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Visible Nonlinear PhotonicsJul 10 2019Over the past decade, remarkable advances have been realized in chip-based nonlinear photonic devices for classical and quantum applications in the near- and mid-infrared regimes. However, few demonstrations have been realized in the visible and near-visible ... More

Modified Apriori Approach for Evade Network Intrusion Detection SystemNov 25 2014Intrusion Detection System or IDS is a software or hardware tool that repeatedly scans and monitors events that took place in a computer or a network. A set of rules are used by Signature based Network Intrusion Detection Systems or NIDS to detect hostile ... More

Frequency Multiplexing for Quasi-Deterministic Heralded Single-Photon SourcesJun 30 2017Sep 01 2017Single-photon sources based on optical parametric processes have been used extensively for quantum information applications due to their flexibility, room-temperature operation and potential for photonic integration. However, the intrinsically probabilistic ... More

The north-south asymmetry of soft X-ray flare index during solar cycles 21, 22 and 23Sep 26 2006In this paper the N-S asymmetry of the soft X-ray flare index during the solar cycles 21, 22 and 23 has been analyzed. The results show the existence of a real N-S asymmetry which is strengthened during solar minimum. The slope of the regression lines ... More

Intermediate-term periodicities in soft X-ray flare index during solar cycles 21, 22 and 23Feb 13 2006Sep 26 2006We have analyzed the intermediate term periodicities in soft X-ray flare index ($FI_{SXR}$) during solar cycles 21, 22 and 23. Power spectral analysis of daily $FI_{SXR}$ reveals a significant period of 161 days in cycle 21 which is absent during cycle ... More

Minimizing Area and Energy of Deep Learning Hardware Design Using Collective Low Precision and Structured CompressionApr 19 2018Deep learning algorithms have shown tremendous success in many recognition tasks; however, these algorithms typically include a deep neural network (DNN) structure and a large number of parameters, which makes it challenging to implement them on power/area-constrained ... More

Contextually proximate approach to develop smart user interfaceAug 17 2015Researchers and experts are taking efforts in delivering an optimal user experience from a long time. Computer interfaces are being developed to keep user 'in the flow' as well as for making users more connected to the real world wile using virtual environment. ... More

A detailed balanced reaction network is sufficient but not necessary for its Markov chain to be detailed balancedDec 15 2013Dec 26 2014Certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics have the property of reaction network detailed balance (RNDB) which is achieved by imposing network-related constraints on the reaction ... More

Complete characterization by multistationarity of fully open networks with one non-flow reactionJul 25 2012Jan 17 2013This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or irreversible) ... More

Stress due to Electric and Magnetic fields in Viscoelastic FluidsMay 18 2013A clear understanding of body force densities due to external electromagnetic fields is necessary to study flow and deformation of materials exposed to the fields. In this paper, we derive an expression for stress in continua with viscous and elastic ... More

Ordinarity of configuration spaces and of wonderful compactificationsMay 17 2010We prove the following: (1) if $X$ is ordinary, the Fulton-MacPherson configuration space $X[n]$ is ordinary for all $n$; (2) the moduli of stable $n$-pointed curves of genus zero is ordinary. (3) More generally we show that a wonderful compactification ... More

A method for construction of rational points over elliptic curvesMay 21 2017Jan 18 2018I provide a systematic construction of points (defined over number fields) on Legendre elliptic curves over $\mathbb{Q}$: for any odd integer $n\geq 3$ my method constructs $n$ points on the Legendre curve and I show that rank of the subgroup of the Mordell-Weil ... More

Crystalline aspects of geography of low dimensional varieties I: NumerologyMar 25 2014Nov 06 2018This is a modest attempt to study, in a systematic manner, the structure of low dimensional varieties in positive characteristics using $p$-adic invariants. The main objects of interest in this paper are surfaces and threefolds. It is known that there ... More

The t-motivic mixed Carlitz zeta category and Carlitz-Thakur multi-zeta valuesJun 11 2013Aug 06 2013We construct the t-motivic mixed Carlitz zeta category over $\F_q(t)$ and show that it contains all the (mixed) t-motives with Carlitz-Thakur multi-zeta values as periods constructed by Anderson and Thakur. Our construction is canonical and our category ... More

