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A group theoretical approach to computing phonons and their interactionsApr 12 2019Here we present four independent advances which facilitate the computation of phonons and their interactions from first-principles. First, we implement a group-theoretical approach to construct the order N Taylor series of a d-dimensional crystal purely ... More

Heat SuperconductivityNov 15 2012Nov 21 2012Electrons/atoms can flow without dissipation at low temperature in superconductors/superfluids. The phenomenon known as superconductivity/superfluidity is one of the most important discoveries of modern physics, and is not only fundamentally important, ... More

1.06 μm Q-switched ytterbium-doped fiber laser using few-layer topological insulator Bi2Se3 as a saturable absorberJul 18 2013Passive Q-switching of an ytterbium-doped fiber (YDF) laser with few-layer topological insulator (TI) is, to the best of our knowledge, experimentally demonstrated for the first time. The few-layer TI: Bi2Se3 (2-4 layer thickness) is fabricated by the ... More

An adaptive significance threshold criterion for massive multiple hypotheses testingOct 27 2006This research deals with massive multiple hypothesis testing. First regarding multiple tests as an estimation problem under a proper population model, an error measurement called Erroneous Rejection Ratio (ERR) is introduced and related to the False Discovery ... More

Single machine slack due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activityMay 04 2014In this paper, we consider the slack due-window assignment model and study a single machine scheduling problem of linear time-dependent deteriorating jobs and a deteriorating maintenance activity. The cost for each job consists of four components: earliness, ... More

Stable Phaseless Sampling and Reconstruction of Real-Valued Signals with Finite Rate of InnovationsJan 17 2018A spatial signal is defined by its evaluations on the whole domain. In this paper, we consider stable reconstruction of real-valued signals with finite rate of innovations (FRI), up to a sign, from their magnitude measurements on the whole domain or their ... More

Collective Excitations of Rotating Dipolar Fermi Gases in the Fractional Quantum Hall RegimeAug 04 2008Aug 22 2008We apply the magneto-roton theory of the fractional quantum Hall effect to study the collective excitation spectrum of rotating dipolar Fermi gases. The predicted spectrum has a finite energy gap in the long wavelength limit and a roton minimum at finite ... More

Static and dynamical properties of a two-dimensional Wigner crystal of rotating dipolar Fermi gasesFeb 13 2009Using an ansatz wave function for the ground state of rotating two-dimensional dipolar fermions, which occupy only partially the lowest Landau level, we study the correlation energy and elastic properties of the Wigner crystal of rotating dipolar Fermi ... More

Excitation Spectrum and Stability from a Filled Landau Level in Rotating Dipolar Fermi GasesSep 29 2008We apply the equation-of-motion method to study the collective excitation spectrum from a filled Landau level in rotating dipolar Fermi gases. The predicted excitation spectrum of rotating dipolar Fermi gases can exhibit a roton-minimum character. This ... More

Universal scaling of Efimov resonance positions in cold atom systemsNov 07 2011Nov 18 2011Recent cold atom experiments report a surprising universal scaling of the first Efimov resonance position a_{-}^1 by the two-body van der Waals length r_{vdW}. The ratio C=-a_{-}^1/r_{vdW}=8.5~9.5 for identical particles appears to be a constant regardless ... More

Faster Approximation of Max Flow for Directed GraphsNov 05 2012Nov 18 2012I extend the methods in "Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs, with Paul Christiano, Jonathan Kelner, Daniel Spielman, and Shang-Hua Teng" to directed graphs with a variation of the framework ... More

Asynchronous Byzantine Agreement with Optimal Resilience and Linear ComplexityJul 22 2015Nov 25 2015Given a system with $n > 3t + 1$ processes, where $t$ is the tolerated number of faulty ones, we present a fast asynchronous Byzantine agreement protocol that can reach agreement in $O(t)$ expected running time. This improves the $O(n^2)$ expected running ... More

The proximity force approximation for the Casimir energy of plate-sphere and sphere-sphere systems in the presence of one extra compactified universal dimensionNov 13 2013The Casimir energies for plate-sphere system and sphere-sphere system under PFA in the presence of one extra compactified universal dimension are analyzed. We find that the Casimir energy between a plate and a sphere in the case of sphere-based PFA is ... More

