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ELF: An Extensive, Lightweight and Flexible Research Platform for Real-time Strategy GamesJul 04 2017Nov 10 2017In this paper, we propose ELF, an Extensive, Lightweight and Flexible platform for fundamental reinforcement learning research. Using ELF, we implement a highly customizable real-time strategy (RTS) engine with three game environments (Mini-RTS, Capture ... More

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

SrRietveld: A program for automating Rietveld refinements for high throughput powder diffraction studiesJun 02 2010Jun 03 2010SrRietveld is a highly automated software toolkit for Rietveld refinement. Compared to traditional refinement programs, it is more efficient to use and easier to learn. It is designed for modern high throughput diffractometers and capable of processing ... 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

Leader-following Consensus Problems with a Time-varying Leader under Measurement NoisesSep 24 2009In this paper, we consider a leader-following consensus problem for networks of continuous-time integrator agents with a time-varying leader under measurement noises. We propose a neighbor-based state-estimation protocol for every agent to track the leader, ... 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

Joint Probability Generating Function for Degrees of Active/Passive Random Intersection GraphsOct 24 2009Correlations of active and passive random intersection graphs are studied in this letter. We present the joint probability generating function for degrees of $G^{active}(n,m,p)$ and $G^{passive}(n,m,p)$, which are generated by a random bipartite graph ... 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

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

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

Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing systemMar 23 2010In this paper, we study a scalar conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. As a generalization of \cite{CKWang}, the velocity function possesses both the local and nonlocal character. ... 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.

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

A Bayesian Splitotic Theory For Nonparametric ModelsAug 17 2015We develop a set of scalable Bayesian inference procedures for a general class of nonparametric regression models based on embarrassingly parallel MCMC. Specifically, we first perform independent nonparametric Bayesian inference on each subset split from ... More

Competition of different evaluation schemes in the continuous variable gameMar 13 2013Jun 25 2013An asymmetric generalization of classical Cournot's duopoly game was introduced and the simulation scheme of its quantized version was analyzed. In this scheme, the player assigned by a 'classical' measurement scheme always wins the player assigned by ... 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

Stochastic heat equations with logarithmic nonlinearityJul 09 2019In this paper, we establish the existence and uniqueness of solutions to stochastic heat equations with logarithmic nonlinearity driven by Brownian motion on a bounded domain $D$ in the setting of $L^2(D)$ space. The result is valid for all initial values ... More

Dirac surface states in intrinsic magnetic topological insulators EuSn2As2 and MnBi2Te4Jul 15 2019In magnetic topological insulators (TIs), the interplay between magnetic order and nontrivial topology can induce fascinating topological quantum phenomena, such as the quantum anomalous Hall effect, chiral Majorana fermions and axion electrodynamics. ... 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

New bounds of Mutually unbiased maximally entangled bases in C^d\otimes C^{kd}Oct 20 2017Jun 08 2018Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in C^d\otimes C^d by properties ... More

Informational work storage in quantum thermodynamicsSep 10 2017Jun 04 2019We present a critical examination of the difficulties with the quantum versions of a lifted weight that are widely used as work storage systems in quantum thermodynamics. To overcome those difficulties, we turn to the strong connections between information ... 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

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

Conservation of Total Escape from Hydrodynamic Planetary AtmospheresAug 02 2013Atmosphere escape is one key process controlling the evolution of planets. However, estimating the escape rate in any detail is difficult because there are many physical processes contributing to the total escape rate. Here we show that as a result of ... More

Tap Density Equations of Granular Powders Based on the Rate Process Theory and the Free Volume ConceptSep 05 2014Tap density of a granular powder is often linked to the flowability via Carr Index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important ... More

Advanced Post-Processing Techniques of Molecular Dynamics Simulations in Studying Strong Anharmonic Thermodynamics of SolidsOct 19 2015While the vibrational thermodynamics of materials with small anharmonicity at low temperatures has been understood well based on the harmonic phonons approximation; at high temperatures, this understanding must accommodate how phonons interact with other ... More

A Classification of (2+1)D Topological Phases with SymmetriesJan 04 2018This thesis aims at concluding the classification results for topological phases with symmetry in 2+1 dimensions. The main result is that topological phases are classified by a triple of unitary braided fusion categories $\mathcal E\subset\mathcal C\subset\mathcal ... More

