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Non-integrated defect relations for the Gauss map of a complete minimal surface with finite total curvature in $\mathbb R^m$Oct 04 2017In this article, we give the non-integrated defect relations for the Gauss map of a complete minimal surface with finite total curvature in $\mathbb R^m.$ This is a continuation of previous work of Ha-Trao [J. Math. Anal. Appl., \textbf{430} (2015), 76-84.], ... More

Local property of maximal plurifinely plurisubharmonic functionsApr 05 2016In this paper, we prove that a continuous $\mathcal F$-plurisubharmonic functions defined in an $\mathcal F$-open set in $\mathbb C^n$ is $\mathcal F$-maximal if and only if it is $\mathcal F$-locally $\mathcal F$-maximal.

Bayesian inverse problems for Burgers and Hamilton-Jacobi equations with white-noise forcingApr 14 2011May 10 2011The paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes formula and the well-posedness of the posterior measure are studied. The abstract theory is ... More

Depth and regularity of powers of sums of idealsJan 24 2015Jan 01 2016Given arbitrary homogeneous ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $k$, we investigate the depth and the Castelnuovo-Mumford regularity of powers of the sum $I+J$ in $A \otimes_k B$ in terms of those of $I$ and $J$. Our results ... More

Homogenization error for two scale Maxwell equationsDec 09 2015For two scale elliptic equations in a domain $D$, standard homogenization errors are deduced with the assumption that the solution $u_0$ of the homogenized equation belongs to $H^2(D)$. For two scale Maxwell equations, the corresponding required regularity ... More

Homogenization of multiscale Maxwell wave equationsMay 21 2017We study homogenization of multiscale Maxwell wave equation that depends on $n$ separable microscopic scales in a domain $D\subset{\mathbb R}^d$ on a finite time interval $(0,T)$. Due to the non-compactness of the embedding of $H_0(\curl,D)$ in $L^2(D)^d$, ... More

Hierarchical multiscale finite element method for multi-continuum mediaJun 11 2019Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum technique, where ... More

Bayesian inverse problems for recovering coefficients of two scale elliptic equationsJul 17 2018Aug 03 2018We consider the Bayesian inverse homogenization problem of recovering the locally periodic two scale coefficient of a two scale elliptic equation, given limited noisy information on the solution. We consider both the uniform and the Gaussian prior probability ... More

High dimensional finite elements for multiscale Maxwell wave equationsAug 07 2017We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain $D\subset{\mathbb R}^d$. The problems depend on $n+1$ scales: one macroscopic scale and $n$ microscopic scales. Solving the macroscopic multiscale ... More

Reconfigurable Multi-UAV Formation Using Angle-Encoded PSOSep 07 2019In this paper, we propose an algorithm for the formation of multiple UAVs used in vision-based inspection of infrastructure. A path planning algorithm is first developed by using a variant of the particle swarm optimisation, named theta-PSO, to generate ... More

Determining White Noise Forcing From Eulerian Observations in the Navier Stokes EquationMar 19 2013Apr 18 2014The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to and the state of a system of interest given noisy observations. Herein we consider the forward problem of the forced 2D Navier Stokes equation. ... More

Enhanced discrete particle swarm optimization path planning for UAV vision-based surface inspectionJun 14 2017In built infrastructure monitoring, an efficient path planning algorithm is essential for robotic inspection of large surfaces using computer vision. In this work, we first formulate the inspection path planning problem as an extended travelling salesman ... More

Complexity Analysis of Accelerated MCMC Methods for Bayesian InversionJul 10 2012Apr 30 2013We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior ... More

Polynomial approximations of a class of stochastic multiscale elasticity problemsNov 28 2015We consider a class of elasticity equations in ${\mathbb R}^d$ whose elastic moduli depend on $n$ separated microscopic scales, are random and expressed as a linear expansion of a countable sequence of random variables which are independently and identically ... More

Real-time Lane Marker Detection Using Template Matching with RGB-D CameraJun 05 2018This paper addresses the problem of lane detection which is fundamental for self-driving vehicles. Our approach exploits both colour and depth information recorded by a single RGB-D camera to better deal with negative factors such as lighting conditions ... More

Parallel Computation of Graph EmbeddingsSep 06 2019Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not scale well to ... More

Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximationOct 25 2017We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of nonparametric estimation ... More

Multiscale simulations for upscaled multi-continuum flowsSep 10 2019We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization was nicely applied, ... More

Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximationOct 25 2017Apr 11 2019We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of nonparametric estimation ... More

Reconciling Bayesian and Total Variation Methods for Binary InversionJun 06 2017Apr 09 2018A central theme in classical algorithms for the reconstruction of discontinuous functions from observational data is perimeter regularization. On the other hand, sparse or noisy data often demands a probabilistic approach to the reconstruction of images, ... More

Estimating the Division Kernel of a Size-Structured PopulationSep 09 2015May 19 2016We consider a size-structured population describing the cell divisions. The cell population is described by an empirical measure and we observe the divisions in the continuous time interval [0, T ]. We address here the problem of estimating the division ... More

A note on independence number, connectivity and $k$-ended treeOct 26 2018A $k$-ended tree is a tree with at most $k$ leaves. In this note, we give a simple proof for the following theorem. Let $G$ be a connected graph and $k$ be an integer ($k\geq 2$). Let $S$ be a vertex subset of $G$ such that $\alpha_{G}(S) \leq k + \kappa_{G}(S)- ... More

Spanning trees in a Claw-free graph whose stems have at most $k$ branch verticesFeb 27 2018Let $T$ be a tree, a vertex of degree one and a vertex of degree at least three is called a leaf and a branch vertex, respectively. The set of leaves of $T$ is denoted by $Leaf(T)$. The subtree $T-Leaf(T)$ of $T$ is called the stem of $T$ and denoted ... More

Modified defect relations of the Gauss map and the total curvature of a complete minimal surfaceOct 09 2017Oct 12 2017In this article, we propose some conditions on the modified defect relations of the Gauss map of a complete minimal surface $M$ to show that $M$ has finite total curvature.

Fast multi-output relevance vector regressionApr 17 2017This paper aims to decrease the time complexity of multi-output relevance vector regression from O(VM^3) to O(V^3+M^3), where V is the number of output dimensions, M is the number of basis functions, and V<M. The experimental results demonstrate that ... More

Learning to Rank Personalized Search Results in Professional NetworksMay 16 2016LinkedIn search is deeply personalized - for the same queries, different searchers expect completely different results. This paper presents our approach to achieving this by mining various data sources available in LinkedIn to infer searchers' intents ... More

Estimates of isospin breaking contributions to baryon massesSep 20 2006Jun 30 2007We estimate the isospin breaking contributions to the baryon masses which we analyzed recently using a loop expansion in the heavy baryon approximation to chiral effective field theory. To one loop, the isospin breaking corrections come from the effects ... More

Any shape can ultimately cross information on two-dimensional abelian sandpile modelsAug 04 2017In this paper we study the abelian sandpile model on the two-dimensional grid with uniform neighborhood, and prove that any family of neighborhoods defined as scalings of a continuous non-flat shape can ultimately perform crossing.

A parametrization of the baryon octet and decuplet massesNov 27 2007May 05 2008We construct a general parametrization of the baryon octet and decuplet mass operators including the three-body terms using the unit operator and the symmetry-breaking factors $M^d=\textrm{diag} (0,1,0)$ and $M^s=\textrm{diag} (0,0,1)$ in conjunction ... More

Decuplet baryon magnetic moments in a QCD-based quark model beyond quenched approximationApr 23 1998We study the decuplet baryon magnetic moments in a QCD-based quark model beyond quenched approximation. Our approach for unquenching the theory is based on the heavy baryon perturbation theory in which the axial couplings for baryon - meson and the meson-meson-photon ... More

A soft-photon theorem for the Maxwell-Lorentz systemAug 07 2019For the coupled system of classical Maxwell-Lorentz equations we show that the quantities \begin{equation*} \mathfrak{F}(\hat x, t)=\lim_{|x|\to \infty} |x|^2 F(x,t), \quad \mathcal{F}(\hat k, t)=\lim_{|k|\to 0} |k| \widehat{F}(k,t), \end{equation*} where ... More

Beyond socket options: making the Linux TCP stack truly extensibleJan 07 2019The Transmission Control Protocol (TCP) is one of the most important protocols in today's Internet. Its specification and implementations have been refined for almost forty years. The Linux TCP stack is one of the most widely used TCP stacks given its ... More

Local property of maximal plurifinely plurisubharmonic functionsApr 05 2016Oct 12 2016In this paper, we prove that a continuous $\mathcal F$-plurisubharmonic functions defined in an $\mathcal F$-open set in $\mathbb C^n$ is $\mathcal F$-maximal if and only if it is $\mathcal F$-locally $\mathcal F$-maximal.

