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Achieving synchronization in arrays of coupled differential systems with time-varying couplingsNov 09 2013In this paper, we study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). The coupling considered here is time-varying in both the network structure and the reaction ... More

Stability of Analytic Neural Networks with Event-triggered Synaptic FeedbacksApr 02 2016In this paper, we investigate stability of a class of analytic neural networks with the synaptic feedback via event-triggered rules. This model is general and include Hopfield neural network as a special case. These event-trigger rules can efficiently ... More

Webly Supervised Learning of Convolutional NetworksMay 07 2015Oct 07 2015We present an approach to utilize large amounts of web data for learning CNNs. Specifically inspired by curriculum learning, we present a two-step approach for CNN training. First, we use easy images to train an initial visual representation. We then ... More

Relay-Assisted and QoS Aware Scheduling to Overcome Blockage in mmWave Backhaul NetworksDec 29 2018In the scenario where small cells are densely deployed, the millimeter wave (mmWave) wireless backhaul network has been widely used. However, mmWave is easily blocked by obstacles, and how to forward the data of the blocked flows is still a significant ... More

nocaps: novel object captioning at scaleDec 20 2018Image captioning models have achieved impressive results on datasets containing limited visual concepts and large amounts of paired image-caption training data. However, if these models are to ever function in the wild, a much larger variety of visual ... More

Multi-Target Embodied Question AnsweringApr 09 2019Embodied Question Answering (EQA) is a relatively new task where an agent is asked to answer questions about its environment from egocentric perception. EQA makes the fundamental assumption that every question, e.g., "what color is the car?", has exactly ... More

Learning a Recurrent Visual Representation for Image Caption GenerationNov 20 2014In this paper we explore the bi-directional mapping between images and their sentence-based descriptions. We propose learning this mapping using a recurrent neural network. Unlike previous approaches that map both sentences and images to a common embedding, ... More

Pull-Based Distributed Event-triggered Consensus for Multi-agent Systems with Directed TopologiesOct 15 2014Apr 24 2015This paper mainly investigates consensus problem with pull-based event-triggered feedback control. For each agent, the diffusion coupling feedbacks are based on the states of its in-neighbors at its latest triggering time and the next triggering time ... More

Learning Visual Storylines with Skipping Recurrent Neural NetworksApr 14 2016Jul 26 2016What does a typical visit to Paris look like? Do people first take photos of the Louvre and then the Eiffel Tower? Can we visually model a temporal event like "Paris Vacation" using current frameworks? In this paper, we explore how we can automatically ... More

Distributed Event-triggered Consensus for Multi-agent Systems with Directed TopologiesJul 11 2014Apr 04 2015In this paper, we study consensus problem in multi-agent system with directed topology by event-triggered feedback control. That is, at each agent, the diffusion coupling feedbacks are based on the information from its latest observations to its in-neighbours. ... More

Event-triggered Consensus for Multi-agent Systems with Asymmetric and Reducible TopologiesJul 05 2014This paper studies the consensus problem of multi-agent systems with asymmetric and reducible topologies. Centralized event-triggered rules are provided so as to reduce the frequency of system's updating. The diffusion coupling feedbacks of each agent ... More

Significance Calculation and a New Analysis Method in Searching for New Physics at the LHCSep 21 2005Dec 16 2005The LHC experiments have great potential in discovering many possible new particles up to the TeV scale. The significance calculation of an observation of a physics signal with known location and shape is no longer valid when either the location or the ... More

PixelNet: Towards a General Pixel-level ArchitectureSep 21 2016We explore architectures for general pixel-level prediction problems, from low-level edge detection to mid-level surface normal estimation to high-level semantic segmentation. Convolutional predictors, such as the fully-convolutional network (FCN), have ... More

Cycle-Consistency for Robust Visual Question AnsweringFeb 15 2019Despite significant progress in Visual Question Answering over the years, robustness of today's VQA models leave much to be desired. We introduce a new evaluation protocol and associated dataset (VQA-Rephrasings) and show that state-of-the-art VQA models ... More

