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A group theoretical approach to computing phonons and their interactionsApr 12 2019Here we present four independent advances which facilitate the computation of phonons and their interactions from first-principles. First, we implement a group-theoretical approach to construct the order N Taylor series of a d-dimensional crystal purely ... More

Uniaxial Strain Tuning of Superconductivity in 2$H$-NbSe$_{2}$Mar 12 2019We explore the effect of lattice anisotropy on the charge-ordered superconductor 2H-NbSe$_{2}$. Using a novel strain apparatus, we measure the superconducting transition temperature $T_{sc}$ as a function of uniaxial strain. It is found that $T_{sc}$ ... More

Lattice QCD study on $K^\ast(892)$ meson decay widthAug 31 2012Sep 06 2012We deliver an exploratory lattice QCD examination of the $K^\ast(892)$ meson decay width with the help of the p-wave scattering phase $\delta_1$ of pion-kaon ($\pi K$) system in the isospin $I=1/2$ channel, which are extracted by the modified Rummukainen-Gottlieb ... More

The Origin of Energy for the Big BangNov 20 2003Our universe is probably a huge black hole. If that is true, all the light and heat ejected by various celestial bodies into the space will be confined within it and shuttling ceaselessly, leading eventually to a uniform equilibrium radiation at certain ... More

Another Way To Realize Maxwell's DemonSep 14 2005Sep 29 2005This is another approach to realize Maxwell's "demon" hypothesis. Two Ag-O-Cs thermal electron ejectors, A and B, are settled in a vacuum tube. A non-uniform magnetic field exerted on the tube provides a one-way channel for the thermal electrons. Ejector ... More

Realization of Maxwell's HypothesisNov 20 2003Nov 20 2012Two similar and parallel Ag-O-Cs surfaces in a vacuum tube ceaselessly eject electrons at room temperature. A static magnetic field applied to the tube plays the role of 'Maxwell's demon'. The thermal electrons are so controlled by the magnetic field ... More

Sublinear Time Motif Discovery from Multiple SequencesJul 15 2010Mar 13 2012A natural probabilistic model for motif discovery has been used to experimentally test the quality of motif discovery programs. In this model, there are $k$ background sequences, and each character in a background sequence is a random character from an ... More

Deformations and Rigidity of $\ell$-adic SheavesNov 12 2016Let $X$ be a smooth connected algebraic curve over an algebraically closed field, let $S$ be a finite closed subset in $X$, and let $\mathcal F_0$ be a lisse $\ell$-torsion sheaf on $X-S$. We study the deformation of $\mathcal F_0$. The universal deformation ... More

Derandomizing Polynomial Identity over Finite Fields Implies Super-Polynomial Circuit Lower Bounds for NEXPNov 11 2013We show that derandomizing polynomial identity testing over an arbitrary finite field implies that NEXP does not have polynomial size boolean circuits. In other words, for any finite field F(q) of size q, $PIT_q\in NSUBEXP\Rightarrow NEXP\not\subseteq ... More

Multivariate Polynomial Integration and Derivative Are Polynomial Time Inapproximable unless P=NPDec 10 2010We investigate the complexity of integration and derivative for multivariate polynomials in the standard computation model. The integration is in the unit cube $[0,1]^d$ for a multivariate polynomial, which has format $f(x_1,\cdots, x_d)=p_1(x_1,\cdots, ... More

Remarks on hard Lefschetz conjectures on Chow groupsMay 26 2009We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.

Inductive characterizations of hyperquadricsMay 21 2007We give two characterizations of hyperquadrics: one as non-degenerate smooth projective varieties swept out by large dimensional quadric subvarieties passing through a point; the other as $LQEL$-manifolds with large secant defects.

Wreath products, nilpotent orbits and symplectic deformationsNov 15 2006We recover a 4-dimensional wreath product X as a transversal slice to a nilpotent orbit in sp_6. By using deformations of Springer resolutions, we construct a symplectic deformation of symplectic resolutions of X.