Beyond socket options: making the Linux TCP stack truly extensibleJan 07 2019May 22 2019The Transmission Control Protocol (TCP) is one of the most important protocols in today's Internet. Its specification and implementations have been refined for almost forty years. The Linux TCP stack is one of the most widely used TCP stacks given its ... More

Polarization of Infrared Emission from Polycyclic Aromatic HydrocarbonsDec 13 2017Polarized infrared emission from polycyclic aromatic hydrocarbons (PAHs) is important for testing the basic physics of alignment of ultrasmall grains and potentially offers a new way to trace magnetic fields. In this paper, a new model of polarized PAH ... More

Heavy diquark in baryons containing a single heavy quark and the weak form factorsNov 10 1993Nov 11 1993It is shown that the number of independent weak form factors collapses if the heavy diquark exists inside the baryons containing a single heavy quark. The relations between the weak form factors are quite different in the case of light diquark. So a careful ... More

Effect of alignment on polarized infrared emission from polycyclic aromatic hydrocarbonsApr 06 2017Polarized emission from polycyclic aromatic hydrocarbons (PAHs) potentially provides a new way to test basic physics of the alignment of ultrasmall grains. In this paper, we present a new model of polarized PAH emission that takes into account the effect ... More

Quantitative Polarimetry: A Unified Model of Dust Grain Alignment by Magnetic Radiative TorquesApr 06 2017Polarization of optical starlight and far-infrared thermal dust emission due to alignment of interstellar grains offers a powerful window to study magnetic fields in the various astrophysical environments, from the diffuse interstellar medium to accretion ... More

Properties and alignment of interstellar dust grains toward Type Ia Supernovae with anomalous polarization curvesOct 07 2015Jan 19 2017Recent photometric and polarimetric observations of type Ia supernovae (SNe Ia) show unusually low total-to-selective extinction ratio ($R_{V}<2$) and wavelength of maximum polarization ($\lambda_{max}<0.4\mu m$) for several SNe Ia, which indicates peculiar ... More

Hopf-Lax formula and generalized characteristicsSep 10 2013Dec 18 2013We study some differential properties of viscosity solution for Hamilton - Jacobi equations defined by Hopf-Lax formula $u(t,x)=\min_{y\in \R^n} \big\{\sigma (y)+tH^*\big (\frac {x-y}{t}\big)\big \}.$ A generalized form of characteristics of the Cauchy ... More

Regularity of viscosity solutions defined by Hopf-type formula for Hamilton-Jacobi equationsAug 16 2012Dec 02 2013Some properties of characteristic curves in connection with viscosity solutions of Hamilton-Jacobi equations defined by Hopf-type formula are studied. We investigate the points where the Hopf-type formula $u(t,x)$ is differentiable, and the strip of the ... More

Modified defect relations of the Gauss map of complete minimal surfaces on annular endsAug 13 2014In this article, we study the modified defect relations of the Gauss map of complete minimal surfaces in $\mathbb R^3$ and $ \mathbb R^4$ on annular ends. We obtain results which are similar to the ones obtained by Fujimoto~[J. Differential Geometry \textbf{29} ... More

An Elementary Approach to a Curious Identity from RamanujanApr 19 2019In his notebooks, Ramanujan wrote the following identity: \begin{equation} \sqrt{2 \left(1 - \frac{1}{3^2}\right) \left(1 - \frac{1}{7^2}\right) \left(1 - \frac{1}{11^2}\right) \left(1 - \frac{1}{19^2}\right)} \ = \ \left(1 + \frac{1}{7}\right) \left(1 ... More

Finite groups whose prime graphs are regularJul 05 2013Aug 23 2013Let G be a finite group and let Irr(G) be the set of all irreducible complex characters of G. Let cd(G) be the set of all character degrees of G and denote by \rho(G) the set of primes which divide some character degrees of G. The prime graph \Delta(G) ... More