From Citation count to Argumentation count: a new metric to indicate the usefulness of an articleJun 26 2014Citation count is a quantifiable measure to indicate the number of times an article is cited by other articles. It is believed that if an article is cited often then it must be an important or influential article; however, there is no guarantee that the ... More

Remarks on methods of Fontaine and FaltingsJan 20 1999In this note we prove the non existence of certain irreducible two dimensional representations of the the absolute Galois group. Such results are predicted by Serre's conjecture and we use Fontaine's methods to verify these predictions in a small number ... More

Remarks on the Fourier coefficients of modular formsMay 17 2010We consider a variant of a question of N. Koblitz. For an elliptic curve $E/\Q$ which is not $\Q$-isogenous to an elliptic curve with torsion, Koblitz has conjectured that there exists infinitely many primes $p$ such that $N_p(E)=#E(\F_p)=p+1-a_p(E)$ ... More

A p-adic proof of Hodge symmetry for threefoldsOct 05 2001In this note we give a p-adic proof of Hodge symmetry for smooth, projective threefolds over complex numbers.

A family of étale coverings of the affine lineSep 02 1993In the note we construct a family of \'etale coverings of the affine line. More specifically, let $F$ be a finite field of characteristic $p$ and suppose that the cardinality of $F$ is at least 4. Let $A = F[T]$ be the polynomial ring in one variable ... More

An Overview of Geometric Asymptotic Analysis of Continuous and Discrete Painlevé EquationsNov 25 2013The classical Painlev\'e equations are so well known that it may come as a surprise to learn that the asymptotic description of its solutions remains incomplete. The problem lies mainly with the description of families of solutions in the complex domain. ... More

Methods for constructing elliptic and hyperelliptic curves with rational pointsNov 16 2017Jan 18 2018I provide methods of constructing elliptic and hyperelliptic curves over global fields with interesting rational points over the given fields or over large field extensions. I also provide a elliptic curves defined over any given number field equipped ... More

Crystalline aspects of geography of low dimensional varieties I: NumerologyMar 25 2014This is a modest attempt to study, in a systematic manner, the structure of low dimensional varieties in positive characteristics using $p$-adic invariants. The main objects of interest in this paper are surfaces and threefolds. It is known that there ... More

Time Series Analysis and Forecasting of the US Housing Starts using Econometric and Machine Learning ModelMay 20 2019In this research paper, I have performed time series analysis and forecasted the monthly value of housing starts for the year 2019 using several econometric methods - ARIMA(X), VARX, (G)ARCH and machine learning algorithms - artificial neural networks, ... More

Some remarks on Hodge symmetryFeb 17 2014I make some remarks on Hodge symmetry, and prove for instance that if $k$ is a perfect field of characteristic $p>0$ and $X/k$ smooth, proper and Hodge-Witt scheme, and Hodge de Rham sequence of $X$ degenerates at $E_1$ and $X$ has torsion-free crystalline ... More

A question about Belyi's TheoremNov 06 2018I discuss a natural version of Belyi's Theorem over $\fq(T)$ and prove that the situation I describe is unique and rigid for $q\geq5$ (in the sense described below).

A method for construction of rational points over elliptic curves II: Points over solvable extensionsJan 18 2018I provide a systematic construction of points, defined over finite radical extensions, on any Legendre curve over any field of characteristic not equal two. This includes as special case Douglas Ulmer's construction of rational points over a rational ... More

Quicksilver Solutions of a q-difference first Painlevé equationJun 21 2013Jul 07 2014In this paper, we present new, unstable solutions, which we call quicksilver solutions, of a $q$-difference Painlev\'e equation in the limit as the independent variable approaches infinity. The specific equation we consider in this paper is a discrete ... More

Direct "Delay" Reductions of the Toda EquationOct 30 2008A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes ... More

Learning in Competitive Network with Haeusslers Equation adapted using FIREFLY algorithmJul 09 2019Many of the competitive neural network consists of spatially arranged neurons. The weigh matrix that connects cells represents local excitation and long-range inhibition. They are known as soft-winner-take-all networks and shown to exhibit desirable information-processing. ... More

