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Strong Feller Continuity of Feller Processes and SemigroupsJun 28 2010May 17 2011We study two equivalent characterizations of the strong Feller property for a Markov process and of the associated sub-Markovian semigroup. One is described in terms of locally uniform absolute continuity, whereas the other uses local Orlicz-ultracontractivity. ... More

On the Coupling Property of Lévy ProcessesJun 28 2010May 15 2011We give necessary and sufficient conditions guaranteeing that the coupling for L\'evy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier ... More

Some Theorems on Feller Processes: Transience, Local Times and UltracontractivityAug 16 2011We present sufficient conditions for the transience and the existence of local times of a Feller process, and the ultracontractivity of the associated Feller semigroup; these conditions are sharp for L\'{e}vy processes. The proof uses a local symmetrization ... More

Lower Bounds of the Hausdorff dimension for Feller processesJun 15 2014Nov 13 2014Let $(X_t)_{t\ge0}$ be a Feller process generated by a pseudo-differential operator whose symbol satisfies $\|p(\cdot,\xi)\|_\infty\le c(1+|\xi|^2)$ and $p(\cdot,0)\equiv0.$ We prove that, for a large class of examples, the Hausdorff dimension of the ... More

Variable selection in nonparametric additive modelsOct 20 2010We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the sample size. ... More

Hydrogen Storage on Platinum-Decorated Carbon Nanotubes with Boron, Nitrogen Dopants or Sidewall VacanciesApr 15 2011The interaction between hydrogen molecules and platinum (Pt)-decorated carbon nanotubes (CNTs) with boron (B)-, nitrogen (N)-dopants or sidewall vacancies is discussed from first-principle calculations. The adsorption patterns of hydrogen molecules on ... More

On generating functions of Hausdorff moment sequencesJan 31 2014Nov 25 2014The class of generating functions for completely monotone sequences (moments of finite positive measures on $[0,1]$) has an elegant characterization as the class of Pick functions analytic and positive on $(-\infty,1)$. We establish this and another such ... More

Asymptotic properties of bridge estimators in sparse high-dimensional regression modelsApr 04 2008We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators to ... More

How does an external electrical field affect adsorption patterns of thiol and thiolate on the gold substrate ?Jan 06 2009The responsive behavior of methanethiol and methylthiolate molecules on the Au(111) surface with an applied electrical potential is studied, and it is shown how the sulfur adsorption site, the S-H bond orientation and the interacting energy change with ... More

Constructions of Coupling Processes for Lévy ProcessesSep 28 2010May 15 2011We construct optimal Markov couplings of L\'{e}vy processes, whose L\'evy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by reflection. ... More

Interference Fragmentation Functions and Valence Quark Spin Distributions in the NucleonOct 31 1997Jan 23 1998We explore further applications of the twist-two quark interference fragmentation functions introduced earlier. We show that semi-inclusive production of two pions in the current fragmentation region in deep inelastic scattering of a longitudinally polarized ... More

Interference Fragmentation Functions and the Nucleon's TransversitySep 12 1997Jan 12 1998We introduce twist-two quark interference fragmentation functions in helicity density matrix formalism and study their physical implications. We show how the nucleon's transversity distribution can be probed through the final state interaction between ... More

Thioglycolic acid on the gold (111) surface and Raman vibrational spectraFeb 05 2010The interaction of thioglycolic acid with the Au(111) surface is investigaged, and it is found that at the low coverage the molecule lies down on the substrate. If the mercaptan-hydrogen atom is eliminated, the resulting SCH_2COOH molecule is randomly ... More

Soft Supersymmetry Breaking, Scalar Top-Charm Mixing and Higgs SignaturesMar 15 2001Feb 05 2002The squark mass-matrix from the soft supersymmetry (SUSY) breaking sector contains a rich flavor-mixing structure that allows O(1) mixings among top- and charm-squarks while being consistent with all the existing theoretical and experimental bounds. We ... More

