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Gated CRF Loss for Weakly Supervised Semantic Image SegmentationJun 11 2019State-of-the-art approaches for semantic segmentation rely on deep convolutional neural networks trained on fully annotated datasets, that have been shown to be notoriously expensive to collect, both in terms of time and money. To remedy this situation, ... More

Unified Hypersphere Embedding for Speaker RecognitionJul 22 2018Incremental improvements in accuracy of Convolutional Neural Networks are usually achieved through use of deeper and more complex models trained on larger datasets. However, enlarging dataset and models increases the computation and storage costs and ... More

Dark Model Adaptation: Semantic Image Segmentation from Daytime to NighttimeOct 05 2018This work addresses the problem of semantic image segmentation of nighttime scenes. Although considerable progress has been made in semantic image segmentation, it is mainly related to daytime scenarios. This paper proposes a novel method to progressive ... More

Unsupervised High-level Feature Learning by Ensemble Projection for Semi-supervised Image Classification and Image ClusteringFeb 02 2016Feb 04 2016This paper investigates the problem of image classification with limited or no annotations, but abundant unlabeled data. The setting exists in many tasks such as semi-supervised image classification, image clustering, and image retrieval. Unlike previous ... More

Real-time 3D Traffic Cone Detection for Autonomous DrivingFeb 06 2019Considerable progress has been made in semantic scene understanding of road scenes with monocular cameras. It is, however, mainly related to certain classes such as cars and pedestrians. This work investigates traffic cones, an object class crucial for ... More

Semantic Foggy Scene Understanding with Synthetic DataAug 25 2017Sep 05 2017This work addresses the problem of semantic foggy scene understanding (SFSU). Although extensive research has been performed on image dehazing and on semantic scene understanding with weather-clear images, little attention has been paid to SFSU. Due to ... More

Semantic Nighttime Image Segmentation with Synthetic Stylized Data, Gradual Adaptation and Uncertainty-Aware EvaluationJan 17 2019This work addresses the problem of semantic segmentation of nighttime images. The main direction of recent progress in semantic segmentation pertains to daytime scenes with favorable illumination conditions. We focus on improving the performance of state-of-the-art ... More

Learning Accurate, Comfortable and Human-like DrivingMar 26 2019Autonomous vehicles are more likely to be accepted if they drive accurately, comfortably, but also similar to how human drivers would. This is especially true when autonomous and human-driven vehicles need to share the same road. The main research focus ... More

Failure Prediction for Autonomous DrivingMay 04 2018The primary focus of autonomous driving research is to improve driving accuracy. While great progress has been made, state-of-the-art algorithms still fail at times. Such failures may have catastrophic consequences. It therefore is important that automated ... More

End-to-End Learning of Driving Models with Surround-View Cameras and Route PlannersMar 27 2018Aug 06 2018For human drivers, having rear and side-view mirrors is vital for safe driving. They deliver a more complete view of what is happening around the car. Human drivers also heavily exploit their mental map for navigation. Nonetheless, several methods have ... More

Fast Optical Flow using Dense Inverse SearchMar 11 2016Most recent works in optical flow extraction focus on the accuracy and neglect the time complexity. However, in real-life visual applications, such as tracking, activity detection and recognition, the time complexity is critical. We propose a solution ... More

Object Referring in Videos with Language and Human GazeJan 04 2018Apr 04 2018We investigate the problem of object referring (OR) i.e. to localize a target object in a visual scene coming with a language description. Humans perceive the world more as continued video snippets than as static images, and describe objects not only ... More

Object Referring in Visual Scene with Spoken LanguageNov 10 2017Dec 05 2017Object referring has important applications, especially for human-machine interaction. While having received great attention, the task is mainly attacked with written language (text) as input rather than spoken language (speech), which is more natural. ... More

PathTrack: Fast Trajectory Annotation with Path SupervisionMar 07 2017Mar 22 2017Progress in Multiple Object Tracking (MOT) has been historically limited by the size of the available datasets. We present an efficient framework to annotate trajectories and use it to produce a MOT dataset of unprecedented size. In our novel path supervision ... 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

Deep Domain Adaptation by Geodesic Distance MinimizationJul 13 2017Oct 10 2017In this paper, we propose a new approach called Deep LogCORAL for unsupervised visual domain adaptation. Our work builds on the recently proposed Deep CORAL method, which proposed to train a convolutional neural network and simultaneously minimize the ... More

