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Secrecy Outage Analysis of Mixed RF-FSO Downlink SWIPT SystemsJun 05 2018We analyze a secure dual-hop mixed radio frequency-free space optical (RF-FSO) downlink simultaneous wireless information and power transfer (SWIPT) systems. The FSO link and all RF links experience Gamma-Gamma, independent and identical Nakagami-$m$ ... More

On Secure Mixed RF-FSO Systems With TAS and Imperfect CSISep 05 2018In this work, we analyze the secrecy outage performance of a dual-hop relay system composed of multiple-input-multiple-output radio-frequency (RF) links and a free-space optical (FSO) link while a multiple-antenna eavesdropper wiretaps the confidential ... More

Secure mmWave Communications in Cognitive Radio NetworksApr 12 2019In this letter, the secrecy performance in cognitive radio networks (CRNs) over fluctuating two-ray (FTR) channels, which is used to model the millimetre wave channel, is investigated in terms of the secrecy outage probability (SOP). Specifically, we ... More

BSDEs and SDEs with time-advanced and -delayed coefficientsJan 18 2017Feb 25 2019This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a sufficiently ... More

Effective Spectral Unmixing via Robust Representation and Learning-based SparsitySep 02 2014Sep 19 2014Hyperspectral unmixing (HU) plays a fundamental role in a wide range of hyperspectral applications. It is still challenging due to the common presence of outlier channels and the large solution space. To address the above two issues, we propose a novel ... More

Insight into the origin of Lithium/Nickel ions exchange in layered Li(NixMnyCoz)O2 cathode materialsApr 12 2018In layered LiNixMnyCozO2 cathode material for lithium-ion batteries, the spins of transition metal (TM) ions construct a two-dimensional triangular networks, which can be considered as a simple case of geometrical frustration. By performing neutron powder ... More

Effective Spectral Unmixing via Robust Representation and Learning-based SparsitySep 02 2014Aug 26 2017Hyperspectral unmixing (HU) plays a fundamental role in a wide range of hyperspectral applications. It is still challenging due to the common presence of outlier channels and the large solution space. To address the above two issues, we propose a novel ... More

Commissioning Progress of the FASTMar 15 2019The Five-hundred-meter Aperture Spherical radio Telescope (FAST) was completed with its main structure installed on September 25, 2016, after which it entered the commissioning phase. This paper aims to introduce the commissioning progress of the FAST ... More

Cyber Epidemic Models with DependencesMar 28 2016Studying models of cyber epidemics over arbitrary complex networks can deepen our understanding of cyber security from a whole-system perspective. In this paper, we initiate the investigation of cyber epidemic models that accommodate the {\em dependences} ... More

The First Pulsar Discovered by FASTMar 15 2019To assist with the commissioning (Jiang et al. 2019) of the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we performed a pulsar search, with the primary goal of developing and testing the pulsar data acquisition and processing pipelines. ... More

DetNAS: Neural Architecture Search on Object DetectionMar 26 2019Object detectors are usually equipped with networks designed for image classification as backbones, e.g., ResNet. Although it is publicly known that there is a gap between the task of image classification and object detection, designing a suitable detector ... More

Joint Neural Architecture Search and QuantizationNov 23 2018Designing neural architectures is a fundamental step in deep learning applications. As a partner technique, model compression on neural networks has been widely investigated to gear the needs that the deep learning algorithms could be run with the limited ... More

Spectral Unmixing via Data-guided SparsityMar 13 2014Nov 17 2014Hyperspectral unmixing, the process of estimating a common set of spectral bases and their corresponding composite percentages at each pixel, is an important task for hyperspectral analysis, visualization and understanding. From an unsupervised learning ... More

Secrecy Outage Analysis for Cooperative NOMA Systems with Relay Selection SchemeNov 08 2018This paper considers the secrecy outage performance of a multiple-relay assisted non-orthogonal multiple access (NOMA) network over Nakagami-$m$ fading channels. Two slots are utilized to transmit signals from the base station to destination. At the first ... More

Toward high-frequency operation of spin lasersAug 17 2015Aug 25 2015Injecting spin-polarized carriers into semiconductor lasers provides important opportunities to extend what is known about spintronic devices, as well as to overcome many limitations of conventional (spin-unpolarized) lasers. By developing a microscopic ... More

A Systematic Analysis for State-of-the-Art 3D Lung Nodule Proposals GenerationJan 09 2018Lung nodule proposals generation is the primary step of lung nodule detection and has received much attention in recent years . In this paper, we first construct a model of 3-dimension Convolutional Neural Network (3D CNN) to generate lung nodule proposals, ... More

