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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

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

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

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.

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

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

Convex Polytopes for the Central Degeneration of the Affine GrassmannianApr 28 2016Aug 30 2016We study the central degeneration (the degeneration that shows up in local models of Shimura varieties and Gaitsgory's central sheaves) of semi-infinite orbits, MV Cycles, and Iwahori orbits in the affine Grassmannian of type A, by considering their moment ... More

Infinite Edge Partition Models for Overlapping Community Detection and Link PredictionJan 25 2015Dec 30 2015A hierarchical gamma process infinite edge partition model is proposed to factorize the binary adjacency matrix of an unweighted undirected relational network under a Bernoulli-Poisson link. The model describes both homophily and stochastic equivalence, ... More

Rational curves and lines on the moduli space of stable bundlesMay 15 2013Aug 06 2014Fix a smooth projetive curve $\mathcal {C}$ of genus $g\geq 2$ and a line bundle $\mathcal{L}$ on $\mathcal{C}$ of degree $d$. Let $M:= \mathcal{SU}_{\mathcal{C}}(r, \mathcal{L})$ be the moduli space of stable vector bundles on $\mathcal{C}$ of rank $r$ ... More

Spherically symmetric Finsler metrics in R^nJun 19 2010In this paper, we give the general form of spherically symmetric Finsler metrics in $R^n$ and surprisedly find that many well-known Finsler metrics belong to this class. Then we explicitly express projective metrics of this type. The necessary and sufficient ... More

Update on two-zero textures of the Majorana neutrino mass matrix in light of recent T2K, Super-Kamiokande and NO$ν$A resultsSep 17 2015Dec 25 2015The latest results from atmospheric and accelerator neutrino experiments indicate that the normal neutrino mass ordering $m^{}_1 < m^{}_2 < m^{}_3$, a maximal leptonic CP-violating phase $\delta = 270^\circ$ and the second octant of neutrino mixing angle ... More

Total perfect codes in Cayley graphsJan 14 2016A total perfect code in a graph $\Gamma$ is a subset $C$ of $V(\Gamma)$ such that every vertex of $\Gamma$ is adjacent to exactly one vertex in $C$. We give necessary and sufficient conditions for a conjugation-closed subset of a group to be a total perfect ... More

Theoretical Results on NeutrinosNov 23 2015In this talk, I first summarize our current knowledge about the fundamental properties of neutrinos and emphasize the remaining unsolved problems in neutrino physics. Then, recent theoretical results on neutrino mass models are introduced. Different approaches ... More

Learning Balanced Mixtures of Discrete Distributions with Small SampleFeb 10 2008We study the problem of partitioning a small sample of $n$ individuals from a mixture of $k$ product distributions over a Boolean cube $\{0, 1\}^K$ according to their distributions. Each distribution is described by a vector of allele frequencies in $\R^K$. ... More

Neutrino Decays and Neutrino Electron Elastic Scattering in Unparticle PhysicsJun 03 2007Oct 30 2007Following Georgi's unparticle scheme, we examine the effective couplings between neutrinos and unparticle operators. As an immediate consequence, neutrinos become unstable and can decay into the unparticle stuff. Assuming the dimension transmutation scale ... More

Legendre Functions, Spherical Rotations, and Multiple Elliptic IntegralsJan 09 2013Apr 29 2013A closed-form formula is derived for the generalized Clebsch-Gordan integral $ \int_{-1}^1 {[}P_{\nu}(x){]}^2P_{\nu}(-x)\D x$, with $ P_\nu$ being the Legendre function of arbitrary complex degree $ \nu\in\mathbb C$. The finite Hilbert transform of $ ... More

Structure Learning of Probabilistic Graphical Models: A Comprehensive SurveyNov 29 2011Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model. Especially, graphical ... More

D4 brane probes in gauge/gravity dualitySep 08 2008Feb 26 2009We propose a DBI vertex brane + $N_c$ fundamental strings configuration for a probe baryon in the finite-temperature thermal gauge field via AdS/CFT correspondence. In particular, we investigate properties of this configuration in QCD_4 and warped AdS_6\times ... More