Curriculum Model Adaptation with Synthetic and Real Data for Semantic Foggy Scene UnderstandingJan 05 2019This work addresses the problem of semantic scene understanding under fog. Although marked progress has been made in semantic scene understanding, it is mainly concentrated on clear-weather scenes. Extending semantic segmentation methods to adverse weather ... More

Ensemble Manifold Segmentation for Model Distillation and Semi-supervised LearningApr 06 2018Manifold theory has been the central concept of many learning methods. However, learning modern CNNs with manifold structures has not raised due attention, mainly because of the inconvenience of imposing manifold structures onto the architecture of the ... More

Model Adaptation with Synthetic and Real Data for Semantic Dense Foggy Scene UnderstandingAug 03 2018This work addresses the problem of semantic scene understanding under dense fog. Although considerable progress has been made in semantic scene understanding, it is mainly related to clear-weather scenes. Extending recognition methods to adverse weather ... More

Learning the Synthesizability of Dynamic Texture SamplesFeb 03 2018A dynamic texture (DT) refers to a sequence of images that exhibit temporal regularities and has many applications in computer vision and graphics. Given an exemplar of dynamic texture, it is a dynamic but challenging task to generate new samples with ... More

Macro pose based non-invasive thermal comfort perception for energy efficiencyNov 12 2018Dec 20 2018Individual thermal comfort perception gives important feedback signals for energy efficient control of smart buildings. However, there is no effective method to measure real-time thermal comfort status of individual occupant until now. For overcoming ... More

Speech-Based Visual Question AnsweringMay 01 2017Sep 16 2017This paper introduces speech-based visual question answering (VQA), the task of generating an answer given an image and a spoken question. Two methods are studied: an end-to-end, deep neural network that directly uses audio waveforms as input versus a ... 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

Gluon Radiation of an Expanding Color Skyrmion in the Quark-Gluon PlasmaApr 02 2007The density of states and energy spectrum of the gluon radiation are calculated for the color current of an expanding hydrodynamic skyrmion in the quark gluon plasma with a semiclassical method. Results are compared with those in literatures.

Quantified separably injective spacesFeb 10 2014Apr 28 2016Let $X$, $Y$ be two Banach spaces. Let $\varepsilon\geq 0$. A mapping $f: X\rightarrow Y$ is said to be a standard $\varepsilon-$ isometry if $f(0)=0$ and $|\|f(x)-f(y)\|-\|x-y\||\leq \varepsilon$. In this paper we first show that if $Y^*$ has the point ... More

Antiferromagnetic order and spin dynamics in iron-based superconductorsMar 08 2015Jun 18 2015High-transition temperature (high-$T_c$) superconductivity in the iron pnictides/chalcogenides emerges from the suppression of the static antiferromagnetic order in their parent compounds, similar to copper oxides superconductors. This raises a fundamental ... More

A New Class of Backward Stochastic Partial Differential Equations with Jumps and ApplicationsMay 04 2011We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion coefficients. ... More

Heavy traffic limit theorems for a queue with Poisson ON/OFF long-range dependent sources and general service time distributionMay 06 2011In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service times) can be generally ... More

Commutative-like Encryption: A New Characterization of ElGamalNov 16 2010Commutative encryption is a useful but rather strict notion in cryptography. In this paper, we deny a loose variation of commutative encryption-commutative-like encryption and give an example: the generalization of ElGamal scheme. The application of the ... More

Viewing the Welch bound inequality from the kernel trick viewpointMar 24 2014Apr 02 2014This brief note views to the Welch bound inequality using the idea of the kernel trick from the machine learning research area. From this angle, some novel insights of the inequality are obtained.

On Qian's problem for $\mathcal{L}_{\infty}$-spacesFeb 10 2014Jan 11 2018In this paper we devote to study Qian's problem for $\mathcal{L}_{\infty}$-spaces. Firstly, a positive answer to Qian's problem for $C(K)$-spaces is given by the assumption that $K$ has the C$\check{e}$ch-Stone property. Secondly, we obtain quantitative ... More

Neutrino in Astrophysics and CosmologySep 23 2003At first we introduce the Neutrino in the standard Model, then the Dirac and Majorana Masses. After introducing the See-Saw Mechanism, we discuss the neutrino oscillations and the neutrino in astrophysics and cosmology. We finish this paper with a brief ... More

Maximum principle and one-sign solutions for the elliptic $p$-LaplacianJul 28 2012In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.

