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Aqua Computing: Coupling Computing and CommunicationsOct 25 2015The authors introduce a new vision for providing computing services for connected devices. It is based on the key concept that future computing resources will be coupled with communication resources, for enhancing user experience of the connected users, ... More

Outage Probability of Dual-Hop Selective AF With Randomly Distributed and Fixed InterferersOct 04 2014The outage probability performance of a dual-hop amplify-and-forward selective relaying system with global relay selection is analyzed for Nakagami-$m$ fading channels in the presence of multiple interferers at both the relays and the destination. Two ... More

Joint Energy Minimization and Resource Allocation in C-RAN with Mobile CloudSep 01 2015Jan 25 2016Cloud radio access network (C-RAN) has emerged as a potential candidate of the next generation access network technology to address the increasing mobile traffic, while mobile cloud computing (MCC) offers a prospective solution to the resource-limited ... More

A balanced rail-to-rail all digital comparator using only standard cellsSep 17 2015May 10 2016An all-digital comparator with full input range is presented. It outperforms the nowaday all-digital comparators with its large rail-to-rail input range. This is achieved by the proposed Yin-yang balance mechanism between the two logic gates: NAND3 and ... More

Energy Efficient Resource Allocation in UAV-Enabled Mobile Edge Computing NetworksFeb 08 2019Feb 13 2019In this paper, we consider the sum power minimization problem via jointly optimizing user association, power control, computation capacity allocation and location planning in a mobile edge computing (MEC) network with multiple unmanned aerial vehicles ... More

Unified Offloading Decision Making and Resource Allocation in ME-RANMay 29 2017Jun 26 2018In order to support communication and computation cooperation, we propose ME-RAN architecture, which consists of mobile edge cloud (ME) as the computation provision platform and radio access network (RAN) as the communication interface. Cooperative offloading ... More

Energy Efficient Resource Allocation in UAV-Enabled Mobile Edge Computing NetworksFeb 08 2019In this paper, we consider the sum power minimization problem via jointly optimizing user association, power control, computation capacity allocation and location planning in a mobile edge computing (MEC) network with multiple unmanned aerial vehicles ... More

A Brief Survey of Image Processing Algorithms in Electrical Capacitance TomographyOct 15 2015To study the fundamental physics of complex multiphase flow systems using advanced measurement techniques, especially the electrical capacitance tomography (ECT) approach, this article carries out an initial literature review of the ECT method from a ... More

Piecewise Toeplitz Matrices-based Sensing for Rank MinimizationJun 01 2014This paper proposes a set of piecewise Toeplitz matrices as the linear mapping/sensing operator $\mathcal{A}: \mathbf{R}^{n_1 \times n_2} \rightarrow \mathbf{R}^M$ for recovering low rank matrices from few measurements. We prove that such operators efficiently ... More

State of the Art and Prospects of Structured Sensing Matrices in Compressed SensingAug 07 2014Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually ... More

A Nonlinear Weighted Total Variation Image Reconstruction Algorithm for Electrical Capacitance TomographyMar 02 2016Nov 21 2016A new iterative image reconstruction algorithm for electrical capacitance tomography (ECT) is proposed that is based on iterative soft thresholding of a total variation penalty and adaptive reweighted compressive sensing. This algorithm encourages sharp ... More

A Robust Compressive Quantum State Tomography Algorithm Using ADMMJan 25 2014The possible state space dimension increases exponentially with respect to the number of qubits. This feature makes the quantum state tomography expensive and impractical for identifying the state of merely several qubits. The recent developed approach, ... More

A Nonlinear Weighted Total Variation Image Reconstruction Algorithm for Electrical Capacitance TomographyMar 02 2016Based on the techniques of iterative soft thresholding on total variation penalty and adaptive reweighted compressive sensing, a new iterative reconstruction algorithm for electrical capacitance tomography (ECT) is proposed. This algorithm encourages ... More

Supervised Fine Tuning for Word Embedding with Integrated KnowledgeMay 29 2015Learning vector representation for words is an important research field which may benefit many natural language processing tasks. Two limitations exist in nearly all available models, which are the bias caused by the context definition and the lack of ... More

Alternating Strategies Are Good For Low-Rank Matrix ReconstructionJul 12 2014This article focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas from the alternating ... More

Orthogonal symmetric Toeplitz matrices for compressed sensing: Statistical isometry propertyDec 29 2010Oct 24 2012Recently, the statistical restricted isometry property (RIP) has been formulated to analyze the performance of deterministic sampling matrices for compressed sensing. In this paper, we propose the usage of orthogonal symmetric Toeplitz matrices (OSTM) ... More

