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Homological Algebra for Persistence ModulesMay 14 2019We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module and sheaf ... More

Small Sets with Large Difference SetsMay 24 2017For every $\epsilon > 0$ and $k \in \mathbb{N}$, Haight constructed a set $A \subset \mathbb{Z}_N$ ($\mathbb{Z}_N$ stands for the integers modulo $N$) for a suitable $N$, such that $A-A = \mathbb{Z}_N$ and $|kA| < \epsilon N$. Recently, Nathanson posed ... More

Contractive Families on Compact SpacesDec 02 2013A family f_1,...,f_n of operators on a complete metric space X is called contractive if there exists lambda < 1 such that for any x,y in X we have d(f_i(x),f_i(y)) leq lambda d(x,y) for some i. Stein conjectured that for any contractive family there is ... More

Alternating direction method of multipliers with variable step sizesApr 20 2017The alternating direction method of multipliers (ADMM) is a flexible method to solve a large class of convex minimization problems. Particular features are its unconditional convergence with respect to the involved step size and its direct applicability. ... More

The automatic creation of concept maps from documents written using morphologically rich languagesOct 29 2012Sep 27 2014Concept map is a graphical tool for representing knowledge. They have been used in many different areas, including education, knowledge management, business and intelligence. Constructing of concept maps manually can be a complex task; an unskilled person ... More

Hardware-Based ADMM-LP DecodingMay 17 2016In this paper we present an FPGA-based implementation of linear programming (LP) decoding. LP decoding frames error correction as an optimization problem. This is in contrast to variants of belief propagation (BP) decoding that view error correction as ... More

On Decay CentralityApr 19 2016We establish a relationship between decay centrality and two widely used and computationally cheaper measures of centrality, namely degree and closeness centrality. We show that for low values of the decay parameter the nodes with maximum decay centrality ... More

Equity forecast: Predicting long term stock price movement using machine learningMar 02 2016Nov 22 2018Long term investment is one of the major investment strategies. However, calculating intrinsic value of some company and evaluating shares for long term investment is not easy, since analyst have to care about a large number of financial indicators and ... More

Maximum range of a projectile thrown from constant-speed circular motionSep 27 2016The problem of determining the angle at which a point mass launched from ground level with a given speed is a standard exercise in mechanics. Similar, yet conceptually and calculationally more difficult problems have been suggested to improve student ... More

Relations between different notions of degrees of freedom of a quantum system and its classical modelNov 17 2014There are at least three different notions of degrees of freedom (DF) that are important in comparison of quantum and classical dynamical systems. One is related to the type of dynamical equations and inequivalent initial conditions, the other to the ... More

Inadequacy of zero-width approximation for a light Higgs boson signalMay 09 2013Jun 05 2013The zero-width approximation (ZWA) restricts the intermediate unstable particle state to the mass shell and, when combined with the decorrelation approximation, fully factorizes the production and decay of unstable particles. The ZWA uncertainty is expected ... More

Hardware-Based Linear Program Decoding with the Alternating Direction Method of MultipliersNov 18 2016We present a hardware-based implementation of Linear Program (LP) decoding for binary linear codes. LP decoding frames error-correction as an optimization problem. In contrast, variants of Belief Propagation (BP) decoding frame error-correction as a problem ... More

Key Reconciliation with Low-Density Parity-Check Codes for Long-Distance Quantum CryptographyFeb 24 2017Apr 17 2017The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuous-variable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms for key reconciliation. ... More

Equity forecast: Predicting long term stock price movement using machine learningMar 02 2016Long term investment is one of the major investment strategies. However, calculating intrinsic value of some company and evaluating shares for long term investment is not easy, since analyst have to care about a large number of financial indicators and ... More

Blocker size via matching minorsJun 20 2016Finding the maximum number of maximal independent sets in an $n$-vertex graph $G$, $i(G)$, from a restricted class is an extensively studied problem. Let $kK_2$ denote the matching of size $k$, that is a graph with $2k$ vertices and $k$ disjoint edges. ... More