On locally solvable subgroups in division ringsOct 16 2018Jul 18 2019Let $D$ be a division ring with center $F$, and $G$ a subnormal subgroup of $D^*$. We show that if $G$ is a locally solvable group such that $G^{(i)}$ is algebraic over $F$, then $G$ must be central. Also, if $M$ is non-abelian locally solvable maximal ... More

Extension of distributions, scalings and renormalization of QFT on Riemannian manifoldsNov 13 2014Let $M$ be a smooth manifold and $X\subset M$ a closed subset of $M$. In this paper, we introduce a natural condition of \emph{moderate growth} along $X$ for a distribution $t$ in $\mathcal{D}^\prime(M\setminus X)$ and prove that this condition is equivalent ... More

The degree sequence of ideals and multiplicitiesMar 10 2015May 05 2015This paper investigates the relationship between multiplicities and the degree sequence of ideals in graded algebras, gives multiplicity equations of graded rings via the degree sequence of ideals, and characterizes mixed multiplicities and multiplicities ... More

Blow-up for biharmonic Schrodinger equation with critical nonlinearityJul 24 2018We consider the minimizers for the biharmonic nonlinear Schr\"odinger functional $$ \mathcal{E}_a(u)=\int_{\mathbb{R}^d} |\Delta u(x)|^2 d x + \int_{\mathbb{R}^d} V(x) |u(x)|^2 d x - a \int_{\mathbb{R}^d} |u(x)|^{q} d x $$ with the mass constraint $\int ... More

Ergodic theory for Riemann surface laminations: a surveyDec 28 2017We survey some recent developments in the ergodic theory for hyperbolic Riemann surface laminations. The emphasis is on singular holomorphic foliations. These results not only illustrate the strong similarity between the ergodic theory of maps and that ... More

Groups whose prime graphs have no trianglesMar 14 2013Let G be a finite group and let cd(G) be the set of all complex irreducible character degrees of G Let \rho(G) be the set of all primes which divide some character degree of G. The prime graph \Delta(G) attached to G is a graph whose vertex set is \rho(G) ... More

Ramification of the Gauss Map of Complete Minimal Surfaces in R^3 and R^4 on Annular EndsApr 26 2013Nov 30 2014In this article, we study the ramification of the Gauss map of complete minimal surfaces in R^3 and R^4 on annular ends. We obtain results which are similar to the ones obtained by Fujimoto and Ru for (the whole) complete minimal surfaces, thus we show ... More

A note on a unicity theorem for the Gauss maps of complete minimal surfaces in Euclidean four-spaceDec 14 2016The classical result of Nevanlinna states that two nonconstant meromorphic functions on the complex plane having the same images for five distinct values must be identically equal to each other. In this paper, we give a similar uniqueness theorem for ... More

Predictions of noncommutative space-timeJul 11 1994Jul 24 1994An unified structure of noncommutative space-time for both gravity and particle physics is presented. This gives possibilities of testing the idea of noncommutative space-time at the currently available energy scale. There are several arguments indicating ... More

Some Remarks on Gravity in Noncommutative Spacetime and a New Solution to the Structure EquationsMar 14 2003In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The diversity in the final ... More

On Sets with More Products than QuotientsJul 31 2019Given a finite set $A\subset \mathbb{R}\backslash \{0\}$, define \begin{align*}&A\cdot A \ =\ \{a_i\cdot a_j\,|\, a_i,a_j\in A\},\\ &A/A \ =\ \{a_i/a_j\,|\,a_i,a_j\in A\}, &A + A \ =\ \{a_i + a_j\,|\, a_i,a_j\in A\},\\ &A - A \ =\ \{a_i - a_j\,|\,a_i,a_j\in ... More

When Sets Are Not Sum-dominantMar 08 2019Given a set $A$ of nonnegative integers, define the sum set $A+A = \{a_i+a_j|a_i,a_j\in A\}$ and the difference set $A-A = \{a_i-a_j|a_i,a_j\in A\}$. The set $A$ is said to be sum-dominant if $|A+A|>|A-A|$. In answering a question by Nathanson, Hegarty ... More

