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Ultrafast dynamic evolution of multilevel systems in medium-strength laser fieldsOct 13 2018The ultrafast dynamic evolution of an atomic system under medium-strength laser fields is studied by performing transient absorption measurement. An analytical model developed from perturbation theory with a modified transition dipole moment is presented ... More

AWG-based Nonblocking Shuffle-Exchange NetworksJul 10 2019Optical shuffle-exchange networks (SENs) have wide application in different kinds of interconnection networks. This paper proposes an approach to construct modular optical SENs, using a set of arrayed waveguide gratings (AWGs) and tunable wavelength converters ... More

Modular AWG-based Optical Shuffle NetworkJul 27 2017This paper proposes an arrayed-waveguide grating (AWG) based wavelength-division-multiplexing (WDM) shuffle network. Compared with previous optical shuffle networks, our proposal is compact, easy to implement, highly scalable, and cost effective.

Fairness of Congestion-Based Congestion Control: Experimental Evaluation and AnalysisJun 28 2017Jul 26 2017BBR is a new congestion-based congestion control algorithm proposed by Google. A BBR flow sequentially measures the bottleneck bandwidth and round-trip delay of the network pipe, and uses the measured results to govern its sending behavior, maximizing ... More

A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret SharingMar 23 2015In this paper, a class of two-weight and three-weight linear codes over $\gf(p)$ is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain bounds on linear ... More

Lasing with cell-endogenous fluorophores: parameters and conditionsJun 30 2017The notion of lasing with biologics has recently been realized and has since rapidly developed with the collective objective of creating lasers $\textit{in vivo}$. One limitation of achieving this goal is the requirement of exogenous laser dyes and fluorescent ... More

Time Consistent Stopping For The Mean-Standard Deviation Problem --- The Discrete Time CaseFeb 23 2018Apr 19 2019Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times ... More

A restriction for singularities on collapsing orbifoldsJan 24 2011Jul 07 2011An orbifold $X$ is locally homeomorphic to $G_x\backslash B_r(0)$, where $G_x$ is a finite group acting on $B_r(0)\subset{\mathbb R}^n$, so that $G_x(0)=0$. For collapsing orbifolds with isolated singularities, we show there is a uniform bound in $|G_x|$. ... More

Semantic Web: Who is who in the field - A bibliometric analysisDec 21 2010The Semantic Web is one of the main efforts aiming to enhance human and machine interaction by representing data in an understandable way for machines to mediate data and services. It is a fast-moving and multidisciplinary field. This study conducts a ... More

On List-decodability of Random Rank Metric CodesJan 13 2014Jan 23 2014In the present paper, we consider list decoding for both random rank metric codes and random linear rank metric codes. Firstly, we show that, for arbitrary $0<R<1$ and $\epsilon>0$ ($\epsilon$ and $R$ are independent), if $0<\frac{n}{m}\leq \epsilon$, ... More

A Construction for Constant-Composition CodesFeb 13 2008By employing the residue polynomials, a construction of constant-composition codes is given. This construction generalizes the one proposed by Xing[16]. It turns out that when d=3 this construction gives a lower bound of constant-composition codes improving ... More

Axiomatization and complexity of modal logic with knowing-what operator on model class KSep 25 2016Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In "Conditionally Knowing ... More

Analogue of Null Geodesic in Quantum SpacetimeJan 23 2018In classical spacetime null geodesics give information on where free massless particles travel. In quantum spacetime where quantum indefiniteness renders spacetime fuzzy null geodesics as sharp trajectories cannot be retained. We propose a "tendency postulate" ... More

Generalizing EntanglementJul 23 2017Feb 24 2018The expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being spacelike and timelike, can they still be entangled? If so, how does one measure ... More

Minimal cones and self-expanding solutions for mean curvature flowsMar 09 2015May 08 2019In this paper, we study self-expanding solutions for mean curvature flows and their relationship to minimal cones in Euclidean space. In [18], Ilmanen proved the existence of self-expanding hypersurfaces with prescribed tangent cones at infinity. If the ... More