The degree of the dormant operatic locusNov 18 2013Mar 30 2016Let $X$ be a smooth, projective curve of genus $g\geq 2$ over an algebraically closed field of characteristic $p>0$. I provide a conjectural formula for the degree of the scheme of dormant ${\rm PGL}(r)$-opers on $X$ where $r\geq 2$ (I assume that $p$ ... More

HAWC High Energy Upgrade with a Sparse ArrayJan 23 2017The High Altitude Water Cherenkov (HAWC) gamma-ray observatory has been fully operational since March 2015. To improve its sensitivity at the highest energies, it is being upgraded with an additional sparse array called outrigger array. We will discuss ... More

Exotic torsion, Frobenius splitting and the slope spectral sequenceOct 05 2001In this note we show that Frobenius split smooth, projective threefolds are Hodge-Witt (using a criterion for the degeneration of the slope spectral sequence of smooth projective threefolds which we prove), and that smooth, projective Frobenius split ... More

Musings on $\Q(1/4)$: Arithmetic spin structures on elliptic curvesMay 17 2010We introduce and study arithmetic spin structures on elliptic curves. We show that there is a unique isogeny class of elliptic curves over $\F_{p^2}$ which carries a unique arithmetic spin structure and provides a geometric object of weight 1/2 in the ... More

Rayleigh-Taylor Instability in Viscoelastic FluidsAug 03 2013In this paper I analyze the onset of Rayleigh-Taylor instability between two linear viscoelastic fluids assuming that the perturbations at the interface are small. In the first half, the paper analyzes a stratified viscoelastic fluid in which I prove ... More

Order of magnitude time-reversible Markov chains and characterization of clustering processesOct 25 2011We introduce the notion of order of magnitude reversibility (OM-reversibility) in Markov chains that are parametrized by a positive parameter $\ep$. OM-reversibility is a weaker condition than reversibility, and requires only the knowledge of order of ... More

On the equation $N_{p_1}(E)\cdot N_{p_2}(E)\cdots N_{p_k}(E)=n$Nov 16 2017For a given elliptic curve $E/\mathbb{Q}$, set $N_p(E)$ to be the number of points on $E$ modulo $p$ for a prime of good reduction for $E$. Given integer $n$, let $G_k(E,n)$ be the number of $k$-tuples of pairwise distinct primes $p_1,\ldots,p_k$ of good ... More

On varieties with trivial tangent bundleMar 30 2016I prove a crystalline characterization of abelian varieties in characteristic $p>0$ amongst the class of varieties with trivial tangent bundle. I show using my characterization that a smooth, projective, ordinary variety with trivial tangent bundle is ... More

Ordinary reductions of abelian varietiesMar 30 2016I show that a conjecture of Joshi-Rajan on primes of Hodge-Witt reduction and in particular a conjecture of Jean-Pierre Serre on primes of good, ordinary reduction for an abelian variety over a number field follows from a certain conjecture on Galois ... More

On the Grothendieck ring of varieties in positive characteristicNov 06 2018Let $k$ be an algebraically closed field of characteristic $p>0$. I prove that the ring of smooth, complete $k$-varieties and Bittner relations contains zero divisors if $p>13$ or $p=11$. In particular it follows, under the same hypothesis, that the isomorphism ... More

A Particle In Cell code development for high current ion beam transport and plasma simulationsJun 20 2016A simulation package employing a Particle in Cell (PIC) method is developed to study the high current beam transport and the dynamics of plasmas. This package includes subroutines those are suited for various planned projects at University of Frankfurt. ... More

The Second Painlevé Equation in the Large-Parameter Limit I: Local Asymptotic AnalysisOct 24 1997In this paper, we find all possible asymptotic behaviours of the solutions of the second Painlev\'e equation $y''=2y^3+xy +\alpha$ as the parameter $\alpha\to\infty$ in the local region $x\ll\alpha^{2/3}$. We prove that these are asymptotic behaviours ... More

