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Clouds of Oriented Gradients for 3D Detection of Objects, Surfaces, and Indoor Scene LayoutsJun 11 2019We develop new representations and algorithms for three-dimensional (3D) object detection and spatial layout prediction in cluttered indoor scenes. We first propose a clouds of oriented gradient (COG) descriptor that links the 2D appearance and 3D pose ... More

A Fusion Approach for Multi-Frame Optical Flow EstimationOct 23 2018Nov 29 2018To date, top-performing optical flow estimation methods only take pairs of consecutive frames into account. While elegant and appealing, the idea of using more than two frames has not yet produced state-of-the-art results. We present a simple, yet effective ... More

Embodied Visual RecognitionApr 09 2019Passive visual systems typically fail to recognize objects in the amodal setting where they are heavily occluded. In contrast, humans and other embodied agents have the ability to move in the environment, and actively control the viewing angle to better ... More

Multi-layer Depth and Epipolar Feature Transformers for 3D Scene ReconstructionFeb 18 2019We tackle the problem of automatically reconstructing a complete 3D model of a scene from a single RGB image. This challenging task requires inferring the shape of both visible and occluded surfaces. Our approach utilizes viewer-centered, multi-layer ... More

Cascaded Scene Flow Prediction using Semantic SegmentationJul 26 2017Oct 05 2017Given two consecutive frames from a pair of stereo cameras, 3D scene flow methods simultaneously estimate the 3D geometry and motion of the observed scene. Many existing approaches use superpixels for regularization, but may predict inconsistent shapes ... More

Half-lives of Double $β^+$-decay with Two NeutrinosJan 07 2015Nuclear double $\beta ^-$-decays with two neutrinos were observed for many years and a systematic law describing the relation between their half-lives and decay energies was also proposed recently [Phys. Rev. C89, 064603 (2014)]. However, double $\beta ... More

Systematic Law for Half-lives of Double $β$-decay with Two NeutrinosJun 04 2014Nuclear double $\beta$-decay with two neutrinos is a rare and important process for natural radioactivity of unstable nuclei. The experimental data of nuclear double $\beta^{-}$-decay with two neutrinos are analyzed and a systematic law to calculate the ... More

Opinion Divergence Reveals the Hierarchical and Overlapping Community Structure in NetworksApr 13 2018Jul 03 2018Often exhibiting hierarchical and overlapping structures, communities or modular groups are fundamental and complex in network science. One of the most exploited tools to detect the mesoscopic structure is synchronization. Several phenomena including ... More

Regular Maps on Cartesian Products and Disjoint Unions of ManifoldsNov 05 2015Jun 08 2016A map from a manifold to a Euclidean space is said to be k-regular if the image of any distinct k points are linearly in- dependent. For k-regular maps on manifolds, lower bounds of the dimension of the ambient Euclidean space have been exten- sively ... More

Coarse embedding into uniformly convex Banach spaceMay 17 2011In this paper, we study the coarse embedding into Banach space. We proved that under certain conditions, the property of embedding into Banach space can be preserved under taking the union the metric spaces. For a group $G$ strongly relative hyperbolic ... More

Interaction solutions for supersymmetric mKdV-B equationJun 25 2015Sep 16 2016The ${\cal N} =1$ supersymmetric mKdV-B system is transformed to a system of coupled bosonic equations by using the bosonization approach. The bosonized supersymmetric mKdV-B (BSmKdV-B) equation can be solved by the usual mKdV equation together with a ... More

Interaction solutions for mKP equation with nonlocal symmetry reductions and CTE methodDec 26 2014May 02 2015The nonlocal symmetries for the modified Kadomtsev-Petviashvili (mKP) equation are obtained with the truncated Painleve method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite ... More

Friedberg-Lee Symmetry for Quark Masses and Flavor MixingJan 03 2008We point out a generic correlation between the Friedberg-Lee symmetry of quark mass operators and the vanishing of quark masses. We make phenomenological explorations on two textures of quark mass matrices with the broken Friedberg-Lee symmetry. We present ... More

