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An Efficient Sufficient Dimension Reduction Method for Identifying Genetic Variants of Clinical SignificanceJan 15 2013Fast and cheaper next generation sequencing technologies will generate unprecedentedly massive and highly-dimensional genomic and epigenomic variation data. In the near future, a routine part of medical record will include the sequenced genomes. A fundamental ... More

Magnetic extraction of energy from accretion disc around a rotating black holeMay 05 2004May 07 2004An analytical expression for the disc power is derived based on an equivalent circuit in black hole (BH) magnetosphere with a mapping relation between the radial coordinate of the disc and that of unknown astrophysical load. It turns out that this disc ... More

Emergent topology and symmetry-breaking order in correlated quench dynamicsMar 21 2019Quenching a quantum system involves three basic ingredients: the initial phase, the post-quench target phase, and the non-equilibrium dynamics which carries the information of the former two. Here we propose to identify both the topology and symmetry-breaking ... More

All-optical production of ${}^6\textrm{Li}$ molecular BEC in excited hyperfine levelsSep 17 2018We present an all-optical method for achieving molecular Bose-Einstein condensates of ${}^6\textrm{Li}$. We demonstrate this with mixtures in the lowest two (1-2), and second lowest two (2-3) hyperfine states. For the 1-2 mixture, we can achieve condensate ... More

Observation of nodal-line semimetal with ultracold fermions in an optical latticeAug 22 2018Aug 28 2018Realization and observation of topological phases beyond two-dimension (2D) have been an open challenge for ultracold atoms. Here we realize for the first time a three-dimensional (3D) nodal-line semimetal phase for ultracold fermions with novel spin-orbit ... More

Topological indexes in symmetry preserving dynamicsFeb 08 2018The quench dynamics of topological phases have received intensive investigations in recent years. In this work, we prove exactly that the topological invariants for both $\mathbb{Z}$ and $\mathbb{Z}_2$ indexes are independent of time in symmetry preserving ... More

CO~($J = 1-0$) Observations of a Filamentary Molecular Cloud in the Galactic Region Centered at $l = 150\arcdeg, b = 3.5\arcdeg$Mar 04 2017Mar 24 2017We present large-field (4.25~$\times$~3.75 deg$^2$) mapping observations toward the Galactic region centered at $l = 150\arcdeg, b = 3.5\arcdeg$ in the $J = 1-0$ emission line of CO isotopologues ($^{12}$CO, $^{13}$CO, and C$^{18}$O), using the 13.7 m ... More

Observation of symmetry-protected topological band with ultracold fermionsJun 02 2017Aug 29 2018Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal invariant topological ... More

Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein CondensatesNov 24 2015Cold atoms with laser-induced spin-orbit (SO) interactions provide intriguing new platforms to explore novel quantum physics beyond natural conditions of solids. Recent experiments demonstrated the one-dimensional (1D) SO coupling for boson and fermion ... More

High Controllable and Robust 2D Spin-Orbit Coupling for Quantum GasesOct 02 2017Nov 07 2018We report the realization of a robust and highly controllable two-dimensional (2D) spin-orbit (SO) coupling with topological non-trivial band structure. By applying a retro-reflected 2D optical lattice, phase tunable Raman couplings are formed into the ... More

Test of Equivalence Principle at $10^{-8}$ Level by a Dual-species Double-diffraction Raman Atom InterferometerMar 02 2015We report an improved test of the weak equivalence principle by using a simultaneous $^{85}$Rb-$^{87}$Rb dual-species atom interferometer. We propose and implement a four-wave double-diffraction Raman transition scheme for the interferometer, and demonstrate ... More

On Hopf algebras over basic Hopf algebras of dimension 24Sep 11 2018We determine finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero, whose Hopf coradical is isomorphic to a non-pointed basic Hopf algebra of dimension $24$ and the infinitesimal braidings are simple objects, under ... More

Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebraJan 18 2018May 15 2018We classify finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradcial is isomorphic to the smallest non-pointed basic Hopf algebra, under the assumption that the diagrams are strictly graded. In particular, ... More

