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A Sunyaev-Zel'dovich take on cluster radio haloes -- I. Global scaling and bi-modality using Planck dataNov 11 2011Apr 13 2012Giant radio haloes in galaxy clusters are the primary evidence for the existence of relativistic particles (cosmic rays) and magnetic fields over Mpc scales. Observational tests for the different theoretical models explaining their powering mechanism ... More

Some results on the radio-SZ correlation for galaxy cluster radio halosOct 11 2012We present correlation results for the radio halo power in galaxy clusters with the integrated thermal Sunyaev-Zel'dovich (SZ) effect signal, including new results obtained at sub-GHz frequencies. The radio data is compiled from several published works, ... More

The impact of the SZ effect on cm-wavelength (1-30 GHz) observation of galaxy cluster radio relicsNov 10 2015Apr 05 2016(Abridged) Radio relics in galaxy clusters are believed to be associated with powerful shock fronts that originate during cluster mergers, and are a testbed for the acceleration of relativistic particles in the intracluster medium. Recently, radio relic ... More

Mpc-scale diffuse radio emission in two massive cool-core clusters of galaxiesOct 25 2016Radio halos are diffuse synchrotron sources on scales of ~1 Mpc that are found in merging clusters of galaxies, and are believed to be powered by electrons re-accelerated by the merger-driven turbulence. We present measurements of extended radio emission ... More

A comparative study of radio halo occurrence in SZ and X-ray selected galaxy cluster samplesJul 11 2013Nov 20 2013We aim at an unbiased census of the radio halo population in galaxy clusters and test whether current low number counts of radio halos have arisen from selection biases. We construct near-complete samples based on X-ray and Sunyaev-Zel'dovich (SZ) effect ... More

Beam energy dependence of pseudorapidity distributions of charged particles produced in heavy-ion collisions at RHIC and LHC energiesApr 29 2016Heavy-ion collisions at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory and the Large Hadron Collider at CERN probe matter at extreme conditions of temperature and energy density. Most of the global properties of the collisions can ... More

A Hybrid Linear Logic for Constrained Transition SystemsMar 08 2016Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic ... More

A Hybrid Linear Logic for Constrained Transition Systems with Applications to Molecular BiologyOct 16 2013Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic ... More

Proceedings Tenth International Workshop on Logical Frameworks and Meta Languages: Theory and PracticeJul 27 2015This volume constitutes the proceedings of LFMTP 2015, the Tenth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, held on August 1st, 2015 in Berlin, Germany. The workshop was a one-day satellite event of CADE-25, ... More

Joint X-ray/Sunyaev-Zel'dovich Analysis of the Intra-Cluster MediumApr 30 2010We present results from a joint X-ray/Sunyaev-Zel'dovich modeling of the intra-cluster gas using XMM-Newton and APEX-SZ imaging data. The goal is to study the physical properties of the intra-cluster gas with a non-parametric de-projection method that ... More

Introducing constrained matched filters for improved separation of point sources from galaxy clustersSep 17 2018Jan 28 2019Matched filters (MFs) are elegant and widely used tools to detect and measure signals that resemble a known template in noisy data. However, they can perform poorly in the presence of contaminating sources of similar or smaller spatial scale than the ... More

Evidence for a pressure discontinuity at the position of the Coma relic from Planck Sunyaev-Zel'dovich effect dataNov 20 2014Jan 16 2015Radio relics are Mpc-scale diffuse synchrotron sources found in galaxy cluster outskirts. They are believed to be associated with large-scale shocks propagating through the intra-cluster medium, although the connection between radio relics and the cluster ... More

Galaxy cluster outskirts from the thermal SZ and non-thermal synchrotron linkNov 25 2016Galaxy cluster merger shocks are the main agent for the thermalization of the intracluster medium and the energization of cosmic ray particles in it. Shock propagation changes the state of the tenuous intracluster plasma, and the corresponding signal ... More

Molecular Assembly on Two-Dimensional MaterialsNov 08 2016Molecular self-assembly is a well-known technique to create highly functional nanostructures on surfaces. Self-assembly on two-dimensional materials is a developing field and has already resulted in the discovery of several rich and interesting phenomena. ... More