Time-Inconsistent Stochastic Linear-quadratic Differential GameJul 03 2016We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We define an ... More

The augmentation category map induced by exact Lagrangian cobordismsJun 19 2016To a Legendrian knot, one can associate an $\mathcal{A}_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and ... More

Joining measures for horocycle flows on abelian coversJul 12 2016Jul 13 2016Let $S_0$ be a $\mathbb{Z}^d$-cover of a compact hyperbolic surface for $d=1,2$. We classify all locally finite joining measures for horocycle flows on the unit tangent bundle of $S_0\times S$ for any hyperbolic surface $S$. We will also discuss several ... More

A Lucas-type congruence for q-Delannoy numbersAug 09 2015We prove a Lucas-type congruence for q-Delannoy numbers.

Ergodic recurrence and bounded gaps between primesAug 14 2016Aug 19 2016Let $(X,B_X,\mu,T)$ be a measure-preserving probability system with $T$ is invertible. Suppose that $A\in B_X$ with $\mu(A)>0$ and $\epsilon>0$. For any $m\geq 1$, there exist infinitely many primes $p_0,p_1,\ldots,p_m$ with $p_0<\cdots<p_m$ such that ... More

A note on the Polignac numbersJun 09 2013Suppose that $k\geq 3.5\times 10^6$ and $\hH=\{h_1,\ldots,h_{k_0}\}$ is admissible. Then for any $m\geq 1$, the set $$ \{m(h_j-h_i):\,h_i<h_j\} $$ contains at least one Polignac number.

Rational Normal Curves on Low Degree Complete IntersectionsOct 13 2013May 24 2016This is the second in a sequence of papers on the geometry of spaces of rational normal curves on smooth complete intersections. For a smooth complete intersection X, we consider a general fiber \mathbb{F} of the evaluation map ev of Kontsevich moduli ... More

The fractional Brownian motion and the halo mass functionOct 16 2006The fractional Brownian motion with index $\alpha$ is introduced to construct the fractional excursion set model. A new mass function with single parameter $\alpha$ is derived within the formalism, of which the Press-Schechter mass function (PS) is a ... More

Equivariant Phantom mapsJun 29 2001A successful generalization of phantom map theory to the equivariant case for all compact Lie groups is obtained in this paper. One of the key observations is the discovery of the fact that homotopy fiber of equivariant completion splits as product of ... More

Having the H-space structure is not a generic propertyJun 29 2001In this note, we answer in negative a question posed by McGibbon about the generic property of H-space structure. In fact we verify the conjecture of Roitberg. Incidentally, the same example also answers in negative the open problem 10 in McGibbon.

The Very Basics of Higher-Spin TheoryFeb 13 2017These notes are based on two lectures given at the Twelfth Modave Summer School in Mathematical Physics 2016. The Fronsdal equation and action for both Minkowski and (A)dS backgrounds are discussed in detail.

Triviality and Split of Vector Bundles on Rationally Connected VarietiesOct 22 2013Feb 07 2014In this paper, we give a simple proof of a triviality criterion due to I.Biswas and J.Pedro and P.Dos Santos. We also prove a vector bundle on a homogenous space is trivial if and only if the restrictions of the vector bundle to Schubert lines are trivial. ... More

p-adic deformation of graph cyclesOct 12 2016Mar 23 2017In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex projective manifolds. ... More

Remarks on 1-D Euler Equations with Time-Decayed DampingOct 27 2015We study the 1-d isentropic Euler equations with time-decayed damping \begin{equation} \left\{ \begin{aligned} &\partial_t \rho+\partial_x(\rho u)=0, \\ &\partial_t(\rho u)+ \partial_x(\rho u^2)+\partial_xp(\rho)=-\frac{\mu}{1+t}\rho u,\\ &\rho|_{t=0}=1+\varepsilon\rho_0(x),u|_{t=0}=\varepsilon ... More

Geometry of Rational Curves on Low degree Complete IntersectionsOct 13 2013Jan 15 2017For a smooth complete intersection X, we consider a general fiber \mathbb{F} of the evaluation map ev of Kontsevich moduli space \bar{M}_{0,m}(X,m)\rightarrow X^m and the forgetful functor F : \mathbb{F} \rightarrow \bar{M}_{0,m}. We prove that a general ... More

The Multiple Permutation Problem and Some ConjecturesJul 27 2010In this paper, we proposed an interesting problem that might be classified into enumerative combinatorics. Featuring a distinctive two-fold dependence upon the sequences' terms, our problem can be really difficult, which calls for novel approaches to ... More

On finite marked length spectral rigidity of hyperbolic cone surfaces and the Thurston metricMar 06 2017We study the geometry of hyperbolic cone surfaces, possibly with cusps or geodesic boundaries. We prove that any hyperbolic cone structure on a surface of non-exceptional type is determined up to isotopy by the geodesic lengths of a finite specific homotopy ... More

Arithmetic properties of q-Fibonacci numbers and q-Pell numbersAug 27 2005Aug 31 2005We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.

