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Object-Aware Guidance for Autonomous Scene ReconstructionMay 20 2018To carry out autonomous 3D scanning and online reconstruction of unknown indoor scenes, one has to find a balance between global exploration of the entire scene and local scanning of the objects within it. In this work, we propose a novel approach, which ... More

A New Kalman Filter Model for Nonlinear Systems Based on Ellipsoidal BoundingFeb 08 2018In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system. The main loop ... More

Choosability in signed planar graphsFeb 16 2015Sep 07 2015This paper studies the choosability of signed planar graphs. We prove that every signed planar graph is 5-choosable and that there is a signed planar graph which is not 4-choosable while the unsigned graph is 4-choosable. For each $k \in \{3,4,5,6\}$, ... More

Equation-free Dynamic Renormalization of a KPZ-type EquationMay 31 2005In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a KPZ type equation to calculate the self-similar solution for its ensemble averaged correlation function. The method involves ... More

Unions of 1-factors in $r$-graphsSep 06 2015The generalized Berge-Fulkerson conjecture states that every $r$-graph has $2r$ 1-factors such that each edge is contained in precisely two of them. This conjecture is shown to be equivalent to the statement that every $r$-graph can be covered by $2r-1$ ... More

Pressure-induced lattice collapse in tetragonal phase and structural phase transition in single crystalline Fe1.05TeMay 20 2009Jul 20 2009We report studies of in-situ x-ray diffraction (XRD) and electronic properties on the single crystalline of Fe1.05Te compound under high pressure. The results demonstrated that the sample undergoes a pressure-induced lattice collapse in tetragonal phase ... More

Petersen cores and the oddness of cubic graphsJan 05 2015Feb 24 2017Let $G$ be a bridgeless cubic graph. Consider a list of $k$ 1-factors of $G$. Let $E_i$ be the set of edges contained in precisely $i$ members of the $k$ 1-factors. Let $\mu_k(G)$ be the smallest $|E_0|$ over all lists of $k$ 1-factors of $G$. If $G$ ... More

Petersen cores and the oddness of cubic graphsJan 05 2015Let $G$ be a bridgeless cubic graph. Consider a list of $k$ 1-factors of $G$. Let $E_i$ be the set of edges contained in precisely $i$ members of the $k$ 1-factors. Let $\mu_k(G)$ be the smallest $|E_0|$ over all lists of $k$ 1-factors of $G$. If $G$ ... More

Precession Effects on Liquid Planetary CoreDec 06 2017Motivated by the desire to understand the rich dynamics of precessionally driven flow in the liquid planetary core, we investigate, through numerical simulations, the precessing fluid motion in a rotating cylindrical annulus which possesses slow precession ... More

Two-Dimensional Diffusion in the Presence of Topological DisorderAug 29 2003How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder leads to a finite ... More

Monte Carlo Methods for Small Molecule High-Throughput ExperimentationJul 23 2001By analogy with Monte Carlo algorithms, we propose new strategies for design and redesign of small molecule libraries in high-throughput experimentation, or combinatorial chemistry. Several Monte Carlo methods are examined, including Metropolis, three ... More

Strategies for High-Throughput, Templated Zeolite SynthesisAug 14 2002How best to design and redesign high-throughput experiments for zeolite synthesis is addressed. A model that relates materials function to chemical composition of the zeolite and the structure directing agent is introduced. Using this model, several Monte ... More

Reaction, Levy Flights, and Quenched DisorderJul 07 2001Aug 13 2002We consider the A + A --> emptyset reaction, where the transport of the particles is given by Levy flights in a quenched random potential. With a common literature model of the disorder, the random potential can only increase the rate of reaction. With ... More

Remarks on planar edge-chromatic critical graphsFeb 24 2017The only open case of Vizing's conjecture that every planar graph with $\Delta\geq 6$ is a class 1 graph is $\Delta = 6$. We give a short proof of the following statement: there is no 6-critical plane graph $G$, such that every vertex of $G$ is incident ... More

Face-degree bounds for planar critical graphsJan 05 2015Aug 24 2016The only remaining case of a well known conjecture of Vizing states that there is no planar graph with maximum degree 6 and edge chromatic number 7. We introduce parameters for planar graphs, based on the degrees of the faces, and study the question whether ... More

