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Creation of User Friendly Datasets: Insights from a Case Study concerning Explanations of Loan DenialsJun 11 2019Most explainable AI (XAI) techniques are concerned with the design of algorithms to explain the AI's decision. However, the data that is used to train these algorithms may contain features that are often incomprehensible to an end-user even with the best ... More

Crowdsourcing in the Absence of Ground Truth -- A Case StudyJun 17 2019Crowdsourcing information constitutes an important aspect of human-in-the-loop learning for researchers across multiple disciplines such as AI, HCI, and social science. While using crowdsourced data for subjective tasks is not new, eliciting useful insights ... More

Generating User-friendly Explanations for Loan Denials using GANsJun 24 2019Financial decisions impact our lives, and thus everyone from the regulator to the consumer is interested in fair, sound, and explainable decisions. There is increasing competitive desire and regulatory incentive to deploy AI mindfully within financial ... More

An Efficient Preprocessing Methodology for Discovering Patterns and Clustering of Web Users using a Dynamic ART1 Neural NetworkSep 06 2011In this paper, a complete preprocessing methodology for discovering patterns in web usage mining process to improve the quality of data by reducing the quantity of data has been proposed. A dynamic ART1 neural network clustering algorithm to group users ... More

Google Cardboard Dates Augmented Reality : Issues, Challenges and Future OpportunitiesJun 05 2017The Google's frugal Cardboard solution for immersive Virtual Reality experiences has come a long way in the VR market. The Google Cardboard VR applications will support us in the fields such as education, virtual tourism, entertainment, gaming, design ... More

Thermal analysis & optimization of a 3 dimensional heterogeneous structureMar 08 2012Besides the lot of advantages offered by the 3D stacking of devices in an integrated circuit there is a chance of device damage due to rise in peak temperature value. Hence, in order to make use of all the potential benefits of the vertical stacking a ... More

Preprocessing: A Prerequisite for Discovering Patterns in WUM ProcessApr 12 2011Web log data is usually diverse and voluminous. This data must be assembled into a consistent, integrated and comprehensive view, in order to be used for pattern discovery. Without properly cleaning, transforming and structuring the data prior to the ... More

Rates of convergence for Smoluchowski's coagulation equationsMay 21 2009Apr 24 2011We establish nearly optimal rates of convergence to self-similar solutions of Smoluchowski's coagulation equation with kernels $K = 2$, $x + y$, and $xy$. The method is a simple analogue of the Berry-Ess\'een theorem in classical probability and requires ... More

An Extension of the Lovasz Local Lemma, and its Applications to Integer ProgrammingJul 18 2003The Lovasz Local Lemma due to Erdos and Lovasz is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events, each of which ... More

Quadratic unipotent blocks in general linear, unitary and symplectic groupsApr 19 2013An irreducible ordinary character of a finite reductive group is called quadratic unipotent if it corresponds under Jordan decomposition to a semisimple element $s$ in a dual group such that $s^2=1$. We prove that there is a bijection between, on the ... More

On CRDAHA and finite general linear and unitary groupsNov 06 2014We show a connection between Lusztig induction operators in finite general linear and unitary groups and parabolic induction in cyclotomic rational double affine Hecke algebras. Two applications are given: an explanation of a bijection result of Brou\'e, ... More

Optimizing the performance of Lattice Gauge Theory simulations with Streaming SIMD extensionsSep 02 2013Two factors, which affect simulation quality are the amount of computing power and implementation. The Streaming SIMD (single instruction multiple data) extensions (SSE) present a technique for influencing both by exploiting the processor's parallel functionalism. ... More

A virtually ample field that is not ampleOct 11 2018A field $K$ is called ample if for every geometrically integral $K$-variety $V$ with a smooth $K$-point, $V(K)$ is Zariski-dense in $V$. A field $K$ is virtually ample if some finite extension of $K$ is ample. We prove that there exists a virtually ample ... More

Conductors and minimal discriminants of hyperelliptic curves with rational Weierstrass pointsAug 21 2015Let $C$ be a hyperelliptic curve of genus $g$ over the fraction field $K$ of a discrete valuation ring $R$. Assume that the residue field $k$ of $R$ is perfect and that $\mathop{\textrm{char}} k \neq 2$. Assume that the Weierstrass points of $C$ are $K$-rational. ... More

