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16-qubit IBM universal quantum computer can be fully entangledJan 11 2018Sep 28 2018Entanglement is an important evidence that a quantum device can potentially solve problems intractable for classical computers. In this paper, we prepare connected graph states involving 8 to 16 qubits on ibmqx5, a 16-qubit superconducting quantum processor ... More

Distributed Bandit Learning: How Much Communication is Needed to Achieve (Near) Optimal RegretApr 12 2019We study the communication complexity of distributed multi-armed bandits (MAB) and distributed linear bandits for regret minimization. We propose communication protocols that achieve near-optimal regret bounds and result in optimal speed-up under mild ... More

Q-learning with UCB Exploration is Sample Efficient for Infinite-Horizon MDPJan 27 2019A fundamental question in reinforcement learning is whether model-free algorithms are sample efficient. Recently, Jin et al. \cite{jin2018q} proposed a Q-learning algorithm with UCB exploration policy, and proved it has nearly optimal regret bound for ... More

Distributed Bandit Learning: Near-Optimal Regret with Efficient CommunicationApr 12 2019May 29 2019We study the problem of regret minimization for distributed bandits learning, in which $M$ agents work collaboratively to minimize their total regret under the coordination of a central server. Our goal is to design communication protocols with near-optimal ... More

Delay-Free Concurrency on Faulty Persistent MemoryJun 12 2018Jan 17 2019Non-volatile memory (NVM) promises persistent main memory that remains correct despite loss of power. This has sparked a line of research into algorithms that can recover from a system crash. Since caches are expected to remain volatile, concurrent data ... More

Space Complexity of Implementing Large Shared RegistersAug 01 2018We prove two new space lower bounds for the problem of implementing a large shared register using smaller physical shared registers. We focus on the case where both the implemented and physical registers are single-writer, which means they can be accessed ... More

Adaptive Gradient Methods with Dynamic Bound of Learning RateFeb 26 2019Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared with SGD or ... More

Robust Lane Detection from Continuous Driving Scenes Using Deep Neural NetworksMar 06 2019Lane detection in driving scenes is an important module for autonomous vehicles and advanced driver assistance systems. In recent years, many sophisticated lane detection methods have been proposed. However, most methods focus on detecting the lane from ... More

Word Segmentation as Graph PartitionApr 05 2018We propose a new approach to the Chinese word segmentation problem that considers the sentence as an undirected graph, whose nodes are the characters. One can use various techniques to compute the edge weights that measure the connection strength between ... More

In-Orbit Instrument Performance Study and Calibration for POLAR Polarization MeasurementsMay 19 2018May 29 2018POLAR is a compact space-borne detector designed to perform reliable measurements of the polarization for transient sources like Gamma-Ray Bursts in the energy range 50-500keV. The instrument works based on the Compton Scattering principle with the plastic ... More

Weighted Mean CurvatureMar 17 2019In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation ... More

Weighted Mean CurvatureMar 17 2019May 07 2019In image processing tasks, spatial priors are essential for robust computations, regularization, algorithmic design and Bayesian inference. In this paper, we introduce weighted mean curvature (WMC) as a novel image prior and present an efficient computation ... More

Learning Deep Image Priors for Blind Image DenoisingJun 04 2019Image denoising is the process of removing noise from noisy images, which is an image domain transferring task, i.e., from a single or several noise level domains to a photo-realistic domain. In this paper, we propose an effective image denoising method ... More

Gradient Distribution Priors for Biomedical Image ProcessingAug 13 2014Sep 03 2014Ill-posed inverse problems are commonplace in biomedical image processing. Their solution typically requires imposing prior knowledge about the latent ground truth. While this regularizes the problem to an extent where it can be solved, it also biases ... More

Side Window FilteringMay 17 2019Local windows are routinely used in computer vision and almost without exception the center of the window is aligned with the pixels being processed. We show that this conventional wisdom is not universally applicable. When a pixel is on an edge, placing ... More

Curve Networks for Surface ReconstructionMar 29 2016Man-made objects usually exhibit descriptive curved features (i.e., curve networks). The curve network of an object conveys its high-level geometric and topological structure. We present a framework for extracting feature curve networks from unstructured ... More

A Low-latency Pipeline for GRB Light Curve and Spectrum using Fermi/GBM Near Real-time DataFeb 26 2018Rapid response and short time latency are very important for Time Domain Astronomy, such as the observations of Gamma-ray Bursts (GRBs) and electromagnetic (EM) counterparts of gravitational waves (GWs). Based on the near real-time Fermi/GBM data, we ... More

