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Automated Parameterized Verification of CRDTsMay 14 2019Maintaining multiple replicas of data is crucial to achieving scalability, availability and low latency in distributed applications. Conflict-free Replicated Data Types (CRDTs) are important building blocks in this domain because they are designed to ... More

Open theoretical problems in the physics of aperiodic systemsJun 23 2010Quasicrystals have intrigued and stimulated research in a large number of disciplines. Mathematicians, physicists, chemists, metallurgists and materials scientists have found in them a fertile ground for new insights and discoveries. In the quarter century ... More

The Dirac equation approach to spin-1/2 particle beam opticsMar 28 1998The traditional approach to accelerator optics, based mainly on classical mechanics, is working excellently from the practical point of view. However, from the point of view of curiosity, as well as with a view to explore quantitatively the consequences ... More

Less singular quasicrystals: life in low codimensionsMay 25 2001Jul 19 2001The Rauzy tilings were proposed recently in a generalisation of the Fibonacci chain by Vidal and Mosseri. These tilings have a particularly simple theoretical description, making them appealing candidates for analytical solutions for electronic properties. ... More

Self-similarity under inflation and level statistics: a study in two dimensionsSep 07 1999Energy level spacing statistics are discussed for a two dimensional quasiperiodic tiling. The property of self-similarity under inflation is used to write a recursion relation for the level spacing distributions defined on square approximants to the perfect ... More

Energy level statistics of electrons in a 2D quasicrystalJan 19 1994A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics for the randomized ... More

Energy levels and their correlations in quasicrystalsNov 03 2006Quasicrystals can be considered, from the point of view of their electronic properties, as being intermediate between metals and insulators. For example, experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have conductivities far smaller ... More

On a nonstandard two-parametric quantum algebra and its connections with $U_{p,q}(gl(2))$ and $U_{p,q}(gl(1|1))$Oct 21 1994Oct 25 1994A quantum algebra $U_{p,q}(\zeta ,H,X_\pm )$ associated with a nonstandard $R$-matrix with two deformation parameters$(p,q)$ is studied and, in particular, its universal ${\cal R}$-matrix is derived using Reshetikhin's method. Explicit construction of ... More

Antiferromagnetism in two-dimensional quasicrystalsOct 13 2008Quasiperiodic structures possess long range positional order, but are freed of constraints imposed by translational invariance. For spins interacting via Heisenberg couplings, one may expect therefore to find novel magnetic configurations in such structures. ... More

The dual $(p,q)$-Alexander-Conway Hopf algebras and the associated universal ${\cal T}$-matrixFeb 07 1996The dually conjugate Hopf algebras $Fun_{p,q}(R)$ and $U_{p,q}(R)$ associated with the two-parametric $(p,q)$-Alexander-Conway solution $(R)$ of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the ... More

On the Hopf structure of $U_{p,q}(gl(1|1))$ and the universal ${\cal T}$-matrix of $Fun_{p,q}(GL(1|1))$Sep 27 1994Using the technique developed by Fronsdal and Galindo (Lett. Math. Phys. 27 (1993) 57) for studying the Hopf duality between the quantum algebras $Fun_{p,q}(GL(2))$ and $U_{p,q}(gl(2))$, the Hopf structure of $U_{p,q}(gl(1|1))$, dual to $Fun_{p,q}(GL(1|1))$, ... More

(p,q)-Rogers-Szego polynomial and the (p,q)-oscillatorMay 24 2010A (p,q)-analogue of the classical Rogers-Szego polynomial is defined by replacing the q-binomial coefficient in it by the (p,q)-binomial coefficient. Exactly like the Rogers-Szego polynomial is associated with the q-oscillator algebra it is found that ... More

Finite Horizon Adaptive Optimal Distributed Power Allocation for Enhanced Cognitive Radio Network in the Presence of Channel UncertaintiesFeb 06 2013In this paper, novel enhanced Cognitive Radio Network is considered by using power control where secondary users are allowed to use wireless resources of the primary users when primary users are deactivated, but also allow secondary users to coexist with ... More

BKM Lie superalgebras from counting twisted CHL dyonsJun 17 2010Jun 02 2011Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, ... More

Punctures in W-string theoryMar 25 1997May 15 1997Using the differential equation approach to W-algebras, we discuss the inclusion of punctures in W-string theory. The key result is the existence of different kinds of punctures in W-strings. This is similar to the NS and R punctures occuring in superstring ... More

