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Hypergeometric function and Modular Curvature I. --Hypergeometric functions in Heat CoefficientsOct 21 2018Jan 13 2019We give a three-fold upgrade to the rearrangement lemma (pioneer by Connes-Tretkoff-Moscovici) base on the functional analytic ground laid by Lesch. First, we show that the building blocks of the spectral functions appeared in the lemma belong to a class ... More

Intelligent Processing in Vehicular Ad hoc Networks: a SurveyMar 28 2019The intelligent Processing technique is more and more attractive to researchers due to its ability to deal with key problems in Vehicular Ad hoc networks. However, several problems in applying intelligent processing technologies in VANETs remain open. ... More

Fine-tune BERT for Extractive SummarizationMar 25 2019BERT, a pre-trained Transformer model, has achieved ground-breaking performance on multiple NLP tasks. In this paper, we describe BERTSUM, a simple variant of BERT, for extractive summarization. Our system is the state of the art on the CNN/Dailymail ... More

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

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

A Hierarchical Butterfly LU Preconditioner for Two-Dimensional Electromagnetic Scattering Problems Involving Open SurfacesJan 31 2019This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations (EFIEs) in electromagnetic scattering problems of perfect electrically ... More

The multiplier and cohomology of Lie superalgebrasNov 01 2018In this paper, all (super)algebras are over a field $\mathbb{F}$ of characteristic different from $2, 3$. We construct the so-called 5-sequences of cohomology for central extensions of a Lie superalgebra and prove that they are exact. Then we prove that ... More

Operator perturbation theory in the backward Heisenberg pictureApr 23 2012We present a simple operator perturbation theory in the backward Heisenberg picture. Compared with the well-known Heisenberg picture, the revised picture is based on the backward time instead of the forward time. The unique feature of the uncommon picture ... More

Orbital-selective Mott phase of Cu-substituted iron-based SuperconductorsJul 07 2016We study the phase transition in Cu-substituted iron-based superconductors with a new developed real-space Green's function method. We find that Cu substitution has strong effect on the orbital-selective Mott transition introduced by the Hund's rule coupling. ... More

Sequential Peer Prediction: Learning to Elicit Effort using Posted PricesNov 28 2016Peer prediction mechanisms are often adopted to elicit truthful contributions from crowd workers when no ground-truth verification is available. Recently, mechanisms of this type have been developed to incentivize effort exertion, in addition to truthful ... More

Proactive rebalancing and speed-up techniques for on-demand high capacity vehicle poolingFeb 09 2019By proposing speed-up techniques and a proactive rebalance algorithm, we improve the Mobility-on-Demand fleet management approach in [1] on both computational performance and system performance. The speed-up techniques comprise search space pruning and ... More

Proceedings Third International Workshop on Engineering Safety and Security SystemsMay 03 2014The International Workshop on Engineering Safety and Security Systems (ESSS) aims at contributing to the challenge of constructing reliable and secure systems. The workshop covers areas such as formal specification, type checking, model checking, program ... More

Multiplex Structures: Patterns of Complexity in Real-World NetworksSep 10 2010Sep 14 2010Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it represents a natural ... More

Global Torelli Theorem for Projective Manifolds of Calabi-Yau TypeMay 18 2012Sep 05 2016We prove that the period maps from the Torelli space and the moduli space with level $m$ structure of Calabi-Yau type manifolds to the corresponding period domain of polarized Hodge structures are injective. The proof is based on the construction of holomorphic ... More

Algebraicity of the image of period mapAug 22 2016We prove that the image of period map is algebraic, as conjectured by Griffiths.