Bias-Compensated Normalized Maximum Correntropy Criterion Algorithm for System Identification with Noisy InputNov 23 2017This paper proposed a bias-compensated normalized maximum correntropy criterion (BCNMCC) algorithm charactered by its low steady-state misalignment for system identification with noisy input in an impulsive output noise environment. The normalized maximum ... More

Multiversion Concurrency with Bounded Delay and Precise Garbage CollectionMar 23 2018May 15 2019In this paper we are interested in bounding the number of instructions taken to process transactions. The main result is a multiversion transactional system that supports constant delay (extra instructions beyond running in isolation) for all read-only ... More

Model-Based Cross-Correlation Search for Gravitational Waves from Scorpius X-1Apr 22 2015May 20 2015We consider the cross-correlation search for periodic GWs and its potential application to the LMXB Sco X-1. This method coherently combines data from different detectors at the same time, as well as different times from the same or different detectors. ... More

Efficient Single Writer ConcurrencyMar 23 2018May 13 2018Most research in concurrency focuses on providing safety and liveness guarantees under the worst possible conditions. However, workloads of many important concurrent applications are much less adversarial, leaving room for optimizations for the common ... More

HLO: Half-kernel Laplacian Operator for Surface SmoothingMay 12 2019This paper presents a simple yet effective method for feature-preserving surface smoothing. Through analyzing the differential property of surfaces, we show that the conventional discrete Laplacian operator with uniform weights is not applicable to feature ... More

Resampling to accelerate cross-correlation searches for continuous gravitational waves from binary systemsDec 18 2017Feb 13 2018Continuous-wave (CW) gravitational waves (GWs) call for computationally-intensive methods. Low signal-to-noise ratio signals need templated searches with long coherent integration times and thus fine parameter-space resolution. Longer integration increases ... More

In-flight energy calibration of the space-borne Compton polarimeter POLAROct 24 2017Dec 18 2017POLAR is a compact wide-field space-borne detector for precise measurements of the linear polarization of hard X-rays emitted by transient sources in the energy range from 50 keV to 500 keV. It consists of a 40$\times$40 array of plastic scintillator ... More

In-flight energy calibration of the space-borne Compton polarimeter POLAROct 24 2017Jun 05 2018POLAR is a compact wide-field space-borne detector for precise measurements of the linear polarisation of hard X-rays emitted by transient sources in the energy range from 50 keV to 500 keV. It consists of a 40$\times$40 array of plastic scintillator ... More

Learning Phase Competition for Traffic Signal ControlMay 12 2019Increasingly available city data and advanced learning techniques have empowered people to improve the efficiency of our city functions. Among them, improving the urban transportation efficiency is one of the most prominent topics. Recent studies have ... 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

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

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

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

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

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

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

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

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

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

Twisted Dirac Operators and the Noncommutative Residue for Manifolds with BoundaryApr 09 2014In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and twisted signature ... More

Deterministic Analysis of Weighted BPDN With Partially Known Support InformationMar 03 2019In this paper, with the aid of the powerful Restricted Isometry Constant (RIC), a deterministic (or say non-stochastic) analysis, which includes a series of sufficient conditions (related to the RIC order) and their resultant error estimates, is established ... More

The parameters of a family of linear codesMar 09 2019A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the sense that ... More

Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equationDec 15 2017Jan 24 2019We investigate the time-asymptotic stability of planar rarefaction wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [24, 22] and our new observations on the underlying wave structures of the equation ... More

A Simple and Space Efficient Segment Tree ImplementationJul 14 2018The segment tree is an extremely versatile data structure. In this paper, a new heap based implementation of segment trees is proposed. In such an implementation of segment tree, the structural information associated with the tree nodes can be removed ... 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

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

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

On the boundary between qualitative and quantitative measures of causal effectsNov 13 2017Jul 09 2018Causal relationships among variables are commonly represented via directed acyclic graphs. There are many methods in the literature to quantify the strength of arrows in a causal acyclic graph. These methods, however, have undesirable properties when ... 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

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

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

In-phase Synchronization of Two Coupled MetronomesMay 01 2018This paper used multi-scale method and KBM method to get approximate solution of coupled Van der Pol oscillators, based on which, researchers investigated the impact several parameters have on the prerequisite of synchronization and the time it takes ... More