Gauge dependence of fermion mass renormalization schemesOct 06 2005Dec 09 2005We discuss the gauge dependence of fermion mass definition and physical result under the conventional on-shell mass renormalization scheme and the recently proposed pole mass renormalization scheme in standard model. By the two-loop calculations of top ... More

Singularity of Feynman propagator and Cutkosky's cutting rulesAug 22 2005May 20 2010We improve on Cutkosky's cutting rules which is used to calculate the contribution of the singularities of Feynman propagators to Feynman amplitude. The correctness of the improved cutting rules is verified by the calculations of the conventional loop ... More

Unstable particle's wave-function renormalization prescriptionFeb 21 2005Dec 17 2005We strictly define two set Wave-function Renormalization Constants (WRC) under the LSZ reduction formula for unstable particles at the first time. Then by introducing antiparticle's WRC and the CPT conservation law we obtain a new wave-function renormalization ... More

The Gauge Dependence of the Imaginary Part of physical amplitude $W^{+}\to u_i \bar{d}_j$ in CKM Matrix RenormalizationDec 10 2003Mar 11 2005This manuscript has been withdrawn due to some default.

Minimal Control Selection for a Networked SystemOct 01 2016Dec 04 2016This paper investigates the minimal number of actuators required to guarantees the controllability of a system, under the condition that its state transition matrix (STM) is prescribed. It has been proved that this minimal number is equal to the maximum ... More

A Rolling PID Control Approach and its ApplicationsApr 09 2016The canonical proportional-integral-derivative (PID) control approach has been widely used in industrial application due to their simplicity and ease of use. However, its corresponding controller parameters are hard to be adjusted, especially for nonlinear ... More

A matlab toolbox for continuous state transition algorithmApr 04 2016State transition algorithm (STA) has been emerging as a novel stochastic method for global optimization in recent few years. To make better understanding of continuous STA, a matlab toolbox for continuous STA has been developed. Firstly, the basic principles ... More

Inverse mean curvature flows in warped product manifoldsSep 30 2016Oct 28 2016We study inverse mean curvature flows of starshaped, mean convex hypersurfaces in warped product manifolds with a positive warping factor $h(r)$. If $h'(r)>0$ and $h"(r)\geq 0$, we show that these flows exist for all times, remain starshaped and mean ... More

Global well-posedness and random attractor of the 3D viscous primitive equations driven by fractional noisesApr 18 2016In this article we study the perturbation of primitive equations (PEs) of large-scale ocean and atmosphere dynamics defined on a bounded open subset $\mho \in \mathbb{R}^{3}$ and driven by infinite-dimensional additive fractional Wiener processes with ... More

Relations among Out-degree, Controllability and Observability of a Networked SystemOct 07 2016Some novel sufficient conditions are derived respectively for the controllability and observability of a networked system, as well as some necessary conditions. These conditions depends only separately on parameters of each subsystem and its out-degree. ... More

Hodge integrals, Hurwitz numbers, and Symmetric GroupsAug 04 2003We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with Chiu-Chu Melissa Liu and Kefeng Liu. ... More

Probing the $P$-wave charmonium decays of $B_c$ mesonDec 24 2017Feb 13 2018Motivated by the large number of $B_c$ meson decay modes observed recently by several detectors at the LHC, we present a detailed analysis of the $B_c$ meson decaying to the $P$-wave charmonium states and a light pseudoscalar($P$) or vector ($V$) meson ... More

Per-Flow Cardinality Estimation Based On Virtual LogLog SketchingNov 30 2018Flow cardinality estimation is the problem of estimating the number of distinct elements in a data flow, often with a stringent memory constraint. It has wide applications in network traffic measurement and in database systems. The virtual LogLog algorithm ... More

Empirical effect of graph embeddings on fraud detection/ risk mitigationMar 05 2019Graph embedding technics are studied with interest on public datasets, such as BlogCatalog, with the common practice of maximizing scoring on graph reconstruction, link prediction metrics etc. However, in the financial sector the important metrics are ... More

Effective upper bound of analytic torsion under Arakelov metricMar 20 2019Mar 26 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

$K$-stable splendid Rickard complexesMar 04 2014In this paper, Brou\'e's conjecture is reduced to simple groups, with an additional stability condition.

