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Low Rank plus Sparse Decomposition of ODFs for Improved Detection of Group-level Differences and Variable Correlations in White MatterMar 15 2018A novel approach is presented for group statistical analysis of diffusion weighted MRI datasets through voxelwise Orientation Distribution Functions (ODF). Recent advances in MRI acquisition make it possible to use high quality diffusion weighted protocols ... More

Identifying Mild Traumatic Brain Injury Patients From MR Images Using Bag of Visual WordsOct 18 2017Feb 14 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests are used to both assess the patient condition and to monitor the patient progress. This work aims ... More

Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph LaplacianOct 25 2018The extraction of clusters from a dataset which includes multiple clusters and another significant portion of "background" samples is a task of practical importance. The traditional spectral clustering algorithm, relying on the leading $K$ eigenvectors ... More

Concentration of the Kirchhoff index for Erdos-Renyi graphsJul 24 2013May 29 2014Given an undirected graph, the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors. Summing these distances over all pairs of nodes yields the so-called Kirchhoff ... More

On the Diffusion Geometry of Graph Laplacians and ApplicationsNov 09 2016We study directed, weighted graphs $G=(V,E)$ and consider the (not necessarily symmetric) averaging operator $$ (\mathcal{L}u)(i) = -\sum_{j \sim_{} i}{p_{ij} (u(j) - u(i))},$$ where $p_{ij}$ are normalized edge weights. Given a vertex $i \in V$, we define ... More

Two-sample Statistics Based on Anisotropic KernelsSep 14 2017Aug 30 2018The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed test can be ... More

Unsupervised Deep Haar Scattering on GraphsJun 09 2014Nov 03 2014The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented with a deep ... More

Butterfly-Net: Optimal Function Representation Based on Convolutional Neural NetworksMay 18 2018Deep networks, especially Convolutional Neural Networks (CNNs), have been successfully applied in various areas of machine learning as well as to challenging problems in other scientific and engineering fields. This paper introduces Butterfly-Net, a low-complexity ... More

The Geometry of Nodal Sets and Outlier DetectionJun 05 2017Let $(M,g)$ be a compact manifold and let $-\Delta \phi_k = \lambda_k \phi_k$ be the sequence of Laplacian eigenfunctions. We present a curious new phenomenon which, so far, we only managed to understand in a few highly specialized cases: the family of ... More

Provable Estimation of the Number of Blocks in Block ModelsMay 24 2017Mar 18 2018Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters $r$ is known apriori. In this paper, we propose an ... More

Deep Haar Scattering NetworksSep 30 2015An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning. It implements ... More

Marchenko-Pastur Law for Tyler's M-estimatorJan 15 2014Apr 01 2016This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples $n$ and their dimension $p$ both go to infinity, and $p/n$ converges to a constant $y$ with $0<y<1$. We prove that when the ... More

DCFNet: Deep Neural Network with Decomposed Convolutional FiltersFeb 12 2018Jul 27 2018Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional ... More

RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep NetworksMay 17 2018Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the convolutional ... More

Cosmological Information in Weak Lensing PeaksSep 28 2011Recent studies have shown that the number counts of convergence peaks N(kappa) in weak lensing (WL) maps, expected from large forthcoming surveys, can be a useful probe of cosmology. We follow up on this finding, and use a suite of WL convergence maps, ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Apr 11 2018Mild traumatic brain injury is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. This work ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests have been used to both assess the patient condition and to monitor the patient progress. This ... More

The Spectrum of Random Inner-product Kernel MatricesFeb 14 2012Mar 22 2012We consider n-by-n matrices whose (i, j)-th entry is f(X_i^T X_j), where X_1, ...,X_n are i.i.d. standard Gaussian random vectors in R^p, and f is a real-valued function. The eigenvalue distribution of these random kernel matrices is studied at the "large ... More

