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On the logical complexity of cyclic arithmeticJul 26 2018Sep 11 2018We study the logical complexity of proofs in cyclic arithmetic ($\mathsf{CA}$), as introduced in Simpson '17, in terms of quantifier alternations of formulae occurring. Writing $C\Sigma_n$ for (the logical consequences of) cyclic proofs containing only ... More

On the relative proof complexity of deep inference via atomic flowsFeb 20 2015Mar 05 2015We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore ... More

A Functional (Monadic) Second-Order Theory of Infinite TreesMar 14 2019This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results concerning the decidability ... More

On linear rewriting systems for Boolean logic and some applications to proof theoryOct 27 2016Dec 27 2016Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can be written as ... More

Securing Tor Tunnels under the Selective-DoS AttackJul 19 2011Dec 18 2012Anonymous communication systems are subject to selective denial-of-service (DoS) attacks. Selective DoS attacks lower anonymity as they force paths to be rebuilt multiple times to ensure delivery which increases the opportunity for more attack. In this ... More

Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequencesApr 01 2016The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. ... More

Fingerprinting Smart Devices Through Embedded Acoustic ComponentsMar 13 2014The widespread use of smart devices gives rise to both security and privacy concerns. Fingerprinting smart devices can assist in authenticating physical devices, but it can also jeopardize privacy by allowing remote identification without user awareness. ... More

Einstein relation and hydrodynamics of nonequilibrium mass transport processesJan 18 2017Jul 05 2017We obtain hydrodynamic descriptions of a broad class of conserved-mass transport processes on a ring. These processes are governed by chipping, diffusion and coalescence of masses, where microscopic probability weights in their nonequilibrium steady states, ... More

Some Fibonacci sequence spaces of non-absolute type derived from $\ell_{p} $ with $(1 \leq p \leq \infty)$ and Hausdorff measure of non-compactness of composition operatorsJun 18 2017The aim of the paper is to introduce the spaces $\ell_{\infty}^{\lambda}(\widehat{F})$ and $\ell_{p}^{\lambda}(\widehat{F})$ derived by the composition of the two infinite matrices $\Lambda=(\lambda_{nk})$ and $\widehat{F}=\left( f_{nk} \right),$ which ... More

Exploring Ways To Mitigate Sensor-Based Smartphone FingerprintingMar 06 2015Modern smartphones contain motion sensors, such as accelerometers and gyroscopes. These sensors have many useful applications; however, they can also be used to uniquely identify a phone by measuring anomalies in the signals, which are a result from manufacturing ... More

On Nested Sequents for Constructive Modal LogicsMay 26 2015Sep 02 2015We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the standard modal ... More

Smartphone Fingerprinting Via Motion Sensors: Analyzing Feasibility at Large-Scale and Studying Real Usage PatternsMay 27 2016Jun 13 2016Advertisers are increasingly turning to fingerprinting techniques to track users across the web. As web browsing activity shifts to mobile platforms, traditional browser fingerprinting techniques become less effective; however, device fingerprinting using ... More

Defending Tor from Network Adversaries: A Case Study of Network Path PredictionOct 07 2014Mar 04 2015The Tor anonymity network has been shown vulnerable to traffic analysis attacks by autonomous systems and Internet exchanges, which can observe different overlay hops belonging to the same circuit. We aim to determine whether network path prediction techniques ... More

On linear rewriting systems for Boolean logic and some applications to proof theoryOct 27 2016Nov 18 2016Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can be written as ... More

On linear rewriting systems for Boolean logic and some applications to proof theoryOct 27 2016Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can be written as ... More

Some new Fibonacci difference spaces of non-absolute type and compact operatorsApr 25 2016The aim of the paper is to introduced the spaces $c_{0}^{\lambda}(\hat{F})$ and $c^{\lambda}(\hat{F})$ which are the BK-spaces of non-absolute type and also derive some inclusion relations. Further, we determine the $\alpha-,\beta-,\gamma-$duals of those ... More

Steady State of an Active Brownian Particle in Two-Dimensional Harmonic TrapFeb 11 2019Mar 14 2019We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions, in the presence of translational diffusion. This series solution allows us to efficiently explore the ... More

