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Topological phases in pyrochlore thallium niobate Tl$_2$Nb$_2$O$_{6+x}$Mar 03 2019Jul 05 2019The discovery of new topological electronic materials brings a chance to uncover novel physics and plays a key role in observing and controlling various intriguing phenomena. Up to now, many materials have been theoretically proposed and experimentally ... More

Weighted Sobolev $L^{p}$ estimates for homotopy operators on strictly pseudoconvex domains with $C^{2}$ boundaryJun 29 2019We derive estimates in a weighted Sobolev space $W^{k,p}_{\mu}(D)$ for a homotopy operator on a bounded strictly pseudoconvex domain $D$ of $C^2$ boundary in ${\C}^n$. As a result, we show that given any $2n < p < \infty$, $k > 1$, $q \geq 1$, and a $\dbar$-closed ... More

Nodal Loop and Nodal Surface States in Ti3Al Family MaterialsMay 04 2018May 09 2018Topological metals and semimetals are new states of matter which attract great interest in current research. Here, based on first-principles calculations and symmetry analysis, we propose that the family of titanium-based compounds Ti3X (X=Al, Ga, Sn, ... More

Convergent Block Coordinate Descent for Training Tikhonov Regularized Deep Neural NetworksNov 20 2017By lifting the ReLU function into a higher dimensional space, we develop a smooth multi-convex formulation for training feed-forward deep neural networks (DNNs). This allows us to develop a block coordinate descent (BCD) training algorithm consisting ... More

Topological Semimetal-Insulator Quantum Phase Transition in Zintl Compounds Ba2X (X=Si, Ge)Oct 17 2016By first-principles calculations, we find that Ba2X(X=Si, Ge) hosts a topological semimetal phase with one nodal ring in the kx=0 plane, which is protected by the glide mirror symmetry when spin-orbit coupling (SOC) is ignored. The corresponding drumheadlike ... More

Quadratic contact point semimetal: Theory and material realizationJun 27 2018Sep 20 2018Most electronic properties of metals are determined solely by the low-energy states around the Fermi level, and for topological metals/semimetals, these low-energy states become distinct because of their unusual energy dispersion and emergent pseudospin ... More

BPGrad: Towards Global Optimality in Deep Learning via Branch and PruningNov 19 2017Understanding the global optimality in deep learning (DL) has been attracting more and more attention recently. Conventional DL solvers, however, have not been developed intentionally to seek for such global optimality. In this paper we propose a novel ... More

Object Proposal Generation using Two-Stage Cascade SVMsJul 20 2014Object proposal algorithms have shown great promise as a first step for object recognition and detection. Good object proposal generation algorithms require high object recall rate as well as low computational cost, because generating object proposals ... More

Triple Point Topological MetalsMay 16 2016Jun 10 2016Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary fermionic particles ... More

Mixed field theoryNov 29 2018We consider scalar field theory defined over a direct product of the real and $p$-adic numbers. An adjustable dynamical scaling exponent $z$ enters into the microscopic lagrangian, so that the Gaussian theories provide a line of fixed points. We argue ... More

Topological phases in pyrochlore thallium niobate Tl$_2$Nb$_2$O$_{6+x}$Mar 03 2019Mar 05 2019The discovery of new topological electronic materials brings a chance to uncover novel physics and plays key rule in observing and controlling various intriguing phenomena. Up to now, many materials have been theoretically proposed and experimentally ... More

Composite Dirac SemimetalApr 12 2019Weak topological insulators and Dirac semimetals are gapped and nodal phases with distinct topological properties, respectively. Here, we propose a novel topological phase that exhibits features of both and is dubbed composite Dirac semimetal (CDSM). ... More

Composite Dirac SemimetalApr 12 2019Apr 16 2019Weak topological insulators and Dirac semimetals are gapped and nodal phases with distinct topological properties, respectively. Here, we propose a novel topological phase that exhibits features of both and is dubbed composite Dirac semimetal (CDSM). ... More

Mechanisms governing phonon scattering by topological defects in graphene nanoribbonsNov 03 2016Understanding phonon scattering by topological defects in graphene is of particular interest for thermal management in graphene-based devices. We present a study that quantifies the roles of the different mechanisms governing defect phonon scattering ... More