Convolutional Compressed Sensing Using Deterministic SequencesOct 28 2012In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier ... 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

Extreme Negative Dependence and Risk AggregationJul 25 2014We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. The END structure, as a new benchmark for negative dependence, is comparable to comonotonicity and independence. ... 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

On explicit factors of Cyclotomic polynomials over finite fieldsNov 22 2010We study the explicit factorization of $2^n r$-th cyclotomic polynomials over finite field $\mathbb{F}_q$ where $q, r$ are odd with $(r, q) =1$. We show that all irreducible factors of $2^n r$-th cyclotomic polynomials can be obtained easily from irreducible ... More

Quantization of adiabatic pumped charge in the presence of superconducting leadFeb 20 2002We investigate the parametric electron pumping of a double barrier structure in the presence of a superconducting lead. The parametric pumping is facilitated by cyclic variation of the barrier heights $x_1$ and $x_2$ of the barriers. In the weak coupling ... More

Non-flow correlations in a cluster modelDec 05 2008Jun 17 2010We derive analytical forms for nonflow contributions from cluster correlation to the measurement of two-particle elliptic flow (v2{2}). We estimate nonflow contribution from rho->pi+pi decays and find it is negative but not a major contributor to the ... More

A Hybridized Weak Galerkin Finite Element Method for the Biharmonic EquationFeb 05 2014This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element boundaries. The Lagrange multiplier ... More

An Efficient Numerical Scheme for the Biharmonic Equation by Weak Galerkin Finite Element Methods on Polygonal or Polyhedral MeshesSep 22 2013This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite element scheme is based on a variational form of the biharmonic equation that is equivalent to the ... More

Oseba: Optimization for Selective Bulk Analysis in Big Data ProcessingJul 12 2017Selective bulk analyses, such as statistical learning on temporal/spatial data, are fundamental to a wide range of contemporary data analysis. However, with the increasingly larger data-sets, such as weather data and marketing transactions, the data organization/access ... 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

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

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

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

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

Nonparametric Additive Model-assisted Estimation for Survey DataJan 04 2011An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson ... 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

Free boundary problems of ecological models with nonlocal and local diffusionsDec 31 2018We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the population dispersal, ... 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

Learning Fine-grained Features via a CNN Tree for Large-scale ClassificationNov 14 2015We propose a novel approach to enhance the discriminability of Convolutional Neural Networks (CNN). The key idea is to build a tree structure that could progressively learn fine-grained features to distinguish a subset of classes, by learning features ... More

Quantitative Density under Higher Rank Abelian Algebraic Toral ActionsApr 01 2010We generalize Bourgain-Lindenstrauss-Michel-Venkatesh's recent one-dimensional quantitative density result to abelian algebraic actions on higher dimensional tori. Up to finite index, the group actions that we study are conjugate to the action of $U_K$, ... More

Forward period analysis and the long term simulation of a periodic Hamiltonian systemOct 23 2014The period of a Morse oscillator and mathematical pendulum system are obtained, accurate to 100 significant digits, by forward period analysis (FPA). From these results, the long-term [0, 10^60] (time unit) solutions, which overlap from the Planck time ... More

Finite Basis for Radical Well-Mixed Difference Ideals Generated by BinomialsOct 22 2016In this paper, we prove a finite basis theorem for radical well-mixed difference ideals generated by binomials. As a consequence, every strictly ascending chain of radical well-mixed difference ideals generated by binomials in a difference polynomial ... More

A theory of nonequilibrium steady states in quantum chaotic systemsJul 18 2016Nonequilibrium steady state (NESS) is a quasistationary state, in which exist currents that continuously produce entropy, but the local observables are stationary everywhere. We propose a theory of NESS under the framework of quantum chaos. In an isolated ... More

The Noncommutative Infinitesimal Equivariant Index FormulaJul 31 2013Mar 17 2015In this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. ... More

The energy of a deterministic Loewner chain: Reversibility and interpretation via SLE$_{0+}$Jan 20 2016We study some features of the energy of a deterministic chordal Loewner chain, which is defined as the Dirichlet energy of its driving function. In particular, using an interpretation of this energy as a large deviation rate function for SLE$_\kappa$ ... More

A Practical Guide to Randomized Matrix Computations with MATLAB ImplementationsMay 28 2015Nov 03 2015Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are prohibitive when the ... More

A Suggestion for Modification of Vafa-Witten TheoryDec 05 1995Using the Mathai-Quillen formalism we reexamine the twisted N=4 supersymmetric model of Vafa-Witten theory. Smooth out the relation between the supersymmetric action and the path integral representation of the Thom class.

