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Discovering and Leveraging the Most Valuable Links for RankingOct 05 2012On the Web, visits of a page are often introduced by one or more valuable linking sources. Indeed, good back links are valuable resources for Web pages and sites. We propose to discovering and leveraging the best backlinks of pages for ranking. Similar ... More

Reinforcement RankingMar 24 2013We introduce a new framework for web page ranking -- reinforcement ranking -- that improves the stability and accuracy of Page Rank while eliminating the need for computing the stationary distribution of random walks. Instead of relying on teleportation ... More

Practical Issues of Action-conditioned Next Image PredictionFeb 08 2018The problem of action-conditioned image prediction is to predict the expected next frame given the current camera frame the robot observes and an action selected by the robot. We provide the first comparison of two recent popular models, especially for ... More

Deep Reinforcement Learning with DecorrelationMar 18 2019Learning an effective representation for high-dimensional data is a challenging problem in reinforcement learning (RL). Deep reinforcement learning (DRL) such as Deep Q networks (DQN) achieves remarkable success in computer games by learning deeply encoded ... More

Deep Reinforcement Learning with DecorrelationMar 18 2019May 08 2019Learning an effective representation for high-dimensional data is a challenging problem in reinforcement learning (RL). Deep reinforcement learning (DRL) such as Deep Q networks (DQN) achieves remarkable success in computer games by learning deeply encoded ... More

ACE: An Actor Ensemble Algorithm for Continuous Control with Tree SearchNov 06 2018In this paper, we propose an actor ensemble algorithm, named ACE, for continuous control with a deterministic policy in reinforcement learning. In ACE, we use actor ensemble (i.e., multiple actors) to search the global maxima of the critic. Besides the ... More

Reinforcing Classical Planning for Adversary Driving ScenariosMar 20 2019Adversary scenarios in driving, where the other vehicles may make mistakes or have a competing or malicious intent, have to be studied not only for our safety but also for addressing the concerns from public in order to push the technology forward. Classical ... More

QUOTA: The Quantile Option Architecture for Reinforcement LearningNov 05 2018Nov 07 2018In this paper, we propose the Quantile Option Architecture (QUOTA) for exploration based on recent advances in distributional reinforcement learning (RL). In QUOTA, decision making is based on quantiles of a value distribution, not only the mean. QUOTA ... More

Negative Log Likelihood Ratio Loss for Deep Neural Network ClassificationApr 27 2018In deep neural network, the cross-entropy loss function is commonly used for classification. Minimizing cross-entropy is equivalent to maximizing likelihood under assumptions of uniform feature and class distributions. It belongs to generative training ... More

Distributional Reinforcement Learning for Efficient ExplorationMay 13 2019In distributional reinforcement learning (RL), the estimated distribution of value function models both the parametric and intrinsic uncertainties. We propose a novel and efficient exploration method for deep RL that has two components. The first is a ... More

A spin-boson theory for charge photogeneration in organic molecules: Role of quantum coherenceSep 13 2014The charge photogeneration process in organic molecules is investigated by a quantum heat engine model, in which two molecules are modeled by a two-spin system sandwiched between two bosonic baths at their own temperatures. The two baths represent the ... More

Asymptotic Behavior for Critical Patlak-Keller-Segel model and an Repulsive-Attractive Aggregation EquationDec 20 2011In this paper we study the long time asymptotic behavior for a class of diffusion-aggregation equations. Most results except the ones in Section 3.3 concern radial solutions. The main tools used in the paper are maximum-principle type arguments on mass ... More

Polaronic quantum diffusion in dynamic localization regimeNov 28 2016We investigate the quantum dynamics in a disordered electronic lattice with Fibonacci sequence of site energy and off-diagonal electron-phonon coupling within a sub-Ohmic bath by the time-dependent density matrix renormalization group algorithm. It is ... More

Coherent dynamics of singlet fission controlled by nonlocal electron-phonon couplingOct 23 2015Oct 28 2015Based on the Frenkel-charge transfer (CT) mixing model of singlet fission (SF), we incorporate both the local and nonlocal phonon baths in the Hamiltonian and adopt the algorithm of time-dependent density matrix renormalization group to simulate the fission ... More

