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Categorization Problem on Controllability of Boolean Control NetworksApr 12 2019A Boolean control network (BCN) is a discrete-time dynamical system whose variables take values from a binary set $\{0,1\}$. At each time step, each variable of the BCN updates its value simultaneously according to a Boolean function which takes the state ... 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

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

An introduction to affine Grassmannians and the geometric Satake equivalenceMar 17 2016Apr 04 2016We introduce various affine Grassmannians, study their geometric properties, and give some applications. We also discuss the geometric Satake equivalence. These are the expanded lecture notes for a mini-course in 2015 PCMI summer school. References updated ... More

Study of an Equivalent Proposition of Riemann HypothesisSep 24 2016Let $H_n = \sum_{k = 1}^{n}\frac{1}{k}$. Using Chebyshev function and prime number theorem, this paper proves that, there exists a positive constant A, such that for all natural numbers $n = q_1 * q_2 *... * q_m$ or $n = q_1^{\alpha_1} * q_2^{\alpha_1} ... More

Low-intensity light switching of cavity-atom polaritonsFeb 03 2010Mar 22 2010I analyze an all-optical switching scheme in a cavity QED system consisting of multiple three-level atoms confined in a cavity mode. A control laser coupled to the atoms from free space induces quantum interference in the coupled cavity-atom system and ... More

The order of the group of self-homotopy equivalence of wedge spacesAug 01 2015In this paper $Aut(\Sigma X\vee \Sigma Y)^\#$ the order of the group of self-homotopy equivalence of wedge spaces is studied. Under the condition of reducibility, we decompose $ Aut(\bigvee\limits_{t=1}^{k}X_{t})$ to the product of subgroups which generalizes ... More

Rigidity of a family of spherical conical metricsFeb 06 2019We study the deformation of spherical conical metrics with at least some of the cone angles larger than $2\pi$. We show in this note via synthetic geometry that for one family of such metrics, there is local rigidity in the choice of cone positions if ... More

Maximal zero sequences for Fock spacesOct 11 2011A sequence $Z$ in the complex plane $\C$ is called a zero sequence for the Fock space $F^p_\alpha$ if there exists a function $f\in F^p_\alpha$, not identically zero, such that $Z$ is the zero set of $f$, counting multiplicities. We show that there exist ... More

Multiqubit Clifford groups are unitary 3-designsOct 09 2015We show that the multiqubit (including qubit) Clifford group in any even prime power dimension is not only a unitary 2-design, but also a unitary 3-design. Moreover, it is a minimal unitary 3-design except for dimension 4. As an immediate consequence, ... More

K3 surfaces associated to Abelian Fourfolds of Mumford's TypeDec 17 2018Mumford 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

Quantitative unique continuation of solutions to higher order elliptic equations with singular coefficientsApr 05 2017Mar 25 2018We investigate the quantitative unique continuation of solutions to higher order elliptic equations with singular coefficients. Quantitative unique continuation described by the vanishing order is a quantitative form of strong unique continuation property. ... More

Area bounds for minimal surfaces in geodesic ball of hyperbolic spaceDec 08 2016In hyperbolic space $H^n$ we set a geodesic ball of radius $\rho$. Consider a $k$ dimensional minimal submanifold passing through the origin of the geodesic ball with boundary lies on the boundary of that geodesic ball. We prove that its area is no less ... More

Two Boundary Centralizer Algebras for $\mathfrak{gl}(n|m)$Sep 21 2018We define an action of the degenerate two boundary braid algebra $\mathcal{G}_d$ on the $\mathbb{C}$-vector space $M\otimes N\otimes V^{\otimes d}$, where $M$ and $N$ are arbitrary modules for the general linear Lie superalgebra $\mathfrak{gl}(n|m)$, ... More

Gradient-based Sampling: An Adaptive Importance Sampling for Least-squaresMar 02 2018In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the input data ... More

Accelerate micromagnetic simulations with GPU programming in MATLABJan 25 2015A finite-difference Micromagnetic simulation code written in MATLAB is presented with Graphics Processing Unit (GPU) acceleration. The high performance of Graphics Processing Unit (GPU) is demonstrated compared to a typical Central Processing Unit (CPU) ... More

