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Human Motion Prediction using Adaptable Neural NetworksOct 01 2018Human motion prediction is an important component to facilitate human robot interaction. Robots need to accurately predict human's future movement in order to efficiently collaborate with humans, as well as to safely plan its own motion trajectories. ... More

SERoCS: Safe and Efficient Robot Collaborative Systems for Next Generation Intelligent Industrial Co-RobotsSep 21 2018Human-robot collaborations have been recognized as an essential component for future factories. It remains challenging to properly design the behavior of those co-robots. Those robots operate in dynamic uncertain environment with limited computation capacity. ... More

Analyzing Traffic Delay at Unmanaged IntersectionsMay 26 2018At an unmanaged intersection, it is important to understand how much traffic delay may be caused as a result of microscopic vehicle interactions. Conventional traffic simulations that explicitly track these interactions are time-consuming. Prior work ... More

Analytically Modeling Unmanaged Intersections with Microscopic Vehicle InteractionsApr 12 2018Sep 06 2018With the emergence of autonomous vehicles, it is important to understand their impact on the transportation system. However, conventional traffic simulations are time-consuming. In this paper, we introduce an analytical traffic model for unmanaged intersections ... More

Algorithms for Verifying Deep Neural NetworksMar 15 2019Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging to verify ... More

Simulating Emergent Properties of Human Driving Behavior Using Multi-Agent Reward Augmented Imitation LearningMar 14 2019Recent developments in multi-agent imitation learning have shown promising results for modeling the behavior of human drivers. However, it is challenging to capture emergent traffic behaviors that are observed in real-world datasets. Such behaviors arise ... More

A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalingsFeb 26 2018Jul 16 2018In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic system and the system with uncertainties, with asymptotic behavior leading to the drift diffusion-Poisson system as the Knudsen number goes to zero. The random inputs ... More

Higher Toda Mechanics and Spectral CurvesJun 01 2003For each one of the Lie algebras $\mathfrak{gl}_{n}$ and $\widetilde {\mathfrak{gl}}_{n}$, we constructed a family of integrable generalizations of the Toda chains characterized by two integers $m_{+}$ and $m_{-}$. The Lax matrices and the equations of ... More

Group Learning and Opinion Diffusion in a Broadcast NetworkSep 14 2013We analyze the following group learning problem in the context of opinion diffusion: Consider a network with $M$ users, each facing $N$ options. In a discrete time setting, at each time step, each user chooses $K$ out of the $N$ options, and receive randomly ... More

Rapid variability of BL Lac 0925+504: interstellar scintillation induced?Apr 25 2018Analysis of rapid variability at 4.85 GHz for the BL BLac object 0925+504 is presented and discussed. The structure functions (SF) are investigated with both refractive and weak interstellar scintillation (RISS/WISS) models analytically. Parameters obtained ... More

Price-Based Distributed Offloading for Mobile-Edge Computing with Computation Capacity ConstraintsDec 02 2017Mobile-edge computing (MEC) is a promising technology to enable real-time information transmission and computing by offloading computation tasks from wireless devices to network edge.

On the $A_α$-characteristic polynomial of a graphNov 09 2017Let $G$ be a graph with $n$ vertices, and let $A(G)$ and $D(G)$ denote respectively the adjacency matrix and the degree matrix of $G$. Define $$ A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G) $$ for any real $\alpha\in [0,1]$. The $A_{\alpha}$-characteristic ... More

On the arithmetic of the endomorphism ring End($\mathbb{Z}_{p}\times\mathbb{Z}_{p^{m}}$)May 03 2016For a prime $p$, let $E_{p,p^m}=\{\begin{pmatrix}a&b\\p^{m-1}c&d\end{pmatrix}|a,b,c\in\mathbb{Z}_{p},~\mathrm{and}~d\in \mathbb{Z}_{p^{m}}\}$. We first establish a ring isomorphism from $\mathrm{End}(\mathbb{Z}_p\times\mathbb{Z}_p^m)$ onto $E_{p,p^m}$. ... More

