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

Computing Lens for Exploring the Historical People's Social NetworkJul 23 2019A typical social research topic is to figure out the influential people's relationship and its weights. It is very tedious for social scientists to solve those problems by studying massive literature. Digital humanities bring a new way to a social subject. ... More

Data Priming Network for Automatic Check-OutApr 10 2019Aug 01 2019Automatic Check-Out (ACO) receives increased interests in recent years. An important component of the ACO system is the visual item counting, which recognizes the categories and counts of the items chosen by the customers. However, the training of such ... More

Data Priming Network for Automatic Check-OutApr 10 2019Automatic Check-Out (ACO) receives increased interests in recent years. An important component of the ACO system is the visual item counting, which recognize the categories and counts of the items chosen by the customers. However, the training of such ... More

Data Priming Network for Automatic Check-OutApr 10 2019Aug 07 2019Automatic Check-Out (ACO) receives increased interests in recent years. An important component of the ACO system is the visual item counting, which recognizes the categories and counts of the items chosen by the customers. However, the training of such ... More

Representation for bounded linear operator on Hilbert spacesNov 07 2016In this paper we construct some $C^{*}$-algebra induced by polar decomposition $T=U|T|$. We get that $T$ is unitary equivalent to $\sqrt{|\eta|}M_{z\phi}$ on $\mathcal{L}^{2}(\sigma(|T|),\mu_{|T|})$, where $\phi\in\mathcal{L}^{\infty}(\sigma(|T|),\mu_{|T|})$ ... More

X-ray emission from magnetic dissipation in the magnetar magnetosphereMay 14 2007Magnetic dissipation through decay of Alfven waves in the magnetar magnetosphere is discussed. Transport of magnetic fields in the star leads to dissipation of the magnetic energy through either direct internal heating or transferring of the energy in ... More

On Generalization of Lax Equivalence Theorem into Unbounded Self-adjoint Operators with Nontrivial KernelAug 15 2017Apr 28 2019For an unbounded self-adjoint operator $ A $ and its resolvent approximation sequence $ \{ A_n \} $, the Moore-Penrose inverse sequence $ \{ A^\dagger_n \}$ is a natural computational scheme of the Moore-Penrose inverse $ A^\dagger $. This paper shows ... More

Minima distribution for global optimizationDec 09 2018May 13 2019This paper establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known first order optimality condition for convex and differentiable functions. By introducing a class ... More

Stable Numerical Differentiation and Generalized Termwise Differentiation on Fourier SeriesMar 10 2019This paper consider the numerical differentiation of first three order via corresponding Fredholm integral equation of first kind in $(0,2\pi)$: Computational schemes with analytic solution formulas are designed using Galerkin method on Fourier basis ... More

A note on Muller's irreducibility criterion for generalized principal seriesMar 18 2019In this paper, via Casselman--Tadic's Jacquet module machine, we reprove I. Muller's irreducibility criterion for principal series, and extend it to generalized principal series. An analogous criterion for covering groups is readily obtained. At last, ... More

Rodier type theorem for generalized principal seriesMar 16 2019In this paper, we extend Rodier's structural theorem for regular principal series to regular generalized principal series of split groups of classical types, which can be viewed as a first step to understand the internal structure of the singular case. ... More

Galerkin Method with Trigonometric Basis on Stable Numerical DifferentiationMar 10 2019Apr 10 2019This paper consider the numerical differentiation of first three order via corresponding Fredholm integral equation of the first kind in $(0,2\pi)$: Computational schemes with analytic solution formulas are designed using Galerkin method on trigonometric ... More

Variational bounds on the ground-state energy of three electrons and one hole in two-dimensionDec 31 2000Jan 09 2001We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon ^2 \hbar ^2 ... More

An Alternative Explanation on the Two Relaxation Rates in Cuprate SuperconductorsNov 22 2000Dec 05 2000Transport properties of high transition temperature (high-Tc) superconductors have been shown to have two distinct relaxation rates. We argue that this apparent inconsistence can be resolved with an effective carrier density n linear in temperature T. ... More

A note on complete hyperbolic structures on ideal triangulated 3-manifoldsOct 18 2010It is a theorem of Casson and Rivin that the complete hyperbolic metric on a cusp end ideal triangulated 3-manifold maximizes volume in the space of all positive angle structures. We show that the conclusion still holds if some of the tetrahedra in the ... More

Automorphisms of Thurston's Space of Measured LaminationsMay 21 1999We give a characterization of the action of the mapping class group on Thurston's space of measured laminations.