History of malwareFeb 21 2013Jan 16 2014In past three decades almost everything has changed in the field of malware and malware analysis. From malware created as proof of some security concept and malware created for financial gain to malware created to sabotage infrastructure. In this work ... More

Signal-background interference in gg --> H --> VVJan 08 2012Sep 20 2012The resonance-continuum interference between the SM Higgs search signal process gg --> H --> VV (V=W,Z) and the irreducible background process gg --> VV is studied at leading order for integrated cross sections and differential distributions in pp collisions ... More

Maximal lower bounds in the Löwner orderDec 15 2016We show that the set of maximal lower bounds of two symmetric matrices with respect to the L\"owner order can be identified to the quotient set $O(p,q)/(O(p)\times O(q))$. Here, $(p,q)$ denotes the inertia of the difference of the two matrices, $O(p)$ ... More

On Decay CentralityApr 19 2016Jan 04 2017We establish a relationship between decay centrality and two widely used and computationally cheaper measures of centrality, namely degree and closeness. We show that for low values of the decay parameter the nodes with maximum decay centrality also have ... More

An Open-Source Monitoring System for Remote Solar Power ApplicationsFeb 12 2015Renewable energy systems are an increasingly popular way to generate electricity. As with any new technological paradigm, new challenges have emerged which are unique to the utilization of renewable energy systems. One of these challenges in particular ... More

Ergodic property of stable-like Markov chainsNov 27 2014A stable-like Markov chain is a time-homogeneous Markov chain on the real line with the transition kernel $p(x,dy)=f_x(y-x)dy$, where the density functions $f_x(y)$, for large $|y|$, have a power-law decay with exponent $\alpha(x)+1$, where $\alpha(x)\in(0,2)$. ... More

On Recurrence and Transience of Two-Dimensional Lévy and Lévy-Type ProcessesSep 03 2015In this paper, we study recurrence and transience of L\'evy-type processes, that is, Feller processes associated with pseudo-differential operators. Since the recurrence property of L\'evy-type processes in dimensions greater than two is vacuous and the ... More

Homogenization of periodic diffusion with small jumpsOct 21 2015In this paper, we study the homogenization of a diffusion process with jumps, that is, Feller process generated by an integro-differential operator. This problem is closely related to the problem of homogenization of boundary value problems arising in ... More

Open Source Remote Monitoring for Rural Solar Electrification ProjectsFeb 12 2015Renewable energy systems are an increasingly popular way to generate electricity around the world. As wind and solar technologies gradually begin to supplant the use of fossil fuels as preferred means of energy production, new challenges are emerging ... More

NLO automated tools for QCD and beyondFeb 21 2012Feb 26 2012Theoretical predictions for scattering processes with multi-particle final states at next-to-leading order (NLO) in perturbative QCD are essential to fully exploit the physics potential of present and future high-energy colliders. The status of NLO QCD ... More

On the size of Diophantine $m$-tuples in imaginary quadratic number ringsJul 05 2018A Diophantine $m$-tuple is a set of $m$ distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers. We study the same problem in ... More

A Note on the Birkhoff Ergodic TheoremApr 12 2017The classical Birkhoff ergodic theorem states that for an ergodic Markov process the limiting behaviour of the time average of a function (having finite $p$-th moment, $p\ge1$, with respect to the invariant measure) along the trajectories of the process, ... More

Ergodicity of Lévy-Type ProcessesMar 24 2016Apr 01 2016In this paper, conditions for transience, recurrence, ergodicity and strong, subexponential (polynomial) and exponential ergodicity of a class of Feller processes are derived. The conditions are given in terms of the coefficients of the corresponding ... More

Long-time behavior of stable-like processesDec 11 2012In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol $p(x,\xi)=-i\beta(x)\xi+\gamma(x)|\xi|^{\alpha(x)},$ where $\alpha(x)\in(0,2)$, $\beta(x)\in\R$ and $\gamma(x)\in(0,\infty)$. ... More