The Dynamic Behavior of Quantum Statistical Entropy in 5D Ricci-flat Black String with Thin-layer ApproachNov 05 2008In this paper, the statistical-mechanical entropies of 5D Ricci-flat black string is calculated through the wave modes of the quantum field with improved thin-layer brick-wall method. The modes along the fifth dimension are semi-classically quantized ... More

Fine Magnetic Characteristics of a Light Bridge by HinodeFeb 01 2019Light bridge (LB) is bright structure crossing the umbra of sunspots and associated to the breakup or assembly of sunspots. In this paper, a LB is presented and studied using the observatory data obtained by {\it Hinode} satellites. Force-free factor ... More

Relationship between Magnetic Field Properties and an X-class Flare in Active Region NOAA 9077Feb 01 2019The magnetic field plays a key role in producing solar flares, so that the investigation on the relationship between the magnetic field properties and flares is significant. In this paper, based on the magnetic field extrapolated from the photospheric ... More

Hypocoercivity for a BGK model for gas mixturesOct 19 2018Jan 08 2019We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we can prove exponential ... More

A blow-up criterion for the compressible liquid crystals systemNov 19 2010Nov 23 2010In this paper, we establish a blow-up criterion for the compressible liquid crystals equations in terms of the gradient of the velocity only, similar to the Beale-Kato-Majda criterion \cite{majda} for ideal incompressible flows and the criterion obtained ... More

On surjectivity of smooth maps into Euclidean spaces and the fundamental theorem of algebraJun 16 2017In this note we obtain the surjectivity of smooth maps into Euclidean spaces under mild conditions. As application we give a new proof of the Fundamental Theorem of Algebra. We also observe that any $C^1$-map from a compact manifold into Euclidean space ... More

$σ$-self-orthogonal constacyclic codes of length $p^s$ over $\mathbb F_{p^m}+u\mathbb F_{p^m}$Jul 25 2018In this paper, we study the $\sigma$-self-orthogonality of constacyclic codes of length $p^s$ over the finite commutative chain ring $\mathbb F_{p^m} + u \mathbb F_{p^m}$, where $u^2=0$ and $\sigma$ is a ring automorphism of $\mathbb F_{p^m} + u \mathbb ... More

Elastic Waves Scattering without Conversion in Metamaterials with Simultaneous Zero Indices for Longitudinal and Transverse wavesMar 08 2015Sep 28 2015We theoretically investigate elastic waves propagating in metamaterials with simultaneous zero indices for both the longitudinal and transverse waves. With scattering objects (here cylinders) present in the metamaterials slabs, while the elastic waves ... More

Exploiting Unlabeled Data for Neural Grammatical Error DetectionNov 28 2016Nov 29 2016Identifying and correcting grammatical errors in the text written by non-native writers has received increasing attention in recent years. Although a number of annotated corpora have been established to facilitate data-driven grammatical error detection ... More

Non-Parametric Variational Inference with Graph Convolutional Networks for Gaussian ProcessesSep 08 2018Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of inducing points. ... More

Lending Orientation to Neural Networks for Cross-view Geo-localizationMar 29 2019This paper studies image-based geo-localization (IBL) problem using ground-to-aerial cross-view matching. The goal is to predict the spatial location of a ground-level query image by matching it to a large geotagged aerial image database (e.g., satellite ... More

Twisted exponential sums of polynomials in one variableDec 10 2009The twisted $T$-adic exponential sum associated to a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function ... More

Letter: Modified normalized Rortex/vortex identification methodMay 08 2019In this paper, a modified normalized Rortex/vortex identification method named Omega_R is presented to improve the original Omega_R method and cure the bulging phenomenon on the iso-surfaces caused by the original Omega_R method. Detailed mathematical ... More

The multiplier and cohomology of Lie superalgebrasNov 01 2018In this paper, all (super)algebras are over a field $\mathbb{F}$ of characteristic different from $2, 3$. We construct the so-called 5-sequences of cohomology for central extensions of a Lie superalgebra and prove that they are exact. Then we prove that ... More

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed ... More

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016Nov 10 2016We consider an inverse acoustic scattering problem in simultaneously recovering an embedded obstacle and its surrounding inhomogeneous medium by formally determined far-field data. It is shown that the knowledge of the scattering amplitude with a fixed ... More

Formula of Volume of Revolution with Integration by Parts and ExtensionSep 04 2016A calculation formula of volume of revolution with integration by parts of definite integral is derived based on monotone function, and extended to a general case that curved trapezoids is determined by continuous, piecewise strictly monotone and differential ... More

A class of cyclic codes whose dual have five zerosFeb 07 2015In this paper, a family of cyclic codes over $\mathbb{F}_{p}$ whose duals have five zeros is presented, where $p$ is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.

