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Complexity, Entropy, and Markov ChainsFeb 26 2019We develop a theory of classical complexity. We study the relations between classical complexity and entropy, and conjecture that in an isolated system, classical absolute complexity always tends to grow, until it reaches its maximum. We calculate some ... More

Transformable topological mechanical metamaterialsOct 21 2015Mechanical metamaterials are engineered materials that gain their remarkable mechanical properties, such as negative Poisson's ratios, negative compressibility, phononic bandgaps, and topological phonon modes, from their structure rather than composition. ... More

Capillary-driven binding of thin triangular prisms at fluid interfacesFeb 08 2018We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 $\mu m$, and the thickness of the prism is varied between 2 and 20 $\mu m$. For thickness ... More

Nonparametric specification for non-stationary time series regressionFeb 04 2014We investigate the behavior of the Generalized Likelihood Ratio Test (GLRT) (Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193]) for time varying coefficient models where the regressors and errors are non-stationary time series and can be cross correlated. ... More

Inference of weighted $V$-statistics for nonstationary time series and its applicationsJan 16 2014We investigate the behavior of Fourier transforms for a wide class of nonstationary nonlinear processes. Asymptotic central and noncentral limit theorems are established for a class of nondegenerate and degenerate weighted $V$-statistics through the angle ... More

Non-zero-sum stopping games in continuous timeAug 17 2015On a filtered probability space $(\Omega ,\mathcal{F}, (\mathcal{F}_t)_{t\in[0,\infty]}, \mathbb{P})$, we consider the two-player non-zero-sum stopping game $u^i := \mathbb{E}[U^i(\rho,\tau)],\ i=1,2$, where the first player choose a stopping strategy ... More

Multi-player stopping games in continuous timeSep 14 2015We consider multi-player stopping games in continuous time. Unlike Dynkin games, in our games the payoff of each player is revealed after all the players stop. Moreover, each player can adjust her own stopping strategy by observing other players' behaviors. ... More

Non-zero-sum stopping games in discrete timeAug 25 2015We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's ... More

Nonparametric inference of quantile curves for nonstationary time seriesOct 19 2010The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence bands and integrated ... More

Channel Estimation for Millimeter Wave MIMO-OFDM Systems via Low-Rank Tensor DecompositionSep 12 2016In millimeter-wave (mmWave) MIMO systems, both the base stations (BS) and the mobile stations (MSs) employ large antenna arrays for directional beamforming. Acquiring channel knowledge for beamforming transmission is challenging due to the large number ... More

On Zero-sum Optimal Stopping GamesAug 16 2014May 08 2015On a filtered probability space $(\Omega,\mathcal{F},P,\mathbb{F}=(\mathcal{F}_t)_{t=0,\dotso,T})$, we consider stopper-stopper games $\overline V:=\inf_{\Rho\in\bT^{ii}}\sup_{\tau\in\T}\E[U(\Rho(\tau),\tau)]$ and $\underline V:=\sup_{\Tau\in\bT^i}\inf_{\rho\in\T}\E[U(\Rho(\tau),\tau)]$ ... More

On utility maximization with derivatives under model uncertaintyJul 18 2013We consider the robust utility maximization using a static holding in derivatives and a dynamic holding in the stock. There is no fixed model for the price of the stock but we consider a set of probability measures (models) which are not necessarily dominated ... More

No-arbitrage and hedging with liquid American optionsMay 04 2016May 27 2016Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this problem has proved ... More

Estimation and inference for precision matrices of non-stationary time seriesMar 03 2018Apr 18 2018In this paper, we consider the estimation and inference of precision matrices of a rich class of locally stationary and nonlinear time series assuming that only one realization of the time series is observed. Using a Cholesky decomposition technique, ... More

Arbitrage, hedging and utility maximization using semi-static trading strategies with American optionsFeb 24 2015Feb 08 2016We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only ... More

On controller-stopper problems with jumps and their applications to indifference pricing of American optionsDec 20 2012Nov 18 2013We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditional ... More

Ground-State Entropy of the Random Vertex-Cover ProblemOct 03 2008Mar 17 2009Counting the number of ground states for a spin-glass or NP-complete combinatorial optimization problem is even more difficult than the already hard task of finding a single ground state. In this paper the entropy of minimum vertex-covers of random graphs ... More

On a Stopping Game in continuous timeSep 23 2014Jul 24 2015We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.

