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Intervention Pathway Discovery via Context-Dependent Dynamic Sensitivity AnalysisFeb 08 2019The sensitivity analysis of biological system models can significantly contribute to identifying and explaining influences of internal or external changes on model and its elements. We propose here a comprehensive framework to study sensitivity of intra-cellular ... More

Deterministic macroscopic quantum superpositions of motion via quadratic optomechanical couplingFeb 28 2013We propose a scheme to prepare macroscopic quantum superpositions of motion in optomachanical nano- or micromechanical oscillators quadratically coupled to an intracavity field. The nonlinear optomechanical coupling leads to an effective degenerate three-wave ... More

Quantum nonlinear cavity QED with coherently prepared atomsJul 06 2015We propose a method to study the quantum nonlinearity and observe the multiphoton transitions in a multiatom CQED system. We show that by inducing simultaneously destructive quantum interference for the single-photon and two-photon excitations in the ... 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

Steady-state one-way Einstein-Podolsky-Rosen steering in optomechanical interfacesNov 28 2014Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlations and its intrinsic asymmetry makes it distinct from entanglement and Bell nonlocality. We propose here a scheme for realizing one-way Gaussian steering of two electromagnetic fields ... More

Dissipation-driven two-mode mechanical squeezed states in optomechanical systemsJan 24 2013In this paper, we propose two quantum optomechanical arrangements that permit the dissipation-enabled generation of steady two-mode mechanical squeezed states. In the first setup, the mechanical oscillators are placed in a two-mode optical resonator while ... 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

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

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

Achieving steady-state entanglement of remote micromechanical oscillators by cascaded cavity couplingOct 08 2012In this paper, we propose a scheme for generating steady-state entanglement of remote micromechanical oscillators in unidirectionally-coupled cavities. For the system of two mechanical oscillators, we show that when two cavity modes in each cavity are ... 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

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

Anomalous Sound Velocity and Dielectric Shift in Glass: a Renormalization Technique for Mechanical and Dielectric Susceptibilities from Generic Coupled Block ModelFeb 15 2016Aug 10 2016Glass sound velocity shift was observed to be longarithmically temperature dependent in both relaxation and resonance regimes: $\Delta c/c=\mathcal{C}\ln T$. It does not monotonically increase with temperature from $T=0$K, but to reach a maximum around ... More

A Modified Kähler-Ricci FlowJan 22 2008In this note, a modified K\"ahler-Ricci flow is introduced and studied. The main point is to show the flexibility of K\"ahler-Ricci flow and summarize some useful techniques.

Convergence Results for Two Kahler-Ricci FlowsNov 09 2013Jul 22 2014In this note, we provide some general discussion on the two main versions in the study of Kahler-Ricci flows over closed manifolds, aiming at smooth convergence to the corresponding Kahler-Einstein metrics with assumptions on the volume form and Ricci ... More

Weighted Sato-Tate Vertical Distribution of the Satake Parameter of Maass Forms on PGL(N)Mar 04 2013Aug 01 2013We formulate a conjectured orthogonality relation between the Fourier coefficients of Maass forms on PGL(N) for N>=2. Based on the work of Goldfeld-Kontorovich and Blomer for N=3, and on our conjecture for N>=4, we prove a weighted vertical equidistribution ... More

Spin-one bosons in low dimensional Mott insulating statesJul 01 2002Jun 05 2003We analyze the strong coupling limit of spin-one bosons in low dimensional Mott insulating states. In 1D lattices, for an odd number of bosons per site ($N_0$), the ground state is a dimerized valence bond crystal state with a two-fold degeneracy; the ... More

Min-max hypersurface in manifold of positive Ricci curvatureApr 04 2015Nov 30 2016In this paper, we study the shape of the min-max minimal hypersurface produced by Almgren-Pitts-Schoen-Simon \cite{AF62, AF65, P81, SS81} in a Riemannian manifold $(M^{n+1}, g)$ of positive Ricci curvature for all dimensions. The min-max hypersurface ... More

Random Walk over Basins of Attraction to Construct Ising Energy LandscapesApr 06 2011An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each ... More

Vortices and phase transitions of interacting bosons in a rotating lattice ringOct 17 2006We investigate the ground state properties of the repulsive interacting bosons in an one dimensional rotating lattice ring, and reveal that the superfluid density of the system and the mass current it can carry in the rotating coordinate are periodic ... More

Excitation function Analysis for Charmonium Production in Heavy-Ion CollisionsSep 17 2015Both color screening and regeneration are hot medium effects on charmonium production in heavy ion collisions. While they affect in an opposite way the charmonium yield, their competition in transverse dynamics bring sensitivity to the ratio of averaged ... More

Uniform annihilators of local cohomologyApr 11 2006May 24 2006In this paper, we study the properties of noetherian rings with uniform annihilators. It turns out that all these rings should be universally catenary and locally equidimensional. We will give a necessary and sufficient condition for these rings, which ... More

Integral dimension of a noetherian ringFeb 29 2016In this paper, we introduce a new notion, called the integral dimension, for noetherian rings. It can be regarded as the weak Briancon-Skoda numbers of rings. The point is that every noetherian local ring has finite integral dimension.