Exploration on Grounded Word Embedding: Matching Words and Images with Image-Enhanced Skip-Gram ModelSep 08 2018Word embedding is designed to represent the semantic meaning of a word with low dimensional vectors. The state-of-the-art methods of learning word embeddings (word2vec and GloVe) only use the word co-occurrence information. The learned embeddings are ... More

On the barycentric extensionMay 02 2019In this paper, we will study the Douady-Earle / barycentric extension of maps on $S^{n-1}$. We will show the extension is uniformly Lipschitz if the map is quasiregular. In particular, we will show the barycentric extension for a rational map $f$ on $S^2$ ... More

A type of globally solvable BSDEs with triangularly quadratic generatorsApr 16 2019The present paper is devoted to the study of the well-posedness of a type of BSDEs with triangularly quadratic generators. This work is motivated by the recent results obtained by Hu and Tang [14] and Xing and \v{Z}itkovi\'{c} [28]. By the contraction ... More

Solving a Mathematical Problem in Square War: a Go-like Board GameJul 26 2015Nov 29 2015In this paper, we present a board game: Square War. The game definition of Square War is similar to the classic Chinese board game Go. Then we propose a mathematical problem of the game Square War. Finally, we show that the problem can be solved by using ... More

On conformal surfaces of annulus typeOct 24 2011Dec 07 2011Let $a>b>0$ and $f$ be a conformal map from $B_a\setminus B_b\subseteq R^2$ into $\R^n$, with $|\nabla f|^2=2e^{2u}$. Then $(e_1, e_2)$ with $e_1=e^{-u}\frac{\partial f}{\partial r},$ and $e_2=r^{-1}e^{-u}\frac{\partial f}{\partial\theta}$ is a moving ... More

Yet another normalisation proof for Martin-Lof's logical framework--Terms with correct arities are strongly normalisingJun 14 2005Jun 15 2005In this paper, we prove the strong normalisation for Martin-L\"{o}f's Logical Framework, and suggest that {}``correct arity'', a condition weaker than well-typedness, will also guarantee the strong normalisation.

Remarks on the nonexistence of biharmonic mapsNov 23 2015Apr 04 2016In this short note we study nonexistence result of biharmonic maps from a complete Riemannian manifold into a Riemannian manifold with nonpositive sectional curvature. Assume that $\phi:(M,g)\to (N, h)$ is a biharmonic map, where $(M, g)$ is a complete ... More

Architectural Techniques for Improving NAND Flash Memory ReliabilityAug 12 2018Raw bit errors are common in NAND flash memory and will increase in the future. These errors reduce flash reliability and limit the lifetime of a flash memory device. We aim to improve flash reliability with a multitude of low-cost architectural techniques. ... More

Zeros of exceptional orthogonal polynomials and the maximum of the modulus of an energy functionJun 24 2017We propose a new property of the zeros of exceptional orthogonal polynomials. It has been known that exceptional orthogonal polynomials (XOP) have both real and complex zeros. By fixing m variables at the imaginary parts of the complex zeros of XOP, we ... More

Variable stars in the open cluster NGC 2141Oct 08 2014Oct 09 2014We report the results of a search for variable stars in the open cluster NGC 2141. Ten variable stars are detected, among which nine are new variable stars and they are classified as three short period W UMa type eclipsing binaries, two EA type eclipsing ... More

On-shell improved lattice QCD with staggered fermionsFeb 13 1997May 23 1997By using Symanzik's improvement program, we study on-shell improved lattice QCD with staggered fermions. We find that there are as many as 15 independent lattice operators of dimension of six~(including both gauge and fermion operators) which must be ... More

Reducing subspaces of multiplication operators on the Dirichlet spaceJun 28 2018In this paper, we study the reducing subspaces for the multiplication operator by a finite Blaschke product $\phi$ on the Dirichlet space $D$. We prove that any two distinct nontrivial minimal reducing subspaces of $M_\phi$ are orthogonal. When the order ... More

