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The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitudeMay 05 2018Recently, a class of binary sequences with optimal autocorrelation magnitude has been presented by Su et al. based on interleaving technique and Ding-Helleseth-Lam sequences (Des. Codes Cryptogr., https://doi.org/10.1007/s10623-017-0398-5). And its linear ... More

Hybrid Neural Network Architecture for On-Line LearningSep 29 2008Approaches to machine intelligence based on brain models have stressed the use of neural networks for generalization. Here we propose the use of a hybrid neural network architecture that uses two kind of neural networks simultaneously: (i) a surface learning ... More

iAQC: The Intensity-Aware Quantum Cryptography ProtocolJun 28 2012Oct 11 2013This paper reports a variant of the three-stage quantum cryptography protocol which can be used in low intensity laser output regimes. The variant, which tracks the intensity of the laser beam at the intermediate stages, makes the task of the eavesdropper ... More

ROAD: Reality Oriented Adaptation for Semantic Segmentation of Urban ScenesNov 30 2017Apr 07 2018Exploiting synthetic data to learn deep models has attracted increasing attention in recent years. However, the intrinsic domain difference between synthetic and real images usually causes a significant performance drop when applying the learned model ... More

Self-supervised Learning with Geometric Constraints in Monocular Video: Connecting Flow, Depth, and CameraJul 12 2019We present GLNet, a self-supervised framework for learning depth, optical flow, camera pose and intrinsic parameters from monocular video -- addressing the difficulty of acquiring realistic ground-truth for such tasks. We propose three contributions: ... More

Learning Semantic Segmentation from Synthetic Data: A Geometrically Guided Input-Output Adaptation ApproachDec 12 2018Jan 13 2019Recently, increasing attention has been drawn to training semantic segmentation models using synthetic data and computer-generated annotation. However, domain gap remains a major barrier and prevents models learned from synthetic data from generalizing ... More

Superlinear elliptic inequalities on manifoldsOct 06 2018Let $M$ be a complete non-compact Riemannian manifold and let $\sigma $ be a Radon measure on $M$. We study the problem of existence or non-existence of positive solutions to a semilinear elliptic inequaliy \begin{equation*} -\Delta u\geq \sigma u^{q}\quad ... More

Semantically-Guided Video Object SegmentationApr 06 2017Jul 17 2018This paper tackles the problem of semi-supervised video object segmentation, that is, segmenting an object in a sequence given its mask in the first frame. One of the main challenges in this scenario is the change of appearance of the objects of interest. ... More

DLOW: Domain Flow for Adaptation and GeneralizationDec 13 2018In this work, we propose a domain flow generation(DLOW) approach to model the domain shift between two domains by generating a continuous sequence of intermediate domains flowing from one domain to the other. The benefits of our DLOW model are two-fold. ... More

Enhanced generative adversarial network for 3D brain MRI super-resolutionJul 10 2019Jul 15 2019Single image super-resolution (SISR) reconstruction for magnetic resonance imaging (MRI) has generated significant interest because of its potential to not only speed up imaging but to improve quantitative processing and analysis of available image data. ... More

DLOW: Domain Flow for Adaptation and GeneralizationDec 13 2018May 13 2019In this work, we present a domain flow generation(DLOW) model to bridge two different domains by generating a continuous sequence of intermediate domains flowing from one domain to the other. The benefits of our DLOW model are two-fold. First, it is able ... More

Blazingly Fast Video Object Segmentation with Pixel-Wise Metric LearningApr 09 2018This paper tackles the problem of video object segmentation, given some user annotation which indicates the object of interest. The problem is formulated as pixel-wise retrieval in a learned embedding space: we embed pixels of the same object instance ... More

Is Image Super-resolution Helpful for Other Vision Tasks?Sep 23 2015Jan 28 2016Despite the great advances made in the field of image super-resolution (ISR) during the last years, the performance has merely been evaluated perceptually. Thus, it is still unclear whether ISR is helpful for other vision tasks. In this paper, we present ... More

Enhanced generative adversarial network for 3D brain MRI super-resolutionJul 10 2019Single image super-resolution (SISR) reconstruction for magnetic resonance imaging (MRI) has generated significant interest because of its potential to not only speed up imaging but to improve quantitative processing and analysis of available image data. ... More

