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New Variables For Graviton Scattering AmplitudesMay 01 2012Motivated by the success of Hodges' momentum twistor variables in planar Yang-Mills, in this note we introduce a set of new variables, the S variables, which are tailored for gravity (or more generally for theories without color ordering). The S variables ... More

Remarks on the Extremal Functions for the Moser-Trudinger InequalitiesApr 15 2005Jul 28 2005We will show in this paper that if $\lambda$ is very close to 1, then $$I(M,\lambda,m)= \sup_{u\in H^{1,n}_0(M) ,\int_M|\nabla u|^ndV=1}\int_\Omega (e^{\alpha_n |u|^\frac{n}{n-1}}-\lambda\sum\limits_{k=1}^m\frac{|\alpha_nu^\frac{n}{n-1}|^k} {k!})dV,$$ ... More

Dark-ages Reionization and Galaxy Formation Simulation - XIII. AGN quenching of high-redshift star formation in ZF-COSMOS-20115Apr 11 2017Aug 25 2017Massive quiescent galaxies (MQGs) are thought to have formed stars rapidly at early times followed by a long period of quiescence. The recent discovery of a MQG, ZF-COSMOS-20115 at $z\sim4$, only 1.5 Gyr after the big bang, places new constraints on galaxy ... More

Dark-ages Reionization and Galaxy Formation Simulation - XIV. Gas accretion, cooling and star formation in dwarf galaxies at high redshiftFeb 12 2018We study dwarf galaxy formation at high redshift ($z\ge5$) using a suite of high-resolution, cosmological hydrodynamic simulations and a semi-analytic model (SAM). We focus on gas accretion, cooling and star formation in this work by isolating the relevant ... More

The UV Emission of Stars in LAMOST Survey I. CatalogsFeb 02 2018We present the ultraviolet magnitudes for over three million stars in the LAMOST survey, in which 2,202,116 stars are detected by $GALEX$. For 889,235 undetected stars, we develop a method to estimate their upper limit magnitudes. The distribution of ... More

Dark-ages Reionization & Galaxy Formation Simulation VIII. Suppressed growth of dark matter halos during the Epoch of ReionizationJan 13 2017Feb 21 2017We investigate how the hydrostatic suppression of baryonic accretion affects the growth rate of dark matter halos during the Epoch of Reionization. By comparing halo properties in a simplistic hydrodynamic simulation in which gas only cools adiabatically, ... More

Dark-ages Reionization and Galaxy Formation Simulation - X. The small contribution of quasars to reionizationMar 15 2017Sep 26 2017Motivated by recent measurements of the number density of faint AGN at high redshift, we investigate the contribution of quasars to reionization by tracking the growth of central supermassive black holes in an update of the Meraxes semi-analytic model. ... More

Solutions for Toda systems on Riemann surfacesApr 19 2005Aug 26 2005In this paper, we study the solutions of Toda systems on Riemann surface in the critical case, we prove a sufficient condition for the existence of solutions of Toda systems.

Bubbling location for $F$-harmonic maps and Inhomogeneous Landau-Lifshitz equationsApr 25 2005Aug 08 2005Let $f$ be a positive smooth function on a close Riemann surface (M,g). The $f-energy$ of a map $u$ from $M$ to a Riemannian manifold $(N,h)$ is defined as $$E_f(u)=\int_Mf|\nabla u|^2dV_g.$$ In this paper, we will study the blow-up properties of Palais-Smale ... More

$W^{2,2}$-conformal immersions of a closed Riemann surface into $\R^n$Jul 22 2010Sep 29 2010We study sequences $f_k:\Sigma_k \to \R^n$ of conformally immersed, compact Riemann surfaces with fixed genus and Willmore energy ${\cal W}(f) \leq \Lambda$. Assume that $\Sigma_k$ converges to $\Sigma$ in moduli space, i.e. $\phi_k^\ast(\Sigma_k) \to ... More

Quantum superreplication of states and gatesDec 18 2015Mar 13 2016While the no-cloning theorem forbids the perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can take place both for ... More

Extremal functions for Moser-Trudinger type inequality on compact closed 4-manifoldsSep 01 2006Sep 14 2006Given a compact closed four dimensional smooth Riemannian manifold, we prove existence of extremal functions for Moser-Trudinger type inequality. The method used is Blow-up analysis combined with capacity techniques.

