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Shimura varieties at level $Γ_1(p^\infty)$ and Galois representationsMar 31 2018Jul 25 2019We show that the compactly supported cohomology of certain $\mathrm{U}(n,n)$ or $\mathrm{Sp}(2n)$-Shimura varieties with $\Gamma_1(p^\infty)$-level vanishes above the middle degree. The only assumption is that we work over a CM field $F$ in which the ... More

Ramification of Hilbert eigenvarieties at classical pointsMay 14 2019Andreatta-Iovita-Pilloni constructed eigenvarieties for cuspidal Hilbert modular forms. The eigenvariety has a natural map to the weight space, called the weight map. At a classical point, we compute a lower bound of the dimension of the tangent space ... More

Linear Dynamics: Clustering without identificationAug 02 2019Clustering time series is a delicate task; varying lengths and temporal offsets obscure direct comparisons. A natural strategy is to learn a parametric model foreach time series and to cluster the model parameters rather than the sequences themselves. ... More

Influence Analysis in the BlogosphereDec 24 2012In this paper we analyze influence in the blogosphere. Recently, influence analysis has become an increasingly important research topic, as online communities, such as social networks and e-commerce sites, playing a more and more significant role in our ... More

A Hybrid Word-Character Approach to Abstractive SummarizationFeb 27 2018Sep 08 2018Automatic abstractive text summarization is an important and challenging research topic of natural language processing. Among many widely used languages, the Chinese language has a special property that a Chinese character contains rich information comparable ... More

Impact of Junction Depth and Abruptness on the Activation and the Leakage Current in Germanium n$^{+}$/p JunctionsMay 18 2017The phosphorous activation in Ge n$^{+}$/p junctions is compared in terms of junction depth, by using laser spike annealing at 860{\deg}C for 400$\mu$s. The reverse junction leakage is found to strongly depend on the abruptness of dopant profiles. A shallow ... More

An Application of Nash-Moser Theorem to Smooth Solutions of One-Dimensional Compressible Euler Equation with GravityAug 18 2012May 28 2013We study one-dimensional motions of polytropic gas governed by the compressible Euler equations. The problem on the half space under a constant gravity gives an equilibrium which has free boundary touching the vacuum and the linearized approximation at ... More

Color Aesthetics and Social Networks in Complete Tang Poems: Explorations and DiscoveriesNov 05 2015The Complete Tang Poems (CTP) is the most important source to study Tang poems. We look into CTP with computational tools from specific linguistic perspectives, including distributional semantics and collocational analysis. From such quantitative viewpoints, ... More

The prism manifold realization problemDec 15 2016The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in $S^3$. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds ... More

Inducing 3-component fermions in centrosymmetric system by breaking TRSSep 22 2017Recent researches show that by breaking inversion symmetry Dirac fermions can split into new fermions with 3-component. In this article, we demonstrate that Dirac fermions can also split into 3-component fermions with time reversal symmetry (TRS) breaking ... More

Hit Song Prediction for Pop Music by Siamese CNN with Ranking LossOct 30 2017A model for hit song prediction can be used in the pop music industry to identify emerging trends and potential artists or songs before they are marketed to the public. While most previous work formulates hit song prediction as a regression or classification ... More

Sleep Apnea Detection Based on Thoracic and Abdominal Movement Signals of Wearable Piezo-Electric BandsNov 22 2016Physiologically, the thoracic (THO) and abdominal (ABD) movement signals, captured using wearable piezo-electric bands, provide information about various types of apnea, including central sleep apnea (CSA) and obstructive sleep apnea (OSA). However, the ... More

Topological superconductor in quasi-one-dimensional Tl2-xMo6Se6Nov 02 2017We propose that the quasi-one-dimensional molybdenum selenide compound Tl2-xMo6Se6 is a time-reversal-invariant topological superconductor induced by inter-sublattice pairing, even in the absence of spin-orbit coupling (SOC). No noticeable change in superconductivity ... More