To Stay Or To Switch: Multiuser Dynamic Channel AccessSep 14 2013In this paper we study opportunistic spectrum access (OSA) policies in a multiuser multichannel random access cognitive radio network, where users perform channel probing and switching in order to obtain better channel condition or higher instantaneous ... More

An Online Approach to Dynamic Channel Access and Transmission SchedulingApr 04 2015Making judicious channel access and transmission scheduling decisions is essential for improving performance as well as energy and spectral efficiency in multichannel wireless systems. This problem has been a subject of extensive study in the past decade, ... More

On a Qualitative Difference between the Dynamics of Particle Production in Soft and Hard Processes of High Energy CollisionsDec 10 1998The qualitative difference between the anomalous scaling properties of hadronic final states in soft and hard processes of high energy collisions is studied in some detail. It is pointed out that the experimental data of e^+e^- collisions at $E_{cm}=$91.2 ... More

Duality-free Methods for Stochastic Composition OptimizationOct 26 2017We consider the composition optimization with two expected-value functions in the form of $\frac{1}{n}\sum\nolimits_{i = 1}^n F_i(\frac{1}{m}\sum\nolimits_{j = 1}^m G_j(x))+R(x)$, { which formulates many important problems in statistical learning and ... More

Constructing a weak subset of a random setFeb 11 2016The tree forcing method given by (Liu 2015) enables the cone avoiding of strong enumeration of a given tree, within a subset or co-subset of an arbitrary given set, provided the given tree does not admit computable strong enumeration. Using this result, ... More

Mixture Diffusion for Asset PricingOct 05 2016Oct 30 2016This paper proposes a general form of mixture diffusion process to model asset price dynamics, using a mixture of infinite number of parametric diffusions. We show that the underlying asset price dynamics of the risk-neutral distributions can be modeled ... More

Lorentz and CPT Violation in Top-Quark ProductionNov 02 2015Signals for Lorentz and CPT violation can appear in a wide range of experiments including hadron colliders like the LHC. We present a calculation of the Lorentz-violating cross section for top-quark pair production via gluon fusion. This process dominates ... More

Contrôle des places non réduitesSep 28 2016In this paper, we give an upper bound of the product of the norms of places such that the reduction over which a pure dimensional reduced projective scheme over a ring of integers is not reduced.

New Coordinates for BTZ Black Hole and Hawking Radiation via TunnellingDec 16 2005Hawking radiation can usefully be viewed as a semi-classical tunnelling process that originates at the black hole horizon. For the stationary axisymmetric BTZ black hole, a generalized Painleve coordinate system (Painleve-BTZ coordinates) is introduced, ... More

A short proof of the HRT conjecture for almost every (1,3) configurationSep 27 2016Based on the proof of Demeter \cite{Dem10}, we establish the HRT conjecture for almost every (1,3) configuration.

Spatial heterodyne scanning laser confocal holographic microscopyOct 11 2016Scanning laser confocal holographic microscopy using a spatial heterodyne detection method is presented. Spatial heterodyne detection technique employs a Mach-Zehnder interferometer with the reference beam frequency shifted by two acousto-optic modulators ... More

Uniqueness in inverse elastic scattering with one incident waveAug 03 2016Oct 03 2016In this paper, we solve a longstanding open problem for determining the shape of an obstacle from the knowledge of the far field pattern for the scattering of time-harmonic elastic wave. We show that the elastic far field pattern by an incoming plane ... More

Theta functions and arithmetic quotients of loop groupsApr 02 2011In this paper we observe that isomorphism classes of certain metrized vector bundles over P^1-{0,infinity} can be parameterized by arithmetic quotients of loop groups. We construct an asymptotic version of theta functions, which are defined on these quotients. ... More