New Braided $T$-Categories over Hopf (co)quasigroupsJan 22 2017Let $H$ be a Hopf quasigroup with bijective antipode and let $Aut_{HQG}(H)$ be the set of all Hopf quasigroup automorphisms of $H$. We introduce a category ${_{H}\mathcal{YDQ}^{H}}(\alpha,\beta)$ with $\alpha,\beta\in Aut_{HQG}(H)$ and construct a braided ... 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

Dirichlet Forms Constructed from Annihilation Operators on Bernoulli FunctionalsFeb 09 2017The annihilation operators on Bernoulli functionals (Bernoulli annihilators, for short) and their adjoint operators satisfy a canonical anti-commutation relation (CAR) in equal-time. As a mathematical structure, Dirichlet forms play an important role ... More

Characterization of Hopf QuasigroupsFeb 26 2019In this paper, we first discuss some properties of the Galois linear maps. We provide some equivalent conditions for Hopf algebras and Hopf (co)quasigroups as its applications. Then let $H$ be a Hopf quasigroup with bijective antipode and $G$ be the set ... More

A primal-dual finite element method for first-order transport problemsJun 18 2019Jun 24 2019This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational formulation of the ... More

Designing Unimodular Sequences with Optimized Auto/cross-correlation Properties via Consensus-ADMM/PDMM ApproachesJul 14 2019Unimodular sequences with good auto/cross-correlation properties are favorable in wireless communication and radar applications. In this paper, we focus on designing these kinds of sequences. The main content is as follows: first, we formulate the designing ... 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

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

Electron Transport in Dirac and Weyl SemimetalsSep 10 2018Recently, the Dirac and Weyl semimetals have attracted extensive attention in condensed matter physics due to both the fundamental interest and the potential application of a new generation of electronic devices. Here we review the exotic electrical transport ... More

Perturbations of Dirac Operators and A KKW Type Theorem for Five Dimensional Manifolds with BoundaryJul 29 2018In this paper, we define lower dimensional volumes of compact Riemannian manifolds with boundary. For five dimensional spin manifolds with boundary, we prove a Kastler-Kalau-Walze type theorem associated with one-form perturbations of Dirac operators ... 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

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

An End-to-End Deep Learning Histochemical Scoring System for Breast Cancer Tissue MicroarrayJan 19 2018One of the methods for stratifying different molecular classes of breast cancer is the Nottingham Prognostic Index Plus (NPI+) which uses breast cancer relevant biomarkers to stain tumour tissues prepared on tissue microarray (TMA). To determine the molecular ... More

Segmentation of Drosophila Heart in Optical Coherence Microscopy Images Using Convolutional Neural NetworksMar 05 2018Jul 21 2018Convolutional neural networks are powerful tools for image segmentation and classification. Here, we use this method to identify and mark the heart region of Drosophila at different developmental stages in the cross-sectional images acquired by a custom ... 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

On the Design of Constant Modulus Probing Waveforms with Good Correlation Properties for MIMO Radar via Consensus-ADMM ApproachJan 16 2019In this paper, we design constant modulus probing waveforms with good correlation properties for collocated multi-input multi-output (MIMO) radar systems. The main content is as follows: first, we formulate the design problem as a fourth order polynomial ... More

An Improved Cost Function for Hierarchical Cluster TreesDec 06 2018Dec 17 2018Hierarchical clustering has been a popular method in various data analysis applications. It partitions a data set into a hierarchical collection of clusters, and can provide a global view of (cluster) structure behind data across different granularity ... 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

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

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

Compatible Matrices of Spearman's Rank CorrelationOct 08 2018Apr 03 2019In this paper, we provide a negative answer to a long-standing open problem on the compatibility of Spearman's rho matrices. Following an equivalence of Spearman's rho matrices and linear correlation matrices for dimensions up to 9 in the literature, ... 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

Compatible Matrices of Spearman's Rank CorrelationOct 08 2018Oct 11 2018In this paper, we provide a negative answer to a long-standing open problem on the compatibility of Spearman's rho matrices. Following an equivalence of Spearman's rho matrices and linear correlation matrices for dimensions up to 9 in the literature, ... More

Thermalization of small quantum systems: From the zeroth law of thermodynamicsMay 15 2019Jun 04 2019Thermalization of isolated quantum systems has been studied intensively in recent years and significant progresses have been achieved. Here, we study thermalization of small quantum systems that interact with large chaotic environments under the consideration ... 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