Contrastive Unsupervised Word Alignment with Non-Local FeaturesOct 08 2014Oct 10 2014Word alignment is an important natural language processing task that indicates the correspondence between natural languages. Recently, unsupervised learning of log-linear models for word alignment has received considerable attention as it combines the ... More

Effective vanishing theorems for ample and globally generated vector bundlesMar 13 2013Jul 22 2015By proving an integral formula of the curvature tensor of $E\ts \det E$, we observe that the curvature tensor of $E\ts \det E$ is very similar to that of a line bundle and obtain certain new Kodaira-Akizuki-Nakano type vanishing theorems for vector bundles. ... More

Global Strong Solution of a 2D coupled Parabolic-Hyperbolic Magnetohydrodynamic SystemJan 29 2017The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic (MHD) model in two dimensional space. Based on Agmon, Douglis and Nirenberg's estimates for the stationary Stokes equation ... More

Magneto-hydrodynamical Model for PlasmaJan 24 2016Dec 08 2016Based on the Newton's second law and the Maxwell equations for the electromagnetic fields, we establish a new 3D incompressible magneto-hydrodynamics(MHD) equations for the motion of plasma under the standard Coulomb gauge. By using the Galerkin method, ... More

On cohomology of filiform Lie superalgebrasSep 03 2018Suppose the ground field $\mathbb{F}$ is an algebraically closed field of characteristic different from 2, 3. We determine the Betti numbers and make a decomposition of the associative superalgebra of the cohomology for the model filiform Lie superalgebra. ... More

A mean value formula of sub-p-Laplace parabolic equations on the Heisenberg groupFeb 03 2013We derive two equivalent definitions of the viscosity solutions to the homogeneous sub-p- Laplace parabolic equations on the Heisenberg group, and characterize the viscosity solutions in terms of an asymptotic mean value formula. Moreover, we construct ... More

Blocks of group algebras are derived simpleApr 04 2011A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This result is ... More

Surrogate Losses in Passive and Active LearningJul 16 2012Mar 14 2015Active learning is a type of sequential design for supervised machine learning, in which the learning algorithm sequentially requests the labels of selected instances from a large pool of unlabeled data points. The objective is to produce a classifier ... More

Validation and Uncertainty Quantification for Wall Boiling Closure Relations in Multiphase-CFD SolverSep 24 2018The two-fluid model based Multiphase Computational Fluid Dynamics (MCFD) has been considered as one of the most promising tools to investigate two-phase flow and boiling system for engineering purposes. The MCFD solver requires closure relations to make ... More

One-loop QCD correction to top pair production in the littlest Higgs model with T-parity at the LHCJul 25 2015In this work, we investigate the one-loop QCD correction to top pair production in the littlest Higgs model with T-parity at the LHC. We calculate the relative correction of the top pair production cross section and top-antitop spin correlation at the ... More

Stochastic Non-convex Optimization with Strong High Probability Second-order ConvergenceOct 25 2017Nov 01 2017In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. ... More

Adaptive Accelerated Gradient Converging Methods under Holderian Error Bound ConditionNov 23 2016May 14 2017Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC). However, the faster ... More

From local Torelli to global TorelliDec 28 2015Sep 05 2016We introduce the notions of strong local Torelli and T-class for polarized manifolds, and prove that strong local Torelli implies global Torelli theorem on the Torelli spaces for polarized manifolds in the T-class. We discuss many new examples of projective ... More

Hodge metric completion of the moduli space of Calabi-Yau manifoldsMay 01 2013Sep 05 2016In this paper, it is proved that the Hodge metric completion of the moduli space of polarized and marked Calabi-Yau manifolds, i.e. the Torelli space, is a complex affine manifold. As applications we prove that the period map from the Torelli space and ... More

Curvatures of direct image sheaves of vector bundles and applications IMar 11 2013Oct 12 2013Let $p:\sXS$ be a proper K\"ahler fibration and $\sE\sX$ a Hermitian holomorphic vector bundle. As motivated by the work of Berndtsson(\cite{Berndtsson09a}), by using basic Hodge theory, we derive several general curvature formulas for the direct image ... More

Rate Adaptive Coded Digital Phase ModulationAug 01 2018In this paper, rate adaptive coded Digital Phase Modulation (DPM) schemes based on punctured ring convolutional codes are presented. We first present an upper bound on symbol error probability for punctured convolutional coded Continuous Phase Modulation ... More

