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Learning Non-Uniform Hypergraph for Multi-Object TrackingDec 10 2018The majority of Multi-Object Tracking (MOT) algorithms based on the tracking-by-detection scheme do not use higher order dependencies among objects or tracklets, which makes them less effective in handling complex scenarios. In this work, we present a ... More

On the dimension of the Hilbert scheme of curvesAug 26 2008Consider a component of the Hilbert scheme whose general point corresponds to a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such a component when X is P^3, P^4 or a smooth ... More

Log Minimal Model Program for the Kontsevich Space of Stable Maps $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$Sep 04 2007This work is inspired by conversations with Izzet Coskun and Joe Harris. We run the log minimal model program for the Kontsevich space of stable maps $\bar{\mathcal M}_{0,0}(\mathbb P^{3}, 3)$ and give modular interpretations to all the intermediate spaces ... More

New Construction of Authentication Codes with Arbitration from Pseudo-Symplectic Geometry over Finite FieldsMay 27 2013A new construction of authentication codes with arbitration from pseudo-symplectic geometry over finite fields is given. The parameters and the probabilities of deceptions of the codes are also computed.

Detaching embedded pointsNov 11 2009Aug 24 2010We show that if $D \subset \mathbb P^N$ is obtained from a codimension two local complete intersection $C$ by adding embedded points of multiplicity $\leq 3$, then $D$ is a flat limit of $C$ and isolated points. As applications, we determine the irreducible ... More

Existence of nontrivial solutions for periodic Schrodinger equations with new nonlinearitiesApr 03 2014We study the Schr\"{o}dinger equation: \begin{eqnarray} - \Delta u+V(x)u+f(x,u)=0,\qquad u\in H^{1}(\mathbb{R}^{N}),\nonumber \end{eqnarray} where $V$ is periodic and $f$ is periodic in the $x$-variables, $0$ is in a gap of the spectrum of the operator ... More

Principal boundary of moduli spaces of abelian and quadratic differentialsNov 05 2016The seminal work of Eskin-Masur-Zorich described the principal boundary of moduli spaces of abelian differentials that parameterizes flat surfaces with a prescribed generic configuration of short parallel saddle connections. In this paper we describe ... More

A Simple Optimal Binary Representation of Mosaic Floorplans and Baxter PermutationsNov 21 2011Nov 22 2011A "floorplan" is a rectangle subdivided into smaller rectangular sections by horizontal and vertical line segments. Each section in the floorplan is called a "block". Two floorplans are considered equivalent if and only if there is a one-to-one correspondence ... More

Competing spreading processes and immunization in multiplex networksAug 03 2016Epidemic spreading on physical contact network will naturally introduce the human awareness information diffusion on virtual contact network, and the awareness diffusion will in turn depress the epidemic spreading, thus forming the competing spreading ... More

On the finiteness of uniform sinksMar 10 2013We study the finiteness of uniform sinks for flow. Precisely, we prove that, for $\alpha>0$ $T>0$, if a vector field $X$ has only hyperbolic singularities or sectionally dissipative singularities, then $X$ can have only finitely many $(\alpha,T)$-uniform ... More

On Pesin's entropy formula for dominated splittings without mixed behaviorDec 28 2015For $C^1$ diffeomorphisms, we prove that the Pesin's entropy formula holds for some invariant measure supported on any topological attractor that admits a dominated splitting without mixed behavior. We also prove Shub's entropy conjecture for diffeomorphisms ... More

Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channelsJun 07 2015Aug 03 2016Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled ... More

A search for evidence of solar rotation in Super-Kamiokande solar neutrino datasetApr 22 2016Jun 06 2016We apply the generalized Lomb-Scargle (LS) periodogram, proposed by Zechmeister and Kurster, to the solar neutrino data from Super-Kamiokande (Super-K) using data from its first five years. For each peak in the LS periodogram, we evaluate the statistical ... 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

Implementation of a Quantum-simulation Algorithm of Calculating Molecular Ground-state Energy on an NMR Quantum ComputerJul 21 2009Jul 22 2009It is exponentially hard to simulate quantum systems by classical algorithms, while quantum computer could in principle solve this problem polynomially. We demonstrate such an quantum-simulation algorithm on our NMR system to simulate an hydrogen molecule ... More

NMR Experimental Demonstration of Probabilistic Quantum CloningApr 19 2011The method of quantum cloning is divided into two main categories: approximate and probabilistic quantum cloning. The former method is used to approximate an unknown quantum state deterministically, and the latter can be used to faithfully copy the state ... More

