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3-D Surface Segmentation Meets Conditional Random FieldsJun 11 2019Automated surface segmentation is important and challenging in many medical image analysis applications. Recent deep learning based methods have been developed for various object segmentation tasks. Most of them are a classification based approach, e.g. ... More

Trust but Verify: An Information-Theoretic Explanation for the Adversarial Fragility of Machine Learning Systems, and a General Defense against Adversarial AttacksMay 25 2019Deep-learning based classification algorithms have been shown to be susceptible to adversarial attacks: minor changes to the input of classifiers can dramatically change their outputs, while being imperceptible to humans. In this paper, we present a simple ... More

Robust Image Segmentation Quality Assessment without Ground TruthMar 20 2019Deep learning based image segmentation methods have achieved great success, even having human-level accuracy in some applications. However, due to the black box nature of deep learning, the best method may fail in some situations. Thus predicting segmentation ... More

Two-dimensional nanoscale nuclear magnetic resonance spectroscopy enhanced by artificial intelligenceFeb 15 2019Two-dimensional Nuclear Magnetic Resonance (NMR) is essential to molecule structure determination. Nitrogen vacancy (NV) center in diamond has been proposed and developed as an outstanding quantum sensor to realize NMR in nanoscale. However, it is still ... More

Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator $\mathrm{MnBi_2Te_4}$Dec 02 2018$\mathrm{MnBi_2Te_4}$ has recently been established as an intrinsic antiferromagnetic (AFM) topological insulator and predicted to be an ideal platform to realize quantum anomalous Hall (QAH) insulator and axion insulator states. We performed comprehensive ... More

Nonparametric specification for non-stationary time series regressionFeb 04 2014We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can be cross correlated. ... More

Inference of weighted $V$-statistics for nonstationary time series and its applicationsJan 16 2014We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics through the angle ... More

Non-zero-sum stopping games in continuous timeAug 17 2015On a filtered probability space $(\Omega ,\mathcal{F}, (\mathcal{F}_t)_{t\in[0,\infty]}, \mathbb{P})$, we consider the two-player non-zero-sum stopping game $u^i := \mathbb{E}[U^i(\rho,\tau)],\ i=1,2$, where the first player choose a stopping strategy ... More

Multi-player stopping games in continuous timeSep 14 2015We consider multi-player stopping games in continuous time. Unlike Dynkin games, in our games the payoff of each player is revealed after all the players stop. Moreover, each player can adjust her own stopping strategy by observing other players' behaviors. ... More

Non-zero-sum stopping games in discrete timeAug 25 2015We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's ... More

Nonparametric inference of quantile curves for nonstationary time seriesOct 19 2010The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence bands and integrated ... More

Arbitrage, hedging and utility maximization using semi-static trading strategies with American optionsFeb 24 2015Feb 08 2016We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only ... More

On controller-stopper problems with jumps and their applications to indifference pricing of American optionsDec 20 2012Nov 18 2013We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditional ... More

Ground-State Entropy of the Random Vertex-Cover ProblemOct 03 2008Mar 17 2009Counting the number of ground states for a spin-glass or NP-complete combinatorial optimization problem is even more difficult than the already hard task of finding a single ground state. In this paper the entropy of minimum vertex-covers of random graphs ... More

On a Stopping Game in continuous timeSep 23 2014Jul 24 2015We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.

Spectral Inference under Complex Temporal DynamicsDec 19 2018Dec 31 2018We develop unified theory and methodology for the inference of evolutionary Fourier power spectra for a general class of locally stationary and possibly nonlinear processes. In particular, simultaneous confidence regions (SCR) with asymptotically correct ... More

Atomic Scale Measurement of Polar EntropyJul 12 2018Jan 10 2019Entropy is a fundamental thermodynamic quantity that is a measure of the accessible microstates available to a system, with the stability of a system determined by the magnitude of the total entropy of the system. This is valid across truly mind boggling ... More

On model-independent pricing/hedging using shortfall risk and quantilesJul 09 2013We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model to call options ... More

On an Optimal Stopping Problem of an InsiderJan 14 2013Apr 06 2015We consider the optimal stopping problem $v^{(\eps)}:=\sup_{\tau\in\mathcal{T}_{0,T}}\mathbb{E}B_{(\tau-\eps)^+}$ posed by Shiryaev at the International Conference on Advanced Stochastic Optimization Problems organized by the Steklov Institute of Mathematics ... More

