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A Neural Network Prediction Based Adaptive Mode Selection Scheme in Full-Duplex Cognitive NetworksApr 12 2019We propose a neural network (NN) predictor and an adaptive mode selection scheme for the purpose of both improving secondary user's (SU's) throughput and reducing collision probability to the primary user (PU) in full-duplex (FD) cognitive networks. SUs ... More

Entanglement negativity and topological orderJun 24 2013Jun 30 2013We use the entanglement negativity, a measure of entanglement for mixed states, to probe the structure of entanglement in the ground state of a topologically ordered system. Through analytical calculations of the negativity in the ground state(s) of the ... More

Quantum coin flipping secure against channel noisesMay 27 2015So far, most of existed single-shot quantum coin flipping(QCF) protocols failed in a noisy quantum channel. Here, we present a nested-structured framework that makes it possible to achieve partially noise-tolerant QCF, due to that there is a trade-off ... More

Pointwise second-order necessary conditions for stochastic optimal controls, Part II: The general caseSep 26 2015Oct 19 2015This paper is the second part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, we consider the general cases, i.e., the control region is allowed to be nonconvex, and the control ... More

Cusp-shaped structure of a jet observed by IRIS and SDONov 15 2016On 29 August 2014, the trigger and evolution of a cusp-shaped jet were captured in detail at 1330 {\AA} by the Interface Region Imaging Spectrograph.At first, two neighboring mini-prominences arose in turn from low solar atmosphere and collided with a ... More

Pixel-wise Regression: 3D Hand Pose Estimation via Spatial-form Representation and Differentiable DecoderMay 06 20193D Hand pose estimation from a single depth image is an essential topic in computer vision and human-computer interaction. Although the rising of deep learning method boosts the accuracy a lot, the problem is still hard to solve due to the complex structure ... More

Crossed modules for Hom-Lie antialgebrasMar 21 2019In this paper, we introduced the concept of crossed module for Hom-Lie antialgebras. It is proved that the category of crossed modules for Hom-Lie antialgebras and the category of $Cat^1$-Hom-Lie antialgebras are equivalent to each other. The relationship ... More

Repeating FRB 121102 : Eight-year Fermi-LAT Upper Limits and ImplicationsMay 11 2017May 29 2017The repeating fast radio burst (FRB) source that produced FRB 121102 was recently localized in a star forming galaxy at $z=0.193$, which is associated with an extended radio source at the burst location. One possibility is that the repeating FRBs are ... More

Trajectory Design for Cellular-Connected UAV Under Outage Duration ConstraintJan 14 2019Mar 14 2019In this paper, we study the trajectory design for a cellular-connected unmanned aerial vehicle (UAV) with given initial and final locations, while communicating with the ground base stations (GBSs) along its flight. We consider delay-limited communications ... More

Minimality of a Kind of Pseudo-Umbilical Totally Real Submanifolds in Non-Flat Complex Space FormsDec 27 2015In this paper, by studying the position of umbilical normal vectors in the normal bundle, we prove that pseudo-umbilical totally real submanifolds with flat normal connection in non-flat complex space forms must be minimal.

Computing Skylines on Distributed DataNov 01 2016In this paper we study skyline queries in the distributed computational model, where we have $s$ remote sites and a central coordinator (the query node); each site holds a piece of data, and the coordinator wants to compute the skyline of the union of ... More

An accelerated proximal iterative hard thresholding method for $\ell_0$ minimizationSep 06 2017Jan 02 2018In this paper, we consider a non-convex problem which is the sum of $\ell_0$-norm and a convex smooth function under box constraint. We propose one proximal iterative hard thresholding type method with extrapolation step used for acceleration and establish ... More

Double Bicrosssum of Braided Lie algebrasJan 08 2007Jan 12 2007The condition for double bicrosssum to be a braided Lie bialgebra is given. The result generalizes quantum double, bicrosssum, bicrosscosum, bisum. The quantum double of braided Lie bialgebras is constructed. The relation between double crosssum of Lie ... More

Sequential Sampling for CGMY Processes via Decomposition of their Time ChangesAug 01 2017Aug 22 2018We present a new and easy-to-implement sequential sampling method for CGMY processes with either finite or infinite variation, exploiting the time change representation of the CGMY model and a decomposition of its time change. We find that the time change ... More