Geometric angle structures on triangulated surfacesJan 20 2006In this paper we characterize a function defined on the set of edges of a triangulated surface such that there is a spherical angle structure having the function as the edge invariant (or Delaunay invariant). We also characterize a function such that ... More

Modular $A_n(V)$ theoryNov 20 2016A series of associative algebras $A_n(V)$ for a vertex operator algebra $V$ over an arbitrary algebraically closed field and nonnegative integers $n$ are constructed such that there is a one to one correspondence between irreducible $A_n(V)$-modules which ... More

Calculus of generalized hyperbolic tetrahedronJul 02 2010We calculate the Jacobian matrix of the dihedral angles of a generalized hyperbolic tetrahedron as functions of edge lengths and find the complete set of symmetries of this matrix.

Primitive prime divisors in the critical orbits of one-parameter families of rational polynomialsMar 04 2019For a rational polynomial $f$ and rational numbers $c, u$, we put $f_c(x):=f(x)+c$, and consider the Zsigmondy set $\mathcal{Z}(f_c,u)$ associated to the sequence $\{f_c^n(u)-u\}_{n\geq 0}$, where $f_c^n$ is the $n$-st iteration of $f_c$. In this paper, ... More

Periodic measures are dense in invariant measures for residually finite amenable group actions with specificationSep 30 2015Oct 18 2015We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.

The Golden Ratio Triple Lattice PETsOct 12 2016We study a one-parameter family of multigraph polytope exchange transformations which were introduced by R. Schwartz in 2013. With the help of computer, we will prove that there exists a renormalization scheme in a neighborhood of the golden ratio $\phi=(\sqrt ... More

Dynamical system based obstacle avoidance via manipulating orthogonal coordinatesFeb 14 2019In this paper, we consider the general problem of obstacle avoidance based on dynamical system. The modulation matrix is developed by introducing orthogonal coordinates, which makes the modulation matrix more reasonable. The new trajectory's direction ... More

Combinatorial Yamabe flow on hyperbolic surfaces with boundaryMar 20 2010This paper studies the combinatorial Yamabe flow on hyperbolic surfaces with boundary. It is proved by applying a variational principle that the length of boundary components is uniquely determined by the combinatorial conformal factor. The combinatorial ... More

Pathwise uniqueness of one-dimensional SDEs driven by one-sided stable processesMay 23 2013For $\alpha\in (0,1)$, we consider stochastic differential equations driven by one-sided stable processes of order $\alpha$: \[dX_t= \phi(X_{t-})\ dZ_t.\] We prove that pathwise uniqueness holds for this equation under the assumptions that $\phi$ is continuous, ... More

The Triple Lattice PETsOct 12 2016Mar 28 2017Polytope exchange transformations (PETs) are higher dimensional generalizations of interval exchange transformations (IETs) which have been well-studied for more than 40 years. A general method of constructing PETs based on multigraphs was described by ... More

A tree augmented naive Bayesian network experiment for breast cancer predictionJun 18 2015In order to investigate the breast cancer prediction problem on the aging population with the grades of DCIS, we conduct a tree augmented naive Bayesian network experiment trained and tested on a large clinical dataset including consecutive diagnostic ... More

Correspondence between 2 Calabi-Yau Categories and QuiversFeb 20 2016This note gives a one-to-one correspondence between the equivalence classes of a certain type of 2-dimensional Calabi-Yau categories, and certain type of quivers, This is an analogue of the result in Stability structures, motivic Donaldson-Thomas invariants ... More

Predicted Rectification and Negative Differential Spin Seebeck Effect at Magnetic InterfacesMay 01 2013Dec 18 2013We study the nonequilibrium Seebeck spin transport across metal-magnetic insulator interfaces. The conjugate-converted thermal-spin transport is assisted by the exchange interaction at the interface, between conduction electrons in the metal lead and ... More