Two-dimensional curvature functionals with superquadratic growthAug 30 2011For two-dimensional, immersed closed surfaces $f:\Sigma \to \R^n$, we study the curvature functionals $\mathcal{E}^p(f)$ and $\mathcal{W}^p(f)$ with integrands $(1+|A|^2)^{p/2}$ and $(1+|H|^2)^{p/2}$, respectively. Here $A$ is the second fundamental form, ... More

Moser-Trudinger inequalities of vector bundle over a compact Riemannian manifold of dimension 2Oct 26 2005Oct 27 2005Let $(M,g)$ be a 2-dimensional compact Riemannian manifold. In this paper, we use the method of blowing up analysis to prove several Moser-Trdinger type inequalities for vector bundle over $(M,g)$. We also derive an upper bound of such inequalities under ... More

Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed statesJul 15 2014Oct 17 2014Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines often remains ... More

Efficient Quantum Compression for Ensembles of Identically Prepared Mixed StatesJun 11 2015Feb 24 2016We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops down discontinuously ... More

Optimal conditions for $L^\infty$-regularity and a priori estimates for elliptic systems, II: $n(\geq 3)$ componentsMay 29 2008In this paper, we present a bootstrap procedure for general elliptic systems with $n(\geq 3)$ components. Combining with the $L^p$-$L^q$-estimates, it yields the optimal $L^\infty$-regularity conditions for the three well-known types of weak solutions: ... More

Optimal conditions for $L^\infty$-regularity and a priori estimates for elliptic systems, I: two componentsMay 29 2008In this paper we present a new bootstrap procedure for elliptic systems with two unknown functions. Combining with the $L^p$-$L^q$-estimates, it yields the optimal $L^\infty$-regularity conditions for the three well-known types of weak solutions: $H_0^1$-solutions, ... More

Weak limit of an immersed surface sequence with bounded Willmore functionalSep 07 2011We will study the blowup behavior of a surface sequence immersed in $R^2$ with bounded Willmore functional and fixed genus.

Si$_3$N$_4$ optomechanical crystals in the resolved-sideband regimeNov 25 2013Nov 26 2013We demonstrate sideband-resolved Si$_3$N$_4$ optomechanical crystals supporting $10^5$ quality factor optical modes at 980 nm, coupled to $\approx4$ GHz frequency mechanical modes with quality factors of $\approx3000$. Optomechanical electromagnetically ... More

MiMatrix: A Massively Distributed Deep Learning Framework on a Petascale High-density Heterogeneous ClusterFeb 07 2018In this paper, we present a co-designed petascale high-density GPU cluster to expedite distributed deep learning training with synchronous Stochastic Gradient Descent~(SSGD). This architecture of our heterogeneous cluster is inspired by Harvard architecture. ... More

Chandra Studies of the X-ray Gas Properties of Fossil SystemsSep 13 2015We study ten galaxy groups and clusters suggested in the literature to be "fossil system (FS)" based on \chandra\ observations. According to the $M_{500}-T$ and $L_{\rm X}-T$ relations, the gas properties of FSs are not physically distinct from ordinary ... More

Farrell cohomology of low genus pure mapping class groups with puncturesJul 22 2002In this paper, we calculate the p-torsion of the Farrell cohomology for low genus pure mapping class groups with punctures, where p is an odd prime. Here, `low genus' means g=1,2,3; and `pure mapping class groups with punctures' means the mapping class ... More

On the Associativity of GluingJul 27 2011This paper studies the associativity of gluing of trajectories in Morse theory. We show that the associativity of gluing follows from of the existence of compatible manifold with face structures on the compactified moduli spaces. Using our previous work, ... More

On the Communication Complexity of Distributed ClusteringJun 30 2015Aug 07 2015In this paper we give a first set of communication lower bounds for distributed clustering problems, in particular, for k-center, k-median and k-means. When the input is distributed across a large number of machines and the number of clusters k is small, ... More

$t$-Analog of $q$-Characters, Bases of Quantum Cluster Algebras, and a Correction TechniqueJul 27 2012Jun 21 2016We first study a new family of graded quiver varieties together with a new $t$-deformation of the associated Grothendieck rings. This provides the geometric foundations for a joint paper by Yoshiyuki Kimura and the author. We further generalize the result ... More