Improving Twitter Sentiment Classification via Multi-Level Sentiment-Enriched Word EmbeddingsNov 01 2016Most of existing work learn sentiment-specific word representation for improving Twitter sentiment classification, which encoded both n-gram and distant supervised tweet sentiment information in learning process. They assume all words within a tweet have ... More

Localized Asymmetric Atomic Matter Waves in Two-Component Bose-Einstein Condensates Coupled with Two Photon Microwave FieldMar 01 2007We investigate localized atomic matter waves in two-component Bose-Einstein condensates coupled by the two photon microwave field. Interestingly, the oscillations of localized atomic matter waves will gradually decay and finally become non-oscillating ... More

Berry-Phase Induced Dynamical Instability and Minimum Conductivity in GrapheneFeb 02 2007Single-layer carbon, or graphene, demonstrates amazing transport properties, such as the minimum conductivity near $\frac{4e^2}{h}$ independent of shapes and mobility of samples. This indicates there exist some unusual effects due to specific Dirac dispersion ... More

A weak second term identity of the regularized Siegel-Weil formula for unitary groupsMay 28 2012Mar 25 2013Following W.T.Gan and S.Takeda, we obtain a weak second term identity of the regularized Siegel-Weil formula for the unitary dual pair $(U(n,n),U(V))$, where $V$ is a split hermitian space of dimension $2r$ with $r+1 \leq n \leq 2r-1$. As an application, ... More

The number of simultaneous core partitionsSep 24 2014Oct 12 2014Amdeberhan conjectured that the number of $(t,t+1, t+2)$-core partitions is $\sum_{0\leq k\leq [\frac{t}{2}]}\frac{1}{k+1}\binom{t}{2k}\binom{2k}{k}$. In this paper, we obtain the generating function of the numbers $f_t$ of $(t, t + 1, ..., t + p)$-core ... More

Finite Groups Whose Character Graphs Associated with Codegrees Have No TrianglesAug 28 2015Mar 19 2017Motivated by the Problem $164$ proposed by Y. Berkovich and E. Zhmud' in their book "Characters of finite groups, Part $1$", we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based on a new kind ... More

Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identitiesJul 26 2016In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family partitions. We give $q$-difference equations for the related generating function ... More

The weight distributions of a class of cyclic codesNov 14 2011Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special case. We make ... More

The graph, range and level set singularity spectra of $b$-adic independent cascade functionNov 06 2009Jan 25 2010With the "iso-H\"older" sets of a function we naturally associate subsets of the graph, range and level set of the function. We compute the associated singularity spectra for a class of statistically self-similar multifractal functions, namely the $b$-adic ... More

A character of Siegel modular group of level 2 from theta constantsJan 10 2017Mar 23 2017Given a characteristic, we define a character of the Siegel modular group of level 2, the computations of their values are also obtained. By using our theorems, some key theorems of Igusa [1] can be recovered.

On positive proportion of rank zero twists of elliptic curves over QNov 20 2013Extending the idea of \cite{dab2} and using the 2-descent method, we provide three general families of elliptic curves over Q such that a positive proportion of prime-twists of such elliptic curves have rank zero simultaneously.

On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley propertyDec 03 2017Jul 02 2018Let $\mathds{k}$ be an algebraically closed field of characteristic zero. We determine all finite-dimensional Hopf algebras over $\mathds{k}$ whose Hopf coradical is isomorphic to the unique $12$-dimensional Hopf algebra $\mathcal{C}$ without the dual ... More

Pointed $p^2q$-dimensional Hopf algebras in positive characteristicApr 30 2017May 16 2017Let $\K$ be an algebraically closed field of positive characteristic $p$. We mainly classify pointed Hopf algebras over $\K$ of dimension $p^2q$, $pq^2$ and $pqr$ where $p,q,r$ are distinct prime numbers. We obtain a complete classification of such Hopf ... More

Edge state transmission, duality relation and its implication to measurementsMar 12 1998The duality in the Chalker-Coddington network model is examined. We are able to write down a duality relation for the edge state transmission coefficient, but only for a specific symmetric Hall geometry. Looking for broader implication of the duality, ... More

