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The independence number of the Birkhoff polytope graph, and applications to maximally recoverable codesFeb 19 2017Mar 31 2017Maximally recoverable codes are codes designed for distributed storage which combine quick recovery from single node failure and optimal recovery from catastrophic failure. Gopalan et al [SODA 2017] studied the alphabet size needed for such codes in grid ... More

Communication and Memory Efficient Testing of Discrete DistributionsJun 11 2019We study distribution testing with communication and memory constraints in the following computational models: (1) The {\em one-pass streaming model} where the goal is to minimize the sample complexity of the protocol subject to a memory constraint, and ... More

Lower Bound on the Redundancy of PIR CodesMay 06 2016We prove that the redundancy of a $k$-server PIR code of dimension $s$ is $\Omega(\sqrt{s})$ for all $k \ge 3$. This coincides with a known upper bound of $O(\sqrt{s})$ on the redundancy of PIR codes. The same lower bound was proved independently by Mary ... More

Lower Bound on the Redundancy of PIR CodesMay 06 2016Feb 28 2017We prove that the redundancy of a $k$-server PIR code of dimension $s$ is $\Omega(\sqrt{s})$ for all $k \ge 3$. This coincides with a known upper bound of $O(\sqrt{s})$ on the redundancy of PIR codes. Moreover, for $k=3$ and $k = 4$, we determine the ... More

A New Upperbound for the Oblivious Transfer Capacity of Discrete Memoryless ChannelsMay 08 2014We derive a new upper bound on the string oblivious transfer capacity of discrete memoryless channels. The main tool we use is the tension region of a pair of random variables introduced in Prabhakaran and Prabhakaran (2014) where it was used to derive ... More

Probabilistic Existence of Large Sets of DesignsApr 26 2017A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been introduced by Kuperberg, Lovett, and Peled (STOC 2012). Using this technique, it can be shown that under certain conditions, a randomly chosen ... More

Torus polynomials: an algebraic approach to ACC lower boundsApr 22 2018Feb 28 2019We propose an algebraic approach to proving circuit lower bounds for ACC0 by defining and studying the notion of torus polynomials. We show how currently known polynomial-based approximation results for AC0 and ACC0 can be reformulated in this framework, ... More

4-particle Amplituhedronics for 3-5 loopsJun 05 2018Jun 14 2018Following the direction of 1712.09990 and 1712.09994, this article continues to excavate more interesting aspects of the 4-particle amplituhedron for a better understanding of the 4-particle integrand of planar N=4 SYM to all loop orders, from the perspective ... More

Local transition gradients determine the global attributes of protein energy landscapesJan 20 2010The dynamical characterization of proteins is crucial to understand protein function. From a microscopic point of view, protein dynamics is governed by the local atomic interactions that, in turn, trigger the functional conformational changes. Unfortunately, ... More

A Theory of Market EfficiencyFeb 09 2017We introduce a mathematical theory called market connectivity that gives concrete ways to both measure the efficiency of markets and find inefficiencies in large markets. The theory leads to new methods for testing the famous efficient markets hypothesis ... More

Simplex-like Structures of Maximally Supersymmetric Scattering AmplitudesDec 28 2017Jun 20 2018We elaborate the two-fold simplex-like structures of tree amplitudes in planar maximally supersymmetric Yang-Mills (N=4 SYM), through its connection to a mathematical structure known as the positive Grassmannian. Exploiting the reduced Grassmannian geometry ... More

Exhaustive search of convex pentagons which tile the planeAug 01 2017We present an exhaustive search of all families of convex pentagons which tile the plane. This research shows that there are no more than the already 15 known families. In particular, this implies that there is no convex polygon which allows only non-periodic ... More

Positivity, Grassmannian Geometry and Simplex-like Structures of Scattering AmplitudesSep 27 2016This article revisits and elaborates the significant role of positive geometry of momentum twistor Grassmannian for planar N=4 SYM scattering amplitudes. First we establish the fundamentals of positive Grassmannian geometry for tree amplitudes. Then we ... More