Crossed modules for Hom-Lie antialgebrasMar 21 2019Apr 03 2019In this paper, we introduced the concept of crossed module for Hom-Lie antialgebras. It is proved that the category of crossed modules for Hom-Lie antialgebras and the category of $Cat^1$-Hom-Lie antialgebras are equivalent to each other. The relationship ... More

Long time well-posdness of Prandtl system with small and analytic initial dataSep 05 2014In this paper, we investigate the long time existence and uniqueness of small solution to $d,$ for $d=2,3,$ dimensional Prandtl system with small initial data which is analytic in the horizontal variables. In particular, we prove that $d$ dimensional ... More

Global well-posedness of 3-D inhomogeneous Navier-Stokes equations with ill-prepared initial dataSep 05 2014In this paper, we investigate the global well-posedness of 3-D incompressible inhomogeneous Navier-Stokes equations with ill-prepared large initial data which are slowly varying in one space variable, that is, initial data of the form $\bigl(1+\e^{\be}a_0(x_{\rm ... More

MinJoin: Efficient Edit Similarity Joins via Local Hash MinimaOct 20 2018May 29 2019We study the problem of computing similarity joins under edit distance on a set of strings. Edit similarity joins is a fundamental problem in databases, data mining and bioinformatics. It finds important applications in data cleaning and integration, ... More

Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequencyMay 23 2018This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern or the ... More

Renormalized solutions for the fractional p(x)-Laplacian equation with L^1 dataAug 15 2017In this paper, we prove the existence and uniqueness of nonnegative renormalized solutions for the fractional p(x)-Laplacian problem with L1 data. Our results are new even in the constant exponent fractional p-Laplacian equation case.

Chaotic transitions of optomechanical resonator modified by the quadratic couplingFeb 06 2016A parametric modification of the dynamical transition from steady-state to limit circles and to chaos by the quadratic coupling in optomechanical system is investigated. Under a weak pumping field, the mechanical resonator damps to a steady state with ... More

Dirac Delta Function of Matrix ArgumentJul 11 2016Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed knowledge about ... More

On the simplicity of induced modules for reductive Lie algebras. IIApr 13 2016A sufficient condition for the simplicity of induced modules of reductive Lie algebras is given.

On the spectrums of ergodic Schrodinger operators with finitely valued potentialsFeb 09 2015Feb 16 2015We show that the measure of the spectrum of Schr\"odinger operator with potential defined by non-constant function over any minimal aperiodic finite subshift tends to zero, as the coupling constant tends to infinity. We also obtained a quantitative upper ... More

A monopole invariant for foliations without transverse invariant measureMar 26 2016Let $Y$ be a closed oriented 3-manifold, and $\mathcal{F}$ a smooth oriented foliation on $Y$. Assume that $\mathcal{F}$ does not admit any transverse invariant measure. This article constructs an invariant $c(\mathcal{F})$ for $\mathcal{F}$ which takes ... More

Book Review: Matrix Theory by X. ZhanDec 08 2014This is a book review for Zhan's Matrix Theory (AMS, GSM 147, 2013).

Abundance of non-uniruled 3-folds with non-trivial Albanese maps in positive characteristicsOct 12 2016In this paper, we prove abundance for non-uniruled 3-folds with non-trivial Albanese maps, over an algebraically closed field of characteristic $p > 5$. As an application we get a characterization of abelian 3-folds.

An Efficient Implementation of Brezzi-Douglas-Marini (BDM) Mixed Finite Element Method in MATLABAug 26 2015In this paper, a MATLAB package bdm_mfem for a linear Brezzi-Douglas- Marini (BDM) mixed finite element method is provided for the numerical solution of elliptic diffusion problems with mixed boundary conditions on unstructured grids. BDM basis functions ... More

Boundary effects on energy dissipation in a cellular automaton modelApr 23 2009Apr 25 2009In this paper, we numerically study energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Numerical results show that there is a nonvanishing energy dissipation rate Ed, and no true free-flow ... More

The efficiency of the molecular motorsOct 07 2008Feb 12 2009Molecular motors convert chemical energy into mechanical work while operating in an environment dominated by Brownian motion. The aim of this paper is to explore the flow of energy between the molecular motors and its surroundings, in particular, its ... More