Stratifications of algebras with two simple modulesOct 13 2013Jun 13 2014Let $A$ be a finite-dimensional algebra with two simple modules. It is shown that if the derived category of $A$ admits a stratification with simple factors being the base field $k$, then $A$ is derived equivalent to a quasi-hereditary algebra. As a consequence, ... More

Examples of finite dimensional algebras which do not satisfy the derived Jordan--Hölder propertyApr 03 2017We construct a matrix algebra $\Lambda(A,B)$ from two given finite dimensional elementary algebras $A$ and $B$ and give some sufficient conditions on $A$ and $B$ under which the derived Jordan--H\"older property (DJHP) fails for $\Lambda(A,B)$. This provides ... More

Genie Tree and Degrees of Freedom of the Symmetric MIMO Interfering Broadcast ChannelSep 26 2013May 26 2016In this paper, we study the information theoretic maximal degrees of freedom (DoF) for the symmetric multi-input-multi-output (MIMO) interfering broadcast channel (IBC) with arbitrary antenna configurations. For the G-cell K-user MXN MIMO-IBC network, ... More

Energy Partition between Energetic Electrons and Turbulent Magnetic Field in Supernova Remnant RX J1713.7-3946Jun 19 2013Current observations of supernova remnant (SNR) RX J1713.7-3946 favor the leptonic scenario for the TeV emission, where the radio to X-ray emission is produced via the synchrotron process and the $\gamma$-ray emission is produced via the inverse Comptonization ... More

Caching Policy Toward Maximal Success Probability and Area Spectral Efficiency of Cache-enabled HetNetsAug 12 2016In this paper, we investigate the optimal caching policy respectively maximizing the success probability and area spectral efficiency (ASE) in a cache-enabled heterogeneous network (HetNet) where a tier of multi-antenna macro base stations (MBSs) is overlaid ... More

Minimax Analysis of Active LearningOct 03 2014This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular, under the noise ... More

Selection by Partitioning the Solution PathsJun 23 2016The performances of penalized likelihood approaches profoundly depend on the selection of the tuning parameter; however there has not been a common agreement on the criterion for choosing the tuning parameter. Moreover, penalized likelihood estimation ... More

Phonon Transport in Amorphous-Coated Nanowires: an Atomistic Green Function ApproachOct 15 2003An approach is presented for the atomistic study of phonon transport in real dielectric nanowires via Green functions. The formalism is applied to investigate the phonon flow through nanowires coated by an amorphous material. Examples for a simple model ... More

Optimal Content Placement for Offloading in Cache-enabled Heterogeneous Wireless NetworksApr 12 2016Caching at base stations (BSs) is a promising way to offload traffic and eliminate backhaul bottleneck in heterogeneous networks (HetNets). In this paper, we investigate the optimal content placement maximizing the successful offloading probability in ... More

Penalized regression adjusted causal effect estimates in high dimensional randomized experimentsSep 24 2018Regression adjustments are often considered by investigators to improve the estimation efficiency of causal effect in randomized experiments when there exists many pre-experiment covariates. In this paper, we provide conditions that guarantee the penalized ... More

Boundedness of the Images of Period MapsDec 09 2014Sep 03 2015We prove a conjecture of Griffiths on simultaneous normalization of all periods which asserts that the image of the lifted period map on the universal cover lies in a bounded domain in complex Euclidean space.

On Noisy Negative Curvature Descent: Competing with Gradient Descent for Faster Non-convex OptimizationSep 25 2017Oct 01 2017The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality). In this paper, we propose to further reduce the number of Hessian-vector ... More

Geometry of Hermitian manifoldsOct 31 2010Nov 13 2010On Hermitian manifolds, the second Ricci curvature tensors of various metric connections are closely related to the geometry of Hermitian manifolds. By refining the Bochner formulas for any Hermitian complex vector bundle (Riemannain real vector bundle) ... More

Contextual Aware Joint Probability Model Towards Question Answering SystemApr 17 2019In this paper, we address the question answering challenge with the SQuAD 2.0 dataset. We design a model architecture which leverages BERT's capability of context-aware word embeddings and BiDAF's context interactive exploration mechanism. By integrating ... More