A Comparative Study of STA on Large Scale Global OptimizationApr 25 2016State transition algorithm has been emerging as a new intelligent global optimization method in recent few years. The standard continuous STA has demonstrated powerful global search ability for global optimization problems whose dimension is no more than ... More

Inverse mean curvature flows in warped product manifoldsSep 30 2016We study inverse mean curvature flows of starshaped, mean convex hypersurfaces in warped product manifolds with a positive warping factor $h(r)$. If $h'(r)>0$ and $h"(r)\geq 0$, we show that these flows exist for all times, remain starshaped and mean ... More

On the free boundary min-max geodesicsApr 04 2015Given a Riemannian manifold and a closed submanifold, we find a geodesic segment with free boundary on the given submanifold. This is a corollary of the min-max theory which we develop in this article for the free boundary variational problem. In particular, ... More

Asymptotic Weights of Syzygies of Toric VarietiesJan 25 2015Jan 27 2015The purpose of the paper is to give a sharp asymptotic description of the weights that appear in the syzygies of a toric variety. We prove that as the positivity of the embedding increases, in any strand of syzygies, torus weights after normalization ... More

The Finsler surface with K=0 and J=0Sep 25 2012In this short note, we verify R. Bryant's claim: there does exist the singular Landsberg Finsler surface with a vanishing flag curvature which is not Berwaldian.

Two dimensional disjoint minimal graphsAug 26 2011Nov 14 2011In this paper, under the assumption of Gauss curvature vanishing at infinity, we will prove Meeks' conjecture: the number of disjointly supported minimal graphs in $\mathbb{R}^3$ is at most two.

Gemini: Graph estimation with matrix variate normal instancesSep 23 2012May 23 2014Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from ... More

Restricted Eigenvalue Conditions on Subgaussian Random MatricesDec 21 2009Dec 27 2009It is natural to ask: what kinds of matrices satisfy the Restricted Eigenvalue (RE) condition? In this paper, we associate the RE condition (Bickel-Ritov-Tsybakov 09) with the complexity of a subset of the sphere in $\R^p$, where $p$ is the dimensionality ... More

Softplus Regressions and Convex PolytopesAug 23 2016To construct flexible nonlinear predictive distributions, the paper introduces a family of softplus function based regression models that convolve, stack, or combine both operations by convolving countably infinite stacked gamma distributions, whose scales ... More

Generalized Negative Binomial Processes and the Representation of Cluster StructuresOct 07 2013The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample ... More

Beta-Negative Binomial Process and Exchangeable Random Partitions for Mixed-Membership ModelingOct 28 2014Dec 31 2014The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable random partitions ... More

Calculations of the Hirzebruch $χ_y$ genera of symmetric products by the holomorphic Lefschetz formulaOct 05 1999We calculate the Hirzebruch $\chi_y$ and $\hat{\chi}_y$-genera of symmetric products of closed complex manifolds by the holomorphic Lefschetz formula of Atiyah and Singer \cite{Ati-Sin}. Such calculation rederive some formulas proved in an earlier paper ... More

Hodge theory and $A_{\infty}$ structures on cohomologyMar 26 1999We use Hodge theory and a construction of Merkulov to construct $A_{\infty}$ structures on de Rham cohomology and Dolbeault cohomology.

Probing the $P$-wave charmonium decays of $B_c$ mesonDec 24 2017Motivated by the large number of $B_c$ meson decay modes observed recently by several detectors at the LHC, we present a detailed analysis of the $B_c$ meson decaying to the $P$-wave charmonium states and a light pseudoscalar ($P$) or vector ($V$) meson ... More

Relative Orbifold Donaldson-Thomas Theory and the Degeneration FormulaApr 09 2015Jun 01 2015We generalize the notion of expanded degenerations and pairs for a simple degeneration or smooth pair to the case of smooth Deligne-Mumford stacks. We then define stable quotients on the classifying stacks of expanded degenerations and pairs and prove ... More

Liouville integrability of the finite dimensional Hamiltonian systems derived from principal chiral fieldMay 15 2002For finite dimensional Hamiltonian systems derived from 1+1 dimensional integrable systems, if they have Lax representations, then the Lax operator creates a set of conserved integrals. When these conserved integrals are in involution, it is believed ... More