ALMA-SZ Detection of a Galaxy Cluster Merger Shock at Half the Age of the UniverseAug 18 2016Sep 06 2016We present ALMA measurement of a merger shock using the thermal Sunyaev-Zel'dovich (SZ) effect signal, at the location of a radio relic in the famous El Gordo galaxy cluster at $z \approx 0.9$. Multi-wavelength analysis in combination with the archival ... More

ALMA-SZ Detection of a Galaxy Cluster Merger Shock at Half the Age of the UniverseAug 18 2016Nov 23 2016We present ALMA measurements of a merger shock using the thermal Sunyaev-Zel'dovich (SZ) effect signal, at the location of a radio relic in the famous El Gordo galaxy cluster at $z \approx 0.9$. Multi-wavelength analysis in combination with the archival ... More

Automating the Construction of Jet Observables with Machine LearningFeb 19 2019Machine-learning assisted jet substructure tagging techniques have the potential to significantly improve searches for new particles and Standard Model measurements in hadronic final states. Techniques with simple analytic forms are particularly useful ... More

Homotopy groups of highly connected manifoldsOct 18 2015In this paper we give a formula for the homotopy groups of $(n-1)$-connected $2n$-manifolds as a direct sum of homotopy groups of spheres in the case the $n^{th}$ Betti number is larger than $1$. We demonstrate that when the $n^{th}$ Betti number is $1$ ... More

Homotopy groups and periodic geodesics of closed 4-manifoldsMar 14 2013Dec 19 2013Given a simply connected, closed four manifold, we associate to it a simply connected, closed, spin five manifold. This leads to several consequences : the stable and unstable homotopy groups of such a four manifold is determined by its second Betti number, ... More

Outskirts of Galaxy ClustersMar 13 2013Until recently, only about 10% of the total intracluster gas volume had been studied with high accuracy, leaving a vast region essentially unexplored. This is now changing and a wide area of hot gas physics and chemistry awaits discovery in galaxy cluster ... More

The SKA Mid-frequency All-sky Continuum Survey: Discovering the unexpected and transforming radio-astronomyDec 18 2014We show that, in addition to specific science goals, there is a strong case for conducting an all-sky (i.e. the visible 3-pi steradians) SKA continuum survey which does not fit neatly into conventional science cases. History shows that the greatest scientific ... More

Submillimeter galaxies behind the Bullet Cluster (1E 0657-56)Mar 03 2010Clusters of galaxies are effective gravitational lenses able to magnify background galaxies and making it possible to probe the fainter part of the galaxy population. Submillimeter galaxies, which are believed to be star-forming galaxies at typical redshifts ... More

Verifying Safety Properties With the TLA+ Proof SystemNov 11 2010TLAPS, the TLA+ proof system, is a platform for the development and mechanical verification of TLA+ proofs written in a declarative style requiring little background beyond elementary mathematics. The language supports hierarchical and non-linear proof ... More

A TLA+ Proof SystemNov 12 2008We describe an extension to the TLA+ specification language with constructs for writing proofs and a proof environment, called the Proof Manager (PM), to checks those proofs. The language and the PM support the incremental development and checking of ... More

HERA Physics - an overview of experimental and theoretical resultsMay 19 1997In this talk I review the low x QCD experimental results from HERA and their theoretical underpinnings. In particular, I discuss the structure function $F_2$, large rapidity gap events, pomeron structure functions and $J/\psi$ production.

Simplifying the one loop five graviton amplitude in type IIB string theoryAug 06 2016We consider the D^8 R^5 and D^{10} R^5 terms in the low momentum expansion of the five graviton amplitude in type IIB string theory at one loop. They involve integrals of various modular graph functions over the fundamental domain of SL(2,Z). Unlike the ... More

A complexity theory of constructible functions and sheavesSep 23 2013Sep 30 2014In this paper we introduce constructible analogs of the discrete complexity classes $\mathbf{VP}$ and $\mathbf{VNP}$ of sequences of functions. The functions in the new definitions are constructible functions on $\mathbb{R}^n$ or $\mathbb{C}^n$. We define ... More

Low temperature properties of holographic condensatesDec 31 2010Jun 16 2011In the current work we study various models of holographic superconductors at low temperature. Generically the zero temperature limit of those models are solitonic solution with a zero sized horizon. Here we generalized simple version of those zero temperature ... More