Analysis of Charge Asymmetry in Rare Dilepton $B$ DecaysMay 16 1995May 16 1995We analyze forward-backward charge asymmetry of the lepton production in rare decays $B\rightarrow X_s l^+l^-$ and $B\rightarrow K^* l^+l^-$, including vector-resonance effects. Certain regions of phase space, in which the asymmetry is sensitive to individual ... More

A time-work uncertainty relation in quantum systemsAug 02 2016In quantum systems, a plausible definition of work is based on two energy measurement scheme. Considering that energy change of quantum system obeys a time-energy uncertainty relation, it shall be interesting to see whether such type of work as well obeys ... More

Py-oopsi: the python implementation of the fast-oopsi algorithmMay 06 2014Fast-oopsi was developed by Joshua Vogelstein in 2009, which is now widely used to extract neuron spike activities from calcium fluorescence signals. Here, we propose detailed implementation of the fast-oopsi algorithm in python programming language. ... More

Optimizing ETL Dataflow Using Shared Caching and Parallelization MethodsSep 05 2014Extract-Transform-Load (ETL) handles large amount of data and manages workload through dataflows. ETL dataflows are widely regarded as complex and expensive operations in terms of time and system resources. In order to minimize the time and the resources ... More

Two-level Data Staging ETL for Transaction DataSep 05 2014Sep 13 2014In data warehousing, Extract-Transform-Load (ETL) extracts the data from data sources into a central data warehouse regularly for the support of business decision-makings. The data from transaction processing systems are featured with the high frequent ... More

Noninformative Bounding in Differential Privacy and Its Impact on Statistical Properties of Sanitized Results in Truncated and Boundary-Inflated-Truncated Laplace MechanismsJul 28 2016Protection of individual privacy is a common concern when releasing and sharing data and information. Differential privacy (DP) formalizes privacy in mathematical terms without making assumptions about the background knowledge of data intruders and thus ... More

An Efficient Implementation for WalkSATOct 25 2015Dec 04 2015Stochastic local search (SLS) algorithms have exhibited great effectiveness in finding models of random instances of the Boolean satisfiability problem (SAT). As one of the most widely known and used SLS algorithm, WalkSAT plays a key role in the evolutions ... More

How to detect super-massive binary black holes at parsec scalesOct 09 2014Jan 05 2015It is difficult to find or identifying the binary black holes in parsec scales, since the dual AGN may be merged quickly. It is required to explore more possibilities to identifying binary black holes in parsec scales, we give some discussions, especially ... More

Quantum walks in the density operator pictureJun 08 2015A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal state is described ... More

Kasami type codes of higher relative dimensionJun 07 2015Jun 10 2015Some new Kasami type codes of higher relative dimension is introduced. Their weight distribution is determined.

From open quantum walks to unitary quantum walksFeb 05 2015We present an idea to convert to a unitary quantum walk any open quantum walk which is defined on lattices as well as on finite graphs. This approach generalizes to the domain of open quantum walks (or quantum Markov chains) the framework introduced by ... More

Defining Concepts of Emotion: From Philosophy to ScienceFeb 11 2016This paper is motivated by a series of (related) questions as to whether a computer can have pleasure and pain, what pleasure (and intensity of pleasure) is, and, ultimately, what concepts of emotion are. To determine what an emotion is, is a matter of ... More

Localization and Conjectures from String DualityJan 23 2007We describe the applications of localization methods, in particular the functorial localization formula, in the proofs of several conjectures from string theory. Functorial localization formula pushes the computations on complicated moduli spaces to simple ... More

Heat kernels, symplectic geometry, moduli spaces and finite groupsOct 19 1999In this note we apply heat kernels to derive some localization formula in sympletcic geometry, to study moduli spaces of flat connections on a Riemann surface, to obtain the push-forward measures for certain maps between Lie groups and to solve equations ... More

On Regularity Property of Retarded Ornstein-Uhlenbeck Processes in Hilbert SpacesJun 08 2011In this work, some regularity properties of mild solutions for a class of stochastic linear functional differential equations driven by infinite dimensional Wiener processes are considered. In terms of retarded fundamental solutions, we introduce a class ... More

Invariant AlgebrasApr 20 2011We introduce invariant algebras and representation$^{(c_1,..., c_8)}$ of algebras, and give many ways of constructing Lie algebras, Jordan algebras, Leibniz algebras, pre-Lie algebras and left-symmetric algebras in an invariant algebras.