A numerical mode matching method for wave scattering in a layered medium with a stratified inhomogeneityApr 23 2018Numerical mode matching (NMM) methods are widely used for analyzing wave propagation and scattering in structures that are piece-wise uniform along one spatial direction. For open structures that are unbounded in transverse directions (perpendicular to ... More

Quantum Factorization of 143 on a Dipolar-Coupling NMR systemNov 16 2011Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its ... More

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

Geometric Hypergraph Learning for Visual TrackingMar 18 2016Graph based representation is widely used in visual tracking field by finding correct correspondences between target parts in consecutive frames. However, most graph based trackers consider pairwise geometric relations between local parts. They do not ... More

Simulation of chemical reaction dynamics on an NMR quantum computerMay 21 2011Quantum simulation can beat current classical computers with minimally a few tens of qubits and will likely become the first practical use of a quantum computer. One promising application of quantum simulation is to attack challenging quantum chemistry ... More

Boundary-sensitive Network for Portrait SegmentationDec 22 2017Apr 09 2018Compared to the general semantic segmentation problem, portrait segmentation has higher precision requirement on boundary area. However, this problem has not been well studied in previous works. In this paper, we propose a boundary-sensitive deep neural ... More

Approximation of Reachable Set for Coherently Controlled Open Quantum Systems: Application to Quantum State EngineeringDec 11 2014Aug 04 2015Precisely characterizing and controlling realistic open quantum systems is one of the most challenging and exciting frontiers in quantum sciences and technologies. In this Letter, we present methods of approximately computing reachable sets for coherently ... More

Quasimodularity and large genus limits of Siegel-Veech constantsJun 13 2016Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich ... More

There is at least one pair of double primes for any even numberOct 16 2005We proved that any even number not less than 6 can be expressed as the sum of two old primes, $2n=p_i+p_j$

On the abundance of SRB measuresApr 10 2018We prove the abundance of Sinai-Ruelle-Bowen measures for diffeomorphisms away from ones with a homoclinic tangency. This is motivated by conjectures of Palis on the existence of physical (Sinai-Ruelle-Bowen) measures for global dynamics. The main novelty ... More

Orthogonal Trigonometric Polynomials: Riemann-Hilbert Analysis and Relations with OPUCMay 17 2008In this paper, we study the theory of orthogonal trigonometric polynomials (OTP). We obtain asymptotics of OTP with positive and analytic weight functions by Riemann-Hilbert approach and find they have relations with orthogonal polynomials on the unit ... More

There are infinitely many cousin primesOct 16 2005Oct 24 2005We proved that there are infinitely many cousin primes.

There are Infinitely Many Pairs of Twin PrimeOct 09 2005We proved that there are infinitely many pairs of twin prime.

Serious Game for Human Environmental Consciousness Education in Residents Daily LifeMar 20 2015It has been challenging to find ways to educate people to have better environmental consciousness. In some cases, people do not know what the right behaviors are to protect the environment. Game engine has been used in the AEC industry for visualization. ... More

Transition state theory: a generalization to nonequilibrium systems with power-law distributionsFeb 17 2011Feb 18 2011Transition state theory (TST) is generalized for the nonequilibrium system with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by the Langevin equations ... More

Recent progress in B physicsSep 10 2007Sep 12 2007We firstly address the recent efforts on calculations of the next-to-leading order corrections to the color-suppressed tree amplitude in QCD factorization method which may be essential to solve the puzzles in $B\to \pi\pi$ and $\pi K$ decays. Then we ... More

Global analysis of B-->PP, PV charmless decays with QCD factorizationNov 11 2003The global analysis of B-->PP, PV charmless decays with QCD factorization (QCDF) is presented. The predictions of QCDF are in good agreement with experiments. The best fitted CKM angel gamma is around 79 degree. The predicted branching ratios of B --> ... More

The Torsion Generating Set Of The Dehn Twist Subgroups Of Non-orientable SurfacesNov 12 2018Nov 19 2018Let $N_g$ be the non-orientable surface with genus $g$, $\text{MCG}(N_g)$ be the mapping class group of $N_g$, $\mathcal{T}(N_g)$ be the index 2 subgroup generated by all Dehn twists of $\text{MCG}(N_g)$. We prove that for odd genus, $\mathcal{T}(N_g)$ ... More