Systematic analysis for triple points in all magnetic symmorphic systems and symmetry-allowed coexistence of Dirac points and triple pointsApr 03 2018Apr 06 2018Similar to Weyl fermions, a recently discovered topological fermion "triple point" can be generated from the splitting of Dirac fermion while the system has inversion symmetry (IS) breaking or time reversal symmetry (TRS) breaking. Inducing triple points ... More

Tellurium substitution effect on superconductivity of the alpha-phase Iron SelenideAug 04 2008Aug 05 2008We have carried out a systematic study of the PbO-type compound FeSe_{1-x}Te_x (x = 0~1), where Te substitution effect on superconductivity is investigated. It is found that superconducting transition temperature reaches a maximum of Tc=15.2K at about ... More

Defect-induced exchange bias in a single SrRuO3 layerSep 28 2018Exchange bias stems from the interaction between different magnetic phases and therefore it generally occurs in magnetic multilayers. Here we present a large exchange bias in a single SrRuO3 layer induced by helium ion irradiation. When the fluence increases, ... More

Photoionization of Xe and Rn from the relativistic random-phase theoryApr 30 2018Feb 14 2019Photoionization cross section $\sigma_{n\kappa}$, asymmetry parameter $\beta_{n\kappa}$, and polarization parameters $\xi_{n\kappa}$, $\eta_{n\kappa}$, $\zeta_{n\kappa}$ of Xe and Rn are calculated in the fully relativistic formalism. To deal with the ... More

Hexagonal-to-Cubic Phase Transformation in GaN Nanowires by Ga+-ImplantationFeb 03 2004Hexagonal to cubic phase transformation is studied in focused ion beam assisted Ga+-implanted GaN nanowires. Optical photoluminescence and cathodoluminescence studies along with high-resolution transmission electron microscopic structural studies are ... More

Disordered Fe vacancies and superconductivity in potassium-intercalated iron selenide (K2-xFe4+ySe5)Feb 04 2015Feb 05 2015The parent compound of an unconventional superconductor must contain unusual correlated electronic and magnetic properties of its own. In the high-Tc potassium intercalated FeSe, there has been significant debate regarding what the exact parent compound ... More

Structural phase transition in TmxFe1-xSe0.85 (Tm = Mn and Cu) and its relation to superconductivityJul 23 2009In this letter, we report the results of detailed studies on Mn- and Cu-substitution to Fe-site of beta-FeSe, namely MnxFe1-xSe0.85 and CuxFe1-xSe0.85. The results show that with only 10 at% Cu-doping the compound becomes a Mott insulator. Detailed temperature ... More

Understanding the Mechanism of Deep Learning Framework for Lesion Detection in Pathological Images with Breast CancerMar 04 2019The computer-aided detection (CADe) systems are developed to assist pathologists in slide assessment, increasing diagnosis efficiency and reducing missing inspections. Many studies have shown such a CADe system with deep learning approaches outperforms ... More

CAPIR: Collaborative Action Planning with Intention RecognitionJun 26 2012We apply decision theoretic techniques to construct non-player characters that are able to assist a human player in collaborative games. The method is based on solving Markov decision processes, which can be difficult when the game state is described ... More

Searching Toward Pareto-Optimal Device-Aware Neural ArchitecturesAug 29 2018Aug 30 2018Recent breakthroughs in Neural Architectural Search (NAS) have achieved state-of-the-art performance in many tasks such as image classification and language understanding. However, most existing works only optimize for model accuracy and largely ignore ... More

Superconductivity in the PbO-type Structure alpha-FeSeJul 15 2008Jul 16 2008The recent discovery of superconductivity with relatively high transition temperature Tc in the layered iron-based quaternary oxypnictides La[ O1-xFx] FeAs was a real surprise. The excitement generated can be seen by the number of subsequent works published ... More

The interplay of mutations and electronic properties in disease-related genesSep 27 2011Electronic properties of DNA are believed to play a crucial role in many phenomena in living organisms, for example the location of DNA lesions by base excision repair (BER) glycosylases and the regulation of tumor-suppressor genes such as p53 by detection ... More