GRB011211: An alternative interpretation of the optical and X-ray spectra in terms of blueshiftsJul 10 2009The redshifts of the gamma ray burst (GRB) GRB 011211 has been determined as 2.14 from several absorption lines seen in the spectrum of its optical afterglow. The spectrum of its X-ray afterglow exhibited several emission lines,and their identification ... More

QSO pairs {\it across} Active galaxies: Evidence of Blueshifts?Jan 08 2007Several QSO pairs have been reported and their redshifts determined, where the two objects in each pair are located {\it across} an active galaxy. The usually accepted explanation of such occurrences is that the pair is ejected from the active galaxy. ... More

Global Seismology of the SunJun 22 2016The seismic study of the Sun and other stars offers a unique window into the interior of these stars. Thanks to helioseismology, we know the structure of the Sun to admirable precision. In fact, our knowledge is good enough to use the Sun as a laboratory. ... More

Perspectives on Low-Mass Star FormationMar 05 2017I review some recent work on low-mass star formation, with an emphasis on theory, basic principles, and unresolved questions. Star formation is both a gravitational fragmentation problem as well as an accretion problem. Molecular cloud structure can be ... More

Molecular Cloud Fragmentation and Core CollapseOct 17 2015I review some steps in the conversion of molecular cloud gas into stars and planets, with an emphasis in this presentation on the early stage molecular cloud fragmentation that leads to elongated filaments/ribbons. Magnetic fields can play a crucial role ... More

Topological Hochschild Homology of $K/p$ as a $K_p^\wedge$ moduleJun 22 2010Dec 03 2010Let $R$ be an $E_\infty$-ring spectrum. Given a map $\zeta$ from a space $X$ to $BGL_1R$, one can construct a Thom spectrum, $X^\zeta$, which generalises the classical notion of Thom spectrum for spherical fibrations in the case $R=S^0$, the sphere spectrum. ... More

What does helioseismology tell us about solar cycle related structural changes in the Sun?May 03 2002Solar oscillations frequencies show a distinct change with solar activity. The changes in frequencies can be used to study the time variation of solar structure. We discuss constraints on the changes in solar structure with time as obtained with helioseismic ... More

Constraints on the Formation and Evolution of Circumstellar Disks in Rotating Magnetized Cloud CoresAug 13 1998We use magnetic collapse models to place some constraints on the formation and angular momentum evolution of circumstellar disks which are embedded in magnetized cloud cores. Previous models have shown that the early evolution of a magnetized cloud core ... More

An exposition of special relativity without appeal to "constancy of speed of light" hypothesesDec 09 2018We present the theory of special relativity here through the lens of differential geometry. In particular, we explicitly avoid any reference to hypotheses of the form "The laws of physics take the same form in all inertial reference frames" and "The speed ... More

Proving relations between modular graph functionsJun 22 2016Dec 03 2016We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the ... More

Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixtureAug 22 2005We elucidate the universal properties of the nonequilibrium steady states (NESS) in a driven symmetric binary fluid mixture, an example of active advection, in its miscible phase. We use the symmetries of the equations of motion to establish the appropriate ... More

Higher Derivative Corrections in Holographic QCDJun 30 2007Dec 03 2007We consider the effect of the R^4 term in type IIA string theory on the supergravity background dual to N_c D4 branes compactified on a circle with supersymmetry breaking boundary conditions. We study the dynamics of D8 branes in this perturbed geometry ... More

Localized Tachyons and the g_cl conjectureApr 29 2002Jul 08 2002We consider C/Z_N and C^2/Z_N orbifolds of heterotic string theories and Z_N orbifolds of AdS_3. We study theories with N=2 worldsheet superconformal invariance and construct RG flows. Following Harvey, Kutasov, Martinec and Moore, we compute g_cl and ... More

Dynamics of geometric phase in the adiabatic limit of quantum phase transitionAug 23 2009May 10 2010The geometric phase associated with a many body ground state exhibits a signature of quantum phase transition. In this context, we have studied the behaviour of the geometric phase during a linear quench caused by a gradual turning off of the magnetic ... More

Topological Aspects of High Temperature Superconductivity and Berry PhaseMay 29 2003We propose a mechanism of high temperature superconductivity from the viewpoint of chirality and Berry phase. It is observed that spin pairing and charge pairing is caused by a gauge force generated by magnetic flux quanta attached to them. From the renormalization ... More