Global Convergence of Analytic Neural Networks with Event-triggered Synaptic FeedbacksApr 30 2015In this paper, we investigate convergence of a class of analytic neural networks with event-triggered rule. This model is general and include Hopfield neural network as a special case. The event-trigger rule efficiently reduces the frequency of information ... More

Optimizing Active Cyber DefenseMar 28 2016Active cyber defense is one important defensive method for combating cyber attacks. Unlike traditional defensive methods such as firewall-based filtering and anti-malware tools, active cyber defense is based on spreading "white" or "benign" worms to combat ... More

PixelNet: Representation of the pixels, by the pixels, and for the pixelsFeb 21 2017We explore design principles for general pixel-level prediction problems, from low-level edge detection to mid-level surface normal estimation to high-level semantic segmentation. Convolutional predictors, such as the fully-convolutional network (FCN), ... More

Iterative Visual Reasoning Beyond ConvolutionsMar 29 2018We present a novel framework for iterative visual reasoning. Our framework goes beyond current recognition systems that lack the capability to reason beyond stack of convolutions. The framework consists of two core modules: a local module that uses spatial ... More

An Efficient Minibatch Acceptance Test for Metropolis-HastingsOct 19 2016Jul 09 2017We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of Metropolis-Hastings tests yield variable data consumed per sample, with only constant factor reductions ... More

An Efficient Minibatch Acceptance Test for Metropolis-HastingsOct 19 2016We present a novel Metropolis-Hastings method for large datasets that uses small expected-size minibatches of data. Previous work on reducing the cost of Metropolis-Hastings tests yield variable data consumed per sample, with only constant factor reductions ... More

TensorMask: A Foundation for Dense Object SegmentationMar 28 2019Sliding-window object detectors that generate bounding-box object predictions over a dense, regular grid have advanced rapidly and proven popular. In contrast, modern instance segmentation approaches are dominated by methods that first detect object bounding ... More

Visualizing and Understanding Neural Models in NLPJun 02 2015Jan 08 2016While neural networks have been successfully applied to many NLP tasks the resulting vector-based models are very difficult to interpret. For example it's not clear how they achieve {\em compositionality}, building sentence meaning from the meanings of ... More

Distributed Finite-time Least Squares Solver for Network Linear EquationsSep 29 2018In this paper, we study the problem of finding the least square solutions of over-determined linear algebraic equations over networks in a distributed manner. Each node has access to one of the linear equations and holds a dynamic state. We first propose ... More

Pythia v0.1: the Winning Entry to the VQA Challenge 2018Jul 26 2018Jul 27 2018This document describes Pythia v0.1, the winning entry from Facebook AI Research (FAIR)'s A-STAR team to the VQA Challenge 2018. Our starting point is a modular re-implementation of the bottom-up top-down (up-down) model. We demonstrate that by making ... More

Grounded Video DescriptionDec 17 2018Video description is one of the most challenging problems in vision and language understanding due to the large variability both on the video and language side. Models, hence, typically shortcut the difficulty in recognition and generate plausible sentences ... More

Towards VQA Models that can ReadApr 18 2019Studies have shown that a dominant class of questions asked by visually impaired users on images of their surroundings involves reading text in the image. But today's VQA models can not read! Our paper takes a first step towards addressing this problem. ... More

Prior-aware Neural Network for Partially-Supervised Multi-Organ SegmentationApr 12 2019Accurate multi-organ abdominal CT segmentation is essential to many clinical applications such as computer-aided intervention. As data annotation requires massive human labor from experienced radiologists, it is common that training data are partially ... More

Device-to-Device Communications Enabled Energy Efficient Multicast Scheduling in mmWave Small CellsDec 14 2017To keep pace with the rapid growth of mobile traffic demands, dense deployment of small cells in millimeter wave (mmWave) bands has become a promising candidate for next generation wireless communication systems. With a greatly increased data rate from ... More

Embodied Visual RecognitionApr 09 2019Passive visual systems typically fail to recognize objects in the amodal setting where they are heavily occluded. In contrast, humans and other embodied agents have the ability to move in the environment, and actively control the viewing angle to better ... More