Probe a family non-universal Z' boson effects in B(s)-> phi mu(+) mu(-)decayJan 06 2011Motivated by the recent measurement on ${\cal B}(\bar{B}_s\to \phi \mu^+\mu^-)$ by CDF collaboration, we study the effects of a family non-universal $Z^{\prime}$ boson on rare semileptonic $\bar{B}_s \to \phi\mu^+\mu^-$ decay. In our evaluations, we analyze ... More

Triangular bases in quantum cluster algebras and monoidal categorification conjecturesJan 16 2015Sep 26 2016We consider the quantum cluster algebras which are injective-reachable and introduce a triangular basis in every seed. We prove that, under some initial conditions, there exists a unique common triangular basis with respect to all seeds. This basis is ... More

Faster Treasure Hunt and Better Strongly Universal Exploration SequencesApr 24 2012In this paper, we investigate the explicit deterministic treasure hunt problem in a $n$-vertex network. This problem was firstly introduced by Ta-Shma and Zwick in \cite{TZ07} [SODA'07]. Note also it is a variant of the well known rendezvous problem in ... More

Quantum Cluster Variables via Serre PolynomialsApr 23 2010Jul 13 2010For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials ... More

Status and prospects for BESIIIDec 01 2013In this paper the status and prospects for BESIII is presented.The BEPCII machine is in good status and recently reached its highest luminosity of 7.08*10^32cm^-2s^-1. The BESIII detectors have been running stably since 2009. Upgrade plans for its sub-detectors ... More

Compare triangular bases of acyclic quantum cluster algebrasJun 17 2016Given a quantum cluster algebra, we show that its triangular bases defined by Berenstein and Zelevinsky and those defined by the author are the same for the seeds associated with acyclic quivers. This result implies that the Berenstein-Zelevinsky's basis ... More

A network model for cellular agingMay 24 2013Dec 17 2013What is aging? Mechanistic answers to this question remain elusive despite decades of research. Here, we propose a mathematical model of cellular aging based on a model gene interaction network. Our network model is made of only non-aging components - ... More

An application of topological equivalence to Morse theoryFeb 14 2011In a previous paper, under the assumption that the Riemannian metric is special, the author proved some results about the moduli spaces and CW structures arising from Morse theory. By virtue of topological equivalence, this paper extends those results ... More

Jordan-Hölder theorems for derived categories of derived discrete algebrasJun 27 2015For any positive integer $n$, $n$-derived-simple derived discrete algebras are classified up to derived equivalence. Furthermore, the Jordan-H\"older theorems for all kinds of derived categories of derived discrete algebras are obtained.

Quantum groups via cyclic quiver varieties IDec 04 2013Mar 10 2015We construct the quantized enveloping algebra of any simple Lie algebra of type ADE as the quotient of a Grothendieck ring arising from certain cyclic quiver varieties. In particular, the dual canonical basis of a one-half quantum group with respect to ... More

Noncommutative maximal ergodic inequality for non-tracial L1-spacesFeb 22 2011We extend the noncommutative L1-maximal ergodic inequality for semifinite von Neumann algebras established by Yeadon in 1977 to the framework of noncommutative L1-spaces associated with sigma-finite von Neumann algebras. Since the semifnite case of this ... More

Performance of a Nonempirical Density Functional on Molecules and Hydrogen-Bonded ComplexesJul 18 2016Aug 11 2016Recently, Tao and Mo (TM) derived a new meta-generalized gradient approximation based on a model exchange hole. In this work, the performance of this functional is assessed on standard test sets, using the 6-311++G(3df,3pd) basis set. These test sets ... More

A sharp Trudinger-Moser type inequality for unbounded domains in $\mathbb{R}^n$Sep 22 2006The Trudinger-Moser inequality states that for functions $u \in H_0^{1,n}(\Omega)$ ($\Omega \subset \mathbb R^n$ a bounded domain) with $\int_\Omega |\nabla u|^ndx \le 1$ one has $\int_\Omega (e^{\alpha_n|u|^{\frac n{n-1}}}-1)dx \le c |\Omega|$, with ... More

Quantum measurements with preselection and postselectionAug 08 2011Nov 15 2011We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive ... More

Accurate semilocal density functional for condensed matter physics and quantum chemistryJul 16 2016Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents ... More

A weak energy identity and the length of necks for a Sacks-Uhlenbeck $α$-harmonic map sequenceApr 28 2008May 30 2008We will give a weak energy identity for Sacks-Uhlenbeck approximation of harmonic maps and calculate the length of the necks.

