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Lectures on Random Voronoi Tessellations

Author : Jesper Moller
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461226529

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Book Lectures on Random Voronoi Tessellations Description/Summary:

Tessellations are subdivisions of d-dimensional space into non-overlapping "cells". Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process. They provide models for many natural phenomena as diverse as the growth of crystals, the territories of animals, the development of regional market areas, and in subjects such as computational geometry and astrophysics. This volume provides an introduction to random Voronoi tessellations by presenting a survey of the main known results and the directions in which research is proceeding. Throughout the volume, mathematical and rigorous proofs are given making this essentially a self-contained account in which no background knowledge of the subject is assumed.

Recent Advances in Applied Probability

Author : Ricardo Baeza-Yates,Joseph Glaz,Henryk Gzyl,Jürg Hüsler,José Luis Palacios
Publisher : Springer Science & Business Media
Release : 2006-02-28
Category : Mathematics
ISBN : 9780387233949

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Book Recent Advances in Applied Probability Description/Summary:

Applied probability is a broad research area that is of interest to scientists in diverse disciplines in science and technology, including: anthropology, biology, communication theory, economics, epidemiology, finance, geography, linguistics, medicine, meteorology, operations research, psychology, quality control, sociology, and statistics. Recent Advances in Applied Probability is a collection of survey articles that bring together the work of leading researchers in applied probability to present current research advances in this important area. This volume will be of interest to graduate students and researchers whose research is closely connected to probability modelling and their applications. It is suitable for one semester graduate level research seminar in applied probability.

Handbook of Discrete and Computational Geometry

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Release : 2017-11-22
Category : Computers
ISBN : 9781498711425

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Book Handbook of Discrete and Computational Geometry Description/Summary:

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Stochastic Geometry, Spatial Statistics and Random Fields

Author : Evgeny Spodarev
Publisher : Springer
Release : 2013-02-11
Category : Mathematics
ISBN : 9783642333057

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Book Stochastic Geometry, Spatial Statistics and Random Fields Description/Summary:

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

An Introduction to Geometrical Probability

Author : A.M. Mathai
Publisher : CRC Press
Release : 1999-12-01
Category : Mathematics
ISBN : 9056996819

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Book An Introduction to Geometrical Probability Description/Summary:

A useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research.

Mathematical Constants II

Author : Steven R. Finch
Publisher : Cambridge University Press
Release : 2018-12-06
Category : Mathematics
ISBN : 9781108604031

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Book Mathematical Constants II Description/Summary:

Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson–Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl–Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton–Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Stochastic Geometry

Author : Wilfrid S. Kendall
Publisher : Routledge
Release : 2019-06-10
Category : Mathematics
ISBN : 9781351413725

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Book Stochastic Geometry Description/Summary:

Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themes o considerations of geometric sampling bias issues o tesselations o shape o random sets o image analysis o spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo

Probabilistic Methods in Telecommunications

Author : Benedikt Jahnel,Wolfgang König
Publisher : Springer Nature
Release : 2020-06-17
Category : Mathematics
ISBN : 9783030360900

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Book Probabilistic Methods in Telecommunications Description/Summary:

Probabilistic modeling and analysis of spatial telecommunication systems have never been more important than they are today. In particular, it is an essential research area for designing and developing next-generation communication networks that are based on multihop message transmission technology. These lecture notes provide valuable insights into the underlying mathematical discipline, stochastic geometry, introducing the theory, mathematical models and basic concepts. They also discuss the latest applications of the theory to telecommunication systems. The text covers several of the most fundamental aspects of quality of service: connectivity, coverage, interference, random environments, and propagation of malware. It especially highlights two important limiting scenarios of large spatial systems: the high-density limit and the ergodic limit. The book also features an analysis of extreme events and their probabilities based on the theory of large deviations. Lastly, it includes a large number of exercises offering ample opportunities for independent self-study.

Burgers-KPZ Turbulence

Author : Wojbor A. Woyczynski
Publisher : Springer
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540494805

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Book Burgers-KPZ Turbulence Description/Summary:

These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.

Stochastic Geometry

Author : W. Weil,A. Baddeley,I. Bárány,R. Schneider
Publisher : Springer
Release : 2006-10-26
Category : Mathematics
ISBN : 9783540381754

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Book Stochastic Geometry Description/Summary:

Stochastic Geometry is the mathematical discipline which studies mathematical models for random geometric structures. This book collects lectures presented at the CIME summer school in Martina Franca in September 2004. The main lecturers covered Spatial Statistics, Random Points, Integral Geometry and Random Sets. These are complemented by two additional contributions on Random Mosaics and Crystallization Processes. The book presents a comprehensive and up-to-date description of important aspects of Stochastic Geometry.

Stochastic Geometry and Its Applications

Author : Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke
Publisher : John Wiley & Sons
Release : 2013-06-27
Category : Mathematics
ISBN : 9781118658253

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Book Stochastic Geometry and Its Applications Description/Summary:

An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. This edition: Presents a wealth of models for spatial patterns and related statistical methods. Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas. Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments. Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes 700 new references. Is written in an accessible style enabling non-mathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.