Cross-Graph Learning of Multi-Relational AssociationsMay 06 2016Cross-graph Relational Learning (CGRL) refers to the problem of predicting the strengths or labels of multi-relational tuples of heterogeneous object types, through the joint inference over multiple graphs which specify the internal connections among ... More

Comprehend DeepWalk as Matrix FactorizationJan 02 2015Word2vec, as an efficient tool for learning vector representation of words has shown its effectiveness in many natural language processing tasks. Mikolov et al. issued Skip-Gram and Negative Sampling model for developing this toolbox. Perozzi et al. introduced ... More

Two and three electrons on a sphere: A generalized Thomson problemJun 21 2018Generalizing the classical Thomson problem to the quantum regime provides an ideal model to explore the underlying physics regarding electron correlations. In this work, we systematically investigate the combined effects of the geometry of the substrate ... More

Caching Policy Toward Maximal Success Probability and Area Spectral Efficiency of Cache-enabled HetNetsAug 12 2016Apr 28 2017In this paper, we investigate the optimal caching policy respectively maximizing the success probability and area spectral efficiency (ASE) in a cache-enabled heterogeneous network (HetNet) where a tier of multi-antenna macro base stations (MBSs) is overlaid ... More

Caching at Base Stations with Heterogeneous User Demands and Spatial LocalityOct 27 2017Oct 26 2018Existing proactive caching policies are designed by assuming that all users request contents with identical activity level at uniformly-distributed or known locations, among which most of the policies are optimized by assuming that user preference is ... More

One-loop effects on top pair production in the littlest Higgs model with T-parity at the LHCOct 18 2012Aug 27 2013In this work, we systematically investigate the one-loop corrections to $t\bar{t}$ production in the littlest Higgs model with T-parity (LHT) at the LHC for $\sqrt{s}=8,14$ TeV. We focus on the effects of LHT particles on $t\bar{t}$ cross section, polarization ... More

Boundedness of the images of period maps and applicationsJun 30 2015Aug 22 2016We prove a conjecture of Griffiths on simultaneous normalization of all periods which asserts that the image of the lifted period map on the universal cover lies in a bounded domain in a complex Euclidean space. As an application we prove that the Teichm\"uller ... More

A Note on Property Testing Sum of Squares and Multivariate Polynomial InterpolationSep 10 2017In this paper, we investigate property testing whether or not a degree d multivariate poly- nomial is a sum of squares or is far from a sum of squares. We show that if we require that the property tester always accepts YES instances and uses random samples, ... More

Recognizing Implicit Discourse Relations via Repeated Reading: Neural Networks with Multi-Level AttentionSep 20 2016Recognizing implicit discourse relations is a challenging but important task in the field of Natural Language Processing. For such a complex text processing task, different from previous studies, we argue that it is necessary to repeatedly read the arguments ... More

A New Fluid Dynamical Model Coupling Heat with Application to Interior SeparationsJun 23 2016Dec 08 2016Based on the Boussinesq equations and the equation of state, a new fluid dynamical model coupling heat is established. Furthermore, the conditions for interior separation, which are determined by the initial conditions, are obtained. This result is derived ... More

The initial boundary value problem for the Boltzmann equation with soft potentialApr 19 2016Aug 02 2016Boundary effects are central to the dynamics of the dilute particles governed by Boltzmann equation. In this paper, we study both the diffuse reflection and the specular reflection boundary value problems for Boltzmann equation with soft potential, in ... More

Hermitian Harmonic maps and non-degenerate curvaturesFeb 15 2014Mar 26 2014In this paper, we study the existence of various harmonic maps from Hermitian manifolds to Kaehler, Hermitian and Riemannian manifolds respectively. By using refined Bochner formulas on Hermitian (possibly non-Kaehler) manifolds, we derive new rigidity ... More

Position Estimation of Camera Based on Unsupervised LearningMay 05 2018It is an exciting task to recover the scene's 3d-structure and camera pose from the video sequence. Most of the current solutions divide it into two parts, monocular depth recovery and camera pose estimation. The monocular depth recovery is often studied ... More