Grain Boundary Shear Coupling is Not a Grain Boundary PropertyOct 10 2018Shear coupling implies that all grain boundary (GB) migration necessarily creates mechanical stresses/strains and is a key component to the evolution of all polycrystalline microstructures. We present MD simulation data and theoretical analyses that demonstrate ... More

Coagulation-fragmentation model for animal group-size statisticsOct 20 2015We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no $H$-theorem, we are able ... More

Light-induced long-ranged disorder effect in ultra-dilute two-dimensional holes in GaAs heterojunction-insulated-gate field-effect-transistorsJun 26 2013Comparing the results of transport measurements of strongly correlated two-dimensional holes in a GaAs heterojunction-insulated-gate field-effect-transistor obtained before and after a brief photo-illumination, the light-induced disorder is found to cause ... More

Electronic States in Two-Dimensional Triangular Cobalt Oxides: Role of Electronic CorrelationJul 23 2003Jul 24 2003We obtain the electronic states and structures of two-dimensional cobalt oxides, Na$_{x}$CoO$_{2}$ (x=0, 0.35, 0.5 and 0.75) by utilizing the full-potential linear muffin-tin orbitals (FP-LMTO) methods, from which some essential electronic interaction ... More

Verification of real-time WSA-ENLIL+Cone simulations of CME arrival-time at the CCMC from 2010-2016Jan 24 2018The Wang-Sheeley-Arge (WSA)-ENLIL+Cone model is used extensively in space weather operations world-wide to model CME propagation. As such, it is important to assess its performance. We present validation results of the WSA-ENLIL+Cone model installed at ... More

Weighted empirical likelihood in some two-sample semiparametric models with various types of censored dataMar 12 2008In this article, the weighted empirical likelihood is applied to a general setting of two-sample semiparametric models, which includes biased sampling models and case-control logistic regression models as special cases. For various types of censored data, ... More

Stochastic Acceleration in the Western Hotspot of Pictor ANov 29 2007Dec 19 2007Chandra's high resolution observations of radio galaxies require a revisit of the relevant electron acceleration processes. Although the diffusive shock particle acceleration model may explain spectra of spatially unresolved sources, it encounters difficulties ... More

Stochastic Electron Acceleration in Shell-Type Supernova RemnantsMay 16 2008Jul 14 2008We study the stochastic electron acceleration by fast mode waves in the turbulent downstream of weakly magnetized collisionless astrophysical shocks. The acceleration is most efficient in a dissipative layer, and the model characteristics are determined ... More

Four-wave mixing with a new phase-matching geometryFeb 27 2019A nondegenerate intensity-squeezed twin beams has been produced with a four-wave mixing (4WM) process driven by two pump fields cross a small angle [Jia \emph{et al.}, Opt. Lett. 42, 4024 (2017)]. We theoretically study this 4WM process and find that ... More

Quantum-oscillation-modulated angular dependences of the positive longitudinal magnetoconductivity and planar Hall effect in Weyl semimetalsJan 29 2019We study the positive longitudinal magnetoconductivity (LMC) and planar Hall effect as emergent effects of the chiral anomaly in Weyl semimetals, following a recent-developed theory by integrating the Landau quantization with Boltzmann equation. It is ... More

Estimating coherence measures from limited experimental data availableJul 10 2017Apr 30 2018Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to estimate these coherence ... More

Neuromimetic Circuits with Synaptic Devices based on Strongly Correlated Electron SystemsNov 15 2014Strongly correlated electron systems such as the rare-earth nickelates (RNiO3, R = rare-earth element) can exhibit synapse-like continuous long term potentiation and depression when gated with ionic liquids; exploiting the extreme sensitivity of coupled ... More

Heliospheric Observations of STEREO-Directed Coronal Mass Ejections in 2008--2010: Lessons for Future Observations of Earth-Directed CMEsMay 11 2012We present a study of coronal mass ejections (CMEs) which impacted one of the STEREO spacecraft between January 2008 and early 2010. We focus our study on 20 CMEs which were observed remotely by the Heliospheric Imagers (HIs) onboard the other STEREO ... More