Vector boson production in association with jets and heavy flavor quarks from CMSJul 06 2016This document is dedicated to recent results on the measurements of a vector boson production associated with jets (V+jets) using CMS detector experiment, with a central proton-proton (pp) collision energy of respectively 8 TeV (RunI) and 13 TeV (RunII). ... More

Entropy in the interior of a black hole and thermodynamicsOct 08 2015Based on a recent proposal for the volume inside a black hole, we calculate the entropy associated with this volume and show that such entropy is proportional to the surface area of the black hole. Together with the consideration of black hole radiation, ... More

Dark Energy and Its Interactions with NeutrinosOct 06 2005In this talk I will firstly review on the current constraints on the equation of state of the dark energy from observational data, then present a new scenario of dark energy dubbed {\it Quintom}. The recent fits to the type Ia supernova data and the cosmic ... More

Performance Improvements in Heterogeneous Wireless Networks for First RespondersNov 07 2016Efficient communications are crucial for disaster response and recovery. However, most current public safety land mobile radio (LMR) networks only provide narrowband voice service with limited support of low-speed data services. In this paper, we study ... More

On the nonexplosion and explosion for nonhomogeneous Markov pure jump processes in Borel spacesNov 16 2015In this paper, we obtain new drift-type conditions for nonexplosion and explosion for nonhomogeneous Markov pure jump processes in Borel state spaces. The conditions are practical and in the meanwhile sharp; e.g., the one for nonexplosion is necessary ... More

The Methicillin-Resistant Staphylococcus Aureus Infection ControlsMay 30 2013Multi-resistant organisms (MROs), the bacteria that are resistant to a number of different antibiotics, have been very popular around the world in recent years. They are very difficult to treat but highly infectious in humans. MRSA (Methicillin-Resistant ... More

The Lennard-Jones Potential Minimization Problem for Prion AGAAAAGA Amyloid Fibril Molecular ModelingJun 08 2011The simplified Lennard-Jones (LJ) potential minimization problem is minimize f(x)=4\sum_{i=1}^N \sum_{j=1,j<i}^N (\tau_{ij}^{-6} -\tau_{ij}^{-3}) subject to x\in \mathbb{R}^n, where $\tau_{ij}=(x_{3i-2}-x_{3j-2})^2 +(x_{3i-1}-x_{3j-1})^2+(x_{3i} -x_{3j})^2$, ... More

Continuous-time Markov decision processes with exponential utilityOct 10 2016In this paper, we consider a continuous-time Markov decision process (CTMDP) in Borel spaces, where the certainty equivalent with respect to the exponential utility of the total undiscounted cost is to be minimized. We establish the optimality equation. ... More

Intrinsic electromagnetic variability in celestial objects containing rapidly spinning black holesFeb 10 2016Analytical studies have raised the concern that a mysterious expulsion of magnetic field lines by a rapidly-spinning black hole (dubbed the black hole Meissner effect) would shut down the Blandford-Znajek process and quench the jets of active galactic ... More

Rademacher Complexity of the Restricted Boltzmann MachineDec 07 2015Boltzmann machine, as a fundamental construction block of deep belief network and deep Boltzmann machines, is widely used in deep learning community and great success has been achieved. However, theoretical understanding of many aspects of it is still ... More

Mixed type multiple orthogonal polynomials associated with the modified Bessel functions and products of two coupled random matricesMay 06 2016Sep 27 2016We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bessel function of the first kind $I_\mu$ and $I_{\mu+1}$, the other vector ... More

Fundamental representations of quantum affine superalgebras and R-matricesJun 19 2015Jul 13 2016We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices between two fundamental ... More

Characterizations and Infinite Divisibility of Extended COM-Poisson DistributionApr 19 2015Aug 25 2015This article provides some characterizations of extended COM-Poisson distribution: conditional distribution given the sum, functional operator characterization (Stein identity). We also give some conditions such that the extended COM-Poisson distribution ... More

On robust width property for Lasso and Dantzig selectorJan 15 2015Apr 03 2016Recently, Cahill and Mixon completely characterized the sensing operators in many compressed sensing instances with a robust width property. The proposed property allows uniformly stable and robust reconstruction of certain solutions from an underdetermined ... More