Microsoft COCO Captions: Data Collection and Evaluation ServerApr 01 2015Apr 03 2015In this paper we describe the Microsoft COCO Caption dataset and evaluation server. When completed, the dataset will contain over one and a half million captions describing over 330,000 images. For the training and validation images, five independent ... More

CoDraw: Collaborative Drawing as a Testbed for Grounded Goal-driven CommunicationDec 15 2017Jan 14 2019In this work, we propose a goal-driven collaborative task that contains language, vision, and action in a virtual environment as its core components. Specifically, we develop a Collaborative image-Drawing game between two agents, called CoDraw. Our game ... More

Event-Triggered Control for Consensus of Multi-Agent Systems with Nonlinear Output and Directed TopologiesApr 12 2019We propose a distributed event-triggered control law to solve the consensus problem for multi-agent systems with nonlinear output. Under the condition that the underlying digraph is strongly connected, we propose some sufficient conditions related to ... More

Distributed Online Optimization for Multi-Agent Networks with Coupled Inequality ConstraintsMay 15 2018This paper investigates the distributed online optimization problem over a multi-agent network subject to local set constraints and coupled inequality constraints, which has a large number of applications in practice, such as wireless sensor networks, ... More

Distributed Robust Dynamic Average Consensus with Dynamic Event-Triggered CommunicationSep 18 2018This paper presents the formulation and analysis of a fully distributed dynamic event-triggered communication based robust dynamic average consensus algorithm. Dynamic average consensus problem involves a networked set of agents estimating the time-varying ... More

Self-Triggered Control for Multi-Agent Systems with Quantized Communication or SensingApr 11 2016The consensus problem for multi-agent systems with quantized communication or sensing is considered. Centralized and distributed self-triggered rules are proposed to reduce the overall need of communication and system updates. It is proved that these ... More

Automorphism group of the subspace inclusion graph of a vector spaceApr 19 2017In a recent paper [Comm. Algebra, 44(2016) 4724-4731], Das introduced the graph $\mathcal{I}n(\mathbb{V})$, called subspace inclusion graph on a finite dimensional vector space $\mathbb{V}$, where the vertex set is the collection of nontrivial proper ... More

Self-Triggered Control for Multi-Agent Systems with Quantized Communication or SensingApr 11 2016Nov 06 2016The consensus problem for multi-agent systems with quantized communication or sensing is considered. Centralized and distributed self-triggered rules are proposed to reduce the overall need of communication and system updates. It is proved that these ... More

Label and Sample: Efficient Training of Vehicle Object Detector from Sparsely Labeled DataAug 26 2018Self-driving vehicle vision systems must deal with an extremely broad and challenging set of scenes. They can potentially exploit an enormous amount of training data collected from vehicles in the field, but the volumes are too large to train offline ... More

Nonlinear consensus protocols with applications to quantized systemsApr 12 2016Two types of general nonlinear consensus protocols are considered in this paper, namely the systems with nonlinear measurement and communication of the agents' states, respectively. The solutions of the systems are understood in the sense of Filippov ... More

A Bayesian Mark Interaction Model for Analysis of Tumor Pathology ImagesFeb 22 2018With the advance of imaging technology, digital pathology imaging of tumor tissue slides is becoming a routine clinical procedure for cancer diagnosis. This process produces massive imaging data that capture histological details in high resolution. Recent ... More

Formation Control for Multi-Agent Systems with Connectivity Preservation and Event-Triggered ControllersNov 10 2016Nov 12 2016In this paper, event-triggered controllers and corresponding algorithms are proposed to establish formation with connectivity preservation for multi-agent systems. Each agent only needs to update its control input and broadcast this control input together ... More

Risk Averse Robust Adversarial Reinforcement LearningMar 31 2019Deep reinforcement learning has recently made significant progress in solving computer games and robotic control tasks. A known problem, though, is that policies overfit to the training environment and may not avoid rare, catastrophic events such as automotive ... More