Effect of Singwi-Tosi-Land-Sjölander local field correction on spin relaxation in $n$-type GaAs quantum wells at low temperatureDec 20 2007Feb 22 2008We study the effect of the Singwi-Tosi-Land-Sj\"{o}lander local field correction on spin relaxation/dephasing in $n$-type GaAs quantum wells at low temperature by constructing and numerically solving the kinetic spin Bloch equations. We calculate the ... More

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulenceAug 01 2013We report a high-resolution numerical study of two-dimensional (2D) miscible Rayleigh-Taylor (RT) incompressible turbulence with the Boussinesq approximation. An ensemble of 100 independent realizations were performed at small Atwood number and unit Prandtl ... More

The first boundary value problem for Abreu's equationSep 09 2010In this paper we prove the existence and regularity of solutions to the first boundary value problem for Abreu's equation, which is a fourth order nonlinear partial differential equation closely related to the Monge-Ampere equation. The first boundary ... More

A Necessary and Sufficient Condition for Stability of Linear Difference Equations with Two DelaysAug 26 2018This note provides a necessary and sufficient condition for guaranteeing exponential stability of the linear difference equation $x(t)=Ax(t-a)+Bx(t-b)$ where $a>0,b>0$ are constants and $A,B$ are $n\times n$ square matrices, in terms of a linear matrix ... More

Stability Analysis of Nonlinear Time-Varying Systems by Lyapunov Functions with Indefinite DerivativesDec 08 2015This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov functions are ... More

Formulation of finite-time singularity for free-surface Euler equationsNov 19 2012Dec 21 2012We give an extremely short proof that the free-surface incompressible, irrotational Euler equations with regular initial condition can form a finite time singularity in 2D or 3D. Thus, we provide a simple view of the problem studied by Castro, Cordoba, ... More

Hohenberg-Kohn Theorem for Coulomb Type SystemsAug 23 2011Density functional theory (DFT) has become a basic tool for the study of electronic structure of matter, in which the Hohenberg-Kohn theorem plays a fundamental role in the development of DFT. Unfortunately, the existing proofs are incomplete even incorrect; ... More

Motivic cohomology of quaternionic Shimura varieties and level raisingJan 07 2019Jan 29 2019We study the motivic cohomology of the special fiber of quaternionic Shimura varieties at a prime of good reduction. We exhibit classes in these motivic cohomology groups and use this to give an explicit geometric realization of level raising between ... More

Boltzmann distribution of free energies in a finite-connectivity spin-glass system and the cavity approachOct 06 2007At sufficiently low temperatures, the configurational phase space of a large spin-glass system breaks into many separated domains, each of which is referred to as a macroscopic state. The system is able to visit all spin configurations of the same macroscopic ... More

Temperature- and Force-Induced beta-Sheet Unfolding in an Exactly Solvable ModelDec 06 2001Mar 18 2002The stability of a $\beta$-sheeted conformation and its transition into a random coil are studied with a 2D lattice biopolymer model. At low temperature and low external force, the polymer folds back and forth on itself and forms a $\beta$-sheet. Our ... More

On the Performance of P2P Network: An Assortment MethodSep 12 2011P2P systems have grown dramatically in recent years. The most popular type of P2P systems are file sharing networks, which are used to share various types of content over the Internet. Due to the increase in popularity of P2P systems, the network performance ... More