Anisotropic model of dark energy dominated universe with hybrid expansion lawOct 08 2010Aug 22 2013The paper deals with the study of the dynamics of Universe within the framework of a spatially homogeneous Bianchi-V space-time filled with a perfect fluid composed of non-interacting matter and dynamical dark energy components. We determine the Bianchi-V ... More

String Cosmology in Anisotropic Bianchi-II Space-timeOct 01 2010Jan 14 2011The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological model representing massive strings. The energy-momentum tensor, as formulated by Letelier (1983), has been used to construct a massive string cosmological model ... More

A Statistical Block Fading Channel Model for Multiuser Massive MIMO SystemMar 04 2016This paper presents a statistical block fading channel model for multiuser massive MIMO system. The proposed channel model is evolved from correlation based stochastic channel model (CBSCM) but in addition to the properties of CBSCM, it has capability ... More

Unravelling Mathieu MoonshineJun 28 2011Apr 23 2012The D1-D5-KK-p system naturally provides an infinite dimensional module graded by the dyonic charges whose dimensions are counted by the Igusa cusp form, Phi_{10}(Z)$. We show that the Mathieu group, M_{24}, acts on this module by recovering the Siegel ... More

Brewing moonshine for MathieuDec 28 2010We propose a moonshine for the sporadic Mathieu group M_12 that relates its conjugacy classes to various modular forms and Borcherds Kac-Moody Lie superalgebras.

On the Geometry of W_n gravityMay 30 1994We report work done with T. Jayaraman (hep-th/9405146) in this talk. In a recent paper, Hitchin introduced generalisations of the Teichmuller space of Riemann surfaces. We relate these spaces to the Teichmuller spaces of W-gravity. We show how this provides ... More

The Graphics Card as a Streaming ComputerOct 05 2003Oct 07 2003Massive data sets have radically changed our understanding of how to design efficient algorithms; the streaming paradigm, whether it in terms of number of passes of an external memory algorithm, or the single pass and limited memory of a stream algorithm, ... More

Some FRW Models of Accelerating Universe with Dark EnergyOct 01 2010The paper deals with a spatially homogeneous and isotropic FRW space-time filled with perfect fluid and dark energy components. The two sources are assumed to interact minimally, and therefore their energy momentum tensors are conserved separately. A ... More

Dispersion Relation for Alfven Waves in a Viscous, Diffusive PlasmaJun 16 2007Propagation of Alfven waves in the solar plasma has been a topic of scientific interest for a long time. We have derived a dispersion relation for shear Alfven waves in a viscous and diffusive plasma.

Pasting pseudofunctorsJun 24 2004We give an abstract criterion for pasting pseudofunctors on two subcategories of a category into a pseudofunctor on the whole category. As an application we extend the variance theory of the twisted inverse image $(-)^!$ over schemes to that over formal ... More

"Improved FCM algorithm for Clustering on Web Usage Mining"Apr 11 2011In this paper we present clustering method is very sensitive to the initial center values, requirements on the data set too high, and cannot handle noisy data the proposal method is using information entropy to initialize the cluster centers and introduce ... More

Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric seriesFeb 27 2006We give a method to embed the q-series in a (p,q)-series and derive the corresponding (p,q)-extensions of the known q-identities. The (p,q)-hypergeometric series, or twin-basic hypergeometric series (diferent from the usual bibasic hypergeometric series), ... More

A note on M(atrix) theory in seven dimensions with eight superchargesMay 15 1997Aug 05 1997We consider M(atrix) theory compactifications to seven dimensions with eight unbroken supersymmetries. We conjecture that both M(atrix) theory on K3 and Heterotic M(atrix) theory on T^3 are described by the same 5+1 dimensional theory with N=2 supersymmetry ... More

Consistency of the nonflat $Λ$CDM model with the new result from BOSSJul 13 2015Dec 01 2015Using 137,562 quasars in the redshift range $2.1\leq z\leq3.5$ from the Data Release 11 (DR11) of the Baryon Oscillation Spectroscopic Survey (BOSS) of Sloan Digital Sky Survey (SDSS)-III, the BOSS-SDSS collaboration estimated the expansion rate $H(z=2.34)=222\pm7$ ... More