Rigidity of formal character of Lie algebras of type AFeb 20 2012Feb 22 2012For a complex simple Lie algebra of type $A$, given a family of elements $f_\lambda\in \mathbb Z[\Lambda],\lambda\in \Lambda^+,$ we show that $f_\lambda$ is just the formal character of the Weyl module $V(\lambda) $ if $f_\lambda$ satisfy two natural ... More

Solutions of the Yang-Mills-Higgs equations in 2+1 dimensional anti-de Sitter space-timeNov 11 2000The solutions of the Bogomolny equation in anti-de Sitter space-time are obtained by using Darboux transformations with both constant spectral parameters and variable "spectral parameters". These solutions give the Yang-Mills-Higgs fields in anti-de Sitter ... More

Viscosity Solutions to Path-Dependent HJB Equation and ApplicationsNov 17 2016In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify the value functional ... More

Curve shortening flows in warped product manifoldsNov 24 2015We study curve shortening flows in two types of warped product manifolds. These manifolds are $S^1\times N$ with two types of warped metrics where $S^1$ is the unit circle in $R^2$ and $N$ is a closed Riemannian manifold. If the initial curve is a graph ... More

Cloud Computing framework for Computer Vision Research:An IntroductionFeb 06 2013Cloud computing offers the potential to help scientists to process massive number of computing resources often required in machine learning application such as computer vision problems. This proposal would like to show that which benefits can be obtained ... More

Efficient programs of NPC problems should be length upper-bounded, and a thought experiment to search for them by machine enumerationApr 25 2012Oct 06 2012This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as: execution time(n) ... More

Property of one-dimensional Coulomb interaction and its possible contribution to strongly correlated systemsAug 21 2011The unique property of Coulomb interaction in strict one-dimensional (1D) system is revealed that the Coulomb repulsion energy of paired electrons is divergent. As consequences, electrons in 1D system can not doubly occupy the same spatial orbital and ... More

Spectral Structure of Electromagnetic Scattering on Arbitrarily Shaped DielectricNov 24 2009Jul 03 2015Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling the interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact and Hilbert--Schmidt operator polynomials are constructed ... More

Withdraw a paper entitled "On the growth rate of solutions for 2D incompressible Euler equations"Dec 04 2008Dec 23 2008This paper has been withdrawn by the author due to a crucial definition error of Triebel space.

Optical theorem and cutting rulesAug 24 2005Apr 17 2007This manuscript has been withdrawn at 17 April, 2007.

A New Renormalization Scheme of Fermion Fields in Electroweak Standard ModelDec 30 2001Jan 04 2002This paper has been withdrawn by the author,due a immature idea.

Boson's field renormalization prescriptionMay 16 2005We discuss the problem of the present boson's field renormalization prescription induced by the imaginary parts of the unstable boson's propagation amplitudes and how to resolve it.

Renormalization of the Cabibbo-Kobayashi-Maskawa Quark Mixing MatrixNov 18 2002Jan 24 2003We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix. When considering the prescription which is formulated with reference to the case of zero mixing we find it doesn't satisfy the unitary condition ... More

Small-time Sampling Behaviour of a Fleming-Viot ProcessJul 02 2013Mar 15 2016The Fleming-Viot process with parent-independent mutation process is one particular neutral population genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high, mutated species ... More

Entanglement Entropy of Local Operators in Quantum Lifshitz TheoryJul 28 2016We study the growth of entanglement entropy(EE) of local operator excitation in the quantum Lifshitz model which has dynamic exponent z = 2. Specifically, we act a local vertex operator on the groundstate at a distance $l$ to the entanglement cut and ... More

Joint User Association and Power Control for Load Balancing in Downlink Heterogeneous Cellular NetworksJul 04 2016Instead of achievable rate in the conventional association, we utilize the effective rate to design two association schemes for load balancing in heterogeneous cellular networks (HCNs), which are both formulated as such problems with maximizing the sum ... More

Asymptotic Behavior of the Pseudo-Covariance Matrix of a Robust State Estimator with Intermittent MeasurementsJan 16 2014Ergodic properties and asymptotic stationarity are investigated in this paper for the pseudo-covariance matrix (PCM) of a recursive state estimator which is robust against parametric uncertainties and is based on plant output measurements that may be ... More