A Modified Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric TermsJan 19 2015Jun 10 2015The Abramov-Petkovsek reduction computes an additive decomposition of a hypergeometric term, which extends the functionality of the Gosper algorithm for indefinite hypergeometric summation. We modify the Abramov-Petkovsek reduction so as to decompose ... More

Refined scattering diagrams and theta functions from asymptotic analysis of Maurer-Cartan equationsFeb 15 2019Mar 27 2019We further develop the asymptotic analytic approach to the study of scattering diagrams. We do so by analyzing the asymptotic behavior of Maurer-Cartan elements of a differential graded Lie algebra constructed from a (not-necessarily tropical) monoid-graded ... More

Sequential Optimization for Efficient High-Quality Object Proposal GenerationNov 14 2015May 22 2017We are motivated by the need for a generic object proposal generation algorithm which achieves good balance between object detection recall, proposal localization quality and computational efficiency. We propose a novel object proposal algorithm, BING++, ... More

Smart Grid Communications: Overview of Research Challenges, Solutions, and Standardization ActivitiesDec 15 2011Optimization of energy consumption in future intelligent energy networks (or Smart Grids) will be based on grid-integrated near-real-time communications between various grid elements in generation, transmission, distribution and loads. This paper discusses ... More

Learning Joint Feature Adaptation for Zero-Shot RecognitionNov 23 2016Zero-shot recognition (ZSR) aims to recognize target-domain data instances of unseen classes based on the models learned from associated pairs of seen-class source and target domain data. One of the key challenges in ZSR is the relative scarcity of source-domain ... More

Zero-Shot Learning via Joint Latent Similarity EmbeddingNov 14 2015Aug 17 2016Zero-shot recognition (ZSR) deals with the problem of predicting class labels for target domain instances based on source domain side information (e.g. attributes) of unseen classes. We formulate ZSR as a binary prediction problem. Our resulting classifier ... More

PRISM: Person Re-Identification via Structured MatchingJun 13 2014May 08 2015Person re-identification (re-id), an emerging problem in visual surveillance, deals with maintaining entities of individuals whilst they traverse various locations surveilled by a camera network. From a visual perspective re-id is challenging due to significant ... More

Learning Joint Feature Adaptation for Zero-Shot RecognitionNov 23 2016Dec 03 2016Zero-shot recognition (ZSR) aims to recognize target-domain data instances of unseen classes based on the models learned from associated pairs of seen-class source and target domain data. One of the key challenges in ZSR is the relative scarcity of source-domain ... More

RAPID: Rapidly Accelerated Proximal Gradient Algorithms for Convex MinimizationJun 13 2014Jun 18 2014In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each proximal gradient ... More

SYZ mirror symmetry from Witten-Morse theoryNov 22 2018This is a survey article on the recent progress in understanding the Strominger-Yau-Zaslow (SYZ) mirror symmetry conjecture, especially on the effect of quantum corrections, via Witten-Morse theory using the program first depicted by Fukaya to obtain ... More

Coloring with Words: Guiding Image Colorization Through Text-based Palette GenerationApr 11 2018Aug 07 2018This paper proposes a novel approach to generate multiple color palettes that reflect the semantics of input text and then colorize a given grayscale image according to the generated color palette. In contrast to existing approaches, our model can understand ... More

Non-local non-linear sigma modelsJun 25 2019We study non-local non-linear sigma models in arbitrary dimension, focusing on the scale invariant limit in which the scalar fields naturally have scaling dimension zero, so that the free propagator is logarithmic. The classical action is a bi-local integral ... More

Zero-Shot Learning via Semantic Similarity EmbeddingSep 15 2015Sep 25 2015In this paper we consider a version of the zero-shot learning problem where seen class source and target domain data are provided. The goal during test-time is to accurately predict the class label of an unseen target domain instance based on revealed ... More

Fukaya's conjecture on $S^1$-equivariant de Rham complexJan 28 2019Getzler-Jones-Petrack introduced $A_\infty$ structures on the equivariant complex for manifold $M$ with smooth $\mathbb{S}^1$ action, motivated by geometry of loop spaces. Applying Witten's deformation by Morse functions followed by homological perturbation ... More