The asymptotic behavior of Casimir force in the presence of compactified universal extra dimensionsSep 14 2006The Casimir effect for parallel plates in the presence of compactified universal extra dimensions within the frame of Kaluza-Klein theory is analyzed. Having regularized and discussed the expressions of Casimir force in the limit, we show that the nature ... More

Energy conservation for the weak solutions of the compressible Navier-Stokes equationsMay 02 2016Nov 01 2016In this paper, we prove the energy conservation for the weak solutions of the compressible Navier-Stokes equations for any time $t>0$, under certain conditions. The results hold for the renormalized solutions of the equations with constant viscosities, ... More

Firing Rate Dynamics in Recurrent Spiking Neural Networks with Intrinsic and Network HeterogeneityMay 12 2015Nov 21 2016Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies ... More

Hausdorff Dimension of Non-Diophantine Points in Finite-Volume Quotients of Rank One Semisimple Lie GroupsOct 06 2016In this note, we give a definition of Diophantine points of type $\gamma$ for $\gamma\geq0$ in a homogeneous space $G/\Gamma$ and we compute Hausdorff dimensions of subsets of points which are not Diophantine of type $\gamma$ when $G$ is a semisimple ... More

Bose-Einstein condensation of photons in the matter-dominated universeDec 30 2014In 1914, Planck introduced the concept of a white body. In nature, no true white bodies are known. We assume that the universe after last-scattering is an ideal white body that contains a tremendously large number of thermal photons and is at an extremely ... More

Permutational behavior of reversed Dickson polynomials over finite fieldsMay 17 2016In this paper, we use the method developed previously by Hong, Qin and Zhao to obtain several results on the permutational behavior of the reversed Dickson polynomial $D_{n,k}(1,x)$ of the $(k+1)$-th kind over the finite field ${\mathbb F}_{q}$. Particularly, ... More

Finding the limit of incompleteness IFeb 15 2019In this paper, I examine the limit of incompleteness w.r.t. interpretation. I first define the notion "G\"{o}del's first incompleteness theorem ($\sf G1$ for short) holds for theory $T$". This paper is motivated by the following question: whether there ... 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

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

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

A relationship between trees and Kelly-Mac Lane graphsApr 21 2003We give a precise description of combed trees in terms of Kelly-Mac Lane graphs. We show that any combed tree is uniquely expressed as an allowable Kelly-Mac Lane graph of a certain shape. Conversely, we show that any such Kelly-Mac Lane graph uniquely ... More

An alternative characterisation of universal cells in opetopic n-categoriesApr 21 2003We address the fact that composition in an opetopic weak n-category is in general not unique and hence is not a well-defined operation. We define composition with a given k-cell in an n-category by a span of (n-k)-categories. We characterise such a cell ... More

The theory of opetopes via Kelly-Mac Lane graphsApr 21 2003This paper follows from two earlier works. In the first we gave an explicit construction of opetopes, the underlying cell shapes in the theory of opetopic n-categories; at the heart of this construction is the use of certain trees. In the second we gave ... More

Opetopic bicategories: comparison with the classical theoryApr 21 2003We continue our previous modifications of the Baez-Dolan theory of opetopes to modify the Baez-Dolan definition of universality, and thereby the category of opetopic n-categories and lax functors. For the case n=2 we exhibit an equivalence between this ... More

On comparing sums of square roots of small integersFeb 28 2006Let $k$ and $n$ be positive integers, $n>k$. Define $r(n,k)$ to be the minimum positive value of $$ |\sqrt{a_1} + ... + \sqrt{a_k} - \sqrt{b_1} - >... -\sqrt{b_k} | $$ where $ a_1, a_2, ..., a_k, b_1, b_2, ..., b_k $ are positive integers no larger than ... More

Hard Problems of Algebraic Geometry CodesJul 08 2005The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for general linear ... More

On Equivalence of MatricesMay 31 2016Sep 19 2017A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related structures ... More

Boolean Algebras and LogicSep 03 2008Dec 03 2011In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness ... More