An Explicit Formula for Likelihood Function for Gaussian Vector Autoregressive Moving-Average Model Conditioned on Initial Observables with Application to Model CalibrationApr 29 2016We derive an explicit formula for likelihood function for Gaussian VARMA model conditioned on initial observables where the moving-average (MA) coefficients are scalar. For fixed MA coefficients the likelihood function is optimized in the autoregressive ... More

The Unmanned Aerial Vehicle Benchmark: Object Detection and TrackingMar 26 2018With the advantage of high mobility, Unmanned Aerial Vehicles (UAVs) are used to fuel numerous important applications in computer vision, delivering more efficiency and convenience than surveillance cameras with fixed camera angle, scale and view. However, ... More

UA-DETRAC: A New Benchmark and Protocol for Multi-Object Detection and TrackingNov 13 2015Sep 04 2016In recent years, numerous effective multi-object tracking (MOT) methods are developed because of the wide range of applications. Existing performance evaluations of MOT methods usually separate the object tracking step from the object detection step by ... More

Solving Quantum Ground-State Problems with Nuclear Magnetic ResonanceJun 02 2011Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground ... More

Robust Mechanisms Under Common ValuationMar 20 2016Nov 19 2016We study robust mechanisms to sell a common-value good. We assume that the mechanism designer knows the prior distribution of the buyers' common value but is unsure of the buyers' information structure about the common value. We use linear programming ... More

On well-conditioned spectral collocation and spectral methods by the integral reformulationNov 04 2015Well-conditioned spectral collocation and spectral methods have recently been proposed to solve differential equations. In this paper, we revisit the well-conditioned spectral collocation methods proposed in [T.~A. Driscoll, {\it J. Comput. Phys.}, 229 ... More

Preconditioning rectangular spectral collocationOct 01 2015Oct 21 2015Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constraints. The involved linear systems in RSC become extremely ill-conditioned ... More

The Extended Mapping Class Group Can Be Generated by Two TorsionsJul 14 2016Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$. When the genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by two torsion elements. One of these ... More

Generating the mapping class groups with torsionsJun 14 2015Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}(S_g)$ be the mapping class group. When the genus is at least 3, $\text{Mod}(S_g)$ can be generated by torsion elements. We prove the follow results. For $g \geq 4$, $\text{Mod}(S_g)$ ... More

Negative frequency communicationDec 07 2010Sep 26 2011Spectrum is the most valuable resource in communication system, but unfortunately, so far, a half of the spectrum has been wasted. In this paper, we will see that the negative frequency not only has a physical meaning but also can be used in communication. ... More

Transport coefficients in Lorentz plasmas with the power-law kappa-distributionJul 15 2013Sep 07 2013Transport coefficients in Lorentz plasma with the power-law kappa-distribution are studied by means of using the transport equation and macroscopic laws of Lorentz plasma without magnetic field. Expressions of electric conductivity, thermoelectric coefficient ... More

Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactionsMar 30 2006Nov 18 2007By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is shown that the ... More

What does the nonextensive parameter q stand for in self-gravitating systems ?Apr 21 2004Apr 06 2010It is natural important question for us to ask what the nonextensive parameter stands for when Tsallis statistics is applied to the self-gravitating systems. In this paper, some properties of the nonextensive parameter and Tsallis equilibrium distribution ... More

The nonextensive parameter and Tsallis distribution for self-gravitating systemsSep 18 2004The properties of the nonextensive parameter q and the Tsallis distribution for self-gravitating systems are studied. A mathematical expression of q is deduced based on the generalized Boltzmann equation, the q-H theorem and the generalized Maxwellian ... More

Optimizing Multi-hop Mechanism for the Long Range Wide Area NetworkNov 13 2018Nov 20 2018Long Range (LoRa) is a modem technology for wireless communication in the Internet of Things (IoT), which trades off low data-rate for low power consumption. Long Range Wide Area Network (LoRaWAN) has an open specification that determines the Medium Access ... More

Surface plasmon resonance under conditions of electromagnetically induced transparencyDec 18 2011A scheme for a surface plasmon resonance system under conditions of electromagnetically induced transparency (EIT) is proposed. The system is composed of three layers: a prism, a thin metal film, and a hybrid dielectric consisting of EIT atoms and a background ... More