Boundedness in a quasilinear fully parabolic Keller-Segel system with logistic sourceApr 06 2015This paper deals with the Neumann boundary value problem for the system $$u_t=\nabla\cdot\left(D(u)\nabla u\right)-\nabla\cdot\left(S(u)\nabla v\right)+f(u) ,\quad x\in\Omega,\ t>0$$ $$v_t=\Delta v-v+u,\quad x\in\Omega,\ t>0$$ in a smooth bounded domain ... More

Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusionJan 21 2015We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-Stokes equations generalizing the porous-medium-type diffusion model $ \quad n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(n\chi(c)\nabla c), $ $ \quad c_t+u\cdot\nabla ... More

Extendability of conformal structures on punctured surfacesSep 27 2015For a smooth immersion $f$ from the punctured disk $D\backslash\{0\}$ into $\mathbb{R}^n$ extendable continuously at the puncture, if its mean curvature is square integrable and the measure of $f(D)\cap B_{r_k}=o(r_k)$ for a sequence $r_k\to 0$, we show ... More

Density profiles and collective modes of a Bose-Einstein condensate with light-induced spin-orbit couplingJun 24 2013Dec 27 2013The phases of a Bose-Einstein condensate (BEC) with light-induced spin-orbit coupling (SOC) are studied within the mean-field approximation. The mixed BEC phase, in which the system condenses in a superposition of two plane wave states, is found to be ... More

$b\to ss{\bar d} $ decay in Randall-Sundrum modelsJul 26 2016The extremely small branching ratio of $b\to ss{\bar d}$ decay in the Standard Model makes it a suitable channel to explore new physics through various extensions of the Standard Model. We study this $\Delta S=2$ process in Randall-Sundrum models, including ... More

Effect of the pseudogap on the infrared response in cuprate superconductorsMar 12 2014One of the most essential aspects of cuprate superconductors is a large pseudogap coexisting with a superconducting gap, then some anomalous properties can be understood in terms of the formation of the pseudogap. Within the kinetic energy driven superconducting ... More

Second Stop and Sbottom Searches with a Stealth StopJul 22 2016The top squarks (stops) may be the most wanted particles after the Higgs boson discovery. The searches for the lightest stop have put strong constraints on its mass. However, there is still a search gap in the low mass region if the spectrum of the stop ... More

Pseudogap and charge dynamics in doped cupratesApr 22 2013Nov 12 2013Within the microscopic theory of the normal-state pseudogap state, the doping and temperature dependence of the charge dynamics in doped cuprates is studied in the whole doping range from the underdoped to heavily overdoped. The conductivity spectrum ... More

Some relations deduced from regularized double shuffle relations of multiple zeta valuesOct 18 2016It is conjectured that the regularized double shuffle relations give all algebraic relations among multiple zeta values. Hence all other algebraic relations should be deduced from the regularized double shuffle relations. In this paper, we recall or prove ... More

Robustness of DC Power Networks under Weight ControlSep 07 2016We study, possibly distributed, robust weight control policies for DC power networks that change link susceptances or weights within specified operational range in response to balanced disturbances to the supply-demand vector. The margin of robustness ... More

Controllable single-photon transport between remote coupled-cavity arraysDec 21 2015Mar 25 2016We develop a new approach for controllable single-photon transport between two remote one-dimensional coupled-cavity arrays, used as quantum registers, mediated by an additional one-dimensional coupled-cavity array, acting as a quantum channel. A single ... More

Implicit Asymptotic Preserving Method for Linear Transport EquationsFeb 01 2016The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the speed of light, ... More

Spin Hall Conductance of the Two Dimensional Hole Gas in a Perpendicular Magnetic FieldFeb 10 2006May 02 2006The charge and spin Hall conductance of the two-dimensional hole gas within the Luttinger model with and without inversion symmetry breaking terms in a perpendicular magnetic field are studied, and two key phenomena are predicted. The sign of the spin ... More

Simulations of a gradual solar energetic particle event observed by Helios 1, Helios 2, and IMP 8May 12 2015Jul 06 2015In this work, a gradual solar energetic particle (SEP) event observed by multispacecraft has been simulated. The time profiles of SEP fluxes accelerated by an interplanetary shock in the three-dimensional interplanetary space are obtained by solving numerically ... More