Voronoi Summation Formulae on GL(n)Oct 13 2014Feb 03 2015We discover new Voronoi formulae for automorphic forms on GL($n$) for $n\geq 4$. There are $[n/2]$ different Voronoi formulae on GL($n$), which are Poisson summation formulae weighted by Fourier coefficients of the automorphic form with twists by some ... More

Spin Ordering and Quasiparticles in Spin Triplet Superconducting LiquidsJan 28 2002Jul 18 2002Spin ordering and its effect on low energy quasiparticles in a p-wave superconducting liquid are investigated. We show that there is a new 2D p-wave superconducting liquid where the ground state is rotation invariant. In quantum spin disordered liquids, ... More

Hidden topological order in $^{23}Na (F=1)$ Bose-Einstein CondensatesJul 12 2001Jul 13 2001We show the existence of a new hidden topological order in $^{23}Na$ (F=1) Bose-Einstein condensates (BEC) with antiferromagnetic interactions. Occurrence of this order is due to the confinement of hedgehogs in BEC where a spin Josephson effect takes ... More

Mott states under the influence of fermion-boson conversion: invasion of superfluidityMay 30 2005Jun 28 2005I study the influence of fermion-boson conversion near Feshbach resonances on Mott states of Cooper pairs and demonstrate possible invasion of superfluidity. The quantum dynamics of Fermi-Bose gases is studied using both an effective coupled $U(1)\otimes ... More

Spin-1/2 Collective Excitations in BEC of Interacting Spin-1 AtomsJun 07 2001We construct spin-1/2 collective excitations in BEC of interacting spin-1 atoms. These excitations exist in states with a maximal global degeneracy. The stability and energy of these objects are determined by interactions with spin fluctuations and are ... More

Spin correlation and Discrete symmetry in Spinor Bose-Einstein CondensatesFeb 21 2001Aug 25 2001We study spin correlations in Bose-Einstein condensates of spin 1 bosons with scatterings dominated by a total spin equal 2 channel. We show the low energy spin dynamics in the system can be mapped into an $o(n)$ nonlinear sigma model(NL$\sigma$M). $n=3$ ... More

On the Equivalence among Three Controllability Problems for a Networked SystemOct 11 2016A new proof is given for the mathematical equivalence among three $k$-sparse controllability problems of a networked system, which plays key roles in Olshevsky,2014, in the establishment of the NP-hardness of the associated minimal controllability problems ... More

Minimal Inputs/Outputs for Subsystems in a Networked SystemOct 07 2016Apr 13 2018Minimal input/output selection is investigated in this paper for each subsystem of a networked system. Some novel sufficient conditions are derived respectively for the controllability and observability of a networked system, as well as some necessary ... More

User Association with Maximizing Sum Energy Efficiency for Massive MIMO Enabled Heterogeneous Cellular NetworksJul 05 2016In this paper, we design an association scheme to maximize the sum energy efficiency for massive multiple-input and multiple-output (MIMO) enabled heterogeneous cellular networks (HCNs). Considering that the final formulated problem is in a sum-of-ratio ... More

Theoretical investigation of the four-layered self-doped high-T$_c$ superconductors: evidence of pair tunneling effectNov 28 2010Mar 29 2011Based on a four-layered self-doped $t-J$ type model and the slave-boson mean-field approach, we study theoretically the superconductivity in the electron-doped and hole-doped layers. The neighbor layers are coupled through both the single electron interlayer ... More

Global Regularity for the Two-dimensional Boussinesq Equations Without Diffusivity in Bounded DomainsOct 07 2015Mar 21 2018We address the well-posedness for the two-dimensional Boussinesq equations with zero diffusivity in bounded domains. We prove global in time regularity for rough initial data: both the initial velocity and temperature have $\epsilon$ fractional derivatives ... More

On the uniqueness conjecture for Markoff triplesOct 13 2000Nov 03 2000This paper has been withdrawn by author due to an error in the proof.