A Network Object Method to Uncover Hidden Disorder-Related Brain ConnectomeSep 01 2016Jan 12 2017Neuropsychiatric disorders impact functional connectivity of the brain at the network level. The identification and statistical testing of disorder-related networks remains challenging. We propose novel methods to streamline the detection and testing ... More

Imaging the formation of high-energy dispersion anomalies in the actinide UCoGa$_5$Jun 06 2012Oct 10 2012We use angle-resolved photoemission spectroscopy (ARPES) to image the emergence of substaintial dispersion anomalies in the electronic renormalization of the actinide compound UCoGa$_5$ which was presumed to belong to a conventional Fermi liquid family. ... More

Kondo-induced hybrid topological insulator in two-dimensional electron system with a quadratic band crossing pointFeb 10 2016We investigate the Kondo effect in the two-dimensional electron system with a non-trivial quadratic energy band crossing point. We show that the Kondo effect can induce a new hybrid topological insulator phase which is a coexistence state of the quantum ... More

General theory of decoy-state quantum cryptography with source errorsFeb 21 2008Apr 30 2008The existing theory of decoy-state quantum cryptography assumes the exact control of each states from Alice's source. Such exact control is impossible in practice. We develop the theory of decoy-state method so that it is unconditionally secure even there ... More

Terahertz multi-heterodyne spectroscopy using laser frequency combsApr 04 2016Frequency combs based on terahertz quantum cascade lasers feature broadband coverage and high output powers in a compact package, making them an attractive option for broadband spectroscopy. Here, we demonstrate the first multi-heterodyne spectroscopy ... More

A C++ library for Multimodal Deep LearningDec 22 2015Apr 12 2016MDL, Multimodal Deep Learning Library, is a deep learning framework that supports multiple models, and this document explains its philosophy and functionality. MDL runs on Linux, Mac, and Unix platforms. It depends on OpenCV.

On Topological 1D Gravity. IDec 04 2014In topological 1D gravity, the genus zero one-point function combined with the gradient of the action function leads to a spectral curve and its special deformation. After quantization, the partition function is identified as an element in the bosonic ... More

The evolution of the small x gluon TMDMar 24 2016We study the evolution of the small $x$ gluon transverse momentum dependent(TMD) distribution in the dilute limit. The calculation has been carried out in the Ji-Ma-Yuan scheme using a simple quark target model. As expected, we find that the resulting ... More

A note on the scale dependence of the Burkardt sum ruleJul 10 2015In this short note, we argue that the Burkardt sum rule for the Sivers functions can be used to check the consistency of evolution equations of three-parton correlators.

Transverse single spin asymmetry in Drell-Yan production in polarized pA collisionsFeb 09 2015We study the transverse single spin asymmetry in Drell-Yan production in pA collisions with incoming protons being transversely polarized. We carry out the calculation using a newly developed hybrid approach. The polarized cross section computed in the ... More

K-Theory of Hilbert Schemes as a Formal Quantum Field TheoryMar 16 2018We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute K-theoretical ... More

Hermitian One-Matrix Model and KP HierarchySep 21 2018The partition functions of Hermitian one-matrix models are known to be tau-functions of the KP hierarchy. In this paper we explicitly compute the elements in Sato grassmannian these tau-functions correspond to, and use them to compute the $n$-point functions ... More

Some integrality properties in local mirror symmetryMay 18 2010Aug 16 2010We prove some integrality properties of the open-closed mirror maps, inverse open-closed mirror maps and mirror curves of some local Calabi-Yau geometries.

Ricci flow and birational surgeryApr 09 2013We study the formation of finite time singularities of the Kahler-Ricci flow in relation to high codimensional birational surgery in algebraic geometry. We show that the Kahler-Ricci flow on an n-dimensionl Kahler manifold contracts a complex submanifold ... More

Game-theoretic Modeling of Players' Ambiguities on External FactorsOct 23 2015Apr 02 2017We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially mappings from ... More

Communication: Words and Conceptual SystemsJul 29 2015Dec 04 2015Words (phrases or symbols) play a key role in human life. Word (phrase or symbol) representation is the fundamental problem for knowledge representation and understanding. A word (phrase or symbol) usually represents a name of a category. However, it ... More

On computations of Hurwitz-Hodge integralsOct 09 2007We describe a method to compute Hurwitz-Hodge integrals.

