total 2273took 0.09s

Information-entropic measures for non-zero l states of confined hydrogen-like ionsApr 04 2019Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials namely, 3D ... More

Information-Entropic Measures in Confined Isotropic Harmonic OscillatorApr 12 2019Information based uncertainty measures like R{\'e}nyi entropy (R), Shannon entropy (S) and Onicescu energy (E) (in both position and momentum space) are employed to understand the influence of radial confinement in isotropic harmonic oscillator. The transformation ... More

Fisher information in confined isotropic harmonic oscillatorApr 04 2019Fisher information ($I$) is investigated in a confined harmonic oscillator (CHO) enclosed in a spherical enclosure, in conjugate $r$ and $p$ spaces. A comparative study between CHO and a free quantum particle in spherical box (PISB), as well as CHO and ... More

Quantum mechanical virial-like theorem for confined quantum systemsApr 04 2019Confinement of atoms inside impenetrable (hard) and penetrable (soft) cavities has been studied for nearly eight decades. However, a unified virial theorem for such systems has not yet been found. Here we provide a general virial-like equation in terms ... More

Some complexity measures in confined isotropic harmonic oscillatorApr 02 2019Various well-known statistical measures like \emph{L\'opez-Ruiz, Mancini, Calbet} (LMC) and \emph{Fisher-Shannon} complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position ($r$) and momentum ($p$) spaces. To ... More

Information-entropic measures in free and confined hydrogen atomJan 16 2018Shannon entropy ($S$), R{\'e}nyi entropy ($R$), Tsallis entropy ($T$), Fisher information ($I$) and Onicescu energy ($E$) have been explored extensively in both \emph{free} H atom (FHA) and \emph{confined} H atom (CHA). For a given quantum state, accurate ... More

Relative Fisher information in some central potentialsApr 04 2019Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials namely, 3D ... More

Quantum confinement in an asymmetric double-well potential through energy analysis and information entropic measureApr 12 2019Localization of a particle in the wells of an asymmetric double-well (DW) potential is investigated here. Information entropy-based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phasespace area, are utilized ... More

Information entropy and complexity measure in generalized Kratzer potentialApr 12 2019Shannon entropy ($S$), Fisher information ($I$) and a measure equivalent to Fisher-Shannon complexity $(C_{IS})$ of a ro-vibrational state of diatomic molecules (O$_2$, O$_2^+$, NO, NO$^+$) with generalized Kratzer potential is analyzed. \emph{Exact} ... More

Information entropy as a measure of tunneling and quantum confinement in a symmetric double-well potentialApr 25 2019Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of this system ... More

Various complexity measures in confined hydrogen atomJan 16 2018Several well-known statistical measures similar to \emph{LMC} and \emph{Fisher-Shannon} complexity have been computed for confined hydrogen atom in both position ($r$) and momentum ($p$) spaces. Further, a more generalized form of these quantities with ... More

Information entropic measures of a quantum harmonic oscillator in symmetric and asymmetric confinement within an impenetrable boxApr 12 2019Information-based uncertainty measures like Shannon entropy, Onicescu energy and Fisher information (in position and momentum space) are employed to understand the effect of \emph{symmetric and asymmetric} confinement in a quantum harmonic oscillator. ... More

Fisher information in confined hydrogen-like ionsNov 04 2017Fisher information (I) is investigated for confined hydrogen atom (CHA)-like systems in conjugate $r$ and $p$ spaces. A comparative study between CHA and free H atom (with respect to $I$) is pursued. In many aspects, inferences in CHA are significantly ... More

Reconstruction of interaction rate in Holographic dark energyAug 01 2016The present work is based on the holographic dark energy model with Hubble horizon as the infrared cut-off. The interaction rate between dark energy and dark matter has been reconstructed for two different parameterizations of the deceleration parameter. ... More

Renyi entropy of the critical O(N) modelDec 03 2015In this article we explore a certain definition of "alternate quantization" for the critical O(N) model. We elaborate on a prescription to evaluate the Renyi entropy of alternately quantized critical O(N) model. We show that there exists new saddles of ... More

Observing the Energetic Universe at Very High Energies with the VERITAS Gamma Ray ObservatorySep 27 2018Very high energy gamma-ray observations offer indirect methods for studying the highest energy cosmic rays in our Universe. The origin of cosmic rays at energies greater than $10^{18}$ eV remains a mystery, and many questions in particle astrophysics ... More

Probability distribution of constrained Random WalksDec 12 2014In this paper we consider a sequence of n coin tosses, whose outcome depends on the previous n-1 tosses. In particular, their distribution is not i.i.d. We compute the limiting distribution of this sequence using the method of images.