Spectral Inference under Complex Temporal DynamicsDec 19 2018Dec 31 2018We develop unified theory and methodology for the inference of evolutionary Fourier power spectra for a general class of locally stationary and possibly nonlinear processes. In particular, simultaneous confidence regions (SCR) with asymptotically correct ... More

On model-independent pricing/hedging using shortfall risk and quantilesJul 09 2013We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model to call options ... More

On an Optimal Stopping Problem of an InsiderJan 14 2013Apr 06 2015We consider the optimal stopping problem $v^{(\eps)}:=\sup_{\tau\in\mathcal{T}_{0,T}}\mathbb{E}B_{(\tau-\eps)^+}$ posed by Shiryaev at the International Conference on Advanced Stochastic Optimization Problems organized by the Steklov Institute of Mathematics ... More

On Arbitrage and Duality under Model Uncertainty and Portfolio ConstraintsFeb 11 2014Mar 27 2015We consider the fundamental theorem of asset pricing (FTAP) and hedging prices of options under non-dominated model uncertainty and portfolio constrains in discrete time. We first show that no arbitrage holds if and only if there exists some family of ... More

Super-hedging American Options with Semi-static Trading Strategies under Model UncertaintyApr 15 2016We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price $\pi$ is given by the supremum ... More

A Microscopic Field Theory for the Universal Shift of Sound Velocity and Dielectric Constant in Low-Temperature GlassesAug 08 2016In low-temperature glasses, the sound velocity changes as the logarithmic function of temperature below $10$K: $[c(T) - c(T_0)]/c(T_0) = \mathcal{C}\ln(T/T_0)$. With increasing temperature starting from $T=0$K, the sound velocity does not increase monotonically, ... More

Exponential Convergence to the Maxwell Distribution For Spatially Inhomogenous Boltzmann EquationsMar 21 2016Nov 08 2016We consider the rate of convergence of solutions of spatially inhomogenous Boltzmann equations, with hard sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially homogenous static Maxwell velocity distributions with different ... More

Scalar Curvature Bound for Kähler-Ricci Flows over Minimal Manifolds of General TypeJan 21 2008In this short note, we use classic computations for K\"ahler-Ricci flow to achieve scalar curvature bound for minimal manifold of general type.

Emergent Geometric Hamiltonian and Insulator-Superfluid Phase TransitionsMar 22 2005May 05 2005I argue that certain bosonic insulator-superfluid phase transitions as an interaction constant varies are driven by emergent geometric properties of insulating states. The {\em renormalized} chemical potential and distribution of disordered bosons define ... More

Quantum Spin Nematic States in Bose-Einstein CondensatesAug 28 2001Dec 19 2002We review some recent results on discrete symmetries and topological order in spinor Bose-Einstein condensates (BECs) of $^{23}Na$. For spin one bosons with two-body scatterings dominated by a total spin equal to two channel, the BECs are in quantum spin ... More

Sparse Group Selection Through Co-Adaptive PenaltiesNov 18 2011Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well approximated by a ... More

Measurement of arbitrary two-photon entanglement state with the photonic Faraday rotationJan 27 2014Feb 05 2014We propose an efficient protocol for measuring the concurrence of arbitrary two-photon pure entangled state with the help of the photonic Faraday rotation. In the protocol, the concurrence of the photonic entangled state can be conversed into the total ... More

Viviani Polytopes and Fermat PointsAug 06 2010Nov 29 2010Given a set of oriented hyperplanes $\mathcal{P}=\{p_1, ..., p_k\}$ in $\mathbb{R}^n$, define $v(P)$ for any point $P\in\mathbb{R}^n$ as the sum of the signed distances from $P$ to $p_1$,..., $p_k$. We give a simple geometric characterization of $\mathcal{P}$ ... More

Projective spherically symmetric Finsler metrics with constant flag curvature in R^nJun 19 2010We investigate projective spherically symmetric Finsler metrics with constant flag curvature in $R^n$ and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk are found to have ... More

Optimal multi-photon entanglement concentration with the photonic Faraday rotationNov 02 2012A recent paper (Phys. Rev. A \textbf{86}, 034305 (2012)) proposed an entanglement concentration protocol (ECP) for distilling one pair of maximally entangled multi-photon Greenberger-Horne-Zeilinger (GHZ) state from two pairs of less-entangled multi-photon ... More

Efficient single-photon entanglement concentration for quantum communicationsSep 28 2012We present two protocols for the single-photon entanglement concentration. With the help of the 50:50 beam splitter, variable beam splitter and an auxiliary photon, we can concentrate a less-entangled single-photon state into a maximally single-photon ... More