A Shrinking Target Problem with Target at Infinity in Rank One Homogeneous SpacesOct 06 2016Oct 08 2018In this paper, we give a definition of Diophantine points of type $\gamma$ for $\gamma\geq0$ in a homogeneous space $G/\Gamma$, and compute the Hausdorff dimension of the subset of points which are not Diophantine of type $\gamma$ when $G$ is a semisimple ... More

Kauffman-Harary conjecture for alternating virtual knotsOct 16 2013In 1999, Kauffman-Harary conjectured that every non-trivial Fox $p$-coloring of a reduced, alternating knot diagram with prime determinant $p$ is heterogeneous. Ten years later this conjecture was proved by W. Mattman and P. Solis. Mathew Williamson generalized ... More

A transcendental function invariant of virtual knotsNov 26 2015In this work we describe a new invariant of virtual knots. We show that this transcendental function invariant generalizes several polynomial invariants of virtual knots, such as the writhe polynomial, the affine index polynomial and the zero polynomial. ... More

QCD Thermodynamics with Domain Wall FermionsOct 07 2008We present our recent studies of the pseudo-critical temperature, $T_c$, of QCD using domain wall fermions. Domain wall fermions have the advantage that they preserve exact SU(2) chiral symmetry at finite lattice spacing in the limit that $L_s \to \infty$. ... More

Fermionic Lieb-Schultz-Mattis Theorems and Weak Symmetry-Protected PhasesApr 26 2018Feb 21 2019The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional generalizations by Oshikawa and Hastings establish that a translation-invariant lattice model of spin-$1/2$'s can not have a non-degenerate ground state preserving both spin and translation ... More

A note on the writhe polynomial and the virtual crossing numberMay 20 2018May 24 2018In this note we give a new lower bound on the virtual crossing number via the writhe polynomial, which refines a result of B. Mellor. The proof is based on a new interpretation of the writhe polynomial. The characterization of the writhe polynomial is ... More

Decoupled oscillations and resonances of three neutrinos in matterApr 04 2001Apr 12 2001In a previous paper, we gave a new theoretical framework in which three neutrino mixing in matter are discussed. Rigorous analytical solutions are obtained. In present paper an approximate method is developed for studying three flavor neutrino oscillations ... More

Iterated distributive lawsOct 05 2007We give a framework for combining $n$ monads on the same category via distributive laws satisfying Yang-Baxter equations, extending the classical result of Barr and Wells which combines two monads via one distributive law. We show that this corresponds ... More

A Global Trace Formula for Reductive Lie Algebras and the Harish-Chandra Transform on the Space of Characteristic PolynomialsOct 01 2014Feb 03 2015In this paper an integral transform between spaces of nonstandard test functions on the affine space of dimension n is constructed. The integral transform satisfies a summation formula of Poisson type, which is derived from an analogue of the Arthur-Selberg ... More

Packing structure of a two-dimensional granular system through the jamming transitionNov 10 2009Jun 23 2010We have performed a novel experiment on granular packs composed of automatically swelling particles. By analyzing the Voronoi structure of packs going through the jamming transition, we show that the local configuration of a jamming pack is strikingly ... More

Low-Mach-number Euler equations with solid-wall boundary condition and general initial dataJun 06 2010Nov 02 2010We prove that the divergence-free component of the compressible Euler equations with solid-wall boundary condition converges strongly towards the incompressible Euler equations at the same order as the Mach number. General initial data are considered ... More

Coalitions in nonatomic network congestion gamesMar 26 2012May 12 2012This work shows that the formation of a finite number of coalitions in a nonatomic network congestion game benefits everyone. At the equilibrium of the composite game played by coalitions and individuals, the average cost to each coalition and the individuals' ... More

Anomalous Dimension in the Solution of the Barenblatt's EquationFeb 28 2001A new method is presented to obtain the anomalous dimension in the solution of the Barenblatt's equation. The result is the same as that in the renormalization group (RG) approach. It gives us insight on the perturbative solution of the Barenblatt's equation ... More

Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two DimensionsFeb 20 2013Apr 11 2014It has been shown that the symmetry-protected topological (SPT) phases with finite Abelian symmetries can be described by Chern-Simons field theory. We propose a topological response theory to uniquely identify the SPT orders, which allows us to obtain ... More