Colouring of generalized signed planar graphsNov 21 2018Assume $G$ is a graph. We view $G$ as a symmetric digraph, in which each edge $uv$ of $G$ is replaced by a pair of opposite arcs $e=(u,v)$ and $e^{-1}=(v,u)$. Assume $S$ is an inverse closed subset of permutations of positive integers. We say $G$ is $S$-$k$-colourable ... More

The 3-colorability of planar graphs without cycles of length 4, 6 and 9Jun 15 2015In this paper, we prove that planar graphs without cycles of length 4, 6, 9 are 3-colorable.

Disorder-Induced Time-Dependent Diffusion in ZeolitesDec 15 1999Apr 03 2000We suggest that disordered framework aluminums and non-framework cations can create a disordered electrostatic potential in zeolites that can lead to a discrepancy between diffusivities measured by microscopic and macroscopic experimental techniques. ... More

The spiral structure of the Milky WayOct 20 2018Nov 17 2018The morphology and kinematics of the spiral structure of the Milky Way is a long-standing problem in astrophysics. In this review we firstly summarize various methods with different tracers used to solve this puzzle. The astrometry of Galactic sources ... More

Cores, joins and the Fano-flow conjecturesJan 21 2016The Fan-Raspaud Conjecture states that every bridgeless cubic graph has three 1-factors with empty intersection. A weaker one than this conjecture is that every bridgeless cubic graph has two 1-factors and one join with empty intersection. Both of these ... More

SPLZ: An Efficient Algorithm for Single Source Shortest Path Problem Using Compression MethodAug 11 2014Jan 11 2015Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning to precomputing ... More

A Perceptual Aesthetics Measure for 3D ShapesAug 17 2016While the problem of image aesthetics has been well explored, the study of 3D shape aesthetics has focused on specific manually defined features. In this paper, we learn an aesthetics measure for 3D shapes autonomously from raw voxel data and without ... More

Collective Multipole excitations of exotic nuclei in relativistic continuum random phase approximationSep 03 2013Journal of Combinatorial Theory, Series B, 98(1):173-225, 2008n exotic nuclei are studied in the framework of a fully self-consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum ... More

Sphere theorems for submanifolds in Kähler ManifoldOct 17 2018In this paper, we prove some differentiable sphere theorems and topological sphere theorems for submanifolds in K\"ahler manifold, especially in complex space forms.

Digital Makeup from Internet ImagesOct 16 2016We present a novel approach of color transfer between images by exploring their high-level semantic information. First, we set up a database which consists of the collection of downloaded images from the internet, which are segmented automatically by ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Aug 16 2016Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

Projective embedding of log Riemann surfaces and K-stabilityMay 03 2016Sep 25 2017Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $\omega$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The ... More

Sphere theorems for Lagrangian and Legendrian submanifoldsOct 22 2018In this paper, we prove some differentiable sphere theorems and topological sphere theorems for Lagrangian submanifolds in K\"ahler manifold and Legendrian submanifolds in Sasaki space form.

Virtual homological eigenvalue and mapping torus of pseudo-Anosov mapsAug 25 2016In this note, we show that, if a pseudo-Anosov map $\phi:S\to S$ admits a finite cover which has a homological eigenvalue with modulus greater than $1$, then the monodromy of any fibered structure of any finite cover of $M_{\phi}$ has this property.

On Noether approach in the cosmological model with scalar and gauge fields: symmetries and the selection ruleApr 18 2015In this paper, based on the works of Capozziello et al., we have studied the Noether symmetry approach in the cosmological model with scalar and gauge fields proposed recently by Soda et al. The correct Noether symmetries and related Lie algebra are given ... More

Decomposition Theorem for Perverse sheaves on Artin stacks over finite fieldsSep 22 2010Mar 11 2012We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.