Egret (GeV) BlazarsJan 17 2001The EGRET instrument on the Compton Gamma Ray Observatory (1991-2000) has positively detected high energy gamma-ray emission from more than 67 active galaxies of the blazar class. The majority of the EGRET blazars are flat-spectrum radio quasars, which ... More

Indexes in Microsoft SQL ServerMar 20 2019Indexes are the best apposite choice for quickly retrieving the records. This is nothing but cutting down the number of Disk IO. Instead of scanning the complete table for the results, we can decrease the number of IO's or page fetches using index structures ... More

Jet rates in the hard scattering process at finite temperatureSep 14 2000We compute the cross-section of the hadronic jets arising from the quark antiquark pair which are produced from a hard photons (of 4-momentum $q$) in the plasma, predominantly consisting of thermalised quarks and gluons. The quark antiquark pair is hard ... More

Poincare gauge theory from higher derivative matter lagrangeanDec 24 2009Aug 10 2010Starting from matter lagrangean containing higher order derivative than the first, we construct the Poincare gauge theory by localising the Poincare symmetry of the matter theory. The construction is shown to follow the usual geometric procedure of gravitational ... More

Enumeration of singular hypersurfaces on arbitrary complex manifoldsOct 15 2014In this paper we obtain an explicit formula for the number of hypersurfaces in a compact complex manifold X (passing through the right number of points), that has a simple node, a cusp or a tacnode. The hypersurfaces belong to a linear system, which is ... More

On cluster systems of tensor product systems of Hilbert spacesFeb 11 2015It is known that the spatial product of two product systems is intrinsic. Here we extend this result by analyzing subsystems of the tensor product of product systems. A relation with cluster systems is established. In a special case, we show that the ... More

Orbit Portraits of Unicritical Anti-polynomialsApr 28 2014May 19 2014Orbit portraits were introduced by Milnor as a combinatorial tool to describe the patterns of all periodic dynamical rays landing on a periodic cycle of a quadratic polynomial. This encodes information about the dynamics and the parameter spaces of these ... More

$C^{1,α}$-Regularity of Quasilinear equations on the Heisenberg GroupMay 09 2018In this article, we reproduce results of classical regularity theory of quasilinear elliptic equations in the divergence form, in the setting of Heisenberg Group. The conditions encompass a very wide class of equations with isotropic growth conditions, ... More

Gibbs measures on mutually interacting Brownian paths under singularitiesOct 15 2015Apr 18 2016We are interested in the analysis of Gibbs measures defined on two independent Brownian paths in $\R^d$ interacting through a mutual self-attraction. This is expressed by the Hamiltonian $\int\int_{\R^{2d}} V(x-y) \mu(\d x)\nu(\d y)$ with two probability ... More

Ashes 2013 - A network theory analysis of Cricket strategiesAug 26 2013We demonstrate in this paper the use of tools of complex network theory to describe the strategy of Australia and England in the recently concluded Ashes 2013 Test series. Using partnership data made available by cricinfo during the Ashes 2013 Test series, ... More

Boundedness of spectral multipliers of generalized Laplacians on compact manifolds with boundaryOct 22 2014Jul 30 2015Consider a second order, strongly elliptic differential operator $L$ (maybe a system) on a compact Riemannian manifold $\overline{M}$ with smooth boundary, where $L$ is defined by coercive boundary conditions. The main result is the $L^\infty - \text{BMO}_L$ ... More

Quantum metrology to probe atomic parity violationJan 13 2009Oct 13 2010An entangled state prepared in the decoherence free sub-space together with a Ramsey type measurement can probe parity violation in heavy alkali ions like Ba+ or Ra+. Here we propose an experiment with Ba+ ions as an example to measure the small parity ... More

