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StRE: Self Attentive Edit Quality Prediction in WikipediaJun 11 2019Wikipedia can easily be justified as a behemoth, considering the sheer volume of content that is added or removed every minute to its several projects. This creates an immense scope, in the field of natural language processing towards developing automated ... More

Stuck? No worries!: Task-aware Command Recommendation and Proactive Help for AnalystsJun 21 2019Data analytics software applications have become an integral part of the decision-making process of analysts. Users of such a software face challenges due to insufficient product and domain knowledge, and find themselves in need of help. To alleviate ... More

Hierarchical Role-Based Access Control with Homomorphic Encryption for Database as a ServiceMar 02 2016Database as a service provides services for accessing and managing customers data which provides ease of access, and the cost is less for these services. There is a possibility that the DBaaS service provider may not be trusted, and data may be stored ... More

Superdense star in a space-time with minimal lengthJan 07 2019In this paper we generalise core-envelope model of superdense star to a non-commutative space-time and study the modifications due to the existence of a minimal length, predicted by various approaches to quantum gravity. We first derive Einstein's field ... More

Neutrino Scattering in a Newly Born Neutron StarOct 15 1996Oct 16 1996We calculate neutrino cross sections from neutral current reactions in the dense matter encountered in the evolution of a newly born neutron star. Effects of composition and of strong interactions in the deleptonization and cooling phases of the evolution ... More

Neutrino Scattering in Strangeness-Rich Stellar MatterDec 07 1995Dec 08 1995We calculate neutrino cross sections from neutral current reactions in dense matter containing hyperons. We show that Sigma- hyperons give significant contributions. To lowest order, the contributions from the neutral Lambda and Sigma0, which have zero ... More

Neutrinos from Protoneutron Stars: A Probe of Hot and Dense matterAug 03 1995Neutrino processes in dense matter play a key role in the dynamics, deleptonization and early cooling of hot protoneutron stars formed in the gravitational collapse of massive stars. Here we calculate neutrino mean free paths from neutrino-hyperon interactions ... More

Geometric Proofs of Horn and Saturation ConjecturesAug 13 2002Jul 21 2005We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also establish transversality ... More

Irredundance in Eigenvalue ProblemsAug 04 2003We show the irredundancy, necessity and sufficiency of inequalities corresponding to intersections whose ``Witten Bundle'' is polyrigid for the product of unitary matrices problem.

Transformation formulas in Quantum CohomologyOct 03 2002The article discusses an action of the center of G on the quantum cohomology of G/P's constructed geometrically. It is shown how to recover Bertram's Quantum Schubert Calculus from this action, and also a refinement of a formula of Fulton and Woodward ... More

Extremal rays in the Hermitian eigenvalue problemMay 30 2017Nov 16 2017The Hermitian eigenvalue problem asks for the possible eigenvalues of a sum of $n\times n$ Hermitian matrices, given the eigenvalues of the summands. The regular faces of the cones $\Gamma_n(s)$ controlling this problem have been characterized in terms ... More

Geometric Proof of a Conjecture of FultonNov 28 2005We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).

Comparative analysis of ADTCP and M-ADTCP: Congestion Control Techniques for improving TCP performance over Ad-hoc NetworksSep 12 2012Identifying the occurrence of congestion in a Mobile Ad-hoc Network (MANET) is a major task. The inbuilt congestion control techniques of existing Transmission Control Protocol (TCP) designed for wired networks do not handle the unique properties of shared ... More

Magneto-optical properties of Europium hexaborideJun 29 2004Full potential spin-polarized self-consistent electronic structure calculation s have been performed on LaB$_{6}$, EuB$_{6}$ and YbB$_{6}$ using Linear Muffin- Tin Orbital Method. The electronic structure of EuB$_{6}$ shows a small overlap near the Fermi ... More

Software Reuse in Medical Database for Cardiac Patients using Pearson Family EquationsDec 03 2012Software reuse is a subfield of software engineering that is used to adopt the existing software for similar purposes. Reuse Metrics determine the extent to which an existing software component is reused in new software with an objective to minimize the ... More