An invariant in shock clustering and Burgers turbulenceJun 15 2011Jan 06 20121-D scalar conservation laws with convex flux and Markov initial data are now known to yield a completely integrable Hamiltonian system. In this article, we rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence from the perspective ... More

On a separation criterion for symmetric elliptic bluff body flowsNov 30 2005Jan 12 2006A new analytical criterion that captures the onset of separation of flow past elliptic cylinders is derived by considering the variation of the wall normal velocity in Reynolds number parameter space. It is shown that this criterion can be used to calculate ... More

Codes on Varieties as Codes on CurvesMar 14 2013The discovery of algebraic geometric codes constructed on curves led to generalizing this construction on higher dimensional varieties. In this paper, we use a theorem of B. Poonen to show that the codes obtained from higher dimensional varieties can ... More

On the Lusternik-Schnirelmann category of Peano continuaDec 04 2012Aug 23 2013We define the LS-category cat_g by means of covers of a space by general subsets, and show that this definition coincides with the classical Lusternik-Schnirelmann category for compact metric ANR spaces. We apply this result to give short dimension theoretic ... More

A complete classification of well-rounded real quadratic ideal latticesFeb 05 2019We provide a complete classification of well-rounded ideal lattices arising from real quadratic fields. We show that the ideals that give rise to such lattices are precisely the ones that correspond to divisors $a$ of the discriminant $d$ that satisfy ... More

Calibrating Black Box Classification Models through the Thresholding MethodMay 20 2017Jun 05 2017In high-dimensional classification settings, we wish to seek a balance between high power and ensuring control over a desired loss function. In many settings, the points most likely to be misclassified are those who lie near the decision boundary of the ... More

On the prime divisors of elements of a $D(-1)$ quadrupleSep 17 2013We show that if {1, b, c, d} is a D(-1) diophantine quadruple with b<c<d and c=1+s^2, then the cases s=p^k, s=2p^k, c=p and c=2p^k do not occur, where p is an odd prime and k is a positive integer. For the integer d=1+x^2, we show that it is not prime ... More

The Mass-Loss Return From Asymptotic Giant Branch Stars to The Large Magellanic Cloud Using Data From The SAGE SurveyNov 04 2009The asymptotic giant branch (AGB) phase is the penultimate stage of evolution for low- and intermediate-mass stars. AGB star outflows inject a significant amount of material into the interstellar medium (ISM), seeding new star formation. AGB mass loss ... More

Dynamic Grouping of Web Users Based on Their Web Access Patterns using ART1 Neural Network Clustering AlgorithmMay 09 2012In this paper, we propose ART1 neural network clustering algorithm to group users according to their Web access patterns. We compare the quality of clustering of our ART1 based clustering technique with that of the K-Means and SOM clustering algorithms ... More

Linear Projections of the Vandermonde PolynomialMay 09 2017An n-variate Vandermonde polynomial is the determinant of the n x n matrix where the ith column is the vector (1, x_i, x_i^2, ...., x_i^{n-1})^T. Vandermonde polynomials play a crucial role in the theory of alternating polynomials and occur in Lagrangian ... More

Limitations of sum of products of Read-Once PolynomialsDec 11 2015We study limitations of polynomials computed by depth two circuits built over read-once polynomials (ROPs) and depth three syntactically multi-linear formulas. We prove an exponential lower bound for the size of the $\Sigma\Pi^{[N^{1/30}]}$ arithmetic ... More

Motivic Decomposition of Projective Pseudo-homogeneous VarietiesSep 21 2015Nov 08 2015Let $G$ be a semi-simple algebraic group over a perfect field $k$. A lot of progress has been made recently in computing the Chow motives of projective $G$-homogenous varieties. When $k$ has positive characteristic, a broader class of $G$-homogeneous ... More

Review on Giant Magnetoelectric effects in Oxide ferromagnetic/ferroelectric Layered StructuresJan 29 2004The synthesis of layered ferrite-lead titanate zirconate (PZT) and lanthanum nanganite-PZT and the observation of giant magneto-electric interactions are discussed. The ferrites used in our studies included pure and Zn substituted cobalt-, nickel- and ... More

Adaptive Greedy Algorithms for Stochastic Set Cover ProblemsMar 20 2018Jun 15 2018We study adaptive greedy algorithms for the problems of stochastic set cover with perfect and imperfect coverages. In stochastic set cover with perfect coverage, we are given a set of items and a ground set B. Evaluating an item reveals its state which ... More

