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The noncommutative Waring problemMar 14 2019This paper poses and treats a noncommutative version of the classical Waring problem for polynomials. That is, for a homogeneous \nc \ polynomial $p$, we find a condition equivalent to $p$ being expressible as sums of powers of homogeneous \nc \ polynomials. ... More

Characterization of Type Ia Supernova Light Curves Using Principal Component Analysis of Sparse Functional DataFeb 16 2018With growing data from ongoing and future supernova surveys it is possible to empirically quantify the shapes of SNIa light curves in more detail, and to quantitatively relate the shape parameters with the intrinsic properties of SNIa. Building such relationship ... More

CSI-Net: Unified Human Body Characterization and Pose RecognitionOct 07 2018Jan 22 2019We build CSI-Net, a unified Deep Neural Network~(DNN), to learn the representation of WiFi signals. Using CSI-Net, we jointly solved two body characterization problems: biometrics estimation (including body fat, muscle, water, and bone rates) and person ... More

Rotation Invariance Neural NetworkJun 17 2017Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol ... More

Fermionic formula for double Kostka polynomialsFeb 29 2016The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\Bla,\Bmu}(t),$ ... More

Large Magellanic Cloud Near-Infrared Synoptic Survey. V. Period-Luminosity Relations of MirasAug 16 2017We study the near-infrared properties of 690 Mira candidates in the central region of the Large Magellanic Cloud, based on time-series observations at JHKs. We use densely-sampled I-band observations from the OGLE project to generate template light curves ... More

Period estimation for sparsely-sampled quasi-periodic light curves applied to MirasSep 21 2016Sep 23 2016We develop a non-linear semi-parametric Gaussian process model to estimate periods of Miras with sparsely-sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum ... More

Period estimation for sparsely-sampled quasi-periodic light curves applied to MirasSep 21 2016Nov 17 2016We develop a non-linear semi-parametric Gaussian process model to estimate periods of Miras with sparsely-sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum ... More

The M33 Synoptic Stellar Survey. II. Mira VariablesMar 03 2017Mar 24 2017We present the discovery of 1847 Mira candidates in the Local Group galaxy M33 using a novel semi-parametric periodogram technique coupled with a Random Forest classifier. The algorithms were applied to ~2.4x10^5 I-band light curves previously obtained ... More

Quasiparticle Band Gaps, Excitonic Effects, and Anisotropic Optical Properties of Monolayer Distorted 1-T Diamond-chain StructuresAug 14 2015Sep 08 2015We report many-body perturbation theory calculations of excited-state properties of distorted 1-T diamond-chain monolayer rhenium disulfide (ReS2) and diselenide (ReSe2). Electronic self-energy substantially enhances their quasiparticle band gaps and, ... More

Combination of e+/e- ratio from AMS-02 and gamma ray line from Fermi-LAT with implication for Dark MatterOct 13 2013Oct 15 2013The precise AMS-02 data provide definite information for the e+/e- ratio in 100 - 350 GeV region. Assuming that the recent gamma ray line observed by Fermi-LAT experiment is product of dark matter in space and taken as input. We make a global fit for ... More

Double Kostka polynomials and Hall bimoduleJan 24 2015Double Kostka polynomials are polynomials indexed by a pair of double partitions. As in the ordinary case, double Kostka polynomials are defined in terms of Schur functions and Hall-Littlewood functions associated to double partitions. In this paper, ... More

Ligand-field helical luminescence in a 2D ferromagnetic insulatorOct 16 2017Bulk chromium triiodide (CrI$_3$) has long been known as a layered van der Waals ferromagnet. However, its monolayer form was only recently isolated and confirmed to be a truly two-dimensional (2D) ferromagnet, providing a new platform for investigating ... More

Diffusion Adaptation Framework for Compressive Sensing ReconstructionDec 03 2017Jun 22 2018Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively studied. Many reconstruction ... 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

