total 1783took 0.18s

Discretization based Solutions for Secure Machine Learning against Adversarial AttacksFeb 08 2019Adversarial examples are perturbed inputs that are designed (from a deep learning network's (DLN) parameter gradients) to mislead the DLN during test time. Intuitively, constraining the dimensionality of inputs or parameters of a network reduces the 'space' ... More

A Photonic In-Memory Computing primitive for Spiking Neural Networks using Phase-Change MaterialsAug 03 2018Oct 24 2018Spiking Neural Networks (SNNs) offer an event-driven and more biologically realistic alternative to standard Artificial Neural Networks based on analog information processing. This can potentially enable energy-efficient hardware implementations of neuromorphic ... More

Capacitively Driven Global Interconnect with Magnetoelectric Switching Based Receiver for Higher Energy EfficiencyFeb 26 2018We propose capacitively driven low-swing global interconnect circuit using a receiver that utilizes magnetoelectric (ME) effect induced magnetization switching to reduce the energy consumption. Capacitively driven wire has recently been shown to be effective ... More

Geodesics in exact plane wave spacetimes and the memory effectJan 31 2019Recently [Phys. Rev. D 96, 064013(2017)], it has been shown how the displacement and velocity memory effects can be analysed by studying geodesics in the exact plane gravitational wave line element. In our work here, we provide simple and largely analytical ... More

Discretization based Solutions for Secure Machine Learning against Adversarial AttacksFeb 08 2019Feb 11 2019Adversarial examples are perturbed inputs that are designed (from a deep learning network's (DLN) parameter gradients) to mislead the DLN during test time. Intuitively, constraining the dimensionality of inputs or parameters of a network reduces the 'space' ... More

Principle bundles admitting a holomorphic structureJan 18 1996Let $M$ be a compact connected K\"ahler manifold and let ${\E}_{l-1}$ be the smallest term in the Harder-Narasimhan filtration of its tangent bundle. Let $G$ be an affine algebraic reductive group over $\C$. We prove the following result: If $M$ satisfies ... More

Stable principal bundles and reduction of structure groupAug 23 2006Let $E_G$ be a stable principal $G$--bundle over a compact connected Kaehler manifold, where $G$ is a connected reductive linear algebraic group defined over the complex numbers. Let $H\subset G$ be a complex reductive subgroup which is not necessarily ... More

On Kaehler structures over symmetric products of a Riemann surfaceJun 19 2011Feb 29 2012Given a positive integer $n$ and a compact connected Riemann surface $X$, we prove that the symmetric product $S^n(X)$ admits a Kaehler form of nonnegative holomorphic bisectional curvature if and only if $\text{genus}(X) \leq 1$. If $n$ is greater than ... More

Technology Aware Training in Memristive Neuromorphic Systems based on non-ideal Synaptic CrossbarsNov 24 2017The advances in the field of machine learning using neuromorphic systems have paved the pathway for extensive research on possibilities of hardware implementations of neural networks. Various memristive technologies such as oxide-based devices, spintronics ... More

Energy-Efficient Memories using Magneto-Electric Switching of FerromagnetsJan 27 2017Voltage driven magneto-electric (ME) switching of ferro-magnets has shown potential for future low-energy spintronic memories. In this paper, we first analyze two different ME devices viz. ME-MTJ and ME-XNOR device with respect to writability, readability ... More

Design of a Low Voltage Analog-to-Digital Converter using Voltage Controlled Stochastic Switching of Low Barrier NanomagnetsMar 04 2018May 23 2018The inherent stochasticity in many nano-scale devices makes them prospective candidates for low-power computations. Such devices have been demonstrated to exhibit probabilistic switching between two stable states to achieve stochastic behavior. Recently, ... More

Quantum Correlations in Quantum CloningJul 13 2010We utilize quantum discord to charecterize the correlation present in Buzek-Hillery quantum copying machine \cite{bh} (not necessarily universal quantum cloning machine). In other words we quantify the correlation present beetween the original and the ... More

On principal bundles over a projective variety defined over a finite fieldJul 07 2009Let M be a geometrically irreducible smooth projective variety, defined over a finite field k, such that M admits a k-rational point x_0. Let \varpi(M,x_0) denote the corresponding fundamental group--scheme introduced by Nori. Let E_G be a principal G-bundle ... More