Quench of non-Markovian coherence in the deep sub-Ohmic spin-boson model: A unitary equilibration schemeSep 10 2014The deep sub-Ohmic spin-boson model shows a longstanding non-Markovian coherence at low temperature. Motivating to quench this robust coherence, the thermal effect is unitarily incorporated into the time evolution of the model, which is calculated by ... More

Mixing and Un-mixing by Incompressible FlowsJul 15 2014We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-in-time constraint $\|\nabla u(\cdot,t)\|_p\leq 1$ we show that any function ... More

A variational surface hopping algorithm for the sub-Ohmic spin-boson modelJun 12 2013Jun 21 2013The Davydov D1 ansatz, which assigns an individual bosonic trajectory to each spin state, is an efficient, yet extremely accurate trial state for time-dependent variation of the sub-Ohmic spin-boson model [J. Chem. Phys. 138, 084111 (2013)]. A surface ... More

Transactive Control of Air Conditioning Loads for Mitigating Microgrid Tie-line Power FluctuationsJan 11 2017This paper presents a distributed control strategy for air conditioning loads (ACLs) to participate in the scheme of mitigating microgrid tie-line power fluctuations. The concept of baseline load is emphasized for ACL control in this paper. To obtain ... More

The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principleFeb 01 2011Nov 10 2011In this paper we investigate qualitative and asymptotic behavior of solutions for a class of diffusion-aggregation equations. Most results except the ones in section 3 and 6 concern radial solutions. The challenge in the analysis consists of the nonlocal ... More

On the polynomial convergence rate to nonequilibrium steady-statesJul 28 2016Aug 24 2016We consider a stochastic energy exchange model that models the 1D microscopic heat conduction. When coupled with heat baths with different temperature, we prove the existence and uniqueness of the nonequilibrium steady-state (NESS), and more important, ... More

Joint pricing and inventory control for a stochastic inventory system with Brownian demandAug 10 2016In this paper, we consider a infinite horizon continuous-review stochastic inventory system in which cumulative customers' demand is price-dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned by selling products ... More

Greatest lower bounds on Ricci curvature of homogeneous toric bundlesAug 07 2016Aug 28 2016For Fano homogeneous toric bundles, we obtain a formula of the greatest lower bound on Ricci curvature. We also give a criteria for the ampleness of a kind of line bundles over general homogeneous toric bundles.

Determinant line bundles on Moduli spaces of pure sheaves on rational surfaces and Strange DualityMay 18 2010Jul 24 2010Let $\mhu$ be the moduli space of semi-stable pure sheaves of class $u$ on a smooth complex projective surface $X$. We specify $u=(0,L,\chi(u)=0),$ i.e. sheaves in $u$ are of dimension $1$. There is a natural morphism $\pi$ from the moduli space $\mhu$ ... More

Existence of Weak Conical Kähler-Einstein Metrics Along Smooth HypersurfacesAug 20 2013The existence of \emph{weak conical K\"ahler-Einstein} metrics along smooth hypersurfaces with angle between $0$ and $2\pi$ is obtained by studying a smooth continuity method and a \emph{local Moser's iteration} technique. In the case of negative and ... More

Tevatron Combination and Higgs Boson PropertiesMay 15 2013We present the Tevatron combination of searches for the Higgs boson and studies of its properties. The searches use up to 10 fb$^{-1}$ of Tevatron collider Run II data. We observe a significant excess of events in the mass range between 115 and 140 GeV/c$^2$. ... More

Many-body singlets by dynamic spin polarizationJan 20 2011We show that dynamic spin polarization by collective raising and lowering operators can drive a spin ensemble from arbitrary initial state to many-body singlets, the zero-collective-spin states with large scale entanglement. For an ensemble of $N$ arbitrary ... More

On the Information of the Second Moments Between Random Variables Using Mutually Unbiased BasesDec 16 2007Dec 19 2007The notation of mutually unbiased bases(MUB) was first introduced by Ivanovic to reconstruct density matrixes\cite{Ivanovic}. The subject about how to use MUB to analyze, process, and utilize the information of the second moments between random variables ... More

Strange duality on rational surfacesApr 19 2016We study Le Potier's strange duality conjecture on a rational surface. We focus on the case involving the moduli space of rank 2 sheaves with trivial first Chern class and second Chern class 2, and the moduli space of 1-dimensional sheaves with determinant ... More