A Note on Lipshitz's Lemma 3Oct 23 2011Nov 06 2011In this note, we give a remark on the proof of Lemma 3 in Lipshitz's paper "The diagonal of a D-Finite power series is D-Finite". This remark is motivated by the observation that the statement from line -8 to -3 on page 375 of that paper seems not completely ... More

Secure Real-Time Monitoring and Management of Smart Distribution Grid using Shared Cellular NetworksJan 13 2017The electricity production and distribution is facing two major changes. First, the production is shifting from classical energy sources such as coal and nuclear power towards renewable resources such as solar and wind. Secondly, the consumption in the ... More

Tropical counting from asymptotic analysis on Maurer-Cartan equationsJul 21 2018Jan 31 2019Let $X = X_\Sigma$ be a toric surface and $(\check{X}, W)$ be its Landau-Ginzburg (LG) mirror where $W$ is the Hori-Vafa potential. We apply asymptotic analysis to study the extended deformation theory of the LG model $(\check{X}, W)$, and prove that ... More

A Wong-Zakai theorem for $Φ^4_3$ modelApr 16 2015We prove a version of the Wong-Zakai theorem for the dynamical $\Phi_3^4$ model driven by space-time white noise on $\mathbb{T}^3$. For the $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed in order to define the nonlinear ... More

Weak universality of the dynamical $Φ_3^4$ model on the whole spaceNov 04 2018Nov 06 2018We prove the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on $\mathbb{R}^3$ to the dynamical $\Phi^4_3$ model by paracontrolled distributions on weighted Besov space. Our approach depends on the delicate ... More

Dirichlet form associated with the $Φ_3^4$ modelMar 29 2017Jun 25 2017We construct the Dirichlet form associated with the dynamical $\Phi^4_3$ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this classical gradient ... More

Random attractor associated with the quasi-geostrophic equationMar 24 2013We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $\alpha>1/2$) by proving the existence of a ... More

Piecewise linear approximation for the dynamical $Φ^4_3$ modelApr 16 2015Oct 22 2017We construct a piecewise linear approximation for the dynamical $\Phi_3^4$ model on $\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to be performed ... More

Dimension reduction-based significance testing in nonparametric regressionOct 13 2015A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a local smoothing ... More

Efficient Training of Very Deep Neural Networks for Supervised HashingNov 14 2015Apr 21 2016In this paper, we propose training very deep neural networks (DNNs) for supervised learning of hash codes. Existing methods in this context train relatively "shallow" networks limited by the issues arising in back propagation (e.e. vanishing gradients) ... More

A Novel Visual Word Co-occurrence Model for Person Re-identificationOct 24 2014Person re-identification aims to maintain the identity of an individual in diverse locations through different non-overlapping camera views. The problem is fundamentally challenging due to appearance variations resulting from differing poses, illumination ... More

Group Membership PredictionSep 16 2015The group membership prediction (GMP) problem involves predicting whether or not a collection of instances share a certain semantic property. For instance, in kinship verification given a collection of images, the goal is to predict whether or not they ... More

Principal Component Analysis of collective flow in Relativistic Heavy-Ion CollisionsMar 23 2019In this paper, we implement Principal Component Analysis (PCA) to study the single particle distributions generated from thousands of {\tt VISH2+1} hydrodynamic simulations with an aim to explore if a machine could directly discover flow from the huge ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jun 10 2015In this paper we study 3D Navier-Stokes (NS) equation driven by space-time white noise by using regularity structure theory introduced in [Hai14] and paracontrolled distribution proposed in [GIP13]. We obtain local existence and uniqueness of solutions ... More

Strong-Feller property for Navier-Stokes equations driven by space-time white noiseSep 27 2017Sep 29 2017In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in ... More

Lattice approximation to the dynamical $Φ_3^4$ modelAug 23 2015We study the lattice approximations to the dynamical $\Phi^4_3$ model by paracontrolled distributions proposed in [GIP13]. We prove that the solutions to the lattice systems converge to the solution to the dynamical $\Phi_3^4$ model in probability, locally ... More