A criterion of simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matricesNov 09 2011In this paper, we consider the simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices.

A Gel'fand-type spectral radius formula and stability of linear constrained switching systemsJul 01 2011Using ergodic theory, in this paper we present a Gel'fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup $\bS^+$ restricted to a subset that need ... More

Dynamics of Bohr almost periodic motions of topological abelian semigroupsJun 09 2016We study the topological and ergodic dynamics of Bohr almost periodic motions of a topological abelian semigroup acting continuously on a compact metric space.

On the Homology of Configuration Spaces Associated to Centers of MassApr 01 2010The aim of this paper is to make sample computations with the Salvetti complex of the "center of mass" arrangement introduced in [arXiv:math/0611732] by Cohen and Kamiyama. We compute the homology of the Salvetti complex of these arrangements with coefficients ... More

Eigenvalue, bifurcation, existence and nonexistence of solutions for Monge-Ampère equationsJul 27 2012In this paper we study the following eigenvalue boundary value problem for Monge-Amp\`{e}re equations: {equation} \{{array}{l} \det(D^2u)=\lambda^N f(-u)\,\, \text{in}\,\, \Omega, u=0,\,\text{on}\,\, \partial \Omega. {array}. {equation} We establish the ... More

Criterion for quasi-anosovian diffeomorphisms of closed manifoldsApr 08 2014Quasi-Anosov diffeomorphism is a kind of important dynamical system due to R. Mane 1970s. In this paper, we present a criterion for such dynamics using ergodic theory.

When is weakly almost periodic equivalent to uniformly almost periodic for semiflows?Dec 15 2017Let $\pi\colon T\times X\rightarrow X$ be a semiflow on a compact Hausdorff space $X$ with phase semigroup $T$. This paper provides us with some conditions under which \textsl{weakly almost periodic} is equivalent to \textsl{uniformly almost periodic} ... More

Eta Invariants for Even Dimensional ManifoldsOct 13 2011In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to $K^1$ representatives on even dimensional manifolds, ... More

Intensity Distribution and Luminosity Function of the Swift Gamma-Ray BurstsDec 24 2008Apr 23 2009Using the sample of long Gamma-ray bursts (GRBs) detected by Swift-BAT before June 2007, we measure the cumulative distribution of the peak photon fluxes (log N - log P) of the Swift bursts. Compared with the BATSE sample, we find that the two distributions ... More

A Positive Mass Theorem for Spaces with Asymptotic SUSY CompactificationAug 26 2003We prove a positive mass theorem for spaces which asymptotically approach a flat Euclidean space times a Calabi-Yau manifold (or any special honolomy manifold except the quaternionic K\"ahler). This is motivated by the very recent work of Hertog-Horowitz-Maeda. ... More

$L^p(Ω)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous DriftApr 09 2014We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$-difference of SDEs using the norm of the difference of coefficients, where the discontinuous ... More

Lower order tensors in non-Kähler geometry and non-Kähler geometric flowMar 21 2015May 31 2016In recent years, Streets and Tian introduced a series of curvature flows to study non-K\"{a}hler geometry. In this paper, we study how to construct second order curvature flows in a uniform way, under some natural assumptions which holds in Streets and ... More

Asymptotics of orthogonal polynomials and the Painlevé transcendentsAug 16 2016Sep 14 2016In this survey, we review asymptotic results of some orthogonal polynomials which are relate to the Painlev\'e transcendents. They are obtained by applying Deift-Zhou's nonlinear steepest descent method for Riemann-Hilbert problems. In the last part of ... More

Ill-posedness of the incompressible magneto-hydrodynamics system in $\dot{B}_{\infty,\infty}^{-1}$Nov 16 2012Jul 25 2014We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed in the largest scaling invariant space $\dot{B}_{\infty,\infty}^{-1}$. The construction method of initial data used in this paper is different from ... More

