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Modeling Rich Contexts for Sentiment Classification with LSTMMay 05 2016Sentiment analysis on social media data such as tweets and weibo has become a very important and challenging task. Due to the intrinsic properties of such data, tweets are short, noisy, and of divergent topics, and sentiment classification on these data ... More

Knowledge Semantic Representation: A Generative Model for Interpretable Knowledge Graph EmbeddingAug 27 2016Knowledge representation is a critical topic in AI, and currently embedding as a key branch of knowledge representation takes the numerical form of entities and relations to joint the statistical models. However, most embedding methods merely concentrate ... More

A Deep Sequential Model for Discourse Parsing on Multi-Party DialoguesDec 01 2018Discourse structures are beneficial for various NLP tasks such as dialogue understanding, question answering, sentiment analysis, and so on. This paper presents a deep sequential model for parsing discourse dependency structures of multi-party dialogues. ... More

Robustly Leveraging Prior Knowledge in Text ClassificationMar 03 2015Prior knowledge has been shown very useful to address many natural language processing tasks. Many approaches have been proposed to formalise a variety of knowledge, however, whether the proposed approach is robust or sensitive to the knowledge supplied ... More

An Interpretable Reasoning Network for Multi-Relation Question AnsweringJan 15 2018Jun 01 2018Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network ... More

SSP: Semantic Space Projection for Knowledge Graph Embedding with Text DescriptionsApr 17 2016Oct 25 2016Knowledge representation is an important, long-history topic in AI, and there have been a large amount of work for knowledge graph embedding which projects symbolic entities and relations into low-dimensional, real-valued vector space. However, most embedding ... More

SSP: Semantic Space Projection for Knowledge Graph Embedding with Text DescriptionsApr 17 2016Knowledge graph embedding represents the entities and relations as numerical vectors, and then knowledge analysis could be promoted as a numerical method. So far, most methods merely concentrate on the fact triples that are composed by the symbolic entities ... More

Linguistically Regularized LSTMs for Sentiment ClassificationNov 12 2016Sentiment understanding has been a long-term goal of AI in the past decades. This paper deals with sentence-level sentiment classification. Though a variety of neural network models have been proposed very recently, however, previous models either depend ... More

From One Point to A Manifold: Knowledge Graph Embedding For Precise Link PredictionDec 15 2015Jun 17 2017Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space. However, existing methods could not characterize the knowledge graph in a fine degree to ... More

KSR: A Semantic Representation of Knowledge Graph within a Novel Unsupervised ParadigmAug 27 2016May 11 2018Knowledge representation is a long-history topic in AI, which is very important. A variety of models have been proposed for knowledge graph embedding, which projects symbolic entities and relations into continuous vector space. However, most related methods ... More

Story Ending Generation with Incremental Encoding and Commonsense KnowledgeAug 30 2018Dec 02 2018Generating a reasonable ending for a given story context, i.e., story ending generation, is a strong indication of story comprehension. This task requires not only to understand the context clues which play an important role in planning the plot but also ... More

Knowledge Semantic Representation: A Generative Model for Interpretable Knowledge Graph EmbeddingAug 27 2016Oct 25 2016Knowledge representation is an important, long-history topic in AI, and there have been a large amount of work for knowledge graph embedding which projects symbolic entities and relations into low-dimensional, real-valued vector space. However, most embedding ... More

From One Point to A Manifold: Knowledge Graph Embedding For Precise Link PredictionDec 15 2015Jan 25 2016Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space. However, existing methods could not characterize the knowledge graph in a fine degree to ... More

SSP: Semantic Space Projection for Knowledge Graph Embedding with Text DescriptionsApr 17 2016Jun 17 2017Knowledge representation is an important, long-history topic in AI, and there have been a large amount of work for knowledge graph embedding which projects symbolic entities and relations into low-dimensional, real-valued vector space. However, most embedding ... More