Symplectic Resolutions for Quotient SingularitiesJun 27 2002Oct 29 2002We give some necessary conditions for the existence of a symplectic resolution for quotient singularities. The McKay correspondence is also worked out for these resolutions.

Symplectic Resolutions for Coverings of Nilpotent OrbitsDec 02 2002Let $\0$ be a nilpotent orbit in a semisimple complex Lie algebra $\g$. Denote by $G$ the simply connected Lie group with Lie algebra $\g$. For a $G$-homogeneous covering $M \to \0$, let $X$ be the normalization of $\bar{\0}$ in the function field of ... More

Hexagonal Warping Effects in the Surface States of Topological Insulator Bi$_2$Te$_3$Aug 10 2009Dec 21 2009A single two-dimensinoal Dirac fermion state has been recently observed on the surface of topological insulator Bi$_2$Te$_3$ by angle-resolved photoemission spectroscopy (ARPES). We study the surface band structure using $k \cdot p$ theory and find an ... More

A Type Checking Algorithm for Higher-rank, Impredicative and Second-order TypesNov 13 2017We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is before each ... More

Representing Nonterminating Rewriting with $\mathbf{F}_2^μ$Jun 02 2017We specify a second-order type system $\mathbf{F}_2^\mu$ that is tailored for representing nonterminations. The nonterminating trace of a term $t$ in a rewrite system $\mathcal{R}$ corresponds to a productive inhabitant $e$ such that $\Gamma_{\mathcal{R}} ... More

Importance sampling-based approximate optimal planning and controlDec 16 2016In this paper, we propose a sampling-based planning and optimal control method of nonlinear systems under non-differentiable constraints. Motivated by developing scalable planning algorithms, we consider the optimal motion plan to be a feedback controller ... More

A Uniform Approach to Random Process ModelJun 23 2019There is a lot of research on probabilistic transition systems. There are not many studies in probabilistic process models. The lack of investigation into the interactive aspect of probabilistic processes is mainly due to the difficulty caused by the ... More

Biharmonic hypersurfaces with three distinct principal curvatures in spheresDec 18 2014Dec 19 2014We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu\c{s}-Montaldo-Oniciuc, we prove that compact ... More

Biharmonic hypersurfaces with three distinct principal curvatures in Euclidean spaceDec 04 2014Dec 18 2014The well known Chen's conjecture on biharmonic submanifolds states that a biharmonic submanifold in a Euclidean space is a minimal one ([10-13, 16, 18-21, 8]). For the case of hypersurfaces, we know that Chen's conjecture is true for biharmonic surfaces ... More

Lattice calculation of $κ$ mesonNov 08 2011We study the $\kappa$ meson in 2+1 flavor QCD with sufficiently light $u/d$ quarks. Using numerical simulation we measure the point-to-point $\kappa$ correlators in the "Asqtad" improved staggered fermion formulation. We analyze those correlators using ... More

Preliminary lattice study of $σ$ meson decay widthFeb 27 2012Jun 10 2012We report an exploratory lattice investigation of $\sigma$ meson decay width using s-wave scattering phase for isospin I=0 pion-pion ($\pi\pi$) system. Rummukainen-Gottlieb formula is used to estimate the scattering phase, which demonstrate the presence ... More

Projective Equivalence for the Roots of UnityMay 04 2019Let $\mu_{\infty}\subseteq\mathbb{C}$ be the collection of roots of unity and $\mathcal{C}_{n}:=\{(s_{1},\cdots,s_{n})\in\mu_{\infty}^{n}:s_{i}\neq s_{j}\text{ for any }1\leq i<j\leq n\}$. Two elements $(s_{1},\cdots,s_{n})$ and $(t_{1},\cdots,t_{n})$ ... More

