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Linear and quadratic in temperature resistivity from holographyJun 25 2016Nov 24 2016We present a new black hole solution in the asymptotic Lifshitz spacetime with a hyperscaling violating factor. A novel computational method is introduced to compute the DC thermoelectric conductivities analytically. We find that both the linear-T and ... More

Design of magnetic spirals in layered perovskites: extending the stability range far beyond room temperatureSep 27 2018In insulating materials with ordered magnetic spiral phases, ferroelectricity can emerge due to the breaking of inversion symmetry. This property is of both fundamental and practical interest, in particular with a view to exploiting it in low-power electronic ... More

Effect of transport-induced charge inhomogeneity on point-contact Andreev reflection spectra at ferromagnet-superconductor interfacesJun 06 2012We investigate the transport properties of a ferromagnet-superconductor interface within the framework of a modified three-dimensional Blonder-Tinkham-Klapwijk formalism. In particular, we propose that charge inhomogeneity forms via two unique transport ... More

Laue three dimensional neutron diffractionFeb 08 2019This article presents a measurement technique and data analysis tool to perform 3D grain distribution mapping and indexing of oligocrystalline samples using neutrons: Laue three-dimensional neutron diffraction (Laue3DND). The approach builds on forward ... More

Channel-Recurrent Autoencoding for Image ModelingJun 12 2017Mar 11 2018Despite recent successes in synthesizing faces and bedrooms, existing generative models struggle to capture more complex image types, potentially due to the oversimplification of their latent space constructions. To tackle this issue, building on Variational ... More

More on the normalized Laplacian Estrada indexJan 07 2014Let $G$ be a simple graph of order $N$. The normalized Laplacian Estrada index of $G$ is defined as $NEE(G)=\sum_{i=1}^Ne^{\lambda_i}$, where $\lambda_1,\lambda_2,\cdots,\lambda_N$ are the normalized Laplacian eigenvalues of $G$. In this paper, we give ... More

Structure and Physical Conditions in MHD Jets from Young StarsDec 28 2001We have constructed the foundations to a series of theoretical diagnostic methods to probe the jet phenomenon in young stars as observed at various optical forbidden lines. We calculate and model in a self-consistent manner the physical and radiative ... More

Estimating the distance Estrada indexJul 20 2014Suppose $G$ is a simple graph on $n$ vertices. The $D$-eigenvalues $\mu_1,\mu_2,\cdots,\mu_n$ of $G$ are the eigenvalues of its distance matrix. The distance Estrada index of $G$ is defined as $DEE(G)=\sum_{i=1}^ne^{\mu_i}$. In this paper, we establish ... More

Cycles in Random Bipartite GraphsOct 13 2013In this paper we study cycles in random bipartite graph $G(n,n,p)$. We prove that if $p\gg n^{-2/3}$, then $G(n,n,p)$ a.a.s. satisfies the following. Every subgraph $G'\subset G(n,n,p)$ with more than $(1+o(1))n^2p/2$ edges contains a cycle of length ... More

Bounds of distance Estrada index of graphsNov 19 2015Let $\lambda_1,\lambda_2,\cdots,\lambda_n$ be the eigenvalues of the distance matrix of a connected graph $G$. The distance Estrada index of $G$ is defined as $DEE(G)=\sum_{i=1}^ne^{\lambda_i}$. In this note, we present new lower and upper bounds for ... More

Bipancyclic subgraphs in random bipartite graphsNov 28 2012Dec 14 2012A bipartite graph on 2n vertices is bipancyclic if it contains cycles of all even lengths from 4 to 2n. In this paper we prove that the random bipartite graph $G(n,n,p)$ with $p(n)\gg n^{-2/3}$ asymptotically almost surely has the following resilience ... More

Bicomp: A Bilayer Scalable Nakamoto Consensus ProtocolSep 05 2018Blockchain has received great attention in recent years and motivated innovations in different scenarios. However, many vital issues which affect its performance are still open. For example, it is widely convinced that high level of security and scalability ... More

Clustering Bioactive Molecules in 3D Chemical Space with Unsupervised Deep LearningFeb 09 2019Unsupervised clustering has broad applications in data stratification, pattern investigation and new discovery beyond existing knowledge. In particular, clustering of bioactive molecules facilitates chemical space mapping, structure-activity studies, ... More

