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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

A Statistical Study of the Magnetic Imprints of X-Class Flares using SDO/HMI Vector MagnetogramsMar 22 2018Magnetic imprints, the rapid and irreversible evolution of photospheric magnetic fields as a feedback from flares in the corona, have been confirmed by many previous studies. These studies showed that the horizontal field will permanently increase near ... 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

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

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

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

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

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

Estimation and inference for precision matrices of non-stationary time seriesMar 03 2018Mar 25 2019In 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

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.

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

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

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

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

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

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

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

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

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

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

Bayesian Nonparametric Models for Biomedical Data AnalysisOct 26 2017In this dissertation, we develop nonparametric Bayesian models for biomedical data analysis. In particular, we focus on inference for tumor heterogeneity and inference for missing data. First, we present a Bayesian feature allocation model for tumor subclone ... 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

Tame the flexibility of circle patternsMay 22 2018This paper proves a deformation circle pattern theorem, which gives a complete description of those circle patterns with interstices in terms of the combinatorial type, the exterior intersections angles and the conformal structures of interstices. As ... More

On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$Dec 07 2017Sep 03 2018We present a universal treatment for imposing superconformal constraints on Mellin amplitudes for $\mathrm{SCFT_d}$ with $3\leq d\leq 6$. This leads to a new technique to compute holographic correlators, which is similar but complementary to the ones ... 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

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

Sorted Range Reporting RevisitedAug 15 2013We consider the two-dimensional sorted range reporting problem. Our data structure requires O(n lglg n) words of space and O(lglg n + k lglg n) query time, where k is the number of points in the query range. This data structure improves a recent result ... 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

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

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

New trial wave function for nuclear cluster structure of nucleiNov 20 2017Mar 06 2018A new trial wave function is proposed for nuclear physics, in which an exact solution to the long-standing center-of-mass problem is given. In the new approach, the widths of the single-nucleon Gaussian wave packets and the widths of the relative Gaussian ... More

Solutions to Linear Bimatrix Equations with Applications to Pole Assignment of Complex-Valued Linear SystemsAug 26 2017We study in this paper solutions to several kinds of linear bimatrix equations arising from pole assignment and stability analysis of complex-valued linear systems, which have several potential applications in control theory, particularly, can be used ... 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

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

Some Moderate Deviations for Ewens-Pitman Sampling ModelNov 15 2018Nov 18 2018Ewens-Pitman model has been successfully applied to various fields including Bayesian statistics. There are four important estimators $K_{n},M_{l,n}$,$K_{m}^{(n)},M_{l,m}^{(n)}$. In particular, $M_{1,n}, M_{1,m}^{(n)}$ are related to discovery probability. ... More

From First-Order Logic to Assertional LogicJan 12 2017Apr 28 2017First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an alternative called assertional ... More

Structured Production System (extended abstract)Apr 26 2017In this extended abstract, we propose Structured Production Systems (SPS), which extend traditional production systems with well-formed syntactic structures. Due to the richness of structures, structured production systems significantly enhance the expressive ... 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

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

On the Homology of the Space of Curves Immersed in The Sphere with Curvature Constrained to a Prescribed IntervalSep 14 2018While the topology of the space of all smooth immersed curves on the $2$-sphere $\mathbb{S}^2$ that start and end at given points in given directions is well known, it is an open problem to understand the homotopy type of its subspaces consisting of the ... 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.

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.

Nonparametric Estimation of Low Rank Matrix Valued FunctionFeb 17 2018Mar 06 2018Let $A:[0,1]\rightarrow\mathbb{H}_m$ (the space of Hermitian matrices) be a matrix valued function which is low rank with entries in H\"{o}lder class $\Sigma(\beta,L)$. The goal of this paper is to study statistical estimation of $A$ based on the regression ... More

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

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.

A description of a space-and-time neighborhood of generic singularities formed by mean curvature flowMar 29 2018Sep 03 2018We consider one of the generic regimes of formation of singularities, and we obtain a detailed description of a possibly small, but fixed, neighborhood of the blowup point, up to (and including) the blowup time. Estimates up to any order of derivatives ... 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

Curve shortening flows in warped product manifoldsNov 24 2015Jan 21 2017We study curve shortening flows in two types of warped product manifolds. These manifolds are $S^1\times N$ with two types of warped metrics where $S^1$ is the unit circle in $R^2$ and $N$ is a closed Riemannian manifold. If the initial curve is a graph ... More

A graph theoretic characterization of the classical generalized hexagon on $364$ verticesOct 17 2018A tetravalent $2$-arc-transitive graph of order $728$ is either the known $7$-arc-transitive incidence graph of the classical generalized hexagon $GH(3,3)$ or a normal cover of a $2$-transitive graph of order $182$ denoted $A[182,1]$ or $A[182,2]$ in ... 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

Sparse Hanson-Wright inequalities for subgaussian quadratic formsOct 19 2015Feb 19 2017In this paper, we provide a proof for the Hanson-Wright inequalities for sparsified quadratic forms in subgaussian random variables. This provides useful concentration inequalities for sparse subgaussian random vectors in two ways. Let $X = (X_1, \ldots, ... 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

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

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

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

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.

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.

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.