Nonparametric Bayesian Negative Binomial Factor AnalysisApr 25 2016A common approach to analyze an attribute-instance count matrix, an element of which represents how many times an attribute appears in an instance, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency for an ... More

(2^n,2^n,2^n,1)-relative difference sets and their representationsNov 13 2012Apr 13 2013We show that every $(2^n,2^n,2^n,1)$-relative difference set $D$ in $\Z_4^n$ relative to $\Z_2^n$ can be represented by a polynomial $f(x)\in \F_{2^n}[x]$, where $f(x+a)+f(x)+xa$ is a permutation for each nonzero $a$. We call such an $f$ a planar function ... More

Spherical Couplings and Multiple Elliptic IntegralsJan 11 2013Various integrals over elliptic integrals are evaluated as couplings on spheres, resulting in some integral and series representations for the mathematical constants $\pi$, $G$ and $\zeta(3)$.

GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold SingularitiesJun 27 2016Aug 18 2016The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral, chain integral ... More

Recent Results in Search for New Physics at the Tevatron (Run 1)May 29 2002We present some new results on searches for new physics at the Tevatron Run 1 (1992 -- 1996). The topics covered are searches for R-Parity violating and conserving mSUGRA, large extra dimensions in di-photon and monojet channels, leptoquark in jets + ... More

On Kadell's two Conjectures for the $q$-Dyson ProductSep 07 2010By extending Lv-Xin-Zhou's first layer formulas of the $q$-Dyson product, we prove Kadell's conjecture for the Dyson product and show the error of his $q$-analogous conjecture. With the extended formulas we establish a $q$-analog of Kadell's conjecture ... More

Two types of glitches in a solid quark star modelJun 09 2015Jun 10 2015Glitch (sudden spinup) is a common phenomenon in pulsar observations. However, the physical mechanism of glitch is still a matter of debate because it depends on the puzzle of pulsar's inner structure, i.e., the equation of state of dense matter. Some ... More

Secure Communication through Wireless-Powered Friendly Jamming: Jointly Online Optimization over Geography, Energy and TimeFeb 17 2016Exploring the interference-emitting friendly jammers to protect the sensitive communications in the presence of eavesdroppers has increasingly being investigated in literature. In parallel, scavenging energy from abient radio signals for energy-constrained ... More

Relatively large theta13 and nearly maximal theta23 from the approximate S3 symmetry of lepton mass matricesJun 23 2011Oct 01 2011We apply the permutation symmetry S_3 to both charged-lepton and neutrino mass matrices, and suggest a useful symmetry-breaking scheme, in which the flavor symmetry is explicitly broken down via S_3 -> Z_3 -> nothing in the charged-lepton sector and via ... More

Thresholded Lasso for high dimensional variable selection and statistical estimationFeb 08 2010Feb 11 2010Given $n$ noisy samples with $p$ dimensions, where $n \ll p$, we show that the multi-step thresholding procedure based on the Lasso -- we call it the {\it Thresholded Lasso}, can accurately estimate a sparse vector $\beta \in \R^p$ in a linear model $Y ... More

Pole wave-function renormalization prescription for unstable particlesOct 19 2005Apr 23 2007We base a new wave-function renormalization prescription on the pole mass renormalization prescription, in which the Wave-function Renormalization Constant (WRC) is extracted by expanding the particle's propagator around its pole, rather than its physical ... More

Renormalization of the Cabibbo-Kobayashi-Maskawa Matrix at One-Loop LevelMay 09 2003May 27 2003We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix at one-loop level. We emphasize at one prescription which is formulated with reference to the case of no mixing of quark's generations and point out ... More

Optical theorem and the cutting rulesApr 04 2004Dec 17 2004The contents of this manuscript has been moved to hep-ph/0412204.