The second largest eigenvalues of some Cayley graphs on alternating groupsNov 24 2017Dec 12 2018Let $A_n$ denote the alternating group of degree $n$ with $n\geq 3$. The alternating group graph $AG_n$, extended alternating group graph $EAG_n$ and complete alternating group graph $CAG_n$ are the Cayley graphs $\mathrm{Cay}(A_n,T_1)$, $\mathrm{Cay}(A_n,T_2)$ ... 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

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

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

Thermodynamics of interacting tachyonic scalar fieldNov 30 2016In this paper we discuss the laws of thermodynamics for interacting tachyonic scalar field. The components of the tachyonic scalar field in the universe are taken to exist in the state of non-equilibrium initially, but due to interaction they undergo ... More

Maximum Correntropy Adaptive Filtering Approach for Robust Compressive Sensing ReconstructionJun 10 2017Robust compressive sensing(CS) reconstruction has become an attractive research topic in recent years. Robust CS aims to reconstruct the sparse signals under non-Gaussian(i.e. heavy tailed) noises where traditional CS reconstruction algorithms may perform ... More

Maximum Total Correntropy Diffusion Adaptation over Networks with Noisy LinksFeb 14 2018Distributed estimation over networks draws much attraction in recent years. In many situations, due to imperfect information communication among nodes, the performance of traditional diffusion adaptive algorithms such as the diffusion LMS (DLMS) may degrade. ... 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

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

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

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

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

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

Fourier coefficients of $\times p$-invariant measuresJun 20 2016We define densities $D_\Sigma(A)$, $\overline{D}_\Sigma(A)$ and $\underline{D}_\Sigma(A)$ for a subset $A$ of $\mathbb{N}$ with respect to a sequence $\Sigma$ of finite subsets of $\mathbb{N}$ and study Fourier coefficients of ergodic, weak-mixing and ... More

A generalized Fejér's theorem for locally compact groupsDec 03 2015Feb 26 2016We prove a generalized Fej\'er's theorem for locally compact groups.

Doubly-nonparametric generalized linear modelsMar 02 2016We extend nonparametric generalized linear models to allow both the mean curve and the response distribution to be nonparametric. The seemingly intractable task of working with two infinite-dimensional parameters is shown to be reducible to a finite optimization ... More

Homological Dimensions Relative to Preresolving SubcategoriesFeb 09 2015We introduce relative preresolving subcategories and precoresolving subcategories of an abelian category and define homological dimensions and codimensions relative to these subcategories respectively. We study the properties of these homological dimensions ... More

The Measure of Strong CP ViolationSep 14 1992We investigate a controversial issue on the measure of CP violation in strong in teractions. In the presence of nontrivial topological gauge configurations, the $\theta$-term in QCD has a profound effect: it breaks the CP symmetry. The CP-violating amplitude ... More

Structure Based Aesthetics and Support of Cognitive Tasks for Graph EvaluationSep 25 2016Drawing principles, or aesthetics, are important in graph drawing. They are used as criteria for algorithm design and for quality evaluation. Current aesthetics are described as visual properties that a drawing is required to have to be visually pleasing. ... More

Non-existence of certain singularities in Legendrian foliationsNov 21 2014In this paper we show that the singular locus of a Legendrian foliation as defined in [Hua13] is a compact submanifold whose connected components are of codimension at most two. As a consequence, given any closed $(n+1)$-dimensional coisotropic submanifold ... More

Exotic $\mathbb{R}^4$'s and positive isotropic curvatureMay 03 2016May 05 2016We show that no exotic $\mathbb{R}^4$ admits a complete Riemannian metric with uniformly positive isotropic curvature and with bounded geometry. This is essentially a corollary of the main result in [Hu1], and was stated in [Hu2] without proof. In the ... More

On the maximum induced density of directed stars and related problemsMar 13 2013Mar 17 2013Let k>=3 be an integer, we prove that the maximum induced density of the k-vertex directed star in a directed graph is attained by an iterated blow-up construction. This confirms a conjecture by Falgas-Ravry and Vaughan, who proved this for k=3, 4. This ... More

