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Condensate Fraction and Pair Coherence Lengths of Two-Dimension Fermi Gases with Spin-Orbit CouplingSep 19 2011The effects of Rashba spin-orbit coupling on BCS-BEC crossover, the condensate fraction and pair coherence lengths for a two-component attractive Fermi gas in two dimension are studied. The results at $T=0K$ indicate that (1) when the strength of SOC ... More

Oscillation of Pauli Paramagnetism in Rotating Two-Component Fermionic Atom GasesNov 24 2008By rotating two-component fermionic atom gases in uniform magnetic field, a similar physical situation with de Haas-van Alphen effect is constructed. We calculate magnetic moment of the system and find that owing to an existence of effective magnetic ... More

Metal-Mott Insulator Transition and Spin Exchange of Two-Component Fermi Gas with Spin-Orbit Coupling in Two-Dimension Square Optical LatticesJul 21 2011Oct 12 2011Effects of spin-orbit coupling (SOC) on metal-Mott insulator transition (MMIT) and spin exchange physics (SEP) of two-component Fermi gases in two-dimension half-filling square optical lattices are investigated. In the frame of Kotliar and Ruckenstein ... More

Excitation Spectrum and Momentum Distribution of Bose-Hubbard Model with On-site Two- and Three-body InteractionDec 16 2012An effective action for Bose-Hubbard model with two- and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis. From this effective action, superfluid-Mott insulator ... More

Finite Temperature Phase Diagram in Rotating Bosonic Optical LatticeNov 24 2008Finite temperature phase boundary between superfluid phase and normal state is analytically derived by studying the stability of normal state in rotating bosonic optical lattice. We also prove that the oscillation behavior of critical hopping matrix directly ... More

Polaron Properties of an Impurity in Bose-Einstein-CondensationNov 24 2008In this paper we study an impurity in Bose-Einstein-Condensate system at $T=0K$ and suppose the contact forms for boson-boson and boson-impurity interactions. Using Bogoliubov theory and a further approximation corresponding to only think over the forward ... More

Phase Diagram of a Spin-Orbit Coupled Fermi Gases in a Bilayer Optical LatticeJan 29 2013We investigate the stability of helical superfluid phase in a spin-orbit coupled Fermi gas loaded in a bilayer optical lattice. The phase diagram of the system is constructed in the mean field framework. We investigate the topological properties of the ... More

A New Non-Abelian Topological Phase of Cold Fermi Gases in Anisotropic and Spin-Dependent Optical LatticesJun 25 2012Jun 26 2012To realize non-Abelian s-wave topological superfluid (TS) of cold Fermi gases, generally a Zeeman magnetic field larger than superfluid pairing gap is necessary. In this paper we find that using an anisotropic and spin-dependent optical lattice (ASDOL) ... More

Topological superfluid of spinless Fermi gases in p-band honeycomb optical lattices with on-site rotationJun 18 2012In this paper, we put forward to another route realizing topological superfluid (TS). In contrast to conventional method, spin-orbit coupling and external magnetic field are not requisite. Introducing an experimentally feasible technique called on-site ... More

BCS-BEC Crossover in Mix-dimensional Fermi GasesApr 13 2011We investigate a mix-dimensional Fermi-Fermi mixture in which one species is confined in two-dimensional(2D) space while the other is free in three-dimensional space(3D). We determine the superfluid transition temperature $T_{c}$ for the entire BCS-BEC ... More

Large Chern Number Topological Superfluids in Coupled Layer SystemAug 13 2014Aug 30 2014We investigate the topological phase transition with large Chern number in a coupled layer system. The topological transitions between different topological superfluids can be realized by controlling the binding energy, interlay tunneling and layer asymmetry ... More

Type-I and type-II topological nodal superconductors with $s$-wave interactionJun 06 2017Topological nodal superconductors are generally realized based on unconventional pairings. In this work, we propose a minimal model to realize these topological nodal phases with only $s$-wave interaction. In our model the linear and quadratic spin-orbit ... More

Dynamical instability towards finite-momentum pairing in quenched BCS superconducting phasesOct 22 2018In this work we numerically investigate the fate of the Bardeen-Cooper-Schrieffer (BCS) pairing in the presence of quenched phase under Peierls substitution using time-dependent real space and momentum space Bogoliubov-de Gennes equation methods and Anderson ... More