Challenges in Building Intelligent Open-domain Dialog SystemsMay 13 2019There is a resurgent interest in developing intelligent open-domain dialog systems due to the availability of large amounts of conversational data and the recent progress on neural approaches to conversational AI. Unlike traditional task-oriented bots, ... More

Personalized Dialogue Generation with Diversified TraitsJan 28 2019Endowing a dialogue system with particular personality traits is essential to deliver more human-like conversations. However, due to the challenge of embodying personality via language expression and the lack of large-scale persona-labeled dialogue data, ... More

Reinforcement Learning for Relation Classification from Noisy DataAug 24 2018Existing relation classification methods that rely on distant supervision assume that a bag of sentences mentioning an entity pair are all describing a relation for the entity pair. Such methods, performing classification at the bag level, cannot identify ... More

Learning to Ask Questions in Open-domain Conversational Systems with Typed DecodersMay 13 2018Asking good questions in large-scale, open-domain conversational systems is quite significant yet rather untouched. This task, substantially different from traditional question generation, requires to question not only with various patterns but also on ... More

TransG : A Generative Mixture Model for Knowledge Graph EmbeddingSep 18 2015Dec 27 2015Recently, knowledge graph embedding, which projects symbolic entities and relations into continuous vector space, has become a new, hot topic in artificial intelligence. This paper addresses a new issue of \textbf{multiple relation semantics} that a relation ... More

Meta-Learning for Low-resource Natural Language Generation in Task-oriented Dialogue SystemsMay 14 2019Natural language generation (NLG) is an essential component of task-oriented dialogue systems. Despite the recent success of neural approaches for NLG, they are typically developed for particular domains with rich annotated training examples. In this ... More

TransG : A Generative Mixture Model for Knowledge Graph EmbeddingSep 18 2015Sep 08 2017Recently, knowledge graph embedding, which projects symbolic entities and relations into continuous vector space, has become a new, hot topic in artificial intelligence. This paper addresses a new issue of multiple relation semantics that a relation may ... More

Knowlege Graph Embedding by Flexible TranslationMay 20 2015Sep 10 2015Knowledge graph embedding refers to projecting entities and relations in knowledge graph into continuous vector spaces. State-of-the-art methods, such as TransE, TransH, and TransR build embeddings by treating relation as translation from head entity ... More

A Hierarchical Framework for Relation Extraction with Reinforcement LearningNov 09 2018Most existing methods determine relation types only after all the entities have been recognized, thus the interaction between relation types and entity mentions is not fully modeled. This paper presents a novel paradigm to deal with relation extraction ... More

Word Embedding based Edit DistanceOct 25 2018Text similarity calculation is a fundamental problem in natural language processing and related fields. In recent years, deep neural networks have been developed to perform the task and high performances have been achieved. The neural networks are usually ... More

Relation Mention Extraction from Noisy Data with Hierarchical Reinforcement LearningNov 03 2018In this paper we address a task of relation mention extraction from noisy data: extracting representative phrases for a particular relation from noisy sentences that are collected via distant supervision. Despite its significance and value in many downstream ... More

Linguistically Regularized LSTMs for Sentiment ClassificationNov 12 2016Apr 25 2017Sentiment understanding has been a long-term goal of AI in the past decades. This paper deals with sentence-level sentiment classification. Though a variety of neural network models have been proposed very recently, however, previous models either depend ... More

TransA: An Adaptive Approach for Knowledge Graph EmbeddingSep 18 2015Sep 28 2015Knowledge representation is a major topic in AI, and many studies attempt to represent entities and relations of knowledge base in a continuous vector space. Among these attempts, translation-based methods build entity and relation vectors by minimizing ... More

Emotional Chatting Machine: Emotional Conversation Generation with Internal and External MemoryApr 04 2017Jun 01 2018Perception and expression of emotion are key factors to the success of dialogue systems or conversational agents. However, this problem has not been studied in large-scale conversation generation so far. In this paper, we propose Emotional Chatting Machine ... More