Four-orbifolds with positive isotropic curvatureJul 07 2011Feb 02 2016We prove the following result: Let $(X,g_0)$ be a complete, connected 4-manifold with uniformly positive isotropic curvature and with bounded geometry. Then there is a finite collection $\mathcal{F}$ of manifolds of the form $\mathbb{S}^3 \times \mathbb{R} ... More

Complete Kähler manifolds with pinched bisectional curvatureAug 17 2006Apr 10 2007This paper has been withdrawn by the author due to a serious gap in the proof of the main theorem.

A note on K$\ddot{a}$hler manifolds with almost nonnegative bisectional curvatureJul 15 2008Nov 10 2008In this note we prove the following result: There is a positive constant $\epsilon(n,\Lambda)$ such that if $M^n$ is a simply connected compact K$\ddot{a}$hler manifold with sectional curvature bounded from above by $\Lambda$, diameter bounded from above ... More

On generalized estimating equations for vector regressionMar 01 2016Jul 26 2016Generalized estimating equations (GEE; Liang & Zeger 1986) for general vector regression settings are examined. When the response vectors are of mixed type (e.g. continuous-binary response pairs), the GEE approach is a semiparametric alternative to full-likelihood ... More

Quasi-isometry classification of right-angled Artin groups II: several infinite out casesMar 08 2016We are motivated by the question that for which class of right-angled Artin groups (RAAG's), the quasi-isometry classification coincides with commensurability classification. This is previously known for RAAG's with finite outer automorphism groups. In ... More

Discovery of Latent Factors in High-dimensional Data Using Tensor MethodsJun 10 2016Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have applications ... More

A Physical Review on CurrencyApr 18 2018A theoretical self-sustainable economic model is established based on the fundamental factors of production, consumption, reservation and reinvestment, where currency is set as a unconditional credit symbol serving as transaction equivalent and stock ... More

Unconventional Color SuperconductorJan 31 2007Superfluidity or superconductivity with mismatched Fermi momenta appears in many systems such as charge neutral dense quark matter, asymmetric nuclear matter, and in imbalanced cold atomic gases. The mismatch plays the role of breaking the Cooper pairing, ... More

Sequential Resource Allocation with Positional CostsApr 22 2014We consider the problem of minimizing the total cost to run a sequence of $n$ tasks in the given order by $k$ agents under the positional cost model. The cost to run a task not only depends on the intrinsic cost of the task itself, but also monotonically ... More

4f fine-structure levels as the dominant error in the electronic structures of binary lanthanide oxidesJul 17 2015Nov 14 2015The ground-state 4f fine-structure levels in the intrinsic optical transition gaps between the 2p and 5d orbitals of lanthanide sesquioxides (Ln2O3, Ln=La...Lu) were calculated by a two-way crossover search for the U parameters for DFT+U calculations. ... More

Exponential sums over primes in short intervals and an application to the Waring--Goldbach problemDec 06 2014May 30 2016Let $\Lambda(n)$ be the von Mangoldt function, $x$ real and $2\leq y \leq x$. This paper improves the estimate on the exponential sum over primes in short intervals \[ S_k(x,y;\alpha) = \sum_{x< n \leq x+y} \Lambda(n) e\left( n^k \alpha \right) \] when ... More

Strong orthogonality between the Mobius function and nonlinear exponential functions in short intervalsDec 06 2014Mar 29 2015Let $\mu(n)$ be the M\"obius function, $e(z) = \exp(2\pi iz)$, $x$ real and $2\leq y \leq x$. This paper proves two sequences $(\mu(n))$ and $(e(n^k \alpha))$ are strongly orthogonal in short intervals. That is, if $k \geq 3$ being fixed and $y\geq x^{1-1/4+\varepsilon}$, ... More