Lie algebras of linear systems and their automorphismsJun 18 2014The objective of this thesis is to study the automorphism groups of the Lie algebras attached to linear systems. A linear system is a pair of vector spaces $(U,W)$ with a nondegenerate pairing $\langle\cdot,\cdot\rangle\colon U\otimes W\to \mathbb{C}$, ... More

New Analysis of Linear Convergence of Gradient-type Methods via Unifying Error Bound ConditionsJun 01 2016Aug 29 2016The subject of linear convergence of gradient-type methods on non-strongly convex optimization has been widely studied by introducing several notions as sufficient conditions. Influential examples include the error bound property, the restricted strongly ... More

The 750GeV diphoton excess: who introduces it?Jan 07 2016Recently, both ATLAS and CMS collaborations report an excess at 750GeV in the diphoton invariant mass spectrum at 13TeV LHC. If it is a new scalar produced via loop induced gluon-gluon fusion process, it is important to know what is the particle in the ... More

Spherical Cap Packing Asymptotics and Rank-Extreme DetectionNov 19 2015We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent ... More

Rank-Extreme Association of Gaussian Vectors and Low-Rank DetectionJun 03 2013Sep 02 2013It is important to detect a low-dimensional linear dependency in high-dimensional data. We provide a perspective on this problem, called the rank-extreme (ReX) association, through studies of the maximum norm of a vector of $p$ standard Gaussian variables ... More

The Limiting Distribution of Decoherent Quantum Random WalksApr 28 2008The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we study the decoherence ... More

On the Concept of Static Structure FactorJun 11 2016Jun 20 2016We clarify the confusion in the expression of the static structure factor S(k) in the study of condensed matters and discuss its explicit form that can be directly used in calculations and computer simulations.

Hyperaccreting Neutron-Star Disks, Magnetized Disks and Gamma-Ray BurstsJun 04 2009Dec 22 2009This thesis focuses on the study of the hyperaccreting neutron-star disks and magnetized accretion flows. It is usually proposed that hyperaccreting disks surrounding stellar-mass black holes with a huge accretion rate are central engines of gamma-ray ... More

Exact Landau Levels in Two-Dimensional Electron Systems with Rashba and Dresselhaus Spin-Orbit Interactions in a Perpendicular Magnetic FieldFeb 20 2006We study a two-dimensional electron system in the presence of both Rashba and Dresselhaus spin-orbit interactions in a perpendicular magnetic field. Defining two suitable boson operators and using the unitary transformations we are able to obtain the ... More

A weighted central limit theorem under sublinear expectationsMay 04 2011In this paper, we investigate a central limit theorem for weighted sums of independent random variables under sublinear expectations. It is turned out that our results are natural extensions of the results obtained by Peng and Li and Shi.

Representations for generalized Drazin inverse of operator matrices over a Banach spaceNov 08 2014In this paper we give expressions for the generalized Drazin inverse of a (2,2,0) operator matrix and a $2\times2$ operator matrix under certain circumstances, which generalizes and unifies several results in the literature.

A Majorization-Minimization Algorithm for Computing the Karcher Mean of Positive Definite MatricesDec 17 2013Jun 04 2015An algorithm for computing the Karcher mean of $n$ positive definite matrices is proposed, based on the majorization-minimization (MM) principle. The proposed MM algorithm is parameter-free, does not need to choose step sizes, and has a theoretical guarantee ... More

Severi inequality for varieties of maximal Albanese dimensionMar 17 2013Let $X$ be a projective, normal, minimal and Gorenstein $n$-dimensional complex variety of general type. Suppose $X$ is of maximal Albanese dimension. We prove that $K^n_X \ge 2 n! \chi(K_X)$

DNF-AF Selection Two-Way RelayingNov 22 2012May 07 2013Error propagation and noise propagation at the relay node would highly degrade system performance in two-way relay networks. In this paper, we introduce DNF-AF selection two-way relaying scheme which aims to avoid error propagation and mitigate noise ... More

The degeneration of convex RP^2 structures on surfacesDec 09 2013Jul 14 2015Let M be a compact surface of negative Euler characteristic and let C(M) be the deformation space of convex real projective structures on M. For every choice of pants decomposition for M, there is a well known parameterization of C(M) known as the Goldman ... More

A note on the asymptotic behavior of conformal metrics with negative curvatures near isolated singularitiesApr 07 2013The asymptotic behavior of conformal metrics with negative curvatures near an isolated singularity for at most second order derivatives was described by Kraus and Roth in one of their papers in 2008. Our work improves one estimate of theirs and shows ... More