Is the GW150914-GBM really associated with the GW150914?May 18 2016Finding the electromagnetic (EM) counterpart is critically important for a gravitational wave event. Although many efforts have been made to search for the purported EM counterpart of GW150914, the first gravitational wave event detected by LIGO, only ... More

A trigonometric integrator for the constrained ring polymer Hamiltonian dynamicsNov 27 2014Jan 04 2016A class of trigonometric integrator is proposed for the constrained ring polymer Hamiltonian dynamics, arising from the path integral molecular dynamics. The integrator is formulated by the composition of flows, thereby integrating the Cartesian equations ... More

The fundamental theorem of affine geometry in $(L^0)^n$Dec 20 2018Let $L^0$ be the algebra of equivalence classes of real valued random variables on a probability space. For each integer $n\geq 2$, we consider $(L^0)^n$--the $n$-ary Cartesian power of $L^0$--as a free $L^0$-module and establish the fundamental theorem ... More

Vibration Induced Non-adiabatic Geometric Phase and Energy Uncertainty of Fermions in GrapheneDec 29 2007We investigate geometric phase of fermion states under relative vibrations of two sublattices in graphene by solving time-dependent Sch\"{o}dinger equation using Floquet scheme. In a period of vibration the fermions acquire different geometric phases ... More

On cyclic codes of composite length and the minimal distanceMar 31 2017In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and dimension ... More

The Graph and Range Singularity Spectra of Random Wavelet Series built from Gibbs measuresJan 25 2010We consider multifractal random wavelet series built from Gibbs measures, and study the singularity spectra associated with the graph and range of these functions restricted to their iso-H\"older sets. To obtain these singularity spectra, we use a family ... More

The weight distributions of a class of cyclic codes IIIOct 10 2012Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a problem of evaluating ... More

The weight distributions of a class of cyclic codes IIOct 10 2012Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we use the method developed before to solve one more special case. We make extensive use of standard tools in number ... More

A Siegel-Weil formula for $(U(1,1), U(V))$ over a function field with $\dim V$ greater than 2Dec 16 2017We establish a Siegel-Weil formula for the dual pair $(U(1,1), U(V))$ over a function field, where $V$ is a hermitian space of dimension greater than 2.

Precision Measurement of the Spin-dependent Asymmetry in the Threshold Region of $^3\vec{\mathrm{He}}(\vec{e},e')$Oct 12 2001We present the first precision measurement of the spin-dependent asymmetry in the threshold region of $^3\vec{\rm He}(\vec{e},e')$ at $Q^2$-values of 0.1 and 0.2 (GeV/c)$^2$. The agreement between the data and non-relativistic Faddeev calculations which ... More

Function Estimation via ReconstructionMay 25 2018This paper introduces an interpolation-based method, called the reconstruction approach, for function estimation in nonparametric models. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction ... More

Better Solution Principle: A Facet of Concordance between Optimization and StatisticsFeb 16 2014Jan 16 2019Many statistical methods require solutions to optimization problems. When the global solution is hard to attain, statisticians always use the better if there are two solutions for chosen, where the word "better" is understood in the sense of optimization. ... More

On best subset regressionDec 05 2011Dec 04 2012In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We prove that ... More

Local optimization-based statistical inferenceFeb 02 2015Apr 20 2015This paper introduces a local optimization-based approach to test statistical hypotheses and to construct confidence intervals. This approach can be viewed as an extension of bootstrap, and yields asymptotically valid tests and confidence intervals as ... More

Why does bulk boundary correspondence fail in some non-hermitian topological modelsMay 17 2017Bulk boundary correspondence is crucial to topological insulator as it associates the boundary states (with zero energy, chiral or helical) to topological numbers defined in bulk. The application of this correspondence needs a prerequisite condition which ... More