A Game-Theoretic Learning Framework for Multi-Agent Intelligent Wireless NetworksDec 04 2018Apr 17 2019In this article, we introduce a game-theoretic learning framework for the multi-agent wireless network. By combining learning in artificial intelligence (AI) with game theory, several promising properties emerge such as obtaining high payoff in the unknown ... More

A Game-Theoretic Learning Framework for Multi-Agent Intelligent Wireless NetworksDec 04 2018In this article, we introduce a game-theoretic learning framework for the multi-agent wireless network. By combining learning in artificial intelligence (AI) with game theory, several promising properties emerge such as obtaining high payoff in the unknown ... More

Domain Adaptive Faster R-CNN for Object Detection in the WildMar 08 2018Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to ... More

Multi-Photon Quantum Key Distribution Based on Double-Lock EncryptionMar 19 2015This paper presents a multi-stage, multi-photon quantum key distribution protocol based on the double-lock cryptography. It exploits the asymmetry in the detection strategies between the legitimate users and the eavesdropper. The security analysis of ... More

Load-aware Dynamic Spectrum Access for Small Cell Networks: A Graphical Game ApproachFeb 24 2015Sep 16 2015In this letter, we investigate the problem of dynamic spectrum access for small cell networks, using a graphical game approach. Compared with existing studies, we take the features of different cell loads and local interference relationship into account. ... More

Efficient and Accurate MRI Super-Resolution using a Generative Adversarial Network and 3D Multi-Level Densely Connected NetworkMar 04 2018Jun 09 2018High-resolution (HR) magnetic resonance images (MRI) provide detailed anatomical information important for clinical application and quantitative image analysis. However, HR MRI conventionally comes at the cost of longer scan time, smaller spatial coverage, ... More

Brain MRI Super Resolution Using 3D Deep Densely Connected Neural NetworksJan 08 2018Magnetic resonance image (MRI) in high spatial resolution provides detailed anatomical information and is often necessary for accurate quantitative analysis. However, high spatial resolution typically comes at the expense of longer scan time, less spatial ... More

The 2018 DAVIS Challenge on Video Object SegmentationMar 01 2018Mar 27 2018We present the 2018 DAVIS Challenge on Video Object Segmentation, a public competition specifically designed for the task of video object segmentation. It builds upon the DAVIS 2017 dataset, which was presented in the previous edition of the DAVIS Challenge, ... More

Video Object Segmentation Without Temporal InformationSep 18 2017May 16 2018Video Object Segmentation, and video processing in general, has been historically dominated by methods that rely on the temporal consistency and redundancy in consecutive video frames. When the temporal smoothness is suddenly broken, such as when an object ... More

Calcium Removal From Cardiac CT Images Using Deep Convolutional Neural NetworkFeb 20 2018Coronary calcium causes beam hardening and blooming artifacts on cardiac computed tomography angiography (CTA) images, which lead to overestimation of lumen stenosis and reduction of diagnostic specificity. To properly remove coronary calcification and ... More

Fully Parallel Architecture for Semi-global Stereo Matching with Refined Rank MethodMay 07 2019Fully parallel architecture at disparity-level for efficient semi-global matching (SGM) with refined rank method is presented. The improved SGM algorithm is implemented with the non-parametric unified rank model which is the combination of Rank filter/AD ... More

Towards Theoretical Understanding of Large Batch Training in Stochastic Gradient DescentDec 03 2018Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received increasing attention. ... More

Heat flow method to Lichnerowicz type equation on closed manifoldsFeb 27 2010In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -\Delta u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\geq0$ are given smooth functions. ... More

Implementation of Secure Quantum Protocol using Multiple Photons for CommunicationAug 30 2012The paper presents the implementation of a quantum cryptography protocol for secure communication between servers in the cloud. As computing power increases, classical cryptography and key management schemes based on computational complexity become increasingly ... More

Inhomogeneous parabolic equations on unbounded metric measure spacesMar 29 2011We study inhomogeneous semilinear parabolic equations with source term f independent of time u_{t}={\Delta}u+u^{p}+f(x) on a metric measure space, subject to the conditions that f(x)\geq 0 and u(0,x)=\phi(x)\geq 0. By establishing Harnack-type inequalities ... More