Virtual reshaping and invisibility in obstacle scatteringNov 09 2008Dec 30 2008We consider reshaping a scattering obstacle virtually by using transformation optics in acoustic and electromagnetic scattering. Among the general virtual reshaping results, the virtual minification and virtual magnification are particularly studied. ... More

The $D^0\bar{D}^0$ Mixing Search --- Current Status and Future ProspectsAug 20 1994The search for $D^0\bar{D}^0$ mixing carries a large discovery potential for new physics since the $D^0\bar{D}^0$ mixing rate is expected to be very small in the Standard Model. The past decade has seen significant experimental progress in sensitivity, ... More

On positive loops of loose Legendrian embeddingsMay 24 2016Jun 03 2016In this paper, via h-principle we prove that there exist contractible positive loops of Legendrian embeddings based at any loose Legendrian submanifold. As an application, we define a new partial order on $\widetilde{Cont}_0(M,\xi)$ and prove that overtwisted ... More

Combined field formulation and a simple stable explicit interface advancing scheme for fluid structure interactionDec 31 2013We develop a combined field formulation for the fluid structure (FS) interaction problem. The unknowns are (u;p;v), being the fluid velocity, fluid pressure and solid velocity. This combined field formulation uses Arbitrary Lagrangian Eulerian (ALE) description ... More

Estimates on singular values of functions of perturbed operatorsMay 12 2016May 17 2016This is a conitunation of [1] and [2]. We prove that if function $f$ belongs to the class $\Lambda_{\omega} \overset{\text{def}}{=} \{f: \omega_{f}(\delta)\leq \text{const} \omega(\delta)\} $ for an arbitrary modulus of continuity $\omega$, then $s_j(f(A)-f(B))\leq ... More

Heavy ion collisions and AdS/CFTFeb 20 2007Feb 20 2007We review some recent applications of the AdS/CFT correspondence to heavy ion collisions including a calculation of the jet quenching parameter in N=4 super-Yang-Mills theory and quarkonium suppression from velocity scaling of the screening length for ... More

No fast food for solving higher curvature gravityMay 24 2011May 25 2011This paper is withdrawn because it was already known in the literature that the single function metric ansatz invalidates the effective action method. (Refs: gr-qc/0306114, gr-qc/0408067,gr-qc/0404120, gr-qc/0506014, 0705.1669, thanks to S. Deser for ... More

Quark orbital motions from Wigner distributionsJun 30 2014We investigate quark Wigner distributions in a light-cone spectator model. Both the scalar and the axial-vector spectators are included. The light-cone wave functions are derived from effective quark-spectator-nucleon vertex and then generalized by adjusting ... More

Energy Flows in the Jupiter-Io SystemMar 18 2016With the laws of mass conservation, momentum conservation and energy conservation, incorporating the processes of neutral gas ionization and ion diffusion, we develop a self-consistent model for the bright ribbon --- the most prominent feature in Io's ... More

Toda-like systems: solutions and symmetriesDec 25 1995This report is consisted of six independent chapters, each chapter (except chapter 1) is a paper carried out in colabouration with others, who's names are indicated in chapter1. The topics included are (1)Overview of general properties of Toda-like systems ... More

Some remarks on log surfacesDec 02 2016Fujino and Tanaka established the minimal model theory for $\mathbb Q$-factorial log surfaces in characteristic $0$ and $p$, respectively. We prove that every intermediate surface has only log terminal singularities if we run the minimal model program ... More

The first moment of central values of symmetric square $L$-functions in the weight aspectOct 24 2016Oct 26 2016In this note we investigate the behavior at the central point of the symmetric square $L$-functions, the most frequently used $\rm{GL}(3)$ $L$-functions. We establish an asymptotic formula with arbitrary power saving for the first moment of $L(\frac{1}{2},{\rm{sym}}^2f)$ ... More

