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Leveraging Unlabeled Data for Crowd Counting by Learning to RankMar 08 2018We propose a novel crowd counting approach that leverages abundantly available unlabeled crowd imagery in a learning-to-rank framework. To induce a ranking of cropped images , we use the observation that any sub-image of a crowded scene image is guaranteed ... More

Exploiting Unlabeled Data in CNNs by Self-supervised Learning to RankFeb 17 2019For many applications the collection of labeled data is expensive laborious. Exploitation of unlabeled data during training is thus a long pursued objective of machine learning. Self-supervised learning addresses this by positing an auxiliary task (different, ... More

Rotate your Networks: Better Weight Consolidation and Less Catastrophic ForgettingFeb 08 2018Dec 12 2018In this paper we propose an approach to avoiding catastrophic forgetting in sequential task learning scenarios. Our technique is based on a network reparameterization that approximately diagonalizes the Fisher Information Matrix of the network parameters. ... More

Rotate your Networks: Better Weight Consolidation and Less Catastrophic ForgettingFeb 08 2018In this paper we propose an approach to avoiding catastrophic forgetting in sequential task learning scenarios. Our technique is based on a network reparameterization that approximately diagonalizes the Fisher Information Matrix of the network parameters. ... More

Learning Metrics from Teachers: Compact Networks for Image EmbeddingApr 07 2019Metric learning networks are used to compute image embeddings, which are widely used in many applications such as image retrieval and face recognition. In this paper, we propose to use network distillation to efficiently compute image embeddings with ... More

Memory Replay GANs: learning to generate images from new categories without forgettingSep 06 2018Oct 29 2018Previous works on sequential learning address the problem of forgetting in discriminative models. In this paper we consider the case of generative models. In particular, we investigate generative adversarial networks (GANs) in the task of learning new ... 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

Power Allocation for Secure SWIPT Systems with Wireless-Powered Cooperative JammingFeb 18 2017This paper considers wireless-powered cooperative jamming (CJ) to secure communication between a transmitter (Tx) and an information receiver (IR), in the presence of an energy receiver (ER) which is termed as a potential eavesdropper. The full-duplex ... 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

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

Critical role of quantum dynamical effects in the Raman spectroscopy of liquid waterDec 29 2017Feb 27 2018Understanding the Raman spectroscopy at the atomistic level is important for the elucidation of dynamical processes in liquid water. Because the polarizability (or its time derivative) is often a highly nonlinear function of coordinates or/and momenta, ... More

$T$-adic exponential sums of polynomials in one variableNov 03 2009The $T$-adic exponential sum of 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 of the T-adic exponential ... More

Relationship between Magnetic Field Properties and an X-class Flare in Active Region NOAA 9077Feb 01 2019May 05 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

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

A bi-fidelity method for the multiscale Boltzmann equation with random parametersMay 22 2019In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [A. Narayan, C. Gittelson and D. Xiu, SIAM J. Sci. Comput., 36 (2014); X. Zhu, A. Narayan ... 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.

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

TeV dark matter and the DAMPE electron excessNov 30 2017The recent high energy electron and positron flux observed by the DAMPE experiment indicates possible excess events near 1.4 TeV. Such an excess may be evidence of dark matter annihilations or decays in a dark matter subhalo that is located close to the ... More

Path Integral Molecular Dynamics for Exact Quantum Statistics of Multi-Electronic-State SystemsOct 11 2017Oct 22 2017An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD) [J. Chem. Phys. 145, 024103 ... 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.