Minor-matching hypertree widthApr 10 2017Jul 04 2017In this paper we present a new width measure for a tree decomposition, minor-matching hypertree width, $\mu\text{-}tw$, for graphs and hypergraphs, such that bounding the width guarantees that set of maximal independent sets has a polynomially-sized restriction ... More

Polarity and Monopolarity of $3$-colourable comparability graphsApr 04 2016Apr 05 2016We sharpen the result that polarity and monopolarity are NP-complete problems by showing that they remain NP-complete if the input graph is restricted to be a $3$-colourable comparability graph. We start by presenting a construction reducing $1$-$3$-SAT ... More

Marvin: Semantic annotation using multiple knowledge sourcesFeb 01 2016Feb 02 2016People are producing more written material then anytime in the history. The increase is so high that professionals from the various fields are no more able to cope with this amount of publications. Text mining tools can offer tools to help them and one ... More

Automated conjecturing of Frobenius numbers via grammatical evolutionOct 02 2014Feb 17 2015Conjecturing formulas and other symbolic relations occurs frequently in number theory and combinatorics. If we could automate conjecturing, we could benefit not only from speeding up, but also from finding conjectures previously out of our grasp. Grammatical ... More

Geometry and Dynamics of Quantum State DiffusionApr 11 2007Riemannian metric on real 2n-dimensional space associated with the equation governing complex diffusion of pure states of an open quantum system is introduced and studied. Examples of a qubit under the influence of dephasing and thermal environments are ... More

Strong, Weak and Branching Bisimulation for Transition Systems and Markov Reward Chains: A Unifying Matrix ApproachDec 10 2009We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic apparatus. Next we ... More

Interference effects for H --> WW/ZZ --> l anti-nu_l anti-l nu_l searches in gluon fusion at the LHCOct 25 2013Dec 02 2013WW/ZZ interference for Higgs signal and continuum background as well as signal-background interference is studied for same-flavour l anti-nu_l anti-l nu_l final states produced in gluon-gluon scattering at the LHC for light and heavy Higgs masses with ... More

On Transience of Lévy-Type ProcessesApr 13 2016In this paper, we study weak and strong transience of a class of Feller processes associated with pseudo-differential operators, the so-called L\'evy-type processes. As a main result, we derive Chung-Fuchs type conditions (in terms of the symbol of the ... More

Recurrence and transience criteria for two cases of stable-like Markov chainsJun 26 2012We give recurrence and transience criteria for two cases of time-homogeneous Markov chains on the real line with transition kernel $p(x,dy)=f_x(y-x)dy$, where $f_x(y)$ are probability densities of symmetric distributions and, for large $|y|$, have a power-law ... More

Stemmer for Serbian languageSep 20 2012In linguistic morphology and information retrieval, stemming is the process for reducing inflected (or sometimes derived) words to their stem, base or root form; generally a written word form. In this work is presented suffix stripping stemmer for Serbian ... More

Recurrence and transience property for a class of Markov chainsMar 02 2012Dec 18 2013We consider the recurrence and transience problem for a time-homogeneous Markov chain on the real line with transition kernel $p(x,\mathrm{d}y)=f_x(y-x)\,\mathrm{d}y$, where the density functions $f_x(y)$, for large $|y|$, have a power-law decay with ... More

Nonlinear evolution of coarse-grained quantum systems with generalized purity constraintsMay 17 2010Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the ... More

Quantum Degrees of Freedom, Quantum Integrability and Entanglment GeneratorsMar 26 2010Dynamical algebra notion of quantum degrees of freedom is utilized to study the relation between quantum dynamical integrability and generalized entanglement. It is argued that a quantum dynamical system generates generalized entanglement by internal ... More

Off-shell Higgs signal and total width determination at the LHCFeb 09 2015Mar 08 2015A substantial off-shell Higgs boson signal in the gluon fusion and vector boson fusion H --> ZZ and H --> WW channels at the Large Hadron Collider (LHC) facilitates a novel, complementary approach to constraining the total Higgs width Gamma_H. With LHC ... More