Probing the matter and dark energy sources in a viable Big Rip model of the UniverseApr 07 2014Aug 13 2014Chevallier-Polarski-Linder (CPL) parametrization for the equation of state of dark energy in terms of cosmic redshift or scale factor have been frequently studied in the literature. In this study, we consider cosmic time based CPL parametrization for ... More

Third Galois cohomology group of function fields of curves over number fieldsJun 09 2017Let F be the function field of a curve over totally imaginary number field. Let p be a prime. If F contains a primitive p th root of unity, then every element in the third Galois cohomology group of F with values in the group of p th roots of unity, is ... More

Compactification for essentially finite-type mapsSep 08 2008We show that any separated essentially finite-type map $f$ of noetherian schemes globally factors as $f = hi$ where $i$ is an injective localization map and $h$ a separated finite-type map. In particular, via Nagata's compactification theorem, $h$ can ... More

Building Resource Adaptive Software Systems (BRASS): Objectives and System EvaluationOct 07 2015As modern software systems continue inexorably to increase in complexity and capability, users have become accustomed to periodic cycles of updating and upgrading to avoid obsolescence -- if at some cost in terms of frustration. In the case of the U.S. ... More

An Attributive Logic of Set Descriptions and Set OperationsMay 30 1994This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted universal role ... More

Heterotic M(atrix) theory at generic points in Narain moduli spaceJul 18 1997Jul 30 1997Type II compactifications with varying string coupling can be described elegantly in F-theory/M-theory as compactifications on U - manifolds. Using a similar approach to describe Super Yang-Mills with a varying coupling constant, we argue that at generic ... More

Higher dimensional uniformisation and W-geometryDec 09 1994Oct 13 1995We formulate the uniformisation problem underlying the geometry of W_n-gravity using the differential equation approach to W-algebras. We construct W_n-space (analogous to superspace in supersymmetry) as an (n-1) dimensional complex manifold using isomonodromic ... More

Notes on higher-dimensional partitionsMar 20 2012We show the existence of a series of transforms that capture several structures that underlie higher-dimensional partitions. These transforms lead to a sequence of triangles whose entries are given combinatorial interpretations as the number of particular ... More

Deterministic Consistency Checking of LP ConstraintsFeb 14 1995Feb 16 1995We provide a constraint based computational model of linear precedence as employed in the HPSG grammar formalism. An extended feature logic which adds a wide range of constraints involving precedence is described. A sound, complete and terminating deterministic ... More

Polynomial deformations of $osp(1/2)$ and generalized parabosonsOct 20 1994We consider the algebra $R$ generated by three elements $A,B,H$ subject to three relations $[H,A]=A$, $[H,B]=-B$ and $\{A,B\}=f(H)$. When $f(H)=H$ this coincides with the Lie superalgebra $osp(1/2)$; when $f$ is a polynomial we speak of polynomial deformations ... More

Contagion processes on urban bus networks in Indian citiesSep 14 2015May 19 2016Bus transportation is considered as one of the most convenient and cheapest modes of public transportation in Indian cities. Due to their cost-effectiveness and wide reachability, they help a significant portion of the human population in cities to reach ... More

Collaborative Learning of Stochastic Bandits over a Social NetworkFeb 29 2016Jul 11 2016We consider a collaborative online learning paradigm, wherein a group of agents connected through a social network are engaged in playing a stochastic multi-armed bandit game. Each time an agent takes an action, the corresponding reward is instantaneously ... More

Finite dimensional representations of the quantum group $GL_{p,q}(2)$ using the exponential map from $U_{p,q}(gl(2))$Nov 28 1994Mar 30 1995Using the Fronsdal-Galindo formula for the exponential mapping from the quantum algebra $U_{p,q}(gl(2))$ to the quantum group $GL_{p,q}(2)$, we show how the $(2j+1)$-dimensional representations of $GL_{p,q}(2)$ can be obtained by `exponentiating' the ... More

Grids versus Graphs: Partitioning Space for Improved Taxi Demand-Supply ForecastsFeb 18 2019Accurate taxi demand-supply forecasting is a challenging application of ITS (Intelligent Transportation Systems), due to the complex spatial and temporal patterns. We investigate the impact of different spatial partitioning techniques on the prediction ... More

Stability, convergence and Hopf bifurcation analyses of the classical car-following modelJul 29 2016Mar 29 2018Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles traversing a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Classical Car-Following ... More