Stochastic Geometry and Wireless Networks

Author : François Baccelli,Bartlomiej Blaszczyszyn
Publisher : Now Publishers Inc
Release : 2010
Category : Technology & Engineering
ISBN : 9781601982643

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Book Stochastic Geometry and Wireless Networks Description/Summary:

This volume bears on wireless network modeling and performance analysis. The aim is to show how stochastic geometry can be used in a more or less systematic way to analyze the phenomena that arise in this context. It first focuses on medium access control mechanisms used in ad hoc networks and in cellular networks. It then discusses the use of stochastic geometry for the quantitative analysis of routing algorithms in mobile ad hoc networks. The appendix also contains a concise summary of wireless communication principles and of the network architectures considered in the two volumes.

Random and Quasi-Random Point Sets

Author : Peter Hellekalek,Gerhard Larcher,P. Diggle,P. Hickernell,S. Fienberg,K. Krickeberg,I. Olkin,N. Wermuth,S. Zeger
Publisher : Springer Science & Business Media
Release : 1998-10-09
Category : Mathematics
ISBN : 0387985549

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Book Random and Quasi-Random Point Sets Description/Summary:

These topics are of theoretical and applied interest in mathematics and statistics. There are applications to mathematical finance, cryptology, and applied statistics. This research-level monograph surveys the theoretical and applied aspects.

Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

Author : Eva B. Vedel Jensen,Markus Kiderlen
Publisher : Springer
Release : 2017-06-10
Category : Mathematics
ISBN : 9783319519517

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Book Tensor Valuations and Their Applications in Stochastic Geometry and Imaging Description/Summary:

The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.

Algorithms and Architectures

Author : Cornelius T. Leondes
Publisher : Elsevier
Release : 1998-02-09
Category : Computers
ISBN : 9780080498980

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Book Algorithms and Architectures Description/Summary:

This volume is the first diverse and comprehensive treatment of algorithms and architectures for the realization of neural network systems. It presents techniques and diverse methods in numerous areas of this broad subject. The book covers major neural network systems structures for achieving effective systems, and illustrates them with examples. This volume includes Radial Basis Function networks, the Expand-and-Truncate Learning algorithm for the synthesis of Three-Layer Threshold Networks, weight initialization, fast and efficient variants of Hamming and Hopfield neural networks, discrete time synchronous multilevel neural systems with reduced VLSI demands, probabilistic design techniques, time-based techniques, techniques for reducing physical realization requirements, and applications to finite constraint problems. A unique and comprehensive reference for a broad array of algorithms and architectures, this book will be of use to practitioners, researchers, and students in industrial, manufacturing, electrical, and mechanical engineering, as well as in computer science and engineering. Radial Basis Function networks The Expand-and-Truncate Learning algorithm for the synthesis of Three-Layer Threshold Networks Weight initialization Fast and efficient variants of Hamming and Hopfield neural networks Discrete time synchronous multilevel neural systems with reduced VLSI demands Probabilistic design techniques Time-based techniques Techniques for reducing physical realization requirements Applications to finite constraint problems Practical realization methods for Hebbian type associative memory systems Parallel self-organizing hierarchical neural network systems Dynamics of networks of biological neurons for utilization in computational neuroscience

Statistical Inference and Simulation for Spatial Point Processes

Author : Jesper Moller,Rasmus Plenge Waagepetersen
Publisher : CRC Press
Release : 2003-09-25
Category : Mathematics
ISBN : 0203496930

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Book Statistical Inference and Simulation for Spatial Point Processes Description/Summary:

Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.

Modeling, Simulation and Optimization of Complex Processes

Author : Hans Georg Bock,Ekaterina Kostina,Xuan Phu Hoang,Rolf Rannacher
Publisher : Springer Science & Business Media
Release : 2008-06-19
Category : Computers
ISBN : 9783540794097

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Book Modeling, Simulation and Optimization of Complex Processes Description/Summary:

This proceedings volume covers the broad interdisciplinary spectrum of scientific computing and presents recent advances in theory, development of methods, and applications in practice.

Progress in Industrial Mathematics at ECMI 2006

Author : Luis L. Bonilla,Miguel Moscoso,Gloria Platero,Jose M. Vega
Publisher : Springer Science & Business Media
Release : 2007-12-24
Category : Mathematics
ISBN : 9783540719922

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Book Progress in Industrial Mathematics at ECMI 2006 Description/Summary:

Proceedings from the 14th European Conference for Mathematics in Industry held in Madrid present innovative numerical and mathematical techniques. Topics include the latest applications in aerospace, information and communications, materials, energy and environment, imaging, biology and biotechnology, life sciences, and finance. In addition, the conference also delved into education in industrial mathematics and web learning.

Stochastic Geometry

Author : David Coupier
Publisher : Springer
Release : 2019-04-09
Category : Mathematics
ISBN : 9783030135478

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Book Stochastic Geometry Description/Summary:

This volume offers a unique and accessible overview of the most active fields in Stochastic Geometry, up to the frontiers of recent research. Since 2014, the yearly meeting of the French research structure GDR GeoSto has been preceded by two introductory courses. This book contains five of these introductory lectures. The first chapter is a historically motivated introduction to Stochastic Geometry which relates four classical problems (the Buffon needle problem, the Bertrand paradox, the Sylvester four-point problem and the bicycle wheel problem) to current topics. The remaining chapters give an application motivated introduction to contemporary Stochastic Geometry, each one devoted to a particular branch of the subject: understanding spatial point patterns through intensity and conditional intensities; stochastic methods for image analysis; random fields and scale invariance; and the theory of Gibbs point processes. Exposing readers to a rich theory, this book will encourage further exploration of the subject and its wide applications.