Low temperature thermal history reconstruction using apatite fission-track length distribution and apatite U-Th/He ageMay 24 2017Low temperature thermochronology plays a key role in the study of tectonic evolution of the upper crust. The general application of thermal history modelling of apatite fission-track analysis requires both the parameters of the apparent age together with ... More

Cosmological Sphaleron from Real Tunneling and Its FateJul 25 1994Aug 05 1994We show that the cosmological sphaleron of Einstein-Yang-Mills system can be produced from real tunneling geometries. The sphaleron will tend to roll down to the vacuum or pure gauge field configuration, when the universe evolves in the Lorentzian signature ... More

Integral Formulas for Higher Order Conformally Invariant Fermionic OperatorsNov 10 2017Mar 25 2019In this paper, we establish higher order Borel-Pompeiu formulas for conformally invariant fermionic operators in higher spin theory, which is the theory of functions on m-dimensional Euclidean space taking values in arbitrary irreducible representations ... More

Borel reducibility and finitely Holder(α) embeddabilityJul 02 2010Let $(X_n,d_n),\,n\in\Bbb N$ be a sequence of pseudo-metric spaces, $p\ge 1$. For $x,y\in\prod_{n\in\Bbb N}X_n$, let $(x,y)\in E((X_n)_{n\in\Bbb N};p)\Leftrightarrow\sum_{n\in\Bbb N}d_n(x(n),y(n))^p<+\infty$. For Borel reducibility between equivalence ... More

Characterization of $\ell_p$-like and $c_0$-like equivalence relationsJun 23 2010Let $X$ be a Polish space, $d$ a pseudo-metric on $X$. If $\{(u,v):d(u,v)<\delta\}$ is ${\bf\Pi}^1_1$ for each $\delta>0$, we show that either $(X,d)$ is separable or there are $\delta>0$ and a perfect set $C\subseteq X$ such that $d(u,v)\ge\delta$ for ... More

Certain Metric Properties of Level HypersurfacesApr 21 2018This note establishes several integral identities relating certain metric properties of level hypersurfaces of Morse functions.

Higher genus Welschinger invariants under real surgeriesOct 09 2017Jan 14 2018According to [3], a real surgery of a real del Pezzo surface $X_\mathbb{R}$ along a real sphere $S$ is a modification of the real structure on $X_\mathbb{R}$ in a neighborhood of $S$. In this paper, we study the behavior of higher genus Welschinger invariants ... More

Hassle-free Approach to Thermal Transport Measurements Using Spatial-Temporal Temperature DataMar 07 2019Nanoscale engineering and novel materials have created interesting effects in thermal transport. Thermal conductivity can now be different due to physical and heating sizes. Also, highly anisotropic thermal conductivity can result from unique material ... More

Companion points and locally analytic socle for $\mathrm{GL}_2(L)$Feb 29 2016Let $p>2$ be a prime number, and $L$ be a finite extension of $\mathbb{Q}_p$, we prove Breuil's locally analytic socle conjecture for $\mathrm{GL}_2(L)$, showing the existence of all the companion points on the definite (patched) eigenvariety. This work ... More

$\mathcal{L}$-invariants, partially de Rham families and local-global compatibilityAug 29 2015Feb 22 2016Let $F_{\wp}$ be a finite extension of $\mathbb{Q}_p$. By considering partially de Rham families, we establish a Colmez-Greenberg-Stevens formula (on Fontaine-Mazur $\mathcal{L}$-invariants) for (general) $2$-dimensional semi-stable non-crystalline $\mathrm{Gal}(\overline{\mathbb{Q}_p}/F_{\wp})$-representations. ... More

Minimal cones and self-expanding solutions for mean curvature flowsMar 09 2015In this paper, we study self-expanding solutions for mean curvature flows and applications to minimal cones in Euclidean space. For an embedded mean convex (but not area-minimizing) cone $C$ pointing into a domain $\Omega$ with $\partial\Omega=C$, there ... More

The Application of Bayesian Technique for Particle IdentificationFeb 24 2006Oct 26 2006The PID problem in high energy physics experiments is analysed with Bayesian technique. The corresponding applicable method is presented.