Charge dynamics of a molecular ion immersed in a Rydberg-dressed atomic lattice gasJan 18 2019Charge dynamics in an ultra-cold setup involving a laser dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange crucially depends ... More

Variation of Laplace spectra of compact "nearly" hyperbolic surfacesJan 27 2016We use the time real analyticity of Ricci flow proved by Kotschwar to extend a result in ~\cite{B}, namely, we prove that the Laplace spectra of negatively curved compact surfaces having same genus $\gamma \geq 2$, same area and same curvature bounds ... More

Gap equation in scalar field theory at finite temperatureMay 23 1997Dec 24 1998We investigate the two-loop gap equation for the thermal mass of hot massless $g^2\phi^4$ theory and find that the gap equation itself has a non-zero finite imaginary part. This indicates that it is not possible to find the real thermal mass as a solution ... More

Phase transition in the two star Exponential Random Graph ModelOct 15 2013This paper gives a way to simulate from the two star probability distribution on the space of simple graphs via auxiliary variables. Using this simulation scheme, the model is explored for various domains of the parameter values, and the phase transition ... More

A Homology Theory For A Special Family Of Semi-groupsNov 17 2016In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the comparison of this ... More

Soliton solutions of a gauged O(3) sigma model with interpolating potentialNov 02 1999Dec 13 2009Soliton modes in a gauged sigma model with interpolating potential have been investigated. Numerical solutions using a fourth order Runge -- Kutta method are discussed. By tuning the interpolation parameter the transition from symmetrybreaking to the ... More

Extremal values of the (fractional) Weinstein functional on the hyperbolic spaceJun 19 2014Jul 11 2015We make a study of Weinstein functionals, first defined in ~\cite{W}, on the hyperbolic space $\mathbb{H}^n$. We are primarily interested in the existence of Weinstein functional maximisers, or, in other words, existence of extremal functions for the ... More

Spacetime Foliations and p-Brane DynamicsMar 01 1998Mar 03 1998This paper has been withdrawn by the author. Proofs of two propositions need more details.

Identifying the greatest team and captain - A complex network approach to cricket matchesJan 05 2012Jan 09 2012We consider all Test matches played between 1877 and 2010 and One Day International (ODI) matches played between 1971 and 2010. We form directed and weighted networks of teams and also of their captains. The success of a team (or captain) is determined ... More

On Local Lipschitz Regularity For Quasilinear equations in the Heisenberg GroupApr 02 2018The goal of this article is to establish local Lipschitz continuity of weak solutions for a class of degenerated elliptic equations of divergence form, in the Heisenberg Group. The considered hypothesis for the growth and ellipticity condition is a natural ... More

Large deviation for the empirical degree distribution of an Erdos-Renyi graphOct 15 2013Oct 26 2013With $(d_1,\cdots,d_n)$ denoting the labeled degrees of an Erdos Renyi graph with parameter $\beta/n$, the large deviation principle for $\frac{1}{n}\sum\limits_{j=1}^n\delta_{d_j}$ (the empirical distribution of the degrees) is derived with a good rate ... More

Charge dynamics of a molecular ion immersed in a Rydberg-dressed atomic lattice gasJan 18 2019Apr 27 2019Charge dynamics in an ultra-cold setup involving a laser dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange crucially depends ... More

Symplectic A-directed ImmersionsJul 20 2015We derive a symplectic analogue of A-directed immersion theorem.

Degeneracy in sparse ERGMs with functions of degrees as sufficient statisticsOct 15 2013May 30 2019A sufficient criterion for "non-degeneracy" is given for Exponential Random Graph Models on sparse graphs with sufficient statistics which are functions of the degree sequence. This criterion explains why statistics such as alternating $k$-star are non-degenerate, ... More

On odd torsion in even Khovanov homologyJun 14 2019This short note resolves the most important part of the PS braid conjecture while introducing the first known examples of knots and links with odd torsion of order 9, 27, 81, and 25 in their even Khovanov homology.