MTBI Identification From Diffusion MR Images Using Bag of Adversarial Visual FeaturesJun 27 2018In this work, we propose bag of adversarial features (BAF) for identifying mild traumatic brain injury (MTBI) patients from their diffusion magnetic resonance images (MRI) (obtained within one month of injury) by incorporating unsupervised feature learning ... More

A Deep Learning Approach to Unsupervised Ensemble LearningFeb 06 2016We show how deep learning methods can be applied in the context of crowdsourcing and unsupervised ensemble learning. First, we prove that the popular model of Dawid and Skene, which assumes that all classifiers are conditionally independent, is {\em equivalent} ... More

Ensemble SamplingMay 20 2017Nov 22 2017Thompson sampling has emerged as an effective heuristic for a broad range of online decision problems. In its basic form, the algorithm requires computing and sampling from a posterior distribution over models, which is tractable only for simple special ... More

NIST: An Image Classification Network to Image Semantic RetrievalJul 02 2016This paper proposes a classification network to image semantic retrieval (NIST) framework to counter the image retrieval challenge. Our approach leverages the successful classification network GoogleNet based on Convolutional Neural Networks to obtain ... More

Defending against Adversarial Images using Basis Functions TransformationsMar 28 2018Apr 16 2018We study the effectiveness of various approaches that defend against adversarial attacks on deep networks via manipulations based on basis function representations of images. Specifically, we experiment with low-pass filtering, PCA, JPEG compression, ... More

Baryon impact on weak lensing peaks and power spectrum: low-bias statistics and self-calibration in future surveysOct 02 2012Peaks in two-dimensional weak lensing (WL) maps contain significant cosmological information, complementary to the WL power spectrum. This has recently been demonstrated using N-body simulations which neglect baryonic effects. Here we employ ray-tracing ... More

Simplification of protein representation from the contact potentials between residuesOct 19 2000Based on the concept of energy landscape a picture of the mismatch between the reduced interaction matrix of residues and the matrix of statistical contact potentials is presented. For the Miyazawa and Jernigan (MJ) matrix, rational groupings of 20 kinds ... More

Global existence of weak solution for the 2-D Ericksen-Leslie systemMay 03 2013Jun 04 2013We prove the global existence of weak solution for two dimensional Ericksen-Leslie system with the Leslie stress and general Ericksen stress under the physical constrains on the Leslie coefficients. We also prove the local well-posedness of the Ericksen-Leslie ... More

Uniformly bounded components of normalityMar 05 2007Jun 09 2007Suppose that $f(z)$ is a transcendental entire function and that the Fatou set $F(f)\neq\emptyset$. Set $$B_1(f):=\sup_{U}\frac{\sup_{z\in U}\log(|z|+3)}{\inf_{w\in U}\log(|w|+3)}$$ and $$B_2(f):=\sup_{U}\frac{\sup_{z\in U}\log\log(|z|+30)}{\inf_{w\in ... More

Classification of pointed Hopf algebras of dimension $p^2$ over any algebraically closed fieldDec 21 2012Mar 12 2015Let $p$ be a prime. We complete the classification on pointed Hopf algebras of dimension $p^2$ over an algebraically closed field $k$. When $\text{char}k \neq p$, our result is the same as the well-known result for $\text{char}k=0$. When $\text{char}k=p$, ... More

Global well-posedness and scattering for Derivative Schrödinger equationSep 20 2009Jun 11 2010In this paper we study the Cauchy problem for the elliptic and non-elliptic derivative nonlinear Schr\"odinger equations in higher spatial dimensions ($n\geq 2$) and some global well-posedness results with small initial data in critical Besov spaces $B^s_{2,1}$ ... More

Indicators of Hopf algebras in positive characteristicApr 18 2017Feb 19 2019The notion of $n$-th indicator for a finite-dimensional Hopf algebra was introduced by Kashina, Montgomery and Ng as gauge invariance of the monoidal category of its representations. The properties of these indicators were further investigated by Shimizu. ... More