Higher order Poisson Kernels and $L^p$ polyharmonic boundary value problems in Lipschitz domainsMar 04 2015Mar 21 2015In this article, we introduce higher order conjugate Poisson and Poisson kernels, which are higher order analogues of the classical conjugate Poisson and Poisson kernels, as well as the polyharmonic fundamental solutions, and define multi-layer potentials ... More

A Polynomial time Algorithm for Hamilton Cycle and Its detailed proofApr 12 2010Nov 10 2016Popular algorithms to find a Hamilton circle in an undirected graph are generally based on the Rotation-Extension method developed by Posa. However, due to the deficiencies of Posa's method, such algorithms are only efficient for graphs that are either ... More

Preconditioning fractional spectral collocationOct 20 2015Fractional spectral collocation (FSC) method based on fractional Lagrange interpolation has recently been proposed to solve fractional differential equations. Numerical experiments show that the linear systems in FSC become extremely ill-conditioned as ... More

Measuring the angle $γ$ of the unitarity triangle in $B_s$ decays into CP eigenstatesJan 16 2007Apr 23 2007In this paper penguin contribution has not been included, so it is not suitable to be published.

A new form of Tsallis distribution based on the probabilistically independent postulateJun 08 2009Apr 01 2010The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. In this letter, the q-exponential of a sum can be applied as the product of the q-exponential based on the ... More

The Chandrasekhar condition of the equilibrium and stability for a star in the nonextensive kinetic theoryFeb 05 2006Jul 26 2006The idea of Chandrasekhar condition of the equilibrium and stability for a star is revisited in the nonextensive kinetic theory based on Tsallis entropy. A new analytical formula generalizing the Chandrasekhar condition is derived by assuming that the ... More

Serious Game for Human Environmental Consciousness Education in Residents Daily LifeMar 20 2015Oct 24 2016It has been challenging to find ways to educate people to have better environmental consciousness. In some cases, people do not know what the right behaviors are to protect the environment. Game engine has been used in the AEC industry for visualization. ... More

On the power-law q-distribution function based on the probabilistically independent postulate in nonextensive statisticsDec 13 2010Dec 25 2010We deal with the power-law q-distribution functions, so-called q-exponentials in nonextensive statistics. The system considered is a many-body Hamiltonian system with arbitrary interacting potentials. We find that the usual form of power-law q-distribution ... More

The hydrostatic equilibrium and Tsallis equilibrium for self-gravitating systemsJun 10 2004Mar 25 2005Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We obtain a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational ... More

Long Range Wide Area Network: A Simulation Module for ns-3Nov 14 2018Nov 20 2018Long Range (LoRa) is a wireless communication technology for the Internet of Things (IoT), able to provide wide coverage networking to devices with low power consumption and low data-rate. This paper~proposes and describes a simulation module of LoRa ... More

Trilateration-based Multi-hop for the Long Range Wide Area NetworkNov 15 2018Nov 20 2018Long Range Wide Area Network (LoRaWAN) has an open specification that defines the Medium Access Control (MAC) protocol for LoRa networks, mainly based on pure-Aloha with beacon option. The LoRaWAN has a star of star topology where end-devices are directly ... More

Refined upper bounds for the convergence of the randomized extended Kaczmarz and Gauss-Seidel algorithmsJan 10 2018The randomized extended Kaczmarz and Gauss-Seidel algorithms have attracted much attention because of their ability to treat all types of linear systems (consistent or inconsistent, full rank or rank-deficient). In this paper, we interpret the randomized ... More

Compactification of strata of abelian differentialsApr 29 2016We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of stable curves with marked points. We provide an explicit characterization ... More

Tautological ring of strata of differentialsAug 01 2017Strata of $k$-differentials on smooth curves parameterize sections of the $k$-th power of the canonical bundle with prescribed orders of zeros and poles. Define the tautological ring of the projectivized strata using the $\kappa$ and $\psi$ classes of ... More

Square-tiled surfaces and rigid curves on moduli spacesMar 03 2010This work is motivated by two central questions in the birational geometry of moduli spaces of curves -- Fulton's conjecture and the effective cone of $\bar M_g$. We study the algebro-geometric aspect of Teichmuller curves parameterizing square-tiled ... More

Model-Based Reinforcement Learning for Whole-Chain RecommendationsFeb 11 2019With the recent prevalence of Reinforcement Learning (RL), there have been tremendous interests in developing RL-based recommender systems. In practical recommendation sessions, users will sequentially access multiple scenarios, such as the entrance pages ... More

Stably weakly shadowing transitive sets and dominated splittingsMar 10 2010We prove that for any $C^1$-stably weakly shadowing transitive set $\Lambda$, either $\Lambda$ is a sink or a source, or $\Lambda$ admits a dominated splitting.