The Dark Side of the Universe after PlanckJun 18 2013Feb 25 2014Recently released Planck data implies a smaller Hubble constant $H_0$ than that from Hubble Space Telescope project (HST) and a larger percentage of the matter components $\Omega_m$ compared to Supernova Legacy Survey (SNLS) in $\Lambda$CDM model. In ... More

Energy conservation for the weak solutions of the compressible Navier-Stokes equationsMay 02 2016In this paper, we prove the energy conservation for the weak solutions of the compressible Navier-Stokes equations for any time $t>0$, under certain conditions. The results hold for the renormalized solutions of the equations with constant viscosities, ... More

On the Type IIb solutions to mean curvature flowMar 19 2016Jul 07 2016In this paper we study the Type IIb mean curvature flow for which has the smooth solution exists for all $t> 0$ and satisfies $\sup\limits_{M^n\times (0,+\infty)}t|A|^2=\infty$, where $A(\cdot,t)$ is the second fundamental form. We prove that the longtime ... More

The Casimir effect for parallel plates in the spacetime with a fractal extra compactified dimensionJun 23 2011The Casimir effect for massless scalar fields satisfying Dirichlet boundary conditions on the parallel plates in the presence of one fractal extra compactified dimension is analyzed. We obtain the Casimir energy density by means of the regularization ... More

The Casimir force on a piston in Randall-Sundrum modelsApr 27 2009Jul 11 2010The Casimir effect of a piston for massless scalar fields which satisfy Dirichlet boundary conditions in the context of five-dimensional Randall-Sundrum models is studied. In these scenarios we derive and calculate the expression for the Casimir force ... More

The Casimir effect for a cavity in the presence of compactified universal extra dimensionOct 13 2004Aug 06 2005We reexamine the Casimir effect for the rectangular cavity with two or three equal edges in the presence of compactified universal extra dimension. We derive the expressions for the Casimir energy and discuss the nature of Casimir force. We show the extra-dimension ... More

A new proof to the energy conservation for the Navier-Stokes equationsApr 19 2016In this paper we give a new proof to the energy conservation for the weak solutions of the incompressible Navier-Stokes equations. This result was first proved by Shinbrot. The new proof relies on a lemma introduced by Lions.

A mean value inequality for the generalized self-expander type submanifolds and its applicationMar 15 2015In this paper we get a version of mean value inequality for generalized self-expander type submanifolds in Euclidean space. As the application, we prove that if mean curvature flow $M(t)$ on the self-expander in Euclidean space subconverges to an $n$-rectifiable ... More

Cowles commission structural equation approach in light of nonstationary time series analysisFeb 27 2007We review the advancement of nonstationary time series analysis from the perspective of Cowles Commission structural equation approach. We argue that despite the rich repertoire nonstationary time series analysis provides to analyze how do variables respond ... More

Internal relation between Personality trait Statistical outcomes among Junior College Divers and their performanceApr 24 2018Objective: Personality trait can predict divers' behavioral performance underwater. However, we know very little about the innate personality of the junior college diving students. To gain a better insight of personality characteristics of them, we carried ... More

Generalization of Mrs. Gerber's LemmaSep 05 2014Sep 11 2014Mrs. Gerber's Lemma (MGL) hinges on the convexity of $H(p*H^{-1}(u))$, where $H(u)$ is the binary entropy function. In this work, we prove that $H(p*f(u))$ is convex in $u$ for every $p\in [0,1]$ provided $H(f(u))$ is convex in $u$, where $f(u) : (a, ... More

A dynamic mechanism of Alzheimer based on artificial neural networkNov 16 2014In this paper, we provide another angle to analyze the reasons why Alzheimer Disease exists. We analyze the dynamic mechanism of Alzheimer Disease based on the cognitive model that established from artificial neural network. We can provide some theoretic ... More

A Constructive Algebraic Proof of Student's TheoremJun 21 2018Student's theorem is an important result in statistics which states that for normal population, the sample variance is independent from the sample mean and has a chi-square distribution. The existing proofs of this theorem either overly rely on advanced ... More