Equilibrium measures of meromorphic self-maps on non-Kahler manifoldsJan 15 2019Apr 17 2019Let $X$ be a compact complex non-K\"ahler manifold and $f$ a dominant meromorphic self-map of $X$. Examples of such maps are self-maps of Hopf manifolds, Calabi-Eckmann manifolds, non-tori nilmanifolds and their blowups. We prove that if $f$ has a dominant ... More

Simple exceptional groups of Lie type are determined by their character degreesFeb 22 2011Let $G$ be a finite group. Denote by $\textrm{Irr}(G)$ the set of all irreducible complex characters of $G.$ Let $\textrm{cd}(G)=\{\chi(1)\;|\;\chi\in \textrm{Irr}(G)\}$ be the set of all irreducible complex character degrees of $G$ forgetting multiplicities, ... More

"Cultural additivity" and how the values and norms of Confucianism, Buddhism, and Taoism co-exist, interact, and influence Vietnamese society: A Bayesian analysis of long-standing folktales, using R and StanMar 05 2018Every year, the Vietnamese people reportedly burned about 50,000 tons of joss papers, which took the form of not only bank notes, but iPhones, cars, clothes, even housekeepers, in hope of pleasing the dead. The practice was mistakenly attributed to traditional ... More

Simple classical groups of Lie type are determined by their character degreesMay 21 2011Feb 22 2012In this paper, we will show that nonabelian simple classical groups of Lie type are uniquely determined by the structure of their complex group algebras.

Solvable-by-finite maximal subgroups of skew linear groupsMar 23 2019Let $D$ be a non-commutative division ring with center $F$, $G$ a subnormal subgroup of $GL_n(D)$. In this note we show that if $G$ contains a non-abelian solvable-by-finite maximal subgroup, then $[D:F]<\infty$, and there exists a maximal subfield $K$ ... More

Grobner bases, local cohomology and reduction numberOct 04 2002D. Bayer and M. Stillman showed that Grobner bases can be used to compute the Castelnuovo-Mumford regularity, which is a measure for the vanishing of graded local cohomology modules. The aim of this paper is to show that the same method can be applied ... More

Castelnuovo-Mumford regularity and related invariantsJul 26 2019These notes are an introduction to some basic aspects of the Castelnuovo-Mumford regularity and related topics such as weak regularity, a*-invariant and partial regularities.

Associated primes of powers of edge ideals and ear decompositions of graphsJun 04 2015Sep 02 2016To compute the local cohomology of a monomial ideal one needs to know its associated primes. In this paper, we give an explicit description of the associated primes of every power of the edge ideal in terms of ear decompositions of the graph. This result ... More

Membership criteria and containments of powers of monomial idealsAug 17 2018Jan 18 2019We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This relationship leads to ... More

NP-completeness of the game KingdominoSep 06 2019Kingdomino is a board game designed by Bruno Cathala and edited by Blue Orange since 2016. The goal is to place $2 \times 1$ dominoes on a grid layout, and get a better score than other players. Each $1 \times 1$ domino cell has a color that must match ... More

Personalized Federated Search at LinkedInFeb 16 2016LinkedIn has grown to become a platform hosting diverse sources of information ranging from member profiles, jobs, professional groups, slideshows etc. Given the existence of multiple sources, when a member issues a query like "software engineer", the ... More

DPG: A Cache-Efficient Accelerator for Sorting and for Join OperatorsAug 02 2003We present a new algorithm for fast record retrieval, distribute-probe-gather, or DPG. DPG has important applications both in sorting and in joins. Current main memory sorting algorithms split their work into three phases: extraction of key-pointer pairs; ... More

Asymptotic behaviour of arithmetically Cohen-Macaulay blow-upsMay 12 2004This paper addresses problems related to the existence of arithmetic Macaulayfications of projective schemes. Let Y be the blow-up of a projective scheme X = Proj R along the ideal sheaf of I \subset R. It is known that there are embeddings Y \cong Proj ... More

Associated primes of powers of edge ideals and ear decompositions of graphsJun 04 2015Jul 17 2018In this paper, we give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establishes a surprising relationship between two seemingly unrelated notions ... More