Fixed points and cycle structure of random permutationsSep 15 2015Jul 13 2016Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions. In particular ... More

Reconstruction of interaction rate in Holographic dark energyAug 01 2016Oct 29 2016The present work is based on the holographic dark energy model with Hubble horizon as the infrared cut-off. The interaction rate between dark energy and dark matter has been reconstructed for three different parameterizations of the deceleration parameter. ... More

Hamiltonicity of the Power Graph of Abelian Groups-IMay 04 2015In this article we discuss the Hamiltonicity of the power graph associated to a finite group.

Search of the ground state(s) of spin glasses and quantum annealingMay 06 2019We review our earlier studies on the order parameter distribution of the quantum Sherrington-Kirkpatrick (SK) model. Through Monte Carlo technique, we investigate the behavior of the order parameter distribution at finite temperatures. The zero temperature ... More

Leadership Network and Team Performance in Interactive ContestsJun 06 2016Over the years, the concept of leadership has experienced a paradigm shift - from solitary leader (centralized leadership) to de-centralized leadership or distributed leadership. This paper explores the idea that centralized leadership, as earlier suggested, ... More

Susceptibilities to order $α_s$ in the high density phase of QCDJun 21 2001We compute the free energy density of QCD to order $\alpha_s$ at very high density and non-zero quark masses. The counterterms needed to renormalise the theory to order $\alpha_s$ is same as the vacuum (non-zero density) theory. We investigate the response ... More

Search of the ground state(s) of spin glasses and quantum annealingMay 06 2019May 08 2019We review our earlier studies on the order parameter distribution of the quantum Sherrington-Kirkpatrick (SK) model. Through Monte Carlo technique, we investigate the behavior of the order parameter distribution at finite temperatures. The zero temperature ... More

Event-by-event multiplicity fluctuations in Pb-Pb collisions in ALICEMar 22 2016Fluctuations of various observables in heavy-ion collisions at ultra-relativistic energies have been extensively studied as they provide important signals regarding the formation of a Quark-Gluon Plasma (QGP). Because of the large number of produced particles ... More

On the Question of Degeneracy of Topological Solitons in a Gauged O(3) Non-Linear Sigma Model with Chern-Simons TermMay 27 1999We show that the degeneracy of topological solitons in the gauged O(3) non-linear sigma model with Chern-Simons term may be removed by chosing a self-interaction potential with symmetry - breaking minima. The topological solitons in the model has energy,charge,flux ... More

Magnetic Vortices in a Gauged O(3) Sigma Model with Symmetry Breaking Self-InteractionMay 26 1997We consider a (2+1) dimensional nonlinear O(3) sigma model with its U(1) subgroup gauged along with the inclusion of a self-interaction having symmetry breaking minima.The gauge field dynamics is governed by the Maxwell term.The model is shown to support ... More

Isoperimetric Inequalities using Varopoulos TransportOct 17 2010Mar 21 2011The main results in this paper provide upper bounds of the second order Dehn functions for three-dimensional groups Nil and Sol. These upper bounds are obtained by using the Varopoulos transport argument on dual graphs. The first step is to start with ... More

On Hamiltonian cycles of power graphs of abelian groupsMay 04 2015May 05 2017In this article we discuss the question of presence of Hamiltonian cycle in the un-directed power graph of a group. In the process we develop weighted Hamiltonian cycle concept and prove a few general results regarding the Hamiltonian question.

Consistent estimation in the two star Exponential Random Graph ModelOct 16 2013This paper explores statistical properties of a particular Exponential Random Graph Model, the two star probability distribution on the space of simple graphs. Non degenerate limiting distributions for the number of edges is derived for all parameter ... More

Weinstein HomotopiesMay 01 2019We give a partial answer to a question asked by Eliashberg in one of his recent papers.