Criteria for Optimal Global Integrability of Hajłasz-Sobolev FunctionsApr 29 2010The author establishes some geometric criteria for a domain of ${\mathbb R}^n$ with $n\ge2$ to support a $(pn/(n-ps),\,p)_s$-Haj{\l}asz-Sobolev-Poincar\'e imbedding with $s\in(0,\,1]$ and $p\in(n/(n+s),\,n/s)$ or an $s$-Haj{\l}asz-Trudinger imbedding ... More

Circle patterns with obtuse exterior intersection anglesMar 06 2017Feb 09 2018Koebe-Andreev-Thurston theorem studies the existence and rigidity of circle patterns of a given combinatorial type and the given non-obtuse exterior intersection angles. By using the topological degree theory and variational principle, this paper derives ... More

Cyclotomic graphs and perfect codesFeb 11 2015Sep 26 2018We study two families of cyclotomic graphs and perfect codes in them. They are Cayley graphs on the additive group of $\mathbb{Z}[\zeta_m]/A$, with connection sets $\{\pm (\zeta_m^i + A): 0 \le i \le m-1\}$ and $\{\pm (\zeta_m^i + A): 0 \le i \le \phi(m) ... More

Single spin asymmetries in forward p-p/A collisions revisited: the role of color entanglementApr 17 2017We calculate the single transverse spin asymmetries(SSA) for forward inclusive particle production in pp and pA collisions using a hybrid approach. It is shown that the Sivers type contribution to the SSA drops out due to color entanglement effect, whereas ... More

Periodic sequences with stable $k$-error linear complexitySep 21 2011The linear complexity of a sequence has been used as an important measure of keystream strength, hence designing a sequence which possesses high linear complexity and $k$-error linear complexity is a hot topic in cryptography and communication. Niederreiter ... More

On Equivariant Elliptic Genera of Toric Calabi-Yau 3-foldsOct 29 2015We show that equivariant elliptic genera of toric Calabi-Yau 3-folds are generalized weak Jacobi forms. We also introduce a notion of averaged equivariant elliptic genera of toric Calabi-Yau 3-folds, and show that they are ordinary weak Jacobi forms given ... More

A Class of Delay Optimal Control Problems and Viscosity Solutions to Associated Hamilton-Jacobi-Bellman EquationsJul 15 2015In this article, a class of optimal control problems of differential equations with delays are investigated for which the associated Hamilton-Jacobi-Bellman (HJB) equations are nonlinear partial differential equations with delays. This type of HJB equation ... More

Emergent Geometry and Mirror Symmetry of A PointJul 07 2015By considering the partition function of the topological 2D gravity, a conformal field theory on the Airy curve emerges as the mirror theory of Gromov-Witten theory of a point. In particular, a formula for bosonic n-point functions in terms of fermionic ... More

Differential Rings from Special Kähler GeometryOct 14 2013Nov 26 2014We study triples of graded rings defined over the deformation spaces for certain one-parameter families of Calabi-Yau threefolds. These rings are analogues of the rings of modular forms, quasi-modular forms and almost-holomorphic modular forms. We also ... More

Resumming subleading Sudakov logarithms in saturation regimeJul 02 2018We investigate the scale dependence of transverse momentum dependent(TMD) gluon distribution in saturation regime. We found that in the Collins-2011 scheme, the scale dependence of small x gluon TMD is governed by the same renormalization group(RG) equation ... More

$A_\infty$-Minimal Model on Differential Graded AlgebrasApr 23 2019For a formal differential graded algebra, if extended by an odd degree element, we prove that the extended algebra has an $A_\infty$-minimal model with only $m_2$ and $m_3$ non-trivial. As an application, the $A_\infty$-algebras constructed by Tsai, Tseng ... More

Local Mirror Symmetry for One-Legged Topological VertexOct 22 2009Oct 30 2009We prove the Bouchard-Mari\~no Conjecture for the framed one-legged topological vertex by deriving the Eynard-Orantin type recursion relations from the cut-and-join equation satisfied by the relevant triple Hodge integrals. This establishes a version ... More

On Degenerated Monge-Ampere Equations over Closed Kähler ManifoldsMar 19 2006Mar 20 2006In this work, we study Monge-Ampere equations over closed K\"ahler manifolds with degenerated cohomology classes. Classic results and arguments in pluripotential theory are generalized a little bit to be applied to our situation.