Positivity, Grassmannian Geometry and Simplex-like Structures of Scattering AmplitudesSep 27 2016Jul 16 2018This article revisits and elaborates the significant role of positive geometry of momentum twistor Grassmannian for planar N=4 SYM scattering amplitudes. First we establish the fundamentals of positive Grassmannian geometry for tree amplitudes. Then we ... More

Soft Theorem of N=4 SYM in Grassmannian FormulationOct 19 2014Feb 19 2015Inspired by the new soft theorem in gravity by Cachazo and Strominger, the soft theorem for color-ordered Yang-Mills amplitudes has also been identified by Casali. In this note, the same content of N=4 SYM using the Grassmannian formulation is studied. ... More

4-particle Amplituhedronics for 3-5 LoopsJun 05 2018May 09 2019Following the direction of 1712.09990 and 1712.09994, this article continues to excavate more interesting aspects of the 4-particle amplituhedron for a better understanding of the 4-particle integrand of planar N=4 SYM to all loop orders, from the perspective ... More

MITOS-RCNN: A Novel Approach to Mitotic Figure Detection in Breast Cancer Histopathology Images using Region Based Convolutional Neural NetworksJul 04 2018Studies estimate that there will be 266,120 new cases of invasive breast cancer and 40,920 breast cancer induced deaths in the year of 2018 alone. Despite the pervasiveness of this affliction, the current process to obtain an accurate breast cancer prognosis ... More

Non-linear sigma model approach to quantum spin chainsDec 05 2005We introduce and motivate the study of quantum spin chains on a one-dimensional lattice. We classify the varieties of methods that have been used to study these models into three categories, - a) exact methods to study specific models b) field theories ... More

Exact Analytic Results for Composite Fermions in a Rajaraman-Sondhi like formulationDec 23 1997Dec 25 1997We obtain the exact spectrum and the unique ground state of two composite fermions (in a Rajaraman - Sondhi like formulation) in an external magnetic field $B$. We show that the energy eigenvalues decrease with increasing angular momentum, thus making ... More

Improved Lower Bounds for the Restricted Isometry Property of Subsampled Fourier MatricesMar 28 2019Let $A$ be an $N \times N$ Fourier matrix over $\mathbb{F}_p^{\log{N}/\log{p}}$ for some prime $p$. We improve upon known lower bounds for the number of rows of $A$ that must be sampled so that the resulting matrix $M$ satisfies the restricted isometry ... More

Weyl semi-metals : a short reviewMar 09 2016Mar 22 2016We begin this review with an introduction and a discussion of Weyl fermions as emergent particles in condensed matter systems, and explain how high energy phenomena like the chiral anomaly can be seen in low energy experiments. We then explain the current ... More

The impact of upper tropospheric friction and Gill-type heating on the location and strength of the Tropical Easterly Jet: Idealized physics in a dry Atmospheric General Circulation ModelMay 19 2015Jun 24 2015An atmospheric general circulation model (AGCM) with idealized and complete physics has been used to evaluate the Tropical Easterly Jet (TEJ) jet. In idealized physics, the role of upper tropospheric friction has been found to be important in getting ... More

An Algebra of Fault ToleranceJul 20 2009Every system of any significant size is created by composition from smaller sub-systems or components. It is thus fruitful to analyze the fault-tolerance of a system as a function of its composition. In this paper, two basic types of system composition ... More

Leveraging human Domain Knowledge to model an empirical Reward function for a Reinforcement Learning problemSep 16 2019Traditional Reinforcement Learning (RL) problems depend on an exhaustive simulation environment that models real-world physics of the problem and trains the RL agent by observing this environment. In this paper, we present a novel approach to creating ... More

Cyclicity of All Anti-NMHV and N$^2$MHV Tree Amplitudes in N=4 SYMJun 05 2018This essay proves the cyclic invariance of anti-NMHV and N$^2$MHV tree amplitudes in N=4 SYM up to any number of external particles as an interesting exercise. In the proof the two-fold simplex-like structures introduced in 1609.08627 (and reviewed in ... More

Cyclicity of All Anti-NMHV and N$^2$MHV Tree Amplitudes in N=4 SYMJun 05 2018May 09 2019This essay proves the cyclic invariance of anti-NMHV and N$^2$MHV tree amplitudes in N=4 SYM up to any number of external particles as an interesting exercise. In the proof the two-fold simplex-like structures introduced in 1609.08627 (and reviewed in ... More