Thurston's h-principle and Flexibility of Poisson StructuresNov 29 2016We prove an analogue of Thurston's h-principle for $2$-dimensional foliations on manifolds of dimension bigger or equal to $4$, in the presence of a fiber-wise non-degenerate $2$-form. This helps us understand the flexibility of rank $2$ regular Poisson ... More

Estimation in exponential families on permutationsJul 03 2013May 13 2015Asymptotics of the normalizing constant is computed for a class of one parameter exponential families on permutations which includes Mallows model with Spearmans's Footrule and Spearman's Rank Correlation Statistic. The MLE, and a computable approximation ... More

Message transport characteristics in communication networksOct 19 2009We study message transport on a $1-d$ ring of nodes and randomly distributed hubs. Messages are deposited on the network at a constant rate. When the rate at which messages are deposited on the lattice is very high, messages start accumulating after a ... More

Statistical Characterizers of Transport in a Communication NetworkOct 22 2008Aug 31 2009We identify the statistical characterizers of congestion and decongestion for message transport in model communication lattices. These turn out to be the travel time distributions, which are Gaussian in the congested phase, and log-normal in the decongested ... More

Precise Variational Calculation For The Doubly Excited State (2p^2)^3P^e of HeliumJun 15 2004Highly precise variational calculations of non-relativistic energies of the (2p^2)^3P^e state of Helium atom are presented.We get an upper bound energy E=-0.71050015565678 a.u.,the lowest yet obtained.

Global Testing Against Sparse Alternatives under Ising ModelsNov 24 2016Oct 05 2017In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the ... More

Detection Thresholds for the $β$-Model on Sparse GraphsAug 05 2016May 27 2017In this paper we study sharp thresholds for detecting sparse signals in $\beta$-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity, and signal strength. In regimes of moderately ... More

A Fast Two Pass Multi-Value Segmentation Algorithm based on Connected Component AnalysisFeb 11 2014Connected component analysis (CCA) has been heavily used to label binary images and classify segments. However, it has not been well-exploited to segment multi-valued natural images. This work proposes a novel multi-value segmentation algorithm that utilizes ... More

Parabolic arcs of the multicorns: Real-analyticity of Hausdorff dimension, and $\mathrm{Per}_n(1)$ curvesOct 05 2014Aug 13 2015The boundaries of the hyperbolic components of odd period of the multicorns contain real-analytic arcs consisting of quasi-conformally conjugate parabolic parameters. The principal result of this paper asserts that the Hausdorff dimension of the Julia ... More

Nonlinear travelling waves on non-Euclidean spacesNov 21 2013Sep 06 2015We study travelling wave solutions, that is, solutions of the form $v(t, x) = e^{i\lambda t}u(g(t)x)$, to nonlinear Schr\"odinger and Klein-Gordon equations on Riemannian manifolds, both compact and non-compact ones, with emphasis on the NLKG. Here $g(t)$ ... More

Involutive Spacetime Distributions and p-Brane DynamicsJul 14 1997We propose a precise definition of multidimensional fluids generated by self-gravitating extended objects such as strings and membranes: a p-dimensional perfect fluid is a smooth involutive p-dimensional distribution on a spacetime, each integral manifold ... More

High Energy Gamma RaysSep 22 2000This article reviews the present status of high energy gamma-ray astronomy at energies above 30 MeV. Observations in the past decade using both space- and ground-based experiments have been primarily responsible for giving a tremendous boost to our knowledge ... More

High Energy Gamma-Ray Emission From Blazars: EGRET ObservationsJan 17 1999We will present a summary of the observations of blazars by the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory (CGRO). EGRET has detected high energy gamma-ray emission at energies greater than 100 MeV from more ... More

Singular Masas and Measure-Multiplicity InvariantApr 18 2011In this paper we study relations between the \emph{left-right-measure} and properties of singular masas. Part of the analysis is mainly concerned with masas for which the \emph{left-right-measure} is the class of product measure. We provide examples of ... More

Masas and Bimodule Decompositions of $\rm{II}_{1}$ FactorsDec 06 2008The measure-multiplicity-invariant for masas in $\rm{II}_{1}$ factors was introduced in \cite{MR2261688} to distinguish masas that have the same Puk\'{a}nszky invariant. In this paper we study the measure class in the measure-multiplicity-invariant. This ... More

Coadjoint orbits for $A_{n-1}^+, B_{n}^{+}$, and $D_{n}^{+}$Jan 20 2005A complete description of the coadjoint orbits for A_{n-1}^{+}, the nilpotent Lie algebra of n-by-n strictly upper triangular matrices, has not yet been obtained, though there has been steady progress on it ever since the orbit method was devised. We ... More

On some representations of nilpotent Lie algebras and superalgebrasSep 24 2004Let $G$ be a simply connected, nilpotent Lie group with Lie algebra $\gee$. The group $G$ acts on the dual space $\gee^*$ by the coadjoint action. %% which partitions $\gee^*$ into coadjoint orbits. By the orbit method of Kirillov, the simple unitary ... More

Seifert's conjecture for almost symplectic foliationsJan 25 2015Oct 25 2016We disproving Seifert's conjecture for almost symplectic foliations with co-dimension bigger or equal to 3.