Mochizuki's anabelian variation of ring structures and formal groupsJun 17 2019I show that there is a universal formal group (over a suitable (non-zero) ring) which is equipped with an action of the multiplicative monoid $\mathcal{O}^\triangleright$ of non-zero elements of the ring of integers of a $p$-adic field. Lubin-Tate formal ... More

On determinantal equations for curves and Frobenius split hypersurfacesJan 10 2019I consider the problem of existence of intrinsic determinantal equations for plane projective curves and hypersurfaces in projective space and prove that in many cases of interest there exist intrinsic determinantal equations. In particular I prove (1) ... More

A remark on Ulrich and ACM bundlesNov 16 2017Jan 10 2019I show that on any smooth, projective ordinary curve of genus at least two and a projective embedding, there is a natural example of a stable Ulrich bundle for this embedding: namely the sheaf $B^1_X$ of locally exact differentials twisted by $\O_X(1)$ ... More

Working women and caste in India: A study of social disadvantage using feature attributionApr 27 2019Women belonging to the socially disadvantaged caste-groups in India have historically been engaged in labour-intensive, blue-collar work. We study whether there has been any change in the ability to predict a woman's work-status and work-type based on ... More

Population I Cepheids and star formation history of the Large Magellanic CloudOct 08 2013Nov 08 2013In this paper we study the Cepheids distribution in the Large Magellanic Cloud (LMC) as a function of their ages using data from the OGLE III photometric catalogue. To determine age of the Pop I Cepheids, we derived a period-age (PA) relationship using ... More

Asteroseismology of Pulsating StarsOct 23 2015The success of helioseismology is due to its capability of measuring p-mode oscillations in the Sun. This allows us to extract informations on the internal structure and rotation of the Sun from the surface to the core. Similarly, asteroseismology is ... More

Dissipation assisted long-range order in coupled qubitsJun 13 2016We theoretically investigate a possibility to establish long-range order in one-dimensional chains of qubits. We combine a reservoir engineering strategy with coherent dynamics to generate multi-qubit entangled states. We find that an interplay between ... More

Stability and locally exact differentials on a curveFeb 23 2004We show that the locally free sheaf of locally exact differentials on a smooth projective curve of genus at least two over an algebraically closed field k of characteristic p is a stable vector bundle. This answers a question of Raynaud.

A General Noether-Lefschetz Theorem and applicationsMay 03 1993May 17 1993In this paper we generalize the classical Noether-Lefschetz Theorem to arbitrary smooth projective threefolds. Let $X$ be a smooth projective threefold over complex numbers, $L$ a very ample line bundle on $X$. Then we prove that there is a positive integer ... More

On Primes of Ordinary and Hodge-Witt ReductionMar 30 2016Jean-Pierre Serre has conjectured, in the context of abelian varieties, that there are infinitely primes of good ordinary reduction for a smooth, projective variety over a number field. We consider this conjecture and its natural variants. In particular ... More

On the construction of Weakly Ulrich bundlesJan 10 2019I provide a construction of intrinsic weakly Ulrich bundles of large rank on any smooth complete surface in ${\bf P}^3$ over fields of characteristic $p>0$ and also for some classes of surfaces of general type in ${\bf P}^n$. I also construct intrinsic ... More

Can Sound Waves be Slowed?Jul 15 2018Jul 21 2018Dielectric fluids experience a striction force in the presence of an external electric field. Although the striction force on the entire body of the fluid is usually zero, it does contribute to its deformations. In this paper, I show that the speed of ... More

Plane Poiseuille flow through a porous medium - an analytical solutionApr 27 2013Jul 15 2016This paper develops a closed-form, analytical expression for the Darcy velocity of a Newtonian fluid flowing through a channel filled with a porous medium, bound by rigid walls and driven by a constant pressure gradient. We express the Darcy velocity ... More

A Quantitative Study of the Impact of Social Media Reviews on Brand PerceptionOct 23 2017This thesis can be categorized under the Influencer Marketing industry with respect to social media initiatives. Influencer marketing is a modern tactic used by brands to enhance their visibility to their target audience by using the services of influential ... More