4-particle Amplituhedron at 3-loop and its Mondrian Diagrammatic ImplicationDec 28 2017Jun 14 2018This article provides a direct calculation of the 4-particle amplituhedron at 3-loop order, by introducing a set of practical tricks. After delicately rearranging each piece of this calculation, we find a suggestive connection between positivity conditions ... More

A Hoeffding inequality for Markov chainsJun 29 2018Mar 29 2019We prove deviation bounds for the random variable $\sum_{i=1}^{n} f_i(Y_i)$ in which $\{Y_i\}_{i=1}^{\infty}$ is a Markov chain with stationary distribution and state space $[N]$, and $f_i: [N] \rightarrow [-a_i, a_i]$. Our bound improves upon previously ... More

Introduction to abelian and non-abelian anyonsOct 28 2016In this set of lectures, we will start with a brief pedagogical introduction to abelian anyons and their properties. This will essentially cover the background material with an introduction to basic concepts in anyon physics, fractional statistics, braid ... More

Finding hitting times in various graphsAug 10 2012The hitting time, h_uv, of a random walk on a finite graph G, is the expected time for the walk to reach vertex v given that it started at vertex u. We present two methods of calculating the hitting time between vertices of finite graphs, along with applications ... More

The Cosmological Evolution of Quasar Damped Lyman-Alpha SystemsSep 06 2000We present results from an efficient, non-traditional survey to discover damped Lyman-alpha (DLA) absorption-line systems with neutral hydrogen column densities N(HI)>2x10^{20} atoms cm^{-2} and redshifts z<1.65. Contrary to previous studies at higher ... More

Coding for SunflowersSep 10 2019A sunflower is a family of sets that have the same pairwise intersections. We simplify a recent result of Alweiss, Lovett, Wu and Zhang that gives an upper bound on the size of every family of sets of size $k$ that does not contain a sunflower. We show ... More

Primitive Indexes, Zsigmondy Numbers, and PrimoverizationOct 25 2018We define a primitive index of an integer in a sequence to be the index of the term with the integer as a primitive divisor. For the sequences $k^u+h^u$ and $k^u-h^u$, we discern a formula to find the primitive indexes of any composite number given the ... More

Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic ThermodynamicsFeb 23 2016May 30 2016We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations satisfying mass action law. Our most general framework considers open ... More

Emergent Structures in an Active Polar Fluid : dynamics of shape, scattering and mergerApr 30 2016Spatially localised defect structures emerge spontaneously in a hydrodynamic description of an active polar fluid comprising polar 'actin' filaments and 'myosin' motor proteins that (un)bind to filaments and exert active contractile stresses. These emergent ... More

Anti-concentration in most directionsNov 15 2018Jan 19 2019We prove an anti-concentration bound for the inner product of two independent random vectors in the discrete cube. If, for example, $A,B$ are subsets of the cube $\{\pm 1\}^n$ with $|A| \cdot |B| \geq 2^{1.01 n}$, and $X \in A$ and $Y \in B$ are sampled ... More

Temperature response of the polarizable SWM4-NDP water modelNov 08 2013Introduction of polarizability in classical molecular simulations holds the promise to increase accuracy as well as prediction power to computer modeling. To introduce polarizability in a straight-forward way one strategy is based on Drude particles: ... More

Controlled dynamics of qubits in the presence of decoherenceJun 19 2007An exactly solvable model for the decoherence of one and two-qubit states interacting with a spin-bath, in the presence of a time-dependent magnetic field is studied. The magnetic field is static along $\hat{z}$ direction and oscillatory in the transverse ... More

A Time-parallel Approach to Strong-constraint Four-dimensional Variational Data AssimilationMay 18 2015A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple sub-intervals that allows to parallelize cost ... More

X-ray Radio Correlation In Black Hole SourcesNov 13 2006We examine the X-ray - radio correlation in Galactic black hole sources. We highlight some of the results which extend the flux-flux relations to sources with very high accretion rates. Some of the recent results indicate that the synchrotron process ... More

Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective AppraisalAug 11 2011According to Hansen, Madow and Tepping [J. Amer. Statist. Assoc. 78 (1983) 776--793], "Probability sampling designs and randomization inference are widely accepted as the standard approach in sample surveys." In this article, reasons are advanced for ... More

Multilateral Index Number Systems for International Price Comparisons: Properties, Existence and UniquenessNov 10 2018Dec 14 2018Over the past five decades a number of multilateral index number systems have been proposed for spatial and cross-country price comparisons. These multilateral indexes are usually expressed as solutions to systems of linear or nonlinear equations. In ... More

An aperiodic set of 11 Wang tilesJun 22 2015Mar 13 2019We present a new aperiodic tile set containing 11 Wang tiles on 4 colors, and show that this tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic. This gives a final ... More

Nonequilibrium phase transitions in active contractile polar filamentsJan 18 2012We study the patterning and fluctuations of a collection of active contractile polar filaments on a two dimensional substrate, using a continuum description in the presence of athermal noise, parameterised by an active temperature $T_A$. The steady states ... More

Interference AutomataJan 22 2007We propose a computing model, the Two-Way Optical Interference Automata (2OIA), that makes use of the phenomenon of optical interference. We introduce this model to investigate the increase in power, in terms of language recognition, of a classical Deterministic ... More

Generalized Counters and Reversal ComplexityOct 25 2004Jun 27 2006We generalize the definition of a counter and counter reversal complexity and investigate the power of generalized deterministic counter automata in terms of language recognition.

Arrested States of SolidsOct 01 1999Solids produced as a result of a fast quench across a freezing or a structural transition get stuck in long-lived metastable configurations of distinct morphology, sensitively dependent on the processing history. {\it Martensites} are particularly well ... More

First Passage Times and Time-Temperature-Transformation curves for MartensitesSep 02 1997Martensites are long-lived nonequilibrium structures produced following a quench across a solid state structural transition. In a recent paper (Phys. Rev. Lett. 78, 2168 (1997)), we had described a mode-coupling theory for the morphology and nucleation ... More

Dynamics of Ordering of Isotropic MagnetsMar 03 1999We study the dynamics of ordering of the nonconserved and conserved Heisenberg magnet. The dynamics consists of two parts - an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. ... More

Approximation properties by generalized Baskakov Kantorovich Stancu type operatorsAug 05 2015In this paper, we introduce generalized Baskakov Kantorovich Stancu type operators and investigate direct result, local approximation and weighted approximation properties of these operators. Modulus of continuity, second modulus of continuity, Peeters ... More

Triangulating an exotic T quarkApr 19 2012Limits on an exotic heavy quark $T$ are broadly generalized by considering the full range of $T\rightarrow Wb, th$ or $tZ$ branching ratios. We combine results of specific $T\rightarrow tZ$ and $T\rightarrow Wb$ searches with limits on various combinations ... More

Geometric progressions in syndetic setsAug 28 2018Apr 28 2019In order to investigate multiplicative structures in additively large sets, Beiglb\"{o}ck et al. raised a significant open question as to whether or not every subset of the natural numbers with bounded gaps (syndetic set) contains arbitrarily long geometric ... More

Towards Neural Co-Processors for the Brain: Combining Decoding and Encoding in Brain-Computer InterfacesNov 28 2018Dec 28 2018The field of brain-computer interfaces is poised to advance from the traditional goal of controlling prosthetic devices using brain signals to combining neural decoding and encoding within a single neuroprosthetic device. Such a device acts as a "co-processor" ... More

Conservation Laws shape DissipationSep 06 2017Feb 06 2018Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the conservative ... More

Universal, transferable and targeted adversarial attacksAug 29 2019Sep 13 2019Deep Neural Network has been found vulnerable recently. A kind of well-designed inputs, which called adversarial examples, can lead the networks to make incorrect predictions. Depending on the different scenarios, goals and capabilities, the difficulty ... More