Strange duality and the Hitchin/WZW connectionMay 04 2007Feb 15 2008For a compact Riemann surface X of positive genus, the space of sections of certain theta bundle on moduli of bundles of rank r and level k admits a natural map to (the dual of) a similar space of sections of rank k and level r (the strange duality isomorphism). ... More

Number of sets with small sumset and the clique number of random Cayley graphsNov 01 2007May 20 2009Let $G$ be a finite abelian group of order $n$. For any subset $B$ of $G$ with $B=-B$, the Cayley graph $G_B$ is a graph on vertex set $G$ in which $ij$ is an edge if and only if $i-j\in B.$ It was shown by Ben Green that when $G$ is a vector space over ... More

Neutron Star News and PuzzlesApr 07 2014Apr 30 2014Gerry Brown has had the most influence on my career in Physics, and my life after graduate studies. This article gives a brief account of some of the many ways in which Gerry shaped my research. Focus is placed on the significant strides on neutron star ... More

Probing Quark Matter In Neutron StarsMay 16 2001The presence of quark matter in neutron star interiors may have distinctive signatures in basic observables such as (i) masses and radii [1], (ii) surface temperatures versus age [2], (iii) spin-down rates of milli-second pulsars [3], and (iv) neutrino ... More

Strange Pathways for Black Hole FormationSep 18 2000Immediately after they are born, neutron stars are characterized by an entropy per baryon of order unity and by the presence of trapped neutrinos. If the only hadrons in the star are nucleons, these effects slightly reduce the maximum mass relative to ... More

Tipping of a classical point mass pendulum: Role of statistical fluctuationsSep 28 2010The behavior of a stationary inverted point mass pendulum pivoted at its lower end in a gravitational potential is studied under the influence of statistical fluctuations. It is shown using purely classical equations that the pendulum eventually tips ... More

The strange duality conjecture for generic curvesFeb 01 2006Feb 22 2006For X a compact Riemann surface of positive genus, the strange duality conjecture predicts that the space of sections of certain theta bundle on moduli of bundles of rank r and level k is naturally dual to a similar space of sections of rank k and level ... More

Quantum Generalization of the Horn ConjectureMar 02 2003Jul 21 2005We prove a theorem which implies a quantum (multiplicative) analogue of the Horn conjecture, and also of the saturation conjecture. We obtain transversality statements for quantum schubert calculus in any characteristic and also determine the smallest ... More

Software Reuse in Cardiology Related Medical Database Using K-Means Clustering TechniqueNov 05 2013Software technology based on reuse is identified as a process of designing software for the reuse purpose. The software reuse is a process in which the existing software is used to build new software. A metric is a quantitative indicator of an attribute ... More

An Influence Diagram-Based Approach for Estimating Staff Training in Software IndustryAug 25 2010The successful completion of a software development process depends on the analytical capability and foresightedness of the project manager. For the project manager, the main intriguing task is to manage the risk factors as they adversely influence the ... More

A Study Of Cyber Security Challenges And Its Emerging Trends On Latest TechnologiesFeb 08 2014Cyber Security plays an important role in the field of information technology .Securing the information have become one of the biggest challenges in the present day. When ever we think about the cyber security the first thing that comes to our mind is ... More

Vortex arrays and ciliary tangles underlie the feeding-swimming tradeoff in starfish larvaeNov 03 2016Many marine invertebrates have larval stages covered in linear arrays of beating cilia, which propel the animal while simultaneously entraining planktonic prey. These bands are strongly conserved across taxa spanning four major superphyla, and they are ... More

Equality of Lyapunov and stability exponents for products of isotropic random matricesJan 12 2016We show that Lyapunov exponents and stability exponents are equal in the case of product of $i.i.d$ isotropic(also known as bi-unitarily invariant) random matrices. We also derive aysmptotic distribution of singular values and eigenvalues of these product ... More

Controlled Quantum Teleportation of Superposed Coherent State using GHZ Entangled Coherent StateApr 26 2019Controlled quantum teleportation of superposed coherent states using GHZ entangled 3-mode coherent states is studied. Proposed scheme can be implemented experimentally using linear optical components such as a symmetric lossless beam splitter, two phase-shifters ... More