Theoretical study of position-dependent defect formation in a single-walled carbon nanotube: Stability towards an open endJul 30 2006Point defects, including atom vacancy, add atom and Stone-Wale defect, close to a (5, 5) single-walled carbon nanotube (SWNT) end were studied by DFT, semi-empirical PM3 method and empirical Brenner Potential. It is found that closer to the SWNT opening ... More

A Note on Kaldi's PLDA ImplementationApr 02 2018Some explanations to Kaldi's PLDA implementation to make formula derivation easier to catch.

High dimensional deformed rectangular matrices with applications in matrix denoisingFeb 22 2017Apr 22 2017We consider the recovery of a low rank $M \times N$ matrix $S$ from its noisy observation $\tilde{S}$ in two different regimes. Under the assumption that $M$ is comparable to $N$, we propose two consistent estimators for $S$. Our analysis relies on the ... More

Quantum field theory with indefinite causal structureMay 22 2018Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may be relevant ... More

Reduction of correlations by quantum indefinite causal structureJun 06 2018We show that quantum indefinite causal structure generically reduce two-party correlations. For significant indefiniteness in the causal structure captured by some general conditions, the correlation is shown to be reduced down to zero. The result offers ... More

A Construction of Binary Linear Codes from Boolean FunctionsNov 01 2015Boolean functions have important applications in cryptography and coding theory. Two famous classes of binary codes derived from Boolean functions are the Reed-Muller codes and Kerdock codes. In the past two decades, a lot of progress on the study of ... More

A Sequence Construction of Cyclic Codes over Finite FieldsNov 20 2016Due to their efficient encoding and decoding algorithms, cyclic codes, a subclass of linear codes, have applications in communication systems, consumer electronics, and data storage systems. There are several approaches to constructing all cyclic codes ... More

Cyclic Codes from APN and Planar FunctionsJun 20 2012Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear functions and planar ... More

On equivalence relations generated by Schauder basesApr 01 2015In this paper, a notion of Schauder equivalence relation $\mathbb R^\mathbb N/L$ is introduced, where $L$ is a linear subspace of $\mathbb R^\mathbb N$ and the unit vectors form a Schauder basis of $L$. The main theorem is to show that the following conditions ... More

Asymptotics of cover times via Gaussian free fields: Bounded-degree graphs and general treesMar 22 2011Feb 25 2014In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field on the graph, ... More

Partial Gauss decomposition, \bf $U_q(\widehat{\frak{gl}(n-1)})\in U_q(\widehat{\frak{gl}(n)}) $ and Zamolodchikov algebraJan 19 1998We use the idea of partial Gauss decomposition to study structures related to $U_q(\widehat{{{\frak{gl}}}(n-1)})$ inside $U_q(\widehat{{{\frak{gl}}}(n)}) $. This gives a description of $U_q(\widehat{{{\frak{gl}}}(n)})$ as an extension of $U_q(\widehat{{{\frak{gl}}}(n-1)})$ ... More

Hopf algebra extension of a Zamolochikov algebra and its doubleDec 04 1996Dec 05 1996The particles with a scattering matrix R(x) are defined as operators $\Phi_i(z)$ satisfying the relation $ R_{i,j}^{j',i'}(x_1/x_2) \Phi_{i'}(x_1)\Phi_{j'}(x_2)= \Phi_i(x_2)\Phi_j(x_1)$. The algebra generated by those operators is called a Zamolochikov ... More

Three Occurrences of the Hyperbolic-Secant DistributionJan 07 2014Although it is the generator distribution of the sixth natural exponential family with quadratic variance function, the Hyperbolic-Secant distribution is much less known than other distributions in the exponential families. Its lack of familiarity is ... More

Connection Cochain of Abelian Extensions and Connection $1$-FormsJul 13 2019In this paper, we consider the concept of connection cochain of central extensions introduced by Moriyoshi and apply it to the abelian case. We will show the relationship between connection cochain and connection $1$-form of a principal bundle whose structure ... More

Variational Analysis of the Ky Fan $k$-normJan 27 2016In this paper, we will study some variational properties of the Ky Fan $k$-norm $\theta=\|\cdot\|_{(k)}$ of matrices, which are closed related to a class of basic nonlinear optimization problems involving the Ky Fan $k$-norm. In particular, for the basic ... More