Relational Constraint Driven Test Case Synthesis for Web ApplicationsSep 20 2010This paper proposes a relational constraint driven technique that synthesizes test cases automatically for web applications. Using a static analysis, servlets can be modeled as relational transducers, which manipulate backend databases. We present a synthesis ... More

Of the Black Hole ThermodynamicsJan 11 2005Jan 12 2005About thirty years ago, Bekenstein and Hawking introduced three basic concepts relating to black hole, namely, the "area entropy", "gravitation temperature" and "thermal radiation". The author analyzes these concepts systematically and concludes that ... More

Hearing the type of a domain in C^2 with the d-bar-Neumann LaplacianAug 24 2005A smooth bounded pseudoconvex domain in two complex variables is of finite type if and only if the number of eigenvalues of the d-bar-Neumann Laplacian that are less than or equal to $\lambda$ has at most polynomial growth as $\lambda$ goes to infinity. ... More

Estimates of invariant metrics on pseudoconvex domains near boundaries with constant Levi ranksMar 08 2012Estimates of the Bergman kernel and the Bergman and Kobayashi metrics on pseudoconvex domains near boundaries with constant Levi ranks are given.

A Tauberian Theorem for $\ell$-adic Sheaves on $\mathbb A^1$Jun 04 2010Let $K\in L^1(\mathbb R)$ and let $f\in L^\infty(\mathbb R)$ be two functions on $\mathbb R$. The convolution $$(K\ast f)(x)=\int_{\mathbb R}K(x-y)f(y)dy$$ can be considered as an average of $f$ with weight defined by $K$. Wiener's Tauberian theorem says ... More

Meta-Key: A Secure Data-Sharing Protocol under Blockchain-Based Decentralised Storage ArchitectureOct 22 2017In this paper a secure data-sharing protocol under blockchain-based decentralised storage architecture is proposed, which fulfils users who need to share their encrypted data on-cloud. It implements a remote data-sharing mechanism that enables data owners ... More

Twisted Exponential SumsJul 06 2006Jan 30 2007Let $k$ be a finite field of characteristic $p$, $l$ a prime number distinct to $p$, $\psi:k\to \bar {\bf Q}_l^\ast$ a nontrivial additive character, and $\chi:{k^\ast}^n\to \bar{\bf Q}_l^\ast$ a character on ${k^\ast}^n$. Then $\psi$ defines an Artin-Schreier ... More

Affine quantum Schur algebras at roots of unityMay 14 2012Aug 06 2012We will classify finite dimensional irreducible modules for affine quantum Schur algebras at roots of unity and generalize \cite[(6.5f) and (6.5g)]{Gr80} to the affine case in this paper.

Non-orthogonal geometric realizations of Coxeter groupsDec 15 2011Feb 28 2013We define in an axiomatic fashion a \emph{Coxeter datum} for an arbitrary Coxeter group $W$. This Coxeter datum will specify a pair of reflection representations of $W$ in two vector spaces linked only by a bilinear paring without any integrality and ... More

Performance of leader-follower multi-agent systems in directed networksJun 07 2016We consider leader-follower multi-agent systems in which the leader executes the desired trajectory and the followers implement the consensus algorithm subject to stochastic disturbances. The performance of the leader-follower systems is quantified by ... More

The comultiplication of modified quantum affine $\frak{sl}_n$Nov 18 2015Let $\dot{\mathbf{U}}(\widehat{\frak{sl}}_n)$ be the modified quantum affine $\frak{sl}_n$ and let ${\bf U}(\widehat{\frak{sl}}_N)^+$ be the positive part of quantum affine $\frak{sl}_N$. Let $\dot{\mathbf{B}}(n)$ be the canonical basis of $\dot{\mathbf{U}}(\widehat{\frak{sl}}_n)$ ... More

Extremal contractions, stratified Mukai flops and Springer mapsMay 16 2006We prove that two Springer maps over a nilpotent orbit closure with the same degree are connected by stratified Mukai flops and the latter is obtained by extremal contractions of a natural resolution of the nilpotent orbit closure.