Topological superfluids with time-reversal symmetry from $s$-wave interaction in a bilayer systemNov 05 2015Topological superconducting phases with time-reversal (TR) symmetry have been widely explored in recent years. However the involved unconventional pairings are generally implausible in realistic materials. Here we demonstrate via detailed self-consistent ... More

Topological indexes in symmetry preserving dynamicsFeb 08 2018The quench dynamics of topological phases have received intensive investigations in recent years. In this work, we prove exactly that the topological invariants for both $\mathbb{Z}$ and $\mathbb{Z}_2$ indexes are independent of time in symmetry preserving ... More

Total Variation Depth for Functional DataNov 15 2016There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the total variation ... More

The $hp$-version Error Analysis of A Mixed DG Method for Linear ElasticityAug 14 2016This paper focuses on the $hp$-version error analysis of a mixed discontinuous Galerkin (DG) method for the linear elasticity problem. We first derive some error estimates for two $L^2$ projection operators in terms of the results in [7,13,23]. Using ... More

Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-DisturbanceJan 01 2017This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a representative agent ... More

Dark Matter Particles with Low Mass (and FTL)Mar 26 2010Apr 17 2012From the observed results of the space distribution of quasars and the mass scale sequence table, we deduced the existence of superstructure (feeble dark structure) with mass scale of 10^(19) solar mass, as well as the lightest stable fermion with mass ... More

Parameter Optimization of Multi-Agent Formations based on LQR DesignJan 24 2011In this paper we study the optimal formation control of multiple agents whose interaction parameters are adjusted upon a cost function consisting of both the control energy and the geometrical performance. By optimizing the interaction parameters and ... More

Automorphism group of the complete alternating group graphMay 21 2016Aug 26 2017Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \emph{complete alternating group graph}, denoted by $CAG_n$, is defined as the Cayley graph ... More

Dark Matter, Mass Scales Sequence, and Superstructure in the Universe (with extension)Sep 18 1999Oct 26 2015There is a category of stable non-baryonic dark matter particles in the universe at the present time: fermions or bosons with mass ~10^(-1) eV. The existence of these do not contradict the dip phenomena of the ultra-high energy primary cosmic ray spectrum ... More

Dark Matter, Quasars, and Superstructures in the UniverseAug 10 2009Feb 02 2016From the observed results of the space distribution of quasars we deduced that neutrino mass is about 10^(-1) eV. The fourth stable elementary paticle (delta particle) with mass about 10^(0) eV can help explain the energy resource mechanism in quasars, ... More

On graphs with three or four distinct normalized Laplacian eigenvaluesNov 16 2016In this paper, we characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues of which one is equal to $1$, determine all connected bipartite graphs with at least one vertex of degree $1$ having exactly four distinct ... More

Automorphism group of the complete alternating group graphMay 21 2016Jun 02 2016Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \emph{complete alternating group graph}, denoted by $CAG_n$, is defined as the Cayley graph ... More

On regular graphs with four distinct eigenvaluesMay 18 2016Sep 17 2016Let $\mathcal{G}(4,2)$ be the set of connected regular graphs with four distinct eigenvalues in which exactly two eigenvalues are simple, $\mathcal{G}(4,2,-1)$ (resp. $\mathcal{G}(4,2,0)$) the set of graphs belonging to $\mathcal{G}(4,2)$ with $-1$ (resp. ... More

On graphs with three or four distinct normalized Laplacian eigenvaluesNov 16 2016Mar 27 2017In this paper, we characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues of which one is equal to $1$, determine all connected bipartite graphs with at least one vertex of degree $1$ having exactly four distinct ... More

Gorenstein Syzygy ModulesMar 26 2009Oct 15 2010For any ring $R$ and any positive integer $n$, we prove that a left $R$-module is a Gorenstein $n$-syzygy if and only if it is an $n$-syzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of finitely generated ... More

Dark energy and normalization of cosmological wave function in modified gravitationsMay 05 2017Based on Wheeler-DeWitt equation derived from general relativity, it had been found that only dark energy can lead to a normalizable cosmological wave function. It is shown in the present work that, for dRGT gravity, Eddington-inspired-Born-Infeld gravity ... More

Hierarchical low rank approximation of likelihoods for large spatial datasetsMay 28 2016Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive computational burden. ... More