A Lane-Change Path Planner and its application with a monocular cameraMar 06 2019Human drivers utilize the visual cues from the road to performance some fundamental driving tasks, e.g. lane keeping and lane change, for the complex driving maneuvers. Lane keeping and lane change can be generalized as one task, because both of them ... More

A Novel Delay-time Enlarged 3-D Gravitational Wave Detection SystemMay 31 2017A novel delay-time enlarged 3-dimensional gravitational wave (GW) detection system is presented. The operation principle is described. The basic specification requirements for all the critical components are analyzed. The whole system consists of three ... More

The 2D Euler-Boussinesq equations in planar polygonal domains with Yudovich's type dataMay 12 2014We address the well-posedness of the 2D (Euler)-Boussinesq equations with zero viscosity and positive diffusivity in the polygonal-like domains with Yudovich's type data, which gives a positive answer to part of the questions raised in 2011 [Lai-Pan-Zhao, ... More

A Note On Go Endgame And Nonstandard AnalysisSep 13 2009Sep 22 2009This paper has been withdrawn by the author, since the relation mentioned in the paper between nonstandard analysis and games is probably useless.

Internal and surface waves in vibrofluidized granular materials: Role of cohesionFeb 26 2018May 18 2018Wave phenomena in vibrofluidized dry and partially wet granular materials confined in a quasi-two-dimensional geometry are investigated with numerical simulations considering individual particles as hard spheres. Short ranged cohesive interactions arising ... More

Growth-Collapse Cycles of a Bose-Einstein Condensate with Attractive InteractionsOct 23 2001A Bose-Einstein condensate of atoms with attractive interactions exhibits growth and collapse cycles, when it is fed by a thermal cloud. Recently this phenomenon has been directly observed in a trapped Li-7 gas. We offer a quantitative explanation of ... More

An Energy Gap for Complex Yang-Mills EquationsJun 13 2016Aug 08 2017We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory Appl. 11 (2012), ... More

Observational effects of a running Planck massNov 09 2015Feb 10 2016We consider observational effects of a running effective Planck mass in the scalar-tensor gravity theory. At the background level, an increasing effective Planck mass allows a larger Hubble constant $H_0$, which is more compatible with the local direct ... More

Positivity for quantum cluster algebras from unpunctured orbifoldsOct 10 2018We give the quantum Laurent expansion formula for the quantum cluster algebras from unpunctured orbifolds with arbitrary coefficients and quantization. As an application, positivity for such class of quantum cluster algebras is given. For technical reasons, ... More

Homotopy types of gauge groups over high dimensional manifoldsMay 13 2018The homotopy theory of gauge groups received considerable attentions in the recent decades, in the theme of which, the works mainly focus on bundles over $4$-dimensional manifolds and vary the structure groups case by case. In this work, we study the ... More

An improved upper bound for the bondage number of graphs on surfacesNov 23 2011May 21 2012The bondage number $b(G)$ of a graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with larger domination number. Recently Gagarin and Zverovich showed that, for a graph $G$ with maximum degree $\Delta(G)$ and embeddable ... More

On Asymptotic Weil-Petersson Geometry of Teichmüller Space of Riemann SurfacesMay 12 2004May 19 2004In this paper, we study the asymptotic geometry of Teichmuller space of Riemann surfaces and give bounds on the Weil-Petersson sectional curvature of Teichmuller space, in terms of the length of the shortest geodesic on the surface. This will also imply ... More

A simple adaptive-feedback controller for high-quality chaos synchronizationMay 08 2004Nov 16 2004Based on the invariance principle of differential equations, a simple adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to ... More

A generalized Fejér's theorem for locally compact groupsDec 03 2015Feb 20 2017We prove a generalized Fej\'er's theorem for locally compact groups.