The finite-step realizability of the joint spectral radius of a pair of $d\times d$ matrices one of which being rank-oneJun 05 2011We study the finite-step realizability of the joint/generalized spectral radius of a pair of real $d\times d$ matrices, one of which has rank 1. Then we prove that there always exists a finite-length word for which there holds the spectral finiteness ... More

Approximation to multifractional Riemann-Liouville Brownian sheetDec 08 2012Dec 25 2012In this paper, we first introduce multifrational Riemann-Liouville Brownian sheets. Then, we show a result of approximation in law of the multifractional Riemann-Liouville Brownian sheet. The construction of these approximations is based on a sequence ... More

Convergence in law to operator fractional Brownian motionsDec 31 2011In this paper, we provide two approximations in law of operator fractional Brownian motions. One is constructed by Poisson processes, and the other generalizes a result of Taqqu (1975).

Continuous dependence for $H^{2}$ critical nonlinear Schrödinger equations in high dimensionsMar 31 2012The global existence of solutions in $H^{2}$ is well known for $H^{2}$ critical nonlinear Schr\"{o}dinger equations with small initial data in high dimensions $d\geq8$. However, even though the solution is constructed by a fixed-point technique, continuous ... More

Unified Systems of FB-SPDEs/FB-SDEs with Jumps/Skew Reflections and Stochastic Differential GamesJun 15 2015Sep 14 2015We study four systems and their interactions. First, we formulate a unified system of coupled forward-backward stochastic partial differential equations (FB-SPDEs) with Levy jumps, whose drift, diffusion, and jump coefficients may involve partial differential ... More

On the Pin(2)-Equivariant Monopole Floer Homology of Plumbed 3-ManifoldsJul 11 2016Sep 23 2016We compute the Pin(2)-equivariant monopole Floer homology for the class of plumbed 3-manifolds with at most one "bad" vertex (in the sense of Oszv\'ath and Szab\'o). We show that for these manifolds, the Pin(2)-equivariant monopole Floer homology can ... More

Stability and Evolution of Color Skyrmions in the Quark-Gluon PlasmaDec 20 2006Feb 01 2007We show the existence of unstable color skyrmions in a class of nonabelian fluid models. Oscillating and expanding solutions are found in the time-dependent case.

Interpreting and Extending The Guided Filter Via Cyclic Coordinate DescentMay 30 2017In this paper, we will disclose that the Guided Filter (GF) can be interpreted as the Cyclic Coordinate Descent (CCD) solver of a Least Square (LS) objective function. This discovery implies a possible way to extend GF because we can alter the objective ... More

The McMahon pseudo-metrics of minimal transformation semigroups with invariant measuresJun 25 2018Let $T\times X\rightarrow X$ be any minimal semiflow with phase semigroup $T$. When $(T,X)$ admits an invariant Borel probability measure, using McMahon pseudo-metrics we mainly show in this paper the following results: \begin{itemize} \item[(1)] $S_{\textit{eq}}(X)=Q(X)$, ... More

The McMahon pseudo-metrics of minimal semiflows with invariant measuresJun 25 2018Mar 29 2019Let $(T,X)$ with phase mapping $(t,x)\mapsto tx$ be any minimal semiflow with phase semigroup $T$ and with compact $\textrm{T}_2$ phase space $X$. When $(T,X)$ admits an invariant Borel probability measure, using McMahon pseudo-metrics we consider the ... More

Mean-variance hedging based on an incomplete market with external risk factors of non-Gaussian OU processesOct 03 2014Aug 26 2015In this paper, we prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semi-explicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian Ornstein-Uhlenbeck ... More

On $\mathrm{C}^1$-class local diffeomorphisms whose periodic points are nonuniformly expandingJun 11 2012Using a sifting-shadowing combination, we prove in this paper that an arbitrary $\mathrm{C}^1$-class local diffeomorphism $f$ of a closed manifold $M^n$ is uniformly expanding on the closure $\mathrm{Cl}_{M^n}(\mathrm{Per}(f))$ of its periodic point set ... More

A positive solution to a conjecture of A. Katok for diffeomorphism caseJun 10 2008In this paper, using Pesin theory and Liao theory, we give a positive solution to a conjecture of A. Katok.