One-dimensional holographic superconductor from AdS_3/CFT_2 correspondenceAug 23 2010Nov 16 2010We obtain a holographical description of a superconductor by using the d=2 case of the AdS_{d+1}/CFT_d correspondence. The gravity system is a (2+1)-dimensional AdS black hole coupled to a Maxwell field and charged scalar. The dual (1+1)-dimensional superconductor ... More

On the torsion subgroups of the modular JacobiansSep 07 2017Nov 28 2017For any positive integer $N$, we prove that the rational torsion subgroup of $J_0(N)$ agrees with its rational cuspidal subgroups up to a factor of $6N\prod_{p\mid N}(p^2-1)$. Moreover, for modular Jacobians of the form $J_0(DC)$ with $D$ a positive square-free ... More

Universal skein theory for group actionsMar 05 2019Given a group action on a finite set, we define the group-action model which consists of tensor network diagrams which are invariant under the group symmetry. In particular, group-action models can be realized as the even part of group-subgroup subfactor ... More

Horizontal Gradient Estimate of Positive Pseudo-Harmonic Functions on Complete Noncompact Pseudo-Hermitian ManifoldsFeb 22 2018In this paper, we will give a horizontal gradient estimate of positive solutions of $\Delta_b u = - \lambda u$ on complete noncompact pseudo-Hermitian manifolds. As a consequence, we recapture the Liouville theorem of positive pseudo-harmonic functions ... More

Generic Newton polygon for exponential sums in $n$ variables with parallelotope baseSep 30 2017Let $p$ be a prime number. Every $n$-variable polynomial $f(\underline x)$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of varieties whose Galois group is isomorphic to $\mathbb{Z}_p$. Our goal of this paper is to study ... More

Newton slopes for twisted Artin--Schreier--Witt TowersApr 24 2017Apr 25 2019We fix a monic polynomial $f(x) \in \mathbb F_q[x]$ over a finite field of characteristic $p$ of degree relatively prime to $p$. Let $a\mapsto \omega(a)$ be the Teichm\"uller lift of $\mathbb F_q$, and let $\chi:\mathbb{Z}\to \mathbb C_p^\times$ be a ... More

Perron's method for viscosity solutions of semilinear path dependent PDEsMar 07 2015This paper proves the existence of viscosity solutions of path dependent semilinear PDEs via Perron's method, i.e. via showing that the supremum of viscosity subsolutions is a viscosity solution. We use the notion of viscosity solutions introduced by ... More

Fermions in a Global Monopole BackgroundDec 10 1993Dec 30 1993We study the scattering of fermions in a ``global monopole'' background metric. This is the four-dimensional analogue of the scattering on a cone in three dimensions. The scattering amplitude is exactly obtained. We then study massless fermion-dyon systems ... More

WZW model based on the extended de Sitter groupMay 17 1995Jul 12 1996We study the WZW model based on the centrally extended 2D de Sitter algebra. We obtain the spacetime metric and its explicitly conformally flat expression. The symmetries of the spacetime are found by identifying the Killing vectors with the group generators. ... More

Local rigidity of inversive distance circle packingMar 08 2009Apr 02 2009A Euclidean (or hyperbolic) circle packing on a closed triangulated surface with prescribed inversive distance is locally determined by its cone angles. We prove this by applying a variational principle.

Semi-supervised Data Representation via Affinity Graph LearningFeb 13 2015We consider the general problem of utilizing both labeled and unlabeled data to improve data representation performance. A new semi-supervised learning framework is proposed by combing manifold regularization and data representation methods such as Non ... More

The spectrum of the singularity category of a category algebraMar 26 2018Let $\C$ be a finite projective EI category and $k$ be a field. The singularity category of the category algebra $k\C$ is a tensor triangulated category. We compute its spectrum in the sense of Balmer.