The strong reflecting property and Harrington's PrincipleMar 13 2015In this paper we characterize the strong reflecting property for $L$-cardinals for all $\omega_n$, characterize Harrington's Principle $HP(L)$ and its generalization and discuss the relationship between the strong reflecting property for $L$-cardinals ... More

Joint source-channel with side information coding error exponentsJan 23 2009In this paper, we study the upper and the lower bounds on the joint source-channel coding error exponent with decoder side-information. The results in the paper are non-trivial extensions of the Csiszar's classical paper [5]. Unlike the joint source-channel ... More

Endpoints of multi-valued weak contractions on the metric space valued in partially ordered groupsMay 31 2014We introduce the metric space valued in partially ordered groups, and define the convergence of sequences and the multi-valued weak contractions, etc., on the space. We then establish endpoint theorems for the defined maps. Our contributions extend the ... More

Approach to Express The Second Moment with A Class of Stochastic Completion TimeJun 28 2011This work presents an approach to express the second moment of the completion time with a preempt-repeat model job processed on a machine subject to stochastic breakdowns by some distribution characters of the uptime, downtime and processing time.

A neural network approach to ordinal regressionApr 08 2007Ordinal regression is an important type of learning, which has properties of both classification and regression. Here we describe a simple and effective approach to adapt a traditional neural network to learn ordinal categories. Our approach is a generalization ... More

On the extension to mean curvature flow in lower dimensionApr 09 2013Jan 03 2014In this paper, we prove that if $M_t\subset \mathbb{R}^{n+1}$, $2\leq n\leq 6$, is the $n$-dimensional closed embedded $\mathcal{F}-$stable solution to mean curvature flow with mean curvature of $M_t$ is uniformly bounded on $[0,T)$ for $T<\infty$, then ... More

Monad interleaving: a construction of the operad for Leinster's weak $ω$-categoriesSep 20 2003Oct 04 2008We show how to "interleave" the monad for operads and the monad for contractions on the category \coll of collections, to construct the monad for the operads-with-contraction of Leinster. We first decompose the adjunction for operads and the adjunction ... More

Dipion light-cone distribution amplitudes and $B \to ππ$ form factorsJan 18 2019Jan 24 2019We suggest to update the expansion coefficients of 2$\pi$DAs with the distribution amplitudes of light mesons evaluated from lattice QCD, with which we revisit $\overline{B}^0 \to \pi^+\pi^0$ transition form factors from light-cone sum rules approach ... More

An Alternative Definition of the Completion of Metric SpacesOct 05 2008Dec 03 2011In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on considerations ... More

The chord index, its definitions, applications and generalizationsJun 05 2016In this paper we study the chord index of virtual knots, which can be thought of as an extension of the chord parity. We show how to use the chord index to define finite type invariants of virtual knots. The notions of indexed Jones polynomial and indexed ... More

Bowling ball representation of virtual string linksJan 21 2015In this paper we investigate the virtual string links via a probabilistic interpretation. This representation can be used to distinguish some virtual string links from classical string links. In order to study the algebraic structure behind this probabilistic ... More

Lattice QCD and Hydro/Cascade Model of Heavy Ion CollisionsMay 11 2010We report here on a recent lattice study of the QCD transition region at finite temperature and zero chemical potential using domain wall fermions (DWF). We also present a parameterization of the QCD equation of state obtained from lattice QCD that is ... More

Error analysis in unconditionally stable coarsening algorithmsApr 08 2008Apr 09 2009In order to quantitatively study the accuracy of the unconditionally stable coarsening algorithms, we calculate the Fourier space multi step error on the order parameter field by explicitly distinguishing the analytic time $\tau$ and the algorithmic time ... More

Lattice Grids and Prisms are AntimagicMar 04 2006An \emph{antimagic labeling} of a finite undirected simple graph with $m$ edges and $n$ vertices is a bijection from the set of edges to the integers $1,...,m$ such that all $n$ vertex sums are pairwise distinct, where a vertex sum is the sum of labels ... More

Strategic decentralization in binary choice composite congestion gamesJun 10 2015Sep 15 2015This paper studies strategic decentralization in binary choice composite network congestion games. A player decentralizes if she lets some autonomous agents to decide respectively how to send different parts of her stock from the origin to the destination. ... More