Modeling study on the validity of a possibly simplified representation of proteinsJun 23 2000The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a ... More

Study of the single neutral top-pion production process at $γγ$ colliderOct 29 2005Nov 18 2005$\gamma\gamma\to \Pi_t^0$ is the major production mechanism of neutral top-pion at the linear colliders. In this paper, we calculate the cross section of the process $\gamma\gamma \to \Pi^0_t$ and discuss the potential to observe the neutral top-pion ... More

Exploring the Systematic Uncertainties of Type Ia Supernovae as Cosmological ProbesJun 27 2013Jul 26 2013We explore the systematic uncertainties of using Type Ia supernovae (SNe Ia) as cosmological probes, using the Supernova Legacy Survey Three Year data (SNLS3). We focus on studying the possible evolution of the stretch-luminosity parameter $\alpha$ and ... More

WISE Detection of the Galactic Low-Mass X-Ray BinariesApr 14 2014We report on the results from our search for the Wide-field Infrared Survey Explorer detection of the Galactic low-mass X-ray binaries. Among 187 binaries catalogued in Liu et al. (2007), we find 13 counterparts and two candidate counterparts. For the ... More

Neural Network-Based Abstract Generation for Opinions and ArgumentsJun 09 2016We study the problem of generating abstractive summaries for opinionated text. We propose an attention-based neural network model that is able to absorb information from multiple text units to construct informative, concise, and fluent summaries. An importance-based ... More

Non-flow, and what flow to subtract in jet-correlationOct 20 2009We derive analytical forms for non-flow contributions from cluster correlation to two-particle elliptic flow (v2{2}) measure. We also derive an analytical form for jet-correlation flow-background with the same cluster approach. We argue that the elliptic ... More

Geometrical quantities on a fuzzy sphereJul 12 2010In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of the energy ... More

Discretization of div-curl Systems by Weak Galerkin Finite Element Methods on Polyhedral PartitionsJan 19 2015In this paper, the authors devise a new discretization scheme for div-curl systems defined in connected domains with heterogeneous media by using the weak Galerkin finite element method. Two types of boundary value problems are considered in the algorithm ... More

Warped cones and proper affine isometric actions of discrete groups on Banach spacesMay 23 2017Warped cones are metric spaces introduced by John Roe from discrete group actions on compact metric spaces to produce interesting examples in coarse geometry. We show that a certain class of warped cones $\mathcal{O}_\Gamma (M)$ admit a fibred coarse ... More

Integrability of scalar curvature and normal metric on conformally flat manifoldsJul 14 2017On a manifold $(\mathbb{R}^n, e^{2u} |dx|^2)$, we say $u$ is normal if the $Q$-curvature equation that $u$ satisfies $(-\Delta)^{\frac{n}{2}} u = Q_g e^{nu}$ can be written as the integral form $u(x)=\frac{1}{c_n}\int_{\mathbb R^n}\log\frac{|y|}{|x-y|}Q_g(y)e^{nu(y)}dy+C$. ... More

Constructing Social Networks From Binary DataJun 11 2018Much of applied network analysis concerns with studying the existing relationships between a set of agents; however, little focus has been given to the considerations of how to represent observed phenomena as a network object. In the case of physical ... More

Optimal Distributed Control for Networked Control Systems with DelaysDec 12 2013In networked control systems (NCS), sensing and control signals between the plant and controllers are typically transmitted wirelessly. Thus, the time delay plays an important role for the stability of NCS, especially with distributed controllers. In ... More

Distance Priors from Planck and Dark Energy Constraints from Current DataApr 16 2013Aug 29 2013We derive distance priors from Planck first data release, and examine their impact on dark energy constraints from current observational data. We give the mean values and covariance matrix of {R, l_a, \Omega_b h^2, n_s}, which give an efficient summary ... More

