total 1303took 0.11s

Decoding Downset codes over a finite gridAug 20 2019In a recent paper, Kim and Kopparty (Theory of Computing, 2017) gave a deterministic algorithm for the unique decoding problem for polynomials of bounded total degree over a general grid. We show that their algorithm can be adapted to solve the unique ... 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

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

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

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

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

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

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

The Remote Point Problem, Small Bias Space, and Expanding Generator SetsSep 29 2009Feb 03 2010Using $\epsilon$-bias spaces over $F_2$, we show that the Remote Point Problem (RPP), introduced by Alon et al [APY09], has an $NC^2$ algorithm (achieving the same parameters as [APY09]). We study a generalization of the Remote Point Problem to groups: ... More

Composition limits and separating examples for some Boolean function complexity measuresJun 04 2013Block sensitivity ($bs(f)$), certificate complexity ($C(f)$) and fractional certificate complexity ($C^*(f)$) are three fundamental combinatorial measures of complexity of a boolean function $f$. It has long been known that $bs(f) \leq C^{\ast}(f) \leq ... More

New results on Noncommutative and Commutative Polynomial Identity TestingJan 03 2008Using ideas from automata theory we design a new efficient (deterministic) identity test for the \emph{noncommutative} polynomial identity testing problem (first introduced and studied in \cite{RS05,BW05}). We also apply this idea to the reconstruction ... More

Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold CircuitsJun 16 2018$ \newcommand{\cclass}[1]{{\normalfont\textsf{##1}}} $We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer $d > 1$, there is a constant ... More

Small-depth Multilinear Formula Lower Bounds for Iterated Matrix Multiplication, with ApplicationsOct 16 2017In this paper, we study the algebraic formula complexity of multiplying $d$ many $2\times 2$ matrices, denoted $\mathrm{IMM}_{d}$, and show that the well-known divide-and-conquer algorithm cannot be significantly improved at any depth, as long as the ... More

Optimal Hitting Sets for Combinatorial ShapesNov 14 2012We consider the problem of constructing explicit Hitting sets for Combinatorial Shapes, a class of statistical tests first studied by Gopalan, Meka, Reingold, and Zuckerman (STOC 2011). These generalize many well-studied classes of tests, including symmetric ... More

On Lower Bounds for Constant Width Arithmetic CircuitsJul 22 2009Aug 14 2009The motivation for this paper is to study the complexity of constant-width arithmetic circuits. Our main results are the following. 1. For every k > 1, we provide an explicit polynomial that can be computed by a linear-sized monotone circuit of width ... More

On the relation between the WRT invariant and the Hennings invariantSep 14 2007Jun 05 2008The purpose of this note is to provide a simple relation between the Witten-Reshetikhin-Turaev SO(3) invariant and the Hennings invariant of 3-manifolds associated to quantum sl_2.

Local decoding and testing of polynomials over gridsSep 18 2017Dec 14 2018The well-known DeMillo-Lipton-Schwartz-Zippel lemma says that $n$-variate polynomials of total degree at most $d$ over grids, i.e. sets of the form $A_1 \times A_2 \times \cdots \times A_n$, form error-correcting codes (of distance at least $2^{-d}$ provided ... More

On polynomial approximations over $\mathbb{Z}/2^k\mathbb{Z}$Jan 23 2017We study approximation of Boolean functions by low-degree polynomials over the ring $\mathbb{Z}/2^k\mathbb{Z}$. More precisely, given a Boolean function $F:\{0,1\}^n \rightarrow \{0,1\}$, define its $k$-lift to be $F_k:\{0,1\}^n \rightarrow \{0,2^{k-1}\}$ ... More

Arithmetic Circuits and the Hadamard Product of PolynomialsJul 23 2009Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our main ... More

Streaming algorithms for recognizing nearly well-parenthesized expressionsJun 01 2012We study the streaming complexity of the membership problem of 1-turn-Dyck2 and Dyck2 when there are a few errors in the input string. 1-turn-Dyck2 with errors: We prove that there exists a randomized one-pass algorithm that given x checks whether there ... More

Time-Reversal Symmetrization of Spontaneous Emission for High Fidelity Quantum State TransferAug 15 2013We demonstrate the ability to control the spontaneous emission from a superconducting qubit coupled to a cavity. The time domain profile of the emitted photon is shaped into a symmetric truncated exponential. The experiment is enabled by a qubit coupled ... More

Andre-Quillen homology of commutative algebrasSep 05 2006These notes are an introduction to basic properties of Andre-Quillen homology for commutative algebras. They are an expanded version of my lectures at the summer school: Interactions between homotopy theory and algebra, University of Chicago, 26th July ... More

Modules and Cohomology over Group Algebras: One Commutative Algebraist's PerspectiveSep 10 2004This article explains basic constructions and results on group algebras and their cohomology, starting from the point of view of commutative algebra. It provides the background necessary for a novice in this subject to begin reading Dave Benson's article ... More