An extension of the Bernoulli polynomials inspired by the Tsallis statisticsDec 22 2016In [Arch. Math. 7, 28 (1956), Utilitas Math. 15, 51 (1979)] Carlitz introduced the degenerate Bernoulli numbers and polynomials by replacing the exponential factors in the corresponding classical generating functions with their deformed analogs: $\exp(t) ... More

The exponential map for representations of $U_{p,q}(gl(2))$Jul 13 1995For the quantum group $GL_{p,q}(2)$ and the corresponding quantum algebra $U_{p,q}(gl(2))$ Fronsdal and Galindo explicitly constructed the so-called universal $T$-matrix. In a previous paper we showed how this universal $T$-matrix can be used to exponentiate ... More

Novel Properties of Frustrated Low Dimensional Magnets with Pentagonal SymmetryJun 23 2010In the context of magnetism, frustration arises when a group of spins cannot find a configuration that minimizes all of their pairwise interactions simultaneously. We consider the effects of the geometric frustration that arises in a structure having ... More

The reduced classical car-following model: stability analyses and design guidelinesJul 29 2016Aug 01 2016Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles driving on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of a recently-proposed car-following ... More

Right buffer sizing matters: stability and queuing dynamics in TCPApr 19 2016Apr 28 2016Motivated by recent concerns that queuing delays in the Internet are on the rise, we conduct a performance evaluation of Compound TCP (C-TCP) in two topologies: a single bottleneck and a multi-bottleneck topology. The first topology consists of a single ... More

Fractal dimensions of the wavefunctions and local spectral measures on the Fibonacci chainJan 04 2016Aug 03 2016We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation ... More

Queuing Approaches to Principal-Agent Communication under Information OverloadMay 03 2016In the information overload regime, human communication tasks such as responding to email are well-modeled as priority queues, where priority is determined by a mix of intrinsic motivation and extrinsic motivation corresponding to the task's importance ... More

Realizations of $su(1,1)$ and $U_q(su(1,1))$ and generating functions for orthogonal polynomialsJul 20 1998Positive discrete series representations of the Lie algebra $su(1,1)$ and the quantum algebra $U_q(su(1,1))$ are considered. The diagonalization of a self-adjoint operator (the Hamiltonian) in these representations and in tensor products of such representations ... More

Nonmonotonic crossover and scaling behaviors in a disordered 1D quasicrystalSep 17 2018Jan 17 2019We consider a noninteracting disordered 1D quasicrystal in the weak disorder regime. We show that the critical states of the pure model approach strong localization in strikingly different ways, depending on their renormalization properties. A finite ... More

Taxi demand forecasting: A HEDGE based tessellation strategy for improved accuracyMay 17 2018May 29 2018A key problem in location-based modeling and forecasting lies in identifying suitable spatial and temporal resolutions. In particular, judicious spatial partitioning can play a significant role in enhancing the performance of location-based forecasting ... More

On Minimizing the Maximum Age-of-Information For Wireless Erasure ChannelsApr 01 2019Age-of-Information (AoI) is a recently proposed metric for quantifying the freshness of information from the UE's perspective in a communication network. Recently, Kadota et al. [1] have proposed an index-type approximately optimal scheduling policy for ... More

Gap structure of 1D cut and project HamiltoniansApr 21 2017We study the gap properties of nearest neighbors tight binding models on quasiperiodic chains. We argue that two kind of gaps should be distinguished: stable and transient. We show that stable gaps have a well defined quasiperiodic limit. We also show ... More

Cardy and KerrSep 06 2009Feb 02 2010The Kerr/CFT correspondence employs the Cardy formula to compute the entropy of the left moving CFT states. This computation, which correctly reproduces the Bekenstein--Hawking entropy of the four-dimensional extremal Kerr black hole, is performed in ... More

New Perspectives on Attractor Flows and Trees from CFTSep 29 2010Oct 24 2011In this note, we use the first order formalism for attractor flows in N=2 SUGRA extremal black hole backgrounds to establish a formal correspondence between the RG flow of moduli in the underlying N=(2,2) SCFT and bulk attractor flows. Starting from a ... More

Estimating the asymptotics of solid partitionsJun 21 2014We study the asymptotic behavior of solid partitions using transition matrix Monte Carlo simulations. If $p_3(n)$ denotes the number of solid partitions of an integer $n$, we show that $\lim_{n\rightarrow\infty} n^{-3/4} \log p_3(n)\sim 1.822\pm 0.001$. ... More