On the algebraic holonomy of stable principal bundlesMar 05 2007Oct 19 2010Apart from math.AG/0608569, it contains the following applications of it. Let M be a simply connected, irreducible smooth complex projective variety of dimension $n$ such that the Picard number of $M$ is one. If the canonical line bundle $K_M$ is ample, ... More

A new line on the wide binary test of gravityFeb 05 2019The relative velocity distribution of wide binary (WB) stars is sensitive to the law of gravity at the low accelerations typical of galactic outskirts. I consider the feasibility of this wide binary test using the `line velocity' method. This involves ... More

Realization of an equivariant holomorphic Hermitian line bundle as a Quillen determinant bundleApr 02 2014Let $M$ be an irreducible smooth complex projective variety equipped with an action of a compact Lie group $G$, and let $({\mathcal L},h)$ be a $G$-equivariant holomorphic Hermitian line bundle on $M$. Given a compact connected Riemann surface $X$, we ... More

Holonomy Quantization of Moduli Spaces & Grothendieck GroupsSep 01 2004Gelfand's charecterization of a topological space M by the duality relationship of M and $\mathcal{A} = \mathcal{F}(M)$, the commutative algebra of functions on this space has deep implications including the development of spectral calculas by Connes ... More

Estimating Vacuum Tunneling RatesOct 18 1996Jan 30 1997We show that in Euclidean field theories that have bounce solutions, the bounce with the least action is the global minimum of the action in an open space of field configurations. A rigorous upper bound on the minimal bounce action can therefore be obtained ... More

Determinant line bundle on moduli space of parabolic bundlesDec 21 2010In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line ... More

Semistability and restrictions of tangent bundle to curvesJan 27 2009We consider all complex projective manifolds X that satisfy at least one of the following three conditions: 1. There exists a pair $(C ,\varphi)$, where $C$ is a compact connected Riemann surface and $\varphi : C\to X$ a holomorphic map, such that the ... More

A remark on the jet bundles over the projective lineJul 03 1996This is a footnote of a recent interesting work of Cohen, Manin and Zagier, where they, among other things, produce a natural isomorphism between the sheaf of (n-1)-th order jets of the n-th tensor power of the tangent bundle of a Riemann surface equipped ... More

The imaginary time Path Integral and non-time-reversal-invariant- saddle points of the Euclidean ActionOct 19 1997Apr 14 1998We discuss new bounce-like (but non-time-reversal-invariant-) solutions to Euclidean equations of motion, which we dub boomerons. In the Euclidean path integral approach to quantum theories, boomerons make an imaginary contribution to the vacuum energy. ... More

Moduli space of $G$-connections on an elliptic curveApr 08 2015Let $X$ be a smooth complex elliptic curve and $G$ a connected reductive affine algebraic group defined over $\mathbb C$. Let ${\mathcal M}_X(G)$ denote the moduli space of topologically trivial algebraic $G$--connections on $X$, that is, pairs of the ... More

Yang-Mills connections on compact complex toriNov 11 2014Let $G$ be a connected reductive complex affine algebraic group and $K\subset G$ a maximal compact subgroup. Let $M$ be a compact complex torus equipped with a flat K\"ahler structure and $(E_G ,\theta)$ a polystable Higgs $G$-bundle on $M$. Take any ... More

Semidirect products and invariant connectionsFeb 18 2015Let $S$ be a complex reductive group acting holomorphically on a complex Lie group $N$ via holomorphic automorphisms. Let $K(S)\subset S$ be a maximal compact subgroup. The semidirect product $G := N\rtimes K(S)$ acts on $N$ via biholomorphisms. We give ... More

Teleportation via a mixture of a two qubit subsystem of a N-qubit W and GHZ stateJan 28 2009Dec 08 2009In this work we study a state which is a random mixture of a two qubit subsystem of a $N$-qubit W state and GHZ state. We analyze several possibilities like separability criterion (Peres-Horodecki criterion [14,15]), non violation of Bell's inequality ... More