Shimura varieties at level $Γ_1(p^\infty)$ and Galois representationsMar 31 2018We show that the compactly supported cohomology of certain $\mathrm{U}(n,n)$ or $\mathrm{Sp}(2n)$-Shimura varieties with $\Gamma_1(p^\infty)$-level vanishes above the middle degree. The only assumption is that we work over a CM field $F$ in which the ... More

Exact Recession Velocity and Cosmic Redshift Based on Cosmological Principle and Yang-Mills GravityAug 01 2019Based on the cosmological principle and quantum Yang-Mills gravity in the super-macroscopic limit, we obtain an exact recession velocity and cosmic redshift z, as measured in an inertial frame $F\equiv F(t,x,y,z).$ For a matter-dominated universe, we ... More

Quantum interference effects in chemical vapor deposited grapheneOct 31 2015We report several quantum interference effects in graphene grown by chemical vapor deposition. A crossover between weak localization and weak antilocalization effects is observed when varying the gate voltage and we discuss the underlying scattering mechanisms. ... More

The metrology cameras for Subaru PFS and FMOSOct 09 2012The Prime Focus Spectrograph (PFS) is a new multi-fiber spectrograph on Subaru telescope. PFS will cover around 1.4 degree diameter field with ~2400 fibers. To ensure precise positioning of the fibers, a metrology camera is designed to provide the fiber ... More

First-order magnetic and structural phase transitions in Fe$_{1+y}$Se$_x$Te$_{1-x}$Nov 02 2008We use bulk magnetic susceptibility, electronic specific heat, and neutron scattering to study structural and magnetic phase transitions in Fe$_{1+y}$Se% $_x$Te$_{1-x}$. Fe$_{1.068}$Te exhibits a first order phase transition near 67 K with a tetragonal ... More

MONAS: Multi-Objective Neural Architecture Search using Reinforcement LearningJun 27 2018Dec 03 2018Recent studies on neural architecture search have shown that automatically designed neural networks perform as good as expert-crafted architectures. While most existing works aim at finding architectures that optimize the prediction accuracy, these architectures ... More

Quasi-particle interferences of the Weyl semimetals TaAs and NbPNov 09 2015The recent discovery of the first Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature. Such a topological semimetal features a novel type of anomalous surface state, the Fermi arc, which connects a pair of Weyl nodes through ... More

Perfect absorption by an atomically thin crystalAug 02 2019Optical absorption is one of fundamental light-matter interactions. In most materials, optical absorption is a weak perturbation to the light. In this regime, absorption and emission are irreversible, incoherent processes due to strong damping. Excitons ... More

Interplay between the magnetic and electric degrees-of-freedom in multiferroic Co3TeO6Mar 28 2012Neutron diffraction, magnetic susceptibility, specific heat, and dielectric constant measurements of single crystal Co3TeO6 have been measured to study the interplay between the ferroelectricity and magnetic order. Long range incommensurate magnetic order ... More

Dynamic Transcript Profiling of Candida Albicans Infection in Zebrafish: a Pathogen-Host Interaction StudyJun 14 2013Candida albicans is responsible for a number of life-threatening infections and causes considerable morbidity and mortality in immunocompromised patients. Previous studies of C. albicans pathogenesis have suggested several steps must occur before virulent ... More

Magnetic tunneling induced Weyl node annihilation in TaPJul 22 2015May 12 2017Weyl nodes are topological objects in three-dimensional metals. Their topological property can be revealed by studying the high-field transport properties of a Weyl semimetal. While the energy of the lowest Landau band (LLB) of a conventional Fermi pocket ... More

K-semistability is equivariant volume minimizationDec 22 2015Sep 27 2016This is a continuation to the paper \cite{Li15a} in which a problem of minimizing normalized volumes over $\mathbb{Q}$-Gorenstein klt singularities was proposed. Here we consider the case when there is a $\mathbb{C}^*$-action on $(X,o)$. In particular, ... More