Analysis of Massive Heterogeneous Temporal-Spatial Data with 3D Self-Organizing Map and Time VectorSep 27 2016Self-organizing map(SOM) have been widely applied in clustering, this paper focused on centroids of clusters and what they reveal. When the input vectors consists of time, latitude and longitude, the map can be strongly linked to physical world, providing ... More

Some results on locally analytic socle for $\mathrm{GL}_n(\mathbb{Q}_p)$Nov 21 2015We study some closed rigid subspaces of the eigenvarieties, constructed by using the Jacquet-Emerton functor for parabolic non-Borel subgroups. As an application (and motivation), we prove some new results on Breuil's locally analytic socle conjecture ... More

An ExpTime Procedure for Description Logic $\mathcal{ALCQI}$ (Draft)Mar 12 2007Mar 18 2007A worst-case ExpTime tableau-based decision procedure is outlined for the satisfiability problem in $\mathcal{ALCQI}$ w.r.t. general axioms.

Testing Lorentz and CPT Symmetries in Penning TrapsOct 28 2016A modified Dirac equation with general Lorentz- and CPT-violating operators in the electromagnetic field is studied. Constraints on and possible sensitivities to Lorentz-violating coefficients in the nonminimal sector up to mass-dimension six can be obtained ... More

On the Conditional Distribution of the Multivariate $t$ DistributionApr 02 2016As alternatives to the normal distributions, $t$ distributions are widely applied in robust analysis for data with outliers or heavy tails. The properties of the multivariate $t$ distribution are well documented in Kotz and Nadarajah's book, which, however, ... More

Causally neutral quantum physicsFeb 15 2019In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present an algebraic ... More

Two paradoxical results in linear models: the variance inflation factor and the analysis of covarianceMar 09 2019A result from a standard linear model course is that the variance of the ordinary least squares (OLS) coefficient of a variable will never decrease if we add additional covariates. The variance inflation factor (VIF) measures the increase of the variance. ... More

Tensor Powers of the Defining Representation of $S_n$Aug 21 2015Feb 05 2016We give a decomposition formula for tensor powers of the defining representation of $S_n$ and apply it to bound the mixing time of a Markov chain on $S_n$.

Dynamics of Yang-Mills Cosmology Bubbles in Bartnik-McKinnon SpacetimesApr 20 1995May 01 1995We investigate the dynamics of a Yang-Mills cosmology (YMC, the FRW type spacetime) bubble in the Bartnik-McKinnon (BK) spacetimes. Because a BK spacetime can be identified to a YMC spacetime with a finite scale factor in the neighborhood of the origin, ... More

$\mathcal{L}$-invariants and local-global compatibility for the group $\mathrm{GL}_2/F$Jan 27 2015Feb 18 2016Let $F$ be a totally real number field, $\wp$ a place of $F$ above $p$. Let $\rho$ be a $2$-dimensional $p$-adic representation of $\mathrm{Gal}(\bar{F}/F)$ which appears in the \'etale cohomology of quaternion Shimura curves (thus $\rho$ is associated ... More

Explicit Blowing-up Solutions to the Schrödinger Maps from ${\bf R}^2$ to the Hyperbolic 2-Space ${\bf H}^2$Dec 01 2003Jun 01 2009In this article, we prove that the equation of the Schr\"odinger maps from ${\bf R}^2$ to the hyperbolic 2-space ${\bf H}^2$ is SU(1,1)-gauge equivalent to the following 1+2 dimensional nonlinear Schr\"odinger-type system of unknown three complex functions ... More

On the Gradient of Harmonic FunctionsNov 10 2018Dec 05 2018For a harmonic function u on Euclidean space, this note shows that its gradient is essentially determined by the geometry of its level hypersurfaces. Specifically, the factor by which |grad(u)| changes along a gradient flow is completely determined by ... More

Asymptotics of empirical eigen-structure for high dimensional sample covariance matrices of general formAug 21 2017Sep 22 2017In this paper, we study the local asymptotics of the eigenvalues and eigenvectors for a general class of sample covariance matrices, where the spectrum of the population covariance matrices can have a finite number of spikes and bulk components. Our paper ... More