Range of Berezin TransformMar 20 2010Let $\ds dA=\frac{dxdy}\pi$ denote the normalized Lebesgue area measure on the unit disk $\disk$ and $u$, a summable function on $\disk$. $$B(u)(z)=\int_\disk u(\zeta)\frac{(1-|z|^2)^2}{|1-\zeta\oln z|^4}dA(\zeta)$$ is called the Berezin transform of ... More

Lipschitz equivalence of fractals and finite state automatonSep 14 2016The study of Lipschitz equivalence of fractals is a very active topic in recent years. Most of the studies in literature concern totally disconnected fractals. In this paper, using finite state automata, we construct a bi-Lipschitz map between two fractal ... More

Higher dimensional Frobenius problem and Lipschitz equivalence of Cantor setsNov 26 2014The higher dimensional Frobenius problem was introduced by a preceding paper [Fan, Rao and Zhang, Higher dimensional Frobenius problem: maximal saturated cones, growth function and rigidity, Preprint 2014]. %the higher dimensional Frobenius problem was ... More

Energy-Efficient Scheduling: Classification, Bounds, and AlgorithmsSep 21 2016The problem of attaining energy efficiency in distributed systems is of importance, but a general, non-domain-specific theory of energy-minimal scheduling is far from developed. In this paper, we classify the problems of energy-minimal scheduling and ... More

Geometric progressions in syndetic setsAug 28 2018In order to investigate multiplicative structures in additively large sets, Beiglb\"{o}ck et al. raised a significant open question as to whether or not every subset of the natural numbers with bounded gaps (syndetic set) contains arbitrarily long geometric ... More

The protein folding networkMar 23 2004The conformation space of a 20-residue antiparallel $\beta$-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Conformations are nodes of the network, and the transitions between them are links. The conformation space network ... More

Efficient parameter sampling for Markov jump processesApr 07 2017Jun 01 2018Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based auxiliary variable ... More

Observing Galactic Black Hole Sources in Hard X-raysOct 01 2013Observations of Galactic black hole sources are traditionally done in the classical X-ray range (2 -- 10 keV) due to sensitivity constraints. Most of the accretion power, however, is radiated above 10 keV and the study of these sources in hard X-rays ... More

Automatic Music AccompanistMar 24 2018Automatic musical accompaniment is where a human musician is accompanied by a computer musician. The computer musician is able to produce musical accompaniment that relates musically to the human performance. The accompaniment should follow the performance ... More

High Energy Transients: the Millisecond DomainNov 01 2017Search for high energy transients in the millisecond domain has come to the focus in recent times due to the detection of Gravitational Wave events and the identification of Fast Radio Bursts as cosmological sources. I will highlight the sensitivity limitations ... More

Actionable and Political Text Classification using Word Embeddings and LSTMJul 08 2016Jul 13 2016In this work, we apply word embeddings and neural networks with Long Short-Term Memory (LSTM) to text classification problems, where the classification criteria are decided by the context of the application. We examine two applications in particular. ... More

Fast extraction of the backbone of projected bipartite networks to aid community detectionDec 07 2015Mar 21 2016This paper introduces a computationally inexpensive method of extracting the backbone of one-mode networks projected from bipartite networks. We show that the edge weights in the one-mode projections are distributed according to a Poisson binomial distribution ... More

Conservation Laws and Work Fluctuation Relations in Chemical Reaction NetworksMay 30 2018Jan 11 2019We formulate a nonequilibrium thermodynamic description for open chemical reaction networks (CRN) described by a chemical master equation. The topological properties of the CRN and its conservation laws are shown to play a crucial role. They are used ... More

Avoiding two consecutive blocks of same size and same sum over $\mathbb{Z}^2$Nov 18 2015Sep 30 2016A long standing question asks whether $\mathbb{Z}$ is uniformly 2-repetitive [Justin 1972, Pirillo and Varricchio, 1994], that is, whether there is an infinite sequence over a finite subset of $\mathbb{Z}$ avoiding two consecutive blocks of same size ... More

Two Modes of Solid State Nucleation - Ferrites, Martensites and Isothermal Transformation CurvesJul 05 2001Aug 17 2001When a crystalline solid such as iron is cooled across a structural transition, its final microstructure depends sensitively on the cooling rate. For instance, an adiabatic cooling across the transition results in an equilibrium `ferrite', while a rapid ... More