Assigning personality/identity to a chatting machine for coherent conversation generationJun 09 2017Jun 21 2017Endowing a chatbot with personality or an identity is quite challenging but critical to deliver more realistic and natural conversations. In this paper, we address the issue of generating responses that are coherent to a pre-specified agent profile. We ... More

Augmenting End-to-End Dialog Systems with Commonsense KnowledgeSep 16 2017Feb 12 2018Building dialog agents that can converse naturally with humans is a challenging yet intriguing problem of artificial intelligence. In open-domain human-computer conversation, where the conversational agent is expected to respond to human responses in ... More

Aggregating E-commerce Search Results from Heterogeneous Sources via Hierarchical Reinforcement LearningFeb 24 2019In this paper, we investigate the task of aggregating search results from heterogeneous sources in an E-commerce environment. First, unlike traditional aggregated web search that merely presents multi-sourced results in the first page, this new task may ... More

Memory-augmented Dialogue Management for Task-oriented Dialogue SystemsMay 01 2018Dialogue management (DM) decides the next action of a dialogue system according to the current dialogue state, and thus plays a central role in task-oriented dialogue systems. Since dialogue management requires to have access to not only local utterances, ... More

Learning to Collaborate: Multi-Scenario Ranking via Multi-Agent Reinforcement LearningSep 17 2018Ranking is a fundamental and widely studied problem in scenarios such as search, advertising, and recommendation. However, joint optimization for multi-scenario ranking, which aims to improve the overall performance of several ranking strategies in different ... More

Domain-Constrained Advertising Keyword GenerationFeb 27 2019Advertising (ad for short) keyword suggestion is important for sponsored search to improve online advertising and increase search revenue. There are two common challenges in this task. First, the keyword bidding problem: hot ad keywords are very expensive ... More

ConvLab: Multi-Domain End-to-End Dialog System PlatformApr 18 2019We present ConvLab, an open-source multi-domain end-to-end dialog system platform, that enables researchers to quickly set up experiments with reusable components and compare a large set of different approaches, ranging from conventional pipeline systems ... 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

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

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

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

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

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

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

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

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

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

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

A heuristic view about the evolution and speciesApr 16 2010The controversy concerning both the definition of the species and methods for inferring the boundaries and numbers of species has occupied biologists for centuries, and the debate itself has become known as the species problem. The modern theory of evolution ... More

On Legendrian foliations in contact manifolds II: Deformation theoryNov 23 2014Using the structural theorems developed in [Hua13], we study the deformation theory of coisotropic submanifolds in contact manifolds, under the assumption that the characteristic foliation is nonsingular. In the "middle" dimensions, we find an interesting ... More

A polynomial-time algorithm for the ground state of one-dimensional gapped HamiltoniansJun 24 2014Oct 26 2015A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let $\epsilon,n,\eta$ be the energy gap, the system size, and the desired precision, respectively. Neglecting ... More

Approximation capability of the convolution methods for fuzzy numbersAug 06 2014This paper shows that how to approximate general fuzzy number by using convolution method.

Convergence of the calabi flow on toric varieties and related Kaehler manifoldsJul 25 2012Let $X$ be a toric variety and $u$ be a normalized symplectic potential of the corresponding polytope $P$. Suppose that the Riemannian curvature is bounded by 1 and $ \int_{\partial P} u ~ d \sigma < C_1, $ then there exists a constant $C_2$ depending ... More

Backwards uniqueness of the mean curvature flowJul 06 2009In this note we prove the backwards uniqueness of the mean curvature flow in codimension one case. More precisely,let $F_t, \widetilde{F}_t:M^n \to \overline{M}^{n+1}$ be two complete solutions of the mean curvature flow on $M^n \times [0,T]$ with bounded ... More