Database-assisted Spectrum Access in Dynamic Networks: A Distributed Learning SolutionFeb 24 2015Jul 03 2015This paper investigates the problem of database-assisted spectrum access in dynamic TV white spectrum networks, in which the active user set is varying. Since there is no central controller and information exchange, it encounters dynamic and incomplete ... More

Autocorrelation and Lower Bound on the 2-Adic Complexity of LSB Sequence of $p$-ary $m$-SequenceFeb 02 2017Dec 10 2017In modern stream cipher, there are many algorithms, such as ZUC, LTE encryption algorithm and LTE integrity algorithm, using bit-component sequences of $p$-ary $m$-sequences as the input of the algorithm. Therefore, analyzing their statistical property ... More

The 2-adic complexity of a class of binary sequences with almost optimal autocorrelationJan 13 2017Mar 18 2017Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been applied in stream cipher. In general, it is difficult to give both the linear complexity and 2-adic complexity ... More

Part-based Visual Tracking via Structural Support Correlation FilterMay 25 2018Recently, part-based and support vector machines (SVM) based trackers have shown favorable performance. Nonetheless, the time-consuming online training and updating process limit their real-time applications. In order to better deal with the partial occlusion ... More

A lower bound on the 2-adic complexity of modified Jacobi sequenceApr 06 2017Dec 10 2017Let $p,q$ be distinct primes satisfying $\mathrm{gcd}(p-1,q-1)=d$ and let $D_i$, $i=0,1,\cdots,d-1$, be Whiteman's generalized cyclotomic classes with $Z_{pq}^{\ast}=\cup_{i=0}^{d-1}D_i$. In this paper, we give the values of Gauss periods based on the ... More

Cyclic Codes from Two-Prime Generalized Cyclotomic Sequences of Order 6Oct 05 2015Cyclic codes have wide applications in data storage systems and communication systems. Employing two-prime Whiteman generalized cyclotomic sequences of order 6, we construct several classes of cyclic codes over the finite field GF}(q) and give their generator ... More

On nonexistence and existence of positive global solutions to heat equation with a potential term on Riemannian manifoldsJan 06 2019We reinvestigate nonexistence and existence of global positive solutions to heat equation with a potential term on Riemannian manifolds. Especially, we give a very natural sharp condition only in terms of the volume of geodesic ball to obtain nonexistence ... More

Isolated sub-100-attosecond pulse generation via controlling electron dynamicsApr 26 2007Jul 10 2008A new method to coherently control the electron dynamics is proposed using a few-cycle laser pulse in combination with a controlling field. It is shown that this method not only broadens the attosecond pulse bandwidth, but also reduces the chirp, then ... More

Distributed Spectrum Access for Cognitive Small Cell Networks: A Robust Graphical Game ApproachFeb 24 2015This letter investigates the problem of distributed spectrum access for cognitive small cell networks. Compared with existing work, two inherent features are considered: i) the transmission of a cognitive small cell base station only interferes with its ... More

Morphological Transformations of Diblock Copolymers in Binary Solvents: A Simulation StudyMar 27 2017Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent (S1) and a selective solvent (S2) for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending ... More

Stackelberg Game Approaches for Anti-jamming Defence in Wireless NetworksMay 31 2018This article investigates the anti-jamming communications problem in wireless networks from a Stackelberg game perspective. By exploring and analyzing the inherent characteristics of the anti-jamming problem, we present and discuss some technical challenges ... More

Unfolding the Labyrinth: Open Problems in Mathematics, Physics, Astrophysics, and Other Areas of ScienceSep 08 2006Sep 10 2006Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either ... More

A lower bound on the 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of period $p^n$Apr 18 2017Apr 24 2017Let $p$ be an odd prime, $n$ a positive integer and $g$ a primitive root of $p^n$. Suppose $D_i^{(p^n)}=\{g^{2s+i}|s=0,1,2,\cdots,\frac{(p-1)p^{n-1}}{2}\}$, $i=0,1$, is the generalized cyclotomic classes with $Z_{p^n}^{\ast}=D_0\cup D_1$. In this paper, ... More

