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Träfflista för sökning "hsv:(NATURVETENSKAP) hsv:(Matematik) hsv:(Sannolikhetsteori och statistik) "

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  • Björnberg, Jakob E., 1983-, et al. (författare)
  • Characterising random partitions by random colouring
  • 2020
  • Ingår i: Electronic Communications in Probability. - 1083-589X. ; 25
  • Tidskriftsartikel (refereegranskat)abstract
    • Let (X-1, X-2, ...) be a random partition of the unit interval [0, 1], i.e. X-i >= 0 and Sigma(i >= 1) X-i = 1, and let (epsilon(1), epsilon(2), ...) be i.i.d. Bernoulli random variables of parameter p is an element of (0, 1). The Bernoulli convolution of the partition is the random variable Z = Sigma(i >= 1) epsilon X-i(i). The question addressed in this article is: Knowing the distribution of Z for some fixed p is an element of (0, 1), what can we infer about the random partition (X-1, X-2, ...)? We consider random partitions formed by residual allocation and prove that their distributions are fully characterised by their Bernoulli convolution if and only if the parameter p is not equal to 1/2.
  • Lundengård, Karl, 1987- (författare)
  • Generalized Vandermonde matrices and determinants in electromagnetic compatibility
  • 2017
  • Licentiatavhandling (övrigt vetenskapligt)abstract
    • <p>Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.</p><p>In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.</p><p>The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.</p><p>The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.</p>
  • Balkanova, Olga, et al. (författare)
  • Prime geodesic theorem in the 3-dimensional hyperbolic space
  • 2019
  • Ingår i: Transactions of the American Mathematical Society. - 0002-9947 .- 1088-6850. ; 372:8, s. 5355-5374
  • Tidskriftsartikel (refereegranskat)abstract
    • For Γ a cofinite Kleinian group acting on H3, we study the prime geodesic theorem on M = Γ\H3, which asks about the asymptotic behavior of lengths of primitive closed geodesics (prime geodesics) on M. Let EΓ(X) be the error in the counting of prime geodesics with length at most log X. For the Picard manifold, Γ = PSL(2, Z[i]), we improve the classical bound of Sarnak, EΓ(X) = O(X5/3+e), to EΓ(X) = O(X13/8+e). In the process we obtain a mean subconvexity estimate for the Rankin-Selberg L-function attached to Maass-Hecke cusp forms. We also investigate the second moment of EΓ(X) for a general cofinite group Γ, and we show that it is bounded by O(X16/5+e).
  • Nyagahakwa, Venuste, et al. (författare)
  • Sets with the Baire property in topologies formed from a given topology and ideals of sets
  • 2017
  • Ingår i: Questions and answers in General Topology. - Osaka : Symposium of General Topology / Iso Shinpojumu. - 0918-4732. ; 35:1, s. 59-76
  • Tidskriftsartikel (refereegranskat)abstract
    • <p>Let X be a set, τ1, τ2 topologies on X and Bp(X, τi) the family of all subsets of X possessing the Baire property in (X, τi), i = 1, 2. In this paper we study conditions on τ1 and τ2 that imply a relationship (for example, inclusion or equality) between the families Bp(X, τ1) and Bp(X, τ2). We are mostly interested in the case where the topology τ2 is formed with the help of a local function defined by the topology τ1 and an ideal of sets I on X. We also consider several applications of the local function defined by the usual topology on the reals and the ideal of all meager sets there, for proving some known facts.</p>
  • Gerlee, Philip, 1980-, et al. (författare)
  • Scientific Models Red Atoms, White Lies and Black Boxes in a Yellow Book
  • 2016
  • Bok (övrigt vetenskapligt)abstract
    • A zebrafish, the hull of a miniature ship, a mathematical equation and a food chain - what do these things have in common? They are examples of models used by scientists to isolate and study particular aspects of the world around us. This book begins by introducing the concept of a scientific model from an intuitive perspective, drawing parallels to mental models and artistic representations. It then recounts the history of modelling from the 16th century up until the present day. The iterative process of model building is described and discussed in the context of complex models with high predictive accuracy versus simpler models that provide more of a conceptual understanding. To illustrate the diversity of opinions within the scientific community, we also present the results of an interview study, in which ten scientists from different disciplines describe their views on modelling and how models feature in their work. Lastly, it includes a number of worked examples that span different modelling approaches and techniques. It provides a comprehensive introduction to scientific models and shows how models are constructed and used in modern science. It also addresses the approach to, and the culture surrounding modelling in different scientific disciplines. It serves as an inspiration for model building and also facilitates interdisciplinary collaborations by showing how models are used in different scientific fields.The book is aimed primarily at students in the sciences and engineering, as well as students at teacher training colleges but will also appeal to interested readers wanting to get an overview of scientific modelling in general and different modelling approaches in particular.
  • Albin, Patrik, 1960- (författare)
  • 2018
  • Ingår i: Esaim-Probability and Statistics. - 1292-8100. ; 22, s. 1-18
  • Tidskriftsartikel (refereegranskat)abstract
    • We study extreme value theory of right stationary Gaussian processes with parameters in open subsets with compact closure of (not necessarily Abelian) locally compact topological groups. Even when specialized to Euclidian space our result extend results on extremes of stationary Gaussian processes and fields in the literature by means of requiring weaker technical conditions as well as by means of the fact that group stationary processes need not be stationary in the usual sense (that is, with respect to addition as group operation).
  • Beilina, Larisa, 1970-, et al. (författare)
  • Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations
  • 2018
  • Ingår i: Inverse Problems. - 0266-5611. ; 34:1
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the recon struction of two unknown coefficients using noisy backscattered data.
  • Björnberg, Jakob E., 1983-, et al. (författare)
  • The interchange process with reversals on the complete graph
  • 2019
  • Ingår i: Electronic Journal of Probability. - 1083-6489. ; 24
  • Tidskriftsartikel (refereegranskat)abstract
    • © 2019, Institute of Mathematical Statistics. All rights reserved. We consider an extension of the interchange process on the complete graph, in which a fraction of the transpositions are replaced by ‘reversals’. The model is motivated by statistical physics, where it plays a role in stochastic representations of xxz-models. We prove convergence to PD(1) of the rescaled cycle sizes, above the critical point 2 for the appearance of macroscopic cycles. This extends a result of Schramm on convergence to PD(1) for the usual interchange process.
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