Distributed Dynamic Event-Triggered Control for Multi-Agent SystemsApr 18 2017We propose two distributed dynamic triggering laws to solve the consensus problem for multi-agent systems with event-triggered control. Compared with existing triggering laws, the proposed triggering laws involve internal dynamic variables which play ... More

Virtual to Real Reinforcement Learning for Autonomous DrivingApr 13 2017Sep 26 2017Reinforcement learning is considered as a promising direction for driving policy learning. However, training autonomous driving vehicle with reinforcement learning in real environment involves non-affordable trial-and-error. It is more desirable to first ... More

Distributed Event-Triggered Control for Global Consensus of Multi-Agent Systems with Input SaturationApr 18 2017We consider the global consensus problem for multi-agent systems with input saturation over digraphs. Under a mild connectivity condition that the underlying digraph has a directed spanning tree, we use Lyapunov methods to show that the widely used distributed ... More

Formation Control for Multi-Agent Systems with Connectivity Preservation and Event-Triggered ControllersNov 10 2016Apr 19 2017In this paper, event-triggered controllers and corresponding algorithms are proposed to establish the formation with connectivity preservation for multi-agent systems. Each agent needs to update its control input and to broadcast this control input together ... More

Distributed Online Convex Optimization with Time-Varying Coupled Inequality ConstraintsMar 06 2019This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local ... More

Formation Control for Multi-Agent Systems with Connectivity Preservation and Event-Triggered ControllersNov 10 2016In this paper, event-triggered controllers and corresponding algorithms are proposed to establish formation with connectivity preservation for multi-agent systems. Each agent only needs to update its control input and broadcast this control input together ... More

Nonlinear consensus protocols with applications to quantized systemsApr 10 2017This paper studies multi-agent systems with nonlinear consensus protocols, i.e., only nonlinear measurements of the states are available to agents. The solutions of these systems are understood in Filippov sense since the possible discontinuity of the ... More

Gravitational instantons with faster than quadratic curvature decay (III)Mar 28 2016Oct 06 2016This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, ... More

Gravitational instantons with faster than quadratic curvature decay (II)Aug 31 2015Jun 23 2016This is our second paper in a series to study gravitational instantons, i.e. complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models ... More

Angora: Efficient Fuzzing by Principled SearchMar 04 2018Mar 27 2018Fuzzing is a popular technique for finding software bugs. However, the performance of the state-of-the-art fuzzers leaves a lot to be desired. Fuzzers based on symbolic execution produce quality inputs but run slow, while fuzzers based on random mutation ... More

Notes on "Einstein metrics on compact simple Lie groups attached to standard triples"Jan 06 2017In the paper "Einstein metrics on compact simple Lie groups attached to standard triples", the authors introduced the definition of standard triples and proved that every compact simple Lie group $G$ attached to a standard triple $(G,K,H)$ admits a left-invariant ... More

Modeling the Annual Growth Rate of Electricity Consumption of China in the 21st Century: Trends and PredictionOct 21 2017In this paper, the annual growth rate of electricity consumption in China in the first 15 years of the 21st century is modeled using multiple linear regression. Historical data and trends of gross domestic product, fixed assets investment and share of ... More

Characterizations of asymptotic distributions of continuous-time Pólya processesNov 29 2016Sep 02 2018We propose an elementary but effective approach to studying a general class of Poissonized tenable and balanced urns on two colors. We characterize the asymptotic behavior of the process via a partial differential equation that governs the process, coupled ... More

Synchronization of Kuramoto oscillators in a bidirectional frequency-dependent tree networkSep 17 2018Dec 09 2018This paper studies the synchronization of a finite number of Kuramoto oscillators in a frequency-dependent bidirectional tree network. We assume that the coupling strength of each link in each direction is equal to the product of a common coefficient ... More

Energy Efficiency Analysis of Heterogeneous Cellular Networks With Extra Cell Range ExpansionJan 05 2018The split control and user plane is key to the future heterogeneous cellular network (HCN), where the small cells are dedicated for the most data transmission while the macrocells are mainly responsible for the control signaling. Adapting to this technology, ... More