Visualising rate of change: application to age-specific fertilityJun 17 2014Dec 09 2015Visualisation methods help in the discovery of characteristics that might not have been apparent using mathematical models and summary statistics, and yet it has not received much attention in demography with the exceptions of scatter plot and Lexis surface. ... More

Nonparametric Bernstein-von Mises Phenomenon: A Tuning Prior PerspectiveNov 13 2014Jul 16 2015Statistical inference on infinite-dimensional parameters in a Bayesian framework is investigated. The main contribution of this paper is to demonstrate that nonparametric Bernstein-von Mises theorem can be established in a {\em general} class of nonparametric ... More

Mortality and life expectancy forecasting for a group of populations in developed countries: A multilevel functional data methodJun 16 2016A multilevel functional data method is adapted for forecasting age-specific mortality for two or more populations in developed countries with high-quality vital registration systems. It uses multilevel functional principal component analysis of aggregate ... More

Selection of the optimal Box-Cox transformation parameter for modelling and forecasting age-specific fertilityMar 08 2015The Box-Cox transformation can sometimes yield noticeable improvements in model simplicity, variance homogeneity and precision of estimation, such as in modelling and forecasting age-specific fertility. Despite its importance, there have been few studies ... More

High-Dimensional Bayesian Inference in Nonparametric Additive ModelsJun 29 2013Sep 23 2013A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small number of components. ... More

Large and moderate deviation principles for Engel continued fractionsApr 18 2016Aug 26 2016Large and moderate deviation principles are proved for Engel continued fractions, a new type of continued fraction expansion with non-decreasing partial quotients in number theory.

A data-driven robust optimization approach to scenario-based stochastic model predictive controlJul 13 2018Jan 14 2019Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive scenarios ... More

A low-redshift galaxy cluster X-ray Temperature Function incorporating Suzaku dataSep 05 2008We present the first results of a survey of 14 low redshift galaxy clusters using Suzaku. Although luminous (L_x> 1\times 10^{43} erg s^{-1} (0.1-2.4 keV)), these clusters have no prior pointed X-ray data. Together with 47 other systems they form a flux ... More

Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentrationAug 25 2016Environmental data often take the form of a collection of curves observed sequentially over time. An example of this includes daily pollution measurement curves describing the concentration of a particulate matter in ambient air. These curves can be viewed ... More

Simulation of continuous variable quantum games without entanglementJan 12 2011Apr 26 2011A simulation scheme of quantum version of Cournot's Duopoly is proposed, in which there is a new Nash equilibrium that may be also Pareto optimal without any entanglement involved. The unique property of this simulation scheme is decoherence-free against ... More

Mean parity of single quantum excitation of some optical fields in thermal environmentsJul 13 2008Jun 11 2010The mean parity (the Wigner function at the origin) of excited binomial states, excited coherent states and excited thermal states in thermal channel is investigated in details. It is found that the single-photon excited binomial state and the single-photon ... More

Nonclassicality of single quantum excitation of a thermal field in thermal environmentsMay 28 2008The nonclassicality of single photon-added thermal states in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function. The Wigner functions become positive when the decay time exceeds a threshold value $\gamma{t}_c$, ... More

Cooperative Change Detection for Online Power Quality MonitoringDec 08 2014This paper considers the real-time power quality monitoring in power grid systems. The goal is to detect the occurrence of disturbances in the nominal sinusoidal voltage/current signal as quickly as possible such that protection measures can be taken ... More

Bayesian bandwidth estimation for a nonparametric functional regression model with mixed types of regressors and unknown error densityMar 08 2014We investigate the issue of bandwidth estimation in a nonparametric functional regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the recent work of ... More

Numerical invariant tori of symplectic integrators for integrable Hamiltonian systemsMay 09 2018In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying R\"{u}ssmann's non-degeneracy condition when symplectic integrators are applied to them. Meanwhile, we give an estimate of the measure of the set occupied ... More

Single-shot work extraction in quantum thermodynamics revisitedMar 14 2017Nov 09 2017We revisit the problem of work extraction from a system in contact with a heat bath to a work storage system, and the reverse problem of state formation from a thermal system state in single-shot quantum thermodynamics. A physically intuitive and mathematically ... More