Stability of the overdamped Langevin equation in double-well potentialJul 28 2018In this article, we discuss stability of the one-dimensional overdamped Lange\-vin equation in double-well potential. We determine unstable and stable equilibria, and discuss the rate of convergence to stable ones. Also, we derive conditions for stability ... More

Long-time behavior for a class of Feller processesJan 12 2014Oct 07 2014In this paper, as a main result, we derive a Chung-Fuchs type condition for the recurrence of Feller processes associated with pseudo-differential operators. In the L\'evy process case, this condition reduces to the classical and well-known Chung-Fuchs ... More

Primal-dual gap estimators for a posteriori error analysis of nonsmooth minimization problemsFeb 11 2019The primal-dual gap is a natural upper bound for the energy error and, for uniformly convex minimization problems, also for the error in the energy norm. This feature can be used to construct reliable primal-dual gap error estimators for which the constant ... More

Capacity of the State-Dependent Half-Duplex Relay Channel Without Source-Destination LinkFeb 15 2013Feb 23 2014We derive the capacity of the state-dependent half-duplex relay channel without source-destination link. The output of the state-dependent half-duplex relay channel depends on the randomly varying channel states of the source-relay and relay-destination ... More

Bifurcations due to small time-lag in coupled excitable systemsNov 13 2003A system of ODE's is used to approximate the dynamics of two delayed coupled FitzHugh-Nagumo excitable units, and study the relevant bifurcations. It is shown that the Bautin bifurcation acts as the organizing center for the dynamics of ODE's for small ... More

Ground state overlap and quantum phase transitionsDec 29 2005Jul 17 2006We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and XY models, we show that the regions of ... More

Quasinormal Modes and Correlators in the Shear Channel of Spacetime-Filling BranesJul 30 2018We study the shear momentum diffusion and related modes of a strongly coupled $(2+1)$-dimensional conformal field theory at finite temperature and chemical potential, using a dual holographic description. We consider a space-time filling charged black ... More

Unsupervised Learning for Color ConstancyDec 01 2017Apr 20 2018Most digital camera pipelines use color constancy methods to reduce the influence of illumination and camera sensor on the colors of scene objects. The highest accuracy of color correction is obtained with learning-based color constancy methods, but they ... More

Specialising Word Vectors for Lexical EntailmentOct 17 2017Apr 19 2018We present LEAR (Lexical Entailment Attract-Repel), a novel post-processing method that transforms any input word vector space to emphasise the asymmetric relation of lexical entailment (LE), also known as the IS-A or hyponymy-hypernymy relation. By injecting ... More

Hankel determinant of second order for some classes of analytic functionsMar 19 2019Let $f$ be analytic in the unit disk $\mathbb D$ and normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order $\alpha$, Ozaki close-to-convex ... More

Robust Learning from Untrusted SourcesJan 29 2019Modern machine learning methods often require more data for training than a single expert can provide. Therefore, it has become a standard procedure to collect data from external sources, e.g. via crowdsourcing. Unfortunately, the quality of these sources ... More

Nonlocal interactions in collapsing condensates in a boxApr 17 2019The collapse of attractive Bose-Einstein condensates in a box with tunable interatomic interactions was studied experimentally recently. Not only were remarkably stable remnant condensates observed, but furthermore they often seem to involve two stable ... More

A New Structural Phase Field Crystal Approach for Modelling GrapheneSep 09 2015Sep 30 2015This paper introduces a new structural phase field crystal (PFC) type model that expands the PFC methodology to a wider class of structurally complex crystal structures than previously possible. Specifically, our new approach allows for stabilization ... More

Classes of Complete Simple Games that are All WeightedJan 07 2014Important decisions are likely made by groups of agents. Thus group decision making is very common in practice. Very transparent group aggregating rules are given by weighted voting, where each agent is assigned a weight. Here a proposal is accepted if ... More

Green Stability Assumption: Unsupervised Learning for Statistics-Based Illumination EstimationFeb 02 2018In the image processing pipeline of almost every digital camera there is a part dedicated to computational color constancy i.e. to removing the influence of illumination on the colors of the image scene. Some of the best known illumination estimation ... More