Random Attractor for Stochastic Hindmarsh-Rose Equations with Multiplicative NoiseAug 03 2019The longtime and global pullback dynamics of stochastic Hindmarsh-Rose equations with multiplicative noise on a three-dimensional bounded domain in neurodynamics is investigated in this work. The existence of a random attractor for this random dynamical ... More

On Multivariate Strong Renewal TheoremDec 05 2014Mar 15 2017This paper takes the so-called probabilistic approach to the Strong Renewal Theorem (SRT) for multivariate distributions in the domain of attraction of a stable law. A version of the SRT is obtained that allows any kind of lattice-nonlattice composition ... More

Uniform convergence of exact large deviations for renewal reward processesJul 31 2007Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname {Pr}\{W(x)\gecx\}-1|=o(1)$, ... More

Large deviations for template matching between point processesMar 22 2005We study the asymptotics related to the following matching criteria for two independent realizations of point processes X\sim X and Y\sim Y. Given l>0, X\cap [0,l) serves as a template. For each t>0, the matching score between the template and Y\cap [t,t+l) ... More

Exact sampling of first passage event of certain symmetric Levy processes with unbounded variationJun 21 2016We show that exact sampling of the first passage event can be done for a Levy process with unbounded variation, if the process can be embedded in a subordinated standard Brownian motion. By sampling a series of first exit events of the Brownian motion ... More

Strong renewal theorems with infinite mean beyond local large deviationsMay 28 2015Let $F$ be a distribution function on the line in the domain of attraction of a stable law with exponent $\alpha\in(0,1/2]$. We establish the strong renewal theorem for a random walk $S_1,S_2,\ldots$ with step distribution $F$, by extending the large ... More

$L_0$ regularized estimation for nonlinear models that have sparse underlying linear structuresOct 14 2009We study the estimation of $\beta$ for the nonlinear model $y = f(X\sp{\top}\beta) + \epsilon$ when $f$ is a nonlinear transformation that is known, $\beta$ has sparse nonzero coordinates, and the number of observations can be much smaller than that of ... More

FDR control for multiple hypothesis testing on composite nullsJul 30 2008Multiple hypothesis testing often involves composite nulls, i.e., nulls that are associated with two or more distributions. In many cases, it is reasonable to assume that there is a prior distribution on the distributions despite it is unknown. When the ... More

Integral criteria for Strong Renewal Theorems with infinite meanDec 20 2013Apr 15 2014Let $F$ be a probability measure on $\mathbb{R}$ in the domain of attraction of a stable law with exponent $\alpha\in (0, 1)$. We establish integral criteria on $F$ that significantly expand the probabilistic approach to Strong Renewal Theorems (SRTs). ... More

On the performance of FDR control: Constraints and a partial solutionOct 17 2007The False Discovery Rate (FDR) paradigm aims to attain certain control on Type I errors with relatively high power for multiple hypothesis testing. The Benjamini--Hochberg (BH) procedure is a well-known FDR controlling procedure. Under a random effects ... More

Big Jets Model with CPT Invariance and Dynamics of Expansion with Quantum Yang-Mills GravityJun 21 2018Based on particle physics, the fundamental CPT invariance suggests a Big Jets model for the beginning of the universe, in which two oppositely directed jets evolved into a gigantic "matter half-universe" and a gigantic "antimatter half-universe" after ... More

Molecular Clock Dating using MrBayesMar 17 2016There are two modern approaches on dating species divergence using molecular data: node dating (e.g., Yang and Rannala, 2006; Drummond et al., 2006) and total-evidence dating (e.g., Ronquist et al., 2012a; Zhang et al., 2016). In a Bayesian framework, ... More

Minimizing normalized volumes of valuationsNov 25 2015Apr 10 2016We propose a problem of minimizing normalized volumes of valuations. For a $\mathbb{Q}$-Gorenstein klt singularity, by proving a key properness estimate, we prove that the set of valuations with uniformly bounded normalized volumes is compact. Under a ... More