Sparse Recovery with Orthogonal Matching Pursuit under RIPMay 13 2010Jun 03 2011This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level $O(\bar{k})$, then OMP can recover a $\bar{k}$-sparse signal in 2-norm. For ... More

On the Linear Convergence of the Cauchy Algorithm for a Class of Restricted Strongly Convex FunctionsNov 01 2016In this short note, we extend the linear convergence result of the Cauchy algorithm, derived recently by E. Klerk, F. Glineur, and A. Taylor, from the case of smooth strongly convex functions to the case of restricted strongly convex functions with certain ... More

A note on Iitaka's conjecture $C_{3,1}$ in positive characteristicsSep 30 2016In this paper, we prove that for a fibration $f:X\to Y$ from a smooth projective 3-fold to a smooth projective curve, over an algebraically closed field $k$ of characteristic $p >5$. If the generic fiber $X_{\eta}$ has big canonical divisor $K_{X_{\eta}}$, ... More

Molecular studies of Planetary NebulaeNov 11 2016Circumstellar envelopes (CEs) around evolved stars are an active site for the production of molecules. After evolving through the Asymptotic Giant Branch (AGB), proto-planetary nebula (PPN), to planetary nebula (PN) phases, CEs ultimately merge with the ... More

Data Partitioning View of Mining Big DataNov 29 2016There are two main approximations of mining big data in memory. One is to partition a big dataset to several subsets, so as to mine each subset in memory. By this way, global patterns can be obtained by synthesizing all local patterns discovered from ... More

Stable multi-instance learning visa causal inferenceFeb 13 2019Multi-instance learning (MIL) deals with tasks where each example is represented by a bag of instances. Unlike traditional supervised learning, only the bag labels are observed whereas the label for each instance in the bags is not available. Previous ... More

The effect of cluster magnetic field on the Sunyaev Zeldovich power spectrumAug 20 2003Nov 26 2003Precision measurements of the Sunyaev Zeldovich (SZ) effect in upcoming blank sky surveys require theoretical understanding of all physical processes with $\ga 10%$ effects on the SZ power spectrum. We show that, observed cluster magnetic field could ... More

Cross correlations of the cosmic infrared backgroundJul 25 2003Mar 09 2004The cosmic infrared background (CIB) is a sensitive measure of the star formation history. But this background is overwhelmed by foregrounds, which bias the CIB mean flux and auto correlation measurement severely. Since dominant foregrounds do not correlate ... More

On Representation of Integers from Thin Subgroups of SL(2,Z) with ParabolicsOct 03 2016Oct 05 2016Let $\Lambda<SL(2,\mathbb{Z})$ be a finitely generated, non-elementary Fuchsian group of the second kind, and $v, w$ be two primitive vectors in $\mathbb{Z}^2-(0,0)$. We consider the set $\mathcal{S}=\{\langle {v}\gamma,{w}\rangle_{\mathbb{R}^2}:\gamma\in\Lambda\}$, ... More

NLO predictions for SMEFT in the top-quark sectorNov 15 2016Predictions for the Standard Model Effective Field Theory at the next-to-leading order accuracy in QCD, including parton-shower effects, have started to become available in the MadGraph5_aMC@NLO framework. In this talk we summarize some recent results ... More

Relative Clifford inequality for varieties fibered by curvesJun 20 2017Mar 07 2018We prove a sharp relative Clifford inequality for relatively special divisors on varieties fibered by curves. It generalizes the classical Clifford inequality about a single curve to a family of curves. It yields a geographical inequality for varieties ... More

Perfect Memory Context Trees in time series modelingOct 17 2016The Stochastic Context Tree (SCOT) is a useful tool for studying infinite random sequences generated by an m-Markov Chain (m-MC). It captures the phenomenon that the probability distribution of the next state sometimes depends on less than m of the preceding ... More

Language in Our Time: An Empirical Analysis of HashtagsMay 11 2019Hashtags in online social networks have gained tremendous popularity during the past five years. The resulting large quantity of data has provided a new lens into modern society. Previously, researchers mainly rely on data collected from Twitter to study ... More