Real Space Renormalization: A Generic Microscopic Theory for Low-Temperature Avalanches in Static Strained Insulating GlassFeb 15 2016Jul 26 2016We propose a microscopic model to study the avalanche problem of insulating glass deformed by external static uniform strain below $T=60$K. We use three-dimensional real-space renormalization procedure to carry out the glass mechanical susceptibility ... More

On Stability of the Linearized Spacecraft Attitude Control SystemApr 01 2015This note is concerned with the stability and stabilization of the linearized spacecraft attitude control system. Necessary and sufficient conditions are respectively provided to guarantee that the considered systems are polynomially stable and stable ... More

Global Structure of Certain Static Spacetimes (I)Apr 13 2001In this paper, static spacetimes with a topological structure of R^2 \times N is studied, where N is an arbitrary manifold. Well known Schwarzschild spacetime and Reissner-Nordstrom spacetime are special cases. It is shown that the existence of a constant ... More

Why the Internet is so 'small'?Mar 30 2010During the last three decades the Internet has experienced fascinating evolution, both exponential growth in traffic and rapid expansion in topology. The size of the Internet becomes enormous, yet the network is very `small' in the sense that it is extremely ... More

Explicit Orbifold Riemann-Roch for quasismooth varietiesJul 22 2014Considering quasismooth varieities as global $\CC^*$ quotients, we present a Riemann-Roch formula via general Riemann-Roch formula for quotient stacks. Furthermore, we give a parcing formula for Hilbert series associated to a polarized quasismooth projectively ... More

The spherically symmetric Finsler metrics with isotropic S-curvatureSep 09 2014Oct 30 2014In this paper, we investigate the spherically symmetric Finsler metrics with isotropic S-curvature and obtain a characterized equation. As an application, we prove that these metrics with Douglas type must be Randers metrics or Berwald metrics. This result ... More

Personalized Web SearchFeb 03 2015Personalization is important for search engines to improve user experience. Most of the existing work do pure feature engineering and extract a lot of session-style features and then train a ranking model. Here we proposed a novel way to model both long ... More

Lusztig's $a$ function for Coxeter groups of rank 3Jul 11 2011We show that Lusztig's $a$-function of a Coxeter group is bounded if the rank of the Coxeter group is 3.

On the Coupling Effects between Elastic and Electromagnetic Fields from the Perspective of Conservation of EnergyNov 29 2015Dec 17 2015In a natural system, coupling effects among different physical fields substantially reflect the conversion of energy from one form to another. According to the law of conservation of energy (LCE), the loss of energy in one field must equal to the gain ... More

Line narrowing via cavity-induced quantum interference in a $Ξ$-type atomMar 20 2000We show that cavity-induced interference may result in spectral line narrowing in the absorption spectrum of a $\Xi$-type atom coupled to a single-mode, frequency-tunable cavity field with a pre-selected polarization at finite temperature.

Supernova Bounds on keV-mass Sterile NeutrinosApr 10 2015Sterile neutrinos of keV masses are one of the most promising candidates for the warm dark matter, which could solve the small-scale problems encountered in the scenario of cold dark matter. We present a detailed study of the production of such sterile ... More

Generic injectivity and stability of inverse problems for connectionsOct 07 2016Oct 17 2016We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral geometry question ... More

A Bernstein type result for graphical self-shrinkers in $\mathbb{R}^4$Apr 26 2015May 08 2015Self-shrinkers are important geometric objects in the study of mean curvature flows, while the Bernstein Theorem is one of the most profound results in minimal surface theory. We prove a Bernstein type result for graphical self-shrinker surfaces with ... More

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

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.

Embedding Constructions of Tail-Biting Trellises for Linear Block CodesSep 06 2011In this paper, embedding construction of tail-biting trellises for linear block codes is presented. With the new approach of constructing tail-biting trellises, most of the study of tail-biting trellises can be converted into the study of conventional ... More

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.