Law of the first passage triple of a spectrally positive strictly stable processJan 21 2018Apr 02 2019For a spectrally positive and strictly stable process with index in (1,2), a series representation is obtained for the joint distribution of the "first passage triple" that consists of the time of first passage and the undershoot and the overshoot at ... More

Nonnormal small jump approximation of infinitely divisible distributionsApr 23 2013We consider a type of nonnormal approximation of infinitely divisible distributions that incorporates compound Poisson, Gamma, and normal distributions. The approximation relies on achieving higher orders of cumulant matching, to obtain higher rates of ... More

Limit laws of estimators for critical multi-type Galton-Watson processesMar 24 2005We consider the asymptotics of various estimators based on a large sample of branching trees from a critical multi-type Galton-Watson process, as the sample size increases to infinity. The asymptotics of additive functions of trees, such as sizes of trees ... More

Random reversible Markov matrices with tunable extremal eigenvaluesMay 08 2015Sep 08 2015Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix of a random ... More

On Multivariate Strong Renewal TheoremDec 05 2014Dec 09 2014This paper takes the so-called probabilistic approach to the Strong Renewal Theorem (SRT) on $\mathbb{R}^d$ for distributions in the domain of attraction without centering of a nondegenerate stable law of exponent $\alpha \in (0, 2]\cap (0,d)$. We obtain ... More

On equivariantly uniform stability and Yau-Tian-Donaldson conjecture for singular Fano varietiesJul 22 2019Let $X$ be a $\mathbb{Q}$-Fano variety and ${\rm Aut}(X)_0$ be the identity component of the automorphism group of $X$. Let $\mathbb{G}$ denote a connected reductive subgroup of ${\rm Aut(X)}_0$. We prove that if $X$ is $\mathbb{G}$-uniformly K-stable, ... More

On exact sampling of the first passage event of Levy process with infinite Levy measure and bounded variationJul 10 2012We present an exact sampling method for the first passage event of a Levy process. The idea is to embed the process into another one whose first passage event can be sampled exactly, and then recover the part belonging to the former from the latter. The ... More

Law of two-sided exit by a spectrally positive strictly stable processJun 19 2018For a spectrally positive strictly stable process with index in (1,2), the paper obtains i) the density of the time when the process makes first exit from an interval by hitting the interval's lower end point before jumping over its upper end point, and ... More

Stochastic Lipschitz continuity for high dimensional Lasso with multiple linear covariate structures or hidden linear covariatesNov 05 2010Two extensions of generalized linear models are considered. In the first one, response variables depend on multiple linear combinations of covariates. In the second one, only response variables are observed while the linear covariates are missing. We ... More

On $\ell_1$-regularized estimation for nonlinear models that have sparse underlying linear structuresNov 25 2009In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important cases can achieve ... More

Sample size and positive false discovery rate control for multiple testingMar 08 2007May 09 2007The positive false discovery rate (pFDR) is a useful overall measure of errors for multiple hypothesis testing, especially when the underlying goal is to attain one or more discoveries. Control of pFDR critically depends on how much evidence is available ... More

Observational approaches to understanding dark energyDec 01 2007Illuminating the nature of dark energy is one of the most important challenges in cosmology today. In this review I discuss several promising observational approaches to understanding dark energy, in the context of the recommendations by the U.S. Dark ... More

Differentiating dark energy and modified gravity with galaxy redshift surveysOct 21 2007Apr 28 2008The observed cosmic acceleration today could be due to an unknown energy component (dark energy), or a modification to general relativity (modified gravity). If dark energy models and modified gravity models are required to predict the same cosmic expansion ... More

Modeling galaxy clustering on small scales to tighten constraints on dark energy and modified gravityJun 26 2016Oct 10 2016We present a new approach to measuring cosmic expansion history and growth rate of large scale structure using the anisotropic two dimensional galaxy correlation function (2DCF) measured from data; it makes use of the empirical modeling of small-scale ... More