Three-dimensional Navier-Stokes equations driven by space-time white noiseMay 31 2014Jan 04 2017In this paper we study 3D Navier-Stokes (NS) equation driven by space-time white noise by using regularity structure theory introduced in [Hai14] and paracontrolled distribution proposed in [GIP13]. We obtain local existence and uniqueness of solutions ... More

Time-Delay Momentum: A Regularization Perspective on the Convergence and Generalization of Stochastic Momentum for Deep LearningMar 02 2019In this paper we study the problem of convergence and generalization error bound of stochastic momentum for deep learning from the perspective of regularization. To do so, we first interpret momentum as solving an $\ell_2$-regularized minimization problem ... More

Additive Decompositions in Primitive ExtensionsFeb 07 2018This paper extends the classical Ostrogradsky-Hermite reduction for rational functions to more general functions in primitive extensions of certain types. For an element $f$ in such an extension $K$, the extended reduction decomposes $f$ as the sum of ... More

Lattice point counting via Einstein metricsMay 21 2013We obtain a growth estimate for the number of lattice points inside any Q-Gorenstein cone. Our proof uses the result of Futaki-Ono-Wang on Sasaki-Einstein metric for the toric Sasakian manifold associated to the cone, a Yau's inequality, and the Kawasaki-Riemann-Roch ... More

Approximating three-dimensional Navier-Stokes equations driven by space-time white noiseSep 17 2014In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in [GIP13]. A solution theory for this equation has been developed recently in [ZZ14] based on regularity ... More

OGNet: Salient Object Detection with Output-guided Attention ModuleJul 17 2019Attention mechanisms are widely used in salient object detection models based on deep learning, which can effectively promote the extraction and utilization of useful information by neural networks. However, most of the existing attention modules used ... More

Dialogue Generation: From Imitation Learning to Inverse Reinforcement LearningDec 09 2018The performance of adversarial dialogue generation models relies on the quality of the reward signal produced by the discriminator. The reward signal from a poor discriminator can be very sparse and unstable, which may lead the generator to fall into ... More

Deformable Part NetworksMay 22 2018In this paper we propose novel Deformable Part Networks (DPNs) to learn {\em pose-invariant} representations for 2D object recognition. In contrast to the state-of-the-art pose-aware networks such as CapsNet \cite{sabour2017dynamic} and STN \cite{jaderberg2015spatial}, ... More

Time-Delay Momentum: A Regularization Perspective on the Convergence and Generalization of Stochastic Momentum for Deep LearningMar 02 2019Jun 01 2019In this paper we study the problem of convergence and generalization error bound of stochastic momentum for deep learning from the perspective of regularization. To do so, we first interpret momentum as solving an $\ell_2$-regularized minimization problem ... More

A Generalization of the Kodaira Vanishing and Embedding TheoremFeb 02 1995We give several generalizations of the Kodaira vanishing and embedding theorems for K\"ahler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg ... More

Spectra and elliptic flow of (multi-)strange hadrons at RHIC and LHC within viscous hydrodynamics+hadron cascade hybrid modelJul 14 2016Aug 15 2016Using the (2+1)-dimensional ultrarelativistic viscous hydrodynamics+hadron cascade, VISHNU, hybrid model, we study the $p_{\rm T}$-spectra and elliptic flow of $\Lambda$, $\Xi$, and $\Omega$ in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV and in Pb+Pb ... More

Log rationally connected surfacesDec 08 2014Jul 02 2015In this paper, combining the works of Miyanishi-Tsunoda and Keel-McKernan, we prove the log Castelnuovo's rationality criterion for smooth quasiprojective surfaces over complex numbers.

Exotic Charmonium-like States at BESIIIMay 18 2015The recent measurement results of exotic charmonium-like states, the so called XYZ particles, at BESIII have been presented. I mainly discussed the charged Zc(3900) state, its neutral partner, and possible excited states.

Charmonium and Light Meson SpectroscopyDec 10 2012This talk reviews recent experimental results on selected topics in the spectroscopy of charmonia, charmonium-like states and light mesons.