Modular Representations, Old and NewAug 16 2011The modular representation theory of finite groups has its origins in the work of Richard Brauer. In this survey article we first discuss the work being done on some outstanding conjectures in the theory. We then describe work done in the eighties and ... More

Good Reduction of Unitary Groups of Quaternionic Skew-Hermitian FormsJun 04 2019Given a field $K$ equipped with a set of discrete valuations $V$, we develop a general theory to relate ramification of skew-hermitian forms over a quaternion $K$-algebra $Q$ to ramification of quadratic forms over the function field $K(Q)$ obtained via ... More

The Lusternik-Schnirelmann category of metric spacesFeb 08 2014Apr 18 2014We extend the theory of the Lusternik-Schnirelmann category to general metric spaces by means of covers by arbitrary subsets. We also generalize the definition of the strict category weight. We show that if the Bockstein homomorphism on a metric space ... More

Strongly Exponential Separation Between Monotone VP and Monotone VNPMar 05 2019We show that there is a sequence of explicit multilinear polynomials $P_n(x_1,\ldots,x_n)\in \mathbb{R}[x_1,\ldots,x_n]$ with non-negative coefficients that lies in monotone VNP such that any monotone algebraic circuit for $P_n$ must have size $\exp(\Omega(n)).$ ... More

CCR and CAR flows over convex conesAug 01 2019Recently it is proved in arXiv:1906.05493v1 [math.OA] that CCR flows over convex cones are cocycle conjugate if and only if the associated isometric representations are conjugate. We provide a very short, simple and direct proof of that. Using the same ... More

Motivic Decomposition of Projective Pseudo-homogeneous VarietiesSep 21 2015Oct 19 2017Let $G$ be a semi-simple algebraic group over a perfect field $k$. A lot of progress has been made recently in computing the Chow motives of projective $G$-homogenous varieties. When $k$ has positive characteristic, a broader class of $G$-homogeneous ... More

Lower bounds for multilinear bounded order ABPsJan 14 2019Proving super-polynomial size lower bounds for syntactic multilinear Algebraic Branching Programs(smABPs) computing an explicit polynomial is a challenging problem in Algebraic Complexity Theory. The order in which variables in $\{x_1,\ldots,x_n\}$ appear ... More

Adaptive Limited Feedback for Sum-Rate Maximizing Beamforming in Cooperative Multicell SystemsDec 04 2009Base station cooperation improves the sum-rates that can be achieved in cellular systems. Conventional cooperation techniques require sharing large amounts of information over finite-capacity backhaul links and assume that base stations have full channel ... More

Pre-Requirement Specification Traceability: Bridging the Complexity Gap through CapabilitiesMar 02 2007Pre-Requirement Specification traceability is the activity of capturing relations between requirements and their sources, in particular user needs. Requirements are formal technical specifications in the solution space; needs are natural language expressions ... More

An optimisation approach for fuel treatment planning to break the connectivity of high-risk regionsDec 22 2015Uncontrolled wildfires can lead to loss of life and property and destruction of natural resources. At the same time, fire plays a vital role in restoring ecological balance in many ecosystems. Fuel management, or treatment planning by way of planned burning, ... More

Scalable production of high sensitivity, label-free DNA biosensors based on back-gated graphene field-effect transistorsAug 29 2017Scalable production of all-electronic DNA biosensors with high sensitivity and selectivity is a critical enabling step for research and applications associated with detection of DNA hybridization. We have developed a scalable and very reproducible (> ... More

Network Analysis and Application Control Software based on Client-Server ArchitectureApr 18 2013This paper outlines a comprehensive model to increase system efficiency, preserve network bandwidth, monitor incoming and outgoing packets, ensure the security of confidential files and reduce power wastage in an organization. This model illustrates the ... More

Lighthouse: A User-Centered Web Service for Linear Algebra SoftwareAug 06 2014Various fields of science and engineering rely on linear algebra for large scale data analysis, modeling and simulation, machine learning, and other applied problems. Linear algebra computations often dominate the execution time of such applications. ... More

Fuel treatment planning: fragmenting high fuel load areas while maintaining availability and connectivity of faunal habitatJan 31 2016Sep 15 2016Reducing the fuel load in fire-prone landscapes is aimed at mitigating the risk of catastrophic wildfires but there are ecological consequences. Maintaining habitat for fauna of both sufficient extent and connectivity while fragmenting areas of high fuel ... More