Time-preserving structural stability of hyperbolic differential dynamics with noncompact phase spacesMay 17 2008In this paper, we study the structural stability of hyperbolic differential systems on Euclidean spaces using Liao theory.

A Note on Positive Energy Theorem for Spaces with Asymptotic SUSY CompactificationJun 01 2004We extend the positive mass theorem proved previously by the author to the Lorentzian setting. This includes the original higher dimensional positive energy theorem whose spinor proof was given by Witten in dimension four and by Xiao Zhang in dimension ... More

The McMahon pseudo-metrics of minimal semiflows with invariant measuresJun 25 2018Apr 17 2019Using McMahon pseudo-metrics, for any minimal semiflow admitting an invariant measure, we study the relationships between its equicontinuous structure relation, regionally proximal relation and Veech's relations; and characterize its weak-mixing. We show ... More

Eigenvalue, global bifurcation and positive solutions for a class of fully nonlinear problemsMar 23 2014In this paper, we shall study global bifurcation phenomenon for the following Kirchhoff type problem \begin{equation} \left\{ \begin{array}{l} -\left(a+b\int_\Omega \vert \nabla u\vert^2\,dx\right)\Delta u=\lambda u+h(x,u,\lambda)\,\,\text{in}\,\, \Omega,\\ ... More

Cosmological magnetic fields: generation during inflation and evolutionSep 23 2003This paper concerns the generation and evolution of the cosmological (large-scale $\sim Mpc$) magnetic fields in an inflationary universe. The universe during inflation is represented by de Sitter space-time. We started with the Maxwell equations in spatially ... More

The Grothendieck Construction and Gradings for Enriched CategoriesJul 01 2009The Grothendieck construction is a process to form a single category from a diagram of small categories. In this paper, we extend the definition of the Grothendieck construction to diagrams of small categories enriched over a symmetric monoidal category ... More

Regularity criterion and energy conservation for the supercritical Quasi-Geostrophic equationMay 09 2015Jul 12 2016This paper studies the regularity and energy conservation problems for the 2D supercritical quasi-geostrophic (SQG) equation. We apply an approach of splitting the dissipation wavenumber to obtain a new regularity condition which is weaker than all the ... More

Existence of regular solutions to the full Liquid Crystal SystemSep 02 2013We study the general Ericksen-Leslie system with non-constant density, which describes the flow of nematic liquid crystal. In particular the model investigated here is associated with Parodi's relation. We prove that: in two dimension, the solutions are ... More

Regularity problem for the nematic LCD system with Q-tensor in $\mathbb R^3$Aug 26 2016We study the regularity problem of a nematic liquid crystal model with local configuration represented by Q-tensor in three dimensions. It was an open question whether the classical Prodi-Serrin condition implies regularity for this model. Applying a ... More

Local well-posedness for the Hall-MHD system in optimal Sobolev SpacesMar 26 2018Jun 08 2018We show that the viscous resistive magneto-hydrodynamics system with Hall effect is locally well-posed in $H^s(\mathbb R^n)\times H^{s+1-\varepsilon}(\mathbb R^n)$ with $s>\frac{n}2-1$ and any small enough $\varepsilon>0$ such that $s+1-\varepsilon>\frac{n}2$. ... More

Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equationsJul 16 2013Dec 17 2013In this paper we show that if a linear cocycle is robustly periodical stable then it is uniformly stable.

Propagation of regularity for the MHD system in optimal Sobolev spaceJul 24 2017Mar 14 2018We study the problem of propagation of regularity of solutions to the incompressible viscous non-resistive magneto-hydrodynamics system. According to scaling, the Sobolev space $H^{\frac n2-1}(\mathbb R^n)\times H^{\frac n2}(\mathbb R^n)$ is critical ... More

On chaotic minimal center of attraction of a Lagrange stable motion for topological semi flowsJul 02 2015Jul 09 2015In this paper, we study the chaotic dynamics of a minimal center of attraction of a Lagrange stable motion for semi flows.

Chaotic dynamics of continuous-time topological semi-flows on Polish spacesJan 09 2015In this paper, we study the chaotic dynamics of a continuous-time topological semi-flow on a Polish space.