Theory of Jet Quenching in Ultra-Relativistic Nuclear CollisionsAug 03 2014We present a short overview of recent progress in the theory of jet quenching in ultra-relativistic nuclear collisions, including phenomenological studies of jet quenching at RHIC and the LHC, development in NLO perburbative QCD calculation of jet broadening ... More

Parton shower evolution in medium and nuclear modification of photon-tagged jets in Pb+Pb collisions at the LHCOct 24 2012Jul 06 2014We study the medium modification of jets correlated with large transverse momentum photons at the LHC via a transport and perturbative QCD hybrid model which incorporates the contributions from both elastic collisions and radiative energy loss experienced ... More

Report on the Workshop on Accelerator R&D for Ultimate Storage RingsMar 19 2013This report summaries the workshop on accelerator R&D for ultimate storage ring, held in Huairou, Beijing, Oct. 30 to Nov. 1, 2012.

Harnack inequalities for $1$-$d$ stochastic Klein-Gordon type equationsOct 31 2013By the coupling method, we establish the Harnack inequalities, derivative formula and Driver's integration by parts formula for the stochastic Klein-Gordon type equations in the interval. We provide a detailed discussion about the nonlinear term. Some ... More

First Principles Study of Bismuth Films on the Nickel(111) SurfaceApr 11 2013A recent experiment(Bollmann11) suggested that bismuth forms hexagonal close packed (HCP) films on the Ni(111) surface, of heights 3, 5 and 7 layers. A quantum size effect based on free electrons was proposed in explanation. To test this idea, we calculate ... More

The Long Bond, Long Forward Measure and Long-Term Factorization in Heath-Jarrow-Morton ModelsOct 04 2016This paper proves existence of the long bond, long forward measure and long-term factorization of the stochastic discount factor (SDF) of Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM) models in the function space ... More

A Family of Compact Complex-Symplectic Calabi-Yau Manifolds that are NonkählerJan 17 2016Jun 05 2016We construct a family of $6$-dimensional compact manifolds $M(A)$, which are simultaneously diffeomorphic to complex Calabi-Yau manifolds and symplectic Calabi-Yau manifolds. They have fundamental groups $\mathbb{Z} \oplus \mathbb{Z}$, their odd-dimensional ... More

A systematic approach to sketch Bethe-Salpeter equationJan 13 2016To study meson properties, one needs to solve the gap equation for the quark propagator and the Bethe-Salpeter (BS) equation for the meson wavefunction, self-consistently. The gluon propagator, the quark-gluon vertex, and the quark--anti-quark scattering ... More

Quantum pumping induced by disorder in one dimensionNov 17 2013Apr 19 2016The topological property in one dimension (1D) is protected by symmetry. Based on a concrete model, we show that since a 1D topological model usually contain two of the three Pauli matrix, the left one automatically become the protecting symmetry. We ... More

Optimal Tracking of Distributed Heavy Hitters and QuantilesDec 01 2008We consider the the problem of tracking heavy hitters and quantiles in the distributed streaming model. The heavy hitters and quantiles are two important statistics for characterizing a data distribution. Let $A$ be a multiset of elements, drawn from ... More

Higher $K$-Groups of Smooth Projective Curves Over Finite FieldsDec 27 2011Let $X$ be a smooth projective curve over a finite field $\mathbb{F}$ with $q$ elements. For $m\geq 1,$ let $X_m$ be the curve $X$ over the finite field $\mathbb{F}_m$, the $m$-th extension of $\mathbb{F}.$ Let $K_n(m)$ be the $K$-group $K_n(X_m)$ of ... More

Necessary conditions for reversed Dickson polynomials of the second kind to be permutationalApr 08 2014In this paper, we present several necessary conditions for the reversed Dickson polynomial $E_{n}(1, x)$ of the second kind to be a permutation of $\mathbb{F}_{q}$. In particular, we give explicit evaluation of the sum $\sum_{a\in \mathbb{F}_{q}}E_{n}(1,a)$. ... More

Joint Variable Selection for Data Envelopement Analysis via Group SparsityFeb 16 2014This study develops a data-driven group variable selection method for data envelopment analysis (DEA), a non-parametric linear programming approach to the estimation of production frontiers. The proposed method extends the group Lasso (least absolute ... More

Construction of Minimal Tail-Biting Trellises for Codes over Finite Abelian GroupsFeb 05 2007May 17 2007A definition of atomic codeword for a group code is presented. Some properties of atomic codewords of group codes are investigated. Using these properties, it is shown that every minimal tail-biting trellis for a group code over a finite abelian group ... More