Radio Continuum and HI study of Blue Compact Dwarf GalaxiesDec 21 2010The multifrequency radio continuum and 21cm HI observations of five blue compact dwarf (BCD) galaxies, Mrk 104, Mrk 108, Mrk 1039, Mrk 1069 and I Zw 97 using the Giant Meterwave Radio Telescope (GMRT) are presented here. Radio continuum emission at 610 ... More

Preprocessing: A Prerequisite for Discovering Patterns in Web Usage Mining ProcessMay 02 2011Web log data is usually diverse and voluminous. This data must be assembled into a consistent, integrated and comprehensive view, in order to be used for pattern discovery. Without properly cleaning, transforming and structuring the data prior to the ... More

Study of star formation in NGC 1084Jul 16 2007We present UBVRI broad band, H$\alpha$ narrow band photometry of the star forming complexes in the infra-red bright galaxy NGC 1084. Results of medium resolution spectroscopy of some of the brighter complexes are also discussed. Spectroscopic data is ... More

Molecular Gas and Star Formation in VoidsNov 07 2014We present the detection of molecular gas using CO(1-0) line emission and follow up Halpha imaging observations of galaxies located in nearby voids. The CO(1-0) observations were done using the 45m telescope of the Nobeyama Radio Observatory (NRO) and ... More

Star formation in bulgeless late type galaxies: clues to their evolutionMay 09 2012We present GMRT 1280 MHz radio continuum observations and follow-up optical studies of the disk and nuclear star formation in a sample of low luminosity bulgeless galaxies. The main aim is to understand bulge formation and overall disk evolution in these ... More

A unified approach to the integrals of Mellin--Barnes--Hecke typeAug 30 2012In this paper we provide a unified approach to a family of integrals of Mellin--Barnes type using distribution theory and Fourier transforms. Interesting features arise in many of the cases which call for the application of pull-backs of distributions ... More

On Polynomial Approximations to ${AC}^0$Apr 27 2016We make progress on some questions related to polynomial approximations of ${\rm AC}^0$. It is known, by works of Tarui (Theoret. Comput. Sci. 1993) and Beigel, Reingold, and Spielman (Proc. $6$th CCC, 1991), that any ${\rm AC}^0$ circuit of size $s$ ... More

A New Approximation Technique for Resource-Allocation ProblemsJan 10 2010We develop a rounding method based on random walks in polytopes, which leads to improved approximation algorithms and integrality gaps for several assignment problems that arise in resource allocation and scheduling. In particular, it generalizes the ... More

Free groups, covering spaces and Artin's theoremApr 13 2019May 05 2019In this expository note we provide a proof of Artin's theorem which states that the commutator subgroup of a free group on two generators is not finitely generated. The proof employs the infinite grid as in two other proofs in the literature mentioned ... More

Homogenization of a locally periodic oscillating boundaryApr 26 2019This paper deals with the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The Neumann condition is prescribed on the oscillating part of the boundary, and the Dirichlet ... More

Bayesian Locality Sensitive Hashing for Fast Similarity SearchOct 06 2011Mar 28 2012Given a collection of objects and an associated similarity measure, the all-pairs similarity search problem asks us to find all pairs of objects with similarity greater than a certain user-specified threshold. Locality-sensitive hashing (LSH) based methods ... More

Adaptive Bayesian Sampling with Monte Carlo EMNov 06 2017We present a novel technique for learning the mass matrices in samplers obtained from discretized dynamics that preserve some energy function. Existing adaptive samplers use Riemannian preconditioning techniques, where the mass matrices are functions ... More

ReStoCNet: Residual Stochastic Binary Convolutional Spiking Neural Network for Memory-Efficient Neuromorphic ComputingFeb 11 2019In this work, we propose ReStoCNet, a residual stochastic multilayer convolutional Spiking Neural Network (SNN) composed of binary kernels, to reduce the synaptic memory footprint and enhance the computational efficiency of SNNs for complex pattern recognition ... More

Structural Instability in Polyacene : A Projector Quantum Monte Carlo StudyJan 24 1997We have studied polyacene within the Hubbard model to explore the effect of electron correlations on the Peierls' instability in a system marginally away from one-dimension. We employ the projector quantum Monte Carlo method to obtain ground state estimates ... More