Posteriori Probabilistic Bounds of Convex Scenario Programs with Validation TestsMar 27 2019Scenario programs have established themselves as efficient tools towards decision-making under uncertainty. To assess the quality of scenario-based solutions a posteriori, validation tests based on Bernoulli trials have been widely adopted in practice. ... More

Cosmology with Standard Sirens: the Importance of the Shape of the Lensing Magnification DistributionApr 20 2010The gravitational waves (GWs) emitted by inspiraling binary black holes, expected to be detected by the Laser Interferometer Space Antenna (LISA), could be used to determine the luminosity distance to these sources with the unprecedented precision of ... More

Mortality and life expectancy forecasting for a group of populations in developed countries: A robust multilevel functional data methodSep 23 2016A robust multilevel functional data method is proposed to forecast age-specific mortality rate and life expectancy for two or more populations in developed countries with high-quality vital registration systems. It uses a robust multilevel functional ... More

Visualising rate of change: application to age-specific fertilityJun 17 2014Jan 25 2018Visualisation methods help in the discovery of characteristics that might not have been apparent using mathematical models and summary statistics. However, visualisation methods have not received much attention in demography, with the exceptions of scatter ... More

Delay-aware data transmission of multi-carrier communications in the presence of renewable energyJul 06 2015In the paper, we investigate the delay-aware data transmission in renewable energy aided multi-carrier system. Besides utilizing the local renewables, the transmitter can also purchase grid power. By scheduling the amount of transmitted data (The data ... More

On the Diophantine Equation 2^a3^b + 2^c3^d = 2^e3^f + 2^g3^hOct 08 2009This paper is a continuation of [1], in which I studied Harvey Friedman's problem of whether the function f(x,y) = x^2 + y^3 satisfies any identities; however, no knowledge of [1] is necessary to understand this paper. We will break the exponential Diophantine ... More

Further Formalization of the Process Algebra CCS in HOL4Jul 16 2017Jul 27 2017In this project, we have extended previous work on the formalization of the process algebra CCS in HOL4. We have added full supports on weak bisimulation equivalence and observation congruence (rooted weak equivalence), with related definitions, theorems ... More

Characterizing the Rate Region of the (4,3,3) Exact-Repair Regenerating CodesDec 03 2013Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a non-vanishing ... More

Latent Capacity Region: A Case Study on Symmetric Broadcast With Common MessagesMar 24 2011We consider the problem of broadcast with common messages, and focus on the case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the message intended for all the receivers in the set $\mathcal{A}$, is the same for all the set $\mathcal{A}$ ... More

Manifestly covariant classical correlation dynamics II. Transport equations and Hakim equilibrium conjectureMay 29 2009This is the second of a series of papers on the special relativistic classical statistical mechanics. Employing the general theory developed in the first paper we rigorously derive the relativistic Vlasov, Landau and Boltzmann equation. The latter two ... More

K-stability and Kähler-Einstein metricsNov 20 2012Jan 28 2013In this new version, we correct some typos. For the readers' convenience, we also added some footnotes and more details for certain lemmas and theorems.

Stability of pairsOct 21 2013This is essentially an expository note based on S. Paul's works on the stability of pairs. Its connection to K-stability will be also discussed.

The stable problem of the black-hole connected region in the Schwarzschild black holeDec 18 2005The stability of the Schwarzschild black hole is studied. Using the Painlev\'{e} coordinate, our region can be defined as the black-hole-connected region(r>2m, see text) of the Schwarzschild black hole or the white-hole-connected region(r>2m, see text) ... More

The last (lost) charge of a black holeApr 01 2018The topological charge of a maximally symmetric black hole naturally arise in holography, which can be viewed as the last (lost) charge of the black hole in the sense that it together with all other known charges satisfies the Gibbs-Duhem-like relation ... More

A categorification of the square root of -1Nov 27 2014We give a graphical calculus for a monoidal DG category $\cal{I}$ whose Grothendieck group is isomorphic to the ring $\mathbb{Z}[\sqrt{-1}]$. We construct a categorical action of $\cal{I}$ which lifts the action of $\mathbb{Z}[\sqrt{-1}]$ on $\mathbb{Z}^2$. ... More