Localizations on Moduli Spaces and Free Field Realizations of Feynman RulesOct 18 2003We prove Iqbal's conjecture on the relationship between the free energy of closed string theory in local toric geometry and the Wess-Zumino-Witten model. This is achieved by first reformulating the calculations of the free energy by localization techniques ... More

Hodge Integrals and Integrable HierarchiesOct 26 2003We show that the generating series of some Hodge integrals involving one or two partitions are tau-functions of the KP hierarchy or the 2-Toda hierarchy respectively. We also formulate a conjecture on the connection between relative invariants and integrable ... More

Fixed-delay Interferometry for Doppler Extra-solar Planet DetectionApr 16 2002We present a new technique based on fixed-delay interferometry for high throughput, high precision and multi-object Doppler radial velocity (RV) surveys for extra-solar planets. The Doppler measurements are conducted through monitoring the stellar fringe ... More

Measure-theoretic sensitivity via finite partitionsJun 12 2016Aug 20 2017For every positive integer $n\geq 2$, we introduce the concept of measure-theoretic $n$-sensitivity for measure-theoretic dynamical systems via finite measurable partitions, and show that an ergodic system is measure-theoretically $n$-sensitive but not ... More

On a Mean Field Theory of Topological 2D GravityMar 30 2015We present a one-dimensional mean field theory for topological 2D gravity. We discuss possible generalizations to other topological field theories, in particular those related to semisimple Frobenius manifolds.

Fermionic Computations for Integrable HierarchiesAug 09 2015We present a unified fermionic approach to compute the tau-functions and the n-point functions of integrable hierarchies related to some infinite-dimensional Lie algebras and their representations.

Quantum Deformation Theory of the Airy Curve and Mirror Symmetry of a PointMay 21 2014We present a quantum deformation theory of the Airy curve and use it to establish a version of mirror symmetry of a point.

Integrality Properties of Open-Closed Mirror MapsJun 28 2010We propose a conjecture on integrality property of the open-closed mirror maps of compact Calabi-Yau manifolds. Some examples are presented.

Explicit Formula for Witten-Kontsevich Tau-FunctionJun 23 2013We present an explicit formula for Witten-Kontsevich tau-function.

Hessian Geometry and Phase Change of Gibbons-Hawking MetricsJan 09 2018We study the Hessian geometry of toric Gibbons-Hawking metrics and their phase change phenomena via the images of their moment maps.

Chaos and Entropy for Interval MapsJul 19 2010Feb 07 2011In this paper, various chaotic properties and their relationships for interval maps are discussed. It is shown that the proximal relation is an equivalence relation for any zero entropy interval map. The structure of the set of $f$-nonseparable pairs ... More

Analysis of Markovian Competitive Situations using Nonatomic GamesOct 23 2015Apr 02 2017For dynamic situations where the evolution of a player's state is influenced by his own action as well as other players' states and actions, we show that equilibria derived for nonatomic games (NGs) can be used by their large finite counterparts to achieve ... More

A Link between Sequential Semi-anonymous Nonatomic Games and their Large Finite CounterpartsOct 23 2015Jun 22 2016We show that equilibria of a sequential semi-anonymous nonatomic game (SSNG) can be adopted by players in corresponding large but finite dynamic games to achieve near-equilibrium payoffs. Such equilibria in the form of random state-to-action rules are ... More

Dirac Composite Fermion - A Particle-Hole SpinorNov 22 2017Jan 10 2018The particle-hole (PH) symmetry at half-filled Landau level requires the relationship between the flux number N_phi and the particle number N on a sphere to be exactly N_phi - 2(N-1) = 1. The wave functions of composite fermions with 1/2 "orbital spin", ... More

Scaling window for mean-field percolation of averagesOct 14 2011Feb 15 2013For a complete graph of size $n$, assign each edge an i.i.d. exponential variable with mean $n$. For $\lambda>0$, consider the length of the longest path whose average weight is at most $\lambda$. It was shown by Aldous (1998) that the length is of order ... More