An $hp$-version error analysis of the discontinuous Galerkin method for linear elasticityAug 14 2016Dec 24 2017An $hp$-version error analysis is developed for the general DG method in mixed formulation for solving the linear elastic problem. First of all, we give the $hp$-version error estimates of two $L^2$ projection operators. Then incorporated with the techniques ... More

Enumerating Cayley (di-)graphs on dihedral groupsDec 12 2016Let $p$ be an odd prime, and $D_{2p}=\langle \tau,\sigma\mid \tau^p=\sigma^2=e,\sigma\tau\sigma=\tau^{-1}\rangle$ the dihedral group of order $2p$. In this paper, we provide the number of (connected) Cayley (di-)graphs on $D_{2p}$ up to isomorphism by ... More

Large Number, Dark Matter, Dark Energy, and the Superstructures in the Universe (with Extension)Apr 16 2008Sep 12 2016Since there are dark matter particles (neutrino) with mass about 10^(-1)eV in the universe, the superstructures with a scale of 10^(19) solar mass [large number A is about 10^(19)] appeared around the era of the hydrogen recombination. The redshift z ... More

Note on the spectra of a class of graphs derived from set inclusion relationsSep 04 2018Sep 08 2018For any given integers $n$, $k$ and $l$ with $n\geq 1$ and $0\leq k<l\leq n$, we denote by $G(n,k,l)$ the graph whose vertex set consists of all $k$- and $l$-subsets of $[n]=\{1,2,\ldots,n\}$, where two distinct vertices are adjacent if one of them is ... More

A Fast HOG Descriptor Using Lookup Table and Integral ImageMar 18 2017The histogram of oriented gradients (HOG) is a widely used feature descriptor in computer vision for the purpose of object detection. In the paper, a modified HOG descriptor is described, it uses a lookup table and the method of integral image to speed ... More

Torsionfree Dimension of Modules and Self-Injective Dimension of RingsJun 06 2009Jan 14 2011Let $R$ be a left and right Noetherian ring. We introduce the notion of the torsionfree dimension of finitely generated $R$-modules. For any $n\geq 0$, we prove that $R$ is a Gorenstein ring with self-injective dimension at most $n$ if and only if every ... More

The Auslander-Type Condition of Triangular Matrix RingsMar 26 2009Let $R$ be a left and right Noetherian ring and $n,k$ any non-negative integers. $R$ is said to satisfy the Auslander-type condition $G_n(k)$ if the right flat dimension of the $(i+1)$-st term in a minimal injective resolution of $R_R$ is at most $i+k$ ... More

Association between Experiences and Representations: Memory, Dreaming, Dementia and ConsciousnessJun 14 2013The mechanisms underlying major aspects of the human brain remain a mystery. It is unknown how verbal episodic memory is formed and integrated with sensory episodic memory. There is no consensus on the function and nature of dreaming. Here we present ... More

Planning Argumentative TextsOct 28 1994This paper presents \proverb\, a text planner for argumentative texts. \proverb\'s main feature is that it combines global hierarchical planning and unplanned organization of text with respect to local derivation relations in a complementary way. The ... More

Coupled beam motion in a storage ring with crab cavitiesOct 16 2015We studied the coupled beam motion in a storage ring between the transverse and longitudinal directions introduced by crab cavities. Analytic form of the linear decoupling transformation is derived. The equilibrium bunch distribution in an electron storage ... More

Programing implementation of the Quine-McCluskey method for minimization of Boolean expressionOct 04 2014A Boolean function is a function that produces a Boolean value output by logical calculation of Boolean inputs. It plays key roles in programing algorithms and design of circuits. Minimization of Boolean function is able to optimize the algorithms and ... More

2D Local Hamiltonian with area laws is QMA-completeNov 24 2014We show that the 2D local Hamiltonian problem with the restriction that the ground state satisfies area laws is QMA-complete. We also prove similar results in 2D translationally invariant systems and for the 3D Heisenberg and Hubbard models. Consequently, ... More

Character-level Convolutional Network for Text Classification Applied to Chinese CorpusNov 14 2016This article provides an interesting exploration of character-level convolutional neural network solving Chinese corpus text classification problem. We constructed a large-scale Chinese language dataset, and the result shows that character-level convolutional ... More