Multi-Channel CNN-based Object Detection for Enhanced Situation AwarenessNov 30 2017Object Detection is critical for automatic military operations. However, the performance of current object detection algorithms is deficient in terms of the requirements in military scenarios. This is mainly because the object presence is hard to detect ... More

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 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

Spectral Numerical Mode Matching Method for 3D Layered Multi-Region StructuresJul 08 2019The spectral numerical mode-matching (SNMM) method is developed to simulate the 3D layered multi-region structures. The SNMM method is a semi-analytical solver having the properties of dimensionality reduction to reduce computational costs; it is especially ... More

Matrix-Product Complementary dual CodesApr 13 2016Linear complementary dual codes (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal matrices. Some ... More

Wake Potential in Strong Coupling Plasma from AdS/CFT CorrespondenceFeb 06 2015With the dielectric function computed from AdS/CFT correspondence, we studied the wake potential induced by a fast moving charge in strong coupling plasma, and compared it with the weak coupling wake potential for different particle velocities as $v=0.55c$ ... More

Quantum Manifestation of Elastic Constants in NanostructuresSep 05 2012Generally, there are two distinct effects in modifying the properties of low-dimensional nanostructures: surface effect (SS) due to increased surface-volume ratio and quantum size effect (QSE) due to quantum confinement in reduced dimension. The SS has ... More

Charge-then-Forward: Wireless Powered Communication for Multiuser Relay NetworksJun 26 2018This paper studies a relay-assisted wireless powered communication network (R-WPCN) consisting of multiple source-destination pairs and a hybrid relay node (HRN). We consider a "charge-then-forward" protocol at the HRN, in which the HRN with constant ... More

Discriminative Cross-View Binary Representation LearningApr 04 2018Learning compact representation is vital and challenging for large scale multimedia data. Cross-view/cross-modal hashing for effective binary representation learning has received significant attention with exponentially growing availability of multimedia ... More

Fine Magnetic Characteristics of a Light Bridge by HinodeFeb 01 2019May 05 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

Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering dataOct 19 2016Jan 04 2017We 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

Upper Beurling Density of Systems formed by Translates of finite Sets of Elements in $L^p(\R^d)$Mar 28 2012In this paper, we prove that if a finite disjoint union of translates $\bigcup_{k=1}^n\{f_k(x-\gamma)\}_{\gamma\in\Gamma_k}$ in $L^p(\R^d)$ $(1<p<\infty)$ is a $p'$-Bessel sequence for some $1<p'<\infty$, then the disjoint union $\Gamma=\bigcup_{k=1}^n\Gamma_k$ ... More

Hypocoercivity based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random InputsSep 30 2017May 22 2018In this paper, we provide a general framework to study general class of linear and nonlinear kinetic equations with random uncertainties from the initial data or collision kernels, and their stochastic Galerkin approximations, in both incompressible Navier-Stokes ... More

Maximal graded subalgebras of Witt and Special superalgebrasNov 18 2009Mar 08 2010This paper has been withdrawn by the author due to that the main results and approaches are closedly parallel to the ones in Lie algebra case.

Derivations from the even parts into the odd parts for Lie superalgebras W and SSep 08 2005Let $\mathcal{W}$ and $\mathcal{S}$ denote the even parts of the general Witt superalgebra $W$ and the special superalgebra $S$ over a field of characteristic $ p>3,$ respectively. In this note, using the method of reduction on $\mathbb{Z}$-gradations, ... 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

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

Uniqueness in inverse elastic scattering with one incident waveAug 03 2016Aug 07 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

A Ranking Algorithm for Re-findingFeb 16 2016Feb 18 2016Re-finding files from a personal computer is a frequent demand to users. When encountered a difficult re-finding task, people may not recall the attributes used by conventional re-finding methods, such as a file's path, file name, keywords etc., the re-finding ... More

On Stability of Nodal $L_k^p$-Maps ISep 24 2015We give a general definition of weakly stable nodal $L_k^p$-maps as a natural generalization of the stability for $J$-holomorphic nodal maps in GW theory. A complete characterization of the weakly stable nodal $L_k^p$-maps are given in term of their isotropy ... More

The first moment of central values of symmetric square $L$-functions in the weight aspectOct 24 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