Grothendieck Duality and Transitivity II: Traces and Residues via Verdier's isomorphismMar 05 2019For a smooth map between noetherian schemes, Verdier relates the top relative differentials of the map with the twisted inverse image functor `upper shriek'. We show that the associated traces for smooth proper maps can be rendered concrete by showing ... More

Gesture based Human-Swarm Interactions for Formation Control using interpretersApr 23 2018We propose a novel Human-Swarm Interaction (HSI) framework which enables the user to control a swarm shape and formation. The user commands the swarm utilizing just arm gestures and motions which are recorded by an off-the-shelf wearable armband. We propose ... More

Planning under risk and uncertainty based on Prospect-theoretic modelsApr 05 2019In this work, we develop a novel sampling-based motion planing approach to generate plans in a risky and uncertain environment. To model a variety of risk-sensitivity profiles, we propose an adaption of Cumulative Prospect Theory (CPT) to the setting ... More

Grothendieck Duality and Transitivity I: Formal SchemesMar 05 2019Mar 22 2019For a proper map $f\colon X\to Y$ of noetherian ordinary schemes, one has a well-known natural transformation, ${\bf L}^*f^*(-)\overset{\bf L}{\otimes} f^!{\mathcal{O}}_Y\to f^!$, obtained via the projection formula, which extends, using Nagata's compactification, ... More

The u-invariant of the function fields of p-adic curvesAug 23 2007The u-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the u-invariant of function fields of p-aidc curves is 8. In this paper, we answer this question in the affirmative for function ... More

A proposal for the geometry of W_n gravityMay 23 1994Oct 06 1994We relate the Teichmuller spaces obtained by Hitchin to the Teichmuller spaces of $WA_{n}$-gravity. The relationship of this space to $W$-gravity is obtained by identifying the flat $PSL(n+1,{\BR})$ connections of Hitchin to generalised vielbeins and ... More

A Calogero formulation for four-dimensional black-hole micro statesSep 10 2015We extract the leading-order entropy of a four-dimensional extremal black hole in ${\cal N}{=}2$ ungauged supergravity by formulating the CFT$_1$ that is holographically dual to its near-horizon AdS$_2$ geometry, in terms of a rational Calogero model ... More

Period of the d-Sequence Based Random Number GeneratorDec 03 2007This paper presents an expression to compute the exact period of a recursive random number generator based on d-sequences. Using the multi-recursive version of this generator we can produce large number of pseudorandom sequences.

Observational constraints on variable equation of state parameters of dark matter and dark energy after PlanckJul 24 2012Sep 03 2014In this paper, we study a cosmological model in general relativity within the framework of spatially flat Friedmann-Robertson-Walker space-time filled with ordinary matter (baryonic), radiation, dark matter and dark energy, where the latter two components ... More

Comment on `Oblique Propagation and Dissipation of Alfvén Waves in Coronal Holes' by Srivastava and DwivediDec 21 2009We comment on the recent paper by Srivastava and Dwivedi (J. Astrophs. Astr. {\bf 28}, 1, 2007). In the said paper the derived dispersion relation $\nu \eta \cos^4 \theta k^4 + [v_A^2 - i \omega (\nu + \eta)] \cos^2 \theta k^2 - \omega^2 = 0$ seems to ... More

Scarring of quasimodes on hyperbolic manifoldsSep 16 2016Let $N$ be a compact hyperbolic manifold, $M\subset N$ an embedded totally geodesic submanifold, and let $-\hbar^2\Delta_{N}$ be the semiclassical Laplace--Beltrami operator. For any $\varepsilon>0$, we explicitly construct families of \emph{quasimodes} ... More

Simulation Study of Two Measures of Integrated InformationJun 29 2017Background: Many authors have proposed Quantitative Theories of Consciousness (QTC) based on theoretical principles like information theory, Granger causality and complexity. Recently, Virmani and Nagaraj (arXiv:1608.08450v2 [cs.IT]) noted the similarity ... More

Two moonshines for $L_2(11)$ but none for $M_{12}$Apr 18 2018Jan 09 2019In this paper, we revisit an earlier conjecture by one of us that related conjugacy classes of $M_{12}$ to Jacobi forms of weight one and index zero. We construct Jacobi forms for all conjugacy classes of $M_{12}$ that are consistent with constraints ... More