Symplectic Resolutions for Nilpotent OrbitsMay 06 2002May 25 2004We prove that any symplectic resolution of the closure of a nilpotent orbit in a semi-simple complex Lie algebra is isomorphic to the collapsing of the cotangent bundle of a projective homogenous variety. Then we give a complete characterization of those ... More

NE is not NP Turing Reducible to Nonexpoentially Dense NP SetsDec 10 2010A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of $NP_T(NP\cap P/poly)$. In this paper, we show that $NE\not\subseteq NP_(NP \cap$ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class ... More

Symplectic Resolutions for Symmetric Products of SurfacesApr 04 2003Let $S$ be a smooth complex connected analytic surface which admits a holomorphic symplectic structure. Let $S^{(n)}$ be its $n$th symmetric product. We prove that every projective symplectic resolution of $S^{(n)}$ is isomorphic to the Douady-Barlet ... More

Factorization of Symmetric Matrices and Actions on Σ_kMar 15 2002In this note, firstly we give an easy proof of the factorization of symmetric matrices (see [Mos] math-ph/0203023), then we use it to prove the well-known fact that the automorphism group of a non-degenerate symmetric bilinear form acts transitively on ... More

Combinatorial bases for multilinear parts of free algebras with double compatible bracketsAug 26 2008Let X be an ordered alphabet. Lie_2(n) (and P_2(n) respectively) are the multilinear parts of the free Lie algebra (and the free Poisson algebra respectively) on X with a pair of compatible Lie brackets. In this paper, we prove the dimension formulas ... More

Moduli of Crude Limit Linear SeriesFeb 25 2009Eisenbud and Harris introduced the theory of limit linear series, and constructed a space parametrizing their limit linear series. Recently, Osserman introduced a new space which compactifies the Eisenbud-Harris construction. In the Eisenbud-Harris space, ... More

The Conley-Zehnder Index of Brownian Paths on Sp(2, R)Oct 27 2016We investigate the probability distribution of Conley-Zehnder indices associated with Brownian random paths on Sp(2n, R) that start at the identity. In the case of n = 1, we prove that the distribution has the same moment asymptotics as the standard random ... More

Rummukainen-Gottlieb's formula on two-particle system with different massOct 03 2011Jun 09 2012L\"uscher established a non-perturbative formula to extract the elastic scattering phases from two-particle energy spectrum in a torus using lattice simulations. Rummukainen and Gottlieb further extend it to the moving frame, which is devoted to the system ... More

Molecular Labor Division: Its Cause and ConsequenceDec 04 2007Aug 21 2011Both external environmental selection and internal lower-level evolution are essential for an integral picture of evolution. This paper proposes that the division of internal evolution into DNA/RNA pattern formation (genotype) and protein functional action ... More

Hearing pseudoconvexity with the Kohn LaplacianMar 22 2004A bounded domain in several complex variables with connected Lipschitz boundary is pseudoconvex if and only if the bottom of the (essential) spectrum of the Kohn Laplacian is positive on all (0, q)-forms with square-integrable coefficients.

An Illustrated Introduction to the Basic Biological PrinciplesDec 13 2007Dec 14 2009Both external environmental selection and internal lower-level evolution are essential for an integral picture of evolution. This paper proposes that the division of internal evolution into DNA/RNA pattern formation (genotype) and protein functional action ... More

Lattice QCD study of the s-wave $ππ$ scattering lengths in the I=0 and 2 channelsMar 03 2013The s-wave pion-pion ($\pi\pi$) scattering lengths are computed below the inelastic threshold by the L\"uscher technique with pion masses ranging from 240 MeV to 463 MeV. In the Asqtad-improved staggered fermion formulation, we calculate the $\pi\pi$ ... More