The spherical part of the local and global Springer actionsJun 11 2011The affine Weyl group acts on the cohomology (with compact support) of affine Springer fibers (local Springer theory) and of parabolic Hitchin fibers (global Springer theory). In this paper, we show that in both situations, the action of the center of ... More

Towards a Global Springer Theory I: The affine Weyl group actionOct 13 2008Apr 22 2009We propose a generalization of Springer representations to the context of groups over a global function field. The global counterpart of the Grothendieck simultaneous resolution is the parabolic Hitchin fibration. We construct an action of the affine ... More

Experimental Twin-Field Quantum Key Distribution Through Sending-or-Not-SendingFeb 17 2019Channel loss seems to be the most severe limitation to the application long distance quantum key distribution in practice. The idea of twin-field quantum key distribution can improve the key rate from the linear scale of channel loss in the traditional ... More

Source attack of decoy-state quantum key distribution using phase informationApr 09 2013Aug 08 2013Quantum key distribution (QKD) utilizes the laws of quantum mechanics to achieve information-theoretically secure key generation. This field is now approaching the stage of commercialization, but many practical QKD systems still suffer from security loopholes ... More

How many variables should be entered in a principal component regression equation?Jun 04 2019We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration coincides with ... More

Curve Shortening Flow and Smooth Projective PlanesAug 16 2013In this paper, we study a family of curves on $S^2$ that defines a two-dimensional smooth projective plane. We use curve shortening flow to prove that any two-dimensional smooth projective plane can be smoothly deformed through a family of smooth projective ... More

Higher-order Alexander Invariants of Hypersurface ComplementsOct 12 2015We define the higher-order Alexander modules $A_{n,i}(\mathcal{U})$ and higher-order degrees $\delta_{n,i}(\mathcal{U})$ which are invariants of a complex hypersurface complement $\mathcal{U}$. These invariants come from the module structure of the homology ... More

Figure of Merit for Dark Energy Constraints from Current Observational DataMar 31 2008Choosing the appropriate figure of merit (FoM) for dark energy (DE) constraints is key in comparing different DE experiments. Here we show that for a set of DE parameters {f_i}, it is most intuitive to define FoM = 1/\sqrt{Cov(f1,f2,f3,...)}, where Cov(f1,f2,f3,...) ... More

Model-Independent Distance Measurements from Gamma-Ray Bursts and Constraints on Dark EnergySep 03 2008Dec 16 2008Gamma-Ray Bursts (GRB) are the most energetic events in the Universe, and provide a complementary probe of dark energy by allowing the measurement of cosmic expansion history that extends to redshifts greater than 6. Unlike Type Ia supernovae (SNe Ia), ... More

Reducts of the random bipartite graphJan 10 2011Aug 18 2011Let $\Gamma$ be the random bipartite graph, a countable graph with two infinite sides, edges randomly distributed between the sides, but no edges within a side. In this paper, we investigate the reducts of $\Gamma$ that preserve sides. We classify the ... More

Model-Independent Measurements of Cosmic Expansion and Growth at z=0.57 Using the Anisotropic Clustering of CMASS Galaxies From the Sloan Digital Sky Survey Data Release 9Apr 21 2014Jul 07 2014We analyze the anisotropic two dimensional galaxy correlation function (2DCF) of the CMASS galaxy sample from the Sloan Digital Sky Survey Data Release 9 (DR9) of the Baryon Oscillation Spectroscopic Survey (BOSS) data. Modeling the 2DCF fully including ... More

A Tale Of Two Amplitudes In High Energy PhysicsMay 27 2013(abbreviated) I will describe my work on proton Compton scattering in a Unified Proton-Delta theory and on the computation of scattering amplitudes in Yang-Mills theory. We study proton Compton scattering in the first resonance region in an effective ... More

The Frenet-Serret formulas of a discrete centroaffine curveJan 25 2016In this paper, we build the fundamental theory of a discrete centroaffine curve. For a discrete plane curve, we define its first and second centroaffine curvatures which are invariant under the affine transformation. Using the centroaffine curvatures, ... More