Spin tunnelling in Molecular MagnetsDec 09 2000We study spin tunneling in magnetic molecules, with special reference to Fe8. The article aims to give a pedagogical discussion of what is meant by the tunneling of a spin, and how tunneling amplitudes or energy level splittings may be calculated using ... More

Vibrational Decoherence in Ion Trap Quantum ComputersOct 22 1997The ion trap quantum computer proposed by Cirac and Zoller is analyzed for decoherence due to vibrations of the ions. An adiabatic approximation exploiting the vast difference between the frequencies of the optical intraionic transition and the vibrational ... More

Decoherence in Ion Trap Quantum ComputersMar 29 1996The {\it intrinsic} decoherence from vibrational coupling of the ions in the Cirac-Zoller quantum computer [Phys. Rev. Lett. {\bf 74}, 4091 (1995)] is considered. Starting from a state in which the vibrational modes are at a temperature $T$, and each ... More

Tunnel splittings for one dimensional potential wells revisitedMar 08 2000The WKB and instanton answers for the tunnel splitting of the ground state in a symmetric double well potential are both reduced to an expression involving only the functionals of the potential, without the need for solving any auxilliary problems. This ... More

Antiferromagnetism and Superconductivity in UPt_3Mar 25 1998The short ranged antiferromagnetism recently seen in UPt_3 is proved incompatible with two dimensional (2D) order parameter models that take the antiferromagnetism as a symmetry breaking field. To adjust to the local moment direction, the order parameter ... More

Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: I. Symmetric ConfigurationsMar 08 2000The perfect quenching of spin tunneling that has previously been discussed in terms of interfering instantons, and has recently been observed in the magnetic molecule \Fe8, is treated using a discrete phase integral (or Wentzel-Kramers-Brillouin) method. ... More

Diabolical points in the magnetic spectrum of Fe_8 moleculesMar 07 2000The magnetic molecule Fe_8 has been predicted and observed to have a rich pattern of degeneracies in its spectrum as an external magnetic field is varied. These degeneracies have now been recognized to be diabolical points. This paper analyzes the diabolicity ... More

Phonoemissive Spin Tunneling in Molecular NanomagnetsOct 15 2011A new mechanism is proposed for the magnetization reversal of molecular nanomagnets such as \Fe8. In this process the spin tunnels from the lowest state near one easy direction to the first excited state near the opposite easy direction, and subsequently ... More

Coherent Magnetic Moment Reversal in Small Particles with Nuclear SpinsJul 13 1999A discrete WKB method is developed for calculating tunnel splittings in spin problems. The method is then applied to the issue of how nuclear spins affect the macroscopic quantum coherence of the total magnetic moment in small magnetic particles. The ... More

Quenched Spin Tunneling and Diabolical Points in Magnetic Molecules: II. Asymmetric ConfigurationsMar 09 2000The perfect quenching of spin tunneling first predicted for a model with biaxial symmetry, and recently observed in the magnetic molecule Fe_8, is further studied using the discrete phase integral (or Wentzel-Kramers-Brillouin) method. The analysis of ... More

Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin ApproachJul 09 1999Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors ... More

Vibrational Decoherence in Ion-Trap Quantum ComputersMar 25 1998Decoherence is studied in an attractive proposal for an actual implementation of a quantum computer based on trapped ions. Emphasis is placed on the decoherence arising from the vibrational motion of the ions, which is compared with that due to spontaneous ... More

Large transverse field tunnel splittings in the Fe_8 spin HamiltonianJun 14 1999The spin Hamiltonian that describes the molecular magnet Fe$_8$ has biaxial symmetry with mutually perpendicular easy, medium, and hard magnetic axes. Previous calculations of the ground state tunnel splittings in the presence of a magnetic field along ... More

Lattice Distortion Mediated Paramagnetic Relaxation in High-Spin High-Symmetry Molecular MagnetsMay 11 1998Field-dependent maxima in the relaxation rate of the magnetic molecules Mn_12-Ac and Fe_8-tacn have commonly been ascribed to some resonant tunneling phenomenon. We argue instead that the relaxation can be understood as purely due to phonons. The rate ... More