Robust Multiplication-based Tests for Reed-Muller CodesDec 09 2016Aug 06 2018We consider the following multiplication-based tests to check if a given function $f: \mathbb{F}_q^n\to \mathbb{F}_q$ is a codeword of the Reed-Muller code of dimension $n$ and order $d$ over the finite field $\mathbb{F}_q$ for prime $q$ (i.e., $f$ is ... More

Nugget Discovery with a Multi-objective Cultural AlgorithmJul 11 2012Partial classification popularly known as nugget discovery comes under descriptive knowledge discovery. It involves mining rules for a target class of interest. Classification "If-Then" rules are the most sought out by decision makers since they are the ... More

On the hardness of the noncommutative determinantOct 13 2009Oct 26 2009In this paper we study the computational complexity of computing the noncommutative determinant. We first consider the arithmetic circuit complexity of computing the noncommutative determinant polynomial. Then, more generally, we also examine the complexity ... More

Iterated Antiderivative ExtensionsFeb 07 2010Let $F$ be a characteristic zero differential field with an algebraically closed field of constants and let $E$ be a no new constants extension of $F$. We say that $E$ is an \textsl{iterated antiderivative extension} of $F$ if $E$ is a liouvillian extension ... More

SER for Optimal Combining in Rician Fading with Co-channel InterferenceAug 14 2017Approximate Symbol error rate (SER) expressions are derived for receive diversity system employing optimum combining, when both the desired and the interfering signals are subjected to Rician fading, for the case of a) equal power uncorrelated interferers ... More

A Social Network Framework to Explore Healthcare CollaborationSep 23 2015A patient-centric approach to healthcare leads to an informal social network among medical professionals. This chapter presents a research framework to: identify the collaboration structure among physicians that is effective and efficient for patients, ... More

On Unimodality of Hilbert Functions of Gorenstein Artin Algebras of Embedding Dimension FourNov 11 2010We prove that the Hilbert functions of codimension four graded Gorenstein Artin algebras R/I are unimodal provided I has a minimal generator in degree less than five. It is an open question whether all Gorenstein h-vectors in codimension four are unimodal. ... More

Co-evolution of Content Popularity and Delivery in Mobile P2P NetworksJul 29 2011Mobile P2P technology provides a scalable approach to content delivery to a large number of users on their mobile devices. In this work, we study the dissemination of a \emph{single} content (e.g., an item of news, a song or a video clip) among a population ... More

Spread of Influence and Content in Mobile Opportunistic NetworksAug 31 2012We consider a setting in which a single item of content (such as a song or a video clip) is disseminated in a population of mobile nodes by opportunistic copying when pairs of nodes come in radio contact. We propose and study models that capture the joint ... More

The complexity of the $q$-analog of the $n$-cubeNov 08 2011Nov 12 2011We present a positive, combinatorial, good formula for the complexity (= number of spanning trees) of the $q$-analog of the $n$-cube. Our method also yields the explicit block diagonalization of the commutant of the $GL(n,F_q)$ action on the $q$-analog ... More

Perturbative solution of Vlasov equation for periodically driven systemsOct 14 2015Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of particles in such a ... More

QoS-Aware Routing in Wireless Networks Using Aerial VehiclesApr 01 2018The next generation wireless networks need efficient mechanisms for data dissemination that should support users with better Quality of Service (QoS). Nevertheless, the existing solutions are unable to handle this demand and require either network redeployment ... More

Dyloc: Dynamic and Collaborative User-controlled AOA based Localizing System with your laptopsMar 22 2018Currently, accurate localization system based on commodity WiFi devices is not broadly available yet. In the literature, the solutions are based on either network infrastructure like WiFi router, which have at least three antennas, or sacrifice accuracy ... More

Design of two-dimensional photonic crystal defect states for quantum cascade laser resonatorsOct 11 2004Current quantum cascade lasers based upon conduction band electron transitions are predominantly TM (electrical field normal to the epitaxial direction) polarized. Here we present a study of localized defect modes, with the requisite TM polarization, ... More

Doing it with Mirrors: Classical analogues for Black Hole radiationDec 27 1998We construct analogues for the quantum phenomena of black hole radiation in the context of {\it classical field theory}. Hawking radiation from a (radially) collapsing star is mathematically equivalent to radiation from a mirror moving along a specific ... More