How the electron-phonon coupling mechanism work in metal superconductorSep 03 2017Superconductivity in some metals at low temperature is known to arise from an electron-phonon coupling mechanism. Such the mechanism enables an effective attraction to bind two mobile electrons together, and even form a kind of pairing system(called Cooper ... More

A data-driven method for the steady state of randomly perturbed dynamicsMay 10 2018Mar 25 2019We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem corresponding to a ... More

Geodesic disks in asymptotic Teichmüller spaceJun 29 2015Let $S$ be a hyperbolic Riemann surface. In a finite-dimensional Teichm\"uller space $T(S)$, it is still an open problem whether the geodesic disk passing through two points is unique. In an infinite-dimensional Teichm\"uller space it is also unclear ... More

A binary infinitesimal form of Teichmuller metricJan 24 2009Feb 16 2009Let $S$ be a Riemann surface of analytic finite type or the unit disk in the complex plane. Let $[\mu]$ denote the Teichm\"uller equivalence classes of Beltrami differentials $\mu $. We apply the Fundamental Inequalities to obtain a binary infinitesimal ... More

Strange duality on rational surfaces II: higher rank casesMar 20 2017Mar 21 2017We study Le Potier's strange duality conjecture on a rational surface. We focus on the strange duality map $SD_{c_n^r,L}$ which involves the moduli space of rank $r$ sheaves with trivial first Chern class and second Chern class $n$, and the moduli space ... More

The Brezis-Browder Theorem revisited and properties of Fitzpatrick functions of order nMay 25 2009In this note, we study maximal monotonicity of linear relations (set-valued operators with linear graphs) on reflexive Banach spaces. We provide a new and simpler proof of a result due to Brezis-Browder which states that a monotone linear relation with ... More

Phase Transition for the Contact Process in a Random Environment on Zd*Z+Feb 27 2018Nov 27 2018We review the results in Chen & Yao(2009,2012) which concern the contact process in a static random environment on the half space Z^d*Z^+ and make some addition to them. Furthermore, we explain why our methods cannot apply to the whole space case and ... More

A doubly exponential upper bound on noisy EPR states for binary gamesApr 18 2019Apr 22 2019This paper initiates the study of a class of entangled-games, mono-state games, denoted by $(G,\psi)$, where $G$ is a two-player one-round game and $\psi$ is a bipartite state independent of the game $G$. In the mono-state game $(G,\psi)$, the players ... More

Devil's Staircase -- Rotation Number of Outer Billiard with Polygonal Invariant CurvesFeb 10 2014In this paper, we discuss rotation number on the invariant curve of a one parameter family of outer billiard tables. Given a convex polygon $\eta$, we can construct an outer billiard table $T$ by cutting out a fixed area from the interior of $\eta$. $T$ ... More

Global solution to the three-dimensional liquid crystal flows of Q-tensor modelJan 28 2016Feb 28 2016A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows. Under suitable ... More

The J-flow On Toric ManifoldsJul 04 2014We study the J-flow on the toric manifolds, through study the transition map between the moment maps induced by two K\"{a}hler metrics, which is a diffeomorphism between polytopes. This is similar to the work of Fang-Lai, under the assumption of Calabi ... More

Moduli spaces of semistable sheaves of dimension 1 on $\mathbb{P}^2$Jun 21 2012Dec 30 2013Let $M(d,\chi)$ be the moduli space of semistable sheaves of rank 0, Euler characteristic $\chi$ and first Chern class $dH (d>0)$, with $H$ the hyperplane class in $\mathbb{P}^2$. We give a description of $M(d,\chi)$, viewing each sheaf as a class of ... More

A data-driven method for the steady state of randomly perturbed dynamicsMay 10 2018We demonstrate a data-driven method to solve the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least square problem corresponding to a reference ... More

Optimal exponentials of thickness in Korn's inequalities for parabolic and elliptic shellsJul 29 2018Sep 01 2018We establish Korn's interpolation inequalities and the rigidity results of the strain tensor of the middle surface for the parabolic and elliptic shells and show that the best constant in Korn's inequalities scales like $h^{3/2}$ for the parabolic shell ... More

Motivic measures of moduli spaces of 1-dimensional sheaves on rational surfacesSep 01 2015We study the moduli space of rank 0 semistable sheaves on some rational surfaces. We show the irreducibility and stable rationality of them under some conditions. We also compute several (virtual) Betti numbers of those moduli spaces by computing their ... More