A categorification of U_q sl(1,1) as an algebraOct 21 2012Feb 18 2013We construct families of differential graded algebras R and R \boxtimes R and give an algebraic formulation of the contact category of a disk through the differential graded category DGP(R) generated by some distinguished projective differential graded ... More

Some Peculiarities of Newton-Hooke Space-TimesSep 18 2011Sep 28 2011Newton-Hooke space-times are the non-relativistic limit of (anti-)de Sitter space-times. We investigate some peculiar facts about the Newton-Hooke space-times, among which the "extraordinary Newton-Hooke quantum mechanics" and the "anomalous Newton-Hooke ... More

Closed-form formulas for calculating the extremal ranks and inertias of a quadratic matrix-valued function and their applicationsJan 11 2013This paper presents a group of analytical formulas for calculating the global maximal and minimal ranks and inertias of the quadratic matrix-valued function $\phi(X) = (\, AXB + C\,)M(\, AXB + C)^{*} + D$ and use them to derive necessary and sufficient ... More

Matrix Representations of Octonions and Their ApplicationsMar 26 2000Apr 01 2000As is well-known, the real quaternion division algebra $ {\cal H}$ is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra ${\cal O}$ can not be algebraically isomorphic to any matrix algebras over the real ... More

Spinor field equations and the problem of prescribing mean curvature on $S^2$Oct 09 2018Let $\Sigma$ denote the class of positive smooth functions on $S^2$, we show that there exists a $C^1$-dense subset $\mathscr{Q}$ of $\Sigma$ such that each $Q\in\mathscr{Q}$ can be prescribed as the mean curvature of a conformal isometric embedding $S^2\hookrightarrow\mathbb{R}^3$. ... More

Universal Similarity Factorization Equalities over Complex Clifford AlgebrasMar 26 2000A set of valuable universal similarity factorization equalities are established over complex Clifford algebras $\Cn.$ Through them matrix representations of complex Clifford algebras $\Cn$ can directly be derived, and their properties can easily be determined. ... More

Rank Equalities Related to Generalized Inverses of Matrices and Their ApplicationsMar 30 2000This paper is divided into two parts. In the first part, we develop a general method for expressing ranks of matrix expressions that involve Moore-Penrose inverses, group inverses, Drazin inverses, as well as weighted Moore-Penrose inverses of matrices. ... More

Classicality of overconvergent Hilbert eigenforms: Case of quadratic residue degreeApr 23 2011Let $F$ be a quadratic real field, $p$ be a rational prime inert in $F$. In this paper, we prove that an overconvergent $p$-adic Hilbert eigenform for $F$ of small slope is actually a classical Hilbert modular form.

Characterization of ${\cal B}(\infty)$ using marginally large tableaux and rigged configurations in the $A_n$ case via integer sequencesNov 14 2016Dec 15 2016Rigged configurations are combinatorial objects prominent in the study of solvable lattice models. Marginally large tableaux are semi-standard Young tableaux of special form that give a realization of the crystals ${\cal B}(\infty)$. We introduce cascading ... More

The Application of Differential Privacy for Rank Aggregation: Privacy and AccuracySep 24 2014The potential risk of privacy leakage prevents users from sharing their honest opinions on social platforms. This paper addresses the problem of privacy preservation if the query returns the histogram of rankings. The framework of differential privacy ... More

Computations of Galois Representations Associated to Modular FormsNov 04 2013Aug 04 2014We propose an improved algorithm for computing mod $\ell$ Galois representations associated to a cusp form $f$ of level one. The proposed method allows us to explicitly compute the case with $\ell=29$ and $f$ of weight $k=16$, and the cases with $\ell=31$ ... More

Configurational space continuity and free energy calculationsFeb 25 2016Aug 20 2016Free energy is arguably the most importance function(al) for understanding of molecular systems. A number of rigorous and approximate free energy calculation/estimation methods have been developed over many decades. One important issue, the continuity ... More

NP=P: From Polynomial Time Approximation Bounded Solutions of TSPMay 20 2016The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, ... More

Linear Upper Bound on the Ribbonlength of Torus Knots and Twist KnotsSep 06 2018Knotted ribbons form an important topic in knot theory. They have applications in natural sciences, such as cyclic duplex DNA modeling. A flat knotted ribbon can be obtained by gently pulling a knotted ribbon tight so that it becomes flat and folded. ... More

On uniform K-stability of pairsDec 14 2018Jan 01 2019In this paper, we discuss stable pairs, which were first studied by S. Paul, and give a proof for a result I learned from him. As a consequence, we will show that the K-stability implies the CM-stability.