Low $x$ physics and Structure FunctionsMay 19 1998In this talk I review the behaviour of structure functions at low values of Bjorken $x$ and discuss the theoretical underpinnings with particular attention to resummation schemes. I present the need for 'less inclusive' events to distinguish between various ... More

Phase Separation Transition in a Nonconserved Two Species ModelOct 27 2016A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show that, in the ... More

A simplifying feature of the heterotic one loop four graviton amplitudeOct 05 2017Dec 08 2017We show that the weight four modular graph functions that contribute to the integrand of the t_8 t_8 D^4 R^4 term at one loop in heterotic string theory do not require regularization, and hence the integrand is simple. This is unlike the graphs that contribute ... More

Simplifying the one loop five graviton amplitude in type IIB string theoryAug 06 2016Apr 11 2017We consider the D^8 R^5 and D^{10} R^5 terms in the low momentum expansion of the five graviton amplitude in type IIB string theory at one loop. They involve integrals of various modular graph functions over the fundamental domain of SL(2,Z). Unlike the ... More

Non--analytic terms from nested divergences in maximal supergravityApr 10 2016The $D^4\mathcal{R}^4$ and $D^6\mathcal{R}^4$ coefficient functions in the effective action of type II string theory compactified on $T^d$ contain terms of the form $\mathcal{E}_1 {\rm ln}g_d$ and $\mathcal{E}_2 ({\rm ln}g_d)^2$ in specific dimensions, ... More

Non-BPS interactions from the type II one loop four graviton amplitudeJan 17 2016We obtain T--duality invariant second order differential equations satisfied by the $D^8\mathcal{R}^4$ and $D^{10} \mathcal{R}^4$ interactions from the low energy expansion of the one loop four graviton amplitude in toroidally compactified type II string ... More

The structure of the R^8 term in type IIB string theoryJun 11 2013Feb 02 2014Based on the structure of the on-shell linearized superspace of type IIB supergravity, we argue that there is a non--BPS 16 derivative interaction in the effective action of type IIB string theory of the form (t_8 t_8 R^4)^2, which we call the R^8 interaction. ... More

The D^6 R^4 term in type IIB string theory on T^2 and U-dualityDec 08 2007We propose a manifestly U-duality invariant modular form for the D^6 R^4 interaction in the effective action of type IIB string theory compactified on T^2. It receives perturbative contributions upto genus three, as well as non-perturbative contributions ... More

Constraining the D3-brane effective actionAug 14 2008We consider higher derivative corrections of the type D^{2k} R^2 in the effective action of the D3-brane with trivial normal bundle. Based on the perturbative disc and annulus amplitudes, and constraints of supersymmetry and duality, we argue that these ... More

Dynamo effect beyond the kinematic approximation: suppression of linear instabilities by non-linear feedbackAug 07 2002The turbulent dynamo effect, which describes the generation of magnetic fields in astrophysical objects, is described by the dynamo equation. This, in the kinematic (linear) approximation gives an unbounded exponential growth of the long wavelength part ... More

The homotopy type of the loops on $(n-1)$-connected $(2n+1)$-manifoldsOct 16 2018For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are determined by ... More

Poisson equation for the three loop ladder diagram in string theory at genus oneJun 07 2016The three loop ladder diagram is a graph with six links and four cubic vertices that contributes to the D^{12} R^4 amplitude at genus one in type II string theory. The vertices represent the insertion points of vertex operators on the toroidal worldsheet ... More

Proving relations between modular graph functionsJun 22 2016We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the ... More

Some explicit computations and models of free productsNov 26 2011In this note, we first work out some `bare hands' computations of the most elementary possible free products involving $\mathbb{C}^2 ~(=\mathbb{C} \oplus \mathbb{C} $) and $M_2 ~(= M_2(\mathbb{C}))$. Using these, we identify all free products $C \ast ... More

The Plancherel Formula for the Universal Covering Group of SL(2,R) RevisitedOct 11 2007Sep 14 2008The Plancherel formula for the universal covering group of $SL(2, R)$ derived earlier by Pukanszky on which Herb and Wolf build their Plancherel theorem for general semisimple groups is reconsidered. It is shown that a set of unitarily equivalent representations ... More

Turbulence and Magnetic Fields in CloudsNov 15 2004We discuss several categories of models which may explain the IMF, including the possible role of turbulence and magnetic fields.