Artificial Neural Networks-based Track Fitting of Cosmic Muons through Stacked Resistive Plate ChambersJul 09 2018Sep 29 2018The India-based Neutrino Observatory (INO) collaboration, as part of its detector R\&D program, has developed prototype stacks of resistive plate chambers (RPCs) to study their performance. These stacks have also been used as testbenches for the development ... More

On the u-Invariant of Function Fields of Curves Over Complete Discretely Valued FieldsApr 13 2014Let K be a complete discretely valued field with residue field k. If char(K) = 0, char(k) = 2 and the 2-rank of k is d, we prove that there exists an integer N depending on d such that the u-invariant of any function field in one variable over K is bounded ... More

On the Landau-Ginzburg description of Boundary CFTs and special Lagrangian submanifoldsMar 27 2000Mar 30 2000We consider Landau-Ginzburg (LG) models with boundary conditions preserving A-type N=2 supersymmetry. We show the equivalence of a linear class of boundary conditions in the LG model to a particular class of boundary states in the corresponding CFT by ... More

Orientifolds of type IIA strings on Calabi-Yau manifoldsMay 13 2003We identify type IIA orientifolds that are dual to M-theory compactifications on manifolds with G_2-holonomy. We then discuss the construction of crosscap states in Gepner models. (Based on a talk presented by S.G. at PASCOS 2003 held at the Tata Institute ... More

D-branes and Vector Bundles on Calabi-Yau Manifolds: a view from the HelixMay 22 2001We review some recent results on D-branes on Calabi-Yau (CY) manifolds. We show the existence of structures (helices and quivers) which enable one to make statements about large families of D-branes in various phases of the Gauged Linear Sigma Model (GLSM) ... More

High Quality of Service on Video Streaming in P2P Networks using FST-MDCMay 27 2011Video streaming applications have newly attracted a large number of participants in a distribution network. Traditional client-server based video streaming solutions sustain precious bandwidth provision rate on the server. Recently, several P2P streaming ... More

Event-Flow Graphs for Efficient Path-Sensitive AnalysesApr 04 2014Mar 08 2015Efficient and accurate path-sensitive analyses pose the challenges of: (a) analyzing an exponentially-increasing number of paths in a control-flow graph (CFG), and (b) checking feasibility of paths in a CFG. We address these challenges by introducing ... More

Perturbation of the semiclassical Schrödinger equation on negatively curved surfacesMay 13 2014Feb 01 2015We consider the semiclassical Schr\"odinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at the quantum evolution (below the Ehrenfest time) under small perturbations ... More

A note on perturbative aspects of Leigh-Strassler deformed N=4 SYM theoryOct 30 2007We carry out a perturbative study of the Leigh-Strassler deformed N=4 SYM theory in order to verify that the trihedral Delta(27) symmetry holds in the quantum theory. We show that the Delta(27) symmetry is preserved to two loops (at finite N) by explicitly ... More

Chiral primaries in the Leigh-Strassler deformed N=4 SYM -- a perturbative studyMar 02 2007May 08 2007We look for chiral primaries in the general Leigh-Strassler deformed N=4 super Yang-Mills theory by systematically computing the planar one-loop anomalous dimension for single trace operators up to dimension six. The operators are organised into representations ... More

Multimodal deep learning for short-term stock volatility predictionDec 25 2018Stock market volatility forecasting is a task relevant to assessing market risk. We investigate the interaction between news and prices for the one-day-ahead volatility prediction using state-of-the-art deep learning approaches. The proposed models are ... More

Evaluation of Complex-Valued Neural Networks on Real-Valued Classification TasksNov 29 2018Complex-valued neural networks are not a new concept, however, the use of real-valued models has often been favoured over complex-valued models due to difficulties in training and performance. When comparing real-valued versus complex-valued neural networks, ... More

Grothendieck Duality and Transitivity II: Traces and Residues via Verdier's isomorphismMar 05 2019Mar 22 2019For a smooth map between noetherian schemes, Verdier relates the top relative differentials of the map with the twisted inverse image functor `upper shriek'. We show that the associated traces for smooth proper maps can be rendered concrete by showing ... More