Characterizations of endograph metric and $Γ$-convergence on fuzzy sets spacesDec 01 2015Jul 07 2016In this paper, it first discusses the continuity of the cut-set functions of fuzzy sets in $F_{USC} (\mathbb{R}^m)$ and $F_{USCB} (\mathbb{R}^m)$ espectively, where $F_{USC} (\mathbb{R}^m)$ is the set of all upper semi-continuous fuzzy sets on $\mathbb{R}^m$, ... More

The Cauchy problem for fully nonlinear parabolic systems on manifoldsJun 16 2015Jul 20 2015We show the short time existence and uniqueness of solutions to the Cauchy problem for fully nonlinear systems of arbitrary even order on closed manifolds which are strongly parabolic at the initial values. The proof uses a linearization procedure and ... More

A matrix differential Harnack estimate for a class of ultraparabolic equationsJun 20 2013Dec 22 2013Let $u$ be a positive solution of the ultraparabolic equation \begin{equation*} \partial_t u=\sum_{i=1}^n \partial_{x_i}^2 u+\sum_{i=1}^k x_i\partial_{x_{n+i}}u \hspace{8mm} \mbox{on} \hspace{4mm} \mathbb{R}^{n+k}\times (0,T), \end{equation*} where $1\leq ... More

Toric Surfaces, K-Stability and Calabi FlowJul 25 2012Let $X$ be a toric surface and $u$ be a normalized symplectic potential on the corresponding polygon $P$. Suppose that the Riemannian curvature is bounded by a constant $C_1$ and $\int_{\partial P} u ~ d \sigma < C_2, $ then there exists a constant $C_3$ ... More

On the Extension of the Calabi Flow on Toric VarietiesJan 04 2011Inspired by recent work of S. K. Donaldson on constant scalar curvature metrics on toric complex surfaces, we study obstructions to the extension of the Calabi flow on a polarized toric variety. Under some technical assumptions, we prove that the Calabi ... More

Message passing algorithms for the Hopfield network reconstruction: threshold behavior and limitationSep 01 2010Oct 25 2010The Hopfield network is reconstructed as an inverse Ising problem by passing messages. The applied susceptibility propagation algorithm is shown to improve significantly on other mean-field-type methods and extends well into the low temperature region. ... More

Notes on branched coverings of Seifert manifoldsMay 30 2014May 11 2016In a paper published in 2002, the author gave a criterion to determine whether there is a fiber-preserving branched covering between two given orientable Seifert manifolds with orientable bases. Here we supply some details of the proof of two claims in ... More

A splitting theorem on toric varietiesDec 15 2012Using the short time existence of the Calabi flow, we prove that any extremal Kaehler metric on a product toric variety is a product extremal Kaehler metric.

Faithful compact quantum group actions on connected compact metrizable spacesFeb 06 2012We construct faithful actions of quantum permutation groups on connected compact metrizable spaces. This disproves a conjecture of Goswami.

Effects of hidden nodes on network structure inferenceJun 01 2015Jul 29 2015Effects of hidden nodes on inference quality of observed network structure are explored based on a disordered Ising model with hidden nodes. We first study analytically small systems consisting of a few nodes, and find that the magnitude of the effective ... More

Compact quantum stabilizer subgroupsJul 13 2016We generalize the concept of stabilizer subgroups to compact quantum groups.

John Ellipsoid and the Center of Mass of a Convex BodyMay 23 2016It is natural to ask whether the center of mass of a convex body $K\subset \mathbb{R}^n$ lies in its John ellipsoid $B_K$, i.e., in the maximal volume ellipsoid contained in $K$. This question is relevant to the efficiency of many algorithms for convex ... More

New Bounds for Hypergeometric Creative TelescopingApr 27 2016May 13 2016Based on a modified version of Abramov-Petkov\v{s}ek reduction, a new algorithm to compute minimal telescopers for bivariate hypergeometric terms was developed last year. We investigate further in this paper and present a new argument for the termination ... More

Theory of population coupling and applications to describe high order correlations in large populations of interacting neuronsFeb 26 2016Jun 21 2016To understand the collective spiking activity in neuronal populations, it is essential to reveal basic circuit variables responsible for these emergent functional states. Here, we develop a mean field theory for the population coupling recently proposed ... More

On the extension and smoothing of the Calabi flow on complex toriSep 07 2016In this paper, we continue to study the Calabi flow on complex tori. We develop a new method to obtain an explicit bound of the curvature of the Calabi flow. As an application, we show that when $n=2$, the Calabi flow starting from a weak K\"ahler metric ... More