Bounding Run-Times of Local Adiabatic AlgorithmsJan 20 2007A common trick for designing faster quantum adiabatic algorithms is to apply the adiabaticity condition locally at every instant. However it is often difficult to determine the instantaneous gap between the lowest two eigenvalues, which is an essential ... More

Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. ISep 27 1997We study the dynamics of ordering of a nonconserved Heisenberg magnet. The dynamics consists of two parts --- an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches to ... More

Note on Identities Inspired by New Soft TheoremsApr 03 2016May 04 2016The new soft theorems, for both gravity and gauge amplitudes, have inspired a number of works, including the discovery of new identities related to amplitudes. In this note, we present the proof and discussion for two sets of identities. The first set ... More

Hierarchical RNN for Information Extraction from Lawsuit DocumentsApr 25 2018Every lawsuit document contains the information about the party's claim, court's analysis, decision and others, and all of this information are helpful to understand the case better and predict the judge's decision on similar case in the future. However, ... More

The 2-domination and Roman domination numbers of grid graphsOct 30 2018May 17 2019We investigate the 2-domination number for grid graphs, that is the size of a smallest set $D$ of vertices of the grid such that each vertex of the grid belongs to $D$ or has at least two neighbours in $D$. We give a closed formula giving the 2-domination ... More

Fractional extensions of some boundary value problems in oil strataJul 13 2007In the present paper, we solve three boundary value problems related to the temperature field in oil strata -- the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of ... More

Irreducible representations for Toroidal Lie algebrasDec 10 2002We study irreducible modules for Toroidal Lie-algebras with finite dimensional weight spaces. First note that Toroidal Lie-algebras have infinite dimensional center. In genaral the infinite dimensional center does not act as scalars on an irreducible ... More

Some Observational Aspects of R Coronae Borealis StarsDec 24 2007Some of the observational aspects related to the evolutionary status and dust production in R Cor Bor stars are discussed. Recent work regarding the surface abundances, stellar winds and evidence for dust production in these high luminosty hydrogen deficient ... More

Failover in cellular automataMay 29 2010A cellular automata (CA) configuration is constructed that exhibits emergent failover. The configuration is based on standard Game of Life rules. Gliders and glider-guns form the core messaging structure in the configuration. The blinker is represented ... More

A-posteriori error estimates for inverse problemsSep 25 2014Jan 30 2015Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This work develops ... More

Where are the Fermi Lines Coming From?Oct 17 2012We estimate the spatial locations of sources of the the observed features in the Fermi-LAT photon spectrum at $E_\gamma=110$ and $E_\gamma=130$ GeV. We determine whether they are consistent with emission from a single source, as would be expected in their ... More

Lattice Boltzmann Models for Micro-tomographic Pore-spacesFeb 28 2019The lattice Boltzmann method (LBM) is a popular numerical framework to investigate single and multiphase flow though porous media. For estimation of absolute permeability based on micro-tomographic images of the porous medium, the single-relaxation time ... More

Central Forests in TreesSep 02 2008A new 2-parameter family of central structures in trees, called central forests, is introduced. Minieka's $m$-center problem and McMorris's and Reid's central-$k$-tree can be seen as special cases of central forests in trees. A central forest is defined ... More

Lipschitz invariance of walk dimension on connected self-similar setsSep 14 2016Walk dimension is an important conception in analysis of fractals. In this paper we prove that the walk dimension of a connected compact set possessing an Alfors regular measure is an invariant under Lipschitz transforms. As an application, we show some ... More

Microsecond long atomistic simulation of supercooled waterJun 04 2012Supercooled water is a metastable phase of liquid water below the melting temperature. An interesting discussion recently developed on the relationship between crystallization rate and the time scales of equilibration within the liquid phase. Calculations ... More

Generalized Casimir OperatorsFeb 25 2016Let G be symmetrizable Kac-Moody Lie algebra. In this paper we describe a new class of central operators generalising the Casimir operator. We also prove some properties of these operators and show that these operators move highest weight vectors to new ... More