On the Phase Space Partition in High Energy CollisionsMar 30 2002In high energy hadron-hadron and e+e- collisions, to isolate a part of the phase space in multi-hadron final states is necessary for exploring the underlying dynamics. It is shown that the partition of phase space according to the value of rapidity, popularly ... More

Estimate the Ranges of rho and eta only from the Kobayashi-Maskawa Matrix Elements of the First Two GenerationsSep 02 1998Based on the relation between weak CP phase and the other three mixing angles in Cabibbo-Kobayashi-Maskawa matrix postulated by us before, the ranges of rho and eta have been estimated by using the best known two KM matrix elements Vud and Vcd (or Vus). ... More

Solutions to the Problem of K-SAT / K-COL Phase Transition LocationJan 19 2016As general theories, currently there are concentration inequalities (of random walk) only for the cases of independence and martingale differences. In this paper, the concentration inequalities are extended to more general situations. In terms of the ... More

A Class of Noncommutative SpectraApr 20 2011We construct a class of noncommutative spectra and give the basic properties of the class of noncommutative spectra.

Sheaf Structures On a Class of Noncommutative SpectraFeb 14 2012We introduce a class of noncommutative spectra and give the sheaf structure on the class of noncommutative spectra.

Some Results about Triangular Representations of Lie AlgebrasJun 21 2014We introduce the concept of a triangular representation of a Lie algebra, give a counterpart of Ado's theorem, and discuss $2$-irreducible triangular modules over a nonreductive Lie algebra.

Modular Invariance and Characteristic NumbersApr 08 1994We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we have shown ... More

Restriction des séries discrètes de SU(2,1) à un sous-groupe exponentiel maximal et à un sous-groupe de BorelAug 05 2012We give an explicit description of the restriction of discrete series representations of SU(2,1) to a Borel subgroup and to a maximal exponential solvable subgroup and we interpret our results in the framework of orbit method, Hamiltonian geometry and ... More

Hidden symmetries for thermodynamics and emergence of relativityFeb 02 2010Apr 16 2010Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment ... More

Fermionic formula for double Kostka polynomialsFeb 29 2016The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\Bla,\Bmu}(t),$ ... More

Functoriality of equivariant eta formsMay 17 2015May 03 2016In this paper, we define the equivariant eta form of Bismut-Cheeger for a compact Lie group and establish a formula about the functoriality of equivariant eta forms with respect to the composition of two submersions.

Relics Theory of Dark Matter in quantum evaporating Black HoleDec 29 2008We introduce first a new road to quantize the Schwarzschild black hole. Then we find that the ground state or relic of the quantum evaporating black hole can be identified as dark matter.

On the Gravitational Wave in de Sitter SpacetimeNov 25 2004For there is always a wrong sign in the mass of graviton in the so-called perturbation expansion approximation of both Minkowski and de Sitter spacetimes, the existence of gravitational wave from the metric perturbation of de Sitter spacetime is doubtful. ... More

Graphical Exponential ScreeningMar 09 2015Jul 03 2016In high dimensions we propose and analyze an aggregation estimator of the precision matrix for Gaussian graphical models. This estimator, called graphical Exponential Screening (gES), linearly combines a suitable set of individual estimators with different ... More

Hawking Radiation as Tunnelling in Static Black HolesDec 16 2005Hawking radiation can usefully be viewed as a semi-classical tunnelling process that originates at the black hole horizon. The conservation of energy implies the effect of self-gravitation. For a static black hole, a generalized Painleve coordinate system ... More

Uniqueness of scatterer in inverse acoustic obstacle scattering with a single incident plane waveOct 11 2016Oct 27 2016In this paper, we give a simple proof for uniqueness of the scatterer in inverse obstacle scattering problem for acoustic wave with a single incident plane wave. That is, we show that the acoustic scattering amplitude $A(\beta, {\alpha}_0, k_0)$, known ... More