Effects of errors in the solar radius on helioseismic inferencesDec 09 1997Frequencies of intermediate-degree f-modes of the Sun seem to indicate that the solar radius is smaller than what is normally used in constructing solar models. We investigate the possible consequences of an error in radius on results for solar structure ... More

Minimalist proof of Fundamental Theorem of Algebra using elementary real analysisApr 26 2017Jun 03 2018The existence of a real quadratic polynomial factor, given any polynomial with real coefficients, is proven using only elementary real analysis. The aim is to provide an approachable proof to anyone familiar with the least upper bound property for real ... More

Computing the Top Betti Numbers of Semi-algebraic Sets Defined by Quadratic Inequalities in Polynomial TimeMar 10 2006Feb 22 2007For any $\ell > 0$, we present an algorithm which takes as input a semi-algebraic set, $S$, defined by $P_1 \leq 0,...,P_s \leq 0$, where each $P_i \in \R[X_1,...,X_k]$ has degree $\leq 2,$ and computes the top $\ell$ Betti numbers of $S$, $b_{k-1}(S), ... More

Eigenvalue equation for genus two modular graphsDec 02 2018Feb 07 2019We obtain a second order differential equation on moduli space satisfied by certain modular graph functions at genus two, each of which has two links. This eigenvalue equation is obtained by analyzing the variations of these graphs under the variation ... More

Perturbative type II amplitudes for BPS interactionsOct 06 2015Jan 20 2016We consider the perturbative contributions to the R^4, D^4 R^4 and D^6 R^4 interactions in toroidally compactified type II string theory. These BPS interactions do not receive perturbative contributions beyond genus three. We derive Poisson equations ... More

Constraining gravitational interactions in the M theory effective actionAug 12 2013Feb 02 2014We consider purely gravitational interactions of the type D^{6n} R^4 in the effective action of M theory which are related to the type IIA interactions of the form e^{2n\phi_A} D^{6n} R^4 where \phi_A is the type IIA dilaton. The coefficients of the M ... More

Statistical properties of driven Magnetohydrodynamic turbulence in three dimensions: Novel universalityDec 04 2003We analyse the universal properties of nonequilibrium steady states of driven Magnetohydrodynamic (MHD) turbulence in three dimensions (3d). We elucidate the dependence of various phenomenologically important dimensionless constants on the symmetries ... More

Algorithms in Real Algebraic Geometry: A SurveySep 04 2014We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for computing topological ... More

Computing the First Few Betti Numbers of Semi-algebraic Sets in Single Exponential TimeMar 10 2006In this paper we describe an algorithm that takes as input a description of a semi-algebraic set $S \subset \R^k$, defined by a Boolean formula with atoms of the form $P > 0, P < 0, P=0$ for $P \in {\mathcal P} \subset \R[X_1,...,X_k],$ and outputs the ... More

A complex analogue of Toda's TheoremDec 14 2009Oct 14 2011Toda \cite{Toda} proved in 1989 that the (discrete) polynomial time hierarchy, $\mathbf{PH}$, is contained in the class $\mathbf{P}^{#\mathbf{P}}$, namely the class of languages that can be decided by a Turing machine in polynomial time given access to ... More

Absence of torsion for NK_1(R) over associative ringsJan 04 2010When R is a commutative ring with identity, and if k is a natural number with kR = R, then C. Weibel proved that SK_1(R[X]) has no k-torsion. We reprove his result for any associative ring R with identity in which kR = R.

Holst-like 2+1 Quantum Gravity with Toric Spatial FoliationFeb 04 2009Sep 23 2009This paper has been withdrawn by the author. A much more revised version is available as arXiv:0909.4238.

Local-global principle for General Quadratic and General Hermitian groups and the nilpotence of KH_1Dec 11 2014In this article we establish an analog of the Quillen---Suslin's local-global principle for the elementary subgroup of the general quadratic group and the general Hermitian group. We show that unstable ${\k}$-groups of general Hermitian groups over module ... More

A note on Quadratic and Hermitian GroupsNov 27 2009In this article we deduce an analogue of Quillen's Local-Global Principle for the elementary subgroup of the general quadratic group and the hermitian group. We show that the unstable K_1-groups of the hermitian groups are nilpotent by abelian. This generalizes ... More

Magic Numbers from New SystematicsFeb 08 2006A new systematics from the separation energy of deuteron is used to examine the magicity of stable as well as nuclei towards dripline.