Affine equivalence and saddle connection graphs of translation surfacesSep 14 2018To every translation surface, we associate a saddle connection graph, which is a subgraph of the arc graph. We prove that every isomorphism between two saddle connection graphs is induced by an affine homeomorphism between the underlying translation surfaces. ... More

On the number of distinct prime factors of $nj+a^hk$Jul 12 2009Aug 06 2009Let $\omega(n)$ denote the number of distinct prime factors of $n$. Then for any given $K\geq 2$, small $\epsilon>0$ and sufficiently large (only depending on $K$ and $\epsilon$) $x$, there exist at least $x^{1-\epsilon}$ integers $n\in[x,(1+K^{-1})x]$ ... More

On the integers not of the form $p+2^a+2^b$May 25 2009Jul 07 2009We prove that |{1<=y<=x: y is odd and not of the form p+2^a+2^b}|>>x^{1-\epsilon} for any \epsilon>0, where the implied constant only depends on \epsilon.

A Nonlinear Singular Diffusion Equation with SourceApr 06 2015In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which depends on initial ... More

On simultaneous conjugation of permutationsOct 21 2018In this paper we give an affirmative answer to a conjecture proposed by Danny Neftin, that is, if the commutator of two permutations has at least n-4 fixed points where two permutations are in degree n symmetric group, then there exists a permutation ... More

Status and Perspectives of the CRAFTS Extra-Galactic HI SurveyMar 15 2019The Five-hundred-meter Aperture Spherical radio Telescope(FAST) is expected to complete its commissioning in 2019. FAST will soon begin the Commensal Radio Astronomy FasT Survey(CRAFTS), a novel and unprecedented commensal drift scan survey of the entire ... More

Status and perspectives of the CRAFTS extra-galactic HI surveyMar 15 2019Mar 21 2019The Five-hundred-meter Aperture Spherical radio Telescope(FAST) is expected to complete its commissioning in 2019. FAST will soon begin the Commensal Radio Astronomy FasT Survey(CRAFTS), a novel and unprecedented commensal drift scan survey of the entire ... More

Effective equidistribution of circles in the limit sets of Kleinian groupsJan 31 2016Consider a general circle packing $\mathcal{P}$ in the complex plane $\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is convex-cocompact or its critical exponent is greater than 1, we obtain an effective equidistribution for small ... More

A note on enumerating colored integer partitionsSep 21 2015In this short note, we give basic enumerative results on colored integer partitions.

A generalized Tian-Todorov theoremOct 27 2013May 24 2016Let X be a smooth proper variety with torsion canonical bundle. Suppose L is a line bundle on X. We prove the pair (X,L) is unobstructed if one of the following conditions holds, (1) the line bundle L is ample, (2) the fundamental group {\pi}_1(X) of ... More

Exact Lagrangian Fillings of Legendrian $(2,n)$ torus linksJul 11 2016For a Legendrian $(2,n)$ torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and K\'alm\'an constructed $C_n$ exact Lagrangian fillings, where $C_n$ is the $n$-th Catalan number. We show that these exact Lagrangian fillings are pairwise ... More

Effective equidistribution of circles in the limit sets of Kleinian groupsJan 31 2016Feb 21 2017Consider a general circle packing $\mathcal{P}$ in the complex plane $\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is convex-cocompact or its critical exponent is greater than 1, we obtain an effective equidistribution for small ... More

Landslide Monitoring based on Terrestrial Laser Scanning: A Novel Semi-automatic WorkflowSep 01 2018In this paper, we propose a workflow that uses Terrestrial Laser Scanning(TLS) to semi-automatically monitor landslide and then test it in practice. Firstly, several groups of TLS stations are set on different time to collect the raw point cloud of the ... More

SAT is a problem with exponential complexity measured by negentropyDec 03 2014Sep 21 2015In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of computation and ... More

Colour Dependence of the Distribution of IRAS Galaxies revealed by Multifractal MeasuresApr 11 2006Jul 04 2006Multifractal measures are applied to three IRAS galaxy subsamples selected by colour from the PSCz catalogue. As shown by generalised dimension spectrum, hot IRAS galaxies are found less clustered than cold galaxies, but the difference is very weak. An ... More

A Proof of Milnor conjecture in dimension 3Mar 23 2017We present a proof of Milnor conjecture in dimension 3 based on Cheeger-Colding theory on limit spaces of manifolds with Ricci curvature bounded below. It is different from [Liu] that relies on minimal surface theory.

Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groupsSep 26 2018Jan 31 2019We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature with additional stability condition on $\widetilde{M}$, the Riemannian universal cover of $M$. We prove that if any tangent cone of $\widetilde{M}$ at infinity is ... More

Non-trivial Kazhdan-Lusztig coefficients of affine Weyl groupsApr 06 2018In this paper we show that the leading coefficients $\mu(y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in the affine Weyl group of type $\widetilde{B_n}$ can be $n$; in the cases of types $\widetilde{C_n}$ and $\widetilde{D_n}$ they can ... More

Vague partition, fuzzy sets and their axiomatical foundationsJun 24 2015Based on the in-depth analysis of the nature and features of vague phenomenon, this paper focuses on establishing the axiomatical foundation of the membership degree theory for vague phenomenon, presents an axiomatic system of governing membership degrees ... More

Spaces of conics on low degree complete intersectionsOct 13 2013Jan 09 2017Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smooth complete intersection. The main ingredients of the proof are a criterion ... More

Derived equivalences for Cohen-Macaulay Auslander algebrasSep 20 2010Mar 29 2011Let $A$ and $B$ be Gorenstein Artin algebras of Cohen-Macaulay finite type. We prove that, if $A$ and $B$ are derived equivalent, then their Cohen-Macaulay Auslander algebras are also derived equivalent.

A remark on Zoloterav's theoremJan 02 2006Let n>=3 be an odd integer. For any integer a prime to n, define the permutation gamma_{a,n} of {1,...,(n-1)/2} by gamma_{a,n}(x)=n-\dec{ax}_n if {ax}_n>=(n+1)/2, and {ax}_n if {ax}_n<=(n-1)/2, where {x}_n denotes the least nonnegative residue of x modulo ... More

A generalization of Carlitz's congruenceMar 21 2006Jul 03 2006In this paper, we propose a generalization of a congruence due to Carlitz.

Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent dampingSep 20 2016We study the isentropic Euler equations with time-dependent damping, given by $\frac{\mu}{(1+t)^\lambda}\rho u$. Here, $\lambda,\mu$ are two non-negative constants to describe the decay rate of damping with respect to time. We will investigate the global ... More

Non-backtracking operator for Ising model and its application in attractor neural networksSep 10 2014The non-backtracking operator was recently shown to give a redemption for spectral clustering in sparse graphs. In this paper we consider non-backtracking operator for Ising model on a general graph with a general coupling distribution by linearizing ... More

The redshift and geometrical aspect of photonsApr 09 2007The cosmological redshift phenomenon can be described by the dark matter field fluid model, the results deduced from this model agree very well with the observations. The observed cosmological redshift of light depends on both the speed of the emitter ... More

Spaces of conics on low degree complete intersectionsOct 13 2013May 23 2016Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smooth complete intersection. The main ingredients of the proof are a criteria ... More

First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p)Oct 11 2015Dec 05 2016We construct some admissible Banach representations of GL_2(Q_p) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of G_{Q_p} via the p-adic local Langlands correspondence. To achieve ... More

Calculating Vacuum Energy as a Possible Explanation of the Dark EnergyJan 20 2011Jun 15 2011We carried out a study of the properties of the $\lambda \phi^4$ field solutions. By constructing Gaussian wave packets to calculate the $S$ matrix, we show that the probability of the vacuum unbroken state transfers to the broken state is about $10^{-52}$. ... More

Meson Mass Spectrum of Heavy-Light Quarks Combinations with Dirac EquationJun 15 2011Nov 23 2011We use the Dirac equation to study the mass spectrum of mesons with heavy-light quark combinations. First we study the Dirac equation with spherically symmetry and funnel potential, and apply them on the hydrogen-like atom problem to check the correctness ... More

Joining measures for horocycle flows on abelian coversJul 12 2016Dec 06 2017A celebrated result of Ratner from the eighties says that two horocycle flows on hyperbolic surfaces of finite area are either the same up to algebraic change of coordinates, or they have no non-trivial joinings. Recently, Mohammadi and Oh extended Ratner's ... More