Moduli spaces of 1-dimensional semi-stable sheaves and Strange duality on $\mathbb{P}^2$Apr 25 2015Jun 11 2017We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We show the conjecture is true for the pair ($W(2,0,2),~M(d,0)$) with $d>0$, where $W(2,0,2)$ is the moduli space of semistable sheaves of rank 2, zero first Chern class and second Chern ... More

A doubly exponential upper bound on noisy EPR states for binary gamesApr 18 2019This paper initiates the study of a class of entangled-games, mono-state games, denoted by $(G,\psi)$, where $G$ is a two-player one-round game and $\psi$ is a bipartite state independent of the game $G$. In the mono-state game $(G,\psi)$, the players ... More

A Theoretical Study of Mafia GamesApr 01 2008Mafia can be described as an experiment in human psychology and mass hysteria, or as a game between informed minority and uninformed majority. Focus on a very restricted setting, Mossel et al. [to appear in Ann. Appl. Probab. Volume 18, Number 2] showed ... More

Existence and stability of periodic planar standing waves in phase-transitional elasticity with strain-gradient effectsOct 31 2011Oct 23 2012Extending investigations of Antman & Malek-Madani, Schecter & Shearer, Slemrod, Barker & Lewicka & Zumbrun, and others, we investigate phase-transitional elasticity models of strain-gradient effect. We prove the existence of non-constant planar periodic ... More

Primary Decomposition: Compatibility, Independence and Linear GrowthSep 20 2002For finitely generated modules $N \subsetneq M$ over a Noetherian ring $R$, we study the following properties about primary decomposition: (1) The Compatibility property, which says that if $\ass (M/N)=\{P_1, P_2, ..., P_s\}$ and $Q_i$ is a $P_i$-primary ... More

Fundamental theorem of hyperbolic geometry without the injectivity assumptionOct 09 2008Feb 16 2009Let $\mathbb{H}^n$ be the $n-$dimensional hyperbolic space. It is well known that, if $f: \mathbb{H}^n\to \mathbb{H}^n$ is a bijection that preserves $r-$dimensional hyperplanes, then $f$ is an isometry. In this paper we make neither injectivity nor $r-$hyperplane ... More

Existence of extremal Beltrami coefficients with non-constant modulusMay 11 2007Jan 24 2009Suppose $[\mu]_{T(\Delta)}$ is a point of the universal Teichm\"uller space $T(\Delta)$. In 1998, it was shown by Bo\v{z}in et al. that there exists $\mu$ such that $\mu$ has non-constant modulus and is uniquely extremal in $[\mu]_{T(\Delta)}$. It is ... More

The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotoneMay 13 2010Aug 14 2010The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of ... More

Propagating stress-pulses and wiggling transition revealed in string dynamicsApr 19 2018Understanding string dynamics yields insights into the intricate dynamic behaviors of various filamentary thin structures in nature and industry covering multiple length scales. In this work, we investigate the planar dynamics of a flexible string where ... More

Topological vacancies in spherical crystal clustersSep 04 2017Understanding geometric frustration of ordered phases in two-dimensional condensed matters on curved surfaces is closely related to a host of scientific problems in condensed matter physics and materials science. Here we show how two-dimensional Lennard-Jones ... More

Glick's conjecture on the point of collapse of axis-aligned polygons under the pentagram mapsOct 28 2014The pentagram map has been studied in a series of papers by Schwartz and others. Schwartz showed that an axis-aligned polygon collapses to a point under a predictable number of iterations of the pentagram map. Glick gave a different proof using cluster ... More

Detecting Potential Instabilities of Numerical AlgorithmsSep 07 2015It has been the standard teaching of today that backward stability analysis is taught as absolute, just as in Newtonian physics time is taught absolute time. We will prove it is not true in general. It depends on algorithms. We will prove that forward ... More

Computer-Aided Annotation for Video Tampering Dataset of Forensic ResearchFeb 07 2018The annotation of video tampering dataset is a boring task that takes a lot of manpower and financial resources. At present, there is no published literature which is capable to improve the annotation efficiency of forged videos. We presented a computer-aided ... More

$L^p$ Solutions of Backward Stochastic Differential Equations with JumpsJul 13 2010Jul 01 2016Given $p \in (1, 2)$, we study $L^p$-solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z,u)$. We show that such a BSDEJ with a p-integrable terminal data ... More