The geometry of the space of branched Rough PathsOct 29 2018Nov 05 2018We construct an explicit transitive free action of a Banach space of H\"older functions on the space of branched rough paths, which yields in particular a bijection between theses two spaces. This endows the space of branched rough paths with the structure ... More

License Plate Recognition with Compressive Sensing Based Feature ExtractionFeb 07 2019License plate recognition is the key component to many automatic traffic control systems. It enables the automatic identification of vehicles in many applications. Such systems must be able to identify vehicles from images taken in various conditions ... More

Hamiltonian Maker-Breaker games on small graphsAug 25 2017Aug 07 2018We look at the unbiased Maker-Breaker Hamiltonicity game played on the edge set of a complete graph $K_n$, where Maker's goal is to claim a Hamiltonian cycle. First, we prove that, independent of who starts, Maker can win the game for $n = 8$ and $n = ... More

Recognition of unipolar and generalised split graphsApr 04 2016A graph is unipolar if it can be partitioned into a clique and a disjoint union of cliques, and a graph is a generalised split graph if it or its complement is unipolar. A unipolar partition of a graph can be used to find efficiently the clique number, ... More

Random Perfect GraphsApr 04 2016Sep 05 2017We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\{1,\ldots,n\}$. Our approach is based on the result of Pr\"omel and Steger that almost all perfect graphs are generalised ... More

Hamilton cycles, minimum degree and bipartite holesApr 04 2016Apr 19 2016We present a tight extremal threshold for the existence of Hamilton cycles in graphs with large minimum degree and without a large ``bipartite hole`` (two disjoint sets of vertices with no edges between them). This result extends Dirac's classical theorem, ... More

Dynamics of FitzHugh-Nagumo excitable systems with delayed couplingMay 07 2003Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in N=2 case are ... More

Bayesian Parameter Inference for Partially Observed Stopped ProcessesJan 18 2012In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally within the context ... More

Characterizing Solute Segregation and Grain Boundary Energy in a Binary Alloy Phase Field Crystal ModelJan 18 2011Apr 08 2013This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elasto-plastic effects on diffusional time ... More

Explicit Formulas for the Scalar Modes in Seiberg-Witten Theory with an Application to the Argyres-Douglas PointSep 24 2004General formulas for the scalar modes a_i and a^i_D in the Seiberg-Witten SU(N) setting are derived in the cases with and without massive hypermultiplets. Subsequently these formulas are applied in a study of the SU(3) Argyres-Douglas point. We use this ... More

New density functional approach for solid-liquid-vapor transitions in pure materialsDec 22 2014Feb 27 2015A new phase field crystal (PFC) type theory is presented, which accounts for the full spectrum of solid-liquid-vapor phase transitions within the framework of a single density order parameter. Its equilibrium properties show the most quantitative features ... More

Grounding object perception in a naive agent's sensorimotor experienceSep 26 2016Artificial object perception usually relies on a priori defined models and feature extraction algorithms. We study how the concept of object can be grounded in the sensorimotor experience of a naive agent. Without any knowledge about itself or the world ... More

Discovering Latent States for Model Learning: Applying Sensorimotor Contingencies Theory and Predictive Processing to Model ContextAug 01 2016Autonomous robots need to be able to adapt to unforeseen situations and to acquire new skills through trial and error. Reinforcement learning in principle offers a suitable methodological framework for this kind of autonomous learning. However current ... More

Gravity-Matter Entanglement in Regge Quantum GravityJan 22 2016We argue that Hartle-Hawking states in the Regge quantum gravity model generically contain non-trivial entanglement between gravity and matter fields. Generic impossibility to talk about "matter in a point of space" is in line with the idea of an emergent ... More

Edge-sum distinguishing labelingApr 15 2018Jan 14 2019We study \emph{edge-sum distinguishing labeling}, a type of labeling recently introduced by Tuza in [Zs. Tuza, \textit{Electronic Notes in Discrete Mathematics} 60, (2017), 61-68] in context of labeling games. An \emph{ESD labeling} of an $n$-vertex graph ... More