Plasmonic Light Trapping in an Ultrathin Photovoltaic Layer with Film-Coupled Metamaterial StructuresSep 11 2014Feb 04 2015A film-coupled metamaterial structure is numerically investigated for enhancing the light absorption in an ultrathin photovoltaic layer of crystalline gallium arsenide (GaAs). The top subwavelength concave grating and the bottom metallic film could not ... More

Hierarchical Spatial Sum-Product Networks for Action Recognition in Still ImagesNov 17 2015Jul 08 2016Recognizing actions from still images is popularly studied recently. In this paper, we model an action class as a flexible number of spatial configurations of body parts by proposing a new spatial SPN (Sum-Product Networks). First, we discover a set of ... More

A Primal-Dual Weak Galerkin Finite Element Method for Fokker-Planck Type EquationsApr 19 2017This paper presents a primal-dual weak Galerkin (PD-WG) finite element method for a class of second order elliptic equations of Fokker-Planck type. The method is based on a variational form where all the derivatives are applied to the test functions so ... More

A Primal-Dual Weak Galerkin Finite Element Method for Second Order Elliptic Equations in Non-Divergence FormOct 13 2015This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The numerical solution ... More

Entanglement in a second order topological insulator on a square latticeAug 03 2018In a $d$-dimensional topological insulator of order $d$, there are zero energy states on its corners which have close relationship with its entanglement behaviors. We studied the bipartite entanglement spectra for different subsystem shapes and found ... More

A Kastler-Kalau-Walze Type Theorem for 5-dimensional Manifolds with BoundaryApr 24 2014The Kastler-Kalau-Walze theorem, announced by Alain Connes, shows that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein-Hilbert action of general relativity. In this paper, we prove a Kastler-Kalau-Walze ... More

Tailoring Thermal Radiative Properties with Film-Coupled Concave Grating MetamaterialsSep 25 2014This work numerically investigates the radiative properties of film-coupled metamaterials made of a two-dimensional metallic concave grating on a continuous metal film separated by an ultrathin dielectric spacer. Spectrally-selective absorption is demonstrated ... More

Coherent Optical DFT-Spread OFDMFeb 28 2011We consider application of the discrete Fourier transform-spread orthogonal frequency-division multiplexing (DFT-spread OFDM) technique to high-speed fiber optic communications. The DFT-spread OFDM is a form of single-carrier technique that possesses ... More

Magnetic interactions in FeSe studied by first principle calculationsOct 19 2015Based on first principle calculations we have investigated the evolution of magnetism in free-standing monolayer FeSe with respect to lattice constant and magnetism in bulk FeSe. The computational results show that the magnetic order in free-standing ... More

Identification of flow-background to subtract in jet-like azimuthal correlationJan 06 2009Jan 28 2010We derive an analytical form for flow-background to jet-like azimuthal correlation in a cluster approach. We argue that the elliptic flow parameter to use in jet-correlation background is that from two-particle method excluding non-flow correlation unrelated ... More

Almost Sure Existence of Global Weak Solutions to the 3D Incompressible Navier-Stokes EquationOct 31 2016In this paper we prove the almost sure existence of global weak solution to the 3D incompressible Navier-Stokes Equation for a set of large data in $\dot{H}^{-\alpha}(\mathbb{R}^{3})$ or $\dot{H}^{-\alpha}(\mathbb{T}^{3})$ with $0<\alpha\leq 1/2$. This ... More

Double Conformal Invariants and the Wodzicki ResidueJan 06 2011For compact real manifolds, a new double conformal invariant is constructed using the Wodzicki residue and the $d$ operator in the framework of Connes. In the flat case, we compute this double conformal invariant, and in some special cases, we also compute ... More

Recognizing number of communities and detecting community structures in complex networksMar 18 2018Recognizing number of communities and detecting community structures of complex network are discussed in this paper. As a visual and feasible algorithm, block model has been successfully applied to detect community structures in complex network. In order ... More

Soft Physics from STAROct 24 2005Oct 27 2005New results on soft hadron distributions and correlations measured with the STAR experiment are presented. Knowledge about the bulk properties of relativistic heavy-ion collisions offered by these results is discussed.