L-series of Artin stacks over finite fieldsAug 22 2010Mar 28 2011We reprove the Lefschetz trace formula for stacks (in the context of derived categories and the six operations for stacks developed by Laszlo and Olsson), and give the meromorphic continuation of L-series (in particular, zeta functions) of Artin stacks ... More

Axisymmetrically Tropical Cyclone-like Vortices with Secondary CirculationsSep 07 2013The secondary circulation of the tropical cyclone (TC) is related to its formation and intensification, thus becomes very important in the studies. The analytical solutions have both the primary and secondary circulation in a three-dimensionally nonhydrostatic ... More

Identify the diapycnical eddy diffusivities by salt fingers and turbulence with vertical microstructure measurementsJun 23 2014Diapycnical eddy diffusivities are formulated from physical relations according to a simple fact that the different formulas are identical for the same parameter. It is found that the dispassion ratio \Gamma is a crucial parameter. When it is above a ... More

Character tables of Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groupsJun 20 2016We determine the character tables of Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groups ${^3}D_4(q^3)$.

NonLERFness of arithmetic hyperbolic manifold groupsAug 17 2016We will show that, for any noncompact arithmetic hyperbolic $m$-manifold with $m\geq 4$, and any compact arithmetic hyperbolic $m$-manifold with $m\geq 5$ which is not a $7$-dimensional arithmetic hyperbolic manifold defined by octonions, its fundamental ... More

Non-elementary convergence groups are acylindrically hyperbolicDec 01 2016We proved that non-elementary discrete convergence groups are acylindrically hyperbolic.

A supercharacter theory for Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groupsNov 28 2016We determine a supercharacter theory for the matrix Sylow $p$-subgroup ${^3}D_4^{syl}(q^3)$ of the Steinberg triality group ${^3}D_4(q^3)$, and establish the supercharacter table of ${^3}D_4^{syl}(q^3)$.

Towards Shockingly Easy Structured Classification: A Search-based Probabilistic Online Learning FrameworkMar 29 2015There are two major approaches for structured classification. One is the probabilistic gradient-based methods such as conditional random fields (CRF), which has high accuracy but with drawbacks: slow training, and no support of search-based optimization ... More

Demosaicing and Superresolution for Color Filter Array via Residual Image Reconstruction and Sparse RepresentationSep 29 2012Jul 04 2013A framework of demosaicing and superresolution for color filter array (CFA) via residual image reconstruction and sparse representation is presented.Given the intermediate image produced by certain demosaicing and interpolation technique, a residual image ... More

Non-elementary convergence groups are acylindrically hyperbolicDec 01 2016Oct 19 2017We proved that non-elementary discrete convergence groups are acylindrically hyperbolic.

Solving the Steiner Tree Problem in Graphs using Physarum-inspired AlgorithmsMar 21 2019Some biological experiments show that the tubular structures of Physarum polycephalum are often analogous to those of Steiner trees. Therefore, the emerging Physarum-inspired Algorithms (PAs) have the potential of computing Steiner trees. In this paper, ... More

Almost linear Nash groupsOct 30 2013Nov 21 2013A Nash group is said to be almost linear if it has a Nash representation with finite kernel. Structures and basic properties of these groups are studied.

Black Hole - Never Forms, or Never EvaporatesFeb 13 2011Mar 21 2011Many discussion about the black hole conundrums, such as singularity and information loss, suggested that there must be some essential irreconcilable conflict between quantum theory and classical gravity theory, which cannot be solved with any semiclassical ... More

Mott-Hubbard Scenario for the Metal-Insulator Transition in the Two Dimensional Electron GasAug 01 2006By comparing the responses to an in-plane magnetic field near the metal-insulator transition (MIT), we find that the observed MIT in Si MOSFETs can be described by the non-perturbative Mott-Hubbard scenario. Interrelations between independent measurables ... More

A note on simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass $L$-functionsSep 10 2016In this note, we prove that given a Hecke-Maass cusp form $f$ for $SL_2(\mathbb{Z})$ and a sufficiently large integer $q=q_1q_2$ with $q_j\asymp \sqrt{q}$ being prime numbers for $j=1,2$, there exists a primitive Dirichlet character $\chi$ of conductor ... More

Libcint: An efficient general integral library for Gaussian basis functionsDec 01 2014An efficient integral library Libcint was designed to automatically implement general integrals for Gaussian-type scalar and spinor basis functions. The library can handle arbitrary integral expressions on top of $\mathbf{p}$, $\mathbf{r}$ and $\sigma$ ... More

