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Mathematical statistics --- Distribution (Probability theory) --- Random variables
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Gegenstand des Buches ist die Lösung einer Reihe von überraschenden mathematischen Aussagen, die leicht zu formulieren sind, die man kaum glaubt (weil sie paradox erscheinen), aber dennoch beweisen kann. Dabei werden elementare Methoden der Kombinatorik, Wahrscheinlichkeitsrechnung, Statistik, Geometrie und Analysis angewendet werden. Das Ziel des Buches besteht darin, dem mathematisch interessierten Leser eine Reihe von kontraintuitiven Aussagen vorzuführen und eingehend zu analysieren. Diese Paradoxa kommen aus verschiedenen Bereichen der Mathematik, wobei jedoch Wahrscheinlichkeitsrechnung und Statistik überwiegen. Behandelt werden u.a. das Geburtstagsparadoxon, Conways Chequerboard-Armee, Torricellis Trompete, nichttransitive Effekte, Verfolgungsprobleme, Parrondo-Spiele, Freitag, der 13., und Fractran. Der Autor baut in jedem Kapitel rund um das jeweilige Paradoxon einen Spannungsbogen auf, der sich im Laufe des Kapitels auf überraschende Weise löst. Zahlreiche Abbildungen und Tabellen illustrieren die Problemstellungen und die wesentlichen Lösungsschritte. Das Buch ist so angelegt, dass es für mathematisch Interessierte mit Oberstufenkenntnissen zugänglich ist.
Combinatorial analysis. --- Distribution (Probability theory) --- Mathematics --- History.
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Mathematical statistics --- Robust statistics. --- kwantitatieve methoden --- regressie-analyse --- lineaire programmering --- Robust statistics --- Statistics, Robust --- Distribution (Probability theory)
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Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern applications. This book presents a coherent and unified treatment of probabilistic techniques for obtaining high probability estimates on the performance of randomized algorithms. It covers the basic toolkit from the Chernoff-Hoeffding bounds to more sophisticated techniques like martingales and isoperimetric inequalities, as well as some recent developments like Talagrand's inequality, transportation cost inequalities and log-Sobolev inequalities. Along the way, variations on the basic theme are examined, such as Chernoff-Hoeffding bounds in dependent settings. The authors emphasise comparative study of the different methods, highlighting respective strengths and weaknesses in concrete example applications. The exposition is tailored to discrete settings sufficient for the analysis of algorithms, avoiding unnecessary measure-theoretic details, thus making the book accessible to computer scientists as well as probabilists and discrete mathematicians.
Random variables. --- Distribution (Probability theory) --- Limit theorems (Probability theory) --- Algorithms. --- Algorism --- Algebra --- Arithmetic --- Probabilities --- Distribution functions --- Frequency distribution --- Characteristic functions --- Chance variables --- Stochastic variables --- Variables (Mathematics) --- Foundations
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Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schrödinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory.
Physics. --- Philosophy of Science. --- Functional Analysis. --- Probability Theory and Stochastic Processes. --- Statistical Physics. --- Mathematical Methods in Physics. --- Quantum Physics. --- Science --- Functional analysis. --- Distribution (Probability theory). --- Quantum theory. --- Mathematical physics. --- Statistical physics. --- Physique --- Sciences --- Analyse fonctionnelle --- Distribution (Théorie des probabilités) --- Théorie quantique --- Physique mathématique --- Physique statistique --- Philosophy. --- Philosophie --- Distribution (Probability theory) --- Quantum theory --- Mathematics.