An Efficient Graph Accelerator with Parallel Data Conflict ManagementJun 03 2018Graph-specific computing with the support of dedicated accelerator has greatly boosted the graph processing in both efficiency and energy. Nevertheless, their data conflict management is still sequential in essential when some vertex needs a large number ... More

Properties of CO Molecular Gas in IR Luminous GalaxiesSep 07 2003We present the properties of the 12CO(1-0) and (3-2) line emission from the nuclei of 60 IR luminous SLUGS galaxies. This subsample is flux limited at S60 > 5.24 Jy with FIR luminosities mostly at LFIR > 10^10 Lo. The emission line strengths of 12CO(1-0) ... More

A Detailed Analysis of Quicksort Algorithms with Experimental MathematicsApr 30 2019We study several variants of single-pivot and multi-pivot Quicksort algorithms and consider them as discrete probability problems. With experimental mathematics, explicit expressions for expectations, variances and even higher moments of their numbers ... More

Infinitesimally extremal Beltrami differentials of non-landslide typeOct 28 2016In this paper, it is shown that there are infinitely many extremal Beltrami differentials of non-landside type and non-constant modulus in an infinitesimal equivalence class unless the class contains a unique extremal.

The Continuity Method to Deform Cone AngleMay 07 2014Nov 08 2014The continuity method is used to deform the cone angle of a weak conical K\"ahler-Einstein metric with cone singularities along a smooth anti-canonical divisor on a smooth Fano manifold. This leads to an alternative proof of Donaldson's Openness Theorem ... More

Strange duality on $\mathbb{P}^2$ via quiver representationsJul 24 2018We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We focus on the strange duality map $SD_{c_n^r,d}$ which involves the moduli space of rank $r$ sheaves with trivial first Chern class and second Chern class $n$, and the moduli space of ... More

A Detailed Analysis of Quicksort Algorithms with Experimental MathematicsApr 30 2019May 02 2019We study several variants of single-pivot and multi-pivot Quicksort algorithms and consider them as discrete probability problems. With experimental mathematics, explicit expressions for expectations, variances and even higher moments of their numbers ... More

Distribution of Normalized Zero-Sets of Random Entire Functions with Small Random PerturbationApr 11 2009In this paper, we extend our earlier result (see [Y-2008]) on the distribution of normalized zero-sets of random entire functions to random entire functions with small random perturbation.

Dressed Active Particles in Spherical CrystalsAug 03 2016We investigate the dynamics of an active particle in two-dimensional spherical crystals, which provide an ideal environment to illustrate the interplay of active particle and crystallographic defects. A moving active particle is observed to be surrounded ... More

Maximality of the sum of the subdifferential operator and a maximally monotone operatorJun 30 2014The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar's constraint qualification holds, which is called the "sum problem". In ... More

Beating maps of singlet fission: Full-quantum simulation of coherent two-dimensional electronic spectroscopy in organic aggregatesJun 02 2017The coherent two-dimensional (2D) electronic spectra with respect to the singlet fission (SF) process in organic molecular aggregates are simulated by the Davydov ansatz combined with the Frenkel-Dirac time-dependent variational algorithm. By virtue of ... More

Signature-Based Gröbner Basis Algorithms --- Extended MMM Algorithm for computing Gröbner basesAug 11 2013Signature-based algorithms is a popular kind of algorithms for computing Gr\"obner bases, and many related papers have been published recently. In this paper, no new signature-based algorithms and no new proofs are presented. Instead, a view of signature-based ... More

Linear Strain Tensors and Optimal Exponential of thickness in Korn's Inequalities for Hyperbolic ShellsJul 29 2018Dec 31 2018We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces to obtain $L^2$ regularity solutions. Then the rigidity results on the strain tensor of the middle surface are implied by the $L^2$ regularity for non-characteristic ... More

Evolving Starburst Modeling of FIR/sub-mm/mm Line Emission. II. Application to M 82Sep 03 2009Sep 10 2009We present starburst models for far-infrared/sub-millimeter/millimeter (FIR/sub-mm/mm) line emission of molecular and atomic gas in an evolving starburst region, which is treated as an ensemble of non-interacting hot bubbles which drive spherical shells ... More