Spin and hyperelliptic structures of log twisted differentialsOct 17 2016Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian ... More

On the Imbedding Problem for Three-state Time Homogeneous Markov Chains with Coinciding Negative EigenvaluesSep 11 2010For an indecomposable $3\times 3$ stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means ... More

Human-Interactive Subgoal Supervision for Efficient Inverse Reinforcement LearningJun 22 2018Humans are able to understand and perform complex tasks by strategically structuring the tasks into incremental steps or subgoals. For a robot attempting to learn to perform a sequential task with critical subgoal states, such states can provide a natural ... More

Distributed Optimization for Second-Order Multi-Agent Systems with Dynamic Event-Triggered CommunicationMar 16 2018Sep 17 2018In this paper, we propose a fully distributed algorithm for second-order continuous-time multi-agent systems to solve the distributed optimization problem. The global objective function is a sum of private cost functions associated with the individual ... More

Faster Deterministic Algorithms for Packing, Matching and $t$-Dominating Set ProblemsJun 15 2013In this paper, we devise three deterministic algorithms for solving the $m$-set $k$-packing, $m$-dimensional $k$-matching, and $t$-dominating set problems in time $O^*(5.44^{mk})$, $O^*(5.44^{(m-1)k})$ and $O^*(5.44^{t})$, respectively. Although recently ... More

Exact Sample Size Methods for Estimating Parameters of Discrete DistributionsNov 08 2012Nov 19 2012In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal property assumptions, ... More

Principal boundary of moduli spaces of abelian and quadratic differentialsNov 05 2016The seminal work of Eskin-Masur-Zorich described the principal boundary of moduli spaces of abelian differentials that parameterizes flat surfaces with a prescribed generic configuration of short parallel saddle connections. In this paper we describe ... More

Gröbner-Shirshov bases for metabelian Lie algebrasJun 13 2011In this paper, we establish the Gr\"{o}bner-Shirshov bases theory for metabelian Lie algebras. As applications, we find the Gr\"{o}bner-Shirshov bases for partial commutative metabelian Lie algebras related to circuits, trees and some cubes.

Gravitational instantons with faster than quadratic curvature decay (I)May 07 2015In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known end----ALE, ALF, ALG or ALH. 2.In ALG and ... More

Exact Methods for Multistage Estimation of a Binomial ProportionFeb 13 2013We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, ... More

Embedding of tenable and balanced urn scheme into continuous-time Pólya processNov 29 2016We study poissonized tenable and balanced urns on two colors, say white and blue. In particular, we look at the process obtained by embedding a generalized P\'{o}lya-Eggenberger urn into continuous time. We analyze the number of white and blue balls after ... More

Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficientsAug 30 2017Sep 24 2017Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide a rigourous mathematical theory of two types of nonequilibrium FDTs for inhomogeneous ... More

On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, IIAug 16 2017By a canonical (resp. terminal) weak $\mathbb{Q}$-Fano $3$-fold we mean a normal projective one with at worst canonical (resp. terminal) singularities on which the anti-canonical divisor is $\mathbb{Q}$-Cartier, nef and big. For a canonical weak $\mathbb{Q}$-Fano ... More

On the anti-canonical geometry of $\mathbb{Q}$-Fano 3-foldsAug 27 2014Feb 02 2015For a $\mathbb{Q}$-Fano 3-fold $X$ on which $K_X$ is a canonical divisor, we investigate the geometry induced from the linear system $|-mK_X|$ in this paper and prove that the anti-$m$-canonical map $\varphi_{-m}$ is birational onto its image for all ... More

Minimum K_2,3-saturated GraphsDec 19 2010Nov 11 2012A graph is K_{2,3}-saturated if it has no subgraph isomorphic to K_{2,3}, but does contain a K_{2,3} after the addition of any new edge. We prove that the minimum number of edges in a K_{2,3}-saturated graph on n >= 5 vertices is sat(n, K_{2,3}) = 2n ... More