On the gluing formula of real analytic torsion formsMay 13 2014In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We assume that ... More

The RPC-based proposal for the ATLAS forward muon trigger upgrade in view of super-LHCOct 25 2012The innermost station of the present ATLAS forward muon detector needs to be upgraded for the super-LHC. We present a proposal to replace it with a sandwiched detector composed of several layers of small-radius Monitored Drift Tube chambers (sMDT) for ... More

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 2019Mar 15 2019We prove that the least area of the non-contractible immersed spheres is no more than $4\pi$ in any oriented compact manifold with dimension $n+2\leq 7$ which satisfies $R\geq 2$ and admits a map to $\mathbf S^2\times T^n$ with nonzero degree. We also ... More

Global classical solutions of 3D compressible viscoelastic system near equilibriumSep 12 2018In this paper, we prove the global existence of general small solutions to compressible viscoelastic system. We remove the "initial state" assumption ($\tilde \rho_0 \det F_0 =1$) and the "div-curl" structure assumption compared with previous works. It ... More

Statistical Physics and Information Theory Perspectives on Linear Inverse ProblemsMay 15 2017Jul 12 2017Many real-world problems in machine learning, signal processing, and communications assume that an unknown vector $x$ is measured by a matrix A, resulting in a vector $y=Ax+z$, where $z$ denotes the noise; we call this a single measurement vector (SMV) ... More

Strongly Unitary Equivalence and Approximately Unitary Equivalence of Normal Compact Operators over Topological SpacesSep 01 2017Let $A$ and $B$ be compact operators over a topological space $X$ and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for $A$ and $B$ to ... More

An axiomatic approach to the roughness measure of rough setsNov 28 2009May 25 2010In Pawlak's rough set theory, a set is approximated by a pair of lower and upper approximations. To measure numerically the roughness of an approximation, Pawlak introduced a quantitative measure of roughness by using the ratio of the cardinalities of ... More

Covering rough sets based on neighborhoods: An approach without using neighborhoodsNov 28 2009Dec 10 2010Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough ... More

The internal structure of $\mathrm{HOD}^{L[x]}$ up to its WoodinNov 06 2017Nov 08 2017Assume $\boldsymbol{\Delta}^1_3$-determinacy. It is shown that for any $x \geq_T M_1^{\#}$, $\mathrm{HOD}^{L[x]}$ is a model of GCH, and in fact, it is a Jensen-Steel core model up to $\omega_2^{L[x]}$.

Conductance in the Helimagnet- and Skyrmion-Lattice-Embedded Electron WaveguideNov 22 2013The helimagnet (HM) and skyrmion lattice (SL) are topologically nontrivial magnetic states. Their spin texture gives rise to finite topological magnetic field and Lorentz force. As a demonstration of the emergent electrodynamics besides the Hall effect, ... More

A scattering matrix approach to quantum pumping: Beyond the small-ac-driving-amplitude limitNov 06 2009In the adiabatic and weak-modulation quantum pump, net electron flow is driven from one reservoir to the other by absorbing or emitting an energy quantum $\hbar \omega $ from or to the reservoirs. In our approach, high-order dependence of the scattering ... More

Spin-dependent electron grating effect from helical magnetization in multiferroic tunnel junctionsApr 27 2012In multiferroic oxides with a transverse helical magnetic order, the magnetization exchange coupling is sinusoidally space-dependent. We theoretically investigate the spin-dependent electron grating effect in normal-metal/helical-multiferroic/ferromagnettic ... More

K3 surfaces associated to Abelian Fourfolds of Mumford's TypeDec 17 2018Apr 15 2019Mumford constructed a family of abelian fourfolds with special stucture not characterized by endomorphism ring. Galluzzi showed that the weight 2 Hodge structure of such a variety decomposes into Hodge substructures via the action of Mumford-Tate group, ... More

Constructing a CM Mumford fourfold from Shioda's fourfoldOct 23 2018Apr 15 2019Shioda proved that the Jacobian $A_S$ of the curve $y^2 = x^9 -1$ is a 4-dimensional CM abelian variety with codimension 2 Hodge cycles not generated by divisors. It was noted by Shioda that this behavior resembles the abelian varieties constructed by ... More

The higher order terms in asymptotic expansion of color Jones polynomialsApr 03 2011Color Jones polynomial is one of the most important quantum invariants in knot theory. Finding the geometric information from the color Jones polynomial is an interesting topic. In this paper, we study the general expansion of color Jones polynomial which ... More