Henri Lebesgue and the End of Classical Theories on CalculusJan 11 2012In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the theories on current ... More

The Radical Mistakes in the Theories on Calculus of Cauchy-Lebesgue SystemDec 10 2011The misunderstanding of the concept of differentials in the theories on calculus of Cauchy-Lebesgue system was exposed in this paper. The defects of the definition of differentials and the associated mistakes in the differentiation of composite functions ... More

Singular vector distribution of sample covariance matricesNov 06 2016Sep 16 2017We consider a class of sample covariance matrices of the form $Q=TXX^{*}T^*,$ where $X=(x_{ij})$ is an $M \times N$ rectangular matrix consisting of i.i.d entries and $T$ is a deterministic matrix satisfying $T^*T$ is diagonal. Assuming $M$ is comparable ... More

Construction of certain rational functions on the moduli stack of Drinfeld shtukasOct 20 2018We construct certain rational functions (modular units) on the moduli stack of Drinfeld shtukas. The divisors of these rational functions are supported on horospherical divisors of the moduli stack. The key to our construction is a vanishing theorem for ... More

A toy model of shtukasFeb 13 2018Nov 02 2018Motivated by the question of constructing certain rational functions (modular units) on the moduli stack of Drinfeld shtukas, we introduce the notion of toy shtukas. We prove basic properties of the moduli scheme of toy shtukas. Analogously to horospherical ... More

Gravitational quasinormal modes of black holes in Einstein-aether theoryDec 18 2018The local Lorentz violation (LV) in gravity sector should show itself in derivation of the characteristic quasinormal modes (QNMs) of black hole mergers from their general relativity case. In this paper, I study QNMs of the gravitational field perturbations ... More

A family of ovoids in PG(3, 2^m) from cyclic codesFeb 10 2018Ovoids in $\PG(3, q)$ have been an interesting topic in coding theory, combinatorics, and finite geometry for a long time. So far only two families are known. The first is the elliptic quadratics and the second is the Tits ovoids. In this article, we ... More

Cyclic Codes from Cyclotomic Sequences of Order FourJul 11 2012Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In this paper, three ... More

Linear Codes from Some 2-DesignsMar 23 2015A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the literature. In this ... More

A Remark On the FRTS realization and Drinfeld Realization of Quantum Affine Superalgebra $U_q(\hat {osp}(1,2))$May 13 1999May 14 1999In this paper, we present the hidden symmetry behind the Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky realization of quantum affine superalgebras $U_q(\hat {osp}(1,2))$ and add the q-Serre relation to the Drinfeld realization of $U_q(\hat {osp}(1,2))$ ... More

Spinor Representations of $U_q(\hat{\frak gl}(n))$ and Quantum Boson-Fermion CorrespondenceOct 17 1995Nov 20 1995This is an extension of quantum spinor construction in \cite{DF2}. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum spinor representations of $U_q(\hat{\frak gl}(n))$ and explain ... More

On some partially de Rham Galois representationsOct 16 2014Sep 01 2015We study some partially de Rham representations of $\mathrm{Gal}(\bar{L}/L)$ for a finite unramified extension $L$ of $\mathbb{Q}_p$. We study some related subspaces of Galois cohomology and of cohomology of $B$-pairs. As an application, we associate ... More

Two Propositions Involving the Standard Representation of $S_n$Feb 10 2013We present here two standalone results from a forthcoming work on the analysis of Markov chains using the representation theory of $S_n$. First, we give explicit formulas for the decompositions of tensor powers of the defining and standard representations ... More

A paradox from randomization-based causal inferenceFeb 02 2014Jun 23 2016Under the potential outcomes framework, causal effects are defined as comparisons between potential outcomes under treatment and control. To infer causal effects from randomized experiments, Neyman proposed to test the null hypothesis of zero average ... More

Selective Radiative Heating of Nanostructures Using Hyperbolic MetamaterialsDec 16 2014Hyperbolic metamaterials (HMM) are of great interest due to their ability to break the diffraction limit for imaging and enhance near-field radiative heat transfer. Here we demonstrate that an annular, transparent HMM enables selective heating of a sub-wavelength ... More