Orthogonal Quantum Group Invariants of LinksJul 09 2010We study the Chern-Simons partition function of orthogonal quantum group invariants, and propose a new orthogonal Labastida-Mari\~{n}o-Ooguri-Vafa conjecture as well as degree conjecture for free energy associated to the orthogonal Chern-Simons partition ... More

Delay-Optimal Buffer-Aware Probabilistic Scheduling with Adaptive TransmissionSep 09 2015Cross-layer scheduling is a promising way to improve Quality of Service (QoS) given a power constraint. In this paper, we investigate the system with random data arrival and adaptive transmission. Probabilistic scheduling strategies aware of the buffer ... More

Fine Residual Carrier Frequency and Sampling Frequency Estimation in Wireless OFDM SystemsNov 08 2012This paper presents a novel algorithm for residual phase estimation in wireless OFDM systems, including the carrier frequency offset (CFO) and the sampling frequency offset (SFO). The subcarriers are partitioned into several regions which exhibit pairwise ... More

Adaptivity vs PostselectionJun 13 2016We study the following problem: with the power of postselection (classically or quantumly), what is your ability to answer adaptive queries to certain languages? More specifically, for what kind of computational classes $\mathcal{C}$, we have $\mathsf{P}^{\mathcal{C}}$ ... More

Bounded Rationality, Strategy Simplification, and EquilibriumFeb 24 2010Jun 26 2011It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with minimization ... More

On the fundamental domain of affine Springer fibersMar 19 2013Mar 11 2014For $G$ a connected reductive group, $\gamma\in \kg(F)$ semisimple regular integral, we introduce a fundamental domain $F_{\gamma}$ for the affine Springer fibers $\xx_{\gamma}$. There is a beautiful way to reduce the purity conjecture of $\xx_{\gamma}$ ... More

Product Formula, Independence and Asymptotic Moment-Independence for Complex Multiple Wiener-Ito IntegralsDec 05 2014We present the product formula for complex multiple Wiener-Ito integrals. As applications, we show the Ustunel-Zakai independent criterion, the Nourdin-Rosinski asymptotic moment-independent criterion and joint convergence criterion for complex multiple ... More

A Geometric Method to Obtain the Generation Probability of a SentenceJun 04 2014"How to generate a sentence" is the most critical and difficult problem in all the natural language processing technologies. In this paper, we present a new approach to explain the generation process of a sentence from the perspective of mathematics. ... More

Optimistic versus Pessimistic--Optimal Judgemental Bias with Reference PointOct 10 2013This paper develops a model of reference-dependent assessment of subjective beliefs in which loss-averse people optimally choose the expectation as the reference point to balance the current felicity from the optimistic anticipation and the future disappointment ... More

The spatial meaning of Pareto's scaling exponent of city-size distributionSep 19 2013The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the fractal dimension. ... More

Localization Formulas About Two Killing Vector FieldsApr 13 2013In this article, we will discuss the smooth $(X_{M}+\sqrt{-1}Y_{M})$-invariant forms on $M$ and to establish a localization formulas. As an application, we get a localization formulas for characteristic numbers.

Sequential change-point detection based on nearest neighborsApr 12 2016We propose a new framework for the detection of change points in online, sequential data analysis. The approach utilizes nearest neighbor information and can be applied to multivariate or object data sequences. Different stopping rules are explored, and ... More

The Cartan Model for Equivariant CohomologyAug 12 2016In this article, we will discuss a new operator $d_{C}$ on $W(\mathfrak{g})\otimes\Omega^{*}(M)$ and to construct a new Cartan model for equivariant cohomology. We use the new Cartan model to construct the corresponding BRST model and Weil model, and ... More

On bootstrap approximations for high-dimensional U-statistics and random quadratic formsSep 30 2016This paper establishes a unified theory of bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when $d$ is large. Specifically, we show that the empirical bootstrap with the ... More

Normalizing and Classifying Shape Indexes of Cities by Ideas from FractalsAug 31 2016A standard scientific study comprises two processes: one is to describe a thing, and the other is to understand how the thing works. In order to understand the principle of urban growth, a number of shape indexes are proposed to describe the size and ... More