Classification of Dermoscopy Images using Deep LearningAug 05 2018Skin cancer is one of the most common forms of cancer and its incidence is projected to rise over the next decade. Artificial intelligence is a viable solution to the issue of providing quality care to patients in areas lacking access to trained dermatologists. ... More

Adjacency Algebra of Unitary Cayley GraphJul 10 2017A few properties of unitary Cayley graphs are explored using their eigenvalues. It is shown that the adjacency algebra of a unitary Cayley graph is a coherent algebra. Finally, a class of unitary Cayley graphs that are distance regular are also obtained. ... More

Valuation Networks and Conditional IndependenceMar 06 2013Valuation networks have been proposed as graphical representations of valuation-based systems (VBSs). The VBS framework is able to capture many uncertainty calculi including probability theory, Dempster-Shafer's belief-function theory, Spohn's epistemic ... More

A Fusion Algorithm for Solving Bayesian Decision ProblemsMar 20 2013This paper proposes a new method for solving Bayesian decision problems. The method consists of representing a Bayesian decision problem as a valuation-based system and applying a fusion algorithm for solving it. The fusion algorithm is a hybrid of local ... More

The multiplicative eigenvalue problem and deformed quantum cohomologyOct 11 2013Nov 01 2013We construct deformations of the small quantum cohomology rings of homogeneous spaces G/P, and obtain an irredundant set of inequalities determining the multiplicative eigenvalue problem for the compact form K of G.

Generalized deconvolution procedure for structural modeling of turbulenceJul 28 2017Approximate deconvolution forms a mathematical framework for the structural modeling of turbulence. The sub-filter scale flow quantities are typically recovered by using the Van Cittert iterative procedure. In this paper, however, we put forth a generalized ... More

Data Privacy for a $ρ$-Recoverable FunctionFeb 21 2018Jan 10 2019A user's data is represented by a finite-valued random variable. Given a function of the data, a querier is required to recover, with at least a prescribed probability, the value of the function based on a query response provided by the user. The user ... More

Perfect Omniscience, Perfect Secrecy and Steiner Tree PackingAug 05 2010We consider perfect secret key generation for a ``pairwise independent network'' model in which every pair of terminals share a random binary string, with the strings shared by distinct terminal pairs being mutually independent. The terminals are then ... More

How Many Queries Will Resolve Common Randomness?May 07 2013A set of m terminals, observing correlated signals, communicate interactively to generate common randomness for a given subset of them. Knowing only the communication, how many direct queries of the value of the common randomness will resolve it? A general ... More

Infinite-message Interactive Function Computation in Collocated NetworksJan 11 2010Jun 01 2010An interactive function computation problem in a collocated network is studied in a distributed block source coding framework. With the goal of computing a desired function at the sink, the source nodes exchange messages through a sequence of error-free ... More

Photon Structure Functions: Target Photon Mass Effects and QCD CorrectionsNov 08 1994We present a systematic analysis of the processes $e^+ ~e^- \rightarrow e^+ ~e^- X$ to study the polarised and unpolarised photon structure functions. The effect of target photon mass, which manifests itself as new singly polarised structure functions ... More

The Local Dimension: a method to quantify the Cosmic WebDec 09 2008It is now well accepted that the galaxies are distributed in filaments, sheets and clusters all of which form an interconnected network known as the Cosmic Web. It is a big challenge to quantify the shapes of the interconnected structural elements that ... More

An Improved Interactive Streaming Algorithm for the Distinct Elements ProblemFeb 27 2014The exact computation of the number of distinct elements (frequency moment $F_0$) is a fundamental problem in the study of data streaming algorithms. We denote the length of the stream by $n$ where each symbol is drawn from a universe of size $m$. While ... More

Eigenvalue problem and a new product in cohomology of flag varietiesJul 02 2004Jul 02 2004Let G be a connected semisimple complex algebraic group and let P be a parabolic subgroup. In this paper we define a new (commutative and associative) product on the cohomology of the homogenous spaces G/P and use this to give a more efficient solution ... More

The Secret Key-Private Key Capacity Region for Three TerminalsNov 12 2005We consider a model for secrecy generation, with three terminals, by means of public interterminal communication, and examine the problem of characterizing all the rates at which all three terminals can generate a ``secret key,'' and -- simultaneously ... More