Active Thermal Extraction of Near-field Thermal RadiationApr 08 2015Radiative heat transport between materials supporting surface-phonon polaritons is greatly enhanced when the materials are placed at sub-wavelength separation as a result of the contribution of near-field surface modes. However, the enhancement is limited ... More

Axiomatization and complexity of modal logic with knowing-what operator on model class KSep 25 2016Nov 25 2016Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In "Conditionally Knowing ... More

Cyclic Codes from Dickson PolynomialsJun 20 2012Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first and second kind ... More

Minimal cones and self-expanding solutions for mean curvature flowsMar 09 2015Jun 05 2017In this paper, we study self-expanding solutions for mean curvature flows and their relationship to minimal cones in Euclidean space. In [17], Ilmanen proved the existence of self-expanding hypersurfaces with prescribed tangent cones at infinity. If the ... More

Quantifying Causality in Quantum and General ModelsJan 19 2018In studies of entanglement, finding out if a state is entangled and quantifying the amount of entanglement contained in a state are related but different questions. Similarly in studies of causality, finding out the causal structures compatible with a ... More

Quantum from principles without assuming definite causal structureAug 01 2018There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational issues. Recent ... More

Graphs without large $K_{2,n}$-minorsFeb 05 2017The purpose of this paper is to characterize graphs that do not have a large $K_{2,n}$-minor. As corollaries, it is proved that, for any given positive integer $n$, every sufficiently large 3-connected graph with minimum degree at least six, every 4-connected ... More

A remark on degenerate singularity in three dimensional Ricci flowSep 05 2007We show that a rescale limit at any degenerate singularity of Ricci flow in dimension 3 is a steady gradient soliton. In particular, we give a geometric description of type I and type II singularities.

Subsequent singularities of mean convex mean curvature flows in smooth manifoldsFeb 09 2015Jan 05 2016For any $n$-dimensional smooth manifold $\Sigma$, we show that all the singularities of the mean curvature flow with any initial mean convex hypersurface in $\Sigma$ are cylindrical (of convex type) if the flow converges to a smooth hypersurface $M_{\infty}$ ... More

A rigidity theorem on the second fundamental form for self-shrinkersJan 27 2017In Theorem 3.1 of [12], we proved a rigidity result for self-shrinkers under the integral condition on the norm of the second fundamental form. In this paper, we relax the such bound to any finite constant (see Theorem 4.4 for details).

Balanced $k$-Center Clustering When $k$ Is A ConstantApr 08 2017The problem of constrained $k$-center clustering has attracted significant attention in the past decades. In this paper, we study balanced $k$-center cluster where the size of each cluster is constrained by the given lower and upper bounds. The problem ... More

Faster Balanced Clusterings in High DimensionSep 04 2018Sep 10 2018The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by the given lower ... More

High dimensional deformed rectangular matrices with applications in matrix denoisingFeb 22 2017Apr 23 2019We consider the recovery of a low rank $M \times N$ matrix $S$ from its noisy observation $\tilde{S}$ in two different regimes. Under the assumption that $M$ is comparable to $N$, we propose two consistent estimators for $S$. Our analysis relies on the ... More

\texttt{GooStats}: A GPU-based framework for multi-variate analysis in particle physicsDec 13 2018\texttt{GooStats} is a software framework that provides a flexible environment and common tools to implement multi-variate statistical analysis. The framework is built upon the \texttt{CERN ROOT}, \texttt{MINUIT} and \texttt{GooFit} packages. Running ... More

Comparative Penning-Trap Tests of Lorentz and CPT SymmetryJun 11 2019The theoretical and experimental prospects for Lorentz- and CPT-violating quantum electrodynamics in Penning traps are reviewed in this work. With the recent reported results for the measurements of magnetic moments for both protons and antiprotons, improvements ... More

Probabilistic Inferences in Bayesian NetworksNov 03 2010Nov 05 2010Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to complex problems. ... More