Diffraction induced Spin Pumping in Normal-Metal/Multiferroic-Helimagnet/Ferromagnet HeterostructuresMay 30 2014Generally the adiabatic quantum pumping phenomenon can be interpreted by the surface integral of the Berry curvature inside the cyclic loop. Spin angular momentum flow without charge current can be pumped out by magnetization precession in ferromagnet-based ... More

Speedup of Micromagnetic Simulations with C++ AMP On Graphics Processing UnitsJun 29 2014A finite-difference Micromagnetic solver is presented utilizing the C++ Accelerated Massive Parallelism (C++ AMP). The high speed performance of a single Graphics Processing Unit (GPU) is demonstrated compared to a typical CPU-based solver. The speed-up ... More

BSDE and generalized Dirichlet forms: the infinite dimensional caseJan 16 2012We consider the following quasi-linear parabolic system of backward partial differential equations on a Banach space $E$: $(\partial_t+L)u+f(\cdot,\cdot,u, A^{1/2}\nabla u)=0$ on $[0,T]\times E,\qquad u_T=\phi$, where $L$ is a possibly degenerate second ... More

On the Complexity of Protein Local Structure Alignment Under the Discrete Fréchet DistanceSep 05 2007We show that given $m$ proteins (or protein backbones, which are modeled as 3D polygonal chains each of length O(n)) the problem of protein local structure alignment under the discrete Fr\'{e}chet distance is as hard as Independent Set. So the problem ... More

Lie II theorem for Lie algebroids via higher groupoidsDec 31 2006May 20 2010Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie groups, Lie algebroids ... More

The higher sharp IV: the higher levelsMay 30 2017We establish the descriptive set theoretic representation of the mouse $M_n^{\#}$, which is called $0^{(n+1)\#}$. This part deals with the case $n>3$.

On the critical branching random walk I: Branching capacity and visiting probabilityNov 30 2016Jan 31 2017We extend the theory of discrete capacity to critical branching random walk. We introduce branching capacity for any finite subset of $\Z^d, d\geq5$. Analogous to the regular discrete capacity, branching capacity is closely related to the asymptotics ... More

On the critical branching random walk II: Branching capacity and branching recurrenceDec 01 2016Jan 31 2017We continue our study of critical branching random walk and branching capacity. In this paper we introduce branching recurrence and branching transience and prove an analogous version of Wiener's Test.

Game Theory for Cyber Deception: A TutorialMar 03 2019Deceptive and anti-deceptive technologies have been developed for various specific applications. But there is a significant need for a general, holistic, and quantitative framework of deception. Game theory provides an ideal set of tools to develop such ... More

A generalized Morse index theoremApr 07 2005In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.

Projective dimension and regularity of the path ideal of the line graphOct 10 2016Oct 26 2016By generalizing the notion of the path ideal of a graph, we study some algebraic properties of some path ideals associated to a line graph. We show that the quotient ring of these ideals are always sequentially Cohen-Macaulay and also provide some exact ... More

Implications of the recent measurement of pure annihilation $B_s \to π^+ π^-$ decays in QCD factorizationJun 23 2011Jul 20 2011The CDF 3.7 sigma evidence of pure annihilation $B_s \to \pi^+ \pi^-$ decays, if confirmed, would imply a large annihilation scenario in the QCD factorization approach. This is somewhat unexpected as the large annihilation scenario was disfavored in previous ... More

B physics constraints on a flavor symmetric scalar model to account for the ttbar asymmetry and Wjj excess at CDFApr 16 2011Jul 22 2011Recently Nelson et al. proposed an interesting flavor symmetric model to account for the top quark forward-backward asymmetry and the dijet anomaly at CDF simultaneously with just three parameters: a coupling constant of order one, and two scalar masses ... More

The Complexity of HCP in Digraps with Degree Bound TwoApr 03 2007Jul 13 2007The Hamiltonian cycle problem (HCP) in digraphs D with degree bound two is solved by two mappings in this paper. The first bijection is between an incidence matrix C_{nm} of simple digraph and an incidence matrix F of balanced bipartite undirected graph ... More

On general (alpha,beta)-metrics with vanishing Douglas curvatureMay 29 2015In this paper, we study a class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$. We find an equation which is necessary and sufficient condition for such Finsler metric ... More

Permutation Symmetry Determines the Discrete Wigner FunctionApr 15 2015Jan 10 2016The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying ... More