Branching laws on the metaplectic cover of ${\rm GL}_{2}$Jun 20 2014Representation theory of $p$-adic groups naturally comes in the study of automorphic forms and one way to understand representations of a group is by restricting to its nice subgroups. D. Prasad studied the restriction for pairs $({\rm GL}_{2}(E), {\rm ... More

A question on splitting of metaplectic coversJun 16 2014Let $E/F$ be a quadratic extension of a non-Archimedian local field. Splitting of the 2-fold metaplectic cover of ${\rm Sp}_{2n}(F)$ when restricted to various subgroups of ${\rm Sp}_{2n}(F)$ plays an important role in application of the Weil representation ... More

A note on lower nil M-Armendariz ringsNov 13 2016May 08 2018In this article, we prove some results for lower nil M-Armendariz ring. Let M be a strictly totally ordered monoid and I be a semicommutative ideal of R. If R/I is a lower nil M-Armendariz ring, then R is lower nil M-Armendariz. Similarly, for above M, ... More

Lyapunov exponents and eigenvalues of products of random matricesJun 24 2016Let $X_1,X_2, \ldots $ be a sequence of $i.i.d$ real (complex) $d \times d $ invertible random matrices with common distribution $\mu$ and $\sigma_1(n), \sigma_2(n), \ldots , \sigma_d(n)$ be the singular values, $\lambda_1(n), \lambda_2(n), \ldots , \lambda_d(n)$ ... More

Few Non-derogatory Directed Graphs from Directed CyclesJul 07 2017We constructed a few non-derogatory digraphs by adding arcs to a directed cycle and computed their characteristic polynomials and exponents.

Reconstructing Faces from fMRI Patterns using Deep Generative Neural NetworksOct 09 2018Feb 17 2019While objects from different categories can be reliably decoded from fMRI brain response patterns, it has proved more difficult to distinguish visually similar inputs, such as different instances of the same category. Here, we apply a recently developed ... More

First Order Phase Transitions in Neutron star Matter: Droplets and Coherent Neutrino ScatteringSep 17 1999A first order phase transition at high baryon density implies that a mixed phase can occupy a significant region of the interior of a neutron star. In this article we investigate the effect of a droplet phase on neutrino transport inside the core. Two ... More

Almost Armendariz RingsFeb 05 2015In this paper, we introduce the notion of almost Armendariz ring which is the generalization of Armendariz ring and discuss some of its properties. We prove that a ring R is almost Armendariz if and only if n X n upper triangular matrix ring T_{n}(R) ... More

Quantum Alternation: Prospects and ProblemsNov 05 2015We propose a notion of quantum control in a quantum programming language which permits the superposition of finitely many quantum operations without performing a measurement. This notion takes the form of a conditional construct similar to the IF statement ... More

The Pervasive Role of the Nuclear Symmetry Energy in the Structure and Evolution of Neutron StarsDec 10 2008The multifaceted role of the density dependent nuclear symmetry energy in the nuclear astrophysics involving neutron stars is highlighted. Efforts toward a model independent determination of the dense matter equation state through a deconstruction of ... More

On the existence and characterization of the maxent distribution under general moment inequality constraintsJun 05 2005A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on the minimum ... More

Simultaneous polarization squeezing in polarized N photon state and diminution on a squeezing operationMar 28 2016We study polarization squeezing of a pure photon number state which is obviously polarized but the mere change in the basis of polarization leads to simultaneous polarization squeezing in all the components of Stokes operator vector except those falling ... More

Alteration in Non-Classicality of Light on Passing Through a Linear Polarization Beam SplitterMar 28 2016Apr 22 2016We observe the polarization squeezing in the mixture of a two mode squeezed vacuum and a simple coherent light through a linear polarization beam splitter. Squeezed vacuum not being squeezed in polarization, generates polarization squeezed light when ... More

A novel quantum grid search algorithm and its applicationMar 18 2019In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items. In one trial ... More

An Auxiliary 'Differential Measure' for $SU(3)$May 27 1996May 29 1996A 'differential measure' is used to cast our calculus for the group $SU(3)$ into a form similar to Schwinger's boson operator calculus for the group $SU(2)$. It is then applied to compute (i) the inner product between the basis states and (ii) an algebraic ... More