Combinational neural network using Gabor filters for the classification of handwritten digitsSep 18 2017A classification algorithm that combines the components of k-nearest neighbours and multilayer neural networks has been designed and tested. With this method the computational time required for training the dataset has been reduced substancially. Gabor ... More

A Local Asymptotic Analysis of the First Discrete Painlevé Equation as the Discrete Independent Variable Approaches InfinityJul 25 1996The first discrete Painlev\'e equation (dPI), which appears in a model of quantum gravity, is an integrable nonlinear nonautonomous difference equation which yields the well known first Painlev\'e equation (PI) in a continuum limit. The asymptotic study ... More

The Origin of Non-chaotic Behavior in Identically Driven SystemsMay 12 1995Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show that the origin ... More

Population I Cepheids and understanding star formation history of the Small Magellanic CloudOct 23 2015In this paper, we study the age and spatial distributions of Cepheids in the Small Magellanic Cloud (SMC) as a function of their ages using the data from the OGLE III photometric catalogue. A period-age (PA) relation derived for the Classical Cepheids ... More

Photometric studies of two W UMa type variables in the field of distant open cluster NGC6866Oct 23 2015Oct 17 2016We present photometric analysis of the two W UMa type binaries identified in the field of distant open star cluster NGC6866. Although these systems, namely ID487 and ID494, were reported in the Joshi et al. (2012), but a detailed study of these stars ... More

Modeling the Spectral Energy Distribution and Variability of 3C 66A during the WEBT campaign of 2003 -- 2004Apr 03 2007The BL Lac object 3C 66A was observed in an extensive multiwavelength monitoring campaign from July 2003 till April 2004. The spectral energy distribution (SED) was measured over the entire electromagnetic spectrum, with flux measurements from radio to ... More

Gravitational Collapse: The Story so farJun 29 2000An outstanding problem in gravitation theory and relativistic astrophysics today is to understand the final outcome of an endless gravitational collapse. Such a continual collapse would take place when stars more massive than few times the mass of the ... More

Signal Processing in the MicroBooNE LArTPCNov 01 2015The MicroBooNE experiment is designed to observe interactions of neutrinos with a Liquid Argon Time Projection Chamber (LArTPC) detector from the on-axis Booster Neutrino Beam (BNB) and off-axis Neutrinos at the Main Injector (NuMI) beam at Fermi National ... More

Stellar Variability with Photometric and Spectroscopic Analysis of five Am Field StarsApr 06 2019Apr 09 2019The spectroscopic and photometric analysis of sample Am stars are carried out to determine the stellar characteristics of each studied star. The CCD photometric analysis of HD 98851 and HD 207561 show clear evidence of pulsation variability of 1.55 hr ... More

Adaptive Communication Strategies to Achieve the Best Error-Runtime Trade-off in Local-Update SGDOct 19 2018Mar 07 2019Large-scale machine learning training, in particular distributed stochastic gradient descent, needs to be robust to inherent system variability such as node straggling and random communication delays. This work considers a distributed training framework ... More

Cross-Domain Transfer in Reinforcement Learning using Target ApprenticeJan 22 2018In this paper, we present a new approach to Transfer Learning (TL) in Reinforcement Learning (RL) for cross-domain tasks. Many of the available techniques approach the transfer architecture as a method of speeding up the target task learning. We propose ... More

TeV Scale Cross-Sections and the Pomeranchuck SingularityAug 02 2010We have investigated the detailed structure of $l$-plane singularities of scattering amplitude saturating the Froissart bound. A self-consistent analysis of these singularities provides us secondary terms in the Froissart bound. These secondary terms ... More

Hate Speech Detection from Code-mixed Hindi-English Tweets Using Deep Learning ModelsNov 13 2018This paper reports an increment to the state-of-the-art in hate speech detection for English-Hindi code-mixed tweets. We compare three typical deep learning models using domain-specific embeddings. On experimenting with a benchmark dataset of English-Hindi ... More

Thermal decoherence in a strongly correlated Bose liquidDec 12 2017We compute the single particle spectral function of a Bose liquid on a lattice, at integer filling, close to the superfluid-Mott transition. We use a `static path approximation' that retains all the classical thermal fluctuations in the problem, and a ... More