Geometry and nonlinear analysisDec 01 2002Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants. Those invariants ... More

A diagrammatic categorification of a Clifford algebraSep 24 2013We give a graphical calculus for a categorification of a Clifford algebra and its Fock space representation via differential graded categories. The categorical action is motivated by the gluing action between the contact categories of infinite strips. ... More

Joint Birkhoff Ergodic Average and Topological PressureAug 18 2014Oct 06 2014In this paper we mainly study the dynamical complexity of Birkhoff ergodic average under the simultaneous observation of any number of continuous functions. These results can be as generalizations of [6,35] etc. to study Birkhorff ergodic average from ... More

Robust Photon Entanglement via Quantum Interference in Optomechanical InterfacesJan 23 2013Jul 03 2013Entanglement is often the key element in quantum information protocols. Here, we present schemes to generate robust photon entanglement in optomechanical interfaces via quantum interference. The schemes explore the excitation of the Bogoliubov dark mode ... More

Cavity cooling of a mechanical resonator in the presence of two-level-system defectsDec 07 2010Jul 22 2011Cavity cooling via quantum backaction force can extract thermal fluctuations from a mechanical resonator to reach the quantum ground state. Surface or bulk two-level-system (TLS) defects in a mechanical resonator can couple with the mechanical mode via ... More

Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2Sep 29 2016In this paper, we deal with limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order 2 by studying expansions of the first order Melnikov functions near the loop and coefficients in these expansions. More precisely, we prove ... More

Topological Pressure for the Completely Irregular Set of Birkhoff AveragesAug 18 2014Feb 24 2017In this paper we mainly study the dynamical complexity of Birkhoff ergodic average under the simultaneous observation of any number of continuous functions. These results can be as generalizations of [6,35] etc. to study Birkhorff ergodic average from ... More

Solutions of the matrix inequalities $BXB^* <=^- A$ in the minus partial ordering and $BXB^* <=^L A$ in the Löwner partial orderingJan 20 2013Two matrices $A$ and $B$ of the same size are said to satisfy the minus partial ordering, denoted by $B\leqslant^{-}A$, iff the rank subtractivity equality ${\rm rank}(\, A - B\,) = {\rm rank}(A) -{\rm rank}(B)$ holds; two complex Hermitian matrices $A$ ... More

Holographic study on the jet quenching parameter in anisotropic systemsSep 13 2016We first calculate the jet quenching parameter of an anisotropic plasma with a U(1) chemical potential via the AdS/CFT duality. The effects of charge, anisotropy parameter and quark motion direction on the jet quenching parameter are investigated. We ... More

RW Aur A from the X-Wind Point of View: General FeaturesSep 11 2012In this paper, the RW Aur A microjet is studied from the point of view of X-wind models. The archived HST/STIS spectra of optical forbidden lines [O I], [S II], and [N II] from RW Aur A, taken in Cycle 8 with seven parallel slits along the jet axis, spaced ... More

The stability, electronic structure, and optical property of TiO2 polymorphsDec 09 2013Phonon density of states calculation shows that a new TiO2 polymorph with tridymite structure is mechanically stable. Enthalpies of 9 TiO2 polymorphs under different pressure are presented to study the relative stability of the TiO2 polymorphs. Band structures ... More

The Electric Dipole Moment and CP Violation in $B \to X_s l^+ l^-$ in SUGRA Models with Nonuniversal Gaugino MassesJan 18 2000May 14 2000The constraints of electric dipole moments (EDMs) of electron and neutron on the parameter space in supergravity (SUGRA) models with nonuniversal gaugino masses are analyzed. It is shown that with a light sparticle spectrum, the sufficient cancellations ... More

$(g-2)_μ$ and CP Asymmetries in $B^0_{d,s} \to l^+ l^-$ and $b \to s γ$ in SUSY modelsJan 14 2002Jun 08 2002We show that with a good fit to the muon $g-2$ constraint, the CP asymmetry can be as large as 25% (15%) for $B^0_d \to \tau^+ \tau^-$ ($B^0_d \to \mu^+ \mu^-$) in SUGRA models with nonuniversal gaugino masses and MSSM. If tau events indentified at B ... More