Curing the acausal behavior of the sound velocity in an excluded volume hadron resonance gas modelOct 15 2015We improve the excluded volume hadron resonances gas model (EHRG) to cure the acausal behavior of the sound velocity which is typical of excluded volume models. We achieve this by including temperature (T) and density ({\mu}) dependent hadron masses in ... More

Interaction Strictly Improves the Wyner-Ziv Rate-distortion functionJan 15 2010Jun 01 2010In 1985 Kaspi provided a single-letter characterization of the sum-rate-distortion function for a two-way lossy source coding problem in which two terminals send multiple messages back and forth with the goal of reproducing each other's sources. Yet, ... More

Neutral Triple Vector Boson Production in Randall-Sundrum Model at the LHCJul 31 2015Nov 04 2015In this paper, triple neutral electroweak gauge boson production processes, viz. \gamma\gamma\gamma, \gamma\gamma Z, \gamma ZZ and ZZZ productions merged to 1-jet have been studied at the leading order in QCD in the context of Randall-Sundrum model at ... More

Asymptotic formula for sum-free sets in abelian groupsJul 13 2005Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. Let SF(G) denotes the set of all sum-free subets of $G$ and $\sigma(G)$ denotes the number ... More

Turning Bitcoins into the Best-coinsDec 23 2014In this paper we discuss Bitcoin, the leader among the existing cryptocurrencies, to analyse its trends, success factors, current challenges and probable solutions to make it even better. In the introduction section, we discuss the history and working ... More

Secret Key and Private Key Constructions for Simple Multiterminal Source ModelsAug 12 2010We propose an approach for constructing secret and private keys based on the long-known Slepian-Wolf code, due to Wyner, for correlated sources connected by a virtual additive noise channel. Our work is motivated by results of Csisz\'ar and Narayan which ... More

Secret Key and Private Key Constructions for Simple Multiterminal Source ModelsNov 13 2005This work is motivated by recent results of Csiszar and Narayan (IEEE Trans. on Inform. Theory, Dec. 2004), which highlight innate connections between secrecy generation by multiple terminals and multiterminal Slepian-Wolf near-lossless data compression ... More

Communication Cost for Updating Linear Functions when Message Updates are Sparse: Connections to Maximally Recoverable CodesMay 03 2016Aug 05 2018We consider a communication problem in which an update of the source message needs to be conveyed to one or more distant receivers that are interested in maintaining specific linear functions of the source message. The setting is one in which the updates ... More

Skew Generalized Cyclic Code over $ R[x_1;σ_1,δ_1][x_2;σ_2,δ_2]$Jul 13 2019Sep 17 2019This article studies two dimensional skew generalized cyclic (SGC) codes, i.e., SGC codes over the ring $ R[x_1;\sigma_1,\delta_1][x_2;\sigma_2,\delta_2]$, where $R$ is a ring with unity. Here, we discuss the structural properties of SGC codes, and a ... More

Extension of Almost Armendariz RingsJul 10 2017A ring $R$ is said to be an almost Armendariz ring if whenever product of two polynomials in $R[x]$ is zero, then product of their coefficients are in $N_{*}(R)$. In this article, for an endomorphism $\alpha$ on $R$, we define an $\alpha$-almost Armendariz ... More

Adjacency Matrix and Energy of the Line Graph of $Γ(\mathbb{Z}_n)$Jun 23 2018Let $\Gamma(\mathbb{Z}_n)$ be the zero divisor graph of the commutative ring $\mathbb{Z}_n$ and $L(\Gamma(\mathbb{Z}_n))$ be the line graph of $\Gamma(\mathbb{Z}_n)$. In this paper, we discuss about the neighborhood of a vertex, the neighborhood number ... More

Developing ZnO Nanoparticle embedded Antimicrobial Starch Biofilm for Food PackagingSep 11 2019Starch based bio-films act as biodegradable packaging material for coating and wrapping food products, which is alternate to the synthetic polymer. Nanoparticles (NPs) are also alternative to antibiotics to target pathogens. Through interaction of nanoparticles ... More