Discussion on the origin of magic numbers in clustersNov 01 2014The distribution of the sizes of clusters is not continuous, but rather has local maxima. The numbers of atoms of those maxima distribution is called magic numbers. Two methods of determining magic numbers are firstly introduced, followed by three different ... More

SNAP: SNowbAll multi-tree Pushing for Peer-to-Peer Media StreamingSep 13 2010Given the respective advantages of the two complimentary techniques for peer-to-peer media streaming (namely tree-based push and mesh-based pull), there is a strong trend of combining them into a hybrid streaming system. Backed by recently proposed mechanisms ... More

Damping Effect of Electromagnetic Radiation and Time-Dependent Schrodinger EquationFeb 05 2010Jun 06 2011The inexactness of the time-dependent Schr\"odinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term representing this effect ... More

Nonlinear Schrodinger equation containing the time derivative of the probability density: A numerical studyDec 29 2009May 11 2014The simplest nonlinear Schrodinger equation that contains the time derivative of the probability density is investigated. This equation has the same stationary solutions as its linear counterpart, and these solutions are the eigenstates of the corresponding ... More

Role of electrical field in quantum Hall effect of grapheneJul 19 2012The ballistic motion of carriers of graphene in an orthogonal electromagnetic field is investigated to explain Hall conductance of graphene under experimental conditions. With the electrical field, all electronic eigen-states have the same expectation ... More

On Low Complexity Maximum Likelihood Decoding of Convolutional CodesNov 20 2007Jul 31 2008This paper considers the average complexity of maximum likelihood (ML) decoding of convolutional codes. ML decoding can be modeled as finding the most probable path taken through a Markov graph. Integrated with the Viterbi algorithm (VA), complexity reduction ... More

Solving Thurston Equation in a Commutative RingJan 11 2012We show that solutions of Thurston equation on triangulated 3-manifolds in a commutative ring carry topological information. We also introduce a homogeneous Thurston equation and a commutative ring associated to triangulated 3-manifolds.

On polynomial representations of classical strange Lie superalgebrasJan 20 2010In this paper, various polynomial representations of strange classical Lie superalgebras are investigated. It turns out that the representations for the algebras of type P are indecomposable, and we obtain the composition series of the underlying modules. ... More

A New Approach to Abstract Machines - Introduction to the Theory of Configuration MachinesJul 19 2010An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these notions as a ... More

Z decays into light gluinos: a calculation based on unitarityJan 08 2003May 11 2003The Z boson can decay to a pair of light gluinos through loop-mediated processes. Based on unitarity of the S-matrix, the imaginary part of the decay amplitude is computed in the presence of a light bottom squark. This imaginary part can provide useful ... More

Character Formulae for Ortho-symplectic Lie Superalgebras $\mathfrak{osp}(n|2)$Sep 17 2009Jan 22 2010The character formula of any finite dimensional irreducible module $L_\lambda$ for Lie superalgebra $\mathfrak{osp}(n|2)$ is computed. As a by-product, the decomposition of tensor module $L_\lambda\otimes \mathbb{C}^{n|2}$, where $\mathbb{C}^{n|2}$ is ... More

Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary ConditionsApr 07 2009In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied ... More

A Counting Lemma for Binary Matroids and Applications to Extremal ProblemsOct 30 2016Nov 20 2018In graph theory, the Szemer\'edi regularity lemma gives a decomposition of the indicator function for any graph $G$ into a structured component, a uniform part, and a small error. This result, in conjunction with a counting lemma that guarantees many ... More

Stochastic Lagrangian flows on the group of volume-preserving homeomorphisms of the spheresDec 09 2013Dec 04 2014We consider stochastic differential equations on the group of volume-preserving homeomorphisms of the sphere $S^d\,(d\geq 2)$. The diffusion part is given by the divergence free eigenvector fields of the Laplacian acting on $L^2$-vector fields, while ... More

Recovering Model Structures from Large Low Rank and Sparse Covariance Matrix EstimationNov 04 2011Mar 16 2013Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to recover such ... More

Multiplicity of normalized solutions for a class of nonlinear Schrodinger-Poisson-Slater equationsSep 27 2013Oct 24 2013In this paper, we prove a multiplicity result of solutions for the following stationary Schr\"odinger-Poisson-Slater equations \begin{equation}\label{eq-abstract} -\Delta u - \lambda u + (\left | x \right |^{-1}\ast \left | u \right |^2) u - |u|^{p-2}u ... More