Hilbert schemes of points on the minimal resolution and soliton equationsApr 29 2004Jun 26 2006The equivariant and ordinary cohomology rings of Hilbert schemes of points on the minimal resolution C^2//G for cyclic G are studied using vertex operator technique, and connections between these rings and the class algebras of wreath products are explicitly ... More

Efficient numerical solution of acoustic scattering from doubly-periodic arrays of axisymmetric objectsJun 12 2015Jun 08 2016We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution operator using ... More

Robustness of DC Power Networks under Weight ControlSep 07 2016Oct 18 2016We study, possibly distributed, robust weight control policies for DC power networks that change link susceptances, or weights in response to balanced disturbances to the supply-demand vector. The margin of robustness for a given control policy is defined ... More

The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gasDec 03 2014We study the regularity of sonic curves to a two-dimensional Riemann problem for the nonlinear wave system of Chaplygin gas, which is an essential step for the global existence of solutions to the two-dimensional Riemann problems. As a result, we establish ... More

Sign changes and resonance of intrinsic spin Hall effect in two-dimensional hole gasJun 03 2006Jul 21 2006The intrinsic spin Hall conductance shows rich sign changes by applying a perpendicular magnetic field in a two-dimensional hole gas. Especially, a notable sign changes can be achieved by adjusting the characteristic length of the Rashba coupling and ... More

Effect of quantum lattice fluctuations on the optical-absorption spectra of halogen-bridged mixed-valence transition-metal complexesJun 01 2001The effect of quantum lattice fluctuations on the optical-absorption spectra in the ground state of halogen-bridged mixed-valence transition-metal linear-chain complexes is studied by using a one-dimensional extended Peierls-Hubbard model. The nonadiabatic ... More

Scheme for the implementation of optimal cloning of arbitrary single particle atomic state into two photonic statesDec 21 2006Dec 22 2006We present a feasible scheme to implement the $1 \to 2$ optimal cloning of arbitrary single particle atomic state into two photonic states, which is important for applications in long distance quantum communication. Our scheme also realizes the tele-NOT ... More

Low Rank and Sparsity Analysis Applied to Speech Enhancement via Online Estimated DictionarySep 29 2016We propose an online estimated dictionary based single channel speech enhancement algorithm, which focuses on low rank and sparse matrix decomposition. In this proposed algorithm, a noisy speech spectral matrix is considered as the summation of low rank ... More

Coherent State Functional Integrals in Quantum CosmologyOct 25 2011Mar 28 2012Coherent state functional integrals for the minisuperspace models of quantum cosmology are studied. By the well-established canonical theories, the transition amplitudes in the path-integral representations of Wheeler-DeWitt quantum cosmology and loop ... More

A Geometric Proof of Removal of Boundary Singularities of Pseudo-Holomorphic CurvesOct 16 2012We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting curves with boundary ... More

Non-vanishing Fourier coefficients of modular formsApr 28 2015Feb 18 2016In this paper, we generalize D. H. Lehmer's result to give a sufficient condition for level one cusp forms $f$ with integral Fourier coefficients such that the smallest $n$ for which the coefficients $a_n(f)=0$ must be a prime. Then we describe a method ... More

Lehmer's totient problem over $\mathbb{F}_q[x]$Dec 11 2013Apr 29 2015In this paper, we consider the function field analogue of the Lehmer's totient problem. Let $p(x)\in\mathbb{F}_q[x]$ and $\varphi(q,p(x))$ be the Euler's totient function of $p(x)$ over $\mathbb{F}_q[x],$ where $\mathbb{F}_q$ is a finite field with $q$ ... More

Homological behavior of Auslander's $k$-Gorenstein ringsSep 09 2004Aug 04 2010In this paper we mainly study the homological properties of dual modules over $k$-Gorenstein rings. For a right quasi $k$-Gorenstein ring $\Lambda$, we show that the right self-injective dimension of $\Lambda$ is at most $k$ if and only if each $M \in$mod ... More

On Okounkov's conjecture connecting Hilbert schemes of points and multiple q-zeta valuesOct 03 2015We compute the generating series for the intersection pairings between the total Chern classes of the tangent bundles of the Hilbert schemes of points on a smooth projective surface and the Chern characters of tautological bundles over these Hilbert schemes. ... More