The dependence of hydrophobic interactions on the solute sizeMay 09 2017Mar 06 2018Based on our recent study on physical origin of hydrophobic effects, this is applied to investigate the dependence of hydrophobic interactions on the solute size. As two same hydrophobic solutes are dissolved into water, the hydration free energy is determined, ... More

Exponential Decay of Lebesgue NumbersFeb 02 2010Nov 20 2010We study the exponential rate of decay of Lebesgue numbers of open covers in topological dynamical systems. We show that topological entropy is bounded by this rate multiplied by dimension. Some corollaries and examples are discussed.

Loss-based risk statistics with set-valued analysisApr 16 2019Since the portfolio has become a hot topic, we wii introduce a special risk statistics from the perspective of loss. This new risk statistic can be uesd for the quantification of portfolio risk. Representation results are provided. Finally, examples are ... More

Loss-based risk statistics with scenario analysisApr 16 2019Since the investors and regulators pay more attention to losses rather than gains, we will study a new class of risk statistics, named loss-based risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension ... More

Confining the light wave by using non-Euclidean transformation opticsFeb 03 2013Sep 24 2013A new way to understand why some inhomogeneous dielectric medium can be used for confining the light wave has been given by using non-Euclidean transformation optics. We show that special inhomogeneous dielectric medium, which corresponds to a dip in ... More

Changes to the t-J Model From Inclusion of Two-Site Nearest-Neighbor Coulomb InteractionsApr 27 2017To date, the Hubbard model and its strong coupling limit, the t-J model, serve as the canonical model for strongly correlated electron systems in solids. Approximating the Coulomb interaction by only the on-site term (Hubbard U-term), however, may not ... More

A Simulation and Modeling of Access Points with Definition LanguageApr 06 2013Apr 11 2013This submission has been withdrawn by arXiv administrators because it contains fictitious content and was submitted under a pseudonym, which is against arXiv policy.

Multiple recurrence and convergence for certain averages along shifted primesMar 15 2013Feb 03 2014We show any subset $A\subset\mathbb{N}$ with positive upper Banach density contains the pattern $\{m,m+[n\alpha],\dots,m+k[n\alpha]\}$, for some $m\in\mathbb{N}$ and $n=p-1$ for some prime $p$, where $\alpha\in\mathbb{R}\backslash\mathbb{Q}$. Making use ... More

Magnetic Manifestation of Discrete Scaling Symmetry in Dirac SemimetalsMay 05 2018Aug 09 2018Two-dimensional and three-dimensional massless Dirac fermions can form a sequence of quasibound states with an attractive charged impurity. These quasibound states exhibit a discrete scaling symmetry, i.e., the energy ratio between two successive states ... More

Why are there strong radio AGNs in the center of "non-cool core" clusters?Oct 05 2009Radio AGN feedback in X-ray cool cores has been proposed as a crucial ingredient in the evolution of baryonic structures. However, it has long been known that strong radio AGNs also exist in "noncool core" clusters, which brings up the question whether ... More

Every BCG with a strong radio AGN has an X-ray cool core: is the cool core - noncool core dichotomy too simple?Apr 13 2009Sep 20 2009Radio AGN feedback in X-ray cool cores has been proposed as a crucial ingredient in the evolution of baryonic structures. However, it has long been known that strong radio AGN also exist in "noncool core" clusters, which brings up the question whether ... More

On the low-regularity global well-posedness of a system of nonlinear Schrodinger EquationApr 17 2017In this article, we study the low-regularity Cauchy problem of a one dimensional quadratic Schrodinger system with coupled parameter $\alpha\in (0, 1)$. When $\frac{1}{2}<\alpha<1$,we prove the global well-posedness in $H^s(\mathbb{R})$ with $s>-\frac{1}{4}$, ... More

Conformally invariant scaling limits in planar critical percolationNov 02 2009Oct 21 2011This is an introductory account of the emergence of conformal invariance in the scaling limit of planar critical percolation. We give an exposition of Smirnov's theorem (2001) on the conformal invariance of crossing probabilities in site percolation on ... More