Partial Swapping, Unitarity and No-signallingJun 27 2007It is a well known fact that an quantum state $|\psi(\theta,\phi)>$ is represented by a point on the Bloch sphere, characterized by two parameters $\theta$ and $\phi$. In a recent work we already proved that it is impossible to partially swap these quantum ... More

Baryogenesis from Cosmic Strings at the Electroweak ScaleApr 19 1996Oct 01 1996We explore the viability of baryogenesis from light scalar decays after the electroweak phase transition. A minimal model of this kind is constructed with new CP violating interactions involving a heavy fourth family. The departure from thermal equilbrium ... More

Homogeneous principal bundles and stabilityMar 25 2009Let G/P be a rational homogeneous variety, where P is a parabolic subgroup of a simple and simply connected linear algebraic group G defined over an algebraically closed field of characteristic zero. A homogeneous principal bundle over G/P is semistable ... More

Efficient Hybrid Network Architectures for Extremely Quantized Neural Networks Enabling Intelligence at the EdgeFeb 01 2019The recent advent of `Internet of Things' (IOT) has increased the demand for enabling AI-based edge computing. This has necessitated the search for efficient implementations of neural networks in terms of both computations and storage. Although extreme ... More

Toward Fast Neural Computing using All-Photonic Phase Change Spiking NeuronsApr 01 2018Aug 28 2018The rapid growth of brain-inspired computing coupled with the inefficiencies in the CMOS implementations of neuromrphic systems has led to intense exploration of efficient hardware implementations of the functional units of the brain, namely, neurons ... More

8T SRAM Cell as a Multi-bit Dot Product Engine for Beyond von-Neumann ComputingFeb 22 2018Oct 16 2018Large scale digital computing almost exclusively relies on the von-Neumann architecture which comprises of separate units for storage and computations. The energy expensive transfer of data from the memory units to the computing cores results in the well-known ... More

Differential geometry of moduli spaces of quiver bundlesJun 05 2016Let P be a parabolic subgroup of a simple affine algebraic group G defined over C and X a compact connected K\"ahler manifold. L. \'Alvarez-C\'onsul and O. Garc\'ia-Prada associated to these a quiver Q and representations of Q into holomorphic vector ... More

Vortex equation and reflexive sheavesNov 28 2011It is known that given a stable holomorphic pair $(E ,\phi)$, where $E$ is a holomorphic vector bundle on a compact K\"ahler manifold $X$ and $\phi$ is a holomorphic section of $E$, the vector bundle $E$ admits a Hermitian metric solving the vortex equation. ... More

A remark on "Connections and Higgs fields on a principal bundle"Feb 21 2011We show that a unipotent vector bundle on a non-Kaehler compact complex manifold does not admit a flat holomorphic connection in general. We also construct examples of topologically trivial stable vector bundle on compact Gauduchon manifold that does ... More

Non Existence of Quantum Mechanical Self Replicating MachineOct 28 2005Jan 14 2007In this letter we establish the impossibility of existence of self replicating machine in the quantum world. We establish this result by three different but consistent approaches of linearity of quantum mechanics, no signalling condition and conservation ... More

Commuting elements in reductive groups and Higgs bundles on abelian varietiesMay 15 2013Let G be a connected real reductive algebraic group, and let K be a maximal compact subgroup of G. We prove that the conjugation orbit space Hom(Z^{2d},K)/K is a strong deformation retract of the space Hom(Z^{2d},G)/G of equivalence classes of representations ... More

A Torelli theorem for moduli spaces of principal bundles over a curveMar 22 2010Feb 11 2011Let X and X' be compact Riemann surfaces of genus at least 3, and let G and G' be nonabelian reductive complex groups. If one component M_G^d(X) of the moduli space for semistable principal G-bundles over X is isomorphic to another component M_{G'}^{d'}(X'), ... More

Thermoelectric Behaviour Near Magnetic Quantum Critical PointApr 19 2001Nov 19 2002We use the coupled 2d-spin-3d-fermion model proposed by Rosch {\sl et. al.} (Phys. Rev. Lett. {\bf 79}, 159 (1997)) to study the thermoelectric behaviour of a heavy fermion compound when it is close to an antiferromagnetic quantum critical point. When ... More