Hitchin-Mochizuki morphism, Opers and Frobenius-destabilized vector bundles over curvesDec 18 2009Jan 15 2015Let X be a smooth projective curve of genus g \textgreater{}1 defined over an algebraically closed field k of characteristic p \textgreater{}0. For p sufficiently large (explicitly given in terms of r,g) we construct an atlas for the locus of all Frobenius-destabilized ... More

A short proof of existence of non-inner automorphism of order $p$ for finite $p$-group of class $2$ for odd prime $p$Jan 11 2019In this note we give a short proof of the existence of a non-inner automorphism of order $p$ of finite $p$-group of class $2$ which fixes the frattini subgroup element wise for $p$ odd. The original proof is due to H. Liebeck.

Consistency around a cuboctahedronJun 16 2019In this paper, we describe new results arising from a search for lattice equations that are consistently placed on cuboctahedra. These results extend the well-known ABS equations that are consistent on cubes. Our search was motivated by $\tau$-functions ... More

Global Asymptotics of the Second Painlevé Equation in Okamoto's SpaceDec 08 2012We study the solutions of the second Painlev\'e equation in the space of initial conditions first constructed by Okamoto, in the limit as the independent variable, x, goes to infinity. Simultaneously, we study solutions of the related equation known as ... More

Asymptotic behaviour of the fifth Painlevé transcendents in the space of initial valuesMar 01 2017Oct 04 2017We study the asymptotic behaviour of the solutions of the fifth Painlev\'e equation as the independent variable approaches zero and infinity in the space of initial values. We show that the limit set of each solution is compact and connected and, moreover, ... More

An Inverse Scattering Transform for the Lattice Potential KdV EquationNov 21 2011The lattice potential Korteweg-de Vries equation (LKdV) is a partial difference equation in two independent variables, which possesses many properties that are analogous to those of the celebrated Korteweg-de Vries equation. These include discrete soliton ... More

On non-QRT Mappings of the PlaneJun 15 2009We construct 9-parameter and 13-parameter dynamical systems of the plane which map bi-quadratic curves to other bi-quadratic curves and return to the original curve after two iterations. These generalize the QRT maps which map each such curve to itself. ... More

Conditions for the Trivers-Willard hypothesis to be valid: A minimal population-genetic modelAug 15 2007The very insightful Trivers-Willard hypothesis, proposed in the early 1970s, states that females in good physiological conditions are more likely to produce male offspring, when the variance of reproductive success amongst males is high. A number of studies, ... More

The Discrete Painlevé I HierarchyOct 24 1997The discrete Painlev\'e I equation (dP$\rm_I$) is an integrable difference equation which has the classical first Painlev\'e equation (P$\rm_I$) as a continuum limit. dP$\rm_I$ is believed to be integrable because it is the discrete isomonodromy condition ... More

Existence and Uniqueness of Tri-tronquée Solutions of the second Painlevé hierarchyDec 09 2002The first five classical Painlev\'e equations are known to have solutions described by divergent asymptotic power series near infinity. Here we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlev\'e ... More

Long Time Response of Aging Glassy PolymersJul 29 2014Aging amorphous polymeric materials undergo free volume relaxation, which causes slowing down of the relaxation dynamics as a function of time. The resulting time dependency poses difficulties in predicting their long time physical behavior. In this work, ... More

Strange Attractors for Asymptotically Zero MapsOct 21 2013A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional hypotheses ... More

A Novel Source of Tagged Low-Energy Nuclear RecoilsMay 25 2011For sufficiently wide resonances, nuclear resonance fluorescence behaves like elastic photo-nuclear scattering while retaining the large cross-section characteristic of resonant photo-nuclear absorption. We show that NRF may be used to characterize the ... More

Weighted geometric distribution with a new characterisation of geometric distributionDec 22 2015Feb 05 2016In this paper, we introduce a new generalization of geometric distribution which can also viewed as discrete analogue of weighted exponential distribution introduced by Gupta and Kundu(2009). We study some basic distributional properties like moments, ... More