Moduli of certain wild covers of curvesApr 07 2019May 05 2019A fine moduli space is constructed, for cyclic-by-$\mathsf{p}$ covers of an affine curve over an algebraically closed field $k$ of characteristic $\mathsf{p}>0$. An intersection of finitely many fine moduli spaces for cyclic-by-$\mathsf{p}$ covers of ... More

Seesaw-Net: Convolution Neural Network With Uneven Group ConvolutionMay 09 2019In this paper, we are interested in boosting the representation capability of convolution neural networks which utilizing the inverted residual structure. Based on the success of Inverted Residual structure[Sandler et al. 2018] and Interleaved Low-Rank ... More

A Note on q-Deformed Two-Dimensional Yang-Mills and Open Topological StringsNov 10 2006In this note we make a test of the open topological string version of the OSV conjecture, proposed in hep-th/0504054, in the toric Calabi-Yau manifold $X= O(-3)\to\mathbf{P}^2$ with background D4-branes wrapped on Lagrangian submanifolds. The D-brane ... More

First-Principles Calculation of Mg(0001) Thin Films: Quantum Size Effect and Adsorption of Atomic HydrogenNov 08 2006We have carried out first-principles calculation of Mg(0001) free-standing thin films to study the oscillatory quantum size effect exhibited in the surface energy, work function, interlayer relaxation, and adsorption energy of the atomic hydrogen adsorbate. ... More

Confronting Four Zero Neutrino Yukawa Textures with $N_2^{}$-dominated LeptogenesisFeb 13 2015Sep 17 2015We consider a restricted Type-I seesaw scenario with four texture zeros in the neutrino Yukawa matrix, in the weak basis where both the charged-lepton Yukawa matrix and the Majorana mass matrix for right-handed neutrinos are diagonal and real. Inspired ... More

Allocations of Standby Redundancies to Coherent Systems with Dependent ComponentsAug 07 2018In the context of industrial engineering, standby allocation strategy is usually adopted by engineers to improve the lifetimes of coherent systems. This paper investigates the optimal allocation strategies of standby redundancies for coherent systems ... More

Principal Postnikov towers and TQ localization of structured ring spectraFeb 09 2019Feb 21 2019The aim of this short paper is to identify a reasonably large class of TQ-local algebras over a spectral operad O. Here TQ is short for topological Quillen homology, which is weakly equivalent to the stabilization of an O-algebra. Our main result is that ... More

Degeneration of shrinking Ricci solitonsSep 12 2009Let $(Y,d)$ be a Gromov-Hausdorff limit of closed shrinking Ricci solitons with uniformly upper bounded diameter and lower bounded volume. We prove that off a closed subset of codimension at least 2, $Y$ is a smooth manifold satisfying a shrinking Ricci ... More

Independent Sets in Direct Products of Vertex-transitive GraphsJul 06 2010The direct product $G\times H$ of graphs $G$ and $H$ is defined by: \[V(G\times H)=V(G)\times V(H)\] and \[E(G\times H)=\left\{[(u_1,v_1),(u_2,v_2)]: (u_1,u_2)\in E(G) \mbox{\ and\ } (v_1,v_2)\in E(H)\right\}.\] In this paper, we will prove that the equality ... More

Efficient active learning of sparse halfspacesMay 07 2018Jun 02 2018We study the problem of efficient PAC active learning of homogeneous linear classifiers (halfspaces) in $\mathbb{R}^d$, where the goal is to learn a halfspace with low error using as few label queries as possible. Under the extra assumption that there ... More

Clustered boundary layer positive solutions for an elliptic Neumann problem with large exponentApr 05 2019Let $\mathcal{D}$ be a smooth bounded domain in $\mathbb{R}^N$ with $N\geq3$, we study the existence and profile of positive solutions for the following elliptic Neumann problem $$\begin{cases}-\Delta \upsilon+\upsilon=\upsilon^p,\quad \upsilon>0 \quad\textrm{in}\ ... More

The Substellar Transition Zone: A Stretched Temperature Canyon in Brown Dwarf Population due to Unsteady Hydrogen FusionOct 16 2018Apr 23 2019I summarize results on transitional and degenerate brown dwarfs presented in a series titled Primeval very low-mass stars and brown dwarfs. I introduce an L subdwarf classification scheme, which classified L subdwarfs into three metal subclasses. I would ... More