Greatest lower bounds on the transverse Ricci curvature of some toric Sasaki manifoldsSep 20 2016We determine the greatest lower bounds on the transverse Ricci curvature of compact toric Sasaki manifolds with positive basic first Chern class and with the first Chern class of the contact bundle being trivial. This is based on Wang-Zhu's and Futaki-Ono-Wang's ... More

Entanglement dynamics in critical random quantum Ising chain with perturbationsNov 15 2016We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with ... More

On plastikstufe, bordered Legendrian open book and overtwisted contact structuresJul 27 2016Oct 06 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

On Structure and History of Space-time with Variable Speed of LightOct 15 2004We apply the variable speed of light into general relativity in order to solve the problems we met in the standard cosmology. We're surprised to find that, the results from the general relativity in cosmology are exactly the same as those we got from ... More

$L^{2}$ harmonic forms on complete special holonomy manifoldsJan 13 2018Apr 01 2018In this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a non-zero parallel form $\omega$. The main result is that if $(X,\omega)$ is a complete $G_{2}$- ( or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- ... More

Extension the Noether's theorem to Lagrangian formulation with nonlocalityMar 06 2012A Lagrangian formulation with nonlocality is investigated in this paper. The nonlocality of the Lagrangian is introduced by a new nonlocal argument that is defined as a nonlocal residual satisfying the zero mean condition. The nonlocal Euler-Lagrangian ... More

Multi-almost periodicity and invariant basins of general neural networks under almost periodic stimuliNov 19 2009In this paper, we investigate convergence dynamics of $2^N$ almost periodic encoded patterns of general neural networks (GNNs) subjected to external almost periodic stimuli, including almost periodic delays. Invariant regions are established for the existence ... More

Do W_L and H form a p-wave bound state?Mar 03 1995We examine the possibility of bound state formation in the W_L H --> W_L H channel. The dynamical calculation using the N/D method indicates that when the interactions among the Goldstone and Higgs bosons become sufficiently strong, a p-wave state [I^G(J^P)=1^-(1^+)] ... More

Lagrangian formulism of elasticity with relevance to surface energyNov 05 2012By introducing the divergence of a vector potential into the Lagrangian, a Lagrangian framework is developed to incorporate surface energy into elasticity. Besides the Euler-Lagrange equation and natural boundary condition, a new boundary constitutive ... More

Magnetic loops above a small flux-emerging region observed by IRIS, Hinode and SDONov 08 2018I report on observations of a set of magnetic loops above a region with late-phase flux emergence taken by IRIS, Hinode and SDO. The loop system consists of many transition region loop threads with size of 5--12\arcsec\ in length and $\sim0.5$\arcsec ... More

On a topology property for moduli space of Kapustin-Witten equationsMar 20 2017Apr 17 2018In this article, we study the Kapustin-Witten equations on a closed, simply-connected, four-manifold. We using a compactness theorem due to Taubes to prove that if $(A,\phi)$ is a solution of Kapustin-Witten equations and the connection $A$ is closed ... More

A Cosmology Forecast Toolkit -- CosmoLibJan 28 2012Jun 11 2012The package CosmoLib is a combination of a cosmological Boltzmann code and a simulation toolkit to forecast the constraints on cosmological parameters from future observations. In this paper we describe the released linear-order part of the package. We ... More

Stabilizing near-nonhyperbolic chaotic systems and its potential applications in neuroscienceMay 08 2004May 11 2004Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly any chaotic systems without any prior analytical knowledge of the systems. ... More

Hall Viscosity Revealed via Density ResponseJan 21 2015Jun 03 2015Quantum Hall systems are recently shown to possess a quantity sensitive to the spatial geometry and topology of the system, dubbed the Hall viscosity $\eta_H$. Despite the extensive theoretical discussions on its properties, the question of how to measure ... More