Arithmetic progressions in amenable groupsJul 25 2016Aug 05 2016We prove that there exist arbitrarily long arithmetic progressions in a subset of an amenable group $\Gamma\supseteq\mathbb{Z}$ with positive upper density with respect to a F{\o}lner sequence. This generalizes Szemer\'edi's theorem to amenable groups. ... More

Commensurability of groups quasi-isometric to RAAG'sMar 28 2016Jun 05 2016Let $G$ be a right-angled Artin group with defining graph $\Gamma$ and let $H$ be a finitely generated group quasi-isometric to $G(\Gamma)$. We show if $G$ satisfies (1) its outer automorphism group is finite; (2) $\Gamma$ does not have induced 4-cycle; ... More

Quantile calculus and censored regressionOct 04 2010Quantile regression has been advocated in survival analysis to assess evolving covariate effects. However, challenges arise when the censoring time is not always observed and may be covariate-dependent, particularly in the presence of continuously-distributed ... More

Anomaly Puzzle, Curved-Spacetime Spinor Hamiltonian, and String PhenomenologyApr 28 2011In the first part of this dissertation, we study two different aspects of string phenomenology. First we discuss the complementary signals of low mass superstrings at the proposed electron-positron facilities (ILC and CLIC), in e+e- and {\gamma} {\gamma} ... More

Theoretical analysis of reflected ray error from surface slope error and their application to the solar concentrated collectorDec 04 2011Surface slope error of concentrator is one of the main factors to influence the performance of the solar concentrated collectors which cause deviation of reflected ray and reduce the intercepted radiation. This paper presents the general equation to calculate ... More

On long time dynamics of perturbed KdV equationsOct 21 2013Dec 06 2013Consider perturbed KdV equations: \[u_t+u_{xxx}-6uu_x=\epsilon f(u(\cdot)),\quad x\in\mathbb{T}=\mathbb{R}/\mathbb{Z},\;\int_{\mathbb{T}}u(x,t)dx=0,\] where the nonlinearity defines analytic operators $u(\cdot)\mapsto f(u(\cdot))$ in sufficiently smooth ... More

A priori bounds for a class of semi-linear degenerate elliptic equationsNov 18 2012In this paper, we mainly discuss a priori bounds of the following degenerate elliptic equation, {equation}\label{000} a^{ij}(x)\partial_{ij}u+b^i(x)\partial_i u +f(x,u)=0,\text{in}\Omega\subset\subset R^n, {equation} where $a^{ij}\partial_i \phi\partial_j ... More

A Liouville theorem of degenerate elliptic equation and its applicationNov 12 2012In this paper, we apply the moving plane method to some degenerate elliptic equations to get a Liouville type theorem. As an application, we derive the a priori bounds for positive solutions of some semi-linear degenerate elliptic equations.

$2^{(\log N)^{1/10-o(1)}}$ Hardness for Hypergraph ColoringApr 15 2015Oct 14 2015We show that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with $2^{(\log N)^{1/10-o(1)}}$ colors, where $N$ is the number of vertices. There has been much focus on hardness of hypergraph coloring recently. Guruswami, H{\aa}stad, Harsha, ... More

Vacuum Misalignment in High Energy CollisionsOct 04 1993Oct 10 1993We study a recent proposal to observe the disoriented chiral condensate in high energy collisions. In order to produce a large fluctuation in pion probability distribution, a large size of the correlated region is essential. We study the role of the intrinsic ... More

On random walk on growing graphsJul 02 2016Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonely to a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple random walk on slowly ... More

An Upper Bound on the Number of $(132,213)$-Avoiding Cyclic PermutationsAug 25 2018We show a $n^2 \cdot 2^{n/2}$ upper bound on the number of $(132,213)$ avoiding cyclic permutations. This is the first nontrivial upper bound on the number of such permutations. We also construct an algorithm to determine whether a $(132,213)$ avoiding ... More

Rational approximations on toric varietiesSep 06 2018Oct 16 2018Using the universal torsor method due to Salberger, we study the approximation of a general fixed point by rational points on split toric varieties. We prove that under certain geometric hypothesis the best approximations (in the sense of McKinnon-Roth's ... More

Growing in time IDLA cluster is recurrentSep 28 2018We show that Internal Diffusion Limited Aggregation (IDLA) on $\mathbb{Z}^d$ has near optimal Cheeger constant when the growing cluster is large enough. This implies, through a heat kernel lower bound derived previously in [H], that simple random walk ... More