$(L^{r}, L^{s})$ Resolvent Estimate for the Sphere off the Line $\frac{1}{r}-\frac{1}{s}=\frac{2}{n}$Mar 22 2017We extend the resolvent estimate on the sphere to exponents off the line $\frac{1}{r}-\frac{1}{s}=\frac{2}{n}$. Since the condition $\frac{1}{r}-\frac{1}{s}=\frac{2}{n}$ on the exponents is necessary for a uniform bound, one cannot expect estimates off ... More

Two Questions about Data-Oriented ParsingJun 17 1996In this paper I present ongoing work on the data-oriented parsing (DOP) model. In previous work, DOP was tested on a cleaned-up set of analyzed part-of-speech strings from the Penn Treebank, achieving excellent test results. This left, however, two important ... More

Parsing with the Shortest DerivationSep 27 2000Common wisdom has it that the bias of stochastic grammars in favor of shorter derivations of a sentence is harmful and should be redressed. We show that the common wisdom is wrong for stochastic grammars that use elementary trees instead of context-free ... More

Gorenstein projective and injective dimensions over Frobenius extensionsJan 22 2018Let $R\subset A$ be a Frobenius extension of rings. We prove that: (1) for any left $A$-module $M$, $_{A}M$ is Gorenstein projective (injective) if and only if the underlying left $R$-module $_{R}M$ is Gorenstein projective (injective). (2) if $\mathrm{G}\text{-}\mathrm{proj.dim}_{A}M<\infty$, ... More

Analytic quantum critical points from holographyOct 09 2012Nov 20 2012We find exact, analytic solutions of the Klein-Gordon equation for a scalar field in the background of the extremal Reissner-Nordstrom-AdS_5 black hole. The Green's function near a quantum critical point for a strongly coupled system can be extracted ... More

A note on circle patterns on surfacesMar 07 2007In this paper we give two different proofs of Bobenko and Springborn's theorem of circle pattern: there exists a hyperbolic (or Euclidean) circle pattern with proscribed intersection angles and cone angles on a cellular decomposed surface up to isometry ... More

Geodesic Acoustic Mode in Toroidally Rotating Anisotropic TokamaksMar 04 2015Effects of anisotropy on the geodesic acoustic mode (GAM) is analyzed by using gyro-kinetic equations applicable to low-frequency microinstabilities in a toroidally rotating tokamak plasma. Dispersion relation in the presence of arbitrary Mach number ... More

On representation theorem of sublinear expectation related to G-Lévy process and paths of G-Lévy processOct 25 2011Nov 04 2011In this paper, we are concerned with the representation of an important sublinear expectation under which framework a new stochastic process G-L\'evy process has been introduced. We show the existence of a weakly compact family of probability measures ... More

Recurrent Soft Attention Model for Common Object RecognitionMay 04 2017May 29 2017We propose the Recurrent Soft Attention Model, which integrates the visual attention from the original image to a LSTM memory cell through a down-sample network. The model recurrently transmits visual attention to the memory cells for glimpse mask generation, ... More

Isometric embeddings of graphs into Riemannian manifoldsApr 19 2018An isometric embedding of a graph into a metric space is an embedding of the vertices such that the smallest number of edges connecting any two vertices equals to the distance in the metric space between the images. In this paper, we study isometric embeddings ... More

Order of the canonical vector bundle over configuration spaces of disjoint unions of spheresMay 16 2016Apr 04 2018Given a vector bundle, its (stable) order is the smallest positive integer n such that the n-fold self-Whitney sum is (stably) trivial. So far, the order and the stable order of the canonical vector bun- dle over configuration spaces of Euclidean spaces ... More

Ordered Partitions and Drawings of Rooted Plane TreesJan 27 2013Jan 27 2014We study the bounded regions in a generic slice of the hyperplane arrangement in $\mathbb{R}^n$ consisting of the hyperplanes defined by $x_i$ and $x_i+x_j$. The bounded regions are in bijection with several classes of combinatorial objects, including ... More