Generalized PMC model for the hybrid diagnosis of multiprocessor systemsSep 17 2017Sep 19 2017Fault diagnosis is important to the design and maintenance of large multiprocessor systems. PMC model is the most famous diagnosis model in the system level diagnosis of multiprocessor systems. Under the PMC model, only node faults are allowed. But in ... More

Branching interlacements and tree-indexed random walks in torusDec 28 2018Jan 15 2019In this article, we introduce a model of branching interlacements made of a countable collection of tree-indexed random walk trajectories on $\mathbb{Z}^d,d\geq 5$ for general critical offspring distributions. We show that this model turns out to be the ... More

Inclined Massive Planets in a Protoplanetary Disc: Gap Opening, Disc Breaking, and Observational SignaturesDec 04 2018We carry out three-dimensional hydrodynamical simulations to study planet-disc interactions for inclined high mass planets, focusing on the disc's secular evolution induced by the planet. We find that, when the planet is massive enough and the induced ... More

A New View of Classification in Astronomy with the Archetype Technique: An Astronomical Case of the NP-complete Set Cover ProblemJun 23 2016We introduce a new generic Archetype technique for source classification and identification, based on the NP-complete set cover problem (SCP) in computer science and operations research (OR). We have developed a new heuristic SCP solver, by combining ... More

WIMPless dark matter and the excess gamma rays from the Galactic centerJan 23 2011Apr 05 2011In this paper we discuss the excess gamma rays from the Galactic center, the WMAP haze and the CoGeNT and DAMA results in WIMPless models. At the same time we also investigate the low energy constraints from the anomalous magnetic moment of leptons and ... More

Some sufficient conditions on Hamiltonian digraphDec 23 2008Z-mapping graph is a balanced bipartite graph $G$ of a digraph $D$ by split each vertex of $D$ into a pair of vertices of $G$. Based on the property of the $G$, it is proved that if $D$ is strong connected and $G$ is Hamiltonian, then $D$ is Hamiltonian. ... More

The Complexity of Determining Existence a Hamiltonian Cycle is $O(n^3)$Jun 19 2007The Hamiltonian cycle problem in digraph is mapped into a matching cover bipartite graph. Based on this mapping, it is proved that determining existence a Hamiltonian cycle in graph is $O(n^3)$.

Deformations of glassy polymers in very low temperature regime within cylindrical microporesAug 28 2008Apr 09 2009The deformation kinetics for glassy polymers confined in microscopic domain at very low temperature regime was investigated using a transition-rate-state dependent model considering the shear thinning behavior which means, once material being subjected ... More

Optimal Strategies for a Long-Term Static InvestorNov 24 2013Oct 14 2014The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitols to maximize the expected long-term growth rate of a utility function of the wealth. When the ... More

Nonexistence of sharply covariant mutually unbiased bases in odd prime dimensionsJun 18 2015Aug 23 2015Mutually unbiased bases (MUB) are useful in a number of research areas. The symmetry of MUB is an elusive and interesting subject. A (complete set of) MUB in dimension $d$ is sharply covariant if it can be generated by a group of order $d(d+1)$ from a ... More

Riesz transform characterization of weighted Hardy spaces associated to Schrödinger operatorsMay 21 2014In this paper, we characterize the weighted local Hardy spaces $h^p_\rho(\omega)$ related to the critical radius function $\rho$ and weights $\omega\in A_{1}^{\rho,\,\infty}(\mathbb{R}^{n})$ by localized Riesz transforms $\widehat{R}_j$, in addition, ... More

Nonuniform Dichotomy Spectrum Intervals: Theorem and ComputationFeb 12 2019Under the condition of nonuniformly bounded growth, %nonuniform exponential dichotomy spectrum for nonautonomous linear system is proposed the relationship of the nonuniform exponential dichotomy spectrum and the other two classical spectrums (the Lyapunov ... More

Robustness of nonuniform mean-square exponential dichotomiesFeb 12 2019Jun 13 2019For linear stochastic differential equations (SDEs) with bounded coefficients, we establish the robustness of nonuniform mean-square exponential dichotomy (NMS-ED) on $[t_{0},+\oo)$, $(-\oo,t_{0}]$ and the whole $\R$ separately, in the sense that such ... More