The quantum group fixing a sequence of finite subsetsJul 25 2016Oct 18 2017Motivated by generalizing Szemer\'edi's theorem, we the elements in a discrete quantum group fixing a sequence of finite subsets and prove that the set of these elements is a quantum subgroup. Using this we obtain a version of mean ergodic theorem for ... More

Proper Resolutions and Gorenstein CategoriesMar 19 2012Let $\mathscr{A}$ be an abelian category and $\mathscr{C}$ an additive full subcategory of $\mathscr{A}$. We provide a method to construct a proper $\mathscr{C}$-resolution (resp. coproper $\mathscr{C}$-coresolution) of one term in a short exact sequence ... More

The Interpretation of Linear Prediction by Interpolation Framework and Two General Constructive MethodsOct 23 2018Dec 23 2018This paper gives a general interpretation of Linear Prediction (LP) by interpolation framework and simultaneously develops a foundation of LP different from the perspective of statistics. The reason of LP's effectiveness, i.e., why linear weighted sum ... More

Syzygy Modules and Injective Cogenerators for Noether RingsAug 11 2013In this paper, we focus on $n$-syzygy modules and the injective cogenerator determined by the minimal injective resolution of a noether ring. We study the properties of $n$-syzygy modules and a category $R_n(\mod R)$ which includes the category consisting ... More

Efficient simulation of many-body localized systemsAug 19 2015An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum) algorithm can ... More

The First Eigenvalue for Compact Minimal Embedded Hypersurface in $S^{n+1}(1)$ ($n\geq 3$) is $n$Nov 04 2004Jun 02 2005I'm sorry that there is a gap in this paper.

Duality Pairs Induced by Auslander and Bass ClassesSep 24 2018Sep 25 2018Let $R$ and $S$ be any rings and $_RC_S$ a semidualizing bimodule, and let $\mathcal{A}_C(R^{op})$ and $\mathcal{B}_C(R)$ be the Auslander and Bass classes respectively. Then both the pairs $$(\mathcal{A}_C(R^{op}),\mathcal{B}_C(R))\ {\rm and}\ (\mathcal{B}_C(R),\mathcal{A}_C(R^{op}))$$ ... More

On Auslander-Type Conditions of ModulesDec 08 2010Mar 20 2014We prove that for a left and right Noetherian ring $R$, $_RR$ satisfies the Auslander condition if and only if so does every flat left $R$-module, if and only if the injective dimension of the $i$th term in a minimal flat resolution of any injective left ... More

Convergence of Maximum Bisection Ratio of Sparse Random GraphsFeb 05 2018Aug 16 2018We consider sequences of large sparse random graphs whose degree distribution approaches a limit with finite mean. This model includes both the random regular graphs and the Erd\"os-Renyi graphs of constant average degree. We prove that the maximum bisection ... More

Wakamatsu Tilting Modules, $U$-Dominant Dimension and $k$-Gorenstein ModulesSep 09 2004Sep 18 2006Let $\Lambda$ and $\Gamma$ be left and right noetherian rings and $_{\Lambda}U$ a Wakamatsu tilting module with $\Gamma ={\rm End}(_{\Lambda}T)$. We introduce a new definition of $U$-dominant dimensions and show that the $U$-dominant dimensions of $_{\Lambda}U$ ... More

The advanced maximum principle for parabolic systems on manifolds with boundaryFeb 10 2008Feb 23 2008In this short note we extend Chow and Lu's advanced maximum principles for parabolic systems on closed manifolds to the case of compact manifolds with boundary, which also generalizes a Hopf type theorem of Pulemotov.