On general $(α,β)$-metrics with isotropic Berwald curvatureJun 05 2015In this paper, we study a class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$. We classify this class of Finsler metrics with isotropic Berwald curvature under certain ... More

Quasiprobability representations of quantum mechanics with minimal negativityApr 24 2016Aug 25 2016Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has profound implications ... More

Stabilization of Damped Waves on Spheres and Zoll Surfaces of RevolutionApr 18 2016Dec 17 2017We study the strong stabilization of wave equations on some sphere-like manifolds, with rough damping terms which do not satisfy the geometric control condition posed by Rauch-Taylor and Bardos-Lebeau-Rauch. We begin with an unpublished result of G. Lebeau, ... More

Preprojective cluster variables of acyclic cluster algebrasNov 29 2005Aug 30 2006For any valued quiver, by using BGP-reflection functors, an injection from the set of preprojective objects in the cluster category to the set of cluster variables of the corresponding cluster algebra is given, the images are called preprojective cluster ... More

Multiple list colouring of planar graphsMay 16 2016This paper proves that for each positive integer $m$, there is a planar graph $G$ which is not $(4m+\lfloor \frac{2m-1}{9}\rfloor,m)$-choosable. Then we pose some conjectures concerning multiple list colouring of planar graphs.

The Lp Minkowski problem for polytopes for 0 < p < 1Jun 29 2014Aug 02 2014Necessary and sufficient conditions are given for the existence of solutions to the discrete Lp Minkowski problem for the critical case where 0 < p < 1.

Rigidity of Area-Minimizing $2$-Spheres in $n$-Manifolds with Positive Scalar CurvatureMar 14 2019Mar 28 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

Neural Architecture Search for Deep Face RecognitionApr 21 2019Apr 26 2019By the widespread popularity of electronic devices, the emergence of biometric technology has brought significant convenience to user authentication compared with the traditional password and mode unlocking. Among many biological characteristics, the ... More

Asymptotic order of the quantization errors for self-affine measures on Bedford-McMullen carpetsApr 19 2016Let $E$ be a Bedford-McMullen carpet determined by a set of affine mappings $(f_{ij})_{(i,j)\in G}$ and $\mu$ a self-affine measure on $E$ associated with a probability vector $(p_{ij})_{(i,j)\in G}$. We prove that, for every $r\in(0,\infty)$, the upper ... More

Convergence order of the geometric mean errors for Markov-type measuresOct 26 2014We study the quantization problem with respect to the geometric mean error for Markov-type measures $\mu$ on a class of fractal sets. Assuming the irreducibility of the corresponding transition matrix $P$, we determine the exact convergence order of the ... More

Asymptotic local uniformity of the quantization error for Ahlfors-David probability measuresAug 25 2017Feb 26 2018Let $\mu$ be an Ahlfors-David probability measure on $\mathbb{R}^q$, namely, there exist some constants $s_0>0$ and $\epsilon_0,C_1,C_2>0$ such that \[ C_1\epsilon^{s_0}\leq\mu(B(x,\epsilon))\leq C_2\epsilon^{s_0},\;\epsilon\in(0,\epsilon_0),\;x\in{\rm ... More

Influence of Stellar Metallicity on Occurrence Rates of Planets and Planetary SystemsAug 28 2018Jan 24 2019We study the influence of stellar metallicity on the fraction of stars with planets (i.e., the occurrence rate of planetary systems) and the average number of planets per star (i.e., the occurrence rate of planets). The former directly reveals the planet ... More

Molecular Model Checking a Temporal LogicAug 05 2016Feb 20 2017The molecular computing has been successfully employed to solve more and more complex computation problems. However, as an important complex problem, the model checking are still far from fully resolved under the circumstance of molecular computing, since ... More

Loss Tomography in General TopologyMar 25 2016Although there are a few works reported in the literature considering loss tomography in the general topology, there is few well established result since all of them rely either on simulations or on experiments that have many random factors affecting ... More

Evidence of Different Formation Mechanisms for Hot versus Warm Super-EarthsMar 05 2015Using the Kepler planet sample from Buchhave et al. and the statistical method clarified by Schlaufman, I show that the shorter-period super-Earths have a different dependence on the host star metallicity from the longer-period super-Earths, with the ... More

Are valence quarks rotating?Oct 27 2012We suggest to compare the deep inelastic scattering structure functions measured in the unpolarized charged-lepton scattering off a transversely polarized proton and off a longitudinally polarized proton at larger Bjorken variable $x$, one may get a direct ... More

