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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

Deep Conversational Recommender in TravelJun 25 2019When traveling to a foreign country, we are often in dire need of an intelligent conversational agent to provide instant and informative responses to our various queries. However, to build such a travel agent is non-trivial. First of all, travel naturally ... 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

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

ChID: A Large-scale Chinese IDiom Dataset for Cloze TestJun 04 2019Jun 08 2019Cloze-style reading comprehension in Chinese is still limited due to the lack of various corpora. In this paper we propose a large-scale Chinese cloze test dataset ChID, which studies the comprehension of idiom, a unique language phenomenon in Chinese. ... 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

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

ChID: A Large-scale Chinese IDiom Dataset for Cloze TestJun 04 2019Cloze-style reading comprehension in Chinese is still limited due to the lack of various corpora. In this paper we propose a large-scale Chinese cloze test dataset ChID, which studies the comprehension of idiom, a unique language phenomenon in Chinese. ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

Stable Yang-Mills connections on Special Holonomy ManifoldsNov 16 2015Jul 19 2016We prove that energy minimizing Yang-Mills connections with certain condition on compact $G_{2}$-manifolds with holonomy equal to $G_{2}$ are $G_{2}$-instantons. We prove related results for compact Calabi-Yau $3$-folds with holonomy equal to $SU(3)$. ... More

Complex flat connections on compact manifoldsJun 13 2016Aug 28 2016We consider a complex flat connection on a principle bundle $P$ over a compact Riemannian manifold $M=M^{n}$,$n\geq5$.First,we prove that the complex part of complex flat connection must with $L^{2}$-bounded from below by some positive constant,if $M$ ... More

Conditional statistical physical properties in two-joint complex systems having long-range interactionsJun 09 2013We propose the sum and the difference of the normalized velocity of two-joint systems to describe its long-range interaction. It is found that the conditional probability distribution function (CPDF) of the normalized velocity between two-joint systems ... More

Distribution locale des points rationnels de hauteur bornée sur une surface de del Pezzo de degré 6Oct 08 2016We establish a measure which describes precisely the local asymptotic distribution of rational points outside the locally accumulating subvarieties around a general rational point on a del Pezzo surface of degree 6 in the sense of diophantine approximation. ... More

Reinterpretation of Thermal Dilepton Emission Rate by Spectral FunctionsJun 22 1995We reinterpret the dilepton emission rate from a hadronic gas expected to be produced in heavy ion collisions in terms of the spectral functions available from the $e^+e^-$ annihilation and the $\tau$ lepton decays experiments. We take into account all ... More

On the Anomalous Discrete SymmetrySep 14 1992We examine an interesting scenario to solve the domain wall problem recently suggested by Preskill, Trivedi, Wilczek and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such ... More

Theoretical analysis of error transfer from surface slope to refractive ray and their application to the solar concentrated collectorDec 06 2011This paper presents the general equation to calculate the standard deviation of reflected ray error from optical error through geometry optics, applying the equation to calculate the standard deviation of reflected ray error for 8 kinds of solar concentrated ... More

Long-time dynamics of resonant weakly nonlinear CGL equationsJul 04 2014Consider a weakly nonlinear CGL equation on the torus~$\mathbb{T}^d$: \[u_t+i\Delta u=\epsilon [\mu(-1)^{m-1}\Delta^{m} u+b|u|^{2p}u+ ic|u|^{2q}u].\eqno{(*)}\] Here $u=u(t,x)$, $x\in\mathbb{T}^d$, $0<\epsilon<<1$, $\mu\geqslant0$, $b,c\in\mathbb{R}$ and ... More

An averaging theorem for nonlinear Schrödinger equations with small nonlinearitiesDec 03 2013Consider nonlinear Schr\"odinger equations with small nonlinearities \[\frac{d}{dt}u+i(-\triangle u+V(x)u)=\epsilon \mathcal{P}(\triangle u,u,x),\quad x\in \mathbb{T}^d.\eqno{(*)}\] Let $\{\zeta_1(x),\zeta_2(x),\dots\}$ be the $L_2$-basis formed by eigenfunctions ... More

New thoughts on an old riddle: what determines genetic diversity within and between species?Oct 20 2015Oct 21 2015The question of what determines genetic diversity both between and within species has long remained unsolved by the modern evolutionary theory (MET). However, it has not deterred researchers from producing interpretations of genetic diversity by using ... More