Characterization of projective spaces and $\mathbb P^r$-bundles as ample divisorsNov 17 2016Let $X$ be a projective manifold of dimension $n$. Suppose that $T_X$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb P^n$. As an application, we derive the classification of projective manifolds containing a $\mathbb P^r$-bundle ... More

Wireless Information and Power Transfer for Multi-Relay Assisted Cooperative CommunicationFeb 22 2016In this paper, we consider simultaneous wireless information and power transfer (SWIPT) in multi-relay assisted two-hop relay system, where multiple relay nodes simultaneously assist the transmission from source to destination using the concept of distributed ... More

Finding binary active galactic nuclei by the centroid shift in imaging surveysAug 21 2015The census of binary active galactic nuclei (AGNs) is important in order to understand the merging history of galaxies and the triggering of AGNs. However, there is still no efficient method for selecting the candidates of binary AGNs. The non-synchronous ... More

Low-Frequency Resonance in Strong HeterogeneityAug 19 2015Sep 14 2016Multiple scattering of wave in strong heterogeneity can cause resonance-like wave phenomenon where signal exhibits low-frequency, high intensity, and slowly propagating wave packet velocity. For example, long period event in volcanic seismology and plasmon ... More

The total Milnor number of the weighted-Le-Yomdin-at-infinity polynomialDec 24 2014Jan 03 2015We give a concrete formula for the total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial in most of the interesting cases. As an application, we give a description of the monodromy fibration at infinity for such kind of polynomial.

Elliptic Curves in Moduli Space of Stable Bundles of Rank 3Dec 08 2012Apr 01 2013Let $M$ be the moduli space of rank 3 stable bundles with fixed determinant of degree 1 on a smooth projective curve of genus $g\geq 2$. When $C$ is generic, we show that any essential elliptic curve on $M$ has degree (respect to anti-canonical divisor ... More

Maxwell Equations and IrreversibilityJun 26 1998Two questions connected to the macroscopic Maxwell equations are addressed: First, which form do they assume in the hydrodynamic regime, for low frequencies, strong dissipation and arbitrary field strengths. Second, what does this tell us about irreversibility ... More

The Range of Validity for the Kelvin ForceOct 18 2000In a recent Letter, Luo, Du and Huang reported a novel convective instability driven by a force rarely studied before -- that exerted by an external magnetic field on a strongly magnetizable liquid. The associated physics is surprisingly rich and promises ... More

Uniqueness of the scatterer for electromagnetic field with one incident plane waveJun 21 2016Oct 03 2016In this paper, we solve a longstanding open problem for determining the shape of an obstacle from the knowledge of the electric (or magnetic) far field pattern for the scattering of time-harmonic electromagnetic field. We show that the electric (or magnetic) ... More

Fujita-type freeness for quasi-log canonical threefoldsFeb 21 2019In this paper, we show that Fujita's basepoint-freeness conjecture for projective quasi-log canonical singularities holds true in dimension three. Immediately, we prove Fujita-type basepoint-freeness for projective semi-log canonical threefolds.

The Poincaré inequality and quadratic transportation-variance inequalitiesFeb 12 2019Feb 14 2019It is known that the Poincar\'e inequality is equivalent to the quadratic transportation-variance inequality (namely $W_2^2(f\mu,\mu) \leqslant C_V \mathrm{Var}_\mu(f)$), see Jourdain \cite{Jourdain} and most recently Ledoux \cite{Ledoux18}. We give an ... More

Gravitational Scattering in the High-Energy LimitNov 28 2018Feb 15 2019Any gravitational scattering amplitude takes a remarkably simple factorized form at tree level in multi-Regge kinematics (MRK), where the produced particles are strongly ordered in rapidity. Very recently, it was shown that also the scattering equations ... More

Proof of Mining in Blockchain SystemsMar 03 2019We propose a proof of mining system. Roughly speaking, in this system the mining stake ${\rm mstak}(A)$ with discrimination index $a\in[0,1]$ of an account $A$ is defined by the formula: $${\rm mstak}(A)=(1-a)\cdot\frac{1}{{\rm NOM}}+a\cdot\frac{{\rm ... More