A Faster Local Algorithm for Detecting Bounded-Size Cuts with Applications to Higher-Connectivity ProblemsApr 17 2019Consider the following "local" cut-detection problem in a directed graph: We are given a starting vertex $s$ and need to detect whether there is a cut with at most $k$ edges crossing the cut such that the side of the cut containing $s$ has at most $\Delta$ ... More

A High Fraction of Double-peaked Narrow Emission Lines in Powerful Active Galactic NucleiJun 21 2016Aug 09 2016One percent of redshift z~0.1 Active Galactic Nuclei (AGNs) show velocity splitting of a few hundred km/s in the narrow emission lines in spatially integrated spectra. Such line profiles have been found to arise from the bulk motion of ionized gas clouds ... More

On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels with Constant CoefficientsJul 06 2012Mar 05 2013In this paper, we analyze the feasibility of linear interference alignment (IA) for multi-input-multi-output (MIMO) interference broadcast channel (MIMO-IBC) with constant coefficients. We pose and prove the necessary conditions of linear IA feasibility ... More

Flexible, solid electrolyte-based lithium battery composed of LiFePO4 cathode and Li4Ti5O10 anode for applications in smart textilesJun 21 2011Nov 28 2011Here we report fabrication of flexible and stretchable battery composed of strain free LiFePO4 cathode, Li4Ti5O10 anode and a solid poly ethylene oxide (PEO) electrolyte as a separator layer. The battery is developed in a view of smart textile applications. ... More

A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional ModelsDec 30 2014Jan 21 2015We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis ... More

Parametric or nonparametric? A parametricness index for model selectionFeb 02 2012In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional (parametric scenario); ... More

A Learning-based Approach to Joint Content Caching and Recommendation at Base StationsJan 22 2018Oct 26 2018Recommendation system is able to shape user demands, which can be used for boosting caching gain. In this paper, we jointly optimize content caching and recommendation at base stations to maximize the caching gain meanwhile not compromising the user preference. ... More

Cache-enabled Heterogeneous Cellular Networks: Comparison and TradeoffsFeb 26 2016Feb 29 2016Caching popular contents at base stations (BSs) is a promising way to unleash the potential of cellular heterogeneous networks (HetNets), where backhaul has become a bottleneck. In this paper, we compare a cache-enabled HetNet where a tier of multi-antenna ... More

Power System Simulation Using the Differential Transformation MethodFeb 12 2018This paper proposes a new semi-analytical approach for online time-domain power system simulation. The approach applies the differential transformation method (DTM) to the power system differential equation model to offline derive a semi-analytical solution ... More

Solving Power System Differential Algebraic Equations Using Differential TransformationMar 03 2019This paper proposes a novel non-iterative approach for solving power system nonlinear differential algebraic equations (DAEs) based on Differential Transformation. The approach has three steps. First, it applies Differential Transformation to transform ... More

Moduli spaces as ball quotients I, local theoryOct 25 2018We give a Hodge theoretic criterion to characterize locally the period domains of certain projective manifolds to be complex balls.

BubGAN: Bubble Generative Adversarial Networks for Synthesizing Realistic Bubbly Flow ImagesSep 07 2018Bubble segmentation and size detection algorithms have been developed in recent years for their high efficiency and accuracy in measuring bubbly two-phase flows. In this work, we proposed an architecture called bubble generative adversarial networks (BubGAN) ... More

Minimal complex surfaces with Levi-Civita Ricci-flat metricsJun 05 2017This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli-Chern class on compact complex manifolds, and proved that the $(1,1)$ curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which ... More

Ricci Curvatures on Hermitian manifoldsApr 09 2014May 21 2016In this paper, we introduce the first Aeppli-Chern class for complex manifolds and show that the $(1,1)$- component of the curvature $2$-form of the Levi-Civita connection on the anti-canonical line bundle represents this class. We systematically investigate ... More