Cyclic Descents for General Skew TableauxAug 14 2018A cyclic descent function on standard Young tableaux of size $n$ is a function that restricts to the usual descent function when $n$ is omitted, such that the number of standard Young tableaux of given shape with cyclic descent set $D\subset[n]$ is invariant ... More

An Averaging Theorem for Perturbed KdV EquationJan 08 2013We consider a perturbed KdV equation: [\dot{u}+u_{xxx} - 6uu_x = \epsilon f(x,u(\cdot)), \quad x\in \mathbb{T}, \quad\int_\mathbb{T} u dx=0.] For any periodic function $u(x)$, let $I(u)=(I_1(u),I_2(u),...)\in\mathbb{R}_+^{\infty}$ be the vector, formed ... More

A Critical History of RenormalizationOct 21 2013The history of renormalization is reviewed with a critical eye, starting with Lorentz's theory of radiation damping, through perturbative QED with Dyson, Gell-Mann & Low, and others, to Wilson's formulation and Polchinski's functional equation, and applications ... More

Protein Folding as a Physical Stochastic ProcessJul 17 2007We model protein folding as a physical stochastic process as follows. The unfolded protein chain is treated as a random coil described by SAW (self-avoiding walk). Folding is induced by hydrophobic forces and other interactions, such as hydrogen bonding, ... More

CSAW: a dynamical model of protein foldingJan 12 2006CSAW (conditioned self-avoiding walk) is a model of protein folding that combines SAW (self-avoiding walk) with Monte-Carlo. It simulates the Brownian motion of a chain molecule in the presence of interactions, both among chain residues, and with the ... More

Connecting phase transition theory with unsupervised learningDec 15 2017Entropy and order parameter are two key concepts in phase transition theory. This paper proposes an unified method to both find order parameter and estimate entropy automatically with unsupervised learning. The contributions of this paper are threefold: ... More

Generalized Greatest Common Divisors for the Orbits under Rational FunctionsFeb 13 2017Aug 08 2018Assume Vojta's Conjecture. Suppose $a, b, \alpha,\beta \in \mathbb{Z}$, and $f(x),g(x) \in \mathbb{Z}[x]$ are polynomials of degree $d \ge 2$. Assume that the sequence $(f^{\circ n}(a), g^{\circ n}(b))_n$ is generic and $\alpha,\beta$ are not exceptional ... More

Bose Condensate in External Potential: A Thomas-Fermi ApproachSep 03 1996The Bose condensate in an external potential is treated in the Thomas-Fermi approximation.

$L^{2}$ vanishing theorem on some Kähler manifoldsNov 27 2018Let $E$ be a Hermitian vector bundle over a complete K\"{a}hler manifold $(X^{2n},\omega)$ with a $d$(bounded) fundamental form $\omega$, $A$ be a Hermitian connection on $E$. The goal of this article is to study the $L^{2}$-Hodge theory on the vector ... More

A compactness theorem of flat $SL(2,\mathbb{C})$ connections on $3$-foldsJun 12 2017In this article, we obtain a compactness theorem of flat $SL(2,\mathbb{C})$-connections by using a compactness theorem of Vafa-Witten equations proved by Tanaka (arXiv:1308.0862). We also using the compactness theorem to study the topology property of ... More

Non-existence of Higgs fields on Calabi-Yau ManifoldsMay 03 2017May 15 2017In this article, we study the Higgs $G$-bundles $(E,\theta)$ on a compact Calabi-Yau manifolds $X$. Our main result is that there is non-existence Higgs fields $\theta$ on a semistable Higgs $G$-bundle over a compact connected Calabi-Yau surface. The ... More

Probing Anomalous Top Quark Couplings at the Future Linear CollidersSep 05 2000Sep 20 2000In terms of an effective Lagrangian we investigate the possibilities of probing anomalous top quark couplings, $t \bar{t} H$, $\gamma t \bar{t}$, $Z t \bar{t}$ and $tWb$ at the future linear colliders. It is found that probing anomalous top quark couplings, ... More