Polarization of light and the spin state of photonOct 11 2011The comparison of the polarization and spin of light is presented in the paper. It is shown that it is more easier and clearer to use the polarization of the light to explain the effect of the interaction of light and atoms than that of spin of the light. ... More

New Investigation on the Spheroidal Wave EquationsApr 09 2010Changing the spheroidal wave equations into new Schro$dinger's form, the super-potential expanded in the series form of the parameter $\alpha$are obtained in the paper. This general form of the super-potential makes it easy to get the ground eigenfunctions ... More

Manifestly covariant classical correlation dynamics I. General theoryJan 11 2009May 29 2009n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing on the action-at-a-distance ... More

Evolution towards Jüttner equilibrium: Manifestly covariant correlation dynamicsJul 09 2008Jan 11 2009Replaced by the new article arXiv:0901.1425 because the J\"uttner distribution has been revised and the second author been removed.

A Note on the Fundamental Limits of Coded CachingFeb 27 2015The fundamental limit of coded caching is investigated for the case with $N=3$ files and $K=3$ users. An improved outer bound is obtained through the computational approach developed by the author in an earlier work. This result is part of the online ... More

A Formalization of Unique Solutions of Equations in Process AlgebraDec 05 2017In this thesis, a comprehensive formalization of Milner's Calculus of Communicating Systems (also known as CCS) has been done in HOL theorem prover (HOL4), based on an old work in HOL88. This includes all classical properties of strong/weak bisimulation ... More

Supersymmetric field theory of local light diffusion in semi-infinite mediaDec 22 2007A supersymmetric field theory of light diffusion in semi-infinite disordered media is presented. With the help of this technique we justify--at the perturbative level--the local light diffusion proposed by Tiggelen, Lagendijk, and Wiersma [Phys. Rev. ... More

Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis systemDec 13 2017It is well-known that the Neumann initial-boundary value problem for the minimal-chemotaxis-logistic system in a 2D bounded smooth domain has no blow-up for any choice of parameters. Here, for a large class of kinetic terms including sub-logistic sources, ... More

Physical-like Measures Coincide with Invariant Measures Supported on Chain Recurrent ClassesJul 20 2019For $C^0$ generic continuous maps or homeomorphisms on compact Riemannian manifold, we prove that (1) the space of physical-like measures coincides with the set of invariant measures supported on chain recurrent classes, (2) every point in the base space ... More

Formulas for calculating the extremal ranks and inertias of a matrix-valued function subject to matrix equation restrictionsJan 14 2013Matrix rank and inertia optimization problems are a class of discontinuous optimization problems in which the decision variables are matrices running over certain matrix sets, while the ranks and inertias of the variable matrices are taken as integer-valued ... More

Analytical solutions to some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix inequalitiesJan 06 2013Matrix rank and inertia optimization problems are a class of discontinuous optimization problems, in which the decision variables are matrices running over certain feasible matrix sets, while the ranks and inertias of the variable matrices are taken as ... 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

A combinatorial algorithm for constrained assortment optimization under nested logit modelMar 30 2016We consider the assortment optimization problem with disjoint-cardinality constraints under two-level nested logit model. To solve this problem, we first identify a candidate set with $O(mn^2)$ assortments and show that at least one optimal assortment ... More

Analogous Viscosity Equations of Granular Powders Based on Eyrings Rate Process Theory and Free Volume ConceptAug 21 2015The viscosity concept of thermal systems is borrowed to describe the flowability of granular powders in this article with the granular temperature is defined analogously. Eyrings rate process theory and free volume concept, which have been proved to be ... More

The dynamics of a qubit coupled strongly with a quantum oscillatorSep 03 2012The dynamics of a qubit coupled with a quantum oscillator is re-studied in the region of strong coupling. The non-degenerate perturbation is added to the usual degenerate one and new results are given.