The excitation operator approach to non-Markovian dynamics of quantum impurity models in the Kondo regimeSep 18 2012We present a numerical method for studying the real time dynamics of a small interacting quantum system coupled to an infinite fermionic reservoir. By building an orthonormal basis in the operator space, we turn the Heisenberg equation of motion into ... More

Variations of Gauss-Codazzi-Ricci Equations in Kaluza-Klein Reduction (String Theory) and Cauchy Problem (General Relativity)May 09 2007We find a kind of variations of Gauss-Codazzi-Ricci equations suitable for Kaluza-Klein reduction and Cauchy problem. Especially the counterpart of extrinsic curvature tensor has antisymmetric part as well as symmetric one. If the dependence of metric ... More

Classification of irreducible modules of W_3 algebra with c = -2Aug 17 1997We construct irreducible modules V_{\alpha}, \alpha \in \C over W_3 algebra with c = -2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W_3 algebra with c = -2. Highest weights of modules V_{\alpha}, ... More

W{1+ \infty} algebra, W_3 algebra, and Friedan-Martinec-Shenker bosonizationAug 07 1997We show that the vertex algebra W{1+ \infty} with central charge -1 is isomorphic to a tensor product of the simple W_3 algebra with central charge -2 and a Heisenberg vertex algebra generated by a free bosonic field. We construct a family of irreducible ... More

Michael-Simon inequalities for $k$-th mean curvaturesMay 14 2013This paper continues the study of Alexandrov-Fenchel inequalities for quermassintegrals for $k$-convex domains. It focuses on the application to the Michael-Simon type inequalities for $k$-curvature operators. The proof uses optimal transport maps as ... More

Isoperimetric inequality, finite total Q-curvature and quasiconformal mapApr 02 2010In this paper, we obtain the isoperimetric inequality on conformally flat manifold with finite total $Q$-curvature. This is a higher dimensional analogue of Li and Tam's result \cite{L-T} on surfaces with finite total Gaussian curvature. The main step ... More

On homogeneous polynomials determined by their Jacobian idealFeb 16 2014Apr 20 2014We investigate which homogeneous polynomials are determined by their Jacobian ideals, and extend and complete previous results due to J. Carlson and Ph. Griffiths, K. Ueda and M. Yoshinaga, and A. Dimca and E. Sernesi.

Isomorphism classes of finite dimensional connected Hopf algebras in positive characteristicOct 26 2013Apr 13 2015We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair associated ... More

Singular and fractional integral operators with variable kernels on the weak Hardy spacesApr 02 2013In this paper, by using the decomposition theorem for weak Hardy spaces, we will obtain the boundedness properties of some integral operators with variable kernels on these spaces, under some Dini type conditions imposed on the variable kernel $\Omega(x,z)$. ... More

Boundedness of singular integral operators with variable kernels on weighted weak Hardy spacesNov 18 2011Dec 26 2012Let $T_\Omega$ be the singular integral operator with variable kernel $\Omega(x,z)$. In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of $T_\Omega$ on these spaces, under ... More

Estimates of some integral operators with bounded variable kernels on the Hardy and weak Hardy spaces over $\mathbb R^n$Oct 05 2010Jan 25 2014In this paper, we first introduce $L^{\sigma_1}$-$(\log L)^{\sigma_2}$ conditions satisfied by the variable kernels $\Omega(x,z)$ for $0\leq\sigma_1\leq1$ and $\sigma_2\geq0$. Under these new smoothness conditions, we will prove the boundedness properties ... More

The boundedness of Bochner-Riesz operators on the weighted weak Hardy spacesNov 06 2011Jun 25 2012Let $w$ be a Muckenhoupt weight and $WH^p_w(\mathbb R^n)$ be the weighted weak Hardy spaces. In this paper, by using the atomic decomposition of $WH^p_w(\mathbb R^n)$, we will show that the maximal Bochner-Riesz operators $T^\delta_*$ are bounded from ... More

Harmonic approximation and improvement of flatness in a singular perturbation problemJan 15 2014We study the De Giorgi type conjecture, that is, one dimensional symmetry problem for entire solutions of an two components elliptic system in $\mathbb{R}^n$, for all $n\geq 2$. We prove that, if a solution $(u,v)$ has a linear growth at infinity, then ... More

Uniform Lipschitz regularity of flat segregated interfaces in a singularly perturbed problemJul 22 2015For the singularly perturbed system \[\Delta u_{i,\beta}=\beta u_{i,\beta}\sum_{j\neq i}u_{j,\beta}^2, \quad 1\leq i\leq N,\] we prove that flat interfaces are uniformly Lipschitz. As a byproduct of the proof we also obtain the optimal lower bound near ... More