Unambiguous discrimination between two unknown qudit statesMay 16 2011Nov 15 2011We consider the unambiguous discrimination between two unknown qudit states in $n$-dimensional ($n\geqslant2$) Hilbert space. By equivalence of unknown pure states to known mixed states and with the Jordan-basis method, we demonstrate that the optimal ... More

Deformation Quantization and Quantum Field Theory on Curved Spaces: the Case of Two-SphereOct 29 2001We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized by $H^2(S^2, ... More

On Ricci flat SupermanifoldsOct 05 2004Oct 07 2004We study the Ricci flatness condition on generic supermanifolds. It has been found recently that when the fermionic complex dimension of the supermanifold is one the vanishing of the super-Ricci curvature implies the bosonic submanifold has vanishing ... More

Primes in higher-order progressions on averageApr 06 2017Mar 10 2018In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.

Cavity implementation of quantum interference in a $Λ$-type atomMar 20 2000Mar 24 2000A scheme for engineering quantum interference in a $\Lambda$-type atom coupled to a frequency-tunable, single-mode cavity field with a pre-selected polarization at finite temperature is proposed. Interference-assisted population trapping, population inversions ... More

Twisted Polytope Sheaves and Coherent-Constructible Correspondence for Toric VarietiesJan 03 2017Given a smooth projective toric variety $X_\Sigma$ of complex dimension $n$, Fang-Liu-Treumann-Zaslow \cite{FLTZ} showed that there is a quasi-embedding of the differential graded (dg) derived category of coherent sheaves $Coh(X_\Sigma)$ into the dg derived ... More

Localizations on Moduli Spaces and Free Field Realizations of Feynman RulesOct 18 2003We prove Iqbal's conjecture on the relationship between the free energy of closed string theory in local toric geometry and the Wess-Zumino-Witten model. This is achieved by first reformulating the calculations of the free energy by localization techniques ... More

A bound on the genus of a curve with Cartier operator of small rankOct 03 2017Ekedahl showed that the genus of a curve in characteristic $p>0$ with zero Cartier operator is bounded by $p(p-1)/2$. We show the bound $p+p(p-1)/2$ in case the rank of the Cartier operator is 1, improving a result of Re.

On the Fenchel Duality between Strong Convexity and Lipschitz Continuous GradientMar 17 2018We provide a simple proof for the Fenchel duality between strong convexity and Lipschitz continuous gradient. To this end, we first establish equivalent conditions of convexity for a general function that may not be differentiable. By utilizing these ... More

Hodge Integrals and Integrable HierarchiesOct 26 2003We show that the generating series of some Hodge integrals involving one or two partitions are tau-functions of the KP hierarchy or the 2-Toda hierarchy respectively. We also formulate a conjecture on the connection between relative invariants and integrable ... More

Efficient entanglement concentration for arbitrary less-entangled N-atom stateOct 23 2012A recent paper (Phys. Rev. A 86, 034305 (2012)) proposed an entanglement concentration protocol (ECP) for less-entangled $N$-atom GHZ state with the help of the photonic Faraday rotation. It is shown that the maximally entangled atom state can be distilled ... More

Spin rotation invariant spin triplet superconducting liquidsFeb 19 2002Mar 26 2002Spin ordering and its effect on the low energy quasiparticles in a p-wave superconducting fluid are investigated. We study the properties of a new 2D quantum spin triplet superconducting liquid where the ground state is spin rotation invariant. In quantum ... More

A novel superconducting glass state in disordered thin films in Clogston limitJun 16 1999A theory of mesoscopic fluctuations in disordered thin superconducting films in a parallel magnetic field is developed. At zero temperature, the superconducting state undergoes a phase transition into a state characterized by superfluid densities of random ... More

Topological spin pumps INov 26 2003Jul 08 2004We have established a semiclassical kinetic approach for various spin correlated pumping phenomena incorporating spin rotation in wave functions into transport equations. We employ this technique to study topological pumps and illustrate spin pumping ... More

The General Solution to Vlasov Equation and Linear Landau DampingOct 14 2015A general solution to linearized Vlasov equation for an electron electrostatic wave in a homogeneous unmagnetized plasma is derived. The quasi-linear diffusion coefficient resulting from this solution is a continuous function of omega in contrast to that ... More