Rank $n$ swapping algebra for GrassmannianApr 15 2019The rank $n$ swapping algebra is the Poisson algebra defined on the ordered pairs of points on a circle using the linking numbers, where a subspace of $(\mathbb{K}^n \times \mathbb{K}^{n*})^r/\operatorname{GL}(n,\mathbb{K})$ is its geometric mode. In ... More

Eisenstein integrals for theta stable parabolic subalgebrasMar 25 2004Nov 28 2004Let $G$ be a connected semisimple Lie group with a finite center, with a maximal compact subgroup $K$. There are two general methods to construct representations of $G$, namely, ordinary parabolic induction and cohomological parabolic induction. We define ... More

Dual pairs and contragredients of irreducible representationsMar 08 2009Dec 08 2009Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over a non-archimedean local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $G$. It is well known that the contragredient of $\pi$ is ... More

Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of SurfacesOct 18 2018Nov 12 2018In this paper we prove that the generic singularity of mean curvature flow of closed embedded surfaces in $\mathbb R^3$ modelled by closed self-shrinkers with multiplicity has multiplicity one. Together with the previous result by Colding-Minicozzi in ... More

The complement value problem for non-local operatorsMar 31 2018Aug 26 2018Let $D$ be a bounded Lipschitz domain of $\mathbb{R}^d$. We consider the complement value problem $$ \left\{\begin{array}{l}(\Delta+a^{\alpha}\Delta^{\alpha/2}+b\cdot\nabla+c)u+f=0\ \ {\rm in}\ D,\\ u=g\ \ {\rm on}\ D^c. \end{array}\right.$$ Under mild ... More

The complement value problem for a class of second order elliptic integro-differential operatorsMay 17 2018We consider the complement value problem for a class of second order elliptic integro-differential operators. Let $D$ be a bounded Lipschitz domain of $\mathbb{R}^d$. Under mild conditions, we show that there exists a unique bounded continuous weak solution ... More

A refined error analysis for fixed-degree polynomial optimization over the simplexDec 20 2013Aug 17 2014We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this paper, we revisit ... More

Carleman Estimate for Surface in Euclidean Space at InfinityMar 26 2017This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads to rigidity ... More

Supercharacter theories for Sylow $p$-subgroups of the Ree groupsAug 19 2018We determine a supercharacter theory for Sylow $p$-subgroups ${^2{G}_2^{syl}(3^{2m+1})}$ of the Ree groups $^2{G}_2(3^{2m+1})$, calculate the conjugacy classes of ${^2{G}_2^{syl}(3^{2m+1})}$, and establish the character table of ${^2{G}_2^{syl}(3)}$.

Localized nonlinear functional equations and two sampling problems in signal processingApr 09 2013Let $1\le p\le \infty$. In this paper, we consider solving a nonlinear functional equation $$f(x)=y,$$ where $x, y$ belong to $\ell^p$ and $f$ has continuous bounded gradient in an inverse-closed subalgebra of ${\mathcal B}(\ell^2)$, the Banach algebra ... More

Wiener's Lemma for Infinite Matrices IIJan 09 2010In this paper, we introduce a class of infinite matrices related to the Beurling algebra of periodic functions, and we show that it is an inverse-closed subalgebra of ${\mathcal B}(\ell^q_w)$, the algebra of all bounded linear operators on the weight ... More

Cohomologically induced distinguished representations and cohomological test vectorsNov 11 2011Jan 30 2015Let $G$ be a real reductive group, and let $\chi$ be a character of a reductive subgroup $H$ of $G$. We construct $\chi$-invariant linear functionals on certain cohomologically induced representations of $G$, and show that these linear functionals do ... More

Geometrically finite amalgamations of hyperbolic 3-manifold groups are not LERFMay 09 2017We prove that, for any two finite volume hyperbolic $3$-manifolds, the amalgamation of their fundamental groups along any nontrivial geometrically finite subgroup is not LERF. This generalizes the author's previous work on nonLERFness of amalgamations ... More

Arithmetic genus of integral space curvesMay 23 2016We give an estimation for the arithmetic genus of an integral space curve, which are not contained in a surface of degree $k-1$. Our main technique is the Bogomolov-Gieseker type inequality for $\mathbb{P}^3$ proved by Macri.