Does the Schwarzschild black hole really exist?Nov 22 2005We use the Kruskal time coordinate T to define the initial time. By this way, it naturally divides the stable study into one connected with the two regions: the white-hole-connected region and the black-hole-connected region. The union of the two regions ... More

Integral equations for the spin-weighted spheroidal wave functionNov 17 2004Nov 25 2004Integral equations for the spin-weighted spheroidal wave functions is given. For the prolate spheroidal wave function with m=0, there exists the integral equation whose kernel is(sin x)/x, and the sinc function kernel (sin x)/x is of great mathematical ... 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

TUNet: Incorporating segmentation maps to improve classificationJan 27 2019Determining the localization of specific protein in human cells is important for understanding cellular functions and biological processes of underlying diseases. Among imaging techniques, high-throughput fluorescence microscopy imaging is an efficient ... More

A theoretical framework for deep locally connected ReLU networkSep 28 2018Understanding theoretical properties of deep and locally connected nonlinear network, such as deep convolutional neural network (DCNN), is still a hard problem despite its empirical success. In this paper, we propose a novel theoretical framework for ... More

An Analytical Formula of Population Gradient for two-layered ReLU network and its Applications in Convergence and Critical Point AnalysisMar 02 2017May 24 2017In this paper, we explore theoretical properties of training a two-layered ReLU network $g(\mathbf{x}; \mathbf{w}) = \sum_{j=1}^K \sigma(\mathbf{w}_j^T\mathbf{x})$ with centered $d$-dimensional spherical Gaussian input $\mathbf{x}$ ($\sigma$=ReLU). We ... More

p-adic Monodromy of the Universal Deformation of a HW-cyclic Barsotti-Tate GroupAug 15 2007Aug 22 2008Let k be an algebraically closed field of characteristic $p>0$, and $G_0$ be a Barsotti-Tate group (or $p$-divisible group) over k. We denote by $S$ the "algebraic" local moduli in characteristic p of $G_0$, by $G$ the universal deformation of $G_0$ over ... More

De Sitter Thermodynamics from Diamonds's TemperatureApr 11 2005Jun 16 2005The thermal time hypothesis proposed by Rovelli [1] regards the physical basis for the flow of time as thermodynamical and provides a definition of the temperature for some special cases. We verify this hypothesis in the case of de Sitter spacetime by ... More

Topological Charge of ADHM Instanton on R^2_{NC}*R^2Apr 19 2004We have calculated the topological charge of U(N) instantons on non-degenerate noncommutative space time to be exactly the instanton number k in a previous paper [Mod.Phys.Lett. A18 1691]. This paper, which deals with the degenerate R^2_{NC}*R^2 case, ... More

Analytic Solution to Geodesic Equations in Lemaître-Tolman-Bondi MetricSep 29 2016May 20 2017In this paper, we use the Taylor expansion method to solve the LTB metric.

On the intrinsic three-dimensionality of the flow normal to a circular diskJun 25 2019Direct numerical simulations are performed for the steady flow normal to a circular disk at the Reynolds number of 1000. Numerical simulations are conducted with different levels of simplification procedure by reducing the azimuthal extension of the disk. ... 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

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

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

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

Disentangling Resonant Scattering and Gas Motions in Galaxy Cluster Emission Line ProfilesNov 11 2012Nov 28 2012Future high spectral resolution telescopes will enable us to place tight constraints on turbulence in the intra-cluster medium through the line widths of strong emission lines. At the same time, these bright lines are the most prone to be optically thick. ... 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

A Formalization of the Process Algebra CCS in HOL4May 20 2017Jun 17 2017An old formalization of the Process Algebra CCS (no value passing, with explicit relabeling operator) on has been ported from HOL88 theorem prover to HOL4 (Kananaskis-11 and later). Transitions between CCS processes are defined by SOS (Structured Operational ... More

Symmetry, Outer Bounds, and Code Constructions: A Computer-Aided Investigation on the Fundamental Limits of CachingOct 31 2016Aug 25 2018We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory literature. The linear ... More

Hydrodynamic and field-theoretic approaches of light localization in open mediaJan 26 2013Many complex systems exhibit hydrodynamic (or macroscopic) behavior at large scales characterized by few variables such as the particle number density, temperature and pressure obeying a set of hydrodynamic (or macroscopic) equations. Does the hydrodynamic ... More

Superdiffusion in the topological metalFeb 15 2012We develop a non-perturbative theory to study large-scale quantum dynamics of Dirac particles in disordered scalar potentials (the so-called "topological metal"). For general disorder strength and carrier doping, we find that at large times, superdiffusion ... More

Weak approximation for cubic hypersurfacesMar 28 2013Jul 29 2014We prove weak approximation for smooth cubic hypersurfaces of dimension at least 2 defined over the function field of a complex curve.