Eigenvalue Computation from the Optimization Perspective: On Jacobi-Davidson, IIGD, RQI, and Newton UpdatesFeb 10 2004We discuss the close connection between eigenvalue computation and optimization using the Newton method and subspace methods. From the connection we derive a new class of Newton updates. The new update formulation is similar to the well-known Jacobi-Davidson ... More

Emergent Geometry of Matrix Models with Even CouplingsMar 26 2019We show that to the modified GUE partition function with even coupling introduced by Dubrovin, Liu, Yang and Zhang, one can associate $n$-point correlation functions in arbitrary genera which satisfy Eynard-Orantin topological recursions. Furthermore, ... More

Hessian Geometry and Phase Change of Gibbons-Hawking MetricsJan 09 2018We study the Hessian geometry of toric Gibbons-Hawking metrics and their phase change phenomena via the images of their moment maps.

On a Mean Field Theory of Topological 2D GravityMar 30 2015We present a one-dimensional mean field theory for topological 2D gravity. We discuss possible generalizations to other topological field theories, in particular those related to semisimple Frobenius manifolds.

Fermionic Computations for Integrable HierarchiesAug 09 2015We present a unified fermionic approach to compute the tau-functions and the n-point functions of integrable hierarchies related to some infinite-dimensional Lie algebras and their representations.

Quantum Deformation Theory of the Airy Curve and Mirror Symmetry of a PointMay 21 2014We present a quantum deformation theory of the Airy curve and use it to establish a version of mirror symmetry of a point.

Explicit Formula for Witten-Kontsevich Tau-FunctionJun 23 2013We present an explicit formula for Witten-Kontsevich tau-function.

On discrete cosine transformSep 02 2011The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating ... More

Integrality Properties of Open-Closed Mirror MapsJun 28 2010We propose a conjecture on integrality property of the open-closed mirror maps of compact Calabi-Yau manifolds. Some examples are presented.

On computations of Hurwitz-Hodge integralsOct 09 2007We describe a method to compute Hurwitz-Hodge integrals.

$T \to 0$ mean-field population dynamics approach for the random 3-satisfiability problemDec 31 2007Sep 25 2008During the past decade, phase-transition phenomena in the random 3-satisfiability (3-SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3-SAT problem by the mean-field first-step replica-symmetry-broken ... More

Criticality and Heterogeneity in the Solution Space of Random Constraint Satisfaction ProblemsNov 23 2009Jul 02 2010Random constraint satisfaction problems are interesting model systems for spin-glasses and glassy dynamics studies. As the constraint density of such a system reaches certain threshold value, its solution space may split into extremely many clusters. ... More

The Cost of Two-dimensional RearrangementOct 02 2005In this paper, we give an estimate for the energy of a highly mixed diffeomorphism on a two-dimensional torus.

Long range frustration in finite connectivity spin glasses: A mean field theory and its application to the random $K$-satisfiability problemNov 03 2004May 19 2005Shortened abstract: A mean field theory of long range frustration is constructed for spin glass systems with quenched randomness of vertex--vertex connections and of spin--spin coupling strengths. This theory is applied to a spin glass model of the random ... More

Vertex cover problem studied by cavity method: Analytics and population dynamicsFeb 14 2003We study the vertex cover problem on finite connectivity random graphs by zero-temperature cavity method. The minimum vertex cover corresponds to the ground state(s) of a proposed Ising spin model. When the connectivity c>e=2.718282, there is no state ... More

Lens rigidity with partial data in the presence of a magnetic fieldMay 20 2016In this paper we consider the lens rigidity problem with partial data for conformal metrics in the presence of a magnetic field on a compact manifold of dimension $\geq 3$ with boundary. We show that one can uniquely determine the conformal factor and ... More

Inverse mean curvature flows in warped product manifoldsSep 30 2016Aug 05 2017We study inverse mean curvature flows of starshaped, mean convex hypersurfaces in warped product manifolds with a positive warping factor $\varphi(r)$. If $\varphi'(r)>0$ and $\varphi''(r)\geq 0$, we show that these flows exist for all times, remain starshaped ... More