Stability of Solutions to the Quasi-Geostrophic Equations in $\mathbb R^2$Mar 16 2015We consider the stationary Quasi-Geostrophic equation in the whole space $\mathbb R^2$ driven by a force $f$. Under certain assumptions of $f$, we establish the existence of solutions with finite $L^2$ norm. This solution is unique among all solutions ... More

Congruences for the number of partitions and bipartitions with distinct even partsApr 22 2014Let $ped(n)$ denote the number of partitions of $n$ wherein even parts are distinct (and odd parts are unrestricted). We show infinite families of congruences for $ped(n)$ modulo $8$. We also examine the behavior of $ped_{-2}(n)$ modulo $8$ in detail ... More

The Exit Distribution for Smart Kinetic Walk with Symmetric Transition ProbabilityNov 29 2016It has been proved that the distribution of the point where the Smart Kinetic Walk (SKW) exits a domain converges in distribution to harmonic measure on the hexagonal lattice. For other lattices, it is believed that this result still holds, and there ... More

Regularity criterion for the 3D Hall-magneto-hydrodynamicsJul 21 2015May 02 2016This paper studies the regularity problem for the 3D incompress- ible resistive viscous Hall-magneto-hydrodynamic (Hall-MHD) system. The Kolmogorov 41 phenomenological theory of turbulence predicts that there exists a critical wavenumber above which the ... More

An Improved Feedback Coding Scheme for the Wire-tap ChannelDec 13 2017Apr 25 2018The model of wiretap channel (WTC) is important as it constitutes the essence of physical layer security (PLS). Wiretap channel with noiseless feedback (WTC-NF) is especially interesting as it shows what can be done when a private feedback is available. ... More

Heterogeneity and aggregation in evolutionary dynamics: a general framework without aggregabilityMay 13 2018We consider general evolutionary dynamics under persistent payoff heterogeneity and study the dynamic relation between the strategy composition over different types and the aggregate strategy distribution of the entire population. It is rigorously proven ... More

Collisionless Magnetic Reconnection via Alfven EigenmodesJul 04 2009We propose an analytic approach to the problem of collisionless magnetic reconnection formulated as a process of Alfven eigenmodes' generation and dissipation. Alfven eigenmodes are confined by the current sheet in the same way that quantum mechanical ... More

Convergence Rates of Finite Difference Stochastic Approximation AlgorithmsJun 30 2015Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various updating schemes ... More

On the E^1-term of the gravity spectral sequenceMar 26 2009The author constructed a spectral sequence strongly converging to h_*(Omega^n Sigma^n X) for any homology theory in [Topology 33 (1994) 631-662]. In this note, we prove that the E^1-term of the spectral sequence is isomorphic to the cobar construction, ... More

An Application of Ubiquitous Video Services and Management Systems in Civil DefenseMar 27 2018This paper proposes a model of ubiquitous video services and management systems for solving current issues of video surveillance services and management in the smart city. The author presents the Enterprise Service Bus (ESB) based methods of integrating ... More

Spectrum of Navier $p$-biharmonic problem with sign-changing weightJul 31 2012Aug 27 2016In this paper, we consider the following eigenvalue problem {{l} (|u"|^{p-2}u")"=\lambda m(x)|u|^{p-2}u, x\in (0,1), u(0)=u(1)=u"(0)=u"(1)=0, where $1<p<+\infty$, $\lambda$ is a real parameter and $m$ is sign-changing weight. We prove there exists a unique ... More

Cellular Stratified Spaces I: Face Categories and Classifying SpacesJun 19 2011Sep 16 2016The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonz\'alez, and Rudyak [1009.1851] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it was shown that ... More

Connected Heegaard Floer homology of sums of Seifert fibrationsApr 17 2018Nov 03 2018We compute the connected Heegaard Floer homology (defined by Hendricks, Hom, and Lidman) for a large class of 3-manifolds, including all linear combinations of Seifert fibered homology spheres. We show that for such manifolds, the connected Floer homology ... More

The Exit Distribution for Smart Kinetic Walk with Symmetric and Asymmetric Transition ProbabilityNov 29 2016Feb 03 2017It has been proved that the distribution of the point where the Smart Kinetic Walk (SKW) exits a domain converges in distribution to harmonic measure on the hexagonal lattice. For other lattices, it is believed that this result still holds, and there ... More