A New Pruning Method for Solving Decision Trees and Game TreesFeb 20 2013The main goal of this paper is to describe a new pruning method for solving decision trees and game trees. The pruning method for decision trees suggests a slight variant of decision trees that we call scenario trees. In scenario trees, we do not need ... More

Triviality properties of principal bundles on singular curvesSep 21 2015Feb 09 2016We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial, provided the order of $\pi_1$ of the group is invertible in the ground field, or if the curve has semi-normal singularities. ... More

Armendariz Property on Weak IFP RingSep 04 2016In this work, we study about the ideals of a ring by introducing a new concept which combines the concept of Armendariz ring and weakly semicommutative (weakly IFP) properties of rings, called weak ideal Armendariz ring. It is a generalisation of ideal ... More

Quantum Teleportation of Single Qubit Mixed Information State with Werner-Like State as ResourceMay 18 2013In this paper we extend our recent results for quantum teleportation of single qubit pure information state using non-maximally entangled pure state resource [Quantum Inf Process, 11 (2012) 1251] to the case of a general mixed information state and mixed ... More

Invariant compact finite difference schemesJan 03 2019In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In this method, ... More

Enforcing causality in nonrelativistic equations of state at finite temperatureFeb 22 2017We present a thermodynamically consistent method by which equations of state based on nonrelativistic potential models can be modified so that they respect causality at high densities, both at zero and finite temperature (entropy). We illustrate the application ... More

Premature Unilateral Ripening in Euonymus alatus: Two Hits Leave(s) a Red FaceOct 12 2017An empirical 2-hit hypothesis is presented to account for premature and unilateral ripening in Euonymus alatus.

Evaluating the Evidence of Multipolar Surface Magnetic Field in PSR J0108$-$1431Aug 17 2019PSR J0108$-$1431 is an old pulsar where the X-ray emission is expected to have a thermal component from the polar cap and a non-thermal component from the magnetosphere. Although the phase-integrated spectra are fit best with a single non-thermal component ... More

Sum-free set in finite abelian groupsFeb 17 2005Dec 06 2005Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. In this paper we shall characterise the largest possible sum-free subsets of G in case the ... More

Trapping/Pinning of colloidal microspheres over glass substrate using surface featuresOct 03 2017Suspensions of micro and nano particles made of Polystyrene, Poly(methyl methacrylate), Silicon dioxide etc. have been a standard model system to understand colloidal physics. . These systems have proved useful insights into phenomena such as self-assembly. ... More

Jordan left {g, h}-derivations over some algebrasMar 21 2018In this article, left {g, h}-derivation and Jordan left {g, h}-derivation on algebras are introduced. It is shown that there is no Jordan left {g, h}-derivation over $\mathcal{M}_n(C)$ and $\mathbb{H}_{\mathbb{R}}$, for g not equal to h. Examples are ... More

3k-4 theorem for ordered groupsFeb 13 2017Recently, G. A. Freiman, M. Herzog, P. Longobardi, M. Maj proved two `structure theorems' for ordered groups \cite{FHLM}. We give elementary proof of these two theorems.

Distribution of prime ideals of higher residue degree across ideal classes in the class groupsJan 29 2017In this article we investigate the distribution of prime ideals of residue degree bigger than one across the ideal classes in the class group of a number field $L$. A criterion for the class group of $L$ being generated by the classes of prime ideals ... More

Remarks on Jordan derivations over matrix algebrasMar 21 2018Let C be a commutative ring with unity. In this article, we show that every Jordan derivation over an upper triangular matrix algebra T_n(C) is an inner derivation. Further, we extend the result for Jordan derivation on full matrix algebra M_n(C).