Localized solitons of hyperbolic su(N) AKNS systemAug 24 1998Using the nonlinear constraint and Darboux transformation methods, the (m_1,...,m_N) localized solitons of the hyperbolic su(N) AKNS system are constructed. Here "hyperbolic su(N)" means that the first part of the Lax pair is F_y=JF_x+U(x,y,t)F where ... More

Predicting Ambulance Demand: Challenges and MethodsJun 16 2016Predicting ambulance demand accurately at a fine resolution in time and space (e.g., every hour and 1 km$^2$) is critical for staff / fleet management and dynamic deployment. There are several challenges: though the dataset is typically large-scale, demand ... More

Success probabilities for universal unambiguous discriminators between unknown pure statesAug 03 2013Dec 06 2013A universal programmable discriminator can perform the discrimination between two unknown states, and the optimal solution can be approached via the discrimination between the two averages over the uniformly distributed unknown input pure states, which ... More

Mixing navigation on networksMay 03 2007May 26 2007In this Letter, we proposed a mixing navigation mechanism, which interpolates between random-walk and shortest-path protocol. The navigation efficiency can be remarkably enhanced via a few routers. Some advanced strategies are also designed: For non-geographical ... More

Partial quantum statistics and its implications for narrow band materialsApr 05 2002Based upon the newly proposed partial quantum statistics [T. Zhou, Solid State Commun. 115, 185 (2000)], some canonical physical properties of partially localized electron systems have been calculated. The calculated transport and superconducting properties ... More

Minimal Inputs/Outputs for a Networked SystemOct 01 2016Mar 18 2017This paper investigates the minimal number of inputs/outputs required to guarantees the controllability/observability of a system, under the condition that its state transition matrix (STM) is prescribed. It has been proved that this minimal number is ... More

Separation of dissipation from diffusionAug 20 2001We study velocity correlations induced by diffusion and dissipation in a simple dissipative dynamical system. We observe that diffusion, as a result of time reversible microscopic processes, leads to correlations with different spatial parity from those ... More

Measuring the Entropy and Testing the Second Law of ThermodynamicsMar 19 2002Evidence implies that basic laws of thermodynamics must be tested by experiments. In this paper, an experiment is designed to measure the entropy of a system with at least one known (measurable) equation of state, especially the gas systems. Since the ... More

Analysis and Design of Complex-Valued Linear SystemsAug 17 2017Aug 08 2018This paper studies a class of complex-valued linear systems whose state evolution dependents on both the state vector and its conjugate. The complex-valued linear system comes from linear dynamical quantum control theory and is also encountered when a ... More

Probability Logic for Harsanyi Type SpacesMay 25 2014Jun 21 2014Probability logic has contributed to significant developments in belief types for game-theoretical economics. We present a new probability logic for Harsanyi Type spaces, show its completeness, and prove both a de-nesting property and a unique extension ... More

Effective Non-vanishing of Asymptotic Adjoint SyzygiesMar 31 2012Apr 08 2014The purpose of this paper is to establish an effective non-vanishing theorem for the syzygies of an adjoint-type line bundle on a smooth variety, as the positivity of the embedding increases. Our purpose here is to show that for an adjoint type divisor ... More

Two Definite Integrals Involving Products of Four Legendre FunctionsMar 11 2016Apr 29 2017The definite integrals $ \int_{-1}^1x[P_\nu(x)]^4\,\mathrm{d} x$ and $ \int_{0}^1x[P_\nu(x)]^2\{[P_\nu(x)]^2-[P_\nu(-x)]^2\}\,\mathrm{d} x$ are evaluated in closed form, where $ P_\nu$ stands for the Legendre function of degree $ \nu\in\mathbb C$. Special ... More

Morse-Bott Cohomology from Homological Perturbation TheoryFeb 18 2019In this paper, we construct cochain complexes generated by cohomology of critical manifolds for Morse-Bott theory under minimum transversality assumptions. We discuss the relations between different constructions of cochain complexes for Morse-Bott theory. ... More

A Mathematical Aspect of Hohenberg-Kohn TheoremSep 21 2017The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become a basic tool for the study of electronic structure of matter. In this article, we study the Hohenberg-Kohn theorem for a class of external potentials based ... More

Collective Effects in Nuclear Collisions: Experimental OverviewOct 16 2018Jan 22 2019These conferences proceedings summarize the experimental findings of collective effects in nuclear collisions, as presented at the Quark Matter 2018 conference.