Minima distribution for global optimizationDec 09 2018Minima distribution (MD) establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known connection $\nabla f(x^*)=0$ between a differentiable convex function $f$ and ... More

Exploring the QCD Phase Structure with Beam Energy Scan in Heavy-ion CollisionsDec 31 2015Mar 15 2016Beam energy scan programs in heavy-ion collisions aim to explore the QCD phase structure at high baryon density. Sensitive observables are applied to probe the signatures of the QCD phase transition and critical point in heavy-ion collisions at RHIC and ... More

Minima distribution for global optimizationDec 09 2018Feb 18 2019Minima distribution (MD) establishes a strict mathematical relationship between an arbitrary continuous function on a compact set and its global minima, like the well-known connection $\nabla f(x^*)=0$ between a differentiable convex function $f$ and ... More

Galerkin Method with Trigonometric Basis on Stable Numerical DifferentiationMar 10 2019May 07 2019This paper consider the numerical differentiation of first three order via corresponding Fredholm integral equation of the first kind in $(0,2\pi)$: Computational schemes with analytic solution formulas are designed using Galerkin method on trigonometric ... More

A Presentation of the Mapping Class GroupsJan 07 1998Using the works of Gervais, Harer, Hatcher and Thurston and others, we show that the mapping class group of a compact orientable surface has a presentation so that the generators are the set of all Dehn twists and the relations are supported in subsurfaces ... More

Some Applications of a Multiplicative Structure on Simple Loops in SurfacesJul 09 1999We discuss some applications of an intrinsic multipication in the space of simple loops in a surface.

Twisted bilayer graphene with Kekule distortion: isolated flat bandMay 17 2019Twisted bilayer graphenes with magical angle exhibit strongly correlated electronic properties because of the isolated flat band at the Fermi level. We studied the twisted bilayer graphene with substrates on both layers. The substrate induce Kekule distortion ... More

Local algebras with radical cubic zero are PCM-freeAug 28 2013Sep 01 2013An artin algebra is said to be PCM-free if every finitely generated Gorenstein projective module with a projective submodule is projective. In this paper, we show that artin local algebras with radical cubic zero are PCM-free.

An approximate solution for solar and supernova neutrino oscillation in matterJun 03 2005By using Laplace transformation we developed an approximate solution to describe neutrino oscillation probabilities in arbitrary density matter. We show that this approximation solution is valid when matter potential V satisfy $V< \Delta m^2/2E$ and $\int ... More

On Generalization of Lax Equivalence Theorem into Unbounded Self-adjoint Operators with Nontrivial KernelAug 15 2017Jun 30 2019For an unbounded self-adjoint operator $ A $ and its resolvent approximation sequence $ \{ A_n \} $, the Moore-Penrose inverse sequence $ \{ A^\dagger_n \}$ is a natural computational scheme of the Moore-Penrose inverse $ A^\dagger $. This paper shows ... More

From Chemically to Physically Induced Pluripotency in Stem CellFeb 09 2015A quantum model on the chemically and physically induced pluripotency in stem cells is proposed. Based on the conformational Hamiltonian and the idea of slow variables (molecular torsions) slaving fast ones the conversion from the differentiate state ... More

Protein Folding as a Quantum Transition Between Conformational StatesJun 13 2009The importance of torsion vibration in the transmission of life information is indicated. The localization of quantum torsion state is proved. Following these analyses a formalism on the quantum theory of conformation-electron system is proposed. The ... More

The maximum number of cliques in graphs without long cyclesJan 25 2017Sep 11 2017The Erd\H{o}s--Gallai Theorem states that for $k\geq 3$ every graph on $n$ vertices with more than $\frac{1}{2}(k-1)(n-1)$ edges contains a cycle of length at least $k$. Kopylov proved a strengthening of this result for 2-connected graphs with extremal ... More

Reflected Stochastic Differential Equations Driven By G-Brownian motion With Nonlinear ResistanceMay 04 2014Sep 23 2014In this paper, we study the uniqueness and existence of solutions of RGSDEs with nonlinear resistance under an integral-Lipschitz condition of coefficients. Moreover we obtain the comparison theorem for RGSDEs with nonlinear resistance.