Particle production and complex path analysisDec 08 1998This paper discusses particle production in Schwarzchild-like spacetimes and in an uniform electric field. Both problems are approached using the method of complex path analysis. Particle production in Schwarzchild-like spacetimes with a horizon is obtained ... More

Separation of AC$^0[\oplus]$ Formulas and CircuitsFeb 13 2017This paper gives the first separation between the power of {\em formulas} and {\em circuits} of equal depth in the $\mathrm{AC}^0[\oplus]$ basis (unbounded fan-in AND, OR, NOT and MOD$_2$ gates). We show, for all $d(n) \le O(\frac{\log n}{\log\log n})$, ... More

Liouvillian Solutions of First Order Non Linear Differential EquationsDec 11 2015Let $k$ be a differential field of characteristic zero and $E$ be a liouvillian extension of $k$. For any differential subfield $K$ intermediate to $E$ and $k$, we prove that there is an element in the set $K-k$ satisfying a linear homogeneous differential ... More

Recalling of Images using Hopfield Neural Network ModelMay 02 2011In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an arbitrary configuration, ... More

Prediction-based Online Trajectory CompressionJan 23 2016Feb 15 2016Recent spatio-temporal data applications, such as car-shar\-ing and smart cities, impose new challenges regarding the scalability and timeliness of data processing systems. Trajectory compression is a promising approach for scaling up spatio-temporal ... More

Maximum Likelihood Estimation for Learning Populations of ParametersFeb 12 2019Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim \text{Binomial}(t, ... More

A note on Gorenstein monomial curvesOct 29 2013Sep 09 2015Let $k$ be an arbitrary field. In this note, we show that if a sequence of relatively prime positive integers ${\bf a}=(a_1,a_2,a_3,a_4)$ defines a Gorenstein non complete intersection monomial curve ${\mathcal C}({\bf a})$ in ${\mathbb A}_k^4$, then ... More

Robust Contextual Outlier Detection: Where Context Meets SparsityJul 28 2016Aug 22 2016Outlier detection is a fundamental data science task with applications ranging from data cleaning to network security. Given the fundamental nature of the task, this has been the subject of much research. Recently, a new class of outlier detection algorithms ... More

Graphical NewtonAug 05 2015Apr 25 2016Computing the Newton step for a generic function $f: \mathbb{R}^N \rightarrow \mathbb{R}$ takes $O(N^{3})$ flops. In this paper, we explore avenues for reducing this bound, when the computational structure of $f$ is known beforehand. It is shown that ... More

Symmetrization for Embedding Directed GraphsNov 06 2018Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs has targeted ... More

Symmetric chains, Gelfand-Tsetlin chains, and the Terwilliger algebra of the binary Hamming schemeJan 02 2010Apr 05 2010The de Bruijn-Tengbergen-Kruyswijk (BTK) construction is a simple algorithm that produces an explicit symmetric chain decomposition of a product of chains. We linearize the BTK algorithm and show that it produces an explicit symmetric Jordan basis (SJB). ... More

Rocking and rolling: a can that appears to rock might actually rollFeb 04 2007Dec 27 2008A beer bottle or soda can on a table, when slightly tipped and released, falls to an upright position and then rocks up to a somewhat opposite tilt. Superficially this rocking motion involves a collision when the flat circular base of the container slaps ... More

A Somewhat Homomorphic Encryption Scheme based on Multivariate Polynomial EvaluationFeb 15 2019We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a generalization ... More

Graphical NewtonAug 05 2015Oct 08 2017Computing the Newton step for a generic function $f: \mathbb{R}^N \rightarrow \mathbb{R}$ takes $O(N^{3})$ flops. In this paper, we explore avenues for reducing this bound, when the computational structure of $f$ is known beforehand. It is shown that ... More

Comments on the paper: Synthesis growth and characterization of copper mercury thiocyanate crystal [Indian J Pure & App Phys 49 (2011) 340-343]Jun 30 2015The unit cell parameters, infrared and UV-Vis spectral data reported in the paper by Vijayabhaskaran et al (Indian J Pure & App Phys 49 (2011) 340-343) cannot belong to the colourless crystalline compound formulated as copper mercury thiocyanate CuHg(SCN)4 ... More