Hasse principle for three classes of varieties over global function fieldsMay 25 2015We give a geometric proof that Hasse principle holds for the following varieties defined over global function fields: smooth quadric hypersurfaces in odd characteristic, smooth cubic hypersurfaces of dimension at least $4$ in characteristic at least $7$, ... 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

The relation between cosmological redshift and scale factor for photonsSep 25 2017The cosmological constant problem has become one of the most important ones in modern cosmology. In this paper, we try to construct a model that can avoid the cosmological constant problem and have the potential to explain the apparent late-time accelerating ... 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

Opinion formation in multiplex networks with general initial distributionsOct 25 2017Jan 29 2018We study opinion dynamics over multiplex networks where agents interact with bounded confidence. Namely, two neighbouring individuals exchange opinions and compromise if their opinions do not differ by more than a given threshold. In literature, agents ... More

On 1-loop diagrams in AdS space and the random disorder problemJul 15 2010Sep 22 2010We study the complex scalar loop corrections to the boundary-boundary gauge two point function in pure AdS space in Poincare coordinates, in the presence of a boundary quadratic perturbation to the scalar. These perturbations correspond to double trace ... More

Profit Incentive In A Secondary Spectrum Market: A Contract Design ApproachJul 27 2012In this paper we formulate a contract design problem where a primary license holder wishes to profit from its excess spectrum capacity by selling it to potential secondary users/buyers. It needs to determine how to optimally price the excess spectrum ... 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

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

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

Defining Temperatures of Granular Powders Analogously with Thermodynamics to Understand the Jamming PhenomenaFeb 26 2016Aug 02 2016For the purpose of applying laws or principles originated from thermal systems to granular athermal systems, we may need to properly define the critical temperature concept in granular powders. The conventional environmental temperature in thermal systems ... More

DroidMeter: A Measurement Tool to Study Embedded Web PagesJan 21 2019Traditional Web browsing involves typing a URL on a browser and loading a Web page. In contrast, there is another form of Web browsing on mobile devices, i.e., embedded Web browsing, which occurs when mobile apps embed a Web page within the app. When ... More

A deformation of Penner's simplicial coordinateNov 07 2010Jul 15 2011We produce a one-parameter family of coordinates $\{\Psi_h\}_{h\in\mathbb{R}}$ of the decorated Teichm\"{u}ller space of an ideally triangulated punctured surface $(S,T)$ with negative Euler characteristic, which is a deformation of Penner's simplicial ... 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

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

Identities of the Function f(x,y) = x^2 + y^3Oct 08 2009Harvey Friedman asked in 1986 whether the function f(x,y) = x^2 + y^3 on the real plane R^2 satisfies any identities; examples of identities are commutativity and associativity. To solve this problem of Friedman, we must either find a nontrivial identity ... More

Detecting gasoline in small public places based on wireless sensor networkJul 09 2018Fire accidents often cause unpredictable catastrophic losses. At present, existing fire prevention measures in public places are mostly based on the emergency treatments after the fire, which have limited protection capability when the fire spreads rapidly, ... 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

Universal Approach to Quantum Adiabaticity via Ancilla CavityFeb 07 2018A central challenge in the successful implementation of adiabatic quantum algorithms is to maintain the quantum adiabaticity during the entire evolution. However, the energy gap between the ground and the excited states of interacting many-body systems ... More

Adiabatic State Conversion and Pulse Transmission in Optomechanical SystemsNov 09 2011Apr 16 2012Optomechanical systems with strong coupling can be a powerful medium for quantum state engineering. Here, we show that quantum state conversion between cavity modes with different wavelengths can be realized with high fidelity by adiabatically varying ... 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

On the Hyperbolic Gluing Equations and Representations of Fundamental Groups of Closed 3-ManifoldsApr 20 2010Apr 22 2010We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many solutions to the ... 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

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.

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

Matrix formulation for non-Abelian familiesAug 07 2019We generalize the $K$ matrix formulation to non-trivial non-Abelian families of 2+1D topological orders. Given a topological order $\mathcal C$, any topological order in the same non-Abelian family as $\mathcal C$ can be efficiently described by $\boldsymbol{a}=(a_I)$ ... More