A lower bound on the solutions of Kapustin-Witten equationsJan 29 2016Sep 23 2016In this article, we consider the Kapustin-Witten equations on a closed $4$-manifold. We study certain analytic properties of solutions to the equations on a closed manifold. The main result is that there exists an $L^{2}$-lower bound on the extra fields ... More

Some Energy Properties of Yang-Mills ConnectionsFeb 11 2015Jun 14 2016We consider a vector bundle $E$ over a compact Riemannian manifold $M$=$M^{n}$,$n\geq 4$,and $A$ is a Yang-Mills connection with $L^{\frac{n}{2}}$ curvature $F_{A}$ on $E$.Then we prove a mean value inequality for the density $|F_{A}|^{\frac{n}{2}}$.This ... More

Instantons on Cylindrical ManifoldsJan 19 2015Mar 07 2016We consider an instanton,$\textbf{A}$,with $L^{2}$-curvature $F_{\textbf{A}}$ on the cylindrical manifold $Z=\mathbf{R}\times M$,where $M$ is a closed Riemannian $n$-manifold, $n\geq 4$.We assume $M$ admits a $3$-form $P$ and a $4$-form $Q$ satisfy $dP=4Q$ ... More

A note on the Ricci flow on noncompact manifoldsJul 01 2008Jul 07 2008Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci flow with initial data $(M^3,g_0)$ ... More

Approximation diophantienne et distribution locale sur une surface torique IIMay 10 2018May 07 2019We propose an empirical formula for the problem of local distribution of rational points of bounded height. This is a local version of the Batyrev-Manin-Peyre principle. We verify this for a toric surface, on which cuspidal rational curves and nodal rational ... More

Impulse response of the Bayreuth FestspielhausMar 21 2017The Bayreuth Festspielhaus is well known for its architecture because its design is heavily influenced by composer Richard Wagner. Due to the special acoustic design, the reverberation time (i.e., time scale for the sound pressure level to decay $60$~dB) ... More

Asymptotic behaviour of instantons on Cylinder ManifoldsJan 22 2018Apr 30 2019IIn this article, we study the instanton equation on the cylinder over a closed manifold $X$ which admits non-zero smooth $3$-form $P$ and $4$-form $Q$. Our results are (1) if $X$ is a \textbf{good} manifold, i.e., $P,Q$ satisfying $d\ast_{X}P=d\ast_{X}Q=0$, ... More

Noncommutative multiplicative norm identities for the quaternions and the octonionsFeb 14 2011We present Capelli type identities associated with the quaternions and the octonions, which are noncommutative versions of multiplicative norm identities for the quaternions and the octonions.

$k$-Gorenstein ModulesSep 10 2004Sep 07 2005Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ and then characterize ... More

On the grade of modules over Noetherian ringsSep 09 2004Sep 02 2007Let $\Lambda$ be a left and right noetherian ring and $\mod \Lambda$ the category of finitely generated left $\Lambda$-modules. In this paper we show the following results: (1) For a positive integer $k$, the condition that the subcategory of $\mod \Lambda$ ... More

The global well-posedness and global attractor for the solutions to the 2D Boussinesq system with variable viscosity and thermal diffusivityMar 06 2014Global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions for the temperature and viscosity and thermal ... More

A Lane-Change Path Planner and its application with a monocular cameraMar 06 2019Mar 10 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

The Interpretation of Linear Prediction by Interpolation Framework and Several following ResultsOct 23 2018Apr 03 2019This paper gives a general interpretation of Linear Prediction (LP) by interpolation framework different from the perspective of statistics. This interpretation is proved to be useful by several following results, such as: The mechanism of widely used ... More

Asymptotic Expansion of Spherical IntegralSep 08 2013Dec 15 2014We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one. We prove the existence of the full asymptotic expansions of these spherical integrals and derive the first and the second term in the asymptotic ... More