Collaborative Recommendation with Auxiliary Data: A Transfer Learning ViewJul 09 2014Intelligent recommendation technology has been playing an increasingly important role in various industry applications such as e-commerce product promotion and Internet advertisement display. Besides users' feedbacks (e.g., numerical ratings) on items ... More

Rational homotopy theory and nonnegative curvatureJun 29 2001In this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact nonnegative curved manifolds ... More

jQuery.Feyn: Drawing Feynman Diagrams with SVGNov 26 2013jQuery.Feyn is a tool for drawing Feynman diagrams with Scalable Vector Graphics (SVG), written in JavaScript and runs in modern browsers. It features predefined propagator styles, vertex types, and symbols. Math formulae can be included as external graphics, ... More

On consecutive happy numbersJul 08 2006Jul 27 2006Let e>=1 and b>=2 be integers. For a positive integer n=\sum_{j=0}^ka_jb^j with 0<=a_j<b, define T_{e,b}(n)=\sum_{j=0}^ka_j^e. n is called (e,b)-happy if T_{e,b}^r(n)=1 for some r>=0, where T_{e,b}^r is the r-th iteration of T_{e,b}. In this paper, we ... More

Robust Spectral Detection of Global Structures in the Data by Learning a RegularizationSep 09 2016Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or ... More

Exact solutions, finite time singularities and non-singular universe models from a variety of $Λ(t)$ cosmologiesDec 04 2017Jan 05 2018Cosmological models with time dependent $\Lambda$ (read as $\Lambda (t)$) have been investigated widely in the literature. Models that solve background dynamics analytically, are of special interest. Additionally, the allowance of past or future singularities ... More

Propagation of Delayed Lattice Differential Equations without Local QuasimonotonicityMay 06 2014This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice ... More

Robust Clustering Oracle and Local Reconstructor of Cluster Structure of GraphsApr 22 2019Due to the massive size of modern network data, local algorithms that run in sublinear time for analyzing the cluster structure of the graph are receiving growing interest. Two typical examples are local graph clustering algorithms that find a cluster ... More

Regularity and geometric character of solution of a degenerate parabolic equationApr 07 2015This work studies the regularity and the geometric significance of solution of the Cauchy problem for a degenerate parabolic equation $u_{t}=\Delta{}u^{m}$. Our main objective is to improve the H$\ddot{o}$lder estimate obtained by pioneers and then, to ... More

A q-analogue of Lehmer's congruenceJul 25 2005Aug 17 2005We establish the q-analogue of a classical congruence of Lehmer. Also, the q-analogues of two congruences of Morley and Granville are given.

A simple proof of Gopakumar-Vafa conjecture for local toric Calabi-Yau manifoldsOct 26 2004Dec 15 2004We prove Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds. It's also proved that the local Gopakumar-Vafa invariants of a given class at large genus vanish.

Factors of Some Lacunary q-Binomial SumsJan 28 2012Jun 03 2012In this paper, we prove a divisibility result for the lacunary $q$-binomial sum $$ \sum_{k\equiv r\pmod{c}}(-1)^kq^{\binom{k}{2}}\qbinom{n}{k}{q}\qbinom{(k-r)/c}{l}{q^{c}}. $$

p-adic deformation of graph cyclesOct 12 2016Oct 14 2016In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. We give a positive answer to Bloch-Esnault-Kerz conjecture for some graph cycles if the infinitesimal Torelli theorem holds.

SAT problem and statistical distanceFeb 26 2015Sep 22 2015In this paper with two equivalent representations of the information contained by a SAT formula, the reason why string generated by succinct SAT formula can be greatly compressed is firstly presented based on Kolmogorov complexity theory. Then what strings ... More

Magnetosphere structure of a Kerr black hole: marginally force-free equatorial boundary conditionJul 15 2018Sep 23 2018The role of equatorial boundary condition in the structure of a force-free black hole magnetosphere was rarely discussed, since previous studies have been focused on the field lines entering the horizon. However, recent high-accuracy force-free electrodynamics ... More

Emergence from Symmetry: A New Type of Cellular AutomataMar 17 2010Jul 25 2010In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich palette of configurations, ... More

Automorphism and Cohomology I: Fano variety of lines and CubicNov 17 2015Oct 12 2016In this paper, we prove a general principle of lifting an automorphism from positive characteristic to zero characteristic. We based on the principle to prove the automorphism group of Fano variety of cubic threefold (fourfold) acts on its cohomology ... More