Nontrivial solutions to Serrin's problem in annular domainsFeb 27 2019Mar 04 2019We construct nontrivial smooth bounded domains $\Omega \subseteq \mathbb{R}^n$ of the form $\Omega_0 \setminus \overline{\Omega}_1$, bifurcating from annuli, for which there exists a positive solution to the overdetermined boundary value problem \[ -\Delta ... More

On Dedekind's problem for complete simple gamesJan 18 2010We combine the parametric Barvinok algorithm with a generation algorithm for a finite list of suitably chosen discrete sub-cases on the enumeration of complete simple games, i.e. a special subclass of monotone Boolean functions. Recently, Freixas et al. ... More

Nontrivial solutions to Serrin's problem in annular domainsFeb 27 2019We construct nontrivial smooth bounded domains $\Omega \subseteq \mathbb{R}^n$ of the form $\Omega_0 \setminus \overline{\Omega}_1$, bifurcating from annuli, for which there exists a positive solution to the overdetermined boundary value problem \[ -\Delta ... More

Fully Statistical Neural Belief TrackingMay 29 2018This paper proposes an improvement to the existing data-driven Neural Belief Tracking (NBT) framework for Dialogue State Tracking (DST). The existing NBT model uses a hand-crafted belief state update mechanism which involves an expensive manual retuning ... More

Dynamical Casimir effect in a periodically changing domain: A dynamical systems approachAug 02 2004We study the problem of the behavior of a quantum massless scalar field in the space between two parallel infinite perfectly conducting plates, one of them stationary, the other moving periodically. We reformulate the physical problem into a problem about ... More

On the extension of $D(-8k^2)$-pair $\{8k^2, 8k^2+1\}$Oct 14 2016Let $n$ be a nonzero integer. A set of $m$ positive integers is called a $D(n)$-$m$-tuple if the product of any two of its distinct elements increased by $n$ is a perfect square. Let $k$ be a positive integer. By elementary means, we show that the $D(-8k^2)$-pair ... More

SYZ mirror symmetry from Witten-Morse theoryNov 22 2018This is a survey article on the recent progress in understanding the Strominger-Yau-Zaslow (SYZ) mirror symmetry conjecture, especially on the effect of quantum corrections, via Witten-Morse theory using the program first depicted by Fukaya to obtain ... More

Finding Endomorphisms of Drinfeld modulesAug 09 2016We give an effective algorithm to determine the endomorphism ring of a Drinfeld module, both over its field of definition and over a separable or algebraic closure thereof. Using previous results we deduce an effective description of the image of the ... More

Using the Random Sprays Retinex Algorithm for Global Illumination EstimationOct 01 2013Oct 02 2013In this paper the use of Random Sprays Retinex (RSR) algorithm for global illumination estimation is proposed and its feasibility tested. Like other algorithms based on the Retinex model, RSR also provides local illumination estimation and brightness ... More

A note on simultaneous representation problem for interval and circular-arc graphsNov 09 2018Nov 27 2018In this short note, we show two NP-completeness results regarding the \emph{simultaneous representation problem}, introduced by Lubiw and Jampani. The simultaneous representation problem for a given class of intersection graphs asks if some $k$ graphs ... More

Random holomorphic iterations and degenerate subdomains of the unit diskMar 04 2005Given a random sequence of holomorphic maps $f_1,f_2,f_3,...$ of the unit disk $\Delta$ to a subdomain $X$, we consider the compositions $$F_n=f_1 \circ f_{2} \circ ... f_{n-1} \circ f_n.$$ The sequence $\{F_n\}$ is called the {\em iterated function system} ... More

A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matricesMay 08 2018We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the ergodic constant of a risk-sensitive control problem, or of an entropy ... More

Uniform a priori estimates for positive solutions of the Lane-Emden equation in the planeFeb 02 2018Mar 29 2018We prove that positive solutions of the Lane-Emden equation in a two-dimensional smooth bounded domain are uniformly bounded for all large exponents.