Effective Primality Test for $p2^n+1$, $p$ prime, $n>1$Nov 14 2018We develop a simple $O((\log n)^2)$ test as an extension of Proth's test for the primality for $p2^n+1$, $p>2^n$. This allows for the determination of large, non-Sierpinski primes $p$ and the smallest $n$ such that $p2^n+1$ is prime. If $p$ is a non-Sierpinski ... More

Listening to the World Improves Speech Command RecognitionOct 23 2017We study transfer learning in convolutional network architectures applied to the task of recognizing audio, such as environmental sound events and speech commands. Our key finding is that not only is it possible to transfer representations from an unrelated ... More

Field Theories of Frustrated Heisenberg AntiferromagnetsJul 02 1995We study the Heisenberg antiferromagnetic chain with both dimerization and frustration. The classical ground state has three phases: a Neel phase, a spiral phase and a colinear phase. In each phase, we discuss a non-linear sigma model field theory governing ... More

Non-linear Field Theory of a Frustrated Heisenberg Spin ChainOct 18 1992We derive a continuum field theory for the Majumdar-Ghosh model in the large-$S$ limit, where the field takes values in the manifold of the $SO(3)$ group. No topological term is induced in the action and the cases for integer spin and half-integer spin ... More

Subsumptive reflection in SNOMED CT: a large description logic-based terminology for diagnosisDec 11 2015Description logic (DL) based biomedical terminology (SNOMED CT) is used routinely in medical practice. However, diagnostic inference using such terminology is precluded by its complexity. Here we propose a model that simplifies these inferential components. ... More

Predicting Item Popularity: Analysing Local Clustering Behaviour of UsersMar 15 2015Sep 17 2015Predicting the popularity of items in rating networks is an interesting but challenging problem. This is especially so when an item has first appeared and has received very few ratings. In this paper, we propose a novel approach to predicting the future ... More

Inner Disk Oscillations and QPOs in Relativistic Jet SourcesDec 01 2000Recent results on the inner disk oscillations found in GRS 1915+105 are reviewed. QPOs during the low state are used as a marker for such oscillations and the physical picture emerging from a combined X-ray spectral and timing analysis is examined. The ... More

Singlet fermion Dark Matter within Left-Right ModelDec 13 2015May 31 2016We discuss singlet fermion dark matter within a left-right symmetric model promoting baryon and lepton numbers as separate gauge symmetries. We add a simple Dirac fermionic dark matter singlet under $SU(2)_{L,R}$ with nonzero and equal baryon and lepton ... More

The impact of latent heating on the location, strength and structure of the Tropical Easterly Jet in the Community Atmosphere Model, version 3.1: Aqua-planet simulationsMay 03 2015Aug 05 2015The Tropical Easterly Jet (TEJ) is a prominent atmospheric circulation feature observed during the Asian Summer Monsoon (ASM). The simulation of TEJ by the Community Atmosphere Model, version 3.1 (CAM-3.1) has been discussed in detail. Although the simulated ... More

Turning Bitcoins into the Best-coinsDec 23 2014In this paper we discuss Bitcoin, the leader among the existing cryptocurrencies, to analyse its trends, success factors, current challenges and probable solutions to make it even better. In the introduction section, we discuss the history and working ... More

Remarks on the Cartan Formula and Its ApplicationsApr 07 2011In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.

Effects of interaction on an adiabatic quantum electron pumpOct 01 2004We study the effects of inter-electron interactions on the charge pumped through an adiabatic quantum electron pump. The pumping is through a system of barriers, whose heights are deformed adiabatically. (Weak) interaction effects are introduced through ... More

Classification of Irreducible integrable modules for toroidal Lie-algebras with finite dimensional weight spacesSep 06 2002Toroidal Lie algebras are universal central extentions of the finite dimensional simple Lie algbera tensored with Laurent Polynomials in several commuteing variables. In this paper we classify irreducible integrable modules for Toroidal Lie algebras with ... More

Application of Fuzzy Logic in Design of Smart Washing MachineJan 04 2017Mar 15 2017Washing machine is of great domestic necessity as it frees us from the burden of washing our clothes and saves ample of our time. This paper will cover the aspect of designing and developing of Fuzzy Logic based, Smart Washing Machine. The regular washing ... More