Long-Term Factorization of Affine Pricing KernelsOct 03 2016This paper constructs and studies the long-term factorization of affine pricing kernels into discounting at the rate of return on the long bond and the martingale component that accomplishes the change of probability measure to the long forward measure. ... More

Automatic finite element implementation of hyperelastic material with a double numerical differentiation algorithmJun 13 2016In order to accelerate implementation of hyperelastic materials for finite element analysis, we developed an automatic numerical algorithm that only requires the strain energy function. This saves the effort on analytical derivation and coding of stress ... More

Self-Retracting Motion of Graphite MicroflakesSep 26 2007We report the observation of a novel phenomenon, the self-retracting motion of graphite, in which tiny flakes of graphite, after being displaced to various suspended positions from islands of highly orientated pyrolytic graphite, retract back onto the ... More

Strong Feller Property and Irreducibility for Non-Linear Monotone SPDEsJul 27 2014Jul 31 2014Strong Feller property and irreducibility are study for a class of non-linear monotone stochastic partial differential equations with multiplicative noise. H\"older continuity of the associated Markov semigroups are discussed in some special cases. The ... More

Regime-switching diffusion processes: strong solutions and strong Feller propertyMar 11 2016We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result is established ... More

Optimal linear codes, constant-weight codes and constant-composition codes over $\Bbb F_{q}$May 13 2016Optimal linear codes and constant-weight codes play very important roles in coding theory and have attached a lot of attention. In this paper, we mainly present some optimal linear codes and some optimal constant-weight codes derived from the linear codes. ... More

Lattice parameters from direct-space images at two tiltsJan 11 2000Oct 29 2001Lattices in three dimensions are oft studied from the ``reciprocal space'' perspective of diffraction. Today, the full lattice of a crystal can often be inferred from direct-space information about three sets of non-parallel lattice planes. Such data ... More

Stability of Wave Patterns to the Inflow Problem of Full Compressible Navier-Stokes EquationsMar 24 2009Mar 25 2009The inflow problem of full compressible Navier-Stokes equations is considered on the half line $(0,+\infty)$. Firstly, we give the existence (or non-existence) of the boundary layer solution to the inflow problem when the right end state $(\rho_+,u_+,\theta_+)$ ... More

On the B-twisted topological sigma model and Calabi-Yau geometryFeb 27 2014We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps. We prove that the first Chern class of the target manifold ... More

A Survey on Distance Vector Routing ProtocolsNov 07 2011In this paper we give a brief introduction to five different distance vector routing protocols (RIP, AODV, EIGRP, RIP-MTI and Babel) and give some of our thoughts on how to solve the count to infinity problem. Our focus is how distance vector routing ... More

Anisotropic Flow and Jet Quenching in Relativistic Nuclear CollisionsFeb 09 2015The exploration of the strong-interaction matter under extreme conditions is one of the main goals of relativistic heavy-ion collisions. We provide some of the main results on the novel properties of quark-gluon plasma, with particular focus given to ... More

Regularized Spectral Clustering under the Degree-Corrected Stochastic BlockmodelSep 16 2013Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for improved statistical ... More

Graded quiver varieties, quantum cluster algebras and dual canonical basisMay 09 2012Jun 12 2012Inspired by a previous work of Nakajima, we consider perverse sheaves over acyclic graded quiver varieties and study the Fourier-Sato-Deligne transform from a representation theoretic point of view. We obtain deformed monoidal categorifications of acyclic ... More

Development of the spectrum of gamma-ray burst pulses influenced by the intrinsic spectral evolution and the curvature effectFeb 16 2009Spectral evolution of gamma-ray burst pulses assumed to arise from emission of fireballs is explored. It is found that, due to the curvature effect, the integrated flux and peak energy are well related by a power law in the decaying phase of pulses, where ... More

The softening phenomenon due to the curvature effect: in the case of extremely short intrinsic emissionJun 20 2008Oct 02 2008The curvature effect is explored in the case of extremely short intrinsic emission. Assuming a $\delta$ function emission we get formulas that get rid of the impacts from the intrinsic emission duration, which are applicable to any forms of continuum. ... More

The full curvature effect expected in early X-ray afterglow emission of gamma-ray burstsApr 14 2008We explore the influence of the full curvature effect on the flux of early X-ray afterglow of gamma-ray bursts (GRBs) in cases when the spectrum of the intrinsic emission is a power-law. We find that the well-known $t^{-(2+\beta)}$ curve is present only ... More