Positive periodic solutions of singular systemsJul 19 2010The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our results provide ... More

Gravitational Collapse and Black Hole Formation in a BraneworldMay 01 2015In this thesis we present the first numerical study of gravitational collapse in braneworlds within the framework of the single brane model proposed by Randall and Sundrum (RSII). We directly show that the evolutions of sufficiently strong initial data ... More

The automorphism groups of Frobenius Groups, and Relative Elementary Abelian GroupsOct 19 2016Motivated by a problem of characterising a family of Cayley graphs, we determine the full automorphism groups of a class of Frobenius groups. As an application, we characterise a type of finite groups $G$ which behave similarly to elementary abelian $p$-groups ... More

Weighted estimates for vector-valued intrinsic square functions and commutators in the Morrey type spacesMar 10 2016In this paper, the boundedness properties of vector-valued intrinsic square functions and their vector-valued commutators with $BMO(\mathbb R^n)$ functions are discussed. We first show the weighted strong type and weak type estimates of vector-valued ... More

Some estimates for commutators of fractional integral operators on weighted Morrey spacesOct 13 2010Jan 22 2013Let $0<\alpha<n$ and $I_\alpha$ be the fractional integral operator. In this paper, we shall use a unified approach to show some boundedness properties of commutators $[b,I_\alpha]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under appropriate conditions ... More

Some estimates for commutators of Calderón-Zygmund operators on the weighted Morrey spacesOct 13 2010Feb 29 2012Let $T$ be a Calder\'on-Zygmund singular integral operator. In this paper, we will show some weighted boundedness properties of commutator $[b,T]$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ under appropriate conditions on the weight $w$, where the ... More

Daya Bay Neutrino Experiment: Goal, Progress and ScheduleSep 15 2011Sep 22 2011Daya Bay Neutrino Experiment is dedicated to measuring the last unobserved neutrino mixing angle theta_13. The predicted precision on sin^2(2theta_13) is 0.01 at 90% confidence level. This document briefly reviews the measurement method and detector construction ... More

Observational Probes of Dark EnergyJan 10 2012Jan 12 2012The cause for the observed acceleration in the expansion of the universe is unknown, and referred to as "dark energy" for convenience. Dark energy could be an unknown energy component, or a modification of Einstein's general relativity. This dictates ... More

Almost strong mixing group actions in topological dynamicsMay 23 2014In ergodic theory, given sufficient conditions on the system, every weak mixing $\mathbb{N}$-action is strong mixing along a density one subset of $\mathbb{N}$. We ask if a similar statement holds in topological dynamics with density one replaced with ... More

Searches for New Physics at the Belle II ExperimentNov 02 2015The Belle II experiment at the SuperKEKB collider is an upgrade of the Belle / KEKB experiment. It will start physics data taking from 2018 and with $40$ times luminosity, its goal is to accumulate 50 $ab^{-1}$ of $e^+e^-$ collision data. The physics ... More

The noncommutative infinitesimal equivariant index formula: part IINov 25 2014Apr 02 2015In this paper, we prove that infinitesimal equivariant Chern-Connes characters are well-defined. We decompose an equivariant index as a pairing of infinitesimal equivariant Chern-Connes characters with the Chern character of an idempotent matrix. We compute ... More

The noncommutative family Atiyah-Patodi-Singer index theoremDec 09 2014Jul 20 2016In this paper, we define the eta cochain form and prove its regularity when the kernel of a family of Dirac operators is a vector bundle. We decompose the eta form as a pairing of the eta cochain form with the Chern character of an idempotent matrix and ... More

An Algebra of Reversible ComputationOct 20 2014May 26 2016We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules, basic reversible processes algebra (BRPA), algebra of reversible communicating processes (ARCP), recursion and abstraction. Just like ... More

The first terms in the expansion of the Bergman kernel in higher degrees: mixed curvature caseJul 18 2014Aug 25 2014We establish the cancellation of the first |2j-q| terms in the diagonal asymptotic expansion of the restriction to the (0, 2j)-forms of the Bergman kernel associated to the modified spin^c Dirac operator on high tensor powers of a line bundle with mixed ... More

Global Well-posedness of the Relativistic Boltzmann Equation with Large Amplitude Initial DataApr 09 2016Jun 23 2016In this paper, we consider the global well-posedness of the special relativistic Boltzmann equation with large amplitude initial data. We proved the global existence and uniqueness of mild solutions to the relativistic Boltzmann equation in both whole ... More