Quantum bit commitment and the reality of the quantum stateAug 16 2017Feb 14 2018Quantum bit commitment (QBC) is insecure in the standard non-relativistic quantum cryptographic framework, essentially because Alice can exploit quantum steering to defer making her commitment. Two assumptions in this framework are that: (a) Alice knows ... More

A #SAT Algorithm for Small Constant-Depth Circuits with PTF gatesSep 16 2018We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of constant-degree ... More

A Tail Bound for Read-k Families of FunctionsApr 25 2012We prove a Chernoff-like large deviation bound on the sum of non-independent random variables that have the following dependence structure. The variables $Y_1,...,Y_r$ are arbitrary Boolean functions of independent random variables $X_1,...,X_m$, modulo ... More

Super-polylogarithmic hypergraph coloring hardness via low-degree long codesNov 28 2013We prove improved inapproximability results for hypergraph coloring using the low-degree polynomial code (aka, the 'short code' of Barak et. al. [FOCS 2012]) and the techniques proposed by Dinur and Guruswami [FOCS 2013] to incorporate this code for inapproximability ... More

On the Probabilistic Degree of OR over the RealsDec 05 2018We study the probabilistic degree over reals of the OR function on $n$ variables. For an error parameter $\epsilon$ in (0,1/3), the $\epsilon$-error probabilistic degree of any Boolean function $f$ over reals is the smallest non-negative integer $d$ such ... More

Almost Settling the Hardness of Noncommutative DeterminantJan 06 2011In this paper, we study the complexity of computing the determinant of a matrix over a non-commutative algebra. In particular, we ask the question, "over which algebras, is the determinant easier to compute than the permanent?" Towards resolving this ... More

Derandomized Graph Product Results using the Low Degree Long CodeNov 13 2014Feb 10 2015In this paper, we address the question of whether the recent derandomization results obtained by the use of the low-degree long code can be extended to other product settings. We consider two settings: (1) the graph product results of Alon, Dinur, Friedgut ... More

A Fixed-Depth Size-Hierarchy Theorem for AC$^0[\oplus]$ via the Coin ProblemSep 11 2018Feb 20 2019We prove the first Fixed-depth Size-hierarchy Theorem for uniform AC$^0[\oplus]$ circuits; in particular, for fixed $d$, the class $\mathcal{C}_{d,k}$ of uniform AC$^0[\oplus]$ formulas of depth $d$ and size $n^k$ form an infinite hierarchy. For this, ... More

A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear CircuitsApr 07 2018We study the size blow-up that is necessary to convert an algebraic circuit of product-depth $\Delta+1$ to one of product-depth $\Delta$ in the multilinear setting. We show that for every positive $\Delta = \Delta(n) = o(\log n/\log \log n),$ there is ... 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

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

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

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

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

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

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

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

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

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

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

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

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

Solvability-Based Comparison of Failure DetectorsJul 11 2014Failure detectors are oracles that have been introduced to provide processes in asynchronous systems with information about faults. This information can then be used to solve problems otherwise unsolvable in asynchronous systems. A natural question is ... More

Fair Scheduling in Networks Through Packet ElectionAug 19 2008Sep 21 2010We consider the problem of designing a fair scheduling algorithm for discrete-time constrained queuing networks. Each queue has dedicated exogenous packet arrivals. There are constraints on which queues can be served simultaneously. This model effectively ... More

A criterion for regularity of local ringsFeb 11 2006Apr 05 2006It is proved that a noetherian commutative local ring A containing a field is regular if there is a complex M of free A-modules with the following properties: M_i=0 for i not in [0,dim A]; the homology of M has finite length; H_0(M) contains the residue ... More

No-signaling from Gleason non-contextuality and the tensor-product structureFeb 08 2012Jun 05 2012The no-signaling principle in quantum mechanics is shown to be a consequence of Gleason non-contextuality and the tensor product structure.

Contextuality and nonlocality of indistinguishable particlesJul 15 2019Unlike in the case of distinguishable particles, the concept of entanglement-- not to mention, nonlocality-- remains debated in case of indistinguishable particles. Here, we show that certain existing all-versus-nothing type of proofs of contextuality ... More

Conformal Riemannian morphisms between Riemannian manifoldsApr 18 2018In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of an isometric immersion, a Riemannian submersion, an isometry, a Riemannian map and a conformal Riemannian map. We show that ... More

Gaps in Hochschild cohomology imply smoothness for commutative algebrasDec 13 2004Aug 06 2005The paper concerns Hochschild cohomology of a commutative algebra S, which is essentially of finite type over a commutative noetherian ring K and projective as a K-module, with coefficients in an S-module M. It is proved that vanishing of HH^n(S|K,M) ... More