Exponential and double exponential tails for maximum of two-dimensional discrete Gaussian free fieldMay 29 2011Sep 25 2012We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double exponential decay ... More

Comparison Theorems for Manifold with Mean Convex BoundaryJun 21 2013Let $M^n$ be an $n$-dimensional Riemannian manifold with boundary $\partial M$. Assume that Ricci curvature is bounded from below by $(n-1)k$, for $k\in \RR$, we give a sharp estimate of the upper bound of $\rho(x)=\dis(x, \partial M)$, in terms of the ... More

Color entanglement effect in collinear twist-3 factorizationJun 09 2017We study color entanglement effect for T-odd cases in collinear twist-3 factorization. As an example, we compute the transverse single spin asymmetry for direct photon production in pp collisions in pure collinear twist-3 approach. By analyzing the gauge ... More

Information Theory and Statistical Mechanics RevisitedApr 29 2016We derive Bose-Einstein statistics and Fermi-Dirac statistics by Principle of Maximum Entropy applied to two families of entropy functions different from the Boltzmann-Gibbs-Shannon entropy. These entropy functions are identified with special cases of ... More

Emergent Geometry of KP Hierarchy. IIDec 10 2015We elaborate on a construction of quantum LG superpotential associated to a tau-function of the KP hierarchy in the case that resulting quantum spectral curve lies in the quantum two-torus. This construction is applied to Hurwitz numbers, one-legged topological ... More

Emergent Geometry of KP HierarchyNov 26 2015We explain how to construct a quantum deformation of a spectral curve to a tau-function of the KP hierarchy. This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of some earlier work. We also apply it to higher ... More

Transverse single spin asymmetries at small x and the anomalous magnetic momentAug 27 2013Apr 10 2014We show that in the Mclerran-Venugopalan model, an axial asymmetrical valence quark distributions in the transverse plane of a transversely polarized proton can give rise to a spin dependent odderon. Such polarized odderon is responsible for the transverse ... More

Solution of W-Constraints for R-Spin Intersection NumbersMay 30 2013We present a solution to the W-constraints satisfied by the intersection numbers on the moduli spaces of r-spin curves. We make use of a grading suggested by the selection rule for the correlators determined by the geometry of the moduli space.

Quantum Mirror Curves for ${\mathbb C}^3$ and the Resolved ConfioldJul 03 2012We establish a conjecture of Gukov and Su{\l}kowski in the following three cases: Lambert curve for Hurwitz numbers, framed mirror curve of ${\mathbb C}^3$, and the framed mirror curve of the resolved conifold.

Integrality Properties of Variations of Mahler MeasuresJun 12 2010We propose some conjectures on the integrality properties related to the variation of Mahler measures, inspired by the results in the elliptic curve case by Rodriguez Villegas, Stienstra and Zagier.

Riemannian geometry of Kahler-Einstein currentsApr 02 2014We study Riemannian geometry of canonical Kahler-Einstein currents on projective Calabi-Yau varieties and canonical models of general type with crepant singularities. We prove that the metric completion of the regular part of such a canonical current ... More

On Quasimodularity of Some Equivariant Intersection Numbers on the Hilbert SchemesJan 27 2018We observe that certain equivariant intersection numbers of Chern characters of tautological sheaves on Hilbert schemes for suitable circle actions can be computed using the Bloch-Okounkov formula, hence they are related to Gromov-Witten invariants of ... More

Frobenius Manifolds, Spectral Curves, and Integrable HierarchiesDec 17 2015We formulate some conjectures that relates semisimple Frobenius manifolds, their spectral curves and integrable hierarchies.