Characterizations of BMO Associated with Gauss Measures via Commutators of Local Fractional IntegralsMar 23 2009Mar 28 2009Let $d\gamma(x)\equiv\pi^{-n/2}e^{-|x|^2}dx$ for all $x\in{\mathbb R}^n$ be the Gauss measure on ${\mathbb R}^n$. In this paper, the authors establish the characterizations of the space BMO$(\gamma)$ of Mauceri and Meda via commutators of either local ... More

Implanting Rational Knowledge into Distributed Representation at Morpheme LevelNov 26 2018Previously, researchers paid no attention to the creation of unambiguous morpheme embeddings independent from the corpus, while such information plays an important role in expressing the exact meanings of words for parataxis languages like Chinese. In ... More

Exact solutions of nonlinear PDE, nonlinear transformations and reduction nonlinear PDE to a quadratureAug 16 2001A method to construct the exact solution of the PDE is presents, which combines the two kind methods(the nonlinear transformation and RQ(Reduction the PDE to a Quadrature problem) method).The nonlinear diffusion equation is chosen to illustrate the method ... More

Universal Correlation between Critical Temperature of Superconductivity and band structure featuresNov 29 2018Dec 14 2018The critical temperature (${T}_\text{c}$) of superconductors varies a lot. The factors governing the ${T}_\text{c}$ may hold key clues to understand the nature of the superconductivity. Thereby, ${T}_\text{c}$-involved correlations, such as Matthias laws, ... More

Analytic Constructions of General n-Qubit Controlled GatesAug 24 2007In this Letter, we present two analytic expressions that most generally simulate $n$-qubit controlled-$U$ gates with standard one-qubit gates and CNOT gates using exponential and polynomial complexity respectively. Explicit circuits and general expressions ... More

Secure Federated Transfer LearningDec 08 2018Machine learning relies on the availability of a vast amount of data for training. However, in reality, most data are scattered across different organizations and cannot be easily integrated under many legal and practical constraints. In this paper, we ... More

Rare Higgs three body decay induced by top-Higgs FCNC coupling in the littlest Higgs Model with T-parityMar 14 2016Feb 18 2017Motivated by the search for flavor-changing neutral current (FCNC) top quark decays at the LHC, we calculate rare Higgs three body decay $H\rightarrow Wbc$ induced by top-Higgs FCNC coupling in the littlest Higgs model with T-parity(LHT). We find that ... More

Asymptotic behavior for 3D stochastic Navier-Stokes equations with memory in unbounded domainsMar 18 2019Mar 31 2019In this paper, we investigate the dynamics of three dimensional stochastic Navier-Stokes equations with memory in unbounded domains. More specifically, we obtain the uniform in time estimates for both $\mathcal{H}$ solutions and $\mathcal{H}^1$ solutions ... More

Rare Higgs three body decay induced by top-Higgs FCNC coupling in the littlest Higgs Model with T-parityMar 14 2016Motivated by the search for flavor-changing neutral current (FCNC) top quark decays at the LHC, we calculate rare Higgs three body decay $H\rightarrow Wbc$ induced by top-Higgs FCNC coupling in the littlest Higgs model with T-parity(LHT). We find that ... More

Revisiting Optimal Power Control: its Dual Effect on SNR and ContentionSep 15 2013In this paper we study a transmission power tune problem with densely deployed 802.11 Wireless Local Area Networks (WLANs). While previous papers emphasize on tuning transmission power with either PHY or MAC layer separately, optimally setting each Access ... More

Generalized Toda mechanics associated with classical Lie algebras and their reductionsJun 10 2003For any classical Lie algebra $g$, we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers $(m,n)$. The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson brackets are provided, ... More

Asymptotic behavior for 3D stochastic Navier-Stokes equations with memory in unbounded domainsMar 18 2019In this paper, we investigate the dynamics of three dimensional stochastic Navier-Stokes equations with memory in unbounded domains. More specifically, we obtain the uniform in time estimates for both $\mathcal{H}$ solutions and $\mathcal{H}^1$ solutions ... More