Lattice study on $πK $ scattering with moving wall sourceOct 07 2011Jan 18 2012The s-wave pion-kaon ($\pi K$) scattering lengths at zero momentum are calculated in lattice QCD with sufficiently light $u/d$ quarks and strange quark at its physical value by the finite size formula. The light quark masses correspond to $m_\pi = 0.330 ... More

Maximal Cost-Bounded Reachability Probability on Continuous-Time Markov Decision ProcessesOct 09 2013Jan 17 2014In this paper, we consider multi-dimensional maximal cost-bounded reachability probability over continuous-time Markov decision processes (CTMDPs). Our major contributions are as follows. Firstly, we derive an integral characterization which states that ... More

BLM realization for the integral form of quantum $\frak{gl}_n$Nov 04 2012Let ${\mathbf U}(n)$ be the quantum enveloping algebra of ${\frak {gl}}_n$ over $\mathbb Q(v)$, where $v$ is an indeterminate. We will use $q$-Schur algebras to realize the integral form of ${\mathbf U}(n)$. Furthermore we will use this result to realize ... More

BLM realization for Frobenius--Lusztig Kernels of type AJan 15 2013The infinitesimal quantum $\frak{gl}_n$ was realized in \cite[\S 6]{BLM}. We will realize Frobenius--Lusztig Kernels of type $A$ in this paper.

Evolution of low mass stars: lithium problem and alpha-enhanced tracks and isochrones (Ph.D. thesis)Feb 09 2017Precise studies on the Galactic bulge, halo, thick disk, and globular clusters require stellar models with alpha enhancement and various He contents. For this purpose we complement existing PARSEC (PAdova-TRieste Stellar Evolution Code) models, which ... More

Logarithmic decay of hyperbolic equations with arbitrary boundary dampingMay 06 2008In this paper, we study the logarithmic stability for the hyperbolic equations by arbitrary boundary observation. Based on Carleman estimate, we first prove an estimate of the resolvent operator of such equation. Then we prove the logarithmic stability ... More

Null controllability for the parabolic equation with a complex principal partMay 25 2008This paper is addressed to a study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish a key weighted identity for partial differential operators $(\a+i\b)\pa_t+\sum\limits_{j,k=1}^n\pa_k(a^{jk}\pa_j)$ ... More

Hall polynomials for representation-finite cluster-tilted algebrasDec 19 2012We show the existence of Hall polynomials for representation-finite cluster-tilted algebras.

$\ell$-adic GKZ hypergeometric sheaf and exponential sumsAug 07 2012Apr 26 2016To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the $\ell$-adic counterpart of the ... More

Calculation of l-adic local Fourier transformationsFeb 15 2007Jun 04 2010We calculate the local Fourier transformations for a class of $\bar{\mathbb Q}_\ell$-sheaves. In particular, we verify a conjecture of Laumon and Malgrange. As an application, we calculate the local monodromy of $\ell$-adic hypergeometric sheaves introduced ... More

On positivity of Ehrhart polynomialsNov 27 2017Aug 31 2018Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart ... More

Beauville-Voisin conjecture for generalized Kummer varietiesSep 19 2013Apr 08 2014Inspired by their results on the Chow rings of projective K3 surfaces, Beauville and Voisin made the following conjecture: given a projective hyperkaehler manifold, for any algebraic cycle which is a polynomial with rational coefficients of Chern classes ... More

Partial Sublinear Time Approximation and Inapproximation for Maximum CoverageApr 05 2016Jul 20 2016We develop a randomized approximation algorithm for the classical maximum coverage problem, which given a list of sets $A_1,A_2,\cdots, A_m$ and integer parameter $k$, select $k$ sets $A_{i_1}, A_{i_2},\cdots, A_{i_k}$ for maximum union $A_{i_1}\cup A_{i_2}\cup\cdots\cup ... More