An approximation scheme for variational inequalities with convex and coercive HamiltoniansOct 20 2018We propose an approximation scheme for a class of semilinear variational inequalities whose Hamiltonian is convex and coercive. The proposed scheme is a natural extension of a previous splitting scheme proposed by Liang, Zariphopoulou and the author for ... More

The Art of Lattice and Gravity Waves from PreheatingFeb 01 2011Jun 07 2011The nonlinear dynamics of preheating after early-Universe inflation is often studied with lattice simulations. In this work I present a new lattice code HLATTICE. It differs from previous public available codes in the following three aspects: (i) A much ... More

Local derivative estimates for the heat equation coupled to the Ricci flowDec 26 2018Jan 17 2019In this note we obtain local derivative estimates of Shi-type for the heat equation coupled to the Ricci flow. As applications, in part combining with Kuang's work, we extend some results of Zhang and Bamler-Zhang including distance distortion estimates ... More

High-redshift Mini-haloes from Modulated PreheatingFeb 26 2019Intermittent type of primordial non-Gaussian fluctuations from modulated preheating can produce an overabundance of $\sim 10^8M_\odot$ mini-haloes at high redshift $z\gtrsim 20$. This may have a significant impact on the formation of high-redshift supermassive ... More

Homotopy of gauge groups over non-simply-connected five dimensional manifoldsMay 13 2018For a principal bundle over a non-simply connected oriented closed $5$-manifold of certain type, we prove various homotopy decompositions of its gauge groups according to the spin and non-spin structure of the manifold. We also show periodicity results ... More

Inverse coefficients problem for a magnetohydrodynamics systemJun 20 2018In this article, we consider a magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. Firstly, we give the stability results for our inverse coefficients problem. Secondly, we establish and prove two Carleman estimates ... More

What will be the maximum Tc in the iron-based superconductors?Aug 29 2008Nov 27 2008Using the newly developed real space vortex-lattice based theory of superconductivity, we study the maximum superconducting transition temperature (T_{c}^{\max}) in the iron-based superconductors. We find that all the reported FeAs superconductors can ... More

Many-body localization with mobility edgesJul 05 2015We construct a solvable spin chain model of many-body localization (MBL) with a tunable mobility edge. This simple model not only demonstrates analytically the existence of mobility edges in interacting one-dimensional (1D) disordered systems, but also ... More

Local derivative estimates for heat equations on Riemannian manifoldsFeb 13 2007In this short note we present local derivative estimates for heat equations on Riemannian manifolds following the line of W.-X. Shi. As an application we generalize a second derivative estimate of R. Hamilton for heat equations on compact manifolds to ... More

Syzygy modules for quasi $k$-Gorenstein ringsSep 10 2004Let $\Lambda$ be a quasi $k$-Gorenstein ring. For each $d$th syzygy module $M$ in mod $\Lambda$ (where $0 \leq d \leq k-1$), we obtain an exact sequence $0 \to B \to M \bigoplus P \to C \to 0$ in mod $\Lambda$ with the properties that it is dual exact, ... More

A General Interpretation of Deep Learning by Affine Transform and Region Dividing without Mutual InterferenceJun 16 2019Jun 24 2019This paper mainly deals with the "black-box" problem of deep learning composed of ReLUs with n-dimensional input space, as well as some discussions of sigmoid-unit deep learning. We prove that a region of input space can be transmitted to succeeding layers ... More

$i$QIST v0.7: An open source continuous-time quantum Monte Carlo impurity solver toolkitAug 24 2017In this paper, we present a new version of the $i$QIST software package, which is capable of solving various quantum impurity models by using the hybridization expansion (or strong coupling expansion) continuous-time quantum Monte Carlo algorithm. In ... More

Domain Specific Distributed Search Engine Based on Semantic P2P NetworksOct 28 2016This paper presents a distributed search engine based on semantic P2P Networks. The user's computers join the domains in which user wants to share information in semantic P2P networks which is domain specific virtual tree (VIRGO ). Each user computer ... More

System Intelligence: Model, Bounds and AlgorithmsMay 09 2016We present a general framework for understanding system intelligence, i.e., the level of system smartness perceived by users, and propose a novel metric for measuring intelligence levels of dynamical human-in-the-loop systems, defined to be the maximum ... More