Space time symmetry in quantum mechanicsFeb 26 2014Mar 12 2014New prescription to treat position and time equally in quantum mechanics is presented. Using this prescription, we could successfully derive some interesting formulae such as time-of-arrival for a free particle and quantum tunneling formula. The physical ... More

Permanence of a general discrete-time two-species-interaction model with non-monotonic per capita growth ratesFeb 28 2011Combined with all density-dependent factors, the per capita growth rate of a species may be non-monotonic. One important consequence is that species may suffer from weak Allee effects or strong Allee effects. In this paper, we study the permanence of ... More

Towards a Global Springer Theory II: the double affine actionApr 22 2009We construct an action of the graded double affine Hecke algebra (DAHA) on the parabolic Hitchin complex, extending the affine Weyl group action constructed in \cite{GSI}. In particular, we get representations of the degenerate DAHA on the cohomology ... More

Horseshoes for $\mathcal{C}^{1+α}$ mappings with hyperbolic measuresNov 25 2014We present here a construction of horseshoes for any $\mathcal{C}^{1+\alpha}$ mapping $f$ preserving an ergodic hyperbolic measure $\mu$ with $h_{\mu}(f)>0$ and then deduce that the exponential growth rate of the number of periodic points for any $\mathcal{C}^{1+\alpha}$ ... More

Towards a Global Springer Theory III: Endoscopy and Langlands dualityApr 22 2009We prove three new results about the global Springer action defined in \cite{GSI}. The first one determines the support of the perverse cohomology sheaves of the parabolic Hitchin complex, which serves as a technical tool for the next results. The second ... More

The fundamental lemma of Jacquet-Rallis in positive characteristicsJan 07 2009Oct 28 2009We prove both the group version and the Lie algebra version of the Fundamental Lemma appearing in a relative trace formula of Jacquet-Rallis in the function field case when the characteristic is greater than the rank of the relevant groups.

Weights of mixed tilting sheaves and geometric Ringel dualityMay 10 2008Nov 22 2008We describe several general methods for calculating weights of mixed tilting sheaves. We introduce a notion called "non-cancellation property" which implies a strong uniqueness of mixed tilting sheaves and enables one to calculate their weights effectively. ... More

Effect of three-particle correlations in low dimensional Hubbard modelsFeb 16 1993A simple approximation which captures some non-perturbative aspects of the one electron Green function of strongly interacting Fermion systems is developed. It provides a way to go one step beyond the usual dilute limit since particle-particle as well ... More

Maximum principle and convergence of fundamental solutions for the Ricci flowNov 08 2007In this paper we will prove a maximum principle for the solutions of linear parabolic equation on complete non-compact manifolds with a time varying metric. We will prove the convergence of the Neumann Green function of the conjugate heat equation for ... More

Uniform Sobolev inequalities for manifolds evolving by Ricci flowAug 07 2007Let M be a compact n-dimensional manifold, $n\ge 2$, with metric g(t) evolving by the Ricci flow $\partial g_{ij}/\partial t=-2R_{ij}$ in (0,T) for some $T\in\Bbb{R}^+\cup\{\infty\}$ with $g(0)=g_0$. Let $\lambda_0(g_0)$ be the first eigenvalue of the ... More

Some results for the Perelman LYH-type inequalityJan 23 2008May 12 2008Let $(M,g(t))$, $0\le t\le T$, $\partial M\ne\phi$, be a compact $n$-dimensional manifold, $n\ge 2$, with metric $g(t)$ evolving by the Ricci flow such that the second fundamental form of $\partial M$ with respect to the unit outward normal of $\partial ... More

On Bifurcation Delay: An Alternative Approach Using Geometric Singular Perturbation TheoryApr 14 2016Jul 29 2016To explain the phenomenon of bifurcation delay, which occurs in planar systems of the form $\dot{x}=\epsilon f(x,z,\epsilon)$, $\dot{z}=g(x,z,\epsilon)z$, where $f(x,0,0)>0$ and $g(x,0,0)$ changes sign at least once on the $x$-axis, we use the Exchange ... More