Study of the family of Nonlinear Schrodinger equations by using the Adler-Kosant-Symes framework and the Tu methodology and their Non-holonomic deformationNov 18 2013May 22 2014The objective of this work is to explore the class of equations of the Non-linear Schrodinger type by employing the Adler-Kostant-Symes theorem and the Tu methodology.In the first part of the work, the AKS theory is discussed in detail showing how to ... More

Holomorphic Cartan geometry on manifolds with numerically effective tangent bundleJan 21 2011Let X be a compact connected Kaehler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly, Peternell and Schenider says that there is a finite unramified Galois covering M --> X, a complex torus T, and a ... More

On the Gieseker Harder-Narasimhan filtration for principal bundlesNov 11 2014We give an example of an orthogonal bundle where the Harder-Narasimhan filtration, with respect to Gieseker semistability, of its underlying vector bundle does not correspond to any parabolic reduction of the orthogonal bundle. A similar example is given ... More

Holomorphic Cartan geometries, Calabi--Yau manifolds and rational curvesSep 29 2010We prove that if a Calabi--Yau manifold $M$ admits a holomorphic Cartan geometry, then $M$ is covered by a complex torus. This is done by establishing the Bogomolov inequality for semistable sheaves on compact K\"ahler manifolds. We also classify all ... More

On the Asymptotic Analysis of Problems Involving Fractional Laplacian in Cylindrical Domains Tending to InfinitySep 22 2015Oct 27 2015The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic problems by ... More

Automorphism group of a moduli space of framed bundles over a curveFeb 06 2018Let $X$ be a smooth complex projective curve of genus $g > 2$, and let $x\in X$ be a point. We compute the automorphism group of the moduli space of framed vector bundles on $X$ with a framing over $x$. It is shown that this group is generated by pullbacks ... More

A vanishing theorem for co-Higgs bundles on the moduli space of bundlesSep 13 2016May 24 2017We consider smooth moduli spaces of semistable vector bundles of fixed rank and determinant on a compact Riemann surface $X$ of genus at least $3$. The choice of a Poincar\'e bundle for such a moduli space $M$ induces an isomorphism between $X$ and a ... More

Electrically Modulated Thin Film Dynamics Controlling Bubble Manipulation in Microfluidic ConfinementMay 12 2013Dec 03 2014Thin film dynamics and associated instability mechanisms have triggered a wide range of scientific innovations, as attributed to their abilities of creating fascinating patterns over small scales. Here, we demonstrate a new thin film instability phenomenon ... More

On the Kähler structures over Quot schemesJan 29 2014Let $S^n(X)$ be the $n$-fold symmetric product of a compact connected Riemann surface $X$ of genus $g$ and gonality $d$. We prove that $S^n(X)$ admits a K\"ahler structure such that all the holomorphic bisectional curvatures are nonpositive if and only ... More

On the Kähler structures over Quot schemes, IIMar 30 2015Let $X$ be a compact connected Riemann surface of genus $g$, with $g \geq 2$, and let ${\mathcal O}_X$ denote the sheaf of holomorphic functions on $X$. Fix positive integers $r$ and $d$ and let ${\mathcal Q}(r,d)$ be the Quot scheme parametrizing all ... More

Geometry of moduli spaces of Higgs bundlesMay 22 2006We construct a Petersson-Weil type K\"ahler form on the moduli spaces of Higgs bundles over a compact K\"ahler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature of a certain ... More

On the exactness of Kostant-Kirillov form and the second cohomology of nilpotent orbitsMar 27 2012We give a criterion for the Kostant-Kirillov form on an adjoint orbit in a real semisimple Lie group to be exact. We explicitly compute the second cohomology of all the nilpotent adjoint orbits in every complex simple Lie algebras.