Conjugacy Classes of Centralizers in $G_2$Apr 23 2008Let $G$ be an algebraic group of type $G_2$ over a field $k$ of characteristic $\neq 2,3$. In this paper we calculate centralizers of semisimple elements in anisotropic $G_2$. Using these, we show explicitly that there are six conjugacy classes of centralizers ... More

Light-cone spreading of perturbations and the butterfly effect in a classical spin chainNov 20 2017Jul 10 2018We find that localised perturbations in a chaotic classical many-body system-- the classical Heisenberg We find that the effects of a localised perturbation in a chaotic classical many-body system--the classical Heisenberg chain at infinite temperature--spread ... More

The Moduli Space of Totally Marked Degree Two Rational MapsAug 17 2014A rational map $\phi: \mathbb{P}^1 \to \mathbb{P}^1$ along with an ordered list of fixed and critical points is called a totally marked rational map. The space of totally marked degree two rational maps, $Rat^{tm}_2$ can be parametrized by an affine open ... More

$e^+ e^- \to μ^+ μ^-$ scattering in the Noncommutative standard modelSep 18 2010We study muon pair production $ e^+ e^- \to \mu^+ \mu^-$ in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps of this to the second order of the noncommutative parameter $\Theta_{\mu \nu}$. Using $\mathcal{O}(\Theta^2)$ ... More

Neutral Higgs boson pair production at the LC in the Noncommutative Standard ModelSep 18 2010We study the Higgs boson pair production through $e^+e^-$ collision in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps of this to the first order of the noncommutative parameter $\Theta_{\mu \nu}$. This process is ... More

Large-field versus discontinuous instantons in spin orientation tunnelingOct 11 2002Tunnel splitting oscillations in magnetic molecules are reconsidered within the simplest model for the problem, which does not contain fourth order anisotropy. It is shown that at large magnetic field, there is only one instanton, and it is continuous. ... More

Deformation and break-up of viscoelastic droplets Using Lattice Boltzmann ModelsNov 09 2014We investigate the break-up of Newtonian/viscoelastic droplets in a viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite ... More

Incoherent Landau-Zener-Stuckelberg Transitions in Single-Molecule MagnetsOct 31 2008Dec 05 2008It is shown that in experiments on single molecule magnets (SMM's) in which transitions between two lowest spin states are induced by sweeping the applied magnetic field along the easy axis, the transitions are fully incoherent. Nuclear spins and the ... More

Computing $n^{\rm th}$ roots in $SL_2(k)$ and Fibonacci polynomialsOct 10 2017Let $k$ be a field of characteristic $\neq 2$. In this paper, we show that computing $n^{\rm th}$ root of an element of the group $SL_2(k)$ is equivalent to finding solutions of certain polynomial equations over the base field $k$. These polynomials are ... More

Spin Tunneling in Magnetic Molecules: Quasisingular Perturbations and Discontinuous SU(2) InstantonsJul 03 2002Spin coherent state path integrals with discontinuous semiclassical paths are investigated with special reference to a realistic model for the magnetic degrees of freedom in the Fe8 molecular solid. It is shown that such paths are essential to a proper ... More

Real Elements and Schur Indices of a GroupApr 20 2011Nov 11 2011In this article we try to explore the relation between real conjugacy classes and real characters of finite groups at more refined level. This refinement is in terms of properties of groups such as strong reality and total orthogonality. In this connection ... More

Nonlocal star as a blackhole mimickerMar 04 2019In the context of ghost-free, infinite derivative gravity, we will provide a quantum mechanical framework in which we can describe astrophysical objects devoid of curvature singularity and event horizon. In order to avoid ghosts and singularity, the gravitational ... More

Real and strongly real classes in finite linear groupsSep 25 2008Nov 03 2009We classify the real and strongly real conjugacy classes in $GL_n(q)$, $SL_n(q)$, $PGL_n(q)$, $PSL_n(q)$, and all quasi-simple covers of $PSL_n(q)$. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. ... More