The Complex Structures on $S^{2n}$Aug 15 2006Jun 28 2008In this paper, we show that the twistor space ${\cal J}(R^{2n+2})$ on Euclidean space $R^{2n+2}$ is a Kaehler manifold and the orthogonal twistor space $\widetilde{\cal J}(S^{2n})$ of the sphere $S^{2n}$ is a Kaehler submanifold of ${\cal J}(R^{2n+2})$. ... More

Curve counting and instanton countingNov 14 2003We prove some combinatorial results required for the proof of the following conjecture of Nekrasov: The generating function of closed string invariants in local Calabi-Yau geometries obtained by appropriate fibrations of $A_N$ singularities over $P^1$ ... More

Homological perturbation theory and mirror symmetryJun 14 1999We explain how deformation theories of geometric objects such as complex structures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson algebras. We use homological perturbation theory to obtain $A_{\infty}$ ... More

A Proof of the Full Marino-Vafa ConjectureJan 13 2010We present a proof of the full Mari\~no-Vafa Conjecture that identifies certain open string invariants of the resolved conifold with the Chern-Simons knot invariant of the unknot, i.e. the quantum dimensions.

Intense Terahertz Laser Fields Induced and Manipulated Pseudospin Polarization in GrapheneJul 04 2008We investigate the pseudospin-dependent density-energy relation (whose differential with respect to energy is density of states) of a monolayer graphene under intense terahertz laser field by exactly solving the time-dependent Schr\"{o}dinger equation ... More

A Conjecture on Hodge IntegralsOct 18 2003We propose a conjectural formula expressing the generating series of some Hodge integrals in terms of representation theory of Kac-Moody algebras. Such generating series appear in calculations of Gromov-Witten invariants by localization techniques. It ... More

Majority Rule for Belief Evolution in Social NetworksSep 03 2013In this paper, we study how an agent's belief is affected by her neighbors in a social network. We first introduce a general framework, where every agent has an initial belief on a statement, and updates her belief according to her and her neighbors' ... More

Extensions of trivial inertial blocksMay 23 2013Aug 16 2013A false application of Proposition 4.10 causes a mistake in the proof of Corollary 4.11

The local $C^1$-density of stable ergodicityDec 24 2011The center bundle of a conservative partially hyperbolic diffeomorphism $f$ is called robustly non-hyperbolic if any conservative diffeomorphism which is $C^1$-close to $f$ has non-hyperbolic center bundle. In this paper, we prove that stable ergodicity ... More

A note on interpreting N M2 branesJul 06 2008Jan 31 2009A new world volume theory with a free scalar field was proposed for Multiple M2 branes recently. By giving the free scalar a large VEV, we can obtain a gauge theory of multiple D2 branes with a coupling constant proportional to the VEV. It is pointed ... More

Information Theoretic Inequalities as Bounds in Superconformal Field TheoryJul 19 2016An 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

Kontsevich-Zagier Integrals for Automorphic Green's Functions. IIJun 01 2015Oct 12 2016We introduce interaction entropies, which can be represented as logarithmic couplings of certain cycles on a class of algebraic curves of arithmetic interest. In particular, via interaction entropies for Legendre-Ramanujan curves $ Y^n=(1-X)^{n-1}X(1-\alpha ... More

Gauge dependence of on-shell and pole mass renormalization prescriptionsAug 22 2005Apr 17 2007We discuss the gauge dependence of physical parameter's definitions under the on-shell and pole mass renormalization prescriptions. By two-loop-level calculations we prove for the first time that the on-shell mass renormalization prescription makes physical ... More

Imaginary part of Feynman amplitude, cutting rules and optical theoremDec 15 2004Jun 13 2005We discuss the algorithm of the cutting rules of calculating the imaginary part of physical amplitude and the optical theorem. We ameliorate the conventional cutting rules to make it suitable for actual calculation and give the right imaginary part of ... More

Singularities of Feynman propagators and Corrections of Cutting rules and usual momentum integral algorism in dimensional regularization prescriptionMar 18 2004Jul 23 2004This manuscript has been removed duo to incorrect contents.

Renormalization of the Cabibbo-Kobayashi-Maskawa Matrix at One-Loop LevelJul 21 2003Dec 09 2003We have investigated the present renormalization prescriptions of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. Based on one prescription which is formulated by comparing with the fictitious case of no mixing of quark generations, we propose ... More

Calculations of the Imaginary Part of Gauge Boson's Wave-function Renormalization Constants and the Modification of hep-ph/0301090Jun 05 2003We have calculated the imaginary part of W and Z gauge boson's wave-function renormalization constants (wrc.) in the complex-pole mass renormalization scheme and made atonement for the paper hep-ph/0301090 where the imaginary part of gauge boson's wrc. ... More

Renormalization of the Cabibbo-Kobayashi-Maskawa Matrix in Standard ModelApr 01 2003Apr 16 2003We have investigated the present renormalization prescriptions of Cabibbo-Kobayashi-Maskawa (CKM) matrix, and found there is still not an integrated prescription to all loop levels. In this paper We propose a new prescription which is designed for all ... More

A Note on the Isotopism of Commutative SemifieldsJun 08 2010Mar 07 2012We present an example of two isotopic but not strongly isotopic commutative semifields. This example shows that a recent result of Coulter and Henderson on semifield of order p^n, n odd, can not be generalized to the case n even.