Gorenstein projective and injective dimensions over Frobenius extensionsJan 22 2018May 06 2018Let $R\subset A$ be a Frobenius extension of rings. We prove that: (1) for any left $A$-module $M$, $_{A}M$ is Gorenstein projective (injective) if and only if the underlying left $R$-module $_{R}M$ is Gorenstein projective (injective). (2) if $\mathrm{G}\text{-}\mathrm{proj.dim}_{A}M<\infty$, ... More

Study of dynamical system based obstacle avoidance via manipulating orthogonal coordinatesFeb 14 2019Feb 16 2019In this paper, we consider the general problem of obstacle avoidance based on dynamical system. The modulation matrix is developed by introducing orthogonal coordinates, which makes the modulation matrix more reasonable. The new trajectory's direction ... More

An index to link scientific productivity with visibilityDec 18 2009I here propose an index that links the number of papers a researcher has published with impact factors (IFs) of the journals that publish these papers. A researcher is said to have an index z if totally z of his/her papers are published in journals with ... More

Gorenstein triangular matrix rings and category algebrasDec 29 2014We give conditions on when a triangular matrix ring is Gorenstein of a given selfinjective dimension. We apply the result to the category algebra of a finite EI category. In particular, we prove that for a finite EI category, its category algebra is 1-Gorenstein ... More

Domain Wall Displacement Detection Technology Research ReportOct 02 2006This article introduce a new data storage method called DWDD(Domain Wall Displacement Detection) and tell you why it succeed.

Generic Newton polygon for exponential sums in two variables with triangular baseJan 01 2017Jan 06 2017Let $p$ be a prime number. Every two-variable polynomial $f(x_1, x_2)$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of surfaces whose Galois group is isomorphic to $\mathbb Z_p$. Our goal of this paper is to study the ... More

Regular Maps on Cartesian Products and Disjoint Unions of ManifoldsNov 05 2015May 20 2017A map from a manifold to a Euclidean space is said to be k-regular if the image of any distinct k points are linearly in- dependent. For k-regular maps on manifolds, lower bounds of the dimension of the ambient Euclidean space have been exten- sively ... More

Quillen equivalence of singular model categoriesJan 08 2019Let $R$ be a left-Gorenstein ring. We construct a Quillen equivalence between singular contraderived model category and singular coderived model category introduced by Becker [Adv. Math., (2014) 187-232]. As an application, we explicitly give an equivalence ... More

Gorenstein projective and injective dimensions over Frobenius extensionsJan 22 2018May 13 2019Let $R\subset A$ be a Frobenius extension of rings. We prove that: (1) for any left $A$-module $M$, $_{A}M$ is Gorenstein projective (injective) if and only if the underlying left $R$-module $_{R}M$ is Gorenstein projective (injective). (2) if $\mathrm{G}\text{-}\mathrm{proj.dim}_{A}M<\infty$, ... More

Time-Dependent Open String Solutions in 2+1 Dimensional GravityDec 10 1993Dec 30 1993We find general, time-dependent solutions produced by open string sources carrying no momentum flow in 2+1 dimensional gravity. The local Poincar\'e group elements associated with these solutions and the coordinate transformations that transform these ... More

Gorenstein projective modules and Frobenius extensionsJul 18 2017We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective, then its underlying module over the the base ring is Gorenstein projective; the converse holds if the Frobenius extension is either left-Gorenstein ... More

Order of the canonical vector bundle over configuration spaces of disjoint unions of spheresMay 16 2016Given a vector bundle, its (stable) order is the smallest positive integer n such that the n-fold self-Whitney sum is (stably) trivial. So far, the order and the stable order of the canonical vector bun- dle over configuration spaces of Euclidean spaces ... More

Topological Pressure and the Variational Principle of Noncompact Sets for Amenable Group ActionsJun 06 2015Jun 14 2016The notion of topological pressure was introduced by Ruell and also he formulated a variational principle for the topological pressure. Pesin and Pitskel introduced a definition of topological on subsets inspired by Hausdorff dimension. In this paper, ... More