Any admissible harmonic Ritz value set is possible for prescribed GMRES residual normsApr 23 2016We show that any admissible harmonic Ritz value set is possible for prescribed GMRES residual norms, which is a complement for the results in [Duintjer Tebbens and Meurant, {\it SIAM J. Matrix Anal. Appl.}, 33 (2012), no. 3, pp. 958--978].

Robust Mechanisms Under Common ValuationMar 20 2016Aug 29 2016We study robust mechanisms to sell a common-value good. We assume that the mechanism designer knows the prior distribution of the buyers' common value but is unsure of the buyers' information structure about the common value. We use linear programming ... More

On Level persistence (Relevant level persistence numbers)Apr 16 2014Apr 20 2014The purpose of this note is to describe of a new set of numerical invariants, the relevant level persistence numbers, and make explicit their relationship with the four types of bar codes, a more familiar set of complete invariants for level persistence. ... More

An Overview of Mobile Capacitive Touch Technologies TrendsDec 25 2016Touch sensing, as a major human/machine interface, is widely used in various commercial products such as smart watches, mobile phones, tablets and TVs. State-of-the-art touch detections are mainly based on mutual capacitive sensing, which requires necessary ... More

Possible dynamics of the Tsallis distribution from a Fokker-Planck equation (I)May 27 2009Jun 01 2009The dynamical property of the Tsallis distribution is studied from a Fokker-Planck equation. For the Langevin dynamical system with an arbitrary potential function, Markovian friction and Gaussian white noise, we show that no possible nonequilibrium dynamics ... More

Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interactionsApr 25 2004The nonextensivity in a non-isothermal plasma system with the Coulombian long-range interactions is studied in the framework of Tsallis statistics. We present for first time a mathematical expression of the nonextensive parameter q based on the mathematical ... More

Jeans criterion in nonextensive statistical mechanicsApr 23 2004The Jeans gravitational instability in nonextensive statistical mechanics is studied and a general form of the generalized Jeans criterion is obtained that is related to the q-function . In this approach, the nonextensive model of classical ideal gas ... More

Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equationsFeb 03 2012Feb 06 2012We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a condition under ... More

Stochastic dynamical theory of power-law distributions induced by multiplicative noiseMar 07 2011Mar 08 2011The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of stationary power-law ... More

Property of Tsallis entropy and principle of entropy increaseFeb 24 2008The property of Tsallis entropy is examined when considering tow systems with different temperatures to be in contact with each other and to reach the thermal equilibrium. It is verified that the total Tsallis entropy of the two systems cannot decrease ... More

Jeans criterion and nonextensive velocity distribution function in kinetic theoryApr 23 2004The effect of nonextensivity of self-gravitating systems on the Jeans criterion for gravitational instability is studied in the framework of Tsallis statistics. The nonextensivity is introduced in the Jeans problem by a generalized q-nonextensive velocity ... More

Ternary quadratic forms and Heegner divisorsApr 19 2014In this paper, I use Siegel-Weil formula and Kudla matching principle to prove some interesting identities between representation number (of ternary quadratic space) and the degree of Heegner divisors.

On the Complexity of Deciding Degeneracy in GamesMay 19 2009We show that it is NP-Complete to decide whether a bimatrix game is degenerate and it is Co-NP-Complete to decide whether a bimatrix game is nondegenerate.

On solvability of an indefinite Riccati equationDec 27 2013This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is derived, based ... More

The Extended Mapping Class Group Can Be Generated by Two TorsionsJul 14 2016Feb 26 2018Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$. When the genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by two torsion elements. One of these ... More

Semi-supervised learning of local structured output predictorsApr 11 2016In this paper, we study the problem of semi-supervised structured output prediction, which aims to learn predictors for structured outputs, such as sequences, tree nodes, vectors, etc., from a set of data points of both input-output pairs and single inputs ... More

Generating the mapping class groups by torsionsJun 14 2015Feb 26 2018Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}(S_g)$ be the mapping class group. When the genus is at least 3, $\text{Mod}(S_g)$ can be generated by torsion elements. We prove the follow results. For $g \geq 4$, $\text{Mod}(S_g)$ ... More