An explicit multistep method for the Wigner problemNov 25 2014Feb 11 2015An explicit multistep scheme is proposed for solving the initial-value Wigner problem. In this scheme, the integrated form of the Wigner equation is approximated by extrapolation or interpolation polynomials on backwards characteristics, and the pseudo-differential ... More

Fano resonances can provide two criteria to distinguish Majorana bound states from other candidates in experimentsDec 14 2015There are still debates on whether the observed zero energy peak in the experiment by Stevan {\it et al.} [Science 346, 602(2014)] reveals the existence of the long pursuing Majorana bound states (MBS). we propose that, by mounting two scanning tunneling ... More

The Beylkin-Cramer Summation Rule and A New Fast Algorithm of Cosmic Statistics for Large Data SetsDec 07 2005Oct 11 2006Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and operators within the ... More

Anderson localization of electron states in graphene in different types of disorderDec 29 2007Anderson localization of electron states on graphene lattice with diagonal and off-diagonal (OD) disorder in the absence of magnetic field is investigated by using the standard finite-size scaling analysis. In the presence of diagonal disorder all states ... More

A representation theorem of the dual of the Orlicz heart of a random normed moduleNov 03 2015In this paper, we introduce the notion of the Orlicz space and the Orlicz heart for a random normed module $E$, and give a representation theorem which identify the dual of the Orlicz heart of $E$ with the Orlicz space generated by the random conjugate ... 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

Probing the Electron States and Metal-Insulator Transition Mechanisms in Atomically Thin MoS2 Based on Vertical HeterostructuresJul 21 2014The metal-insulator transition (MIT) is one of the remarkable electrical transport properties of atomically thin molybdenum disulphide (MoS2). Although the theory of electron-electron interactions has been used in modeling the MIT phenomena in MoS2, the ... More

Three-body system of $ππΣ_c$Sep 27 2016The existence of near-threshold charmed baryon $\Lambda_c^+(2595)$ implies the pion and the lightest, isospin-$1$ charmed baryon $\Sigma_c$ interact very strongly at extremely low energies. Using the two-flavor version of heavy hadron chiral perturbation ... More

Forbidding intersection patterns between layers of the cubeNov 22 2013Mar 20 2015A family ${\mathcal A} \subset {\mathcal P} [n]$ is said to be an antichain if $A \not \subset B$ for all distinct $A,B \in {\mathcal A}$. A classic result of Sperner shows that such families satisfy $|{\mathcal A}| \leq \binom {n}{\lfloor n/2\rfloor}$, ... More

Robust Strictly Positive Real Synthesis for Polynomial Families of Arbitrary OrderNov 01 2002For any two $n$-$th$ order polynomials $a(s)$ and $b(s),$ the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial $c(s)$ such that $c(s)/a(s)$ and $c(s)/b(s)$ are both strictly positive real.

Estimates at or beyond endpoint in harmonic analysis: Bochner-Riesz means and spherical meansMar 03 2011We introduce some new functions spaces to investigate some problems at or beyond endpoint. First, we prove that Bochner-Riesz means $B_R^\lambda$ are bounded from some subspaces of $L^p_{|x|^\alpha}$ to $L^p_{|x|^\alpha}$ for $ \frac{n-1}{2(n+1)}<\lambda ... More

Parisian ruin of Brownian motion risk model over an infinite-time horizonFeb 20 2017Let $B(t), t\in \mathbb{R}$ be a standard Brownian motion. In this paper, we derive the exact asymptotics of the probability of Parisian ruin on infinite time horizon for the following risk process \begin{align}\label{Rudef} R_u^{\delta}(t)=e^{\delta ... More

Extremes of multifractional Brownian motionNov 15 2017Let $B_{H}(t), t\geq [0,T], T\in(0,\infty)$ be the standard Multifractional Brownian Motion(mBm), in this contribution we are concerned with the exact asymptotics of \begin{eqnarray*} \mathbb{P}\left\{\sup_{t\in[0,T]}B_{H}(t)>u\right\} \end{eqnarray*} ... More