A Bernstein Polynomial Collocation Method for the Solution of Elliptic Boundary Value ProblemsNov 15 2012In this article, a formulation of a point-collocation method in which the unknown function is approximated using global expansion in tensor product Bernstein polynomial basis is presented. Bernstein polynomials used in this study are defined over general ... More

Numerical Approach to Painlevé Transcendents on Unbounded DomainsJul 12 2018A multidomain spectral approach for Painlev\'e transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a, possibly divergent, asymptotic series valid near infinity in a sector and approximates ... More

Tropical Kraus maps for optimal control of switched systemsJun 14 2017Nov 10 2017Kraus maps (completely positive trace preserving maps) arise classically in quantum information, as they describe the evolution of noncommutative probability measures. We introduce tropical analogues of Kraus maps, obtained by replacing the addition of ... More

A Coherent Perceptron for All-Optical LearningJan 07 2015Mar 28 2015We present nonlinear photonic circuit models for constructing programmable linear transformations and use these to realize a coherent Perceptron, i.e., an all-optical linear classifier capable of learning the classification boundary iteratively from training ... More

Eye of the BeholderMay 30 2014We show that the real line R viewed as a vector space is of uncountable (algebraic) dimension over the scalar field Q of rational numbers. We then build an operator J which maps {R, Q} onto {R, Q}, is Q-linear and whose graph is scattered all over the ... More

Calculating principal eigen-functions of non-negative integral kernels: particle approximations and applicationsFeb 29 2012Sep 27 2016Often in applications such as rare events estimation or optimal control it is required that one calculates the principal eigen-function and eigen-value of a non-negative integral kernel. Except in the finite-dimensional case, usually neither the principal ... More

Relative entropy as a measure of inhomogeneity in general relativityAug 31 2010We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike slices. The resulting ... More

A Compact Codimension Two Braneworld with Precisely One BraneApr 11 2010Jun 29 2010Building on earlier work on football shaped extra dimensions, we construct a compact codimension two braneworld with precisely one brane. The two extra dimensions topologically represent a 2-torus which is stabilized by a bulk cosmological constant and ... More

PhD thesis: Homological Quantum Codes Beyond the Toric CodeFeb 05 2018PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and enumerate all ... More

Context Discovery for Model Learning in Partially Observable EnvironmentsAug 02 2016The ability to learn a model is essential for the success of autonomous agents. Unfortunately, learning a model is difficult in partially observable environments, where latent environmental factors influence what the agent observes. In the absence of ... More

Inadequacy of zero-width approximation for a light Higgs boson signalJun 21 2012Aug 02 2012In the Higgs search at the LHC, a light Higgs boson (115 GeV <~ M_H <~ 130 GeV) is not excluded by experimental data. In this mass range, the width of the Standard Model Higgs boson is more than four orders of magnitude smaller than its mass. The zero-width ... More

The rate of convergence of the hyperbolic density on sequences of domainsOct 05 2012It is known that if a sequence of domains $U_n$ converges to a domain $U$ in the Caratheodory sense then the hyperbolic densities on $U_n$ converge to the hyperbolic density on $U$. In this paper, we study the rate of convergence of the hyperbolic density ... More

Some properties of the class $\mathcal{U}$Dec 20 2018Dec 21 2018In this paper we study the class $\mathcal{U}$ of functions that are analytic in the open unit disk ${\mathbb D}=\{z:|z|<1\}$, normalized such that $f(0)=f'(0)-1=0$ and satisfy \[\left|\left [\frac{z}{f(z)} \right]^{2}f'(z)-1 \right|<1\quad\quad (z\in ... More

A class of univalent functions with real coefficientsOct 09 2018Oct 16 2018In this paper we study class $\mathcal{S}^+$ of univalent functions $f$ such that $\frac{z}{f(z)}$ has real and positive coefficients. For such functions we give estimates of the Fekete-Szeg\H{o} functional and sharp estimates of their initial coefficients ... More