Stability of Solutions to the Quasi-Geostrophic Equations in $\mathbb R^2$Mar 16 2015Feb 16 2017We consider the stationary Quasi-Geostrophic equation in the whole space $\mathbb R^2$ driven by a force $f$. Under certain smallness assumptions of $f$, we establish the existence of solutions with finite $L^2$ norm. This solution is unique among all ... More

Equations For Parseval's Frame Wavelets In $L^2(\R^d)$ With Compact SupportsJul 31 2016Let $d\geq 1$ be a natural number and $A_0$ be a $d\times d$ expansive integral matrix with determinant $\pm 2.$ Then $A_0$ is integrally similar to an integral matrix $A$ with certain additional properties. A finite solution to the system of equations ... More

Spectra of Cantor measuresJan 19 2014Feb 09 2015Let $\mu_{q, b}$ be the Cantor measure associated with the iterated function system $f_i(x)=x/b+i/q, 0\le i\le q-1$, where $2\le q, b/q\in \Z$. In this paper, we consider spectra and maximal orthogonal sets of the Cantor measure $\mu_{q, b}$ and their ... More

Eta Invariant and Conformal CobordismJun 20 2001Jun 21 2001In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an abelian group, the conformal cobordism group, which classifies ... More

Criteria of stabilizability for switching-control systems with solvable linear approximationsJan 10 2012We study the stability and stabilizability of a continuous-time switched control system that consists of the time-invariant $n$-dimensional subsystems \dot{x}=A_ix+B_i(x)u\quad (x\in\mathbb{R}^n, t\in\mathbb{R}_+ \textrm{and} u\in\mathbb{R}^{m_i}),\qquad ... More

A Curvature Flow Unifying Symplectic Curvature Flow And Pluriclosed FlowNov 28 2013Mar 21 2015Streets and Tian introduced pluriclosed flow and symplectic curvature flow in recent years. Here we construct a curvature flow to unify these two flows. We show the short time existence of our flow and exhibit an obstruction to long time existence.

Uniform positive recursion frequency of any minimal dynamical system on a compact spaceJun 25 2018Using Gottschalk's notion\,---\,weakly locally almost periodic point, we show in this paper that if $f\colon X\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage $\varepsilon$ of $X$, ... More

Almost automorphy of surjective semiflows on compact Hausdorff spacesJun 15 2018Mar 29 2019Let $(T,X)$ with phase mapping $(t,x)\mapsto tx$ be a semiflow on a compact $\textrm{T}_2$-space $X$ with phase semigroup $T$ such that $tX=X$ for each $t$ of $T$. An $x\in X$ is called an \textit{a.a. point} if $t_nx\to y, x_n^\prime\to x^\prime$ and ... More

Characterizations of function spaces on the sphere using framesOct 04 2005In this paper we introduce a polynomial frame on the unit sphere $\sph$ of $\mathbb{R}^d$, for which every distribution has a wavelet-type decomposition. More importantly, we prove that many function spaces on the sphere $\sph$, such as $L^p$, $H^p$ and ... More

Pointwise convergence of ergodic averages of bounded measurable functions for amenable groupsApr 03 2016Jun 16 2016Given any amenable group $G$ (with a left Haar measure $|\cdot|$ or $dg$), we can select out a \textit{F{\o}lner subnet} $\{F_\theta,\theta\in\Theta\}$ from any left F{\o}lner net in $G$, which is \textit{$L^\infty$-admissible}, namely, for any Borel ... More

Some Results on the Scattering Theory for Nonlinear Schrödinger Equations in Weighted $L^{2}$ SpaceAug 16 2011We investigate the scattering theory for the nonlinear Schr\"{o}dinger equation $i \partial_{t}u+ \Delta u+\lambda|u|^\alpha u=0$ in $\Sigma=H^{1}(\mathbb{R}^{d})\cap L^{2}(|x|^{2};dx)$. We show that scattering states $u^{\pm}$ exist in $\Sigma$ when ... More

Non-uniqueness of Leray-Hopf weak solutions of the 3D Hall-MHD systemDec 29 2018Jan 11 2019Non-uniqueness of Leray-Hopf type of solutions is obtained for the three dimensional magneto-hydrodynamics with Hall effect. It seems to be the first result in the literature on non-uniqueness of Leray-Hopf weak solutions for dissipative equations. As ... More