Parabolic arcs of the multicorns: Real-analyticity of Hausdorff dimension, and singularities of $\mathrm{Per}_n(1)$ curvesOct 05 2014May 17 2017The boundaries of the hyperbolic components of odd period of the multicorns contain real-analytic arcs consisting of quasi-conformally conjugate parabolic parameters. One of the main results of this paper asserts that the Hausdorff dimension of the Julia ... More

On Local Lipschitz Regularity For Quasilinear equations in the Heisenberg GroupApr 02 2018Mar 06 2019The goal of this article is to establish local Lipschitz continuity of weak solutions for a class of degenerated elliptic equations of divergence form, in the Heisenberg Group. The considered hypothesis for the growth and ellipticity condition is a natural ... More

Global Testing Against Sparse Alternatives under Ising ModelsNov 24 2016In this paper, we study the effect of dependence on detecting sparse signals. In particular, we focus on global testing against sparse alternatives for the means of binary outcomes following an Ising model, and establish how the interplay between the ... More

Birthday Paradox, Monochromatic Subgraphs, and the Second Moment PhenomenonNov 04 2017What is the chance that among a group of $n$ friends, there are $s$ friends all of whom have the same birthday? This is the celebrated birthday problem which can be formulated as the existence of a monochromatic $s$-clique $K_s$ ($s$-matching birthdays) ... More

Intensity-Intensity Correlations of Classically Entangled LightJan 03 2014An experiment is proposed to show that after initial frequency and polarization selection, classical thermal light from two independent sources can be made path-polarization entangled. Such light will show new intensity-intensity correlations involving ... More

Consistent clustering using an $\ell_1$ fusion penaltyDec 02 2014Feb 23 2016We study the large sample behavior of a convex clustering framework, which minimizes the sample within cluster sum of squares under an~$\ell_1$ fusion constraint on the cluster centroids. This recently proposed approach has been gaining in popularity, ... More

Positive solutions for nonlinear Choquard equation with singular nonlinearitySep 23 2016Nov 02 2016In this article, we study the following nonlinear Choquard equation with singular nonlinearity \begin{equation*} \quad -\De u = \la u^{-q} + \left( \int_{\Om}\frac{|u|^{2^*_{\mu}}}{|x-y|^{\mu}}\mathrm{d}y \right)|u|^{2^*_{\mu}-2}u, \quad u>0 \; \text{in}\; ... More

Critical growth fractional elliptic problem with singular nonlinearitiesFeb 25 2016In this article, we study the following fractional Laplacian equation with critical growth and singular nonlinearity $$\quad (-\Delta)^s u = \lambda a(x) u^{-q} + u^{2^*_s-1}, \quad u>0 \; \text{in}\; \Omega,\quad u = 0 \; \mbox{in}\; \mathbb{R}^n \setminus\Omega,$$ ... More

Determinants of the hypergeometric period matrices of an arrangement and its dualFeb 28 2006We fix three natural numbers $k, n, N$, such that $n+k+1=N$, and introduce the notion of two dual arrangements of hyperplanes. One of the arrangements is an arrangement of $N$ hyperplanes in a $k$-dimensional affine space, the other is an arrangement ... More

The Information Geometry of Mirror DescentOct 29 2013Apr 29 2014Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections between the ... More

Discrete $z$-filters and rings of analytic functionsOct 12 2015Jul 17 2016Consider rings of single variable real analytic or complex entire functions, denoted by $\mathbb{K}\langle z\rangle$. We study "discrete $z$-filters" on $\mathbb{K}$ and their connections with the space of maximal ideals of $\mathbb{K}\langle z\rangle$, ... More