An ultimate storage ring lattice with vertical emittance generated by damping wigglersSep 26 2014Oct 07 2014We discuss the approach of generating round beams for ultimate storage rings using vertical damping wigglers (with horizontal magnetic field). The vertical damping wigglers provide damping and excite vertical emittance. This eliminates the need to generate ... More

Code optimization, frozen glassy phase and improved decoding algorithms for low-density parity-check codesJul 03 2014Sep 18 2014The statistical physics properties of low-density parity-check codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function ... More

Sparse Hopfield network reconstruction with $\ell_{1}$ regularizationDec 26 2012Nov 14 2013We propose an efficient strategy to infer sparse Hopfield network based on magnetizations and pairwise correlations measured through Glauber samplings. This strategy incorporates the $\ell_{1}$ regularization into the Bethe approximation by a quadratic ... More

Characterizations of precompact sets in fuzzy star-shaped numbers space with Lp-metricJul 23 2015In this paper, we consider the characterizations of precompact sets in fuzzy star-shaped number space with Lp-metric.

Continuous $\times p,\times q$-invariant measures on the unit circleJul 09 2016We express continuous $\times p,\times q$-invariant measures on the unit circle via some simple forms. On one hand, a continuous $\times p,\times q$-invariant measure is the weak-$*$ limit of average of Dirac measures along an irrational orbit. On the ... More

Certainty Equivalence, Separation Principle, and Cooperative Output Regulation of Multi-Agent Systems by Distributed Observer ApproachAug 18 2015The cooperative output regulation problem of linear multi-agent systems was formulated and studied by the distributed observer approach in [20, 21]. Since then, several variants and extensions have been proposed, and the technique of the distributed observer ... More

Notes on Ricci flows with collapsing initial data (I): Distance distortionAug 22 2018Sep 06 2018In this note, we prove a uniform distance distortion estimate for Ricci flows with uniformly bounded scalar curvature, independent of the lower bound of the initial $\mu$-entropy. Our basic principle tells that once correctly renormalized, the metric-measure ... More

Non-equilibrium relaxation process of complex systems and its statistical physical propertiesJan 31 2019We constructed a model that evolved from a non-equilibrium state to an equilibrium state. The model only needs two basic coefficients, including self-similar coefficients and non-equilibrium coefficients. The coefficients of the model can be obtained ... More

Aut($Γ$)=det($M_Γ$)Jul 03 2018In this article, we will show that the automorphism group of any hypergraph is essentially equal to the determinant of some matrix over a ring generated from the set of ground points. With this, we are also able to determine whether two graphs are isomorphic. ... More

Computing energy density in one dimensionMay 04 2015We study the problem of computing energy density in one-dimensional quantum systems. We show that the ground-state energy per site or per bond can be computed in time (i) independent of the system size and subexponential in the desired precision if the ... More

Two extremal problems on intersecting familiesApr 30 2018In this short note, we address two problems in extremal set theory regarding intersecting families. The first problem is a question posed by Kupavskii: is it true that given two disjoint cross-intersecting families $\mathcal{A}, \mathcal{B} \subset \binom{[n]}{k}$, ... More

Large dimensional analysis of general margin based classification methodsJan 23 2019Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a particular classification ... More

On random walk on growing graphsJul 02 2016Oct 07 2018Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple random walk ... More

A remark on odd dimensional normalized Ricci flowOct 24 2007Dec 17 2007Let $(M^n,g_0)$ ($n$ odd) be a compact Riemannian manifold with $\lambda(g_0)>0$, where $\lambda(g_0)$ is the first eigenvalue of the operator $-4\Delta_{g_0}+R(g_0)$, and $R(g_0)$ is the scalar curvature of $(M^n,g_0)$. Assume the maximal solution $g(t)$ ... More

The powers of smooth words over arbitrary 2-letter alphabetsApr 03 2009Aug 09 2011Carpi (1993) and Lepisto (1994) proved independently that smooth words are cube-free for the alphabet {1, 2}, but nothing is known on whether for the other 2-letter alphabets, smooth words are k-power-free for some suitable positive integer k. In this ... More

Generalized tilting modules with finite injective dimensionFeb 25 2006Dec 31 2006Let $R$ be a left noetherian ring, $S$ a right noetherian ring and $_RU$ a generalized tilting module with $S={\rm End}(_RU)$. The injective dimensions of $_RU$ and $U_S$ are identical provided both of them are finite. Under the assumption that the injective ... More

Some gradient estimates for a diffusion equation on Riemannian manifoldsJul 27 2007Apr 24 2008In this note we present some gradient estimates for the diffusion equation $\partial_t u=\Delta u-\nabla \phi \cdot \nabla u $ on Riemannian manifolds, where $\phi $ is a C^2 function, which generalize estimates of R. Hamilton's and Qi S. Zhang's on the ... More