Lehmer's type congruences for lacunary harmonic sumsMay 07 2009Oct 10 2009In this paper, we study the Lehmer's type congruences for lacunary harmonic sums.

q-Analogue of Gauss' Divisibility TheoremApr 05 2008We give a q-analogue of Gauss' divisibility theorem

Relative derived equivalences and relative homological dimensionsJan 25 2014Let $\mathscr{A}$ be a small abelian category. For a closed subbifunctor $F$ of $\Ext_{\mathscr{A}}^{1}(-,-)$, Buan has generalized the construction of the Verdier's quotient category to get a relative derived category, where he localized with respect ... More

The augmentation category map induced by exact Lagrangian cobordismsJun 19 2016May 23 2017To a Legendrian knot, one can associate an $\mathcal{A}_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and ... More

Spectral estimation of the percolation transition in clustered networksOct 04 2017There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight when the network ... More

T2Ku: Building a Semantic Wiki of MathematicsJan 27 2012We introduce T2Ku, an open source project that aims at building a semantic wiki of mathematics featuring automated reasoning(AR) techniques. We want to utilize AR techniques in a way that truly helps mathematical researchers solve problems in the real ... More

Evaluating accuracy of community detection using the relative normalized mutual informationJan 15 2015Oct 28 2015The Normalized Mutual Information (NMI) has been widely used to evaluate the accuracy of community detection algorithms. However in this article we show that the NMI is seriously affected by systematic errors due to finite size of networks, and may give ... More

Inference of kinetic Ising model on sparse graphsJul 23 2012Based on dynamical cavity method, we propose an approach to the inference of kinetic Ising model, which asks to reconstruct couplings and external fields from given time-dependent output of original system. Our approach gives an exact result on tree graphs ... More

On divisibility of sums of Apery polynomialsAug 07 2011For any positive integers $m$ and $\alpha$, we prove that $$\sum_{k=0}^{n-1}\epsilon^k(2k+1)A_k^{(\alpha)}(x)^m\equiv0\pmod{n}, $$ where $\epsilon\in\{1,-1\}$ and $$ A_n^{(\alpha)}(x)=\sum_{k=0}^n\binom{n}{k}^{\alpha}\binom{n+k}{k}^{\alpha}x^k.$$

First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p)Oct 11 2015We construct some admissible Banach representations of GL_2(Q_p) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of G_{Q_p} via the p-adic local Langlands correspondence. To achieve ... More

The evolution of the Earth-Moon system based on the dark matter field fluid modelApr 01 2007Jan 13 2008The evolution of Earth-Moon system is described by the dark matter field fluid model proposed in the Meeting of Division of Particle and Field 2004, American Physical Society. The current behavior of the Earth-Moon system agrees with this model very well ... More

Local mixing on abelian covers of hyperbolic surfaces with cuspsDec 16 2017We prove the local mixing theorem for geodesic flows on abelian covers finite volume hyperbolic surfaces with cusps, which is a continuation of the work of Oh-Pan. We also describe applications to counting problems and the prime geodesic theorem.

A note on enumerating colored integer partitionsSep 21 2015Mar 28 2018In this short note, we give basic enumerative results on colored integer partitions.

Tensor Transpose and Its PropertiesNov 06 2014Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor ... More

Growth Estimates and Integral Representations of Harmonic and Subharmonic FunctionsJun 09 2009There are ten chapters in this dissertation, which focuses on nine contents: growth estimates for a class of subharmonic functions in the half plane; growth estimates for a class of subharmonic functions in the half space; a generalization of harmonic ... More

Using Malware Self-Defence Mechanism to Harden Defence and Remediation ToolsJan 06 2018Malware are becoming a major problem to every individual and organization in the cyber world. They are advancing in sophistication in many ways. Besides their advanced abilities to penetrate and stay evasive against detection and remediation, they have ... More

Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groupsOct 16 2017Oct 18 2017We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature. We show that if there is an integer $k$ such that any tangent cone at infinity of the Riemannian universal cover of $M$ is a metric cone, whose maximal Euclidean ... More

Balance functions of (un)identified hadrons in Pb--Pb, p--Pb, and pp collisions at the LHCJul 26 2018In ultrarelativistic heavy-ion collisions, correlations of particles with opposite quantum numbers provide insight into quark production mechanisms and time scales, collective motion, and re-scattering in the hadronic phase. The longitudinal and azimuthal ... More