Strong contraction mapping and topological non-convex optimizationJul 08 2018Mar 22 2019The strong contraction mapping, a self-mapping that the range is always a subset of the domain, admits a unique fixed-point which can be pinned down by the iteration of the mapping. We introduce a topological non-convex optimization method as an application ... More

The corona theorem and Bass stable rank for $M(D(\sum_{i=1}^k a_i δ_{ζ_i}))$Jan 28 2014In this paper, we prove the corona theorem for $M(D(\mu_k))$ in two different ways, where $\mu_k = \sum_{i=1}^k a_i \delta_{\zeta_i}$. Then we prove that the Bass stable rank of $M(D(\mu_k))$ is one.

Dirac Lepton Angle Matrix v.s. Majorana Lepton Angle Matrix and Their Renormalization Group Running BehavioursSep 20 2011Dec 14 2011Enlightened by the idea of the 3 times 3 CKM angle matrix proposed recently by Harrison et al., we introduce the Dirac angle matrix Phi and the Majorana angle matrix Psi in the lepton sector for Dirac and Majorana neutrinos respectively. We show that ... More

Rank-determining sets of metric graphsJun 15 2009Oct 04 2009A metric graph is a geometric realization of a finite graph by identifying each edge with a real interval. A divisor on a metric graph $\Gamma$ is an element of the free abelian group on $\Gamma$. The rank of a divisor on a metric graph is a concept appearing ... More

Weakly convex biharmonic hypersurfaces in nonpositive curvature space forms are minimalMay 30 2013Jan 17 2014A submanifold $M^m$ of a Euclidean space $R^{m+p}$ is said to have harmonic mean curvature vector field if $\Delta \vec{H}=0$, where $\vec{H}$ is the mean curvature vector field of $M\hookrightarrow R^{m+p}$ and $\Delta$ is the rough Laplacian on $M$. ... More

Galerkin Method with Trigonometric Basis on Stable Numerical DifferentiationMar 10 2019Jul 20 2019This paper considers the $ p $ ($ p=1,2,3 $) order numerical differentiation on function $ y $ in $ (0,2\pi) $. They are transformed into corresponding Fredholm integral equation of the first kind. Computational schemes with analytic solution formulas ... More

Trees, length spectra for rational maps via barycentric extensions and Berkovich spacesJul 14 2019In this paper, we study the dynamics of degenerating sequences of rational maps on Riemann sphere $\hat{\mathbb{C}}$ using $\mathbb{R}$-trees. Given a sequence of degenerating rational maps, we give two constructions for limiting dynamics on $\mathbb{R}$-trees: ... More

Classical LQG's limitation and modification in stochastic vibration systemNov 07 2011The function of control force is deduced by stochastic averaging method in shochastic vibration system.It is found that classical LQG is not full optimization because control force from displacement is of no effect to depress stochastic response.A modified ... More

One-dimensional electronic solitons of graphene in an electromagnetic fieldApr 05 2013May 03 2013Electronic energy-eigen-states of graphene in an orthogonal electromagnetic field with relative magnitude beta=E/vf*B>=1 or in a pure electric field are obtained by a differential-equation method. Gaussian wave packets of probability density are constructed ... More

Differential Transfer Relations of Physical Flux Density Between Time Domains of the Flux Source and ObserverApr 08 2003Differential transfer relations of flux density, general physics quantities' and its corresponding energy's, between time domains of source and observer are derived from conservative rule of various physical quantities and time function between the two ... More

Electronic orbital angular momentum and magnetism of grapheneAug 10 2013May 23 2014Orbital angular momentum (OAM) of graphene electrons in a perpendicular magnetic field is calculated and corresponding magnetic moment is used to investigate the magnetism of perfect graphene. Variation in magnetization demonstrates its decrease with ... More

The Weitzenbock formula on the Wiener space and its application to the asymptotic estimate of entropyFeb 21 2011We consider the Fokker-Planck equation on the abstract Wiener space associated to the Ornstein-Uhlenbeck operator. Using the Weitzenb\"ock formula, we prove an explicit estimate on the time derivative of the entropy of the solution to the Fokker-Planck ... More