Moment Consistency of the Exchangeably Weighted Bootstrap for Semiparametric M-EstimationSep 20 2011Sep 21 2014The bootstrap variance estimate is widely used in semiparametric inferences. However, its theoretical validity is a well known open problem. In this paper, we provide a {\em first} theoretical study on the bootstrap moment estimates in semiparametric ... More

Mixing of three neutrinos in matterApr 04 2001Apr 12 2001Explicit analytical expression is derived for mixing matrix of three neutrinos in matter using a set of direct vacuum physical parameters. Results are presented in simple, symmetrical form. The physical contents are more clear than using of traditional ... More

How Many Iterations are Sufficient for Semiparametric Estimation?Sep 10 2010Sep 22 2010A common practice in obtaining a semiparametric efficient estimate is through iteratively maximizing the (penalized) log-likelihood w.r.t. its Euclidean parameter and functional nuisance parameter via Newton-Raphson algorithm. The purpose of this paper ... More

Modeling of fracture geometry alteration and fracture flow evolution under geostress and water-rock interactionApr 11 2019A coupled mech-hydro-chemical model for rock geometry alteration of fractures under water-rock interaction (WRI) and geostress is developed. Processes including WRI, asperity deformation, mineral chemical dissolution and pressure dissolution etc., are ... More

An almost-Schur type lemma for symmetric $(2,0)$ tensors and applicationsAug 10 2012In our previous paper in \cite{C}, we generalized the almost-Schur lemma of De Lellis and Topping for closed manifolds with nonnegative Rcci curvature to any closed manifolds. In this paper, we generalize the above results to symmetric $(2,0)$-tensors ... More

Improved Accuracy of Incompressible Approximation of Compressible Euler EquationsFeb 03 2014Aug 29 2014This article addresses a fundamental concern regarding the incompressible approximation of fluid motions, one of the most widely used approximations in fluid mechanics. Common belief is that its accuracy is $O(\epsilon)$ where $\epsilon$ denotes the Mach ... More

Bounded Composition Operators and Multipliers of Some Reproducing Kernel Hilbert Spaces on the BidiskSep 12 2017Jun 29 2018We study the boundedness of composition operators on the bidisk using reproducing kernels. We show that a composition operator is bounded on the Hardy space of the bidisk if some associated function is a positive kernel. This positivity condition naturally ... More

Normal Truncated Toeplitz OperatorsSep 12 2017Oct 16 2017The characterization of normal truncated Toepltiz operators is first given by Chalendar and Timotin. We give an elementary proof of their result without using the algebraic properties of truncated Toeplitz operators.

Asymptotic Bohr Radius for the Polynomials in One Complex VariableMar 25 2014Apr 03 2014We consider the Bohr radius $R_n$ for the class of complex polynomials in one variable of degree at most $n$. It was conjectured by R. Fournier in 2008 that $R_n={1\over 3}+{\pi^2\over {3n^2}}+o({1\over n^2})$. We shall prove this conjecture is true in ... More

Phase-resolved imaging of edge-mode spin waves using scanning transmission x-ray microscopyApr 25 2014Oct 02 2016We have imaged the excitation of small-amplitude spin-wave eigenmodes, localized within $\sim$ 100 nm of the vertices of nanoscale Ni$_{81}$Fe$_{19}$ ellipses, using time-resolved scanning transmission x-ray microscopy (STXM) at 2 GHz and resolution of ... More

Probing the primordial Universe from the low-multipole CMB dataMay 02 2014Since the temperature fluctuations in cosmic microwave background (CMB) on large-angular scales probe length scales that were super-horizon sized at photon decoupling and hence insensitive to microphysical processes, the low-multipole CMB data are supposed ... More

Constraint on inflation model from BICEP2 and WMAP 9-year dataApr 04 2014Apr 08 2014Even though Planck data released in 2013 (P13) is not compatible with Background Imaging of Cosmic Extragalactic Polarization (B2) and some local cosmological observations, including Supernova Legacy Survey (SNLS) samples and $H_0$ prior from Hubble Space ... More

A simple model of Feshbach moleculesJun 14 2005Jun 21 2005We present a two-channel model to describe the quantum state of two atoms with finite-range interaction near a Feshbach resonance. This model provides a simple picture to analytically derive the wave function and the binding energy of the molecular bound ... More