MOR Cryptosystem and classical Chevalley groups in odd characteristicAug 27 2014In this paper we study the MOR cryptosystem using finite classical Chevalley groups over a finite field of odd characteristic. In the process we develop an algorithm for these Chevalley groups in the same spirit as the row-column operation for special ... More

Probing the Supersymmetric Inflaton and Dark Matter link via the CMB, LHC and XENON1T experimentsMay 12 2012Feb 05 2013The primordial inflation dilutes all matter except the quantum fluctuations which we see in the cosmic microwave background (CMB) radiation. Therefore the last phases of inflation must be embedded within a beyond the Standard Model (SM) sector where the ... More

Surface superconductivity and $H_{c3}$ in UPt$_3$Sep 12 1995Surface superconductivity is studied within Ginzburg-Landau theory for two classes of models for the order parameter of UPt$_{3}$. The first class assumes two independent one-dimensional order parameters ($AB$ models), while the second assumes a single ... More

The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flowsAug 13 1997We argue that important elements of the dynamics of wall-bounded flows reside at the wall-normal position $y_p^+$ corresponding to the peak of the Reynolds shear stress. Specializing to pipe and channel flows, we show that the mean momentum balance in ... More

Interaction Rates in String Gas CosmologySep 15 2004We study string interaction rates in the Brandenberger-Vafa scenario, the very early universe cosmology of a gas of strings. This cosmology starts with the assumption that all spatial dimensions are compact and initially have string scale radii; some ... More

Towards (1+ε)-Approximate Flow SparsifiersOct 11 2013A useful approach to "compress" a large network $G$ is to represent it with a {\em flow-sparsifier}, i.e., a small network $H$ that supports the same flows as $G$, up to a factor $q \geq 1$ called the quality of sparsifier. Specifically, we assume the ... More

Inflation, baryogenesis and gravitino dark matter at ultra low reheat temperaturesMay 11 2009It is quite possible that the reheat temperature of the universe is extremely low close to the scale of Big Bang nucleosynthesis, i.e. $T_{R}\sim 1-10$ MeV. At such low reheat temperatures generating matter anti-matter asymmetry and synthesizing dark ... More

Low-Temperature Magnetization Dynamics of Magnetic Molecular Solids in a Swept FieldDec 20 2012Oct 02 2015The swept-field experiments on magnetic molecular solids such as \Fe8 are studied using Monte Carlo simulations. A kinetic equation is developed to understand the phenomenon. It is found that the simulations provide a quantitatively accurate account of ... More

The Semiclassical Propagator for Spin Coherent StatesApr 14 2000We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the ``extra phase'' discovered by Solari and Kochetov, and show that this correction is related to an ... More

Exact Steady State of Active Brownian Particles in a 2D Harmonic TrapFeb 11 2019We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions, in the presence of translational diffusion. This series solution allows us to efficiently explore the ... More

Field Theoretical Methods in CosmologySep 07 1995To optimally utilize all the exciting cosmological data coming in we need to sharpen also the theoretical tools available to cosmologists. One such indispensible tool to understand hot big bang cosmology is finite temperature field theory. We review and ... More

Quasar Production:Topological Defect Formation due to a Phase Transition linked with Massive NeutrinosApr 29 1994Recent observations of the space distribution of quasars indicate a very notable peak in space density at a redshift of $2$ to $3$.It is pointed out in this article that this may be the result of a phase transition which has a critical temperature of ... More

Losing Treewidth by Separating SubsetsApr 04 2018Oct 23 2018We study the problem of deleting the smallest set $S$ of vertices (resp. edges) from a given graph $G$ such that the induced subgraph (resp. subgraph) $G \setminus S$ belongs to some class $\mathcal{H}$. We consider the case where graphs in $\mathcal{H}$ ... More

On collisions driven negative energy waves and Weibel instability of a relativistic electron beam in a quasi-neutral plasmaAug 29 2008Sep 02 2008A new quasi-neutral model describing the Weibel instability of a high-current relativistic beam propagating through a resistive plasma is developed. It treats beam electrons as kinetic particles, and ambient plasma as a non-relativistic fluid. For a finite-temperature ... More