Goldbach Conjecture and the least prime number in an arithmetic progressionDec 25 2008Feb 23 2010In this Note, we try to study the relations between the Goldbach Conjecture and the least prime number in an arithmetic progression. We give a new weakened form of the Goldbach Conjecture. We prove that this weakened form and a weakened form of the Chowla ... More

A Note on Hardness Frameworks and Computational Complexity of Xiangqi and JanggiMar 30 2019We review NP-hardness framework and PSPACE-hardness framework for a type of 2D platform games. We introduce a EXPTIME-hardness framework by defining some new gadgets. We use these hardness frameworks to analyse computational complexity of Xiangqi (Chinese ... More

The $P=W$ identity for cluster varietiesMar 17 2019We find new examples of the $P=W$ identity of de Cataldo-Hausel-Migliorini by studying cluster varieties. We prove that the weight filtration of 2D cluster varieties correspond to the perverse filtration of elliptic fibrations which are deformation equivalent ... More

Scattering in periodic waveguide: integral representation and spectrum decompositionMay 27 2019Scattering problems in periodic waveguides are interesting but challenging topics in mathematics, both theoretically and numerically. Due to the existence of eigenvalue, the unique solvability of such problems is not always guaranteed. To obtain a unique ... More

Thermal Casimir Effect in Kerr Space-timeOct 06 2017We investigate the thermal Casimir effect of a massless scalar field for two parallel plates moving in the equatorial orbit in Kerr space-time. Under the assumption that the typical cavity size is much smaller than the orbital radius, proposed by Sorge, ... More

Cross: Efficient Low-rank Tensor CompletionNov 03 2016Nov 27 2018The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required number of measurements ... More

FRB Energetics and detectability from high redshiftsAug 15 2018Oct 16 2018We estimate the upper limit redshifts of known FRBs using the dispersion measure (DM) - redshift ($z$) relation and derive the upper limit peak luminosity $L_p$ and energy $E$ of FRBs within the observational band. The average $z$ upper limits range from ... More

The behavior of $f(R)$ gravity in the solar system, galaxies and clustersJan 23 2007Jun 08 2007For cosmologically interesting $f(R)$ gravity models, we derive the complete set of the linearized field equations in the Newtonian gauge, under environments of the solar system, galaxies and clusters respectively. Based on these equations, we confirmed ... More

On bodies with congruent sections or projectionsNov 28 2017In this paper, we construct two convex bodies $K$ and $L$ in $\mathbb{R}^n$, $n\geq 3$, such that their projections $K|H$, $L|H$ onto every subspace $H$ are congruent, but nevertheless, $K$ and $L$ do not coincide up to a translation or a reflection in ... More

Expected Dimensions of Higher-rank Brill-Noether LociDec 05 2013Apr 02 2015In this paper, we prove a new expected dimension formula for certain rank two Brill-Noether loci with fixed special determinant. This answers a question asked by Osserman and also leads to a new and much simpler proof of a theorem of Osserman. Our result ... More

An update on a few permanent conjecturesAug 09 2016We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture${}^\dagger$, Lieb permanent dominance conjecture, Bapat and ... More

Scalar Curvature Behavior for Finite Time Singularity of Kähler-Ricci FlowJan 11 2009In this short paper, we show that K\"ahler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.

The relation between the decomposition of comodules and coalgebrasNov 28 2003T. Shudo and H. Miyamito \cite{SM78} showed that $C$ can be decomposed into a direct sum of its indecomposable subcoalgebras of $C$. Y.H. Xu \cite {XF92} showed that the decomposition was unique. He also showed that $M$ can uniquely be decomposed into ... More

On representations of certain pseudo-Anosov maps of Riemann surfaces with puncturesAug 28 2007Jan 16 2008Let $S$ be a Riemann surface of type $(p,n)$ with $3p+n>4$ and $n\geq 1$. Let $\alpha_1,\alpha_2\subset S$ be two simple closed geodesics such that $\{\alpha_1, \alpha_2\}$ fills $S$. It was shown by Thurston that most maps obtained through Dehn twists ... More

Representations for the restricted Lie color algebrasNov 08 2010The generalized p-characters for the restricted Lie color are defined. The simplicity of the induced modules for the FP triples are determined. As applications, we have obtained an analogue of the Kac-Weisfiler theorem for the algebraic Lie color algebra ... More