Efficient Algorithms for Parsing the DOP Model? A Reply to Joshua GoodmanMay 24 1996This note is a reply to Joshua Goodman's paper "Efficient Algorithms for Parsing the DOP Model" (Goodman, 1996; cmp-lg/9604008). In his paper, Goodman makes a number of claims about (my work on) the Data-Oriented Parsing model (Bod, 1992-1996). This note ... More

Extremum problems for eigenvalues of discrete Laplace operatorsJun 29 2011The discrete Laplace operator on a triangulated polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the discrete Laplace operators. Among all triangles, an equilateral triangle ... More

Effects of Circulating Energetic Ions on Geodesic Acoustic Modes with Finite Wave NumbersDec 16 2013May 06 2014Effects of circulating energetic particles on the geodesic acoustic modes (GAMs) with finite wave numbers are analyzed by using the hybrid kinetic-fluid model. The dispersion relation is derived by adopting the slowing beam ions distribution function ... More

The Tetrahedral TwistsSep 10 2016We introduce a family of piecewise isometries $f_s$ parametrized by $s \in [0,1)$ on the surface of a regular tetrahedron, which we call the tetrahedral twists. This family of maps is similar to the PETs constructed by Patrick Hooper. We study the dynamics ... More

Regular Maps on Euclidean Spaces and ToriNov 05 2015Oct 04 2016A map from a manifold to a Euclidean space is said to be k-regular if the image of any distinct k points are linearly independent. In this paper, we give some lower bounds of the dimension of the ambient Euclidean space for complex k-regular maps on Euclidean ... More

Crowd collectiveness measure via graph-based node clique learningDec 19 2016Collectiveness motions of crowd systems have attracted a great deal of attentions in recently years. In this paper, we try to measure the collectiveness of a crowd system by the proposed node clique learning method. The proposed method is a graph based ... More

The Third Way of Thermal-Electric Conversion beyond Seebeck and Pyroelectric EffectsFeb 15 2014Thermal-electric conversion is crucial for smart energy control and harvesting, such as thermal sensing and waste heat recovering. So far, people are aware of only two ways of direct thermal-electric conversion, Seebeck and pyroelectric effects, each ... More

Effcient simulation of the adaptive time-dependent density-matrix renormalization-group with periodic boundary conditionsMay 30 2011May 31 2011We introduce a numerical method of the adaptive time-dependent density-matrix renormalization-group to compute one-dimensional quantum spin systems with periodic boundary condition. We check our algorithm to study the dynamic correlation in spin-1/2 Heisenberg ... More

Anatomy of a Burning 2-2-holeMay 23 2019We are entering a new era to test the strong gravity regime around astrophysical black holes. The possibility that they are actually horizonless ultracompact objects and then free from the information loss paradox can be examined more closely with observational ... More

Quadratic torsion subgroups of modular Jacobian varietiesJan 27 2019Let $D$ be an odd positive square-free integer. In this paper, we prove that the $\chi$-part of the torsion subgroup of $J_0(D^2)$ agrees with the $\chi$-part of its cuspidal subgroup up to a factor of $6D$, where $\chi$ is the quadratic character of ... More

Applications of cotorsion triplesApr 30 2014Mar 15 2018We study homotopy categories of model categories arising from a cotorsion triple, and the equivalences between corresponding stable categories. We characterize homological dimensions with respect to a cotorsion triple. Then, we lift cotorsion triple to ... More

On parameterizations of Teichmüller spaces of surfaces with boundaryDec 08 2006In \cite{rigidity}, Luo introduced a $\psi_{\lambda}$ edge invariant which turns out to be a coordinate of the Teichm\"uller space of a surface with boundary. And he proved that for $\lambda \geq 0$, the image of the Teichm\"uller space under $\psi_{\lambda}$ ... More

Arithmetic of Eisenstein quotientsDec 27 2016In this paper, we will study the arithmetic of the Eisenstein part of the modular Jacobians. In the first section, we introduce some general preliminaries of the arithmetic theory of modular curves that we will need later. In the second section, we give ... More

