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Saddlepoint Approximation for Calculating Performance of Spectrum-Sliced WDM SystemsTeotia, Seemant 06 August 1999 (has links)
Spectrum slicing is a novel technique for the implementation of wavelength-division multiplexing (WDM). While conventional WDM systems employ laser diodes operating at discrete wavelengths as carriers for the different data channels that are to be multiplexed, spectrum-sliced systems make use of spectral slices of a broadband noise source for the different data channels, thus being economically attractive.
In spectrum-sliced WDM systems with an optical preamplifier receiver there is an optimum m=BoT (Bo = optical channel bandwidth, T = bit duration) to minimize the average number of photons-per-bit (Np) required at the receiver for a given error probability (Pe). Both the optimum m and the minimum increase as interchannel interference increases. This has been analyzed previously by using the Gaussian approximation, or by assuming that the signals at the decision point are chi-square distributed. Although the chi-square distribution is valid in the case where there is no interference, it is not valid in the presence of interference, since the interference from the neighboring channel has a smaller bandwidth than the signal. In this thesis, a different method is used to analyze this problem. This method is called the Saddlepoint Approximation, and while the exact analysis required determination of the probability density function (pdf) of the received signal, the saddlepoint method makes use of moment generating functions (MGFs) which have a much simpler form and don't require the convolution operations the pdfs require.
The saddlepoint method is validated by comparing results obtained with the chi-square analysis for the no interchannel interference case when a rectangular shaped filter is used. The effect of non-rectangular spectra on receiver sensitivity with the use of the Saddlepoint Approximation is also investigated. After verifying its validity, the method is applied to the interchannel interference case caused by filter overlap. It is shown that for small filter overlap, use of an equivalent chi-square distribution is valid, but when the overlap becomes larger, the performance approaches that calculated using the Gaussian distribution. It is shown that there is an optimum filter overlap to maximize the total system throughput when total bandwidth is constrained. Operating at this optimum, the total system throughput is 135 Gbits/s when the total system bandwidth is 4.4 THz (35 nm) for a Bit Error Rate (BER) of 10e-9. / Master of Science
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Relativistic distorted wave analysis of neutrino-induced strange particle production on nucleiAdera, Gashaw Bekele 12 1900 (has links)
Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: See fulltext for abstract. / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming.
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Best Approximations, Lethargy Theorems and SmoothnessCase, Caleb 01 January 2016 (has links)
In this paper we consider sequences of best approximation. We first examine the rho best approximation function and its applications, through an example in approximation theory and two new examples in calculating n-widths. We then further discuss approximation theory by examining a modern proof of Weierstrass's Theorem using Dirac sequences, and providing a new proof of Chebyshev's Equioscillation Theorem, inspired by the de La Vallee Poussin Theorem. Finally, we examine the limits of approximation theorem by looking at Bernstein Lethargy theorem, and a modern generalization to infinite-dimensional subspaces. We all note that smooth functions are bounded by Jackson's Inequalities, but see a newer proof that a single non-differentiable point can make functions again susceptible to lethargic rates of convergence.
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Approximation Algorithms for Rectangle Piercing ProblemsMahmood, Abdullah-Al January 2005 (has links)
Piercing problems arise often in facility location, which is a well-studied area of computational geometry. The general form of the piercing problem discussed in this dissertation asks for the minimum number of facilities for a set of given rectangular demand regions such that each region has at least one facility located within it. It has been shown that even if all regions are uniform sized squares, the problem is NP-hard. Therefore we concentrate on approximation algorithms for the problem. As the known approximation ratio for arbitrarily sized rectangles is poor, we restrict our effort to designing approximation algorithms for unit-height rectangles. Our e-approximation scheme requires <I>n</I><sup><I>O</I>(1/ε??)</sup> time. We also consider the problem with restrictions like bounding the depth of a point and the width of the rectangles. The approximation schemes for these two cases take <I>n</I><sup><I>O</I>(1/ε)</sup> time. We also show how to maintain a factor 2 approximation of the piercing set in <I>O</I>(log <I>n</I>) amortized time in an insertion-only scenario.