Vacuum Stability Bounds On Higgs Mass With Gravitational ContributionsDec 06 2013May 22 2014We calculate the gravitational contributions to $\phi^4$ theory with general $R_\xi$ gauge-fixing choice and find that the result is gauge independent. Based on weak coupling expansion of gravity and ignoring the possible higher dimensional operators ... More

In-Medium Properties of JetsJul 05 2007Modifications of jet-like azimuthal correlations have revealed novel properties of the medium created in relativistic heavy-ion collisions. Experimental results on jet-like 2- and 3-particle correlations, specificly "punch-through" at high transverse ... More

Under-approximation of the Greatest Fixpoints in Real-Time System VerificationJan 22 2005Techniques for the efficient successive under-approximation of the greatest fixpoint in TCTL formulas can be useful in fast refutation of inevitability properties and vacuity checking. We first give an integrated algorithmic framework for both under and ... More

Measurement of Jet Modification at RHICApr 06 2004Charged hadrons (0.15 < pt < 4 GeV/c) associated with a large pt trigger particle (4 < pt < 6 GeV/c) are statistically reconstructed in the large acceptance STAR TPC for p+p and Au+Au collisions at sqrt(s_NN)=200 GeV. Preliminary results on transverse ... More

Numerical simulations of Ising spin glasses with free boundary conditions: the role of droplet excitations and domain wallsOct 25 2016The relative importance of the contributions of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses in three and four dimensions is studied. We compare the overlap distributions of periodic and free boundary ... More

Quantum Cosmology: Theory of General System (III)May 15 1996The concepts of the perfect system and degeneracy are introduced. A special symmetry is found which is related to the entropy invariant. The inversion relation of system is obtained which is used to give the oppsite direction of time to classical sencond ... More

Total coloring of 1-toroidal graphs of maximum degree at least 11 and no adjacent trianglesJun 18 2012Sep 16 2013A {\em total coloring} of a graph $G$ is an assignment of colors to the vertices and the edges of $G$ such that every pair of adjacent/incident elements receive distinct colors. The {\em total chromatic number} of a graph $G$, denoted by $\chiup''(G)$, ... More

Antiferromagnetic Dirac Semimetals in Two DimensionsSep 12 2016The search for symmetry-protected 2D Dirac semimetals analogous to graphene is important both for fundamental and practical interest. The 2D Dirac cones are protected by crystalline symmetries and magnetic ordering may destroy their robustness. Here we ... More

Transport equation for plasmas in a stationary-homogeneous turbulenceDec 04 2015For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose symmetry has been ... More

Energy-Based Analysis of Crowd Self-Driven MotionSep 11 2013Jul 06 2015For centuries, how an object moves given external forces is characterized by physical laws. As for creatures like human, their movements are self-driven, and the driving forces are generated by intention of people in a psychological sense. How to capture ... More

DIY the Integrated Climate Model and its computational performanceMay 29 2014Aug 25 2014This article describes the software engineering framework and computation performance of a global climate system model which helps the user to understand the step-by-step technical to DIY(do it yourself) a climate model by your own. The model integrates ... More

Covering with Excess One: Seeing the TopologyDec 28 2013We have initiated the study of topology of the space of coverings on grid domains. The space has the following constraint: while all the covering agents can move freely (we allow overlapping) on the domain, their union must cover the whole domain. A minimal ... More

Dynamical Trading Mechanism in Limit Order MarketsMar 13 2013This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of trading processes, ... More

Concurrent Processing MemoryAug 15 2006Sep 25 2010A theoretical memory with limited processing power and internal connectivity at each element is proposed. This memory carries out parallel processing within itself to solve generic array problems. The applicability of this in-memory finest-grain massive ... More