Application of Jet Trimming in Boosted Higgs SearchJul 09 2011We present the study of the $WH$ and $ZH$ search with the Higgs Boson decayed to $b\bar{b}$ at the Large Hadron Collider. The Higgs Boson and the Vector Boson are required to be boosted, and the Higgs Boson is reconstructed with Jet Trimming Technique. ... More

A Closed Form Maximum Likelihood Estimator to End-to-End Loss Rate EstimationApr 30 2011Oct 01 2012Loss tomography has been studied for more than 10 years and a number of estimators have been proposed. The estimators can be divided into two classes: maximum likelihood and non-maximum likelihood. The maximum likelihood estimators rely on the maximum ... More

Loss Rate Inference in Multi-Sources and Multicast-Based General TopologySep 14 2010Jul 20 2011Loss tomography has received considerable attention in recent years and a number of estimators have been proposed. Unfortunately, almost all of them are devoted to the tree topology despite the general topology is more common in practice. In addition, ... More

Experimental Study on CTL model checking using Machine LearningFeb 23 2019The existing core methods, which are employed by the popular CTL model checking tools, are facing the famous state explode problem. In our previous study, a method based on the Machine Learning (ML) algorithms was proposed to address this problem. However, ... More

Analyzing DNA Hybridization via machine learningMar 27 2018Jul 02 2018In DNA computing, it is impossible to decide whether a specific hybridization among complex DNA molecules is effective or not within acceptable time. In order to address this common problem, we introduce a new method based on the machine learning technique. ... More

An Energy Reducing Flow for Multiple-Valued FunctionsJun 20 2006By the method of discrete Morse flows, we construct an energy reducing multiple-valued function flow. The flow we get is Holder continuous with respect to the L-2 norm. We also give another way of constructing flows in some special cases, where the flow ... More

A note on the quantization error for in-homogeneous self-similar measuresAug 31 2016We further study the asymptotics of quantization errors for two classes of in-homogeneous self-similar measures $\mu$. We give a new sufficient condition for the upper quantization coefficient for $\mu$ to be finite. This, together with our previous work, ... More

Several Conclusions on another site setting problemJun 02 2018Let $S = \{ {A_1},{A_2}, \cdots ,{A_n}\} $ be a finite point set in m-dimensional Euclidean space ${E^m}$, and$\left\| {{A_i}{A_j}} \right\|$ be the distance between $A_i$ and $A_j$. Define $\sigma (S) = \sum\limits_{1 \le i < j \le n} {\left\| {{A_i}{A_j}} ... More

Prescribing integral curvature equationJul 10 2014Feb 07 2015In this paper we formulate new curvature functions on $\mathbb{S}^n$ via integral operators. For certain even orders, these curvature functions are equivalent to the classic curvature functions defined via differential operators, but not for all even ... More

Regular representations of the quantum groups at roots of unityNov 20 2007Dec 03 2007We study the bimodule structure of the quantum function algebra at roots of 1 and prove that it admits an increasing filtration with factors isomorphic to the tensor products of the dual of Weyl modules $V_\lambda^* \otimes V_{- \omega_0 \lambda}^*$. ... More

Regularity for harmonic maps into certain Pseudo-Riemannian manifoldsJan 10 2011Mar 20 2012In this article, we investigate the regularity for certain elliptic systems without a $L^2$-antisymmetric structure. As applications, we prove some $\epsilon$-regularity theorems for weakly harmonic maps from the unit ball $B= B(m) \subset \mathbb{R}^m ... More

Depth and Stanley depth of the path ideal associated to an $n$-cyclic graphDec 24 2016We compute the depth and Stanley depth for the quotient ring of the path ideal of length $3$ associated to a $n$-cyclic graph, given some precise formulas for depth when $n\not\equiv 1\,(\mbox{mod}\ 4)$, tight bounds when $n\equiv 1\,(\mbox{mod}\ 4)$ ... 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

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

Local Quantum Criticality of a One-Dimensional Kondo Insulator ModelMar 17 2018The continuous quantum phase transition and the nature of quantum critical point (QCP) in a modified Kondo lattice model with Ising anisotropic exchange interactions is studied within the density-matrix renormalization group algorithm. We investigate ... 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