A Coalition-Based Communication Framework for Intelligent Flying Ad-Hoc NetworksDec 03 2018In this paper, we develop the intelligent networking framework for Flying Ad-hoc Networks (FANETs), where a coalition-based model is designed. Firstly, we present a brief survey to show the state-of-the art studies on the intra-communication of unmanned ... More

Anti-jamming Communications Using Spectrum Waterfall: A Deep Reinforcement Learning ApproachOct 13 2017This letter investigates the problem of anti-jamming communications in dynamic and unknown environment through on-line learning. Different from existing studies which need to know (estimate) the jamming patterns and parameters, we use the spectrum waterfall, ... More

Carrier-envelope phase measurement from half-cycle high harmonicsJan 04 2008We present a method to distinguish the high harmonics generated in individual half-cycle of the driving laser pulse by mixing a weak ultraviolet pulse, enabling one to observe the cutoff of each half-cycle harmonic. We show that the detail information ... More

Quantum oscillations and nontrivial topological state in a compensated semimetal TaP2May 31 2019We report systematic magneto-transport measurements and ab initio calculations on single-crystalline TaP2, a new member of the transition-metal dipnictides. We observed unsaturated magnetoresistance (MR) reaching ~ 700% at a magnetic field (B) of 9 T ... More

Density functional study of X monodoped and codoped (X=C, N, S, F) anatase TiO2Nov 30 2013Using density-functional theory calculations within the generalized gradient corrected approximation, the models that nonmetallic impurities X substituted for O or Ti sites in anatase TiO2 were investigated. The conclusion of the valence states of nonmetallic ... More

Linear complexity of generalized cyclotomic sequences of order 4 over F_lMar 26 2013May 17 2016Generalized cyclotomic sequences of period pq have several desirable randomness properties if the two primes p and q are chosen properly. In particular,Ding deduced the exact formulas for the autocorrelation and the linear complexity of these sequences ... More

On Providing Downlink Services in Collocated Spectrum-Sharing Macro and Femto NetworksMay 19 2012Femtocells have been considered by the wireless industry as a cost-effective solution not only to improve indoor service providing, but also to unload traffic from already overburdened macro networks. Due to spectrum availability and network infrastructure ... More

$p$-ary sequences with six-valued cross-correlation function: a new decimation of Niho typeMay 13 2011For an odd prime $p$ and $n=2m$, a new decimation $d=\frac{(p^{m}-1)^{2}}{2}+1$ of Niho type of $m$-sequences is presented. Using generalized Niho's Theorem, we show that the cross-correlation function between a $p$-ary $m$-sequence of period $p^{n}-1$ ... 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

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

Dynamic Spectrum Access with Statistical QoS Provisioning: A Distributed Learning Approach Beyond Expectation OptimizationFeb 24 2015Mar 25 2015This article investigates the problem of dynamic spectrum access with statistical quality of service (QoS) provisioning for dynamic canonical networks, in which the channel states are time-varying from slot to slot. In the existing work with time-varying ... More

A Game Theoretic Perspective on Self-organizing Optimization for Cognitive Small CellsMar 01 2015Mar 05 2015In this article, we investigate self-organizing optimization for cognitive small cells (CSCs), which have the ability to sense the environment, learn from historical information, make intelligent decisions, and adjust their operational parameters. By ... More

Distributed Relay Selection for Heterogeneous UAV Communication Networks Using A Many-to-Many Matching Game Without SubstitutabilityDec 22 2017This paper proposes a distributed multiple relay selection scheme to maximize the satisfaction experiences of unmanned aerial vehicles (UAV) communication networks. The multi-radio and multi-channel (MRMC) UAV communication system is considered in this ... More

Gradient Scheduling with Global Momentum for Non-IID Data Distributed Asynchronous TrainingFeb 21 2019Distributed asynchronous offline training has received widespread attention in recent years because of its high performance on large-scale data and complex models. As data are processed from cloud-centric positions to edge locations, a big challenge for ... More

A Necessary and Sufficient Condition for Having Independent TE and TM Modes in an Anisotropic WaveguideAug 02 2016Whether there exist independent transverse electric (TE) and transverse magnetic (TM) modes in a metallic waveguide filled with an anisotropic medium is a fundamental question in electromagnetics waveguide theory, but so far no definitive answers have ... More