Kontsevich-Zagier Integrals for Automorphic Green's Functions. IDec 22 2013Nov 23 2014In the framework of Kontsevich-Zagier periods, we derive integral representations for weight-$k$ automorphic Green's functions invariant under modular transformations in $\varGamma_0(N)$ ($N\in\mathbb Z_{\geq1} $), provided that there are no cusp forms ... More

Information Theoretic Inequalities as Bounds in Superconformal Field TheoryJul 19 2016Feb 24 2017An information theoretic approach to bounds in superconformal field theories is proposed. It is proved that the supersymmetric R\'enyi entropy $\bar S_\alpha$ is a monotonically decreasing function of $\alpha$ and $(\alpha-1)\bar S_\alpha$ is a concave ... More

Measurements of correlations of anisotropic flow harmonics in Pb--Pb Collisions with ALICEDec 16 2015We report the first measurements of the correlation strength between various anisotropic flow harmonics, using ALICE data. This correlation strength is characterized with multi-particle cumulants of mixed harmonics, which by construction depend only on ... More

Future Communication Model for High-speed Railway Based on Unmanned Aerial VehiclesNov 13 2014High-speed railway is playing an important role in mass transportation, due to its lower energy consumption, less environmental pollution, larger capacity and higher safety features. The development of high-speed railway makes people's life more and more ... More

Ramanujan Series for Epstein Zeta FunctionsOct 30 2014Mar 28 2015In the spirit of Ramanujan, we derive exponentially fast convergent series for Epstein zeta functions $ E^{\varGamma_0(N)}(z,s)$ on the Hecke congruence groups $ \varGamma_0(N),N\in\mathbb Z_{>0}$, where $z$ is an arbitrary point in the upper half-plane ... More

Ergodic Inequality of Three Population Genetic ModelsJul 03 2013Nov 19 2013In this article, three models are considered, they are the infinitely-many-neutral-alleles model \cite{MR615945}, infinite dimensional diffusion associated with two-parameter Poisson-Dirichlet distribution \cite{MR2596654} and the infinitely-many-alleles ... More

A Note on Characteristic ClassesAug 03 2006This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

Grassmann Manifold G(2,8) and Complex Structure on $S^6$Aug 02 2006Aug 18 2006In this paper, we use Clifford algebra and the spinor calculus to study the complex structures on Euclidean space $R^8$ and the spheres $S^4,S^6$. By the spin representation of $G(2,8)\subset Spin(8)$ we show that the Grassmann manifold G(2,8) can be ... More

A fast algorithm for determining the linear complexity of periodic sequencesDec 10 2005A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m, where p is a prime, q is a prime and a primitive root modulo p2. The algorithm presented here generalizes ... More

Crepant Resolutions, Quivers and GW/NCDT DualityJul 01 2009We propose a conjecture that relates some local Gromov-Witten invariants of some crepant resolutions of Calabi-Yau 3-folds with isolated singularities with some Donaldson-Thomas type invariants of the moduli spaces of representations of some quivers with ... More

Regularity/Controllability/Observability of an NDS with Descriptor Form Subsystems and Generalized LFTsMar 13 2019This paper investigates regularity, controllability and observability for a networked dynamic system (NDS) with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized linear fractional ... More

Hilbert Transforms and Sum Rules of Bessel MomentsJun 04 2017Jul 13 2017Using Hilbert transforms, we establish two families of sum rules involving Bessel moments, which are integrals associated with Feynman diagrams in two-dimensional quantum field theory. With these linear relations among Bessel moments, we verify and generalize ... More

Convex Polytopes for the Central Degeneration of the Affine GrassmannianApr 28 2016Jun 15 2018We study algebraic geometry and combinatorics of the central degeneration (the degeneration that shows up in local models of Shimura varieties and Gaitsgory's central sheaves) in type A. More specifically, we elucidate the central degeneration of semi-infinite ... More

Multi-Domain Sampling With Applications to Structural Inference of Bayesian NetworksOct 15 2011When a posterior distribution has multiple modes, unconditional expectations, such as the posterior mean, may not offer informative summaries of the distribution. Motivated by this problem, we propose to decompose the sample space of a multimodal distribution ... More

The Voronoi formula on GL(3) with ramificationJun 28 2018Sep 16 2018Firstly we prove that the Voronoi formula of Miller-Schmid type applies to automorphic forms on GL(3) for the congruence subgroup $\Gamma_0(N)$, when the conductor of the additive character in the formula is a multiple of $N$. As an application, we produce ... More

Finite dimensionality of global attractor for the solutions to 3D viscous primitive equations of large-scale moist atmosphereOct 22 2016Under general boundary conditions we consider the finiteness of the Hausdorff and fractal dimensions of the global attractor for the strong solution of the 3D moist primitive equations with viscosity. Firstly, we obtain time-uniform estimates of the first-order ... More