Path integral approach to analytic continuation of Liouville theory: the pencil regionSep 23 2018We study the problem of analytic continuation of Liouville Conformal Field Theory using the probabilistic approach of David, Kupiainen, Rhodes and Vargas [DKRV16] based on the theory of Gaussian Multiplicative Chaos. The key idea is to apply stochastic ... More

Efficient Time-Evolving Stream Processing at ScaleJun 03 2018Time-evolving stream datasets exist ubiquitously in many real-world applications where their inherent hot keys often evolve over times. Nevertheless, few existing solutions can provide efficient load balance on these time-evolving datasets while preserving ... More

Hopf Ore ExtensionsFeb 06 2019Brown, O'Hagan, Zhang, and Zhuang gave a set of conditions on an automorphism $\sigma$ and a $\sigma$-derivation $\delta$ of a Hopf $k$-algebra $R$ for when the skew polynomial extension $T=R[x, \sigma, \delta]$ of $R$ admits a Hopf algebra structure ... More

On plastikstufe, bordered Legendrian open book and overtwisted contact structuresJul 27 2016Aug 03 2016In this paper we prove the presence of an embedded plastikstufe implies overtwistedness of the contact structure in any dimension. Moreover, we show in dimension 5 that the presence of an embedded bordered Legendrian open book (bLob) also implies overtwistedness. ... More

The properties of sendograph metric on fuzzy number spacesJul 24 2013This paper discusses the variation of sendograph distances under some algebra operations.

Equidistribution and measure rigidity under $\times p,\times q$Nov 17 2014Jun 08 2015We show that equidistribution of irrational orbits on the unit circle implies Furstenberg's conjecture.

The transverse Chern-Ricci flowJun 08 2015We introduce transverse Chern-Ricci flow for transversely Hermitian foliations, which is analogous to the Chern-Ricci flow. We show that when $\mathcal{F}$ is homologically orientable and the basic first Bott-Chern class is zero, starting at any transversely ... More

Sasaki manifolds with positive transverse orthogonal bisectional curvatureJan 07 2013Jan 09 2013In this short note we show the following result: Let $(M^{2n+1},g)$ ($n \geq 2$) be a compact Sasaki manifold with positive transverse orthogonal bisectional curvature. Then $\pi_1(M)$ is finite, and the universal cover of $(M^{2n+1},g)$ is isomorphic ... More

Three-orbifolds with positive scalar curvatureOct 27 2012We prove the following result: Let $(\mathcal{O},g_0)$ be a complete, connected 3-orbifold with uniformly positive scalar curvature, with bounded geometry, and containing no bad 2-suborbifolds. Then there is a finite collection $\mathcal{F}$ of spherical ... More

Ricci flow on open 4-manifolds with positive isotropic curvatureAug 15 2011Aug 30 2011In this note we prove the following result: Let $X$ be a complete, connected 4-manifold with uniformly positive isotropic curvature, with bounded geometry and with no essential incompressible space form. Then $X$ is diffeomorphic to $\mathbb{S}^4$, or ... More

State sampling dependence of the Hopfield network inferenceApr 26 2011Aug 31 2011The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the ... More

The $L^{3/2}$-norm of the scalar curvature under the Ricci flow on a 3-manifoldJan 04 2011Feb 28 2011Assume $M$ is a closed 3-manifold whose universal covering is not $S^3$. We show that the obstruction to extend the Ricci flow is the boundedness $L^{3/2}$-norm of the scalar curvature $R(t)$, i.e, the Ricci flow can be extended over time $T$ if and only ... More

Reconstructing the Hopfield network as an inverse Ising problemSep 10 2009Dec 14 2009We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing technique is adopted. ... More

A countable set derived by fuzzy setOct 19 2015In this paper, it shows that for each fuzzy set $u$ on $\mathbb{R}^m$, the set $D(u)$ is at most countable. Based on this, it modifies the proof of assertion (I) in step 2 of the sufficiency part of Theorem 4.1 in paper: Characterizations of compact sets ... More

A note on Morse's index theorem for Perelman's $\mathcal{L}$-lengthFeb 06 2006This is essentially a note on Section 7 of Perelman's first paper on Ricci flow. We list some basic properties of the index form for Perelman's $ \mathcal{L} $-length, which are analogous to the ones in Riemannian case (with fixed metric), and observe ... More

Log-linear Conway-Maxwell-Poisson models for dispersed countsJun 10 2016Conway-Maxwell-Poisson (COMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to directly model the ... More