Supersymmetric CP Violation in $B \to X_s l^+ l^-$ in Minimal Supergravity ModelAug 04 1999Mar 01 2000Direct CP asymmetries and the CP violating normal polarization of lepton in inclusive decay B \to X_s l^+ l^- are investigated in minimal supergravity model with CP violating phases. The contributions coming from exchanging neutral Higgs bosons are included. ... More

On Equivalent Color Transform and Four Coloring TheoremOct 06 2016In this paper, we apply an equivalent color transform (ECT) for a minimal $k$-coloring of any graph $G$. It contracts each color class of the graph to a single vertex and produces a complete graph $K_k$ for $G$ by removing redundant edges between any ... More

The Distance of 4 kpc to the SNR CTB 109/AXP 1E 2259+586 systemNov 15 2007Feb 08 2010We suggest a revised distance to the supernova remnant (SNR) G109.1-1.0 (CTB 109) and its associated anomalous X-ray pulsar (AXP) 1E 2259+586 by analyzing 21cm HI-line and 12CO-line spectra of CTB 109, HII region Sh 152, and the adjacent molecular cloud ... More

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

Characterization of ${\cal B}(\infty)$ using marginally large tableaux and rigged configurations in the $A_n$ case via integer sequencesNov 14 2016Rigged configurations are combinatorial objects prominent in the study of solvable lattice models. Marginally large tableaux are semi-standard Young tableaux of special form that give a realization of the crystals ${\cal B}(\infty)$. We introduce cascading ... More

How to solve three fundamental linear matrix inequalities in the Löwner partial orderingJan 28 2013This paper shows how to solve analytically the three fundamental linear matrix inequalities $$ AXB \succcurlyeq C \, (\succ C), \ \ AXA^*\succcurlyeq B \, (\succ B), \ \ AX +(AX)^{*} \succcurlyeq B \, (\succ B) $$ in the L\"owner partial ordering by using ... More

Similarity and Consimilarity of Elements in Real Cayley-Dickson AlgebrasMar 26 2000A set of valuable universal similarity factorization equalities is established over complex Clifford algebras $\Cn.$ Through them matrix representations of complex Clifford algebras $\Cn$ can directly be derived, and their properties can easily be determined. ... More

Multi-center SuperstrataJul 29 2016Aug 05 2016We construct a new class of superstrata, the regular supergravity solutions describing the microstates of D1-D5-P black holes. Our solutions are obtained by adding momentum charge to the D1-D5 geometries based on multiple concentric Kaluza-Klein monopoles. ... More

On the conjecture by Demyanov-Ryabova in converting finite exhaustersJan 24 2016Apr 04 2016In this paper, we prove the conjecture of Demyanov and Ryabova on the length of cycles in converting exhausters in an affinely independent setting and obtain a combinatorial reformulation of the conjecture. Given a finite collection of polyhedra, we can ... More

Symmetry, Outer Bounds, and Code Constructions: A Computer-Aided Investigation on the Fundamental Limits of CachingOct 31 2016We considered the optimal memory-transmission-rate tradeoff of caching systems. Different from the conventional analytical approach usually seen in the information theory literature, we rely on a computer-aided approach in this investigation. The linear ... More

On the Hybrid Mean Value of Generalized Dedekind Sums, Generalized Hardy Sums and Kloosterman SumsSep 20 2018The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums, and give some exact computational formulae for them by using the properties of Gauss sums and the ... More

On the Archimedean Local Gamma Factors for Adjoint Representation of $\mathrm{GL}_3$, Part INov 07 2018Studying the analytic properties of the partial Langlands $L$-function via Rankin-Selberg method has been proved to be successful in various cases. Yet in few cases is the local theory studied at the archimedean places, which causes a tremendous gap to ... More

How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?Dec 09 2016Dec 15 2016In this paper, we study the minimal Keller-Segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and other ingredient, especially, chemotactic aggregation to guarantee boundedness ... More

Hyperbolic Periodic Points and Hyperbolic Measures with Dominated SplittingNov 28 2010Nov 20 2015In this paper we consider a non-atomic invariant hyperbolic measure $\mu$ of a $C^1$ diffeomorphsim on a compact manifold, in whose Oseledec splitting the stable bundle dominates the unstable bundle on $\mu$ a.e. points. We show an \textit{exponentially} ... More