Saturation and associated primes of powers of edge idealsNov 28 2014For the edge ideal I of an arbitrary simple graph G we describe the monomials of the saturation of a power of I in terms of (vertex) weighted graphs associated with the monomials. This description allows us to characterize the embedded associated primes ... More

An Enciphering Scheme Based on a Card ShuffleAug 06 2012Nov 21 2014We introduce the swap-or-not shuffle and show that the technique gives rise to a new method to convert a pseudorandom function (PRF) into a pseudorandom permutation (PRP) (or, alternatively, to directly build a confusion/diffusion blockcipher). We then ... More

Fixed Parameter Polynomial Time Algorithms for Maximum Agreement and Compatible SupertreesFeb 20 2008Consider a set of labels $L$ and a set of trees ${\mathcal T} = \{{\mathcal T}^{(1), {\mathcal T}^{(2), ..., {\mathcal T}^{(k) \$ where each tree ${\mathcal T}^{(i)$ is distinctly leaf-labeled by some subset of $L$. One fundamental problem is to find ... More

Hilbert polynomials of non-standard bigraded algebrasNov 11 2002This paper is a systematic study of the Hilbert polynomial of a bigraded algebra R which are generated by elements of bidegrees (1,0), (d_1,1),...,(d_r,1), where d_1,...,d_r are non-negative integers. The obtained results can be applied to study Rees ... More

Formation Control of Rigid Graphs with a Flex Node AdditionJun 05 2017This paper examines stability properties of distance-based formation control when the underlying topology consists of a rigid graph and a flex node addition. It is shown that the desired equilibrium set is locally asymptotically stable but there exist ... More

Spectral analysis of morse-smale flows ii: resonances and resonant statesMar 23 2017The goal of the present work is to compute explicitely the correlation spectrum of a Morse-Smale flow in terms of the Lyapunov exponents of the Morse--Smale flow, the topology of the flow around periodic orbits and the monodromy of some given flat connection. ... More

Autocovariance Varieties of Moving Average Random FieldsMar 20 2019We study the autocovariance functions of moving average random fields over the integer lattice $\mathbb{Z}^d$ from an algebraic perspective. These autocovariances are parametrized polynomially by the moving average coefficients, hence tracing out algebraic ... More

Estimation of causal CARMA random fieldsFeb 13 2019We estimate model parameters of L\'evy-driven causal CARMA random fields by fitting the empirical variogram to the theoretical counterpart using a weighted least squares (WLS) approach. Subsequent to deriving asymptotic results for the variogram estimator, ... More

Passive Tracer Dynamics in Slow-Bond ProblemApr 30 2019Asymptotic Kardar-Parisi-Zhang (KPZ) properties are investigated in the totally asymmetric simple exclusion process (TASEP) with a localized geometric defect. In particular, we focus on the universal nature of nonequilibrium steady states of the modified ... More

A new theorem for black holesMar 26 2007A new theorem for black holes is established. The mass of a black hole depends on where the observer is. The horizon mass theorem states that for all black holes: neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed ... More

Horizon Mass TheoremSep 15 2005A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes: neutral, charged or rotating, the horizon mass is always twice the irreducible ... More

The size function of quadratic extensions of complex quadratic fieldsApr 04 2015Dec 22 2015The function $h^0$ for a number field is an analogue of the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. In this paper, we prove the conjecture of van der Geer and Schoof about the maximality of $h^0$ at the trivial Arakelov ... More

Empirical formula for the excitation energies of the first $2^+$ and $3^-$ states in even-even nucleiDec 02 2006Mar 13 2007We report empirical findings that a simple formula in terms of the mass number $A$, the valence proton number $N_p$, and the valence neutron number $N_n$ can describe the essential trends of excitation energies $E_x$ of the first $2^+$ and $3^-$ states ... More

Stabilization/destabilization of cell membranes by multivalent ions: Implications for membrane fusion and divisionMay 31 2000Jun 02 2000We propose a mechanism for the stabilization/destabilization of cell membranes by multivalent ions with an emphasis on its implications for the division and fusion of cells. We find that multivalent cations preferentially adsorbed onto a membrane dramatically ... More

Quantum Black Holes As Elementary ParticlesDec 30 2008Are black holes elementary particles? Are they fermions or bosons? We investigate the remarkable possibility that quantum black holes are the smallest and heaviest elementary particles. We are able to construct various fundamental quantum black holes: ... More