LOO and WAIC as Model Selection Methods for Polytomous ItemsJun 26 2018Watanabe-Akaike information criterion (WAIC; Watanabe, 2010) and leave-one-out cross validation (LOO) are two fully Bayesian model selection methods that have been shown to perform better than other traditional information-criterion based model selection ... More

Clone Theory and Algebraic LogicJul 27 2009The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other. Left and right ... More

Clones and Genoids in Lambda Calculus and First Order LogicDec 19 2007Sep 07 2012A genoid is a category of two objects such that one is the product of itself with the other. A genoid may be viewed as an abstract substitution algebra. It is a remarkable fact that such a simple concept can be applied to present a unified algebraic approach ... More

On Willmore Legendrian surfaces in $\mathbb{S}^5$ and the contact stationary Legendrian Willmore surfacesMay 31 2017In this paper we study Willmore Legendrian surfaces (that is Legendrian surfaces which are critical points of the Willmore functional). We use an equality proved in \cite{Luo} to get a relation between Willmore Legendrian surfaces and contact stationary ... More

Spectral viscosity method with generalized Hermite functions for nonlinear conservation lawsFeb 16 2014Oct 06 2017In this paper, we propose new spectral viscosity methods based on the generalized Hermite functions for the solution of nonlinear scalar conservation laws in the whole line. It is shown rigorously that these schemes converge to the unique entropy solution ... More

Unified Description of Efficiency Correction and Error Estimation for Moments of Conserved Quantities in Heavy-Ion CollisionsOct 15 2014Apr 05 2015I provide a unified description of efficiency correction and error estimation for moments of conserved quantifies in heavy-ion collisions. Moments and cumulants are expressed in terms of the factorial moments, which can be easily corrected for the efficiency ... More

A Framework for Solving Turing Kernel (Compression) Lower Bound Problem and Finding Natural Candidate Problems in NP-intermediateSep 18 2016Kernelization is a significant topic in parameterized complexity. Turing kernelization is a general form of kernelization. For kernelization, It has been established a nice hardness theory [Bodlaender etc. (ICALP 2008, JCSS2009), Fortnow and Santhanam ... More

Weak contraction map and topological non-convex optimizationJul 08 2018Nov 11 2018The definition of weak contraction map and the existence and uniqueness of the fixed-point of weak contraction map is discussed. A stochastic contour-based optimization method based on weak contraction map is proposed to achieve global minimum convergence. ... More

Coherent synchrotron emission from cosmic ray air showersJun 01 2006Coherent synchrotron emission by particles moving along semi-infinite tracks is discussed, with a specific application to radio emission from air showers induced by high-energy cosmic rays. It is shown that in general, radiation from a particle moving ... More

Triangulated 3-Manifolds: from Haken's normal surfaces to Thurston's algebraic equationMar 23 2010Jul 23 2010We give a brief summary of some of our work and our joint work with Stephan Tillmann on solving Thurston's equation and Haken equation on triangulated 3-manifolds in this paper. Several conjectures on the existence of solutions to Thurston's equation ... More

Automorphisms of the Complex of CurvesApr 04 1999This goal of the paper is to show that the automorphisms of the complex of curves in a surface are induced by the self-homeomorphisms of the surface except the surface is the 2-holed torus.

Geodesic Length Functions and Teichmüller SpacesJan 07 1998Given a compact orientable surface with finitely many punctures $\Sigma$, let $\Cal S(\Sigma)$ be the set of isotopy classes of essential unoriented simple closed curves in $\Sigma$. We determine a complete set of relations for a function from $\Cal S(\Sigma)$ ... More

3-Dimensional Schlaefli Formula and Its GeneralizationFeb 19 2008Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.