Probabilistic Relational Planning with First Order Decision DiagramsJan 16 2014Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on symbolic dynamic ... More

DCT and Eigenvectors of Covariance of 1st and 2nd order Discrete fractional Brownian motionFeb 22 2013This paper establishes connection between discrete cosine transform (DCT) and 1st and 2nd order discrete-time fractional Brownian motion process. It is proved that the eigenvectors of the auto-covariance matrix of a 1st and 2nd order discrete-time fractional ... More

Lectures on Pseudo-differential OperatorsJun 23 1999This lecture notes cover a Part III (first year graduate) course that was given at Cambridge University over several years on pseudo-differential operators. The calculus on manifolds is developed and applied to prove propagation of singularities and the ... More

Pinaka: Symbolic Execution meets Incremental Solving (Competition Contribution)Mar 06 2019Many modern-day solvers offer functionality for incremental SAT solving, which preserves the state of the solver across invocations. This is beneficial when multiple, closely related SAT queries need to be fed to the solver. Pinaka is a symbolic execution ... More

Spacetime SingularitiesNov 03 2013We present here an overview of our basic understanding and recent developments on spacetime singularities in the Einstein theory of gravity. Several issues related to physical significance and implications of singularities are discussed. The nature and ... More

On the genericity of spacetime singularitiesFeb 21 2007We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational ... More

The Rainbows of GravityMay 05 2013We present here a spectrum of developments and predictions in gravitation theory in recent years which appear to be amongst some of the most exciting directions. These include the spacetime singularities, gravitational collapse final states, and the deep ... More

Key problems in black hole physics todayApr 19 2011We review here some of the major open issues and challenges in black hole physics today, and the current progress on the same. It is pointed out that to secure a concrete foundation for the basic theory as well as astrophysical applications for black ... More

Gravitational Collapse End StatesDec 17 2004Recent developments on the final state of a gravitationally collapsing massive matter cloud are summarized and reviewed here. After a brief background on the problem, we point out how the black hole and naked singularity end states arise naturally in ... More

Gravitational CollapseFeb 19 1997We review here some recent developments on the issue of final fate of gravitational collapse within the framework of Einstein theory of gravity. The structure of collapsed object is discussed in terms of either a black hole or a singularity having causal ... More

Intranight optical variability of radio-loud broad absorption line quasarsNov 20 2012We present the results of an optical photometric monitoring program of 10 extremely radio loud broad absorption line quasars (RL-BALQSOs) with radio-loudness parameter, R, greater than 100 and magnitude g_i < 19. Over an observing run of about 3.5-6.5 ... More

Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD AlgorithmsAug 22 2018Jan 25 2019Communication-efficient SGD algorithms, which allow nodes to perform local updates and periodically synchronize local models, are highly effective in improving the speed and scalability of distributed SGD. However, a rigorous convergence analysis and ... More

Open star cluster: formation, parameters, membership and importanceJun 23 2016We have been represented the collective information of estimation procedures of parameters of the open clusters and put them together for showing the importance of clusters to understand their role in stellar evolution phenomenon. Moreover, we have been ... More

Dynamical properties and search of variable stars: NGC 1960Dec 11 2015The total-to-selective extinction RV in the direction of a cluster is found to be 3.12 +/- 0.2 (close to its normal value). We derive the luminosity and mass functions for the cluster main sequence stars. The mass function slope is found to be -2.29 +/- ... More

Complexity of Scrambling: A New Twist to the Competence - Performance DistinctionNov 29 1994Nov 30 1994In this paper we discuss the following issue: How do we decide whether a certain property of language is a competence property or a performance property? Our claim is that the answer to this question is not given a-priori. The answer depends on the formal ... More

Which small reaction networks are multistationary?Mar 21 2016Sep 19 2016Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the following ... More

Global Guarantees for Blind Demodulation with Generative PriorsMay 29 2019We study a deep learning inspired formulation for the blind demodulation problem, which is the task of recovering two unknown vectors from their entrywise multiplication. We consider the case where the unknown vectors are in the range of known deep generative ... More