Large Extra Dimension effects through Light-by-Light Scattering at the CERN LHCJun 16 2014Jul 31 2014Observing light-by-light scattering at the Large Hadron Collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the ... More

Note on geodesic rays tamed by simple test configurationsJun 17 2008Nov 08 2009In this short note, we give a new proof of a theorem of Arezzo-Tian on the existence of smooth geodesic rays tamed by a special degeneration.

Large Two-loop Effects in the Higgs Sector as New Physics ProbesOct 08 2015We consider a simple Higgs portal model in beyond the standard model scenario: an extra real gauge singlet scalar that couples to the Higgs. We calculate the higher-loop corrections to the cross section of the Higgsstrahlung process $e^+e^- \rightarrow ... More

Little Flavor: Heavy Leptons, Z' and Higgs PhenomenologyNov 01 2014Jan 22 2016The Little Flavor model is a close cousin of the Little Higgs theory which aims to generate flavor structure around TeV scale. While the original Little Flavor only included the quark sector, here we build the lepton part of the Little Flavor model and ... More

Multi-view Laplacian Support Vector MachinesJul 26 2013We propose a new approach, multi-view Laplacian support vector machines (SVMs), for semi-supervised learning under the multi-view scenario. It integrates manifold regularization and multi-view regularization into the usual formulation of SVMs and is a ... More

Size Information Obtained by Using Static Light Scattering TechniqueJul 01 2004Dec 08 2004Detailed investigation of static light scattering $(SLS) $ has been attempted in this work using dilute water dispersions of homogenous spherical particles, poly($N$-isopropylacrylamide) microgels and simulated data. When Rayleigh-Gan-Debye approximation ... More

Analysis of Fully Preconditioned ADMM with Relaxation in Hilbert SpacesNov 15 2016Alternating direction method of multipliers (ADMM) is a powerful first order methods for various applications in signal processing and imaging. However, there is no clear result on the weak convergence of ADMM with relaxation studied by Eckstein and Bertsakas ... More

Co-iterative augmented Hessian method for orbital optimizationOct 26 2016Orbital optimization procedure is widely called in electronic structure simulation. To efficiently find the orbital optimization solution, we developed a new second order orbital optimization algorithm, co-iteration augmented Hessian (CIAH) method. In ... More

Stability of direct images under Frobenius morphismAug 02 2006Aug 18 2006Let $X$ be a smooth projective variety over an algebraically field $k$ with ${\rm char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. When ${\rm dim}(X)=1$, we prove that $F_*W$ is a stable bundle for any stable bundle $W$ (Theorem \ref{thm1.3}). ... More

Root Mean Square Minimum Distance: a Quality Metric for Localization Nanoscopy ImagingJan 06 2018A localization algorithm in optical localization nanoscopy plays an important role in obtaining a high-quality image. A universal and objective metric, which is crucial and necessary to evaluate qualities of nanoscopy images and performances of localization ... More

Notes on MVW-extensionsMar 02 2011We review certain basic geometric and analytic results concerning MVW-extensions of classical groups, following Moeglin-Vigneras-Waldspurger. The related results for Jacobi groups, metaplectic groups, and special orthogonal groups are also included.

Cohen-Lyndon type theorem for group theoretic Dehn fillingsSep 24 2018Nov 13 2018The classical Cohen-Lyndon property of a free group describes the structure of the normal closure of a non-trivial element, and computes the relation module of the corresponding quotient group. Realizing that this result is, in fact, about the kernel ... More

Kepler's third law of n-body periodic orbits in a Newtonian gravitation fieldJul 25 2018This study considers the periodic orbital period of an n-body system from the perspective of dimension analysis. According to characteristics of the n-body system with point masses $(m_1,m_2,...,m_n)$, the gravitational field parameter, $\alpha \sim Gm_im_j$, ... More

Bounded t-structures on the bounded derived category of coherent sheaves over a weighted projective lineAug 17 2017Jun 20 2018We use recollement and HRS-tilt to describe bounded t-structures on the bounded derived category $\mathcal{D}^b(\mathbb{X})$ of coherent sheaves over a weighted projective line $\mathbb{X}$ of virtual genus $\leq 1$. We will see from our description that ... More