Phase Diffusion in Quantum Dissipative SystemsJun 25 2007Nov 27 2007We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via a quantum ... More

An environment-mediated quantum deleterNov 27 2006Apr 24 2007Environment-induced decoherence presents a great challenge to realizing a quantum computer. We point out the somewhat surprising fact that decoherence can be useful, indeed necessary, for practical quantum computation, in particular, for the effective ... More

Inferring Rankings Using Constrained SensingOct 06 2009Jun 19 2011We consider the problem of recovering a function over the space of permutations (or, the symmetric group) over $n$ elements from given partial information; the partial information we consider is related to the group theoretic Fourier Transform of the ... More

Connecting the Random Connection ModelOct 19 2015Consider the random graph $G({\mathcal P}_{n},r)$ whose vertex set ${\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \frac{1}{2}, \frac{1}{2}]^d$, $d \geq 2$. Any two vertices $X_i,X_j \in {\mathcal P}_{n}$ are connected by an edge ... More

Coherent Control of a Superconducting Qubit with Dynamically Tunable Qubit-cavity CouplingAug 12 2011We demonstrate coherent control and measurement of a superconducting qubit coupled to a superconducting coplanar waveguide resonator with a dynamically tunable qubit-cavity coupling strength. Rabi oscillations are measured for several coupling strengths ... More

High fidelity single-shot readout of a transmon qubit using a SLUG μwave amplifierJan 21 2014We report high-fidelity, quantum nondemolition, single-shot readout of a superconducting transmon qubit using a DC-biased superconducting low-inductance undulatory galvanometer(SLUG) amplifier. The SLUG improves the system signal-to-noise ratio by 7 dB ... More

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness DistributionNov 03 2016We study the seasonal changes in the thickness distribution of Arctic sea ice, $g(h)$, under climate forcing. Our analytical and numerical approach is based on a Fokker-Planck equation for $g(h)$ (Toppaladoddi \& Wettlaufer \emph{Phys. Rev. Lett.} {\bf ... More

Gorenstein dimension of modules over homomorphismsApr 16 2005Nov 18 2005Given a homomorphism of commutative noetherian rings R --> S and an S-module N, it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated ... More

The Jacobian ideal of a commutative ring and annihilators of cohomologyOct 09 2016Aug 03 2018It is proved that for a ring $R$ that is either an affine algebra over a field, or an equicharacteristic complete local ring, some power of the Jacobian ideal of $R$ annihilates $\mathrm{Ext}^{d+1}_{R}(-,-)$, where $d$ is the Krull dimension of $R$. Sufficient ... More

Openness of the regular locus and generators for module categoriesAug 10 2018This work clarifies the relationship between the openness of the regular locus of a commutative Noetherian ring R and the existence of generators for the category of finitely generated R-modules, the corresponding bounded derived category, and for the ... More

New upper bounds for Ramanujan primesJun 22 2017For $n\ge 1$, the $n^{\rm th}$ Ramanujan prime is defined as the smallest positive integer $R_n$ such that for all $x\ge R_n$, the interval $(\frac{x}{2}, x]$ has at least $n$ primes. We show that for every $\epsilon>0$, there is a positive integer $N$ ... 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

Grand canonical partition functions for multi level para Fermi systems of any orderAug 22 1996A general formula for the grand canonical partition function for a para Fermi system of any order and of any number of levels is derived.

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

Role of electron inertia and electron/ion finite Larmor radius effects in low-beta, magneto-Rayleigh-Taylor instabilitySep 12 2018The magneto-Rayleigh-Taylor (MRT) instability has been investigated in great detail in previous work using magnetohydrodynamic and kinetic models for low-beta plasmas. The work presented here extends previous studies of this instability to regimes where ... More

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

Semantic Web Techniques for Yellow Page Service ProvidersAug 09 2012Use of web pages providing unstructured information poses variety of problems to the user, such as use of arbitrary formats, unsuitability for machine processing and likely incompleteness of information. Structured data alleviates these problems but we ... 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

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

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

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

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

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

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

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

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

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

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

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

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

Picard-Vessiot Extensions For Unipotent Algebraic GroupsFeb 15 2011Let F be a differential field of characteristic zero. In this article, we construct Picard-Vessiot extensions of F whose differential Galois group is isomorphic to the full unipotent subgroup of the upper triangular group defined over the field of constants ... More

Molecular gas associated with the IRAS-Vela shellJun 11 1999We present a survey of molecular gas in the J = 1 -> 0 transition of 12CO towards the IRAS Vela shell. The shell, previously identified from IRAS maps, is a ring-like structure seen in the region of the Gum Nebula. We confirm the presence of molecular ... More

Polynomial mechanics and optimal controlNov 01 2014Apr 01 2015We describe a new algorithm for trajectory optimization of mechanical systems. Our method combines pseudo-spectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical quantities such as ... More