On Q-factorial terminalizations of nilpotent orbitsSep 30 2008Nov 24 2008In a recent preprint, Y. Namikawa proposed a conjecture on Q-factorial terminalizations and their birational geometry of nilpotent orbits. He proved his conjecture for classical simple Lie algebras. In this note, we prove his conjecture for exceptional ... More

Contact resolutions of projectivised nilpotent orbit closuresFeb 06 2006Jun 07 2007The projectivised nilpotent orbit closure P(\bar{O}) carries a natural contact structure on its smooth part. A resolution X \to P(\bar{O}) is called contact if the contact structure on P(O) extends to a contact structure on X. It turns out that contact ... More

Parity-breaking phases of spin-orbit-coupled metals with gyrotropic, ferroelectric and multipolar ordersJan 30 2015Jun 30 2015We study Fermi liquid instabilities in spin-orbit-coupled metals with inversion symmetry. By introducing a canonical basis for the doubly degenerate Bloch bands in momentum space, we derive the general form of interaction functions. A variety of time-reversal-invariant, ... More

Topological Crystalline InsulatorsOct 09 2010Mar 12 2011The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point group symmetry ... More

Odd-parity topological superconductor with nematic order: Application to CuxBi2Se3Aug 27 2014CuxBi2Se3 was recently proposed as a promising candidate for time-reversal-invariant topological superconductors[1]. In this work, we argue that the unusual anisotropy of the Knight shift observed by Zheng[2], taken together with specific heat measurements, ... More

Performance of leader-follower multi-agent systems in directed networksJun 07 2016Dec 23 2016We consider leader-follower multi-agent systems in which the leader executes the desired trajectory and the followers implement the consensus algorithm subject to stochastic disturbances. The performance of the leader-follower systems is quantified by ... More

An explicit divergence-free DG method for incompressible flowAug 14 2018Nov 10 2018We present an explicit divergence-free DG method for incompressible flow based on velocity formulation only. A globally divergence-free finite element space is used for the velocity field, and the pressure field is eliminated from the equations by design. ... More

On Blockwise Symmetric Matchgate Signatures and Higher Domain \#CSPJul 03 2017For any $n\geq 3$ and $ q\geq 3$, we prove that the {\sc Equality} function $(=_n)$ on $n$ variables over a domain of size $q$ cannot be realized by matchgates under holographic transformations. This is a consequence of our theorem on the structure of ... More

Hybrid meson decay from lattice QCDMar 08 2011Sep 10 2012Besides the conventional hadrons containing valence quarks and valence antiquarks, quantum chromodynamics (QCD) suggests the existence of the hybrid hadrons containing valence gluons in addition to the quarks and antiquarks, and some experiments may have ... More

The Universal ProcessAug 20 2017Nov 16 2017A universal process of a process calculus is one that, given the G\"{o}del index of a process of a certain type, produces a process equivalent to the encoded process. This paper demonstrates how universal processes can be formally defined and how a universal ... More

BLM realization for ${\mathcal U}_{\mathbb Z}(\hat{\frak{gl}}_n)$Apr 14 2012In 1990, Beilinson-Lusztig-MacPherson (BLM) discovered a realization \cite[5.7]{BLM} for quantum $\frak{gl}_n$ via a geometric setting of quantum Schur algebras. We will generailze their result to the classical affine case. More precisely, we first use ... More

The Kobayashi metric in the normal direction and the mapping problemOct 06 2008Estimates of the Kobayashi metric in the normal direction are used to study the mapping problem in several complex variables.

A Thom-Sebastiani Theorem in Characteristic pMay 26 2011Dec 30 2013Let $k$ be a perfect field of characteristic $p$, let $f_i:X_i\to\mathbb A_k^1$ $(i=1,2)$ be two $k$-morphism of finite type, and let $f:X_1\times_k X_2\to \mathbb A_k^1$ be the morphism defined by $f(z_1,z_2)=f_1(z_1)+f_2(z_2)$. For each $i\in\{1,2\}$, ... More

On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic modelJun 21 2018In this paper, we consider a stochastic epidemic model with time delay and general incidence rate. We first prove the existence and uniqueness of the global positive solution. By using the Krylov-Bogoliubov method, we obtain the existence of invariant ... More

Positivity of the $\bar\partial$-Neumann LaplacianJun 21 2010We study the $\bar\partial$-Neumann Laplacian from spectral theoretic perspectives. In particular, we show how pseudoconvexity of a bounded domain is characterized by positivity of the $\bar\partial$-Neumann Laplacian.