Researches on Dynamic Load Balancing Algorithms and hp-Adaptivity in 3-D Parallel Adaptive Finite Element ComputationsNov 24 2016This work is related to PHG (Parallel Hierarchical Grid). PHG is a toolbox for developing parallel adaptive finite element programs, which is under active development at the State Key Laboratory of Scientific and Engineering Computing. The main results ... More

A note on discrete monotonic dynamical systemsJul 29 2004Aug 10 2004We give a upper bound of Lebesgue measure $V(S(f,h,\Omega))$ of the set $S(f,h,\Omega)$ of points $q\in Q_h^d$ for which the triple $(h,q,\Omega)$ is dynamically robust when $f$ is monotonic and satisfies certain condition on some compact subset $\Omega ... More

The Poincaré inequality and quadratic transportation-variance inequalitiesFeb 12 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 Ledoux \cite{Ledoux18} most recently. We give an alternative proof to this fact. ... More

Scalar curvature in conformal geometry of Connes-Landi noncommutative manifoldsNov 27 2016We first propose a conformal geometry for Connes-Landi noncommutative manifolds and study the associated scalar curvature. The new scalar curvature contains its Riemannian counterpart as the commutative limit. Similar to the results on noncommutative ... More

Kernelized Deep Convolutional Neural Network for Describing Complex ImagesSep 15 2015With the impressive capability to capture visual content, deep convolutional neural networks (CNN) have demon- strated promising performance in various vision-based ap- plications, such as classification, recognition, and objec- t detection. However, ... More

Height fluctuations of stationary TASEP on a ring in relaxation time scaleOct 14 2016We consider the totally asymmetric simple exclusion process on a ring with stationary initial conditions. The crossover between KPZ dynamics and equilibrium dynamics occurs when time is proportional to the $3/2$ power of the ring size. We obtain the limit ... More

On the Algebraic Representation of One-Tape Deterministic Turing MachineJul 13 2016An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to model the ... More

Quantile tests in frequency domain for sinusoid modelsMay 11 2016For second order stationary processes, the spectral distribution function is uniquely deter- mined by the autocovariance functions of the processes. We define the quantiles of the spectral distribution function and propose two estimators for the quantiles. ... More

On chromatic functors and stable partitions of graphsMar 28 2016Jul 17 2016The chromatic functor of a simple graph is a functorization of the chromatic polynomial. M. Yoshinaga showed in \cite{Yoshinaga2015} that two finite graphs have isomorphic chromatic functors if and only if they have the same chromatic polynomial. The ... More

Strong solutions to the Cauchy problem of the two-dimensional compressible Navier-Stokes-Smoluchowski equations with vacuumAug 29 2016This paper studies the local existence of strong solutions to the Cauchy problem of the 2D fluid-particle interaction model with vacuum as far field density. Notice that the technique used by Ding et al.\cite{SBH} for the corresponding 3D local well-posedness ... More

A new characterization of quadratic transportation-information inequalitiesJun 08 2015Jun 07 2016It is known that a quadratic transportation-information inequality $\mathrm{W_2I}$ interpolates between the Talagrand's inequality $\mathrm{W_2H}$ and the log-Sobolev inequality (LSI for short). The aim of the present paper is threefold: (1) To prove ... More

Harnessing Low-Fidelity Data to Accelerate Bayesian Optimization via Posterior RegularizationFeb 11 2019Feb 14 2019Bayesian optimization (BO) is a powerful paradigm for derivative-free global optimization of a black-box objective function (BOF) that is expensive to evaluate. However, the overhead of BO can still be prohibitive if the maximum number of allowed function ... More

On invariant subspaces for the shift operator on Bergman spaces and Hardy spacesJun 09 2018It is well known that the structure of nontrival invariant subspaces for the shift operator on the Bergman space is extremely complicated and very little is known about their specific structures. In this paper, we give a explicit description of the specific ... More

New integral inequalities via $(α,m)$-convexity and quasi-convexityJan 25 2012In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.