Flocking of Active Particles in a Turbulent FlowDec 26 2018We investigate the effect of cooperative interactions in an ensemble of microorganisms, modelled as self-propelled disk-like and rod-like particles, in a three-dimensional turbulent flow to show flocking as an emergent phenomenon. Building on the work ... More

Performance Analysis of Energy Harvesting Underlay Cooperative Cognitive Radio Relay Networks with Randomly Located NodesMar 04 2019In this work, we investigate the successful data communication probability of an energy harvesting co-operative cognitive radio network (CRN) in the presence of Poisson field of primary users (PU). We consider the scenario where, after harvesting energy ... More

Non-singular metric for an electrically charged point-source in ghost-free infinite derivative gravityApr 25 2018Dec 04 2018In this paper we will construct a linearized metric solution for an electrically charged system in a {\it ghost-free} infinite derivative theory of gravity which is valid in the entire region of spacetime. We will show that the gravitational potential ... More

Post-inflationary brane cosmologyAug 09 2000Feb 25 2001The brane cosmology has invoked new challenges to the usual Big Bang cosmology. In this paper we present a brief account on thermal history of the post-inflationary brane cosmology. We have realized that it is not obvious that the post-inflationary brane ... More

Interesting consequences of brane cosmologyJul 24 2000Apr 09 2001We discuss cosmology in four dimensions within a context of brane-world scenario.Such models can predict chaotic inflation with very low reheat temperature depending on the brane tension. We notice that the gravitino abundance is different in the brane-world ... More

Extra Dimensions and InflationFeb 17 1999Oct 26 1999It has been proposed that, without invoking supersymmetry, it is possible to solve the hierarchy problem provided the fundamental scale in the higher dimensional theory is at a much lower scale than the Planck scale. In this paper we consider a toy model ... More

The origin of dark matter, matter-anti-matter asymmetry, and inflationJun 27 2011A rapid phase of accelerated expansion in the early universe, known as inflation, dilutes all matter except the vacuum induced quantum fluctuations. These are responsible for seeding the initial perturbations in the baryonic matter, the non-baryonic dark ... More

Ribet's construction of a suitable cusp eigenformOct 08 2009Oct 16 2009This article gives a self-contained exposition on Ribet's construction of a Hecke eigenform of weight 2 with certain congruence properties.

A customized flocking algorithm for swarms of sensors tracking a swarm of targetsNov 13 2013Wireless mobile sensor networks (WMSNs) are groups of mobile sensing agents with multi-modal sensing capabilities that communicate over wireless networks. WMSNs have more flexibility in terms of deployment and exploration abilities over static sensor ... More

Three dimensional filamentary structures of a relativistic electron beam in Fast Ignition plasmasSep 23 2008Nov 13 2008The filamentary structures and associated electromagnetic fields of a relativistic electron beam have been studied by three dimensional particle-in-cell (PIC) simulations in the context of Fast Ignition fusion. The simulations explicitly include collisions ... More

Discrete phase integral method for five-term recursion relationsMar 08 2000A formalism is developed to study certain five-term recursion relations by discrete phase integral (or Wentzel-Kramers-Brillouin) methods. Such recursion relations arise naturally in the study of the Schrodinger equation for certain spin Hamiltonians. ... More

Low scale inflation with large number of e-foldingsOct 16 2003Oct 25 2003In this paper we illustrate an interesting example of low scale inflation with an extremely large number of e-foldings. This realization can be implemented easily in hybrid inflation model where usually inflation ends via phase transition. However this ... More

A model for fluctuating inflaton coupling: (s)neutrino induced adiabatic perturbations and non-thermal leptogenesisJun 03 2003Mar 26 2004We discuss an unique possibility of generating adiabatic density perturbations and leptogenesis from the spatial fluctuations of the inflaton decay rate. The key assumption is that the initial isocurvature perturbations are created in the right handed ... More

Inflatonic Q-ball evaporation: A new paradigm for reheating the UniverseNov 15 2002We show that the inflaton condensate associated with a global symmetry can fragment into quasi stable Q balls after the end of inflation, provided the inflaton oscillations give rise to an effective equation of state with negative pressure. We argue that ... More