Exact decay rate of a nonlinear elliptic equation related to the Yamabe flowNov 14 2012Jan 12 2013Let 0<m<(n-2)/n, n>2, $\alpha=(2\beta +\rho)/(1-m)$ and $\beta>m\rho/(n-2-mn)$ for some constant $\rho>0$. Suppose v is a radially symmetric symmetric solution of $\frac{n-1}{m}\Delta v^m+\alpha v+\beta x\cdot\nabla v=0$, v>0, in $R^n$. When m=(n-2)/(n+2), ... More

RL-Based Method for Benchmarking the Adversarial Resilience and Robustness of Deep Reinforcement Learning PoliciesJun 03 2019This paper investigates the resilience and robustness of Deep Reinforcement Learning (DRL) policies to adversarial perturbations in the state space. We first present an approach for the disentanglement of vulnerabilities caused by representation learning ... More

A harmonic map flow associated with the standard solution of Ricci flowFeb 07 2007Let $(\Bbb{R}^n,g(t))$, $0\le t\le T$, $n\ge 3$, be a standard solution of the Ricci flow with radially symmetric initial data $g_0$. We will extend a recent existence result of P. Lu and G. Tian and prove that for any $t_0\in [0,T)$ there exists a solution ... More

Number and Stability of Relaxation Oscillations for Predator-Prey Systems with Small Death RatesJan 08 2018Oct 29 2018We consider planar systems of predator-prey models with small predator death rate $\epsilon>0$. Using geometric singular perturbation theory and Floquet theory, we derive characteristic functions that determines the location and the stability of relaxation ... More

The Interactions of Solitons in the Novikov-Veselov EquationOct 15 2013Aug 07 2014Using the reality condition of the solutions, one constructs the real Pfaffian N-solitons solutions of the Novikov-Veselov (NV) equation using the $\tan$ function and the Schur identity. By the minor-summation formula of the Pfaffian, we can study the ... More

Existence and properties of ancient solutions of the Yamabe flowJun 09 2016Jun 11 2016Let $n\ge 3$ and $m=\frac{n-2}{n+2}$. We construct $5$-parameters, $4$-parameters, $3$-parameters ancient solutions of the equation $v_t=(v^m)_{xx}+v-v^m$, $v>0$, in $\mathbb{R}\times (-\infty,T)$ for some $T\in\mathbb{R}$. This equation arises in the ... More

Rotational symmetry and properties of the ancient solutions of Ricci flow on surfacesMar 11 2010We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of P.Daskalopoulos, R.Hamilton and N.Sesum on the a priori estimates for the ancient solutions ... More

Super fast vanishing solutions of the fast diffusion equationFeb 25 2019We will extend a recent result of B.Choi, P.Daskalopoulos and J.King. For any $n\ge 3$, $0<m<\frac{n-2}{n+2}$ and $\gamma>0$, we will construct subsolutions and supersolutions of the fast diffusion equation $u_t=\frac{n-1}{m}\Delta u^m$ in $\mathbb{R}^n\times ... More

Viscous singular shock profiles for a system of conservation laws modeling two-phase flowDec 01 2015This paper is concerned with singular shocks for a system of conservation laws modeling incompressible two-phase fluid flow. We prove the existence of viscous profiles using the Geometric Singular Perturbation Theory. Weak convergence and growth rates ... More

Adversarial Exploitation of Policy ImitationJun 03 2019This paper investigates a class of attacks targeting the confidentiality aspect of security in Deep Reinforcement Learning (DRL) policies. Recent research have established the vulnerability of supervised machine learning models (e.g., classifiers) to ... More

A pseudolocality theorem for Ricci flowAug 06 2009Oct 06 2010In this paper we will give a simple proof of a modification of a result on pseudolocality for the Ricci flow by P.Lu without using the pseudolocality theorem 10.1 of Perelman [P1]. We also obtain an extension of a result of Hamilton on the compactness ... More