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This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of one science into another. It updates an earlier successful edition and greatly expands the concept of the "computer biology laboratory," giving students a general perspective of the field before proceeding to more specialized topics. The book focuses on problems of contemporary interest, such as cancer, genetics, and the rapidly growing field of genomics. It includes new chapters on parasites, cancer, and phylogenetics, along with an introduction to online resources for DNA, protein lookups, and popular pattern matching tools such as BLAST. In addition, the emerging field of algebraic statistics is introduced and its power illustrated in the context of phylogenetics. A unique feature of the book is the integration of a computer algebra system into the flow of ideas in a supporting but unobtrusive role. Syntax for both the Maple and Matlab systems is provided in a tandem format. The use of a computer algebra system gives the students the opportunity to examine "what if" scenarios, allowing them to investigate biological systems in a way never before possible. For students without access to Maple or Matlab, each topic presented is complete. Graphic visualizations are provided for all mathematical results. Mathematical Biology includes extensive exercises, problems and examples. A year of calculus with linear algebra is required to understand the material presented. The biology presented proceeds from the study of populations down to the molecular level; no previous coursework in biology is necessary. The book is appropriate for undergraduate and graduate students studying mathematics or biology and for scientists and researchers who wish to study the applications of mathematics and computers in the natural sciences.
Biomathematics. Biometry. Biostatistics --- Mathematics. --- Mathematical Biology in General. --- Computer Appl. in Life Sciences. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Computer Applications. --- Computer science. --- Biology --- Distribution (Probability theory). --- Mathématiques --- Informatique --- Biologie --- Distribution (Théorie des probabilités) --- Data processing.
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Mathematical statistics --- #SBIB:303H520 --- Methoden sociale wetenschappen: techniek van de analyse, algemeen --- Statistical hypothesis testing --- Statistical power analysis --- Power analysis (Statistics) --- Hypothesis testing (Statistics) --- Significance testing (Statistics) --- Statistical significance testing --- Testing statistical hypotheses --- Distribution (Probability theory) --- Hypothesis
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Ce cours, qui s'adresse aux étudiants des universités et des grandes écoles, donne les éléments de la théorie des probabilités utiles à la compréhension des modèles probabilistes de leurs spécialités respectives, ainsi que la pratique du calcul des probabilités nécessaire à l'exploitation de ces modèles. Cette initiation aux probabilités comporte trois degrés: le calcul des probabilités, la théorie des probabilités, les chaînes de Markov. La première partie du cours introduit les notions essentielles: événements, probabilité, variable aléatoire, probabilité conditionnelle, indépendance. L'accent est mis sur les outils de base (fonction génératrice, fonction caractéristique) et le calcul des probabilités (règles de Bayes, changement de variable, calcul sur les matrices de covariance et les vecteurs gaussiens). Un court chapitre est consacré à la notion d'entropie et à sa signification en théorie des communications et en physique statistique. Le seul prérequis pour cette première étape est une connaissance pratique des séries, de l'intégrale de Riemann et de l'algèbre matricielle. La deuxième partie concerne la théorie des probabilités proprement dite. Elle débute par un résumé motivé des résultats de la théorie de l'intégration de Lebesgue, qui fournit le cadre mathématique de la théorie axiomatique des probabilités et précise les points techniques laissés provisoirement dans l'ombre dans la première partie. Puis vient un chapitre où sont étudiées les différentes notions de convergence, et dans lequel sont présentés les deux sommets de la théorie, la loi forte des grands nombres et le théorème de la limite gaussienne. Le chapitre final, qui constitue à lui seul la troisième étape de l'initiation, traite des chaînes de Markov, la plus importante classe de processus stochastiques pour les applications. En fin de chaque chapitre se trouve une section d'exercices, la plupart corrigés, sauf ceux marqués d'un astérisque.
statistisch onderzoek --- stochastische analyse --- kansrekening --- Statistical science --- Operational research. Game theory --- Probabilities --- Markov processes --- Probabilités --- Markov, Processus de --- Problems, exercises, etc --- Problèmes et exercices --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Mathematics --- Distribution (Probability theory) --- Mathematical statistics
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The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein-Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados. The second main objective is to provide a study of the approximation and geometric proper
Approximation theory. --- Operator theory. --- Bernstein polynomials. --- Convolutions (Mathematics) --- Convolution transforms --- Transformations, Convolution --- Distribution (Probability theory) --- Functions --- Integrals --- Transformations (Mathematics) --- Polynomials, Bernstein --- Convergence --- Probabilities --- Series --- Functional analysis --- Theory of approximation --- Polynomials --- Chebyshev systems
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