Quasinormal ringing of black holes in Einstein aether theoryJul 21 2017Oct 24 2017The gravitational consequence of local Lorentz violation (LV) should show itself in derivation of the characteristic quasinormal ringing of black hole mergers from their general relativity case. In this paper, we study quasinormal modes (QNMs) of the ... More

An infinite family of Steiner systems $S(2, 4, 2^m)$ from cyclic codesJan 21 2017Steiner systems are a fascinating topic of combinatorics. The most studied Steiner systems are $S(2, 3, v)$ (Steiner triple systems), $S(3, 4, v)$ (Steiner quadruple systems), and $S(2, 4, v)$. There are a few infinite families of Steiner systems $S(2, ... More

Hawking radiation and total entropy change as tunnelingFeb 02 2013Oct 21 2013In the frame of Hamilton-Jacobi method, the back-reactions of the radiating particles together with the total entropy change of the whole system are investigated. The emission probability from this process is found to be equivalent to the null geodesic ... More

A trichotomy for a class of equivalence relationsJan 06 2010Let $X_n, n\in\Bbb N$ be a sequence of non-empty sets, $\psi_n:X_n^2\to\Bbb R^+$. We consider the relation $E((X_n,\psi_n)_{n\in\Bbb N})$ on $\prod_{n\in\Bbb N}X_n$ by $(x,y)\in E((X_n,\psi_n)_{n\in\Bbb N})\Leftrightarrow\sum_{n\in\Bbb N}\psi_n(x(n),y(n))<+\infty$. ... More

Smallest Irreducible of the Form $x^2-dy^2$Mar 01 2016It is a classical result that prime numbers of the form $x^2+ny^2$ can be characterized via class field theory for an infinite set of $n$. In this paper we derive the function field analogue of the classical result. Then we apply an effective version ... More

Several Metric Properties of Level CurvesApr 21 2018This article establishes several remarkably simple identities relating certain metric invariants of level curves of real and complex functions. In particular, we relate lengths of level curves to their curvature and to the gradient field of the function. ... More

Bayesian Robust Inference of Sample Selection Using Selection-t ModelsJan 07 2014Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton proposed a selection-t ... More

Infinite families of $t$-designs from a type of five-weight codesJul 17 2016It has been known for a long time that $t$-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a $t$-design. While a lot of progress in the direction of constructing codes from ... More

Characterizing Level-set Families of Harmonic FunctionsDec 05 2018Families of hypersurfaces that are level-set families of harmonic functions are characterized by a simple analytic condition. Harmonic functions with a specified level-set family are constructed from geometric data. Emphasis is placed on the two-variable ... More

On cover times for 2D latticesOct 15 2011Jun 05 2012We study the cover time $\tau_{\mathrm{cov}}$ by (continuous-time) random walk on the 2D box of side length $n$ with wired boundary or on the 2D torus, and show that in both cases with probability approaching 1 as $n$ increases, $\sqrt{\tau_{\mathrm{cov}}}=\sqrt{2n^2}[\sqrt{2/\pi} ... More

Inverse of a matrix related to double zeta values of odd weightOct 21 2015In this paper, we give a proof of a conjecture made by Zagier about the inverse of some matrix related to double zeta values of parity $(\mathrm{even},\mathrm{odd})$. As a result, we obtain a family of Bernoulli number identities. We further generalize ... More

Renormalization and alpha-limit set for expanding Lorenz mapsMar 27 2007Jun 17 2009We show that there is a bijection between the renormalizations and proper completely invariant closed sets of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. Based on the properties of periodic orbit of ... More

Applying weighted PageRank to author citation networksFeb 09 2011This paper aims to identify whether different weighted PageRank algorithms can be applied to author citation networks to measure the popularity and prestige of a scholar from a citation perspective. Information Retrieval (IR) was selected as a test field ... More

Singular vector distribution of covariance matricesNov 06 2016We consider a class of covariance matrices of the form $Q=\Sigma^{\frac{1}{2}}XX^{*} \Sigma^{\frac{1}{2}},$ where $X=(x_{ij})$ is an $M \times N$ rectangle matrix consisting of i.i.d entries and $\Sigma$ is a diagonal positive definite matrix satisfying ... More