Iteration of Polynomials $AX^d+C$ Over Finite FieldsJul 15 2018Jul 17 2018For a polynomial $f(X)=AX^d+C \in \mathbb{F}_p[X]$ with $A\neq 0$ and $d\geq 2$, we prove that if $d\;|\;p-1$ and $f^i(0)\neq f^j(0)$ for $0\leq i<j\leq N$, then $\#f^N(\mathbb{F}_p) \sim \frac{2p}{(d-1)N},$ where $f^N$ is the $N$-th iteration of $f$. ... More

On Stochastic Belief Revision and Update and their CombinationApr 07 2016I propose a framework for an agent to change its probabilistic beliefs when a new piece of propositional information $\alpha$ is observed. Traditionally, belief change occurs by either a revision process or by an update process, depending on whether the ... More

Newton slopes for twisted Artin--Schreier--Witt TowersApr 24 2017We fix a monic polynomial $f(x) \in \mathbb F_q[x]$ over a finite field of characteristic $p$ of degree relatively prime to $p$. Let $a\mapsto \omega(a)$ be the Teichm\"uller lift of $\mathbb F_q$, and let $\chi:\mathbb{Z}\to \mathbb C_p^\times$ be a ... More

Finite-orbit-width effects on the geodesic acoustic mode in the toroidally rotating tokamak plasmaNov 16 2016The Landau damping of geodesic acoustic mode (GAM) in a torodial rotating tokamak plasma is analytically investigated by taking into account the finite-orbit-width (FOW) resonance effect to the 3rd order. The analytical result is shown to agree well with ... More

A survey of quantum Teichmüller space and Kashaev algebraJul 25 2011Sep 16 2011In this chapter, we survey the algebraic aspects of quantum Teichm\"uller space, generalized Kashaev algebra and a natural relationship between the two algebras.

Viscosity Solutions of Fully Nonlinear Elliptic Path Dependent PDEsJan 21 2014Feb 11 2016This paper introduces a convenient solution space for the uniformly elliptic fully nonlinear path dependent PDEs. It provides a wellposedness result under standard Lipschitz-type assumptions on the nonlinearity and an additional assumption formulated ... More

Asymptotically AdS spacetimes with a timelike Kasner singularityMar 25 2016Aug 01 2016Exact solutions to Einstein's equations for holographic models are presented and studied. The IR geometry has a timelike cousin of the Kasner singularity, which is the less generic case of the BKL (Belinski-Khalatnikov-Lifshitz) singularity, and the UV ... More

Correlating Features and Code by Dynamic and Semantic AnalysisDec 12 2015One major problem in maintaining a software system is to understand how many functional features in the system and how these features are implemented. In this paper a novel approach for locating features in code by semantic and dynamic analysis is proposed. ... More

Topological Pressure and the Variational Principle of Noncompact Sets for Amenable Group ActionsJun 06 2015Dec 20 2016The notion of topological pressure was introduced by Ruell and also he formulated a variational principle for the topological pressure. Pesin and Pitskel introduced a definition of topological on subsets inspired by Hausdorff dimension. In this paper, ... More

From skein theory to presentations for Thompson groupSep 14 2016Sep 29 2016Jones introduced unitary representations of Thompson group $F$ starting from a given subfactor planar algebra, and all unoriented links arise as matrix coefficients of these representations. Moreover, all oriented links arise as matrix coefficients of ... More

Ideal structures and rigidity of uniform Roe algebrasSep 22 2015Jun 02 2016In this paper, we study the rigidity of uniform Roe algebras via the ideal structures. We showed that for given metric spaces X and Y with bounded geometry, if their uniform Roe algebras are isomorphic, then they are coarse equivalent.

The tensor product of Gorenstein-projective modules over category algebrasJan 16 2017For a finite free and projective EI category, we prove that Gorenstein-projective modules over its category algebra are closed under the tensor product if and only if each morphism in the given category is a monomorphism.