Simple Loops on Surfaces and Their Intersection NumbersJan 06 1998Given a compact orientable surface $\Sigma$, let $\Cal S(\Sigma)$ be the set of isotopy classes of essential simple loops on $\Sigma$. We determine a complete set of relations for a function from $\Cal S(\Sigma)$ to $\bold Z$ to be a geometric intersection ... More

Galerkin Method with Trigonometric Basis on Stable Numerical DifferentiationMar 10 2019Jun 30 2019This paper consider the numerical differentiation of first three order via corresponding Fredholm integral equation of the first kind in $(0,2\pi)$: Computational schemes with analytic solution formulas are designed using Galerkin method on trigonometric ... More

Multivariate Feedback Particle Filter via F-divergence and the Well-posedness of its Admissible Control InputFeb 23 2019In this paper, we shall first derive the admissible control input of the multivariate feedback particle filter (FPF) by minimizing the f-divergence of the posterior conditional density function and the empirical conditional density of the controlled particles. ... More

Quantum Theory on Glucose Transport Across MembraneJul 27 2014Nov 26 2014After a brief review of the protein folding quantum theory and a short discussion on its experimental evidences the mechanism of glucose transport across membrane is studied from the point of quantum conformational transition. The structural variations ... More

A Unified Theory on Construction and Evolution of the Genetic CodeAug 21 2009A quantitative theory on the construction and the evolution of the genetic code is proposed. Through introducing the concept of mutational deterioration (MD) and developing a theoretical formalism on MD minimization we have proved: 1, the redundancy distribution ... More

On the Law of Directionality of Genome EvolutionMay 08 2008Aug 04 2011The problem of the directionality of genome evolution is studied from the information-theoretic view. We propose that the function-coding information quantity of a genome always grows in the course of evolution through sequence duplication, expansion ... More

Entropy Production in a Cell and Reversal of Entropy Flow as an Anticancer TherapyFeb 01 2008The entropy production rate of cancer cell is always higher than healthy cell under the case of no external field applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is ... More

Abelian Ideals and Cohomology of Symplectic TypeApr 08 2008For symplectic Lie algebras $\mathfrak{sp}(2n,\mathbb{C})$, denote by $\mathfrak{b}$ and $\mathfrak{n}$ its Borel subalgebra and maximal nilpotent subalgebra, respectively. We construct a relationship between the abelian ideals of $\mathfrak{b}$ and the ... More

Loops and autonomy promote evolvability of ecosystem networksJul 10 2015The structure of ecological networks, in particular food webs, determines their ability to evolve further, i.e. evolvability. The knowledge about how food web evolvability is determined by the structures of diverse ecological networks can guide human ... More

Improvement of the Staggered Fermion OperatorsApr 30 1996We present a complete and detailed derivation of the finite lattice spacing corrections to staggered fermion matrix elements. Expanding upon arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order ... More

Optical injection of spin current in zigzag nanoribbon of monolayer MoS2 with antiferromagnetic Kekule distortionJul 19 2019Kekule pattern of (anti)ferromagnetic exchange field on the monolayer $MoS_{2}$ could be induced by proximity to the $(111)$ surface of $BiFeO_{3}$ on both sides. The magnetization orientations of the substrates control the pattern of exchange field, ... More

On Graph Cohomology and Betti Numbers of Hamiltonian GKM ManifoldsJun 26 2012In this paper we introduce the concept of characteristic number that are proven to be useful in the study of the combinatorics of graph cohomology. We claim that it is a good combinatorial counterpart for geometric Betti numbers. We then use this concept ... More

Structure of polynomial representations for orthosymplectic Lie superalgebrasJan 20 2010Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the structure of their ... More

Non-unitary deviation from the tri-bimaximal lepton mixing and its implications on neutrino oscillationsApr 30 2008Jul 05 2008We propose a new pattern of the neutrino mixing matrix which can be parametrized as the product of an arbitrary Hermitian matrix and the well-known tri-bimaximal mixing matrix. In this scenario, nontrivial values of the smallest neutrino mixing angle ... More

Short Zero-Sum Sequences Over Abelian $p$-Groups of Large ExponentAug 18 2016Let $G$ be a finite abelian group with exponent $n$. Let $\eta(G)$ denote the smallest integer $\ell$ such that every sequence over $G$ of length at least $\ell$ has a zero-sum subsequence of length at most $n$. We determine the precise value of $\eta(G)$ ... More

Volume Optimization, Normal Surfaces and Thurston's Equation on Triangulated 3-ManifoldsMar 06 2009Jun 19 2010We propose a finite dimensional variational principle on triangulated 3-manifolds so that its critical points are related to solutions to Thurston's gluing equation and Haken's normal surface equation. The action functional is the volume. This is a generalization ... More