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Improved Approximation Algorithms for Geometric Packing Problems With Experimental EvaluationSong, Yongqiang 12 1900 (has links)
Geometric packing problems are NP-complete problems that arise in VLSI design. In this thesis, we present two novel algorithms using dynamic programming to compute exactly the maximum number of k x k squares of unit size that can be packed without overlap into a given n x m grid. The first algorithm was implemented and ran successfully on problems of large input up to 1,000,000 nodes for different values. A heuristic based on the second algorithm is implemented. This heuristic is fast in practice, but may not always be giving optimal times in theory. However, over a wide range of random data this version of the algorithm is giving very good solutions very fast and runs on problems of up to 100,000,000 nodes in a grid and different ranges for the variables. It is also shown that this version of algorithm is clearly superior to the first algorithm and has shown to be very efficient in practice.
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Approximation uniforme par fonctions aléatoiresManka, Sébastien January 2003 (has links)
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
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Caractérisation optique et géométrique des agrégats submicroniques multi-échelles de particules sphériques très diffusantes / Optical and geometrical characterization of submicron milti-scale aggregates of spherical particles quite scatteringLagarrigue, Marthe 18 April 2011 (has links)
Les agrégats multi-échelles (sulfure de zinc: ZnS, ...) ont des propriétés physiques et physicochimiques présentant un grand intérêt industriel (industrie pharmaceutique, matériau, environnement...). L'objectif général de cette thèse est de caractériser ces agrégats multi-échelles par une méthode optique d'une part, et par une étude géométrique d'autre part. Le but est de trouver des relations simples entre propriétés optiques et géométriques. Les résultats présentés sont valables pour tout matériau à haut indice de réfraction.Ce travail comporte une première étape de modélisation en étudiant tout d'abord des modèles simples d'agrégats multi-échelles (agencement ordonné de particules élémentaires sphériques). Différents agrégats sont alors géométriquement modélisés suivant des paramètres de construction prédéfinis (volume global des agrégats, rayon des particules primaires...). Une analyse préliminaire optique puis une analyse géométrique sont alors effectuées afin de déterminer les paramètres respectifs à étudier: la section efficace moyenne de diffusion (...), calculée au moyen d'une extension de la théorie de Mie (GMM pour Generalized Multiparticle Mie) d'Y-L Xu, et des caractéristiques géométriques spécifiques (volume de matière, compacité...).Une seconde étape consiste à étudier les variations de la valeur de ... en fonction de celles des paramètres géométriques des agrégats. Des relations caractérisant ces variations sont établies. Enfin, une expression approchées pour la valeur de ... est recherchée sous la forme d'une loi de puissance, reposant sur des méthodes optiques approchées existantes et sur la sélection de caractéristiques géométriques pertinentes. Le modèle mis en place est robuste et présente un compromis entre précision et complexité. Le travail réalisé ouvre diverses perspectives comme la confrontation du modèle mathématique théorique obtenu, avec l'expérience. / Multiscale aggregates (zinc sulfide: ZnS, ...) havephysical and physicochemical properties of great industrial interest (e.g. pharmaceutical industriy, material, environment). The overall objective of this thesis is to characterize these multiscale aggregates by an optical method on the one hand, and a geometric study of the other. The goal is to find simple relations between optical and geometrical properties. The results presented are valid for any material with high refractive index.The first step of this work is to build in a simple way the multiscale aggregate (like ordered arrangement of spherical elementary particles). Different aggregates are then geometrically modeled thanks to predefined design parameters (e.g. particles radius, aggregates overall volume). A preleminary analysis of optical and geometrical analysis is then performed to determine the relevant parameters: the average scattering cross section (...), calculed using a generalization of the Mie theory (GMM for Generalized Multiparticle Mie) developped by Y.L. Xu, and specific geometric values features. An analysis of the behavior of the optical parameter and the geometrical characteristic (e.g. compactness, volume of matter...), with respect to the construction parameters of the aggregates, is then performed.A second step is to study variations of ... value versus the variation of the geometrical parameter of aggregates. Mathematical relations characterizing these variations are established. Finally, a study on the approximation of the ... value is carried out. A power law is proposed which is basedon previous optical approximate methods and on the selection of geometrical characteristics of the aggregates. The optical properties and geometrical characteristics of the clusters are fairly extensive and contrasted to give a general groundwork to this study. The work done opens various perspectives such as the confrontation of the theorical mathematical model obtained, with experiment.