Universal Logarithmic Scrambling in Many Body LocalizationAug 09 2016Aug 28 2016Out of time ordered correlator (OTOC) is recently introduced as a powerful diagnose for quantum chaos. To go beyond, here we present an analytical solution of OTOC for a non-chaotic many body localized (MBL) system, showing distinct feature from quantum ... More

Equivalent Relation between Normalized Spatial Entropy and Fractal DimensionAug 06 2016Sep 25 2016Fractal dimension is defined on the base of entropy, including macro state entropy and information entropy. The generalized dimension of multifractals is based on Renyi entropy. However, the mathematical transform from entropy to fractal dimension is ... More

Non-divergence Parabolic Equations of Second Order with Critical Drift in Lebesgue SpacesNov 04 2015Feb 02 2016We consider uniformly parabolic equations and inequalities of second order in the non-divergence form with drift \[-u_{t}+Lu=-u_{t}+\sum_{ij}a_{ij}D_{ij}u+\sum b_{i}D_{i}u=0\,(\geq0,\,\leq0)\] in some domain $Q\subset \mathbb{R}^{n+1}$. We prove growth ... More

Wave equations with moving potentialsOct 30 2016In this paper, we study the endpoint reversed Strichartz estimates along general time-like trajectories for wave equations in $\mathbb{R}^{3}$. We also discuss some applications of the reversed Strichartz estimates and the structure of wave operators ... More

von Neumann-Landau equation for wave functions, wave-particle duality and collapses of wave functionsMar 22 2007Sep 29 2007It is shown that von Neumann-Landau equation for wave functions can present a mathematical formalism of motion of quantum mechanics. The wave functions of von Neumann-Landau equation for a single particle are `bipartite', in which the associated Schr\"{o}dinger's ... More

Variants of Bell inequalitiesNov 13 2006A family of Bell-type inequalities is present, which are constructed directly from the "standard" Bell inequalities involving two dichotomic observables per site. It is shown that the inequalities are violated by all the generalized Greenberger-Horne-Zeilinger ... More

Deeply Virtual Compton Scattering and Skewed Parton DistributionAug 02 2000An overview of the current status of and possible future theoretical, phenomenological and experimental studies of DVCS and SPD's is presented.

Strong laws of large numbers for capacitiesJun 03 2010In this paper, with the notion of independent identically distributed random variables under sub-linear expectations initiated by Peng, we derive three kinds of strong laws of large numbers for capacities. Moreover, these theorems are natural and fairly ... More

Machine Translation Model based on Non-parallel Corpus and Semi-supervised Transductive LearningMay 22 2014Although the parallel corpus has an irreplaceable role in machine translation, its scale and coverage is still beyond the actual needs. Non-parallel corpus resources on the web have an inestimable potential value in machine translation and other natural ... More

Sub-Gaussian heat kernel estimates and quasi Riesz transforms for $1\leq p\leq 2$Jan 10 2014On a complete non-compact Riemannian manifold $M$, we prove that a so-called quasi Riesz transform is always $L^p$ bounded for $1<p\leq 2$. If $M$ satisfies the doubling volume property and the sub-Gaussian heat kernel estimate, we prove that the quasi ... More

Electron and phonon correlations in systems of one-dimensional electrons coupled to phononsJun 02 2008Aug 16 2008Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2k_F$-wave components of the electron ... More

Hsiao-Code Check Matrices and Recursively Balanced MatricesMar 08 2008The key step of generating the well-known Hsiao code is to construct a {0,1}-check-matrix in which each column contains the same odd-number of 1's and each row contains the same number of 1's or differs at most by one for the number of 1's. We also require ... More

The curvature of spectral energy distribution of blazarsMay 06 2014The SED of blazars show significant curvature. In this paper, we study the curvature properties for a large sample of Fermi/LAT bright blazars based on quasi-simultaneous SED. Both SEDs of synchrotron and inverse Compton (IC) components are fitted by ... More