Relation between concurrence and Berry phase of an entangled state of two spin 1/2 particlesFeb 10 2006We have studied here the influence of the Berry phase generated due to a cyclic evolution of an entangled state of two spin 1/2 particles. It is shown that the measure of formation of entanglement is related to the cyclic geometric phase of the individual ... More

Energy scales in a holographic black hole and conductivity at finite momentumNov 26 2009Nov 28 2009In this work we discuss the low temperature ($T$) behavior of gauge field correlators with finite momentum (k) in a $AdS^4$ black hole background. At low temperature, a substantial non-zero conductivity is only possible for a frequency range $\omega>\omega_g=k$. ... More

Low momentum expansion of one loop amplitudes in heterotic string theoryAug 28 2017Sep 04 2017We consider the low momentum expansion of the four graviton and the two graviton--two gluon amplitudes in heterotic string theory at one loop in ten dimensions, and analyze contributions upto the D^2 R^4 interaction from the four graviton amplitude, and ... More

Constraining non--BPS interactions from counterterms in three loop maximal supergravityAug 01 2014Oct 10 2015The structure of one, two and three loop counterterms imposes strong constraints on several non--BPS interactions in the low momentum expansion of the three loop four graviton amplitude in maximal supergravity. The constraints are imposed by demanding ... More

The D^6 R^4 term from three loop maximal supergravityJul 02 2014Oct 12 2014We consider the D^6 R^4 term which is the leading contribution in the low momentum expansion of the three loop, four graviton amplitude in maximal supergravity. We calculate the moduli dependent coefficient of this term in 11 dimensional supergravity ... More

Supersymmetry constraints on the R^4 multiplet in type IIB on T^2Jul 18 2011Jul 19 2011We consider a class of eight derivative interactions in the effective action of type IIB string theory compactified on T^2. These 1/2 BPS interactions have moduli dependent couplings. We impose the constraints of supersymmetry to show that each of these ... More

The D^4 R^4 term in type IIB string theory on T^2 and U-dualityAug 22 2007Aug 14 2008We propose a manifestly U-duality invariant modular form for the D^4 R^4 interaction in type IIB string theory compactified on T^2. It receives perturbative contributions upto two loops, and non-perturbative contributions from D-instantons and (p,q) string ... More

Phase transitions and noise crosscorrelations in a model of directed polymers in a disordered mediumJul 12 2000We show that effective interactions mediated by disorder between two directed polymers can be modelled as the crosscorrelation of noises in the Kardar-Parisi-Zhang (KPZ) equations satisfied by the respective free energies of these polymers. When there ... More

Decaying magnetohydrodynamics: effects of initial conditionsOct 11 1999We study the effects of homogenous and isotropic initial conditions on decaying Magnetohydrodynamics (MHD). We show that for an initial distribution of velocity and magnetic field fluctuations, appropriately defined structure functions decay as power ... More

Of Sullivan models, Massey products, and twisted Pontrjagin productsSep 14 2012Sep 27 2012Associated to every connected, topological space $X$ there is a Hopf algebra - the Pontrjagin ring of the based loop space of the configuration space of two points in X. We prove that this Hopf algebra is not a homotopy invariant of the space. We also ... More

A complexity theory of constructible functions and sheavesSep 23 2013Oct 06 2017In this paper we introduce constructible analogs of the discrete complexity classes $\mathbf{VP}$ and $\mathbf{VNP}$ of sequences of functions. The functions in the new definitions are constructible functions on $\mathbb{R}^n$ or $\mathbb{C}^n$. We define ... More

Eigenvalue equation for the modular graph $C_{a,b,c,d}$Jun 06 2019The modular graph $C_{a,b,c,d}$ on the torus is a three loop planar graph in which two of the vertices have coordination number four, while the others have coordination number two. We obtain an eigenvalue equation satisfied by $C_{a,b,c,d}$ for generic ... More

