13,875 research outputs found
Universal Electromagnetic Waves in Dielectric
The dielectric susceptibility of a wide class of dielectric materials
follows, over extended frequency ranges, a fractional power-law frequency
dependence that is called the "universal" response. The electromagnetic fields
in such dielectric media are described by fractional differential equations
with time derivatives of non-integer order. An exact solution of the fractional
equations for a magnetic field is derived. The electromagnetic fields in the
dielectric materials demonstrate fractional damping. The typical features of
"universal" electromagnetic waves in dielectric are common to a wide class of
materials, regardless of the type of physical structure, chemical composition,
or of the nature of the polarizing species, whether dipoles, electrons or ions.Comment: 19 pages, LaTe
Analytic urns
This article describes a purely analytic approach to urn models of the
generalized or extended P\'olya-Eggenberger type, in the case of two types of
balls and constant ``balance,'' that is, constant row sum. The treatment starts
from a quasilinear first-order partial differential equation associated with a
combinatorial renormalization of the model and bases itself on elementary
conformal mapping arguments coupled with singularity analysis techniques.
Probabilistic consequences in the case of ``subtractive'' urns are new
representations for the probability distribution of the urn's composition at
any time n, structural information on the shape of moments of all orders,
estimates of the speed of convergence to the Gaussian limit and an explicit
determination of the associated large deviation function. In the general case,
analytic solutions involve Abelian integrals over the Fermat curve x^h+y^h=1.
Several urn models, including a classical one associated with balanced trees
(2-3 trees and fringe-balanced search trees) and related to a previous study of
Panholzer and Prodinger, as well as all urns of balance 1 or 2 and a sporadic
urn of balance 3, are shown to admit of explicit representations in terms of
Weierstra\ss elliptic functions: these elliptic models appear precisely to
correspond to regular tessellations of the Euclidean plane.Comment: Published at http://dx.doi.org/10.1214/009117905000000026 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Distinguishing noise from chaos: objective versus subjective criteria using Horizontal Visibility Graph
A recently proposed methodology called the Horizontal Visibility Graph (HVG)
[Luque {\it et al.}, Phys. Rev. E., 80, 046103 (2009)] that constitutes a
geometrical simplification of the well known Visibility Graph algorithm [Lacasa
{\it et al.\/}, Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to
study the distinction between deterministic and stochastic components in time
series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)].
Specifically, the authors propose that the node degree distribution of these
processes follows an exponential functional of the form , in which is the node degree and is a
positive parameter able to distinguish between deterministic (chaotic) and
stochastic (uncorrelated and correlated) dynamics. In this work, we investigate
the characteristics of the node degree distributions constructed by using HVG,
for time series corresponding to chaotic maps and different stochastic
processes. We thoroughly study the methodology proposed by Lacasa and Toral
finding several cases for which their hypothesis is not valid. We propose a
methodology that uses the HVG together with Information Theory quantifiers. An
extensive and careful analysis of the node degree distributions obtained by
applying HVG allow us to conclude that the Fisher-Shannon information plane is
a remarkable tool able to graphically represent the different nature,
deterministic or stochastic, of the systems under study.Comment: Submitted to PLOS On
Fractional Hida Malliavin Derivatives and Series Representations of Fractional Conditional Expectations
We represent fractional conditional expectations of a functional of
fractional Brownian motion as a convergent series in L^2 space. When the target
random variable is some function of a discrete trajectory of fractional
Brownian motion, we obtain a backward Taylor series representation; when the
target functional is generated by a continuous fractional filtration, the
series representation is obtained by applying a "frozen path" operator and an
exponential operator to the functional. Three examples are provided to show
that our representation gives useful series expansions of ordinary expectations
of target random variables
Conditioning bounds for traveltime tomography in layered media
This paper revisits the problem of recovering a smooth, isotropic, layered
wave speed profile from surface traveltime information. While it is classic
knowledge that the diving (refracted) rays classically determine the wave speed
in a weakly well-posed fashion via the Abel transform, we show in this paper
that traveltimes of reflected rays do not contain enough information to recover
the medium in a well-posed manner, regardless of the discretization. The
counterpart of the Abel transform in the case of reflected rays is a Fredholm
kernel of the first kind which is shown to have singular values that decay at
least root-exponentially. Kinematically equivalent media are characterized in
terms of a sequence of matching moments. This severe conditioning issue comes
on top of the well-known rearrangement ambiguity due to low velocity zones.
Numerical experiments in an ideal scenario show that a waveform-based model
inversion code fits data accurately while converging to the wrong wave speed
profile
Calculation of solvency capital requirements for non-life underwriting risk using generalized linear models
The paper presents various GLM models using individual rating factors to calculate the solvency capital requirements for non-life underwriting risk in insurance. First, we consider the potential heterogeneity of claim frequency and the occurrence of large claims in the models. Second, we analyse how the distribution of frequency and severity varies depending on the modelling approach and examine how they are projected into SCR estimates according to the Solvency II Directive. In addition, we show that neglecting of large claims is as consequential as neglecting the heterogeneity of claim frequency. The claim frequency and severity are managed using generalized linear models, that is, negative-binomial and gamma regression. However, the different individual probabilities of large claims are represented by the binomial model and the large claim severity is managed using generalized Pareto distribution. The results are obtained and compared using the simulation of frequency-severity of an actual insurance portfolio.Web of Science26446645
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