Anonymous Information DeliveryJun 14 2018We introduce the problem of anonymous information delivery (AID), comprised of $K$ messages, a user, and $N$ servers (each holds $M$ messages) that wish to deliver one out of $K$ messages to the user anonymously, i.e., without revealing the delivered ... More

Intrinsic Universal Measurements of Non-linear EmbeddingsNov 05 2018A basic problem in machine learning is to find a mapping $f$ from a low dimensional latent space to a high dimensional observation space. Equipped with the representation power of non-linearity, a learner can easily find a mapping which perfectly fits ... More

Exponential Decay of Expansive ConstantsJan 04 2011A map $f$ on a compact metric space is expansive if and only if $f^n$ is expansive. We study the exponential rate of decay of the expansive constant of $f^n$. A major result is that this rate times box dimension bounds topological entropy.

The Structural Origin of Hydration Repulsive ForceMar 22 2018In our recent works, based on the structural studies on water and interfacial water (topmost water layer at the solute/water interface), hydration free energy is derived and utilized to investigate the physical origin of hydrophobic interactions. In this ... More

Averages of shifted convolution sums for $GL(3) \times GL(2)$Jan 08 2017Let $A_f(1,n)$ be the normalized Fourier coefficients of a $GL(3)$ Maass cusp form $f$ and let $a_g(n)$ be the normalized Fourier coefficients of a $GL(2)$ cusp form $g$. Let $\lambda(n)$ be either $A_f(1,n)$ or the triple divisor function $d_3(n)$. It ... More

Sparse approximation property and stable recovery of sparse signals from noisy measurementsJul 26 2011In this paper, we introduce a sparse approximation property of order $s$ for a measurement matrix ${\bf A}$: $$\|{\bf x}_s\|_2\le D \|{\bf A}{\bf x}\|_2+ \beta \frac{\sigma_s({\bf x})}{\sqrt{s}} \quad {\rm for\ all} \ {\bf x},$$ where ${\bf x}_s$ is the ... More

Cyclotomic Temperley-Lieb algebra of type D and its representation theoryNov 17 2010Nov 19 2010We define a new class of algebras, cyclotomic Temperley-Lieb algebras of type D, in a diagrammatic way, which is a generalization of Temperley-Lieb algebras of type D. We prove that the cyclotomic Temperley-Lieb algebras of type D are cellular. In fact, ... More

Landau Level to Efimov-like Bound State Crossover in Two-dimensional Dirac SemimetalsJul 18 2018In two-dimensional Dirac semimetals, massless Dirac fermions can form a series of Efimov-like quasibound states in an attractive Coulomb potential. In an applied magnetic field, these quasibound states can become bound states around the Dirac point, due ... More

Noncommutative Ergodic Theorems for Connected Amenable GroupsMay 11 2016This paper is devoted to the study of noncommutative ergodic theorems for connected amenable locally compact groups. For a dynamical system $(\mathcal{M},\tau,G,\sigma)$, where $(\mathcal{M},\tau)$ is a von Neumann algebra with a normal faithful finite ... More

Convergence of incremental adaptive systemsOct 03 2013Feb 21 2014In this paper, incremental adaptive mechanisms are presented and characterized, to provide design hints for the development of continuous-time adaptive systems. The comparison with the conventional integral adaptive systems indicates that the suggested ... More

Hot Gas in Galaxy Groups: Recent ObservationsMar 19 2012Galaxy groups are the least massive systems where the bulk of baryons begin to be accounted for. Not simply the scaled-down versions of rich clusters following self-similar relations, galaxy groups are ideal systems to study baryon physics, which is important ... More

Swapping algebra, Virasoro algebra and discrete integrable systemDec 14 2014Sep 22 2016We induce a Poisson algebra $\{\cdot,\cdot\}_{\mathcal{C}_{n,N}}$ on the configuration space $\mathcal{C}_{n,N}$ of $N$ twisted polygons in $\mathbb{RP}^{n-1}$ from the swapping algebra \cite{L12}, which is found coincide with Faddeev-Takhtajan-Volkov ... More