Higher Spin de Sitter Quantum GravityJul 16 2015Jul 21 2015We consider Einstein gravity with positive cosmological constant coupled with higher spin interactions and calculate Euclidean path integral perturbatively. We confine ourselves to the static patch of the 3 dimensional de Sitter space. This geometry, ... More

Communities of dense weighted networks: MicroRNA co-target network as an exampleJan 15 2014Complex networks are intrinsically modular. Resolving small modules is particularly difficult when the network is densely connected; wide variation of link weights invites additional complexities. In this article we present an algorithm to detect community ... More

The D^{10} R^4 term in type IIB string theoryOct 31 2006Nov 02 2006The modular invariant coefficient of the D^{2k} {\cal{R}}^4 term in the effective action of type IIB superstring theory is expected to satisfy Poisson equation on the fundamental domain of SL(2,Z). Under certain assumptions, we obtain the equation satisfied ... More

Dynamo mechanism: Effects of correlations and viscositiesFeb 23 2004We analyze the effects of the background velocity and the initial magnetic field correlations, and viscosities on the turbulent dynamo and the \alpha-effect. We calculate the \alpha-coefficients for arbitrary magnetic and fluid viscosities, background ... More

Scaling and noise-crosscorrelations in a Burgers-like model for MagnetohydrodynamicsSep 06 2000Sep 07 2000We study the effects of crosscorrelations of noises on the scaling properties of the correlation functions in a reduced model for Magnetohydrodynamic (MHD) turbulence [A. Basu, J.K Bhattacharjee and S. Ramaswamy [{\em Eur. Phys. J B} {\bf 9}, 725 (1999)]. ... More

Algorithmic Semi-algebraic Geometry and Topology -- Recent Progress and Open ProblemsAug 21 2007Sep 15 2007We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from describing these ... More

Revisiting Absorbing Phase Transition in Energy Exchange ModelsJun 13 2012Jul 13 2013A recent study of conserved Manna model, with both discrete and continuous variable, indicates that absorbing phase transitions therein belong to the directed percolation (DP) universality class. In this context we revisit critical behaviour in energy ... More

Discontinuous Absorbing State Transition in $(1+1)$ DimensionOct 11 2010A $(1+1)$ dimensional model of directed percolation is introduced where sites on a tilted square lattice are connected to their neighbours by $N$ channels, operated at both ends by valves which are either open or closed. The spreading fluid is assumed ... More

On The Injection Spectrum of Ultrahigh Energy Cosmic Rays in the Top-Down ScenarioMar 31 2004May 13 2004We analyze the uncertainties involved in obtaining the injection spectra of UHECR particles in the top-down scenario of their origin. We show that the DGLAP $Q^2$ evolution of fragmentation functions (FF) to $Q=M_X$ (mass of the X particle) from their ... More

Spectral Sequences, Exact Couples and Persistent Homology of filtrationsAug 04 2013Feb 01 2016In this paper we study the relationship between a very classical algebraic object associated to a filtration of spaces, namely a spectral sequence introduced by Leray in the 1940's, and a more recently invented object that has found many applications ... More

Statistics of Quasiparticles in Fractional Quantum Hall StatesFeb 16 2004We have considered here the statistics parameter for quasiparticles in FQH states from an analysis of these states in the framework of chiral anomaly and Berry phase. It is shown that we have a generalized relation such that the statistical phase of a ... More

$SO(N)$ Lattice Gauge Theory, planar and beyondAug 15 2016Lattice Gauge theories have been studied in the physics literature as discrete approximations to quantum Yang-Mills theory for a long time. Primary statistics of interest in these models are expectations of the so called "Wilson loop variables". In this ... More

Multi-parameter deformed and nonstandard $Y(gl_M)$ Yangian symmetry in integrable variants of Haldane-Shastry spin chainFeb 10 1998By using `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable variants of Haldane-Shastry (HS) spin chain. Lax equations for these ... More

On the equivariant Betti numbers of symmetric semi-algebraic sets: vanishing, bounds and algorithmsOct 17 2016Let $\mathrm{R}$ be a real closed field. We prove that for any fixed $d$, the equivariant rational cohomology groups of closed symmetric semi-algebraic subsets of $\mathrm{R}^k$ defined by polynomials of degrees bounded by $d$ vanishes in dimensions $d$ ... More