1,721,092 research outputs found
SMUTHI: A python package for the simulation of light scattering by multiple particles near or between planar interfaces
Full text linkSMUTHI is a python package for the efficient and accurate simulation of electromagnetic scattering by one or multiple wavelength-scale objects in a planarly layered medium. The software combines the T-matrix method for individual particle scattering with the scattering matrix formalism for the propagation of the electromagnetic field through the planar interfaces. In this article, we briefly introduce the relevant theoretical concepts and present the main features of SMUTHI. Simulation results obtained for several benchmark configurations are validated against commercial software solutions. Owing to the generality of planarly layered geometries and the availability of different particle shapes and light sources, possible applications of SMUTHI include the study of discrete random media, meta-surfaces, photonic crystals and glasses, perforated membranes and plasmonic systems, to name a few relevant examples at visible and near-visible wavelengths
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Analytical Methods For Levy Processes With Applications To Finance
Full text linkThis dissertation is divided into two parts: the first part is a literature review and the second describes three new contributions to the literature. The literature review aims to provide a self-contained introduction to some popular Levy models and to two key objects from the theory of Levy processes: the Wiener-Hopf factors and the exponential functional. We pay special attention to techniques and results associated with two “analytically tractable” families of processes known as the meromorphic and hyper-exponential families. We also demonstrate some important numerical techniques for working with these families and for solving numerical integration and rational approximation problems.
In the second part of the dissertation we prove that the exponential functional of a meromorphic Levy process is distributed like an infinite product of independent Beta random variables. We also identify the Mellin transform of the exponential functional, and then, under the assumption that the log-stock price follows a meromorphic process, we use this to develop a fast and accurate algorithm for pricing continuously monitored, fixed strike Asian call options. Next, we answer an open question about the density of the supremum of an alpha-stable process. We find that the density has a conditionally convergent double series representation when alpha is an irrational number. Lastly, we develop an effective and simple algorithm for approximating any process in the class of completely monotone processes –some members of this class include the popular variance gamma, CGMY, and normal inverse Gaussian processes – by a hyper-exponential process. Under the assumption that the log-stock price follows a variance gamma or CGMY process we use this
approximation to price several exotic options such as Asian and barrier options. Our algorithms are easy to implement and produce accurate prices
On Laplace transforms, generalized gamma convolutions, and their applications in risk aggregation
No full textThis dissertation begins with two introductory chapters to provide some relevant background information: an introduction on the Laplace transform and an introduction on Generalized Gamma Convolutions (GGCs). The heart of this dissertation is the final three chapters comprised of three contributions to the literature.
In Chapter 3, we study the analytical properties of the Laplace transform of the log-normal distribution. Two integral expressions
for the analytic continuation of the Laplace transform of the log-normal distribution are provided, one of which takes the form of a Mellin-Barnes integral. As
a corollary, we obtain an integral expression for the characteristic function; we show that the integral expression derived by Leipnik in \cite{Leipnik1991} is
incorrect. We present two approximations for the Laplace transform of the log-normal distribution, both valid in \C \setminus(-\infty,0].
In the last section, we discuss how one may use our results to compute the density of a sum of independent log-normal random variables.
In Chapter 4, we explore the topic of risk aggregation with moment matching \\approximations. We put forward a refined moment matching approximation (MMA) method for approximating the distributions of the sums of insurance risks. Our method approximates the distributions of interest to any desired precision, works equally well for light and heavy-tailed distributions, and is reasonably fast irrespective of the number of the involved summands.
In Chapter 5, we study the convergence of the Gaver-Stehfest algorithm. The Gaver-Stehfest algorithm is widely used for numerical inversion of Laplace transform. In this chapter we provide the first rigorous study of the rate of convergence of the Gaver-Stehfest algorithm. We prove that the Gaver-Stehfest approximations of order converge exponentially fast if the target function is analytic in a neighbourhood of a point and they converge at a rate if the target function is -times differentiable at a point
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Mode-resolved analysis of pump and Stokes beams in LD-pumped GRIN fiber Raman lasers
Full text linkAll-fiber Raman lasers have demonstrated their potential for efficient conversion of highly multimode pump beams into high-quality Stokes beams. However, the modal content of these beams has not yet been investigated. In this work, based on a mode decomposition technique, we are able to reveal the details of intermodal interactions in the different operation regimes of continuous wave multimode graded-index fiber Raman lasers. We observed that, above the laser threshold, the residual pump beam is strongly depleted in its transverse modes with principal quantum number below 10. However, the generated Stokes signal beam mainly consists of the fundamental mode, but higher-order modes are also present, albeit with exponentially decreasing population
Mechanism of brightness enhancement in multimode LD-pumped graded-index fiber Raman lasers. Numerical modeling
Full text linkWe develop a comprehensive theory for describing the experimental beam profiles from multimode fiber Raman lasers. We take into account the presence of random linear mode
coupling, Kerr beam self-cleaning and intra-cavity spatial filtering. All of these factors play a decisive role in shaping the Stokes beam, which has a predominant fundamental mode content.
Although the highly multimode pump beam is strongly depleted, it remains almost insensitive to the different physical effects. As a result, the intensity of the output Stokes beam is an order of
magnitude higher than the pump intensity at its maximum, in quantitative agreement with the experimental results and in contrast with the simplified balance model
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On Guaranteed Minimum Maturity Benefits and First-to-Default Type Problems
Full text linkA new class of exponential functionals arises when pricing certain equity-linked insurance products.We study the distribution of these exponential functionals using tools from Probability and Complex Analysis. In the case of the Kou process we obtain an explicit formula for the probability density function of the exponential functional and we apply this result to pricing equity-linked insurance products. As a by-product of this research we have also derived a new class of duality relations for hypergeometric functions.
In the second part of the thesis, we study correlation uncertainty in Credit Risk. The goal is to price analogues of first-to-default options under the assumption that the assets follow correlated stochastic processes with known marginal distributions and unknown dependence structure. We solve this problem using tools from Stochastic Analysis and Optimal Control Theory. We provide explicit solutions in some specific examples and numerical approximations in the more general case
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