Information complementarity: A new paradigm for decoding quantum incompatibilityJun 26 2014Sep 14 2015The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality ... More

A note on eigenvalues of a class of singular continuous and discrete linear Hamiltonian systemsAug 01 2018In this paper, we show that the analytic and geometric multiplicities of an eigenvalue of a class of singular linear Hamiltonian systems are equal, where both endpoints are in the limit circle cases. The proof is fundamental and is given for both continuous ... More

Integral Solutions to Linear Indeterminate EquationMar 08 2011In this paper, using Euler's function, we give a formula of all integral solutions to linear indeterminate equation with $s$-variables $a_1x_1+a_2x_2+...+a_sx_s=n$. It is a explicit formula of the coefficients $a_1$, $a_2$,..., $a_s$ and the free term ... More

n-Groupoids and Stacky GroupoidsJan 14 2008Jun 29 2009We discuss two generalizations of Lie groupoids. One consists of Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. The other consists of stacky Lie groupoids $\cG\rra M$ with $\cG$ a differentiable stack. We build a 1-1 ... More

Lie n-groupoids and stacky Lie groupoidsSep 14 2006Nov 13 2006We discuss two sorts of generalization of Lie groupoids. One is Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. The other is the stacky Lie groupoid $\cG\rra M$ with $\cG$ a differentiable stack. We build 1-1 correspondence ... More

Integrating Lie algebroids via stacks and applications to Jacobi manifoldsMay 09 2005Lie algebroids can not always be integrated into Lie groupoids. We introduce a new object--``Weinstein groupoid'', which is a differentiable stack with groupoid-like axioms. With it, we have solved the integration problem of Lie algebroids. It turns out ... More

The Lp Minkowski problem for polytopes for negative pFeb 25 2016May 07 2016Existence of solutions to the Lp Minkowski problem is proved for all p less than 0. For the cirtical case of p=-n, which is known as the centro-affine Minkowski problem, this paper contains the main result in [71] as a special case.

The optimal control related to Riemannian manifolds and the viscosity solutions to H-J-B equationsJan 16 2010This paper is concerned with the Dynamic Programming Principle (DPP in short) with SDEs on Riemannian manifolds. Moreover, through the DPP, we conclude that the cost function is the unique viscosity solution to the related PDEs on manifolds.

The quantization for in-homogeneous self-similar measures with in-homogeneous open set conditionJul 05 2014Let $(g_i)_{i=1}^M$ be a family of contractive similitudes satisfying the open set condition. Let $\nu$ be a self-similar measure associated with $(g_i)_{i=1}^M$. We study the quantization problem for the in-homogeneous self-similar measure $\mu$ associated ... More

The Laplace transform of the cut-and-join equation of Mariño-Vafa formula and its applicationsJan 05 2010By the same method introduced in [9], we calculate the Laplace transform of the celebrated cut-and-join equation of Mari\~no-Vafa formula discovered by C. Liu, K. Liu and J. Zhou [17]. Then, we study the applications of the polynomial identity (1) obtained ... More

On a proof of the Bouchard-Sulkowski conjectureAug 14 2011In this short note, we give a proof of the free energy part of the BKMP conjecture of C^3 proposed by Bouchard and Sulkowski [4]. Hence the proof of the full BKMP conjecture for the case of C^3 has been finished.

Jet schemes and singularities of W^r_d(C) lociDec 05 2012Kempf proved that the theta divisor of a smooth projective curve C has rational singularities. In this paper we estimate the dimensions of the jet schemes of the theta divisor and show that all these schemes are irreducible. In particular, we recover ... More

On the Well-posedness of a Generalized Moment Problem and Its Numerical SolutionFeb 26 2018We show that the unique solution to a parametric version of the generalized moment problem depends continuously on the prior function, and thus the problem is well-posed in the sense of Hadamard. Based on this result, the problem is reparametrized via ... More

Constructing a CM Mumford fourfold from Shioda's fourfoldOct 23 2018Jun 06 2019Shioda proved that the Jacobian $A_S$ of the curve $y^2 = x^9 -1$ is a 4-dimensional CM abelian variety with codimension 2 Hodge cycles not generated by divisors. It was noted by Shioda that this behavior resembles the abelian varieties constructed by ... More