Staggered chiral perturbation theory in the two-flavor caseNov 13 2009Nov 08 2010I study two-flavor staggered chiral perturbation theory in the light pseudoscalar sector. The pion mass and decay constant are calculated through NLO in the partially-quenched case. In the limit where the strange quark mass is large compared to the light ... More

A Polynomial time Algorithm for Hamilton Cycle and Its detailed proofApr 12 2010Aug 29 2016Popular algorithms to find a Hamilton circle in an undirected graph are generally based on the Rotation-Extension method developed by Posa. However, due to the deficiencies of Posa's method, such algorithms are only efficient for graphs that are either ... More

Higher Groupoid Actions, Bibundles, and DifferentiationDec 14 2015In this thesis, we employ simplicial methods to study actions, principal bundles, and bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher groupoids, we use pairs of a Kan fibration and a special acyclic fibration to ... More

Random Walks on Dicyclic GroupMar 16 2009This paper works out the rate of convergence of two "natural" random walks on the dicyclic group.

Quantum-State Purity of Heralded Single Photons Produced from Frequency-Anti-Correlated BiphotonsJul 13 2015Sep 15 2015We analyze the quantum-state purity of heralded single photons produced from frequency-anti-correlated biphotons. We find that the quantum-state purity in time-frequency domain depends strongly on the response time uncertainty of the trigger-photon detector ... More

Two spectral methods for 2D quasi-periodic scattering problemsJul 06 2015Jul 12 2015We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product spectral method ... More

CP violation for neutral charmed meson decays to CP eigenstatesAug 30 2006Nov 06 2006CP asymmetries for neutral charmed meson decays to CP eigenstates are carefully studied. The formulas and numerical results are presented. The impact on experiments is briefly discussed.

Test of Nonextensive Statistical Mechanics by Solar Sound SpeedsFeb 05 2006Jul 26 2006To check the validity of the theory of nonextensive statistical mechanics, we have investigated the nonextensive degree of the solar interior and have tried to find the experimental evidence by helioseismological measurements that q is different from ... More

On Graph Isomorphism ProblemOct 26 2017Let $G$ and $H$ be two simple graphs. A bijection $\phi:V(G)\rightarrow V(H)$ is called an isomorphism between $G$ and $H$ if $(\phi v_i)(\phi v_j)\in E(H)$ $\Leftrightarrow$ $v_i v_j\in E(G)$, $\forall v_i,v_j \in V(G)$. In the case that $G = H$, we ... More

On the Automorphism Group of a GraphJul 02 2016An automorphism of a graph $G$ with $n$ vertices is a bijective map $\phi$ from $V(G)$ to itself such that $\phi(v_i)\phi(v_j)\in E(G)$ $\Leftrightarrow$ $v_i v_j\in E(G)$ for any two vertices $v_i$ and $v_j$ of $G$. Denote by $\mathfrak{G}$ the group ... More

Favard, Baxter, Geronimus, Rakhmanov, Szegö and the strong Szegö theorems for orthogonal trigonometric polynomialsJul 23 2008In this paper, we obtain some analogs of Favard, Baxter, Geronimus, Rakhmanov, Szeg\"o and the strong Szeg\"o theorems appeared in the theory of orthogonal polynomials on the unit circle (OPUC) for orthogonal trigonometric polynomials (OTP). The key tool ... More

Application of Autoencoder-Assisted Recurrent Neural Networks to Prevent Cases of Sudden Infant Death SyndromeApr 28 2019This project develops and trains a Recurrent Neural Network (RNN) that monitors sleeping infants from an auxiliary microphone for cases of Sudden Infant Death Syndrome (SIDS), manifested in sudden or gradual respiratory arrest. To minimize invasiveness ... More

Degenerations of Abelian DifferentialsApr 08 2015Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate differentials, ... More

Covers of the projective line and the moduli space of quadratic differentialsMay 18 2010Consider the 1-dimensional Hurwitz space parameterizing covers of P^1 branched at four points. We study its intersection with divisor classes on the moduli space of curves. As an application, we calculate the slope of the Teichmuller curve parameterizing ... More

An extremal effective survey about extremal effective cycles in moduli spaces of curvesNov 01 2017We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces of curves.

A note on resolution quiversNov 26 2012Recently, Ringel introduced the resolution quiver for a connected Nakayama algebra. It is known that each connected component of the resolution quiver has a unique cycle. We prove that all cycles in the resolution quiver are of the same size. We introduce ... More