Weight Agnostic Neural NetworksJun 11 2019Sep 05 2019Not all neural network architectures are created equal, some perform much better than others for certain tasks. But how important are the weight parameters of a neural network compared to its architecture? In this work, we question to what extent neural ... More

Metal Artifact Reduction in Cone-Beam X-Ray CT via Ray Profile CorrectionAug 06 2018In computed tomography (CT), metal implants increase the inconsistencies between the measured data and the linear attenuation assumption made by analytic CT reconstruction algorithms. The inconsistencies give rise to dark and bright bands and streaks ... More

The $a$-values of the Riemann zeta function near the critical lineNov 24 2017We study the value distribution of the Riemann zeta function near the line $\Re s = 1/2$. We find an asymptotic formula for the number of $a$-values in the rectangle $ 1/2 + h_1 / (\log T)^\theta \leq \Re s \leq 1/2+ h_2 /(\log T)^\theta $, $T \leq \Im ... More

On normal subgroups of division rings which are radical over a proper division subringDec 18 2012Dec 11 2013We introduce Kurosh elements in division rings based on the idea of a conjecture of Kurosh. Using this, we generalize a result of Faith in [3] and of Herstein in [6].

Un-normalized hypergraph p-Laplacian based semi-supervised learning methodsNov 06 2018Most network-based machine learning methods assume that the labels of two adjacent samples in the network are likely to be the same. However, assuming the pairwise relationship between samples is not complete. The information a group of samples that shows ... More

Hilbert functions of socle idealsAug 12 2015In this paper, we explore a relationship between Hilbert functions and the irreducible decompositions of ideals in local rings. Applications are given to characterize the regularity, Gorensteinness, Cohen-Macaulayness and sequentially Cohen-Macaulayness ... More

Tensor Sparse PCA and Face Recognition: A Novel ApproachApr 12 2019Face recognition is the important field in machine learning and pattern recognition research area. It has a lot of applications in military, finance, public security, to name a few. In this paper, the combination of the tensor sparse PCA with the nearest-neighbor ... More

Volterra-type Ornstein-Uhlenbeck processes in space and timeSep 22 2016Nov 06 2017We propose a novel class of tempo-spatial Ornstein-Uhlenbeck processes as solutions to L\'evy-driven Volterra equations with additive noise and multiplicative drift. After formulating conditions for the existence and uniqueness of solutions, we derive ... More

Renormalization of Feynman amplitudes on manifolds by spectral zeta regularization and blow-upsDec 10 2017Our goal in this paper is to present a generalization of the spectral zeta regularization for general Feynman amplitudes. Our method uses complex powers of elliptic operators but involves several complex parameters in the spirit of the analytic renormalization ... More

Some results on abstract stochastic semilinear evolution equationsAug 28 2015This paper devotes to studying abstract semilinear stochastic evolution equations with additive noise in Hilbert spaces. First, we investigate a special case, namely linear evolution equations. Results on existence and uniqueness of strict and mild solutions ... More

Enhancement of Real Time EPICS IOC PV Management for Data Archiving SystemJul 31 2015For operating a 100MeV linear proton accelerator, the major driving values and experimental data need to be archived. According to the experimental conditions, different data are required. It is necessary to implement functions that can add new data and ... More

Origin of $2_1^+$ Excitation Energy Dependence on Valence Nucleon NumbersMar 13 2007Apr 17 2007It has been shown recently that a simple formula in terms of the valence nucleon numbers and the mass number can describe the essential trends of excitation energies of the first $2^+$ states in even-even nuclei. By evaluating the first order energy shift ... More

Baryon Magnetic Moments in a QCD-based Quark Model with loop correctionsApr 23 1998We study meson loop corrections to the baryon magnetic moments starting from a QCD-based quark model derived earlier in a quenched approximation to QCD. The model reproduces the standard quark model with extra corrections for the binding of the quarks. ... More

Bosonization and Lie Group StructureSep 25 2015We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the group parameters. ... More

Symmetries in BosonizationDec 27 2013Two-dimensional quantum field theories are important in many problems in physics because they contain exact symmetries and are often completely integrable. We demonstrate the power of bosonization in elucidating the structure of a multi-component fermion ... More