A Class of degenerate Stochastic differential equations with non-Lipschitz coefficientsApr 17 2009We obtain sufficient condition for SDEs to evolve in the positive orthant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs with non-Lipschitz ... More

Applications of duality theory to cousin complexesDec 05 2005Jul 10 2007We use the anti-equivalence between Cohen-Macaulay complexes and coherent sheaves on formal schemes to shed light on some older results and prove new results. We bring out the relations between a coherent sheaf M satisfying an S_2 condition and the lowest ... More

Three dimensional quadratic algebras: Some realizations and representationsAug 31 2001Four classes of three dimensional quadratic algebras of the type $\lsb Q_0 , Q_\pm \rsb$ $=$ $\pm Q_\pm$, $\lsb Q_+ , Q_- \rsb$ $=$ $aQ_0^2 + bQ_0 + c$, where $(a,b,c)$ are constants or central elements of the algebra, are constructed using a generalization ... More

A LEO-Based Solar-Shade System to Mitigate Global WarmingApr 20 2015The development of a Low-Earth-Orbit (LEO) based solar-shade system, as part of a technically- and financially-viable multipurpose system to provide long-term solutions to global warming and the energy crisis is discussed. The proposed solar-shade and ... More

Period-index and u-invariant questions for function fields over complete discretely valued fieldsApr 08 2013Let K be a complete discretely valued field and F the function field of a curve over K. If the characteristic of the residue field k of K is p > 0, then we give a bound for the Brauer p-simension of F in terms of the p-rank of k. If k is a perfect field ... More

Power to the Points: Validating Data Memberships in ClusteringsMay 21 2013A clustering is an implicit assignment of labels of points, based on proximity to other points. It is these labels that are then used for downstream analysis (either focusing on individual clusters, or identifying representatives of clusters and so on). ... More

Binary Random Sequences Obtained From Decimal SequencesSep 03 2008This paper presents a twist to the generation of binary random sequences by starting with decimal sequences. Rather than representing the prime reciprocal sequence directly in base 2, we first right the prime reciprocal in base 10 and then convert it ... More

Strong Scarring of Logarithmic QuasimodesJul 30 2015We consider a semiclassical (pseudo)differential operator on a compact surface $(M,g)$, such that the Hamiltonian flow generated by its principal symbol admits a hyperbolic periodic orbit $\gamma$ at some energy $E_0$. For any $\epsilon>0$, we then explicitly ... More

Failure of the local-global principle for isotropy of quadratic forms over rational function fieldsSep 12 2017We prove the failure of the local-global principle, with respect to all discrete valuations, for isotropy of quadratic forms over a rational function field of transcendence degree at least 2 over the complex numbers. Our construction involves the generalized ... More

BKM Lie superalgebras from counting twisted CHL dyons -- IIMay 15 2019We revisit our earlier work which lead to a periodic table of Borcherds-Kac-Moody algebras that appeared in the context of the refined generating function of quarter-BPS (dyons) in $\mathcal{N}=4$ supersymmetric four-dimensional string theory. We make ... More

Why does Deep Learning work? - A perspective from Group TheoryDec 20 2014Feb 28 2015Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning. One factor ... More

Degree three cohomology of function fields of surfacesDec 24 2010Jun 05 2014Let F be a finite field and l a prime not equal to the characteristic of F. Let K be the function field of a surface over F. Assume that K contains a primitive lth root of unity. In the paper we prove a certain local-global principle for elements of H^3(K, ... More

Effective superpotentials for B-branes in Landau-Ginzburg modelsAug 03 2006We compute the partition function for the topological Landau-Ginzburg B-model on the disk. This is done by treating the worldsheet superpotential perturbatively. We argue that this partition function as a function of bulk and boundary perturbations may ... More

Crosscaps in Gepner Models and Type IIA OrientifoldsJun 26 2003Feb 24 2004As a first step to a detailed study of orientifolds of Gepner models associated with Calabi-Yau manifolds, we construct crosscap states associated with anti-holomorphic involutions (with fixed points) of Calabi-Yau manifolds. We argue that these orientifolds ... More

Boundary Fermions, Coherent Sheaves and D-branes on Calabi-Yau manifoldsApr 14 2001Apr 19 2001We construct boundary conditions in the gauged linear sigma model for B-type D-branes on Calabi-Yau manifolds that correspond to coherent sheaves given by the cohomology of a monad. This necessarily involves the introduction of boundary fields, and in ... More