The MCM-approximation of the trivial module over a category algebraJan 12 2016For a finite free EI category, we construct an explicit module over its category algebra. If in addition the category is projective over the ground field, the constructed module is Gorenstein-projective and is a maximal Cohen-Macaulay approximation of ... More

A Novel Deep Neural Network Based Approach for Sparse Code Multiple AccessJun 04 2019Sparse code multiple access (SCMA) has been one of non-orthogonal multiple access (NOMA) schemes aiming to support high spectral efficiency and ubiquitous access requirements for 5G wireless communication networks. Conventional SCMA approaches are confronting ... More

A Hybrid POMDP-BDI Agent Architecture with Online Stochastic Planning and Plan CachingJul 03 2016This article presents an agent architecture for controlling an autonomous agent in stochastic environments. The architecture combines the partially observable Markov decision process (POMDP) model with the belief-desire-intention (BDI) framework. The ... More

Computing tropical points and tropical linksNov 09 2016In this article, we apply some basic results on triangular decomposition and Newton polygons to construct fast algorithms for computing non-trivial points on and codimension one links of tropical varieties. Using them, we show that the tropical Grassmannians ... More

Cotorsion triple and applicationsApr 30 2014Jul 31 2015The triple $(\mathcal{X}, \mathcal{Z}, \mathcal{Y})$ of subcategories of an abelian category $\mathcal{A}$ is called a cotorsion triple if $(\mathcal{X}, \mathcal{Z})$ and $(\mathcal{Z}, \mathcal{Y})$ are cotorsion pairs in $\mathcal{A}$. The aim of this ... More

Information Conservation, Entropy Increase and the Statistical Irreversibility for an Isolated SystemFeb 05 2009We consider the statistical irreversibility and its compatibility with the reversible dynamics. The role played by the observation is analyzed in detail. It makes our previous proof for the second law of thermodynamics clearer. On this basis, we emphasize ... More

Qualitative picture of a new mechanism for high-Tc superconductorsMay 19 2003Xu et al. observed enhanced Nernst effect and Iguchi et al. observed patched diamagnetism, both well above $T_c$ in underdoped high-$T_c$ superconductors (HTSCs). A new mechanism is proposed here, which seems to naturally explain, at least qualitatively, ... More

The Kohnen plus space for Hilbert-Siegel modular formsJul 31 2015The Kohnen plus space, roughly speaking, is a space consisting of modular forms of half integral weight with some property in Fourier coefficients. For example, the $n$-th coefficient of a normal modular form of weight $k+1/2$ in the plus space is $0$ ... More

Boson-Fermion Model of High-T_C Superconductivity ----A Progress ReportNov 16 1998Nov 18 1998This is an invited lecture at the XXII International School of Theoretical Physics, Ustron, Poland, 9/10-9/15, 1998. The boson-fermion model of high T_C superconductivity is reviewed. Its applications to the pseudo-gap and DC transport coefficients are ... More

Path Integrals, BRST Identities and Regularization Schemes in Nonstandard GaugesNov 20 1998The path integral of a gauge theory is studied in Coulomb-like gauges. The Christ-Lee terms of operator ordering are reproduced {\it{within}} the path integration framework. In the presence of fermions, a new operator term, in addition to that of Christ-Lee, ... More

Two types of electronic states in one dimensional crystals of finite lengthApr 09 2002Exact and general results on the electronic states in one dimensional crystals bounded at tau and tau+L - where L=Na, N is a positive integer and a is the potential period - are presented. Corresponding to each energy band of Bloch wave, there are N-1 ... More

Phase Quantization Study of Spatial Light Modulator for Extreme High contrast ImagingSep 15 2016Nov 21 2016Direct imaging of exoplanets by reflected starlight is extremely challenging due to the large luminosity ratio to the primary star. Wave-front control is a critical technique to attenuate the speckle noise in order to achieve an extremely high contrast. ... More