Minimal Diffeomorphisms cannot satisfy Generalized Dominated SplittingJun 19 2011We introduce a new notion called generalized dominated splitting which is weaker than classical dominated splitting. We use this notion to generalize a result of Zhang\cite{Zh}: every diffeomorphism with nontrivial global generalized dominated splitting ... More

Different Asymptotic Behavior versus Same Dynamical ComplexityNov 04 2013Jan 14 2015For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense in the space ... More

Analytical formulas for calculating the extremal ranks of the matrix-valued function $A + BXC$ when the rank of $X$ is fixedJan 16 2013One of the simplest matrix-valued function with a single variable matrix $X$ is given by $A + BXC$. In this this note, analytical formulas are established for calculating the maximal and minimal ranks of $A + BXC$ when the rank of the variable matrix ... More

Equalities and inequalities for Hermitian solutions and Hermitian definite solutions of the two matrix equations $AX = B$ and $AXA^* = B$Jan 17 2013This paper studies algebraic properties of Hermitian solutions and Hermitian definite solutions of the two types of matrix equation $AX = B$ and $AXA^* = B$. We first establish a variety of rank and inertia formulas for calculating the maximal and minimal ... More

Generalizations of an Expansion Formula for Top to Random ShufflesOct 25 2014In the top to random shuffle, the first a cards are removed from a deck of n cards 12 \cdots n and then inserted back into the deck. This action can be studied by treating the top to random shuffle as an element B_a, which we define formally in Section ... More

Signature candidate of quantum chaos far from the semiclassical regimeApr 23 2013Feb 24 2014We numerically investigated the entanglement product in the simplest coupled kicked top model with the spin $j=1$. Different from the dynamical pattern of entanglement in the semiclassical regime, two similar initial states may have discordant entanglement ... More

Paths Beyond Local Search: A Nearly Tight Bound for Randomized Fixed-Point ComputationFeb 16 2007In 1983, Aldous proved that randomization can speedup local search. For example, it reduces the query complexity of local search over [1:n]^d from Theta (n^{d-1}) to O (d^{1/2}n^{d/2}). It remains open whether randomization helps fixed-point computation. ... More

A plug-in bandwidth selection procedure for long run covariance estimation with stationary functional time seriesApr 10 2016In arenas of application including environmental science, economics, and medicine, it is increasingly common to consider time series of curves or functions. Many inferential procedures employed in the analysis of such data involve the long run covariance ... More

Games on the Sperner TriangleFeb 26 2007We create a new two-player game on the Sperner Triangle based on Sperner's lemma. Our game has simple rules and several desirable properties. First, the game is always certain to have a winner. Second, like many other interesting games such as Hex and ... More

Probing Gas Motions in the Intra-Cluster Medium: A Mixture Model ApproachApr 26 2012Upcoming high spectral resolution telescopes, particularly Astro-H, are expected to finally deliver firm quantitative constraints on turbulence in the intra-cluster medium (ICM). We develop a new spectral analysis technique which exploits not just the ... More

Spending is not Easier than Trading: On the Computational Equivalence of Fisher and Arrow-Debreu EquilibriaJul 23 2009It is a common belief that computing a market equilibrium in Fisher's spending model is easier than computing a market equilibrium in Arrow-Debreu's exchange model. This belief is built on the fact that we have more algorithmic success in Fisher equilibria ... More

A Complexity View of Markets with Social InfluenceSep 02 2010In this paper, inspired by the work of Megiddo on the formation of preferences and strategic analysis, we consider an early market model studied in the field of economic theory, in which each trader's utility may be influenced by the bundles of goods ... More

Model confidence sets and forecast combination: An application to age-specific mortalitySep 28 2018Model averaging combines forecasts obtained from a range of models, and it often produces more accurate forecasts than a forecast from a single model. The crucial part of forecast accuracy improvement in using the model averaging lies in the determination ... More

Grouped multivariate and functional time series forecasting: An application to annuity pricingMay 22 2017Age-specific mortality rates are often disaggregated by different attributes, such as sex, state, ethnic group and socioeconomic status. In making social policies and pricing annuity at national and subnational levels, it is important not only to forecast ... More