Stationary Solutions of Neutral Stochastic Partial Differential Equations with Delays in the Highest-Order DerivativesJul 25 2017In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially concerned about ... More

Image Retrieval using Histogram Factorization and Contextual Similarity LearningApr 07 2013Apr 09 2013Image retrieval has been a top topic in the field of both computer vision and machine learning for a long time. Content based image retrieval, which tries to retrieve images from a database visually similar to a query image, has attracted much attention. ... More

Sublattices of finite indexDec 15 2006Jan 05 2007Assuming the Gowers Inverse conjecture and the M\"{o}bius conjecture for the finite parameter $s$, Green-Tao verified Dickson's conjecture for lattices which are ranges of linear maps of complexity at most $s$. In this paper, we reformulate Green-Tao's ... More

Composed inclusions of $A_3$ and $A_4$ subfactorsAug 26 2013In this article, we classify all standard invariants that can arise from a composed inclusion of an $A_3$ with an $A_4$ subfactor. More precisely, if $\mathcal{N}\subset \mathcal{P}$ is the $A_3$ subfactor and $\mathcal{P}\subset\mathcal{M}$ is the $A_4$ ... More

The Pointwise Estimates of Solutions for Semilinear Dissipative Wave EquationApr 02 2008Jan 06 2010In this paper we focus on the global-in-time existence and the pointwise estimates of solutions to the initial value problem for the semilinear dissipative wave equation in multi-dimensions. By using the method of Green function combined with the energy ... More

Combinatorial bases for multilinear parts of free algebras with double compatible bracketsAug 26 2008Let X be an ordered alphabet. Lie_2(n) (and P_2(n) respectively) are the multilinear parts of the free Lie algebra (and the free Poisson algebra respectively) on X with a pair of compatible Lie brackets. In this paper, we prove the dimension formulas ... More

Binary matrix completion with nonconvex regularizersApr 08 2019Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case of BMC problem, ... More

Mathematical results inspired by physicsApr 28 2003I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of intersection ... More

Generalization of One of Lie's TheoremsFeb 26 2008Feb 28 2008We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.

Lie-like Algebras (Superalgeras)Feb 11 2008We introduce the notion of a Lie-like algebra$^{\diamond}$ (superalgebra$^{\diamond}$) for $\diamond\in\{^{1-st}, ^{2-nd}, ^{3-rd} \}$.

Even (Odd) Roots and Simple Leibniz Algebras with Lie Factor $s\ell_2$Dec 31 2006We introduce 3-irreducible modules, even roots and odd roots for Leibniz algebras, produce a basis for a root space of a Leibniz algebra with a semisimple Lie factor, and classify finite dimensional simple Leibniz algebras with Lie factor $s\ell_2$.

Algebraic Regularity over Quaternions and Regular Four-ManifoldsNov 27 2015Based on a new generalization of Cauchy-Riemann system presented in this paper, we introduce a class of quaternion-valued functions of a quaternionic variable, which are called algebraic regular functions. The set of algebraic regular functions is not ... More

Local model of Hilbert-Siegel moduli schemes in $Γ_1(p)$-levelFeb 12 2019We construct a local model for Hilbert-Siegel moduli schemes with $\Gamma_1(p)$-level bad reduction over $\text{Spec }\mathbb{Z}_{q}$, where $p$ is a prime unramified in the totally real field and $q$ is the residue cardinality over $p$. Our main tool ... More

A classification result on prime Hopf algebras of GK-dimension oneApr 24 2018Apr 27 2018In this paper, we classify all prime Hopf algebras $H$ of GK-dimension one satisfying the following two conditions: 1) $H$ has a 1-dimensional representation of order PI.deg$(H)$ and 2) the invariant components of $H$ with respect to this 1-dimensional ... More

Variational characterization of H^pJun 06 2017In this paper we obtain the variational characterization of Hardy space $H^p$ for $p\in(\frac n{n+1},1]$ and get estimates for the oscillation operator and the $\lambda$-jump operator associated with approximate identities acting on $H^p$ for $p\in(\frac ... More