Spectrum of the d-bar-Neumann Laplacian on polydiscsSep 06 2005The spectrum of the d-bar-Neumann Laplacian on a polydisc in several complex variables is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, some of which, in particular the smallest ones, are of infinite multiplicity. ... More

Deformation of $\ell$-adic sheaves with Undeformed Local MonodromyMar 06 2011Sep 29 2012Let $X$ be a smooth connected algebraic curve over an algebraically closed field $k$. We study the deformation of $\ell$-adic Galois representations of the function field of $X$ while keeping the local Galois representations at all places undeformed.

Deformations and Rigidity of $\ell$-adic SheavesNov 12 2016May 21 2019Let $X$ be a smooth connected projective algebraic curve over an algebraically closed field, and let $S$ be a finite nonempty closed subset in $X$. We study deformations of $\overline{\mathbb F}_\ell$-sheaves. The universal deformation space is a formal ... More

The dominance hierarchy in root systems of Coxeter groupsAug 15 2011May 14 2012If $x$ and $y$ are roots in the root system with respect to the standard (Tits) geometric realization of a Coxeter group $W$, we say that $x$ \emph{dominates} $y$ if for all $w\in W$, $wy$ is a negative root whenever $wx$ is a negative root. We call a ... More

Deep Q-Networks for Accelerating the Training of Deep Neural NetworksJun 05 2016Nov 11 2016In this paper, we propose a principled deep reinforcement learning (RL) approach that is able to accelerate the convergence rate of general deep neural networks (DNNs). With our approach, a deep RL agent (synonym for \emph{optimizer} in this work) is ... More

Direct linearisation of the discrete-time two-dimensional Toda latticesFeb 18 2018Jul 08 2018The discrete-time two-dimensional Toda lattice of $A_\infty$-type is studied within the direct linearisation framework, which allows us to deal with several nonlinear equations in this class simultaneously and to construct more general solutions of these ... More

On the hyperalgebra of the loop algebra ${\widehat{\frak{gl}}_n}$Nov 18 2015Let $\widetilde{\mathcal U}_{\mathbb Z}({\widehat{\frak{gl}}_n})$ be the Garland integral form of ${\mathcal U}(\widehat{{\frak{gl}}}_n)$ introduced by Garland \cite{Ga}, where ${\mathcal U}(\widehat{{\frak{gl}}}_n)$ is the universal enveloping algebra ... More

Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersectionsSep 25 2012On one hand, for a general Calabi-Yau complete intersection X, we establish a decomposition, up to rational equivalence, of the small diagonal in X^3, from which we deduce that any decomposable 0-cycle of degree 0 is in fact rationally equivalent to 0, ... More

On the coniveau of certain sub-Hodge structuresApr 10 2012Sep 19 2012We study the generalized Hodge conjecture for certain sub-Hodge structure defined as the kernel of the cup product map with a big cohomology class, which is of Hodge coniveau at least 1. As predicted by the generalized Hodge conjecture, we prove that ... More

A survey on symplectic singularities and resolutionsOct 17 2005This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.