Density estimates for sdes driven by tempered stable processesApr 16 2015Jan 29 2016We study a class of stochastic differential equations driven by a possibly tempered L{\'e}vy process, under mild conditions on the coefficients. We prove the well-posedness of the associated martingale problem as well as the existence of the density of ... More

Fast-Convergent Learning-aided Control in Energy Harvesting NetworksMar 19 2015Mar 20 2015In this paper, we present a novel learning-aided energy management scheme ($\mathtt{LEM}$) for multihop energy harvesting networks. Different from prior works on this problem, our algorithm explicitly incorporates information learning into system control ... More

QCD phase diagram at high temperature and densityJan 19 2010This article reviews recent progress of QCD phase structure, including color superconductor at high baryon density and strongly interacting quark-gluon plasma (sQGP) at high temperature created through relativistic heavy ion collision. A brief overview ... More

Sign-preserving of principal eigenfunctions in P1 finite element approximation of eigenvalue problems of second-order elliptic operatorsJun 09 2013This paper is concerned with the P1 finite element approximation of the eigenvalue problem of second-order elliptic operators subject to the Dirichlet boundary condition. The focus is on the preservation of basic properties of the principal eigenvalue ... More

Entropic uncertainty in the background of expanding de Sitter space-timeMay 01 2019We study the dynamics of quantum-memory-assisted entropic uncertainty for a hybrid qutrit-qubit system interacting with fluctuating quantum scalar field in the background of expanding de Sitter space. We firstly derive the master equation that the system ... More

A General Interpretation of Deep Learning by Affine Transform and Region Dividing without Mutual InterferenceJun 16 2019This paper mainly deals with the "black-box" problem of deep learning composed of ReLUs with n-dimensional input space, as well as some discussions of sigmoid-unit deep learning. We prove that a region of input space can be transmitted to succeeding layers ... More

On Learning to ProveApr 24 2019Apr 26 2019In this paper, we consider the problem of learning a (first-order) theorem prover where we use a representation of beliefs in mathematical claims instead of a proof system to search for proofs. The inspiration for doing so comes from the practices of ... More

Stable Yang-Mills connections on Special Holonomy ManifoldsNov 16 2015Feb 10 2017We prove that energy minimizing Yang-Mills connections on a compact $G_{2}$-manifold has holonomy equal to $G_{2}$ are $G_{2}$-instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing connections on a compact ... More

A generalized Lieb's theorem and its applications to spectrum estimates for a sum of random matricesAug 10 2018Nov 30 2018In this paper we prove the concavity of the $k$-trace functions, $A\mapsto (\text{Tr}_k[\exp(H+\ln A)])^{1/k}$, on the convex cone of all positive definite matrices. $\text{Tr}_k[A]$ denotes the $k_{\mathrm{th}}$ elementary symmetric polynomial of the ... More

Homotopy of gauge groups over non-simply-connected five dimensional manifoldsMay 13 2018May 10 2019Both the gauge groups and $5$-manifolds are important in physics and mathematics. In this paper, we combine them together to study the homotopy aspects of gauge groups over $5$-manifolds. For principal bundles over non-simply connected oriented closed ... More

$1/f$ noise on the brink of wet granular meltingFeb 17 2015Jul 23 2015The collective behavior of a two-dimensional wet granular cluster under horizontal swirling motions is investigated experimentally. Depending on the balance between the energy injection and dissipation, the cluster evolves into various nonequilibrium ... More

Dark Energy and Dark Matter in a Superfluid UniverseSep 23 2013The vacuum is filled with complex scalar fields, such as the Higgs field. These fields serve as order parameters for superfluidity (quantum phase coherence over macroscopic distances), making the entire universe a superfluid. We review a mathematical ... More

Spatial Throughput of Mobile Ad Hoc Networks Powered by Energy HarvestingNov 24 2011Jun 27 2013Designing mobiles to harvest ambient energy such as kinetic activities or electromagnetic radiation will enable wireless networks to be self sustaining besides alleviating global warming. In this paper, the spatial throughput of a mobile ad hoc network ... More

An Asymptotically Free Phi4 TheoryOct 06 1993The Phi4 theory in 4-epsilon dimensions has two fixed points, which coincide in the limit epsilon->0. One is a Gaussian UV fixed point, and the other a non-trivial IR fixed point. They lead to two different continuum field theories. The commonly adopted ... More