Gravitational Collapse of Dark Energy Field ConfigurationsJul 29 2010It is now a well established fact based on several observations that we live in a Universe dominated by dark energy. The most natural candidates for dark energy are fields in curved space-time. We develop the formalism to study the gravitational collapse ... More

A small non-vanishing cosmological constant from vacuum energy: physically and observationally desirableDec 05 1994Dec 15 1995Increasing improvements in the independent determinations of the Hubble constant and the age of the universe now seem to indicate that we need a small non-vanishing cosmological constant to make the two independent observations consistent with each other. ... More

On units generated by Euler systemsOct 08 2009In the context of cyclotomic fields, it is still unknown whether there exist Euler systems other than the ones derived from cyclotomic units. Nevertheless, we first give an exposition on how norm-compatible units are generated by any Euler system, following ... More

Welfare and Profit Maximization with Production CostsOct 22 2011Combinatorial Auctions are a central problem in Algorithmic Mechanism Design: pricing and allocating goods to buyers with complex preferences in order to maximize some desired objective (e.g., social welfare, revenue, or profit). The problem has been ... More

Spatiotemporal Feature Learning for Event-Based VisionMar 16 2019Unlike conventional frame-based sensors, event-based visual sensors output information through spikes at a high temporal resolution. By only encoding changes in pixel intensity, they showcase a low-power consuming, low-latency approach to visual information ... More

Rotating metric in Non-Singular Infinite Derivative Theories of GravityOct 05 2017Apr 12 2018In this paper we will provide a non-singular rotating space time metric for a ghost free infinite derivative theory of gravity. We will provide the predictions for the Lense-Thirring effect for a slowly rotating system, and how it is compared with that ... More

Baryogenesis, dark matter and inflation in the Next-to-Minimal Supersymmetric Standard ModelSep 19 2013Sep 23 2013Explaining baryon asymmetry, dark matter and inflation are important elements of a successful theory that extends beyond the Standard Model of particle physics. In this paper we explore these issues within the Next-to-Minimal Supersymmetric Standard Model ... More

How Difficult is it to Develop a Perfect Spell-checker? A Cross-linguistic Analysis through Complex Network ApproachMar 21 2007The difficulties involved in spelling error detection and correction in a language have been investigated in this work through the conceptualization of SpellNet - the weighted network of words, where edges indicate orthographic proximity between two words. ... More

Time auto-correlation function and Green-Kubo formula: A study on disordered harmonic chainSep 02 2010Feb 18 2014We have considered heat conduction in a one-dimensional mass disordered harmonic chain of $N$ particles connected to two Langevin type reservoirs at different temperatures. An exact expression for the boundary heat current-current auto-correlation function ... More

Representation Theory of Finite GroupsJan 04 2010The point of view of these notes on the topic is to bring out the flavor that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of base field. These notes cover completely the theory over complex ... More

Binary-Fluid Turbulence: Signatures of Multifractal Droplet Dynamics and Dissipation ReductionDec 31 2015Apr 09 2016We present an extensive direct numerical simulation of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction by using the Cahn-Hilliard-Navier-Stokes equations. We choose parameters, ... More

Early Universe cosmology and supergravityJun 30 2003In this talk I will describe the role of supersymmetric flat directions in the early Universe cosmology. Particularly I will discuss how supergravity effects lift the flat direction potential and leads to interesting cosmological consequences.

Selmer Groups of Elliptic Curves with Complex MultiplicationOct 08 2009This paper contains some results regarding the Iwasawa module structure of Selmer groups of elliptic curves with complex multiplication.