On Geometry and Symmetry of Kepler Systems. IAug 18 2017We study the Kepler metrics on Kepler manifolds from the point of view of Sasakian geometry and Hessian geometry. This establishes a link between the problem of classical gravity and the modern geometric methods in the study of AdS/CFT correspondence ... More

Transitive points via Furstenberg familyMar 17 2011Jul 30 2011Let $(X,T)$ be a topological dynamical system and $\mathcal{F}$ be a Furstenberg family (a collection of subsets of $\mathbb{Z}_+$ with hereditary upward property). A point $x\in X$ is called an $\mathcal{F}$-transitive one if $\{n\in\mathbb{Z}_+:\, T^n ... More

Regularity of Leray-Hopf solutions to Navier-Stokes equations (II)-Blow up rate with small L^2(R^3) dataNov 30 2006Sep 07 2007An upper bound of blow up rate for the Navier-Stokes equations with small data in L^2(R^3) is obtained.

Open String Invariants and Mirror Curve of the Resolved ConifoldJan 04 2010For the resolved conifold with one outer D-brane in arbitrary framing, we present some results for the open string partition functions obtained by some operator manipulations. We prove some conjectures by Aganagic-Vafa and Aganagic-Klemm-Vafa that relates ... More

Local Mirror Symmetry for the Topological VertexNov 12 2009For three-partition triple Hodge integrals related to the topological vertex, we derive Eynard-Orantin type recursion relations from the cut-and-join equation. This establishes a version of local mirror symmetry for the local $C^3$ geometry with three ... More

Crepant resolution conjecture in all genera for type A singularitiesNov 13 2008We prove an all genera version of the Crepant Resolution Conjecture of Ruan and Bryan-Graber for type A surface singularities. We are based on a method that explicitly computes Hurwitz-Hodge integrals described in an earlier paper and some recent results ... More

Arithmetic McKay correspondenceDec 22 2008We propose an arithmetic McKay correspondence which relates suitably defined zeta functions of some Deligne-Mumford stacks to the zeta functions of their crepant resolutions. Some examples are discussed.

On a deformed topological vertexApr 22 2005We introduce a deformed topological vertex and use it to define deformations of the topological string partition functions of some local Calabi-Yau geometries. We also work out some examples for which such deformations satisfy a deformed Gopakumar-Vafa ... More

The α-Invariant on Toric Fano ManifoldsJul 22 2003The global holomorphic \alpha-invariant introduced by Tian is closely related with the study in the existence of Kahler-Einstein metric. We apply the result of Tian, Lu and Zelditch on polarized Kahler metrics to approximate plurisubharmonic functions ... More

A remark on the convergence of inverse $σ_k$-flowMay 19 2015We study the positivity of related cohomology classes concerning the convergence problem of inverse $\sigma_k$-flow in the conjecture proposed by Lejmi and Sz\'{e}kelyhidi.

Asymptotic Behavior of Solutions for Competitive Models with Free BoundariesDec 16 2013In this paper, we study a competitive model involving two species. When the competition is strong enough, the two species are separated by a free boundary. If the initial data has a positive bound at infinity. We prove that the solution will converge, ... More

Intersection numbers on Deligne-Mumford moduli spaces and quantum Airy curveJun 26 2012We establish the Airy curve case of a conjecture of Gukov and Su{\l}kowski by reducing to Dijkgraaf-Verlinde-Verlinde Virasoro constraints satisfied by the intersection numbers on moduli spaces of algebraic curves.

Rationality for subgroups of S_6Aug 02 2013Sep 04 2013For a transitive subgroup $G \le S_6$ which contain $C_3 \times C_3$ as subgroup, we prove that $K(x_1,\dots,x_6)^G$ is rational over $K$, where $K$ is any field, and $G$ acts naturally on $K(x_1,\dots,x_6)$ by permutations on the variables. We also give ... More

Genus Expansions of Hermitian One-Matrix Models: Fat Graphs vs. Thin GraphsSep 28 2018We consider two different genus expansions of the free energy functions of Hermitian one-matrix models, one using fat graphs, one using ordinary graphs (thin graphs). Some structural results are first proved for the thin version of genus expansion using ... More

Hessian Geometry and Phase Changes of Multi-Taub-NUT MetricsJan 20 2018We study the Hessian geometry of toric multi-Taub-NUT metrics and their phase change phenomena via the images of their moment maps. This generalizes an earlier paper on toric Gibbons-Hawking metrics.