Extremes of $α(t)$-Locally stationary Gaussian processes with non-constant variancesJun 22 2016Aug 21 2016With motivation from K. D\c{e}bicki and P. Kisowski (2007), in this paper we derive the exact tail asymptotics of $\alpha(t)$-locally stationary Gaussian processes with non-constant variance functions. We show that some certain variance functions lead ... More

Estimation of Change-point ModelsMay 01 2018May 08 2018We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of observations. Motivated by this problem, in this contribution we first investigate the extremes of Gaussian fields with trend ... More

The effective dynamics of loop quantum $R^2$ cosmologyNov 20 2018The effective dynamics of loop quantum $f (R)$ cosmology in Jordan frame is considered by using the dynamical system method and numerical method. To make the analyze in detail, we focus on $R^2$ model since it is simple and favored from observations. ... More

Differentiation of IntegralsJul 08 2014No functions class for general measurable sets classes are known whose functions have the property of differentiability of integrals associated to such sets classes. In this paper,we give some subspaces of $L^s$ with $1<s<\infty$, whose functions are ... More

Convexity, translation invariance and subadditivity for $g$-expectations and related risk measuresJan 22 2008Under the continuous assumption on the generator $g$, Briand et al. [Electron. Comm. Probab. 5 (2000) 101--117] showed some connections between $g$ and the conditional $g$-expectation $({\mathcal{E}}_g[\cdot|{\mathcal{F}}_t])_{t\in[0,T]}$ and Rosazza ... More

Made-to-measure galaxy modelling utilising absorption line strength dataSep 06 2016We enhance the Syer & Tremaine made-to-measure (M2M) particle method of stellar dynamical modelling to model simultaneously both kinematic data and absorption line strength data thus creating a `chemo-M2M' modelling scheme. We apply the enhanced method ... More

Finite index subgroups of the modular group and their modular formsJul 23 2007Classically, congruence subgroups of the modular group, which can be described by congruence relations, play important roles in group theory and modular forms. In reality, the majority of finite index subgroups of the modular group are noncongruence. ... More

A note on the Brown-Erdős-Sós conjecture in finite groupsFeb 20 2019Mar 01 2019We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some $k$, or the entire multiplication table of a certain large abelian group, as a subgrid. As a ... More

Programming of Finite Element Methods in MATLABApr 14 2018We discuss how to implement the linear finite element method for solving the Poisson equation. We begin with the data structure to represent the triangulation and boundary conditions, introduce the sparse matrix, and then discuss the assembling process. ... More

Large unavoidable subtournamentsFeb 18 2015Mar 11 2016Let $D_k$ denote the tournament on $3k$ vertices consisting of three disjoint vertex classes $V_1, V_2$ and $V_3$ of size $k$, each of which is oriented as a transitive subtournament, and with edges directed from $V_1$ to $V_2$, from $V_2$ to $V_3$ and ... More

Edge Theorem for Multivariable SystemsNov 01 2002This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.

Robust Performance of A Class of Control SystemsFeb 23 2002Some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications ... More

Neutrino Factory R&DOct 17 2005Elegant experiments are being carried out, or are in preparation, to improve the precision with which the solar and atmospheric neutrino-oscillation parameters are known, and to attempt to make a first measurement of the small mixing angle $\theta_{13}$. ... More

Subharmonicity of conic Mabuchi's functional, IOct 31 2015Mar 01 2016The purpose of this paper is to generalize the convexity of Mabuchi's functional to the conic setting. We first established a frame to study conic cscK metrics, and then the conic Mabuchi functional was introduced in such a way that conic cscK metrics ... More

Extremes of $L^p$-norm of Vector-valued Gaussian processes with TrendJun 26 2017Jun 01 2018Let $\boldsymbol{X}(t)=(X_1(t),\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\left\|\boldsymbol{X}(t)\right\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector, have been ... More

Higher Spin Entanglement EntropyAug 06 2014Dec 04 2014In this paper, we develop a perturbation formulation to calculate the single interval higher spin R$\acute{e}$nyi and entanglement entropy for two dimensional conformal field theory with $\mathcal{W}_{\infty}(\lambda)$ symmetry. The system is at finite ... More