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Reduced Ideals and Periodic Sequences in Pure Cubic FieldsJacobs, G. Tony 08 1900 (has links)
The “infrastructure” of quadratic fields is a body of theory developed by Dan Shanks, Richard Mollin and others, in which they relate “reduced ideals” in the rings and sub-rings of integers in quadratic fields with periodicity in continued fraction expansions of quadratic numbers. In this thesis, we develop cubic analogs for several infrastructure theorems. We work in the field K=Q(), where 3=m for some square-free integer m, not congruent to ±1, modulo 9. First, we generalize the definition of a reduced ideal so that it applies to K, or to any number field. Then we show that K has only finitely many reduced ideals, and provide an algorithm for listing them. Next, we define a sequence based on the number alpha that is periodic and corresponds to the finite set of reduced principal ideals in K. Using this rudimentary infrastructure, we are able to establish results about fundamental units and reduced ideals for some classes of pure cubic fields. We also introduce an application to Diophantine approximation, in which we present a 2-dimensional analog of the Lagrange value of a badly approximable number, and calculate some examples.
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Wiener's Approximation Theorem for Locally Compact Abelian GroupsShu, Ven-shion 08 1900 (has links)
This study of classical and modern harmonic analysis extends the classical Wiener's approximation theorem to locally compact abelian groups. The first chapter deals with harmonic analysis on the n-dimensional Euclidean space. Included in this chapter are some properties of functions in L1(Rn) and T1(Rn), the Wiener-Levy theorem, and Wiener's approximation theorem. The second chapter introduces the notion of standard function algebra, cospectrum, and Wiener algebra. An abstract form of Wiener's approximation theorem and its generalization is obtained. The third chapter introduces the dual group of a locally compact abelian group, defines the Fourier transform of functions in L1(G), and establishes several properties of functions in L1(G) and T1(G). Wiener's approximation theorem and its generalization for L1(G) is established.
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Probabilistic matching systems : stability, fluid and diffusion approximations and optimal controlChen, Hanyi January 2015 (has links)
In this work we introduce a novel queueing model with two classes of users in which, instead of accessing a resource, users wait in the system to match with a candidate from the other class. The users are selective and the matchings occur probabilistically. This new model is useful for analysing the traffic in web portals that match people who provide a service with people who demand the same service, e.g. employment portals, matrimonial and dating sites and rental portals. We first provide a Markov chain model for these systems and derive the probability distribution of the number of matches up to some finite time given the number of arrivals. We then prove that if no control mechanism is employed these systems are unstable for any set of parameters. We suggest four different classes of control policies to assure stability and conduct analysis on performance measures under the control policies. Contrary to the intuition that the rejection rate should decrease as the users become more likely to be matched, we show that for certain control policies the rejection rate is insensitive to the matching probability. Even more surprisingly, we show that for reasonable policies the rejection rate may be an increasing function of the matching probability. We also prove insensitivity results related to the average queue lengths and waiting times. Further, to gain more insight into the behaviour of probabilistic matching systems, we propose approximation methods based on fluid and diffusion limits using different scalings. We analyse the basic properties of these approximations and show that some performance measures are insensitive to the matching probability agreeing with the results found by the exact analysis. Finally we study the optimal control and revenue management for the systems with the objective of profit maximization. We formulate mathematical models for both unobservable and observable systems. For an unobservable system we suggest a deterministic optimal control, while for an observable system we develop an optimal myopic state dependent pricing.
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