016Nov 17 2016We develop a non-linear semi-parametric Gaussian process model to estimate periods of Miras with sparsely-sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum ... More

Edge-Insensitive Magnetism and Half Metallicity in Graphene NanoribbonsOct 09 2018Realizing magnetism in graphene/carbon nanostructures is a decade-long challenge. The magnetic edge state and half metallicity in zigzag graphene nanoribbons are particularly promising [Y.-W. Son, et al., Nature 444, 347 (2006)]. However, its experimental ... More

Renormalization of quasiparticle band gap in doped two-dimensional materials from many-body calculationsDec 13 2017Doped free carriers can substantially renormalize electronic self-energy and quasiparticle band gaps of two-dimensional (2D) materials. However, it is still challenging to quantitatively calculate this many-electron effect, particularly at the low doping ... More

Double Kostka polynomials and Hall bimoduleJan 24 2015Double Kostka polynomials are polynomials indexed by a pair of double partitions. As in the ordinary case, double Kostka polynomials are defined in terms of Schur functions and Hall-Littlewood functions associated to double partitions. In this paper, ... More

Combination of e+/e- ratio from AMS-02 and gamma ray line from Fermi-LAT with implication for Dark MatterOct 13 2013Oct 15 2013The precise AMS-02 data provide definite information for the e+/e- ratio in 100 - 350 GeV region. Assuming that the recent gamma ray line observed by Fermi-LAT experiment is product of dark matter in space and taken as input. We make a global fit for ... 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

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

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

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

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

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

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

Quasiparticle Band Gaps, Excitonic Effects, and Anisotropic Optical Properties of Monolayer Distorted 1-T Diamond-chain StructuresAug 14 2015Sep 08 2015We report many-body perturbation theory calculations of excited-state properties of distorted 1-T diamond-chain monolayer rhenium disulfide (ReS2) and diselenide (ReSe2). Electronic self-energy substantially enhances their quasiparticle band gaps and, ... More

Application of support vector machine for the fast and accurate reconstruction of nanostructures in optical scatterometryMay 15 2019Nonlinear regression methods, such as local optimization algorithms, are widely used in the extraction of nanostructure profile parameters in optical scatterometry. The success of local optimization algorithms heavily relies on the estimated initial solution. ... 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

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

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

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

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

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

Thermodynamics of interacting tachyonic scalar fieldNov 30 2016In this paper we discuss the laws of thermodynamics for interacting tachyonic scalar field. The components of the tachyonic scalar field in the universe are taken to exist in the state of non-equilibrium initially, but due to interaction they undergo ... 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

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

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

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

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.

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

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

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.

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

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

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

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

Stability of stochastic impulsive differential equations: integrating the cyber and the physical of stochastic systemsApr 29 2019According to Newton's second law of motion, we humans describe a dynamical system with a differential equation, which is naturally discretized into a difference equation whenever a computer is used. The differential equation is the continuous-time model ... More

Optimizing Your Online-Advertisement AsynchronouslyMar 23 2014We consider the problem of designing optimal online-ad investment strategies for a single advertiser, who invests at multiple sponsored search sites simultaneously, with the objective of maximizing his average revenue subject to the advertising budget ... More

Directory Service Provided by DSCloud PlatformOct 23 2017When there are huge volumes of information dispersing in the various machines, global directory services are required for the users. DSCloud Platform provides the global directory service, in which the directories are created and maintained by the users ... More

Density stability for some Lévy-driven Stochastic Differential EquationsMar 16 2016We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the distance between ... More

Global Solution to a nonlinear wave equation of liquid crystal in the constant electric fieldJun 14 2018Oct 10 2018We construct a global conservative weak solution to the Cauchy problem for the non-linear variational wave equation $v_{tt} - c(v)(c(v)v_x)_x + \frac{1}{2}(v+v^3)= 0$ where $c(\cdot)$ is any smooth function with uniformly positive bounded value. This ... 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

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

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.

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

On Formation of Singularity of Spherically Symmetric Nonbarotropic FlowsDec 31 2014We study an initial boundary value problem on a ball for the heat-conductive system of compressible Navier-Stokes-Fourier equations, in particular, a criterion of breakdown of the classical solution. For smooth initial data away from vacuum, it is proved ... 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

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

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

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 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