Search for Lorentz Violation using Short-Range Tests of GravityJul 24 2016Experimental tests of the newtonian inverse square law at short range, one at Indiana University and the other at the Huazhong University of Science and Technology, have been used to set limits on Lorentz violation in the pure gravity sector of the nonminimal ... More

Exponential decay and symmetry of solitary waves to the Degasperis-Procesi equationJan 20 2019Jan 24 2019We prove that solitary waves to the steady Degasperis-Procesi equation, if they exist, decay as $e^{-|x|}$ for large $|x|$ and are symmetric with respect to the unique symmetry axis located at the only crest (although only peaked solitary waves are allowed). ... More

Scalar-Invariant Test for High-Dimensional Regression CoefficientsFeb 16 2015This article is concerned with simultaneous tests on linear regression coefficients in high-dimensional settings. When the dimensionality is larger than the sample size, the classic $F$-test is not applicable since the sample covariance matrix is not ... More

QCD at high energy (experiments)Dec 04 2002Recent measurements of QCD interactions involving large momentum transfers are reviewed. The status of measurements of the strong coupling constant is summarised. Recent developments in the measurement and interpretation of deep inelastic scattering, ... More

H-infinity Performance of Interval SystemsNov 01 2002In this paper, we study $H^{\infty}$ performance of interval systems. We prove that, for an interval system, the maximal $H^{\infty}$ norm of its sensitivity function is achieved at twelve (out of sixteen) Kharitonov vertices.

Improved Results on Robust Stability of Multivariable Interval Control SystemsNov 01 2002For interval polynomial matrices, we identify the minimal testing set, whose stability can guarantee that of the whole uncertain set. Our results improve the conclusions given by Kamal and Dahleh.

Multigrid Methods for Constrained Minimization Problems and Application to Saddle Point ProblemsJan 15 2016The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace optimization method ... More

Robust Strictly Positive Real Synthesis for Convex Combination of Sixth-Order PolynomialsNov 01 2002For the two sixth-order polynomials $a(s)$ and $b(s),$ Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial $c(s)$ such that $c(s)/a(s)$ and $c(s)/b(s)$ are both strictly positive real. Our reasoning ... More

A Recipe for Construction of the Critical Vertices for Left-Sector Stability of Interval PolynomialsFeb 23 2002For the left-sector stability of interval polynomials, it suffices to check a subset of its vertex polynomials. This paper provides a recipe for construction of these critical vertices. Illustrative examples are presented.

Complete Solution to the General Robust Strictly Positive Real Synthesis Problem for Polynomial SegmentsOct 30 2002For any two n-th order polynomials a(s) and b(s), the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real.

Regularity of relativistic modelsMar 06 2018May 19 2018The electronic relativistic equation is one kind of relativistic equation with the Coulomb forces in the field. It is more general than the electronic schr\"odinger equation which has been analyzed by Harry Yserentant with the Pauli principle by Hardy ... More

A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential EquationsSep 02 2018In this work, we study solving (decoupled) forward-backward stochastic differential equations FBSDEs numerically using the regression trees. For the one-step scheme, we apply firstly the the general theta-discretization for the time-integrands and show ... More

On the Spectrum of weighted Laplacian operator and its application to uniqueness of Kähler Einstein metricsOct 31 2013Nov 08 2013The purpose of this paper is to provide a new proof of Bando-Mabuchi's uniqueness theorem of K\"ahler Einstein metrics on Fano manifolds, based on Chen's weak C^{1,1} geodesic without using any further regularities. Unlike the smooth case, the lack of ... More

The 90/10 phenomenon in directed signed social networksApr 14 2016We empirical study the signs' property in the directed signed social networks of Slashdot and Epinions by using an reshuffled approach. Through calculating the entropy $S_{out}$ and the giant component $G$, we find an interesting 90/10 phenomenon: each ... More