Wrońskian factorizations and Broadhurst-Mellit determinant formulaeNov 06 2017Feb 02 2018Drawing on Vanhove's contributions to mixed Hodge structures for Feynman integrals in two-di\-men\-sion\-al quantum field theory, we compute two families of determinants whose entries are Bessel moments. Via explicit factorizations of certain Wro\'nskian ... More

On Borwein's conjectures for planar uniform random walksAug 09 2017Let $ p_n(x)=\int_0^\infty J_0(xt)[J_0(t)]^n xt\,\mathrm{d}\, t$ be Kluyver's probability density for $n$-step uniform random walks in the Euclidean plane. Through connection to a similar problem in 2-dimensional quantum field theory, we evaluate the ... More

Wick rotations, Eichler integrals, and multi-loop Feynman diagramsJun 26 2017Dec 04 2017Using contour deformations and integrations over modular forms, we compute certain Bessel moments arising from diagrammatic expansions in two-dimensional quantum field theory. We evaluate these Feynman integrals as either explicit constants or critical ... More

Scaling exponents and clustering coefficients of a growing random networkMar 26 2003The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidden of self-connection and multiple links ... More

Network Landscape from a Brownian Particle's PerspectiveFeb 11 2003Given a complex biological or social network, how many clusters should it be decomposed into? We define the distance $d_{i,j}$ from node $i$ to node $j$ as the average number of steps a Brownian particle takes to reach $j$ from $i$. Node $j$ is a global ... More

The curve shortening flow with parallel 1-formDec 21 2012Dec 26 2012Let $M$ be a closed Riemannian manifold with a parallel 1-form $\Omega$. We prove two theorems about the curve shortening flow in $M$. One is that the {\csf} $\ct$ in $M$ exists for all $t$ in $[0, \infty)$, if it satisfies $\Omega(T)\geq 0$ on the initial ... More

Solution space heterogeneity of the random K-satisfiability problem: Theory and simulationsJan 18 2010Jul 02 2010The random K-satisfiability (K-SAT) problem is an important problem for studying typical-case complexity of NP-complete combinatorial satisfaction; it is also a representative model of finite-connectivity spin-glasses. In this paper we review our recent ... More

Long Range Frustrations in a Spin Glass Model of the Vertex Cover ProblemNov 03 2004Nov 06 2012In a spin glass system on a random graph, some vertices have their spins changing among different configurations of a ground--state domain. Long range frustrations may exist among these unfrozen vertices in the sense that certain combinations of spin ... More

Rigidity of formal characters of Lie algebras (II)Dec 04 2012For a complex simple Lie algebra of type A_l,B_l,C_l or D_l, given a family of elements f_\lambda\ in commutative ring Z[\Lambda], we show that f_\lambda\ is just the formal character of the Weyl module V(\lambda) if f_\lambda\ satisfy several natural ... More

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

Viscosity Solutions to Path-Dependent HJB Equation and ApplicationsNov 17 2016Jan 06 2017In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify the value functional ... 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.

Effective upper bound of analytic torsion under Arakelov metricMar 20 2019Given a choice of metric on the Riemann surface, the regularized determinant of Laplacian (analytic torsion) is defined via the complex power of elliptic operators: $$ \det(\Delta)=\exp(-\zeta'(0)) $$ In this paper we gave an asymptotic effective estimate ... More

On representation and regularity of viscosity solutions to degenerate Isaacs equations and certain nonconvex Hessian equationsNov 25 2013We study the smoothness of the upper and lower value functions of stochastic differential games in the framework of time-homogeneous (possibly degenerate) diffusion processes in a domain, under the assumption that the diffusion, drift and discount coefficients ... More

The inverse problem for the local ray transformApr 25 2013Jul 20 2013In this paper we consider the local X-ray transform for general flows. We extend the results on the local and global invertibility of the geodesic ray transform proved by Uhlmann and Vasy \cite{UV} to the X-ray transform for a general flow. The key improvement ... More

The Poincare center-focus problem for a class of higher order polynomial differential systemsNov 29 2018In this paper, I have proved that for a class of polynomial differential systems of degree n+1 ( where n is an arbitrary positive integer) the composition conjecture is true. I give the sufficient and necessary conditions for these differential systems ... More

Generalized solutions to the Dirichlet problem of translating mean curvature equationsFeb 05 2019Mar 18 2019In this paper we study the Dirichlet problem of translating mean curvature equations over domains in Riemannian manifolds with dimension $n$. Imitating the generalized solution theory of Miranda-Giusti, we define a new conformal area functional and a ... More