Evolving Starburst Modeling of FIR/sub-mm/mm Line Emission. III. Application to Nearby Luminous Infrared GalaxiesSep 08 2009Apr 23 2010In a previous work, we showed that the observed FIR/sub-mm/mm line spectra of a starburst galaxy (M 82) can be successfully modeled in terms of the evolutionary scheme of an ensemble of giant molecular clouds (GMCs) and shells, and such studies can usefully ... More

Motivic measures of the moduli spaces of pure sheaves on $\mathbb{P}^2$ with all degreesMar 21 2015Mar 31 2015Let $\mathcal{M}(d,\chi)$ be the moduli stack of stable sheaves of rank 0, Euler characteristic $\chi$ and first Chern class $dH~(d>0)$, with $H$ the hyperplane class in $\mathbb{P}^2$. We compute the $A$-valued motivic measure $\mu_A(\mathcal{M}(d,\chi))$ ... More

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current SingularitiesAug 28 2017Coronal heating has been a long-standing conundrum in solar physics. Parker's conjecture that spontaneous current singularities lead to nanoflares that heat the corona has been controversial. In ideal magnetohydrodynamics (MHD), can genuine current singularities ... More

Non-decreasable extremal Beltrami differentials of non-landslide typeJun 22 2016In this paper, we deform a uniquely-extremal Beltrami differential into different non-decreasable Beltrami differentials, and then construct non-unique extremal Beltrami differentials such that they are both non-landslide and non-decreasable.

Quantum phase transition of the 103mRh spin-density waveJun 30 2009We induce a quantum phase transition of the 103mRh excitation at the critical density of 10^{12} cm^{-3} by bremsstrahlung pumping at 300 K. A massive 103mRh spin-density wave carrying a spin current moves on the identical 103Rh matrix like a quantum ... More

Nuclear spin-density wave theoryJul 09 2009Sep 15 2009Recently [arXiv:0906.5417], we reported a quantum phase transition of 103mRh excited by bremsstrahlung pumping. The long-lived Moessbauer excitation is delocalized as a neutral quasiparticle carrying a spin current. This letter gives a general theory ... More

Special value formula for the twisted triple product and applicationsOct 31 2018Nov 27 2018We establish explicit Ichino's formulae for the central values of the triple product $L$-functions with emphasis on the calculations for the real place. The key ingredient for our computations is Proposition 4.5 for the real place which is the main novelty ... More

Distribution of Normalized Zero-Sets of Random Entire FunctionsNov 20 2008This paper is concerned with the distribution of normalized zero-sets of random entire functions. The normalization of the zero-set is performed in the same way as that of the counting function for an entire function in Nevanlinna theory. The result generalizes ... More

The Breuil--Mézard conjecture for function fieldsAug 28 2018Let $K$ be a local function field of characteristic $l$, $\mathbb{F}$ be a finite field over $\mathbb{F}_p$ where $l \ne p$, and $\overline{\rho}: G_K \rightarrow \text{GL}_n (\mathbb{F})$ be a continuous representation. We apply the Taylor-Wiles-Kisin ... More

Logarithmic de Rham--Witt complexes via the Décalage operatorAug 28 2018Feb 25 2019We provide a new formalism of de Rham--Witt complexes in the logarithmic setting. This construction generalizes a result of Bhatt--Lurie--Mathew, and agrees with those of Hyodo--Kato and Matsuue for log-smooth schemes of log-Cartier type. We then apply ... More

$L^p$ Solutions of Backward Stochastic Differential Equations with JumpsJul 13 2010Feb 10 2017Given $p \in (1, 2)$, we study $L^p$-solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z)-$variables. We show that such a BSDEJ with a p-integrable terminal ... More

Characterizations of ultramaximally monotone operatorsJan 29 2014In this paper, we study properties of ultramaximally monotone operators. We characterize the interior and the closure of the range of an ultramaximally monotone operator. We establish the Brezis--Haraux condition in the setting of a general Banach space. ... More

The sum of a maximally monotone linear relation and the subdifferential of a proper lower semicontinuous convex function is maximally monotoneOct 21 2010The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of ... More

Unsupervised Learning on Neural Network Outputs: with Application in Zero-shot LearningJun 02 2015May 23 2016The outputs of a trained neural network contain much richer information than just an one-hot classifier. For example, a neural network might give an image of a dog the probability of one in a million of being a cat but it is still much larger than the ... More