Polarized 3He(e,e'n) Asymmetries in Three Orthogonal MeasurementsSep 12 2012Asymmetry measurements were conducted in Jefferson Lab's experimental Hall A through electron scattering from a polarized $^3$He target in the quasi-elastic $^3\mathrm{He}(e,e'n)$ reaction. Measurements were made with the target polarized in the longitudinal ... More

Scattering Resonances of Convex Obstacles for general boundary conditionsJan 19 2014We study the distribution of resonances for smooth strictly convex obstacles under general boundary conditions. We show that under a pinched curvature condition for the boundary of the obstacle, the resonances are separated into cubic bands and the distribution ... More

Resonance-free Region in scattering by a strictly convex obstacleAug 27 2012Sep 01 2012We prove the existence of a resonance free region in scattering by a strictly convex obstacle with the Robin boundary condition. More precisely, we show that the scattering resonances lie below a cubic curve which is the same as in the case of the Neumann ... More

Equivalence of Weak Galerkin Methods and Virtual Element Methods for Elliptic EquationsMar 16 2015We propose a modification of the weak Galerkin methods and show its equivalence to a new version of virtual element methods. We also show the original weak Galerkin method is equivalent to the non-conforming virtual element method. As a consequence, ideas ... More

On co-dimension two defect operatorsNov 08 2016Conformal symmetry is broken by a flat or spherical defect operator $\mathcal{D}$. We show that this defect operator, may be identified as a pair of twist operators which are inserted at the tips of its causal diamond. Any $k-$point correlation function ... More

Equivalence of Weak Galerkin Methods and Virtual Element Methods for Elliptic EquationsMar 16 2015Apr 14 2018We propose a modification of the weak Galerkin methods and show its equivalence to a new version of virtual element methods. We also show the original weak Galerkin method is equivalent to the non-conforming virtual element method. As a consequence, ideas ... More

Index iteration theory for symplectic paths with applications to nonlinear Hamiltonian systemsApr 18 2003In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.

A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential EquationsSep 02 2018Mar 21 2019In this work, we study solving (decoupled) forward-backward stochastic differential equations (FBSDEs) numerically using the regression trees. Based on the general theta-discretization for the time-integrands, we show how to efficiently use regression ... More

Vortical Motions of Baryonic Gas in the Cosmic Web: Growth History and Scaling RelationAug 27 2015The vortical motions of the baryonic gas residing in large scale structures are investigated by cosmological hydrodynamic simulations. Proceeding in the formation of the cosmic web, the vortical motions of baryonic matter are pumped up by baroclinity ... More

Enhancement of coherent energy transfer by disorder and temperature in light harvesting processesAug 27 2012We investigate the influence of static disorder and thermal excitations on excitonic energy transport in the light-harvesting apparatus of photosynthetic systems by solving the Schr\"{o}dinger equation and taking into account the coherent hoppings of ... More

Continuous local time of a purely atomic immigration superprocess with dependent spatial motionFeb 07 2008A purely atomic immigration superprocess with dependent spatial motion in the space of tempered measures is constructed as the unique strong solution of a stochastic integral equation driven by Poisson processes based on the excursion law of a Feller ... More

Geometric coherence and quantum state discriminationJan 18 2018Sep 18 2018The operational meaning of coherence measure lies at very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to the minimum ... More

A Harnack inequality for fractional Laplace equations with lower order termsDec 29 2010We establish a Harnack inequality of fractional Laplace equations without imposing sign condition on the coefficient of zero order term via the Moser's iteration and John-Nirenberg inequality.

Operator-valued Triebel-Lizorkin spacesApr 05 2018This paper is devoted to the study of operator-valued Triebel-Lizorkin spaces. We develop some Fourier multiplier theorems for square functions as our main tool, and then study the operator-valued Triebel-Lizorkin spaces on $\mathbb{R}^d$. As in the classical ... More

Electron-electron interactions, quantum Coulomb gap, and dynamical scaling near integer quantum Hall transitionsOct 15 2001Mar 05 2002The effects of electron-electron interactions on the bulk tunneling density of states (TDOS) are studied near the integer quantum Hall transitions (IQHT). Taking into account the dynamical screening of the interactions in the critical conducting state, ... More