On semistable principal bundles over a complex projective manifoldMar 28 2008Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold ... More

A construction of Chern classes of parabolic vector bundlesSep 14 2012Given a parabolic vector bundle, we construct for it a projectivization and tautological line bundle. These are analogs of the projectivization and tautological line bundle for an usual vector bundle. Using these we give a construction of the parabolic ... More

Higgs bundles on Sasakian manifoldsJul 25 2016We extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact K\"ahler manifolds to compact quasi-regular Sasakian manifolds. A particular consequence is the translation of restrictions on K\"ahler ... More

Fractional Order Fuzzy Control of Hybrid Power System with Renewable Generation Using Chaotic PSONov 29 2016This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer ... More

Rigidity of holomorphic maps between fiber spacesSep 16 2013Dec 19 2013In the study of holomorphic maps, the term "rigidity" refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this theme, we begin ... More

Atiyah sequences, connections and Chern-Weil theory for algebraic and differentiable stacksNov 19 2013Nov 26 2013We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah sequences associated to transversal tangential distributions.

Coupled vortex equations and Moduli: Deformation theoretic Approach and Kaehler GeometryAug 24 2008We investigate differential geometric aspects of moduli spaces parametrizing solutions of coupled vortex equations over a compact Kaehler manifold X. These solutions are known to be related to polystable triples via a Kobayashi-Hitchin type correspondence. ... More

Yang-Mills equation for stable Higgs sheavesMar 31 2008We establish a Kobayashi-Hitchin correspondence for the stable Higgs sheaves on a compact Kaehler manifold. Using it, we also obtain a Kobayashi-Hitchin correspondence for the stable Higgs G-sheaves, where G is any complex reductive linear algebraic group. ... More

Inverses of structured vector bundlesJan 31 2015Apr 22 2015We prove that structured vector bundles whose holonomies lie in GL(N,C), SO(N,C), or Sp(2N,C) have structured inverses. This generalizes a theorem of Simons and Sullivan.

On semistable principal bundles over a complex projective manifold, IISep 25 2009Let (X, \omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following ... More

Nakano positivity and the L2-metric on the direct image of an adjoint positive line bundleOct 28 1999Apr 10 2000We prove that the $L^2$ metric on the direct image of an adjoint positive line bundle by a locally trivial submersion between projective manifolds is Nakano positive, under the assumption that the typical fiber has zero first Betti number. As a consequence, ... More

Brauer Group of Moduli Spaces of PGL(r)-Bundles over a curveApr 29 2009Apr 27 2010We compute the Brauer group of the moduli stack of stable PGL(r)-bundles on a curve $X$ over an algebraically closed field of characteristic zero. We also show that the Brauer group of such a moduli stack coincides with the Brauer group of the smooth ... More

The Nori fundamental gerbe of tame stacksFeb 25 2015Sep 09 2015Given an algebraic stack, we compare its Nori fundamental group with that of its coarse moduli space. We also study conditions under which the stack can be uniformized by an algebraic space.

Higgs bundles and representation spaces associated to morphismsJul 16 2015Let $G$ be a connected reductive affine algebraic group defined over the complex numbers, and $K\subset G$ be a maximal compact subgroup. Let $X , Y$ be irreducible smooth complex projective varieties and $f: X \rightarrow Y$ an algebraic morphism, such ... More

Weil-Petersson geometry and determinant bundles on inductive limits of moduli spacesOct 31 1996In an earlier paper [Acta Mathematica, v. 176, 1996, 145-169, alg-geom/9505024 ] the present authors and Dennis Sullivan constructed the universal direct system of the classical Teichm\"uller spaces of Riemann surfaces of varying genus. The direct limit, ... More

Ice Shelves as Floating Channel Flows of Viscous Power-Law FluidsOct 30 2013Dec 07 2013We attempt to better understand the flow of marine ice sheets. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases - the presence or absence of contact with sidewalls. Most real-world situations ... More

Effects of Fluid Composition on Spherical Flows around Black HolesDec 14 2008Steady, spherically symmetric, adiabatic accretion and wind flows around non-rotating black holes were studied for fully ionized, multi-component fluids, which are described by a relativistic equation of state (EoS). We showed that the polytropic index ... More

Binary String DynamicsOct 01 1996In this paper we investigate the dynamical properties of binary cosmic strings. We find extrinsic curvature dependence of the string action and show that kinks on binary strings are eroded while cusps can play a major role in their evolution.