Polynomial Structure of Topological String Partition FunctionsJan 02 2015Sep 07 2015We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special K\"ahler geometry and the ring of almost-holomorphic ... More

Stepping-stone model with circular Brownian migrationSep 16 2005In this paper we consider a stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow and the marginal distribution of this model. We then give a new representation for the stepping-stone model ... More

The localisation of low-temperature interfaces in $d$ dimensional Ising modelJan 17 2019We study the Ising model in a box $\Lambda$ in $\mathbb{Z}^d$ (not necessarily parallel to the directions of the lattice) with Dobrushin boundary conditions at low temperature. We couple the spin configuration with the configurations under $+$ and $-$ ... More

On the Multiplicity One Conjecture in Min-max theoryJan 04 2019Feb 05 2019We prove that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity one. This confirms ... More

Can One Design a Series of Brains for Neuromorphic Computing to solve complex inverse problemsFeb 02 2019In this position paper, we present a discussion on neuromorphic computing and especially the learning/training algorithm to design a series of brains with different memristive values to solve complex ill-posed inverse problems based on a Finite Element(FE) ... More

Return Probabilities of Random WalksDec 14 2015Associated to a random walk on $\mathbb{Z}$ and a positive integer $n$, there is a return probability of the random walk returning to the origin after $n$ steps. An interesting question is when the set of return probabilities uniquely determines the random ... More

Mod-$p$ isogeny classes on Shimura varieties with parahoric level structureJul 31 2017Feb 15 2018We study the special fiber of the integral models for Shimura varieties of Hodge type with parahoric level structure constructed by Kisin and Pappas in [KP]. We show that when the group is residually split, the points in the mod $p$ isogeny classes have ... More

Kähler-Ricci Flow with Degenerate Initial ClassSep 29 2009In an earlier work joint with X. X. Chen and G. Tian, we introduced the weak K\"ahler-Ricci flow for various geometric motivations. In the current work, we take further consideration on setting up the weak flow. Namely, the initial class is allowed to ... More

Scalar Curvature Behavior for Finite Time Singularity of Kähler-Ricci FlowJan 11 2009In this short paper, we show that K\"ahler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.

Exponential Convergence to the Maxwell Distribution For Spatially Inhomogenous Boltzmann EquationsMar 21 2016Apr 07 2017We consider the rate of convergence of solutions of spatially inhomogenous Boltzmann equations, with hard sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially homogenous static Maxwell velocity distributions with different ... More

On the Vertices of Indecomposable Modules Over Dihedral 2-GroupsSep 02 2007Sep 13 2007Let $k$ be an algebraically closed field of characteristic 2. We compute the vertices of all indecomposable $kD_8$-modules for the dihedral group $D_8$ of order 8. We also give a conjectural formula of the induced module of a string module from $kT_0$ ... More

The Moduli Space of Hyperbolic Cone StructuresMay 28 1998Let $\Sigma$ be a hyperbolic link with $m$ components in a 3-dimensional manifold $X$. In this paper, we will show that the moduli space of marked hyperbolic cone structures on the pair $(X, \Sigma)$ with all cone angle less than $2\pi /3$ is an $m$-dimensional ... More

Probing non-linearity of higher order anisotropic flow in Pb--Pb collisionsApr 24 2017The second and the third order anisotropic flow, $V_{2}$ and $V_3$, are determined by the corresponding initial spatial anisotropy coefficients, $\varepsilon_{2}$ and $\varepsilon_{3}$, in the initial density distribution. On the contrary, the higher ... More

A Set Theoretic Approach for Knowledge Representation: the Representation PartMar 11 2016In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by equality assertions. ... More

Review of anisotropic flow correlations in ultrarelativistic heavy-ion collisionsJul 19 2016Anisotropic flow phenomena is a key probe of the existence of Quark-Gluon Plasma. Several new observable associated with correlations between anisotropic flow harmonics are developed, which are expected to be sensitive to the initial fluctuations and ... More

Searches for $p_{\rm T}$ dependent fluctuations of flow angle and magnitude in Pb--Pb and p--Pb collisionsJul 29 2014Anisotropic azimuthal correlations are used to probe the properties and the evolution of the system created in heavy-ion collisions. Two-particle azimuthal correlations were used in the searches of $p_{\rm T}$ dependent fluctuations of flow angle and ... More