Duality and Recycling Computing in Quantum ComputersAug 15 2007Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static ... More

Unexpected universality in static and dynamic avalanchesFeb 23 2010We find that some equilibrium systems and their non-equilibrium counterparts actually show the same jerky response or avalanche behavior on many scales in response to slowly changing external conditions. In other words, their static and dynamic avalanches ... More

Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulatorsAug 15 2014We propose a general framework of nonlinear optics induced by non-Abelian Berry curvature in time-reversal-invariant (TRI) insulators. We find that the third-order response of a TRI insulator under optical and terahertz light fields is directly related ... More

Berry phases of quantum trajectories in semiconductors under strong terahertz fieldsNov 13 2012Quantum evolution of particles under strong fields can be essentially captured by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integrals. The quantum trajectories are the key concept to ... More

Irreducible Projective Representations and Their Physical ApplicationsMay 19 2016Dec 16 2017An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and modified Schur's ... More

On Picard Type Theorems and Entire Solutions of Differential EquationsSep 14 2018We give a connection between the Picard type theorem of Polya-Saxer-Milliox and characterization of entire solutions of a differential equation and then their higher dimensional extensions, which leads further results on both (ordinary and partial) differential ... More

Ultra-high mechanical stretchability and controllable topological phase transitions in two-dimensional arsenicJan 18 2015The mechanical stretchability is the magnitude of strain which a material can suffer before it breaks. Materials with high mechanical stretchability, which can reversibly withstand extreme mechanical deformation and cover arbitrary surfaces and movable ... More

Deleting a marked item from an unsorted database with a single queryOct 17 2007In this Letter we present a quantum deletion algorithm that deletes a marked state from an unsorted database of $N$ items with only a single query. This algorithm achieves exponential speedup compared with classical algorithm where O(N) number of query ... More

Revealing the intricate effect of collaboration on innovationSep 09 2013We study the Japan and U.S. patent records of several decades to demonstrate the effect of collaboration on innovation. We find that statistically inventor teams slightly outperform solo inventors while company teams perform equally well as solo companies. ... More

Quantum many-body theory of qubit decoherence in a finite-size spin bathMay 31 2008Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. We develop a cluster-correlation expansion (CCE) theory for the spin bath dynamics relevant to the qubit decoherence problem. A cluster correlation ... More

Quantum many-body theory of qubit decoherence in a finite-size spin bath. II. Ensemble dynamicsFeb 18 2009Decoherence of a center spin or qubit in a spin bath is essentially determined by the many-body bath evolution. The bath dynamics can start either from a pure state or, more generally, from a statistical ensemble. In the preceding article [W. Yang and ... More

Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decayApr 30 2016Motivated by the paper by D. Gerard-Varet and E. Dormy [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal variable, and the recent study of well-posedness on the Prandtl equations ... More

Direct calculation of the linear thermal expansion coefficients of MoS2 via symmetry-preserving deformationsAug 30 2016Using density-functional perturbation theory and the Gr\"uneisen formalism, we directly calculate the linear thermal expansion coefficients (TECs) of a hexagonal bulk system MoS2 in the crystallographic $a$ and $c$ directions. The TEC calculation depends ... More

Lyapunov instabilities of Lennard-Jones fluidsApr 14 2004Recent work on many particle system reveals the existence of regular collective perturbations corresponding to the smallest positive Lyapunov exponents (LEs), called hydrodynamic Lyapunov modes. Until now, however, these modes are only found for hard ... More

Robust Variable and Interaction Selection for High-Dimensional Classification via Logistic RegressionNov 26 2016Discriminant analysis and logistic regression are fundamental tools for classification problems. Quadratic discriminant analysis has the ability to exploit interaction effects of predictors, but the selection of interaction terms is non-trivial and the ... More

Imaginary geometric phases of quantum trajectoriesJun 11 2014A quantum object can accumulate a geometric phase when it is driven along a trajectory in a parameterized state space with non-trivial gauge structures. Inherent to quantum evolutions, a system can not only accumulate a quantum phase but may also experience ... More