MathGR: a tensor and GR computation package to keep it simpleJun 06 2013Aug 18 2014We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices to partially ... More

$L^p$-Wasserstein distance for stochastic differential equations driven by Lévy processesMar 17 2016Coupling by reflection mixed with synchronous coupling is constructed for a class of stochastic differential equations (SDEs) driven by L\'{e}vy noises. As an application, we establish the exponential contractivity of the associated semigroups $(P_t)_{t\ge0}$ ... More

Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equationsMay 29 2008In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct concerning geometric ... More

Some aspects of color superconductivity: an introductionDec 13 2009A pedagogical introduction to color superconductivity in the weak coupling limit is given. The focus is on the basic tools of thermal field theory necessary to compute observables of color superconductivity. The rich symmetry structure and symmetry breaking ... More

A Numerical Scheme for BSVIEsMay 16 2016In this paper, we consider the Euler method for backward stochastic Volterra integral equations. First, we approximate the original equation by a family of backward stochastic equations (BSDEs, for short). Then we solve the BSDEs by the Euler method. ... More

Beyond knowing that: a new generation of epistemic logicsMay 06 2016Jun 17 2016Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka (1962). Despite its various successful applications in theoretical computer science, AI, and game theory, the technical development of the field ... More

Core-EP Decomposition and its ApplicationsJun 30 2016In this paper, we introduce the notion of the core-EP decomposition and some of its properties. By using the decomposition, we derive several characterizations of the core-EP inverse, introduce a pre-order(i.e. the core-EP order) and a partial order(i.e. ... More

Simulating thermal boundary conditions of spin-lattice models with weighted averagesJul 30 2015Mar 23 2016Thermal boundary conditions has played an increasingly important role in revealing the nature of short-range spin glasses and is likely to be relevant also for other disordered systems. Diffusion method initializing each replica with a random boundary ... More

Rational curves on hypersurfacesApr 15 2016Let $(X,D)$ be a pair where $X$ is a projective variety. We study in detail how the behavior of rational curves on $X$ as well as the positivity of $-(K_X+D)$ and $D$ influence the behavior of rational curves on $D$. In particular we give criteria for ... More

Cyclotomy and permutation polynomials of large indicesSep 18 2012We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.

Minimal Root's embeddings for general starting and target distributionsJan 28 2016Oct 04 2016Recent works (Dupire (2005), Cox and Wang (2013), Gassiat et al. (2015)) have studied the construction of Root's embedding. However, all the results so far rely on the assumption that the corresponding stopped process is uniformly integrable, which is ... More

Intrinsic Lorentz violation in Doppler effect from a moving point light sourceJul 06 2010Apr 09 2012Einstein's Doppler formula is not applicable when a moving point light source is close enough to the observer; for example, it may break down or cannot specify a determinate value when the point source and the observer overlap. In this paper, Doppler ... More

Another proof of Masuoka's Theorem for semisimple irreducible Hopf algebrasDec 04 2012Feb 28 2013Masuoka proved (2009) that a finite-dimensional irreducible Hopf algebra $H$ in positive characteristic is semisimple if and only if it is commutative semisimple if and only if the Hopf subalgebra generated by all primitives is semisimple. In this paper, ... More

One New Blowup Criterion for the 2D Full Compressible Navier-Stokes SystemOct 24 2012Jan 30 2013We establish a blowup criterion for the two-dimensional (2D) full compressible Navier-Stokes system. The criterion is given in terms of the divergence of the velocity field only, and is independent of the temperature. It is almost the same as that of ... More

On Zeilberger ConjectureJan 31 2014Feb 14 2014We prove a conjecture by D. Zeilberger on the determinant of a certain matrix and relate it to a problem of non-existence of 1-cycles in this note.