On Regularized Elliptic Genera of ALE SpacesNov 04 2015We define regularized elliptic genera of ALE space of type A by taking some regularized nonequivariant limits of their equivariant elliptic genera with respect to some torus actions. They turn out to be multiples of the elliptic genus of a K3 surface. ... More

The elliptic gluon GTMD inside a large nucleusNov 08 2016We evaluate the elliptic gluon Generalized Transverse Momentum Dependent(GTMD) distribution inside a large nucleus using the McLerran-Venugopalan model. We further show that this gluon distribution can be probed through the angular correlation in virtual ... More

Fat and Thin Emergent Geometries of Hermitian One-Matrix ModelsOct 09 2018We use genus zero free energy functions of Hermitian matrix models to define spectral curves and their special deformations. They are special plane curves defined by formal power series with integral coefficients generalizing the Catalan numbers. This ... More

The rectifiability of singular sets for geometric flows (I)--Yang-Mills flowJun 03 2007We prove that monotonicity of density and energy inequality imply the rectifiability of the singular sets for Yang-Mills flow.

Localization of mixing property via Furstenberg familiesSep 30 2014This paper is devoted to studying the localization of mixing property via Furstenberg families. It is shown that there exists some $\mathscr{F}_{pubd}$-mixing set in every dynamical system with positive entropy, and some $\mathscr{F}_{ps}$-mixing set ... More

Probing the Nucleon's Transversity Via Two-Meson Production in Polarized Nucleon-Nucleon CollisionsJul 30 1998We explore the possibility of probing the nucleon's transversity distribution $\delta q(x)$ through the final state interaction between two mesons ($\pi^+\pi^-$, $\pi K$, or $K\bar K$) produced in transversely polarized nucleon-nucleon collisions. We ... More

Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theoremSep 30 2014It is proved by Kawamata that the canonical bundle of a projective manifold is semi-ample if it is big and nef. We give an analytic proof using the Ricci flow, degeneration of Riemannian manifolds and $L^2$-theory. Combined with our earlier results, we ... More

Degeneration of Kahler-Einstein manifolds of negative scalar curvatureJun 05 2017Let $\pi: \mathcal{X}^* \rightarrow B^*$ be an algebraic family of compact K\"ahler manifolds of complex dimension $n$ with negative first Chern class over a punctured disc $B^*\in \mathbb{C}$. Let $g_t$ be the unique K\"ahler-Einstein metric on $\mathcal{X}_t= ... More

On a class of stochastic partial differential equationsMar 23 2015Jan 28 2016In this paper, we study the stochastic partial differential equation with multiplicative noise $\frac{\partial u}{\partial t} =\mathcal L u+u\dot W$, where $\mathcal L$ is the generator of a symmetric L\'evy process $X$ and $\dot W$ is a Gaussian noise. ... More

Dynamical characterization of C-sets and its applicationOct 25 2011Jan 10 2012In this paper, we set up a general correspondence between the algebra properties of $\bN$ and the sets defined by dynamical properties. In particular, we obtain a dynamical characterization of C-sets, where C-sets are the sets satisfying the strong Central ... More

Particle-Hole Symmetry and the Fractional Quantum Hall States at 5/2 Filling FactorJan 13 2017We propose a derivative operator formed as a function of derivatives of the electron coordinates. When the derivative operator is applied to the Laughlin wave function, two new wave functions in the lowest Landau level at filling factor 1/2 are generated. ... More

Statistical inference for template-based protein structure predictionJun 19 2013Protein structure prediction is one of the most important problems in computational biology. The most successful computational approach, also called template-based modeling, identifies templates with solved crystal structures for the query proteins and ... More

Regularity of Leray-Hopf solutions to Navier-Stokes equations (I)-Critical interior regularity in weak spacesNov 30 2006Dec 29 2006We consider the interior regularity of Leray-Hopf solutions to Navier-Stokes equations on critical case L^2_w(0,T;L^\infty(R^3)). Particularly, an open problem proposed in [KK] was solved.