Semistability criterion for parabolic vector bundles on curvesMar 07 2011Oct 24 2011We give a cohomological criterion for a parabolic vector bundle on a curve to be semistable. It says that a parabolic vector bundle $E$ with rational parabolic weights is semistable if and only if there is another parabolic vector bundle $F$ with rational ... More

Differential geometry of moduli spaces of quiver bundlesJun 05 2016Nov 21 2016Let P be a parabolic subgroup of a simple affine algebraic group G defined over C and X a compact connected K\"ahler manifold. L. \'Alvarez-C\'onsul and O. Garc\'ia-Prada associated to these a quiver Q and representations of Q into holomorphic vector ... More

The Weil-Petersson current for moduli of vector bundles and applications to orbifoldsSep 01 2015May 11 2016We investigate stable holomorphic vector bundles on a compact complex K\"ahler manifold and more generally on an orbifold that is equipped with a K\"ahler structure. We use the existence of Hermite-Einstein connections in this set-up and construct a generalized ... More

Deligne pairing and Quillen metricJan 12 2015Let $X\rightarrow S$ be a smooth projective surjective morphism of relative dimension $n$, where $X$ and $S$ are integral schemes over $\mathbb C$. Let $L\rightarrow X$ be a relatively very ample line bundle. For every sufficiently large positive integer ... More

Principal bundles over a real algebraic curveAug 01 2011Sep 25 2012Let X be a compact connected Riemann surface equipped with an anti-holomorphic involution \sigma. Let G be a connected complex reductive affine algebraic group, and let \sigma_G be a real form of G. We consider holomorphic principal G-bundles on X satisfying ... More

Equivariant bundles and connectionsNov 27 2016Let $X$ be a connected complex manifold equipped with a holomorphic action of a complex Lie group $G$. We investigate conditions under which a principal bundle on $X$ admits a $G$--equivariance structure.

Low dimensional projective groupsMar 20 2012Feb 26 2014We initiate the study of holomorphically convex groups: groups that can be realized as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers. If $G$ is a holomorphically convex group of cohomological dimension ... More

Fuzzy Bayesian LearningOct 28 2016In this paper we propose a novel approach for learning from data using rule based fuzzy inference systems where the model parameters are estimated using Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques. We show the applicability of the ... More

Estimation of mass outflow rates from viscous relativistic accretion discs around black holesMay 03 2016We investigated flow in Schwarzschild metric, around a non-rotating black hole and obtained self-consistent accretion - ejection solution in full general relativity. We covered the whole of parameter space in the advective regime to obtain shocked, as ... More

Multi-standard programmable baseband modulator for next generation wireless communicationSep 09 2010Considerable research has taken place in recent times in the area of parameterization of software defined radio (SDR) architecture. Parameterization decreases the size of the software to be downloaded and also limits the hardware reconfiguration time. ... More

H_1-semistability for projective groupsMar 09 2014We initiate the study of the asymptotic topology of groups that can be realized as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers (these are called here as holomorphically convex groups). We prove ... More

A note on real algebraic groupsNov 12 2013The efficacy of using complexifications to understand the structure of real algebraic groups is demonstrated. In particular the following results are proved: a) If L is an algebraic subgroup of a connected real algebraic group G such that the complexification ... More

Hermitian-Einstein connections on polystable parabolic principal Higgs bundlesSep 01 2011Given a smooth complex projective variety X and a smooth divisor D on X, we prove the existence of Hermitian-Einstein connections, with respect to a Poincar\'e-type metric on X - D, on polystable parabolic principal Higgs bundles with parabolic structure ... More

Vector bundles on Sasakian manifoldsSep 23 2008Mar 20 2009We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds.

Symplectic Structures on Moduli Spaces of Parabolic Higgs Bundles and Hilbert SchemeFeb 18 2003Parabolic triples of the form $(E_*,\theta,\sigma)$ are considered, where $(E_*,\theta)$ is a parabolic Higgs bundle on a given compact Riemann surface $X$ with parabolic structure on a fixed divisor $S$, and $\sigma$ is a nonzero section of the underlying ... More

Quasiprojective three-manifold groups and complexification of three-manifoldsFeb 26 2014Dec 12 2014We characterize the quasiprojective groups that appear as fundamental groups of compact $3$-manifolds (with or without boundary). We also characterize all closed $3$-manifolds that admit good complexifications. These answer questions of Friedl--Suciu, ... More