Context-aware Group Buying in Ultra-dense Small Cell Networks: Unity is StrengthJul 23 2018The ultra-dense small cell networks (SCNs) have been regarded as a promising technology to solve the data traffic explosion in future. However, the complicated relationships among large scale users and cells practically demand a cooperative grouping mechanism ... More

Dynamic Spectrum Access with Statistical QoS Provisioning: A Distributed Learning Approach Beyond Expectation OptimizationFeb 24 2015Oct 08 2016This article investigates the problem of dynamic spectrum access with statistical quality of service (QoS) provisioning for dynamic canonical networks, in which the channel states are time-varying from slot to slot. In the existing work with time-varying ... More

Dynamic Spectrum Access in Time-varying Environment: Distributed Learning Beyond Expectation OptimizationFeb 24 2015Jul 28 2017This article investigates the problem of dynamic spectrum access for canonical wireless networks, in which the channel states are time-varying. In the most existing work, the commonly used optimization objective is to maximize the expectation of a certain ... 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

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

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

Estimates of Dirichlet Eigenvalues for a Class of Sub-elliptic OperatorsMay 31 2019Let $\Omega$ be a bounded connected open subset in $\mathbb{R}^n$ with smooth boundary $\partial\Omega$. Suppose that we have a system of real smooth vector fields $X=(X_{1},X_{2},$ $\cdots,X_{m})$ defined on a neighborhood of $\overline{\Omega}$ that ... 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

Gradient Scheduling with Global Momentum for Non-IID Data Distributed Asynchronous TrainingFeb 21 2019Mar 29 2019Distributed asynchronous offline training has received widespread attention in recent years because of its high performance on large-scale data and complex models. As data are processed from cloud-centric positions to edge locations, a big challenge for ... More

Inferring topologies via driving-based generalized synchronization of two-layer networksDec 08 2015Feb 16 2016The interaction topology among the constituents of a complex network plays a crucial role in the network's evolutionary mechanisms and functional behaviors. However, some network topologies are usually unknown or uncertain. Meanwhile, coupling delay are ... More

D2D Big Data: Content Deliveries over Wireless Device-to-Device Sharing in Large Scale Mobile NetworksFeb 03 2018Recently the topic of how to effectively offload cellular traffic onto device-to-device (D2D) sharing among users in proximity has been gaining more and more attention of global researchers and engineers. Users utilize wireless short-range D2D communications ... More

Self-Organizing Relay Selection in UAV Communication Networks: A Matching Game PerspectiveMay 19 2018For large unmanned aerial vehicle (UAV) networks, the timely communication is needed to accomplish a series of missions accurately and effectively. The relay technology will play an important role in UAV networks by helping drones communicating with long-distance ... More

Cognitive Internet of Things: A New Paradigm beyond ConnectionMar 11 2014Current research on Internet of Things (IoT) mainly focuses on how to enable general objects to see, hear, and smell the physical world for themselves, and make them connected to share the observations. In this paper, we argue that only connected is not ... More

Gradient Scheduling with Global Momentum for Non-IID Data Distributed Asynchronous TrainingFeb 21 2019Apr 23 2019Distributed asynchronous offline training has received widespread attention in recent years because of its high performance on large-scale data and complex models. As data are distributed from cloud-centric to edge nodes, a big challenge for distributed ... 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

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

HSEARCH: fast and accurate protein sequence motif search and clusteringJan 02 2017Protein motifs are conserved fragments occurred frequently in protein sequences. They have significant functions, such as active site of an enzyme. Search and clustering protein sequence motifs are computational intensive. Most existing methods are not ... More

Some sufficient conditions for infinite collisions of simple random walks on a wedge combOct 26 2010In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile $\{f(n), n\in \ZZ\}$. One interesting result is that if $f(n)$ has a growth order as $n\log n$, then two independent ... 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

The Noether inequality for algebraic threefolds (With an Appendix by János Kollár)Mar 15 2018Jul 19 2018We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq ... 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

Scalar field quasinormal frequencies of Reissner-Nordström black hole surrounded by quintessenceMay 27 2016Jun 03 2016We evaluate the quasinormal modes of massless scalar field around Reissner-Nordstr$\ddot{\text{o}}$m black hole surrounded by a static and spherically symmetric quintessence by using the continued fraction method. The appropriate Frobenius series for ... 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

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