Supervising Feature InfluenceMar 28 2018Apr 07 2018Causal influence measures for machine learnt classifiers shed light on the reasons behind classification, and aid in identifying influential input features and revealing their biases. However, such analyses involve evaluating the classifier using datapoints ... More

On Shalev's conjecture for type $A_n$ and ${}^{2}A_n$May 12 2018In the paper we consider images of finite simple projective special linear and unitary groups under power words. In particular, we show that if $G\simeq \PSL_n^\varepsilon (q)$, then for every power words of type $x^M$ there exist constant $c$ and $N$ ... More

Projective varieties covered by isotrivial familiesOct 25 2011Jan 24 2013Let X,Y be projective schemes over a discrete valuation ring R, where Y is generically smooth and g:X \to Y a surjective R-morphism such that g_*\mathcal{O}_X = \mathcal{O}_Y. We show that if the family X \to Spec(R) is isotrivial, then the generic fiber ... More

Nanodot to Nanowire: A strain-driven shape transition in self-organized endotaxial CoSi2 on Si (100)May 04 2012We report a phenomenon of strain-driven shape transition in the growth of nanoscale self-organized endotaxial CoSi2 islands on Si (100) substrates. Small square shaped islands as small as 15\times15 nm2 have been observed. Islands grow in the square shape ... More

Dynamical Theory of the Inverted Cheerios EffectApr 06 2017Recent experiments have shown that liquid drops on highly deformable substrates exhibit mutual interactions. This is similar to the Cheerios effect, the capillary interaction of solid particles at a liquid interface, but now the roles of solid and liquid ... More

Application of the discrete Wentzel-Kramers-Brillouin method to spin tunnelingJul 13 1999A discrete version of the WKB method is developed and applied to calculate the tunnel splittings between classically degenerate states of spin Hamiltonians. The results for particular model problems are in complete accord with those previously found using ... More

Spin tunnelling in mesoscopic systemsDec 09 2000We study spin tunnelling in molecular magnets as an instance of a mesoscopic phenomenon, with special emphasis on the molecule Fe8. We show that the tunnel splitting between various pairs of Zeeman levels in this molecule oscillates as a function of applied ... More

CMB constraints on non-thermal leptogenesisAug 02 2003Nov 22 2003Leptogenesis is at the heart of particle cosmology which requires physics beyond the Standard Model. There are two possibilities of realizing leptogenesis; thermal and non-thermal. Both are viable given the scale of inflation and the constraint on the ... More

Real Elements in Spin GroupsApr 08 2008Let $F$ be a field of characteristic $\neq 2$. Let $G$ be an algebraic group defined over $F$. An element $t\in G(F)$ is called {\bf real} if there exists $s\in G(F)$ such that $sts^{-1}=t^{-1}$. A semisimple element $t$ in $GL_n(F), SL_n(F), O(q), SO(q), ... More

Audit Games with Multiple Defender ResourcesSep 16 2014Mar 01 2015Modern organizations (e.g., hospitals, social networks, government agencies) rely heavily on audit to detect and punish insiders who inappropriately access and disclose confidential information. Recent work on audit games models the strategic interaction ... More

Effect of Human Learning on the Transient Performance of Cloud-based Tiered ApplicationsAug 27 2016Cloud based tiered applications are increasingly becoming popular, be it on phones or on desktops. End users of these applications range from novice to expert depending on how experienced they are in using them. With repeated usage (practice) of an application, ... More

Performance Analysis of Ultra Wideband Receivers for High Data Rate Wireless Personal Area Network SystemMar 18 2010For high data rate ultra wideband communication system, performance comparison of Rake, MMSE and Rake-MMSE receivers is attempted in this paper. Further a detail study on Rake-MMSE time domain equalizers is carried out taking into account all the important ... More

On the Extension of the Gaussian Moat ProblemJan 28 2019In this paper, we have developed an algorithm for the prime searching in $\mathbb{R}^3$. This problem was proposed by M. Das [Arxiv,2019]. This paper is an extension of her work. As we know the distribution of primes will get more irregular as we are ... More

Almost-sure quasiperiodicity in countably many co-existing circlesDec 09 2016In many dynamical systems, countably infinitely many invariant tori co-exist. The occurrence of quasiperiodicity on any one of these tori is sometimes sufficient to establish strong global properties, like dense trajectories and periodic points. In this ... More

Bound state solutions of square root power law potential--Wavefunction ansatz method on $D$-dimensional Schrödinger equationMar 25 2015$D$-dimensional Schr\"{o}dinger equation is addressed for square root power law potential. Bound state unnormalized eigenfunctions and the energy eigenvalues are obtained using wave function ansatz method. Some special cases are studied at the end to ... More