One-relator Kaehler groupsJan 27 2012Aug 04 2012We prove that a one-relator group $G$ is K\"ahler if and only if either $G$ is finite cyclic or $G$ is isomorphic to the fundamental group of a compact orbifold Riemann surface of genus $g > 0$ with at most one cone point of order $n$: $$< a_1\, b_1\, ... More

Automorphisms of the generalized quot schemesJan 18 2016Given a compact connected Riemann surface $X$ of genus $g \geq 2$, and integers $r\geq 2$, $d_p > 0$ and $d_z > 0$, in \cite{BDHW}, a generalized quot scheme ${\mathcal Q}_X(r,d_p,d_z)$ was introduced. Our aim here is to compute the holomorphic automorphism ... More

Principal bundles over finite fieldsMar 19 2010Let M be an irreducible smooth projective variety defined over \bar{{\mathbb F}_p}. Let \pi(M, x_0) be the fundamental group scheme of M with respect to a base point x_0. Let G be a connected semisimple linear algebraic group over \bar{{\mathbb F}_p}. ... More

Generalized Holomorphic Cartan geometriesFeb 18 2019This is largely a survey paper, dealing with Cartan geometries in the complex analytic category. We first remind some standard facts going back to the seminal works of F. Klein, E. Cartan and C. Ehresmann. Then we present the concept of a branched holomorphic ... More

Physical Biomodeling: a new field enabled by 3-D printing in biomodelingFeb 16 2015Jul 12 2015Accurate physical modeling with 3D-printing techniques could lead to new approaches to study structure and dynamics of biological systems complementing computational methods. Computational biology has become an important part of research over the last ... More

Fundamental theorem of Algebra - A Nevanlinna theoretic proofDec 08 2016The aim of this short note is to produce a new proof of Fundamental Theorem of Algebra using Nevanlinna Theory.

Leveraging disjoint communities for detecting overlapping community structureApr 14 2015Network communities represent mesoscopic structure for understanding the organization of real-world networks, where nodes often belong to multiple communities and form overlapping community structure in the network. Due to non-triviality in finding the ... More

Authorship Identification in Bengali Literature: a Comparative AnalysisAug 30 2012Feb 24 2013Stylometry is the study of the unique linguistic styles and writing behaviors of individuals. It belongs to the core task of text categorization like authorship identification, plagiarism detection etc. Though reasonable number of studies have been conducted ... More

Accelerating Expansion of the UniverseMay 04 2011This thesis concentrates on the accelerated expansion of the Universe recently explored by measurements of redshift and luminosity-distance relations of type Ia Supernovae. We have considered a model of the universe filled with modified Chaplygin gas ... More

PeppyChains: Simplifying the assembly of 3D-printed generic protein modelsFeb 16 2015Peppytides is a coarse-grained, accurate, physical model of the polypeptide chain. I have shared instructions to make your own polypeptide chain and STL files of Peppytides in MAKE magazine in Jan 2014 issue. However, Peppytides involves a lot of steps ... More

Contractive properties of multifunctions related to uniformityFeb 02 2005Here I prove some extension theorem for multifunctions in a space with an arbitrary uniform structure and orbital completeness. The motivation comes from a fixed point theorem due to Dhage which is proved as a special case of the theorem presented here. ... More

Boundary terms of the Einstein-Hilbert actionJul 19 2016The Einstein-Hilbert action for general relativity is not well posed in terms of the metric $g_{ab}$ as a dynamical variable. There have been many proposals to obtain an well posed action principle for general relativity, e.g., addition of the Gibbons-Hawking-York ... More

An Extension Of Weiler-Atherton Algorithm To Cope With The Self-intersecting PolygonMar 04 2014In this paper a new algorithm has been proposed which can fix the problem of Weiler Atherton algorithm. The problem of Weiler Atherton algorithm lies in clipping self intersecting polygon. Clipping self intersecting polygon is not considered in Weiler ... More

Effective Thermal Diffusivity in Real SolidMay 28 2015The effective thermal diffusivity is evaluated for a two dimensional real solid and the real solid is modeled with periodic surface. The result contain the scale factor for the conformal transformation that flattens the surface. We find that the effective ... More