Comment on the paper: Synthesis, growth and characterization of cadmium manganese thiocyanate (CMTC) crystalJun 06 2015The authors of the title paper (Spectrochim. Acta 79A (2011) 340-343) report the crystal growth of cadmium manganese thiocyanate CdMn(SCN)4 and its characterization by single crystal X-ray diffraction and infrared spectrum. Many points of criticism, concerning ... More

Free groups, covering spaces and Artin's theoremApr 13 2019May 14 2019In this expository note we provide a proof of Artin's theorem which states that the commutator subgroup of a free group on two generators is not finitely generated. The proof employs the infinite grid as in two other proofs in the literature mentioned ... More

Linear and nonlinear optical spectroscopy of a strongly-coupled microdisk-quantum dot systemJul 23 2007Jul 27 2007A fiber taper waveguide is used to perform direct optical spectroscopy of a microdisk-quantum-dot system, exciting the system through the photonic (light) channel rather than the excitonic (matter) channel. Strong coupling, the regime of coherent quantum ... More

Facets of Tunneling: Particle production in external fieldsJul 23 1998This paper presents a critical review of particle production in an uniform electric field and Schwarzchild-like spacetimes. Both problems can be reduced to solving an effective one-dimensional Schrodinger equation with a potential barrier. In the electric ... More

Optical fiber taper coupling and high-resolution wavelength tuning of microdisk resonators at cryogenic temperaturesNov 14 2006A system for studying microcavity resonators at cryogenic temperatures (~10 K) through evanescent coupling via optical fiber taper waveguides is reported, and efficient fiber coupling to AlGaAs microdisk cavities with embedded quantum dots is demonstrated. ... More

Mode Coupling and Cavity-Quantum-Dot Interactions in a Fiber-Coupled Microdisk CavityJun 17 2006Jan 26 2007A quantum master equation model for the interaction between a two-level system and whispering-gallery modes (WGMs) of a microdisk cavity is presented, with specific attention paid to current experiments involving a semiconductor quantum dot (QD) embedded ... More

A novel approach to particle production in an uniform electric fieldNov 07 1999We outline a different method of describing scalar field particle production in a uniform electric field. In the standard approach, the (analytically continued) harmonic oscillator paradigm is important in describing particle production. However, there ... More

The Impact of Orography and Latent Heating on the Location of the Tropical Easterly JetAug 01 2013The Tropical Easterly Jet (TEJ) is a prominent atmospheric circulation feature observed during the Asian Summer Monsoon. It is generally assumed that Tibet is an essential ingredient in determining the location of the TEJ. However studies have also suggested ... More

On Polynomial Approximations to ${AC}^0$Apr 27 2016Aug 06 2018We make progress on some questions related to polynomial approximations of ${\rm AC}^0$. It is known, by works of Tarui (Theoret. Comput. Sci. 1993) and Beigel, Reingold, and Spielman (Proc. $6$th CCC, 1991), that any ${\rm AC}^0$ circuit of size $s$ ... More

On Cooperative Behavior of Open Homogeneous Chemical Reaction Systems in the Extent DomainNov 20 2015Material balance equations describe the dynamics of the species in open reaction systems and contain information regarding reaction topology, kinetics and operation mode. For reaction systems, the state variables (the numbers of moles, or concentrations) ... More

Cultural Algorithm Toolkit for Multi-objective Rule MiningSep 12 2012Cultural algorithm is a kind of evolutionary algorithm inspired from societal evolution and is composed of a belief space, a population space and a protocol that enables exchange of knowledge between these sources. Knowledge created in the population ... More

Circuit Lower Bounds, Help Functions, and the Remote Point ProblemNov 23 2009We investigate the power of Algebraic Branching Programs (ABPs) augmented with help polynomials, and constant-depth Boolean circuits augmented with help functions. We relate the problem of proving explicit lower bounds in both these models to the Remote ... More

Codes on Planar GraphsApr 05 2009May 15 2009Codes defined on graphs and their properties have been subjects of intense recent research. On the practical side, constructions for capacity-approaching codes are graphical. On the theoretical side, codes on graphs provide several intriguing problems ... More

Robust Contextual Outlier Detection: Where Context Meets SparsityJul 28 2016Dec 22 2016Outlier detection is a fundamental data science task with applications ranging from data cleaning to network security. Given the fundamental nature of the task, this has been the subject of much research. Recently, a new class of outlier detection algorithms ... More