Successive Difference Substitution Based on Column Stochastic Matrix and Mechanical Decision for Positive Semi-definite FormsApr 27 2009Apr 02 2010The theory part of this paper is sketched as follows. Based on column stochastic average matrix $T_n$ selected as a basic substitution matrix, the method of advanced successive difference substitution is established. Then, a set of necessary and sufficient ... More

Moduli spaces of 1-dimensional semi-stable sheaves and Strange duality on $\mathbb{P}^2$Apr 25 2015We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We show the conjecture is true for the pair ($M(2,0,2),~M(d,0)$) with $d>0$, where $M(2,0,2)$ is the moduli space of semistable sheaves of rank 2, zero first Chern class and second Chern ... More

A New Hypothesis On The Origin and Formation of The Solar And Extrasolar Planetary SystemsMar 02 2014A new theoretical hypothesis on the origin and formation of the solar and extrasolar planetary systems is summarized and briefly discussed in the light of recent detections of extrasolar planets, and studies of shock wave interaction with molecular clouds, ... More

Joint pricing and inventory control for a stochastic inventory system with Brownian motion demandAug 10 2016Jul 11 2017In this paper, we consider an infinite horizon, continuous-review, stochastic inventory system in which cumulative customers' demand is price-dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned by selling ... More

Parity Decision Tree Complexity and 4-Party Communication Complexity of XOR-functions Are Polynomially EquivalentJun 09 2015Jun 28 2015In this note, we study the relation between the parity decision tree complexity of a boolean function $f$, denoted by $\mathrm{D}_{\oplus}(f)$, and the $k$-party number-in-hand multiparty communication complexity of the XOR functions $F(x_1,\ldots, x_k)= ... More

Studies of measuring Higgs self-coupling with $HH\rightarrow b\bar b γγ$ at the future hadron collidersAug 28 2013Sep 11 2013We present a feasibility study of observing $HH\rightarrow b\bar b\gamma\gamma$ at the future hadron colliders with $\sqrt{s}=$14, 33, and 100 TeV. The measured cross section then can be used to constrain the Higgs self-coupling directly in the standard ... More

Quantum computing with single electron bubbles in heliumOct 27 2005An electron inside liquid helium forms a bubble of 17 \AA in radius. In an external magnetic field, the two-level system of a spin 1/2 electron is ideal for the implementation of a qubit for quantum computing. The electron spin is well isolated from other ... More

Towards Quantum Field Theory in Curved Spacetime for an Arbitrary ObserverJul 15 2009We propose a new framework of quantum field theory for an arbitrary observer in curved spacetime, defined in the spacetime region in which each point can both receive a signal from and send a signal to the observer. Multiple motivations for this proposal ... More

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H. TongJan 06 2012Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H. Tong [arXiv:1104.3073]

An affirmative answer to a problem posed by ZalinescuNov 10 2009Recently, in [5] Zalinescu posed a question about the characterization of the intrinsic core of the Minkowski sum of two graphs associated with two maximal monotone operators. In this note we give an affirmative answer.

On infinitesimally weakly non-decreasable Beltrami differentialsOct 28 2016Z. Zhou et al. proved that in a Teichm\"uller equivalence class, there exists an extremal quasiconformal mapping with a weakly non-decreasable dilatation. In this paper, we prove that in an infinitesimal equivalence class, there exists a weakly non-decreasable ... More

On nonuniqueness of geodesics in asymptotic Teichmüller spaceJun 29 2015In an infinite-dimensional Teichm\"uller space, it is known that the geodesic connecting two points can be unique or not. In this paper, we study the situation on the geodesic in the universal asymptotic Teichm\"uller space $AT(\Delta)$. We introduce ... More

A note on a Marčenko-Pastur type theorem for time seriesSep 08 2011In this note we develop an extension of the Mar\v{c}enko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for its Stieltjes ... More

On the polynomial convergence rate to nonequilibrium steady-statesJul 28 2016Jun 06 2018We consider a stochastic energy exchange model that models the 1D microscopic heat conduction in the nonequilibrium setting. In this paper, we prove the existence and uniqueness of the nonequilibrium steady state (NESS) and, furthermore, the polynomial ... More

Emergent dynamic structures and statistical law in spherical lattice gas automataDec 26 2017Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate ... More