Black chain of pearls in 5D de Sitter spacetimeJun 29 2007Jul 01 2007We analyze some exact chain-shaped black hole solutions in 5-dimensional spacetime. Unlike usual black string and black ring solutions, the topology of the horizons of the new solutions are neither $\mathbb{R}\times R^{2}$ nor $S^1\times S^2$ but rather ... More

Tangent-like Spaces to Local MonoidsJul 26 2005The main new notions are the notions of tangent-like spaces and local monoids. The main result is the pasage from a local monoid to its tangent-like space which is a local Leibniz algebra.

On noncommutative distributional symmetries and de Finetti type theorems associated with themNov 18 2015We prove general de Finetti theorems for classical, free and boolean independence. Our general de Finetti theorems work for non-easy quantum groups, which generalizes a recent work of Banica, Curran and Speicher. For infinite sequences, we will determine ... More

Some remarks on log surfacesDec 02 2016Dec 16 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

On Hausdorff dimension of radial projectionsMar 28 2019Apr 03 2019For any $x\in\mathbb{R}^d$, $d\geq 2$, denote $\pi^x: \mathbb{R}^d\backslash\{x\}\rightarrow S^{d-1}$ as the radial projection $$\pi^x(y)=\frac{y-x}{|y-x|}. $$ Given a Borel set $E\subset{\Bbb R}^d$, $\dim_{\mathcal{H}} E\leq d-1$, in this paper we investigate ... More

Stationary one-sided area-minimizing hypersurfaces with isolated singularitiesApr 04 2019We extend the results of Hardt and Simon on area-minimizing cones to prove that isolated singularities of stationary one-sided area-minimizing hypersurfaces can be locally perturbed away on the side that they are minimizing.

The Existence of Embedded $G$-Invariant Minimal HypersurfaceDec 04 2018Dec 14 2018For a compact connected Lie group $G$ acting as isometries on a compact orientable Riemannian manifold $M^{n+1},$ we prove the existence of a nontrivial embedded $G$-invariant minimal hypersurface, that is smooth outside a set of Hausdorff dimension at ... More

On instability and mixing on the UK Continental ShelfDec 22 2015The stability of stratified flows at locations in the Clyde, Irish and Celtic Seas on the UK Continental Shelf is examined. Flows are averaged over periods of 12-30 min in each hour, corresponding to the times taken to obtain reliable estimates of the ... More

A Monte Carlo Study of Erraticity Behavior in Nucleus-Nucleus Collisions at High EnergiesOct 10 2001It is demonstrated using Monte Carlo simulation that in different nucleus$-$nucleus collision samples, the increase of the fluctuation of event factorial moments with decreasing phase space scale, called erraticity, is still dominated by the statistical ... More

Weight decomposition of de Rham cohomology sheaves and tropical cycle classes for non-Archimedean spacesJan 31 2017We construct a functorial decomposition of de Rham cohomology sheaves, called weight decomposition, for smooth analytic spaces over non-Archimedean fields embeddable into $\mathbf{C}_p$, which generalizes a construction of Berkovich and solves a question ... More

Well-posedness of strong solutions to the anelastic equations for viscous flowsMar 04 2019We address the local and global well-posedness issues of strong solutions to the anelastic equations for viscous flows. The density profile is taken to satisfy physical vacuum singularity, and the interaction of the density profile with the velocity fields ... More

Generalized Cohn's TheoremDec 02 2007We introduce the notion of a free associative $\mathcal{Z}_2$-algebra on the union of two disjoint sets and prove a generalization of Cohn's Theorem on Jordan algebras.

Locally analytic vectors of some crystabelian representations of GL_2(Qp)Oct 04 2009Jan 11 2011For V a 2-dimensional p-adic representation of G_Qp, we denote by B(V) the admissible unitary representation of GL_2(Qp) attached to V under the p-adic local Langlands correspondence of GL_2(Qp) initiated by Breuil. In this article, building on the works ... More