A gluing construction for polynomial invariantsMay 17 2010Sep 15 2010We give a polynomial gluing construction of two groups $G_X\subseteq GL(\ell,\mathbb F)$ and $G_Y\subseteq GL(m,\mathbb F)$ which results in a group $G\subseteq GL(\ell+m,\mathbb F)$ whose ring of invariants is isomorphic to the tensor product of the ... More

The Value-of-Information in Matching with QueuesMar 27 2015We consider the problem of \emph{optimal matching with queues} in dynamic systems and investigate the value-of-information. In such systems, the operators match tasks and resources stored in queues, with the objective of maximizing the system utility ... More

Authorization Policies and Co-Operating Strategies of DSCloud PlatformJan 07 2018Jan 13 2018One of the services of DSCloud Platform is to provide the global directory service to solve the problems of dispersed, difficult retrieved and isolated information. In this paper, we describe DSCloud Platform's authorization policies and co-operating ... More

Integration Checker of JAVA P2P distributed System with Auto Source Code CompositionOct 28 2016This paper presents an integrity checker of JAVA P2P distributed system with auto source code composition. JAVA distributed system must guarantee the integrity of program itself and the system components of JAVA virtual machine against attackers, hackers, ... More

On a topology property for the moduli space of Kapustin-Witten equationsMar 20 2017Apr 30 2019In this article, we study the Kapustin-Witten equations on a closed, simply-connected, four-dimensional manifold which were introduced by Kapustin and Witten. We use the Taubes' compactness theorem in arXiv:1307.6447v4 to prove that if $(A,\phi)$ is a ... More

A proof on energy gap for Yang-Mills connectionApr 10 2017Aug 03 2017In this note, we prove an ${L^{\frac{n}{2}}}$-energy gap result for Yang-Mills connections on a principal $G$-bundle over a compact manifold without using Lojasiewicz-Simon gradient inequality (arXiv:1502.00668).

Learning Efficient Representations for Reinforcement LearningAug 28 2015Markov decision processes (MDPs) are a well studied framework for solving sequential decision making problems under uncertainty. Exact methods for solving MDPs based on dynamic programming such as policy iteration and value iteration are effective on ... More

A new conception for computing gröbner basis and its applicationsDec 24 2010Dec 28 2010This paper presents a conception for computing gr\"{o}bner basis. We convert some of gr\"{o}bner-computing algorithms, e.g., F5, extended F5 and GWV algorithms into a special type of algorithm. The new algorithm's finite termination problem can be described ... More

Simplifying Local BRST Cohomology Calculation via Spectral SequenceAug 30 2010We simplify some crucial calculations in \cite{1} by using the technique of spectral sequence of a double complex.

Some Extensions of Witt's TheoremMay 25 2007We extend Witt's theorem to several kinds of simultaneous isometries of subspaces. We determine sufficient and necessary conditions for the extension of an isometry of subspaces $\phi:E\to E'$ to an isometry $\phi_V:V\to V'$ that also sends a given subspace ... More

Domination ratio of integer distance digraphsMar 05 2019An integer distance digraph is the Cayley graph $\Gamma(\mathbb{Z},S)$ of the additive group $\mathbb{Z}$ of all integers with respect to some finite subset $S \subseteq \mathbb{Z}$. The domination ratio of $\Gamma(\mathbb{Z},S)$ is the minimum density ... More

Quantum cluster algebras from unpunctured triangulated surfaces: arbitrary coefficients and quantizationJul 18 2018Jan 08 2019We study quantum cluster algebras from unpunctured surfaces with arbitrary coefficients and quantization. We first give a new proof of the Laurent expansion formulas for commutative cluster algebras from unpunctured surfaces, we then give the quantum ... More

Provably efficient neural network representation for image classificationNov 13 2017The state-of-the-art approaches for image classification are based on neural networks. Mathematically, the task of classifying images is equivalent to finding the function that maps an image to the label it is associated with. To rigorously establish ... More

Entanglement dynamics in critical random quantum Ising chain with perturbationsNov 15 2016Apr 22 2017We 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

Approximating local properties by tensor network states with constant bond dimensionMar 24 2019Suppose we would like to approximate all local properties of a quantum many-body state to accuracy $\delta$. In one dimension, we prove that an area law for the Renyi entanglement entropy $R_\alpha$ with index $\alpha<1$ implies a matrix product state ... More