Searching for Debris Disks around Isolated PulsarsFeb 20 2014Apr 08 2014Different pieces of observational evidence suggest the existence of disks around isolated neutron stars. Such disks could be formed from supernova fallback when neutron stars are born in core-collapse supernova explosions. Efforts have been made to search ... More

An Algebra of Reversible Quantum ComputingJan 17 2015Based on the axiomatization of reversible computing RACP, we generalize it to quantum reversible computing which is called qRACP. By use of the framework of quantum configuration, we show that structural reversibility and quantum state reversibility must ... More

Entanglement in Quantum Process AlgebraMar 17 2014Jul 13 2015We explicitly model entanglement in quantum processes by treating entanglement as a kind of parallelism. We introduce a shadow constant quantum operation and a so-called entanglement merge into quantum process algebra qACP. The transition rules of the ... More

Formal Model of Web Service Composition: An Actor-Based Approach to Unifying Orchestration and ChoreographyDec 03 2013Web Service Composition creates new composite Web Services from the collection of existing ones to be composed further and embodies the added values and potential usages of Web Services. Web Service Composition includes two aspects: Web Service orchestration ... More

Faster Approximation of Max Flow for Directed GraphsNov 05 2012Nov 18 2012I extend the methods in "Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs, with Paul Christiano, Jonathan Kelner, Daniel Spielman, and Shang-Hua Teng" to directed graphs with a variation of the framework ... More

Common Signal AnalysisMar 22 2011Mar 24 2011A common signal is defined for any two signals which have non-zero correlation. A mathematical method is provided to extract the best obtainable common signal between the two signals. This analysis is extended to extracting common signal among three signals. ... More

Braiding statistics and classification of two-dimensional charge-$2m$ superconductorsJan 08 2016Aug 16 2016We study braiding statistics between quasiparticles and vortices in two-dimensional charge-$2m$ (in units of $e$) superconductors that are coupled to a $\mathbb Z_{2m}$ dynamical gauge field, where $m$ is any positive integer. We show that there exist ... More

Asynchronous Byzantine Agreement with Optimal Resilience and Linear ComplexityJul 22 2015Nov 25 2015Given a system with $n > 3t + 1$ processes, where $t$ is the tolerated number of faulty ones, we present a fast asynchronous Byzantine agreement protocol that can reach agreement in $O(t)$ expected running time. This improves the $O(n^2)$ expected running ... More

Pullback Attractors for Non-autonomous Reaction-Diffusion Equations on R^nMar 29 2009We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space R^n when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established ... More

Optimal Throughput for Covert Communication Over a Classical-Quantum ChannelMar 18 2016Jun 16 2016This paper considers the problem of communication over a memoryless classical-quantum wiretap channel subject to the constraint that the eavesdropper on the channel should not be able to learn whether the legitimate parties are using the channel to communicate ... More

Strong law of large number for branching Hunt processesOct 19 2014In this paper we prove that, under certain conditions, a strong law of large number holds for a class of branching particle systems $X$ corresponding to the parameters $(Y,\beta,\psi)$, where $Y$ is a Hunt process and $\psi$ is the generating function ... More

Hamilton-Jacobi Theorems for Regular Reducible Hamiltonian Systems on a Cotangent BundleMar 23 2013Jul 28 2016In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden ... More

Magnetic Reduction of Regular Controlled Hamiltonian System with Symmetry of the Heisenberg GroupJun 11 2015Aug 16 2015In this paper, we study the regular point reduction of a regular controlled Hamiltonian system with magnetic symplectic form and the symmetry of the Heisenberg group. We give the reduced regular controlled Hamiltonian system on the generalization of coadjoint ... More

Davenport constant for semigroups IISep 07 2014Mar 09 2015Let $\mathcal{S}$ be a finite commutative semigroup. The Davenport constant of $\mathcal{S}$, denoted ${\rm D}(\mathcal{S})$, is defined to be the least positive integer $\ell$ such that every sequence $T$ of elements in $\mathcal{S}$ of length at least ... More