Random Packing and Random Covering Sequences
Random Packing and Random Covering Sequences

Author: Stanford University. Department of Statistics

Publisher:

Published: 1987

Total Pages: 312

ISBN-13:

DOWNLOAD EBOOK

In a sequential packing problem, random objects are uniformly and independently selected from some space. A selected object is either packed or rejected, depending on the distance between it and the nearest object which has been previously packed. A saturated packing is said to exist when it is no longer possible to pack any additional selections. The random packing density is the average proportion of the space which is occupied by the packed objects at saturation. Results concerning the time of the first rejection in a packing sequence are given in Chapter 1. The accuracy of some common approximation formulas is investigated for several settings. The problems considered may be thought of as generalizations of the classical birthday problem. Exact results concerning random packing densities are generally known only for some packing sequences in one-dimensional spaces. In Chapter 2, the packing densities of various computer generated codes are examined. These stochastically constructed codes provide a convenient way to study packing in multidimensional spaces. Asymptotic approximation formulas are given for the packing densities which arise from several different coding schemes. In Chapter 3 the distribution of the number of random selections needed to achieve a saturated packing is considered. In each of the settings examined, the results are compared with analogous results from an associated random covering problem.

Finite Packing and Covering
Finite Packing and Covering

Author: K. Böröczky

Publisher: Cambridge University Press

Published: 2004-08-02

Total Pages: 406

ISBN-13: 9780521801577

DOWNLOAD EBOOK

This book provides an in-depth discussion of the theory of finite packings and coverings by convex bodies.

Morphological Models of Random Structures
Morphological Models of Random Structures

Author: Dominique Jeulin

Publisher: Springer Nature

Published: 2021-06-01

Total Pages: 919

ISBN-13: 3030754529

DOWNLOAD EBOOK

This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.

Recent Developments in Fractals and Related Fields
Recent Developments in Fractals and Related Fields

Author: Julien Barral

Publisher: Birkhäuser

Published: 2017-08-23

Total Pages: 320

ISBN-13: 3319578057

DOWNLOAD EBOOK

This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

Scientific and Technical Aerospace Reports
Scientific and Technical Aerospace Reports

Author:

Publisher:

Published: 1982

Total Pages: 666

ISBN-13:

DOWNLOAD EBOOK

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Bandit Algorithms
Bandit Algorithms

Author: Tor Lattimore

Publisher: Cambridge University Press

Published: 2020-07-16

Total Pages: 538

ISBN-13: 1108687490

DOWNLOAD EBOOK

Decision-making in the face of uncertainty is a significant challenge in machine learning, and the multi-armed bandit model is a commonly used framework to address it. This comprehensive and rigorous introduction to the multi-armed bandit problem examines all the major settings, including stochastic, adversarial, and Bayesian frameworks. A focus on both mathematical intuition and carefully worked proofs makes this an excellent reference for established researchers and a helpful resource for graduate students in computer science, engineering, statistics, applied mathematics and economics. Linear bandits receive special attention as one of the most useful models in applications, while other chapters are dedicated to combinatorial bandits, ranking, non-stationary problems, Thompson sampling and pure exploration. The book ends with a peek into the world beyond bandits with an introduction to partial monitoring and learning in Markov decision processes.

Network Information Theory
Network Information Theory

Author: Abbas El Gamal

Publisher: Cambridge University Press

Published: 2011-12-08

Total Pages: 666

ISBN-13: 1139503146

DOWNLOAD EBOOK

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Adventures Between Lower Bounds and Higher Altitudes
Adventures Between Lower Bounds and Higher Altitudes

Author: Hans-Joachim Böckenhauer

Publisher: Springer

Published: 2018-09-04

Total Pages: 658

ISBN-13: 3319983555

DOWNLOAD EBOOK

This Festschrift volume is published in honor of Juraj Hromkovič on the occasion of his 60th birthday. Juraj Hromkovič is a leading expert in the areas of automata and complexity theory, algorithms for hard problems, and computer science education. The contributions in this volume reflect the breadth and impact of his work. The volume contains 35 full papers related to Juraj Hromkovič’s research. They deal with various aspects of the complexity of finite automata, the information content of online problems, stability of approximation algorithms, reoptimization algorithms, computer science education, and many other topics within the fields of algorithmics and complexity theory. Moreover, the volume contains a prologue and an epilogue of laudatios from several collaborators, colleagues, and friends.