A high-order HDG method for the Biot's consolidation modelApr 27 2018We propose a novel high-order HDG method for the Biot's consolidation model in poroelasticity. We present optimal error analysis for both the semi-discrete and full-discrete (combined with temporal backward differentiation formula) schemes. Numerical ... More

An explicit divergence-free DG method for incompressible magnetohydrodynamicsAug 23 2018We extend the recently introduced explicit divergence-free DG scheme for incompressible hydrodynamics [arXiv:1808.04669]. to the incompressible magnetohydrodynamics (MHD). A globally divergence-free finite element space is used for both the velocity and ... More

Classification of polarized symplectic automorphisms of Fano varieties of cubic fourfoldsMar 09 2013Mar 13 2013We classify the polarized symplectic automorphisms of Fano varieties of smooth cubic fourfolds (equipped with the Pl\"ucker polarization) and study the fixed loci.

Approximating Acceptance Probabilities of CTMC-Paths on Multi-Clock Deterministic Timed AutomataOct 17 2012Feb 01 2013We consider the problem of approximating the probability mass of the set of timed paths under a continuous-time Markov chain (CTMC) that are accepted by a deterministic timed automaton (DTA). As opposed to several existing works on this topic, we consider ... More

On biharmonic hypersurfaces with constant scalar curvatures in $\mathbb E^5(c)$Dec 23 2014We prove that proper biharmonic hypersurfaces with constant scalar curvature in Euclidean sphere $\mathbb S^5$ must have constant mean curvature. Moreover, we also show that there exist no proper biharmonic hypersurfaces with constant scalar curvature ... More

Studying $κ$ meson with a MILC fine latticeMay 20 2013May 31 2013Using the lattice simulations in the Asqtad-improved staggered fermion formulation we compute the point-to-point $\kappa$ correlators, which are analyzed by the rooted staggered chiral perturbation theory (rS$\chi$PT). After chiral extrapolation, we secure ... More

Preliminary lattice study of the I=1 $K \bar{K}$ scattering lengthJan 18 2012Jun 25 2012The s-wave kaon-antikaon ($K \bar{K}$) elastic scattering length is investigated by lattice simulation using pion masses $m_\pi = 330 - 466$ MeV. Through moving wall sources without gauge fixing, we calculate $K \bar{K}$ four-point correlation functions ... More

Blocks of affine quantum Schur algebrasApr 21 2013The affine quantum Schur algebra is a certain important infinite dimensional algebra whose representation theory is closely related to that of quantum affine $\frak{gl}_n$. Finite dimensional irreducible modules for the affine quantum Schur algebra ${\mathcal ... More

A combinatorial analysis of Severi degreesApr 04 2013Jan 06 2014Based on results by Brugall\'e and Mikhalkin, Fomin and Mikhalkin give formulas for computing classical Severi degrees $N^{d, \delta}$ using long-edge graphs. In 2012, Block, Colley and Kennedy considered the logarithmic version of a special function ... More

On the action of symplectic automorphisms on the $CH_0$-groups of some hyper-Kähler fourfoldsFeb 26 2013Nov 10 2014We prove that for any polarized symplectic automorphism of the Fano variety of lines of a cubic fourfold (equipped with the Pl\"ucker polarization), the induced action on the Chow group of 0-cycles is identity, as predicted by Bloch-Beilinson conjecture. ... More

A note on lattice-face polytopes and their Ehrhart polynomialsOct 26 2008We give a new definition of lattice-face polytopes by removing an unnecessary restriction in the paper "Ehrhart polynomials of lattice-face polytopes", and show that with the new definition, the Ehrhart polynomial of a lattice-face polytope still has ... More

Hook length polynomials for plane forests of a certain typeNov 02 2005The original motivation for study for hook length polynomials was to find a combinatorial proof for a hook length formula for binary trees given by Postnikov, as well as a proof for a hook length polynomial formula conjectured by Lascoux. In this paper, ... More

Coxeter groups, imaginary cones and dominanceAug 26 2011Oct 19 2012Brink and Howlett have introduced a partial ordering, called dominance, on the positive roots in the Tits realization of Coxeter groups (Math. Ann. 296 (1993), 179--190). Recently a concept called $\infty$-height is introduced to each reflection in an ... More