Representation and regularity for the Dirichlet problem for real and complex degenerate Hessian equationsNov 25 2013We consider the Dirichlet problem for positively homogeneous, degenerate elliptic, concave (or convex) Hessian equations. Under natural and necessary conditions on the geometry of the domain, with the $C^{1,1}$ boundary data, we establish the interior ... More

Random attractor of the 3D viscous primitive equations driven by fractional noisesApr 18 2016May 19 2017We develop a new and general method to prove the the existence of the random attractor (strong attractor) for the primitive equations (PEs) of large-scale ocean and atmosphere dynamics under $non$-$periodic$ boundary conditions and driven by infinite-dimensional ... More

A note on the degree-diameter problem for arc-transitive graphsDec 22 2013We give two lower bounds on the largest order of an arc-transitive graph of diameter two and a given degree.

A remark on Rickard complexesMay 21 2013In this paper, we characterize a Rickard complex, which induces a Rickard equivalence between the block algebras of a block $b$ and its Brauer correspondent and whose vertices have the same order as defect groups of the block $b$. The homology of such ... More

Overview of recent azimuthal correlation measurements from ALICEOct 26 2016Azimuthal correlations are a powerful tool to probe the properties and the evolution of the collision system. In this proceedings, we will review the recent azimuthal correlation measurements from ALICE at the LHC. The comparison to other experimental ... More

Constraining the Higgs Boson Coupling to Light Quarks in the $H\to ZZ$ Final StatesMay 23 2015Feb 14 2016We constrain the Higgs boson (Yukawa) coupling to quarks in the first two generations in the $H\to ZZ$ final states. Deviation of these couplings from the Standard Model values leads to change in the Higgs boson width and in the cross sections of relevant ... More

Cluster structures and subfans in scattering diagramsJan 14 2019We give more precise statements of Fock-Goncharov duality conjecture for cluster varieties parametrizing $PGL_{2}$-local systems on once punctured torus. Then we prove these statements. Along the way, using disjoint subfans in the scattering diagram, ... More

Clickbait Detection in Tweets Using Self-attentive NetworkOct 15 2017Clickbait detection in tweets remains an elusive challenge. In this paper, we describe the solution for the Zingel Clickbait Detector at the Clickbait Challenge 2017, which is capable of evaluating each tweet's level of click baiting. We first reformat ... More

$3d$ One-form Mixed Anomaly and Entanglement EntropyApr 15 2019We study mixed anomaly between $G_1$ and $G_2$ of one-form finite symmetry $G_1\times G_2$ in $3d$ Chern-Simons theories. We assign a quantum entanglement structure to two linked $G$-symmetry lines (Wilson loops) and compute the entanglement entropy $S[G]$. ... More

Globally Existing Kähler-Ricci FlowsAug 26 2014May 15 2015We consider the general K\"ahler-Ricci flows which exist for all time. The zeroth order control on the flow metric potential for various infinite time singularities is the focus. The possible semi-amplness for numerically effective classes serves as the ... More

General Weak Limit for Kahler-Ricci FlowApr 15 2011Apr 10 2015Consider the Kahler-Ricci flow with finite time singularities over any closed Kahler manifold. We prove the existence of the flow limit in the sense of current towards the time of singularity. This answers affirmatively a problem raised by Tian on the ... More

The Complex Structures on $S^{2n}$Aug 15 2006Dec 11 2017Let $\widetilde{\cal J}(S^{2n})$ be the set of orthogonal complex structures on $TS^{2n}$. We show that the twistor space $\widetilde{\cal J}(S^{2n})$ is a Kaehler manifold. Then we show that an orthogonal almost complex structure $J_f$ on $S^{2n}$ is ... More