Fully Abstract Game Semantics for ActorsMar 26 2014Apr 10 2014Along the way paved by the recent concurrent game semantics for process algebra CCS and $\pi$-calculus, based on the basic characteristics of the actor computational model and the very reductive semantics for actors, we establish a fully abstract concurrent ... More

An Axiomatization for Quantum Processes to Unifying Quantum and Classical ComputingNov 11 2013We establish an axiomatization for quantum processes, which is a quantum generalization of process algebra ACP (Algebra of Communicating Processes). We use the framework of a quantum process configuration $\langle p, \varrho\rangle$, but we treat it as ... More

Quantitative stratification of stationary Yang-Mills fieldsOct 02 2016In this paper we study the singular set of a stationary Yang-Mills connection $A$ and prove the rectifiability of the $k^{th}$ stratification $S^k(A)$ for all integer $k$, the set where no tangent measure is $k+1$-symmetric. In order to do this we introduce ... More

Spectator fields and their imprints on the Cosmic Microwave BackgroundOct 10 2016When a subdominant light scalar field ends slow roll during inflation, but well after the Hubble exit of the pivot scales, it may determine the cosmological perturbations. This thesis investigates how such a scalar field, the spectator, may leave its ... More

Maximum likelihood degree of Fermat hypersurfaces via Euler characteristicsSep 12 2015Maximum likelihood degree of a projective variety is the number of critical points of a general likelihood function. In this note, we compute the Maximum likelihood degree of Fermat hypersurfaces. We give a formula of the Maximum likelihood degree in ... More

The Belle II Experiment and SuperKEKB UpgradeNov 30 2015Apr 26 2016The Belle II / SuperKEKB experiment is an $e^+e^-$ collider running at the $\Upsilon(4S)$ resonance energy to produce B meson pairs. As an upgrade of the Belle / KEKB experiment, it will start physics data taking from 2018 and with $\sim 40$ times luminosity, ... More

Rational curves on hypersurfaces of a projective varietyNov 20 2014In this paper, we extend our result in [3] to hypersurfaces of any smooth projective variety $Y$. Precisely we let $X_0$ be a generic hypersurface of $Y$ and $c_0:\mathbf P^1\to X_0$ be a generic birational morphism to its image, i.e. $c_0\in Hom_{bir}(\mathbf ... More

Detecting CMB modulations and non-Gaussianities from power multipolesJan 08 2014By decomposing the CMB temperature fluctuations \emph{squared} into spherical harmonics, we can define the \emph{CMB power multipoles} as the fundamental observables to quantify any generic modulations in the CMB. This allows for simple direct measurements ... More

Pullback Attractors for the Non-autonomous FitzHugh-Nagumo System on Unbounded DomainsMay 24 2008The existence of a pullback attractor is established for the singularly perturbed FitzHugh-Nagumo system defined on the entire space $R^n$ when external terms are unbounded in a phase space. The pullback asymptotic compactness of the system is proved ... More

New Congruences on Multiple Harmonic Sums and Bernoulli NumbersApr 13 2015Jan 27 2016Let ${\mathcal{P}_{n}}$ denote the set of positive integers which are prime to $n$. Let $B_{n}$ be the $n$-th Bernoulli number. For any prime $p \ge 11$ and integer $r\ge 2$, we prove that $$ \sum\limits_{\begin{smallmatrix} {{l}_{1}}+{{l}_{2}}+\cdots ... More

A New Super Congruence Involving Multiple Harmonic SumsOct 07 2014Oct 12 2014Let ${\mathcal{P}_{n}}$ denote the set of positive integers which are prime to $n$. Let $B_{n}$ be the $n$-th Bernoulli number. For any prime $p\ge 5$ and $r\ge 2$, we prove that \begin{equation} \sum\limits_{\begin{smallmatrix} {{l}_{1}}+{{l}_{2}}+\cdots ... More

Estimation of nonlinear models with Berkson measurement errorsAug 30 2005This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not necessarily normal. ... More

Rainbow Ramsey theorem for triples is strictly weaker than the Arithmetic Comprehension AxiomMar 14 2013We prove that $\RCA + \RRT^3_2 \not\vdash \ACA$ where $\RRT^3_2$ is the Rainbow Ramsey Theorem for 2-bounded colorings of triples. This reverse mathematical result is based on a cone avoidance theorem, that every 2-bounded coloring of pairs admits a cone-avoiding ... More

Global solutions of a Keller--Segel system with saturated logarithmic sensitivity functionDec 01 2013Feb 07 2015We study a Keller-Segel type chemotaxis model with a modified sensitivity function in a bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq2$. The global existence of classical solutions to the fully parabolic system is established provided that the ratio ... More