A Note on Wilson Loop in N=2 Quiver/M theory Gravity DualityOct 22 2009Nov 26 2009We study Wilson loops in the 4-dimensional N=2 supersymmetric quiver/M theory duality recently constructed by Gaiotto and Maldacena, that is conjectured to be dual to M2 branes on AdS_5\times S^4 fibered over \Sigma_2. We use the localization method raised ... More

Hardcore bosons on checkerboard lattices near half filling: geometric frustration, vanishing charge order and fractional phaseJun 25 2008We study a spinless hardcore boson model on checkerboard lattices by Green function Monte Carlo method. At half filling, the ground state energy is obtained up to $28\times 28$ lattice and extrapolated to infinite size, the staggered pseudospin magnetization ... More

The quantum entanglement contained in density matricesOct 22 2007Dec 24 2010We point out that density matrices can only be used to describe quantum states, so the entanglement contained in a density matrix is just quantum entanglement. This means a bipartite state described by a density matrix contains quantum entanglement, unless ... More

Intense terahertz laser fields on a two-dimensional hole gas with Rashba spin-orbit couplingSep 18 2007We investigate the influence on the density of states and the density of spin polarization for a two-dimensional hole gas with Rashba spin-orbit coupling under intense terahertz laser fields. Via Floquet theorem, we solve the time-dependent Schr\"{o}dinger ... More

Robust Recursive State Estimation with Random Measurements DroppingsJan 16 2014A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent observations, ... More

Reconstructing electromagnetic obstacles by the enclosure methodAug 27 2009Aug 28 2009We present a reconstruction algorithm for recovering both "magnetic-hard" and "magnetic-soft" obstacles in a background domain with known isotropic medium from the boundary impedance map. We use in our algorithm complex geometric optics solutions constructed ... More

Donaldson-Thomas theory of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$Oct 03 2015May 16 2016We study the relative orbifold Donaldson-Thomas theory of $[\mathbb{C}^2/\mathbb{Z}_{n+1}]\times \mathbb{P}^1$. We establish a correspondence between the DT theory relative to 3 fibers to quantum multiplication by divisors in the Hilbert scheme of points ... More

Darboux transformations for twisted so(p,q) system and local isometric immersion of space formsAug 17 1998For the n-dimensional integrable system with a twisted so(p,q) reduction, Darboux transformations given by Darboux matrices of degree 2 are constructed explicitly. These Darboux transformations are applied to the local isometric immersion of space forms ... More

Lattice Calculations of B to K/K*l+l- form factorsJan 04 2013This paper gives a brief review on the recent lattice QCD calculations of the B to K/K*l+l- semi-leptonic decay form factors.

r-Matrix for the restricted KdV Flows with the Neumann constraintsApr 01 1998Under the Neumann constraints, each equation of the KdV hierarchy is decomposed into two finite dimensional systems, including the well-known Neumann model. Like in the case of the Bargmann constraint, the explicit Lax representations are deduced from ... More

The Quenching Problem in the Nonlinear Heat EquationsDec 05 2006Dec 06 2006In this paper we study the quenching problem in nonlinear heat equations with power nonlinearities. For nonlinearities of power p<0 and for an open set of slowly varying initial conditions we prove that the solutions will collapse in a finite time. We ... More

Measuring the transmission matrix for microwave radiation propagating through random waveguides: fundamentals and applicationsFeb 14 2014This thesis describes the measurement and analysis of the transmission matrix (TM) for microwave radiation propagating through multichannel random waveguides in the crossover to Anderson localization. Eigenvalues of the transmission matrix and the associated ... More

Almost Complex Structure on $S^{2n}$Apr 04 2011We show that there is no complex structure in a neighborhood of the space of orthogonal almost complex structures on the sphere $S^{2n}, \ n>1$. The method is to study the first Chern class of vetcor bundle $T^{(1,0)}S^{2n}$.

Harder-Narasimhan Filtrations and K-Groups of an Elliptic CurveSep 02 2007Sep 10 2007Let $X$ be an elliptic curve over an algebraically closed field. We prove that some exact sub-categories of the category of vector bundles over $X$, defined using Harder-Narasimhan filtrations, have the same K-groups as the whole category.

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

Weak metacirculants of odd prime power orderNov 18 2016Nov 18 2017Metacirculants are a basic and well-studied family of vertex-transitive graphs, and weak metacirculants are generalizations of them. A graph is called a weak metacirculant if it has a vertex-transitive metacyclic automorphism group. This paper is devoted ... 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

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 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.

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

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

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

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

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

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