The weak solution to a Boltzmann type equation and its energy conservationMar 22 2016Apr 07 2016In this paper, we study the initial value problem of a Boltzmann type equation with a nonlinear degenerate damping. We prove the existence of global weak solutions with large initial data, in three dimensional space. We rely on a variant version of the ... More

$\mathcal{N}=(0,2)$ SYK, Chaos and Higher-SpinsMay 23 2018We study a 2-dimensional SYK model with $\mathcal{N}=(0,2)$ supersymmetry. The model describes $N$ chiral supermultiplets and $M$ Fermi supermultiplets with a $(q+1)$-field interaction. We solve the model analytically and numerically in the $N\gg 1$, ... More

Improved critical eigenfunction restriction estimates on Riemannian manifolds with constant negative curvatureJul 25 2016Apr 22 2017We show that one can obtain logarithmic improvements of $L^2$ geodesic restriction estimates for eigenfunctions on 3-dimensional compact Riemannian manifolds with constant negative curvature. We obtain a $(\log\lambda)^{-\frac12}$ gain for the $L^2$-restriction ... More

Optimal Dividends in the Dual Risk Model under a Stochastic Interest RateMay 23 2017Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual risk model, under ... More

Space-Efficient Karatsuba Multiplication for Multi-Precision IntegersMay 22 2016The traditional Karatsuba algorithm for the multiplication of polynomials and multi-precision integers has a time complexity of $O(n^{1.59})$ and a space complexity of $O(n)$. Roche proposed an improved algorithm with the same $O(n^{1.59})$ time complexity ... More

Context-Dependent SimilarityMar 27 2013Attribute weighting and differential weighting, two major mechanisms for computing context-dependent similarity or dissimilarity measures are studied and compared. A dissimilarity measure based on subset size in the context is proposed and its metrization ... More

Note on some misinterpretations of Gödel's incompleteness theoremsFeb 14 2019In this paper, I evaluate some formal and informal misinterpretations of G\"{o}del's incompleteness theorems from the literature and the folklore, as well as clarify some misunderstandings about G\"{o}del's incompleteness theorems based on the current ... More

A Mathematically Sensible Explanation of the Concept of Statistical PopulationApr 06 2017In statistics education, the concept of population is widely felt hard to grasp, as a result of vague explanations in textbooks. Some textbook authors therefore chose not to mention it. This paper offers a new explanation by proposing a new theoretical ... More

Sparse Range-constrained Learning and Its Application for Medical Image GradingJul 11 2018Sparse learning has been shown to be effective in solving many real-world problems. Finding sparse representations is a fundamentally important topic in many fields of science including signal processing, computer vision, genome study and medical imaging. ... More

AI Reasoning Systems: PAC and Applied MethodsJul 09 2018Learning and logic are distinct and remarkable approaches to prediction. Machine learning has experienced a surge in popularity because it is robust to noise and achieves high performance; however, ML experiences many issues with knowledge transfer and ... More

Long time existence of smooth solutions to semigeostrophic equations on a torusFeb 26 2015Oct 04 2015In this work,we show the long time existence of smooth solu- tions to semigeostrophic equations on a torus when the initial dual density is bounded between two positive constants and smooth.The key ingredient is a more precise estimate on C 2 norm of ... More

On the rate distortion function of Bernoulli Gaussian sequencesJan 24 2009In this paper, we study the rate distortion function of the i.i.d sequence of multiplications of a Bernoulli $p$ random variable and a gaussian random variable $\sim N(0,1)$. We use a new technique in the derivation of the lower bound in which we establish ... More

Enhanced Magnetization and Conductivity in NiFe2O4May 08 2011Different configurations of magnetic orders and cation distributions for NiFe2O4 are studied by the density functional based methods with the possible inclusion of the on-site Coulomb interaction U. The lowest energy state is an inverse spinel structure ... More

Long-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4Apr 25 2008Jul 15 2008For the first time, the Fe-Fe interactions in the geometrically frustrated antiferromagnetic systems of zinc and cadmium ferrites are determined quantitatively by the first-principles methods of density functional theory. Both the generalized gradient ... More