Trajectory optimization using quantum computingJan 14 2019Feb 13 2019We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization of the optimization ... More

Planar Algebra of the Subgroup-SubfactorJun 11 2008We give an identification between the planar algebra of the subgroup-subfactor $R \rtimes H \subset R \rtimes G$ and the $G$-invariant planar subalgebra of the planar algebra of the bipartite graph $\star_n$, where $n = [G : H]$. The crucial step in this ... More

Extremal rays in the Hermitian eigenvalue problem for arbitrary typesMar 09 2018Mar 28 2018The Hermitian eigenvalue problem asks for the possible eigenvalues of a sum of Hermitian matrices given the eigenvalues of the summands. This is a problem about the Lie algebra of the maximal compact subgroup of $G=\operatorname{SL}(n)$ . There is a polyhedral ... More

Universal dynamics of dilute and semidilute solutions of flexible linear polymersJan 21 2019Mar 01 2019Experimental observations and computer simulations have recently revealed universal aspects of polymer solution behaviour that were previously unknown. This progress has been made possible due to developments in experimental methodologies and simulation ... More

Rough differential equations with power type nonlinearitiesAug 15 2017In this note we consider differential equations driven by a signal $x$ which is $\gamma$-H\"older with $\gamma>1/3$, and is assumed to possess a lift as a rough path. Our main point is to obtain existence of solutions when the coefficients of the equation ... More

Derivations of the Lie algebra of strictly block upper triangular matricesMar 25 2016Let ${\mathcal N}$ be the Lie algebra of all $n\times n$ strictly block upper triangular matrices over a field ${\mathbb F}$ relative to a given partition. In this paper, we give an explicit description of all derivations of ${\mathcal N}$.

Benefit of Delay on the Diversity-Multiplexing Tradeoffs of MIMO Channels with Partial CSIJul 14 2007This paper re-examines the well-known fundamental tradeoffs between rate and reliability for the multi-antenna, block Rayleigh fading channel in the high signal to noise ratio (SNR) regime when (i) the transmitter has access to (noiseless) one bit per ... More

Matroids, motives and conjecture of KontsevichDec 20 2000Let G be a finite connected graph. The Kirchhoff polynomial of G is a certain homogeneous polynomial whose degree is equal to the first betti number of G. These polynomials appear in the study of electrical circuits and in the evaluation of Feynman amplitudes. ... More

Armendariz ring with weakly semicommutativitySep 04 2016Jan 20 2018In this article, we introduce the weak ideal-Armendariz ring which combines Armendariz ring and weakly semicommutative properties of rings. In fact, it is a generalisation of an ideal-Armendariz ring. We investigate some properties of weak ideal Armendariz ... More

A novel quantum grid search algorithm and its applicationMar 18 2019Sep 09 2019In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items. In one trial ... More

Triviality properties of principal bundles on singular curves-IIJan 15 2018For $G$ a split semi-simple group scheme and $P$ a principal $G$-bundle on a relative curve $X\to S$, we study a natural obstruction for the triviality of $P$ on the complement of a relatively ample Cartier divisor $D \subset X$. We show, by constructing ... More

On finite generation of the section ring of the determinant of cohomology line bundleJun 28 2016Jul 26 2016For $C$ a stable curve of arithmetic genus $g\ge 2$, and $\mathcal{D}$ the determinant of cohomology line bundle on $\operatorname{Bun}_{\operatorname{SL}(r)}(C)$, we show the section ring for the pair $(\operatorname{Bun}_{\operatorname{SL}(r)}(C), \mathcal{D})$ ... More

Divisor graph of complement of Gamma(R)Nov 03 2017Let overline{\Gamma(R)} be the complement of zero divisor graph of a finite commutative ring R. In this article, we have provided the answer of the question (ii) raised by Osba and Alkam in their paper and prove that overline{\Gamma(R)} is a divisor graph ... More

Pancyclic zero divisor graph over the ring $\mathbb{Z}_n[i]$Jun 21 2018Let $\Gamma(\mathbb{Z}_n[i])$ be the zero divisor graph over the ring $\mathbb{Z}_n[i]$. In this article, we study pancyclic properties of $\Gamma(\mathbb{Z}_n[i])$ and $\overline{\Gamma(\mathbb{Z}_n[i])}$ for different $n$. Also, we prove some results ... More

Color-Neutral Superconducting Quark MatterMay 18 2002Sep 29 2002We investigate the consequences of enforcing local color neutrality on the color superconducting phases of quark matter by utilizing the Nambu-Jona-Lasinio model supplemented by diquark and the t'Hooft six-fermion interactions. In neutrino free matter ... More