Consensus over Weighted Directed Graphs: A Robustness PerspectiveSep 01 2016The present paper investigates the robustness of the consensus protocol over weighted directed graphs using the Nyquist criterion. The limit to which a single weight can vary, while consensus among the agents can be achieved, is explicitly derived. It ... More

Helicity-dependent Twist-two and Twist-three Generalized Parton Distributions in Light-front QCDNov 25 2002Mar 03 2003We investigate the helicity dependent twist-two and twist-three generalized parton distributions in light-front Hamiltonian QCD for a massive dressed quark target. Working in the kinematical region $\xi< x <1$, we obtain the splitting functions for the ... More

A Real Space Description of Magnetic Field Induced Melting in the Charge Ordered Manganites: I. The Clean LimitNov 21 2008Oct 21 2014We study the melting of charge order in the half doped manganites using a model that incorporates double exchange, antiferromagnetic superexchange, and Jahn-Teller coupling between electrons and phonons. We primarily use a real space Monte Carlo technique ... More

WikiSent : Weakly Supervised Sentiment Analysis Through Extractive Summarization With WikipediaSep 12 2012Sep 18 2012This paper describes a weakly supervised system for sentiment analysis in the movie review domain. The objective is to classify a movie review into a polarity class, positive or negative, based on those sentences bearing opinion on the movie alone. The ... More

A Scaling Relation in Inhomogeneous Cosmology with k-essence scalar fieldsFeb 03 2016We obtain a scaling relation for spherically symmetric k-essence scalar fields $\phi(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman- Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous ... More

Enhancement of Image Resolution by BinarizationNov 21 2011Image segmentation is one of the principal approaches of image processing. The choice of the most appropriate Binarization algorithm for each case proved to be a very interesting procedure itself. In this paper, we have done the comparison study between ... More

Impact Parameter Dependent Parton Distributions for a Relativistic Composite SystemOct 08 2004We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We express them in terms of overlaps of light-cone wave functions for a self consistent two-body spin-1/2 state, namely an ... More

In search of the dark matter dark energy interaction: a kinematic approachOct 14 2016The present work deals with a kinematic approach to the modelling the late time dynamics of the universe. This approach is based upon the assumption of constant value of cosmological jerk parameter, which is the dimensionless representation of the 3rd ... More

Large Deviations for Brownian Intersection MeasuresMay 05 2011Jul 11 2012We consider $p$ independent Brownian motions in $\R^d$. We assume that $p\geq 2$ and $p(d-2)<d$. Let $\ell_t$ denote the intersection measure of the $p$ paths by time $t$, i.e., the random measure on $\R^d$ that assigns to any measurable set $A\subset ... More

Probing TMDs in heavy quarkonium production in $pp$ collisionOct 18 2016We present a recent calculation of $J/\psi$ and $\Upsilon$ production in unpolarized $pp$ collision and show that this can be used to probe the unpolarized gluon as well as the linearly polarized gluon transverse momentum dependent parton distributions ... More

On Concentration of least energy solutions for magnetic critical Choquard equationsNov 17 2016In the present paper, we consider the following magnetic nonlinear Choquard equation $$ \left\{ \begin{array}{ll} & (-i \nabla+A(x))^2u + \mu g(x)u = \la u + (|x|^{-\alpha} * |u|^{2^*_\alpha})|u|^{2^*_\alpha-2}u ,\; u>0 \;\text{in} \; \mb R^n , & u \in ... More

Aspect Specific Opinion Expression Extraction using Attention based LSTM-CRF NetworkFeb 07 2019Opinion phrase extraction is one of the key tasks in fine-grained sentiment analysis. While opinion expressions could be generic subjective expressions, aspect specific opinion expressions contain both the aspect as well as the opinion expression within ... More

Mean-field interaction of Brownian occupation measures, I: uniform tube property of the Coulomb functionalSep 22 2015We study the transformed path measure arising from the self-interaction of a three-dimensional Brownian motion via an exponential tilt with the Coulomb energy of the occupation measures of the motion by time $t$. The logarithmic asymptotics of the partition ... More