Random Explorations
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Author | : Gregory F. Lawler |
Publisher | : American Mathematical Society |
Total Pages | : 215 |
Release | : 2022-12-06 |
Genre | : Mathematics |
ISBN | : 1470467666 |
The title “Random Explorations” has two meanings. First, a few topics of advanced probability are deeply explored. Second, there is a recurring theme of analyzing a random object by exploring a random path. This book is an outgrowth of lectures by the author in the University of Chicago Research Experiences for Undergraduate (REU) program in 2020. The idea of the course was to expose advanced undergraduates to ideas in probability research. The book begins with Markov chains with an emphasis on transient or killed chains that have finite Green's function. This function, and its inverse called the Laplacian, is discussed next to relate two objects that arise in statistical physics, the loop-erased random walk (LERW) and the uniform spanning tree (UST). A modern approach is used including loop measures and soups. Understanding these approaches as the system size goes to infinity requires a deep understanding of the simple random walk so that is studied next, followed by a look at the infinite LERW and UST. Another model, the Gaussian free field (GFF), is introduced and related to loop measure. The emphasis in the book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution (SLE), and the continuous Gaussian free field. A number of exercises scattered throughout the text will help a serious reader gain better understanding of the material.
Author | : Melanie Mitchell |
Publisher | : Oxford University Press |
Total Pages | : 367 |
Release | : 2009-04-01 |
Genre | : Science |
ISBN | : 0199741026 |
What enables individually simple insects like ants to act with such precision and purpose as a group? How do trillions of neurons produce something as extraordinarily complex as consciousness? In this remarkably clear and companionable book, leading complex systems scientist Melanie Mitchell provides an intimate tour of the sciences of complexity, a broad set of efforts that seek to explain how large-scale complex, organized, and adaptive behavior can emerge from simple interactions among myriad individuals. Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. Richly illustrated, Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.
Author | : Burkhart Wolff |
Publisher | : Springer Science & Business Media |
Total Pages | : 235 |
Release | : 2011-10-21 |
Genre | : Computers |
ISBN | : 364224579X |
This book constitutes the refereed proceedings of the 23rd IFIP WG 6.1 International Conference on Testing Software and Systems, ICTSS 2011, held in Paris, France, in November 2011. The 13 revised full papers presented together with 2 invited talks were carefully selected from 40 submissions. The papers address the conceptual, theoretic, and practical problems of testing software systems, including communication protocols, services, distributed platforms, middleware, controllers, and security infrastructures.
Author | : Bruce Hajek |
Publisher | : Cambridge University Press |
Total Pages | : 429 |
Release | : 2015-03-12 |
Genre | : Technology & Engineering |
ISBN | : 1316241246 |
This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).
Author | : Martin Gogolla |
Publisher | : Springer Science & Business Media |
Total Pages | : 215 |
Release | : 2011-06-22 |
Genre | : Computers |
ISBN | : 3642217672 |
This book constitutes the refereed proceedings of the 5th International Conference on Tests and Proofs, TAP 2011, held in Zurich, Switzerland in June/July 2011. The 12 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 27 submissions. Among the topics covered are model checking, testing systems, test generation, symbolic testing, SAT solvers, SMT solvers, property-based testing, automated test generation, learning-based testing, UML, OCL, specification-based testing, and network testing.
Author | : Khaled El-Fakih |
Publisher | : Springer |
Total Pages | : 271 |
Release | : 2015-11-07 |
Genre | : Computers |
ISBN | : 3319259458 |
This book constitutes the refereed proceedings of the 27th IFIP WG 6.1 International Conference on Testing Software and Systems, ICTSS 2015, held in Sharjah and Dubai, United Arab Emirates, in November 2015. The 14 revised full papers and 4 short papers presented were carefully reviewed and selected from 42 submissions. The papers are organized in topical sections on model based testing, test derivation methods, monitoring and fault localization, model and system testing, and real-time systems.
Author | : James Wei |
Publisher | : Oxford University Press |
Total Pages | : 376 |
Release | : 2007-01-04 |
Genre | : Science |
ISBN | : 0195159179 |
'Product Engineering' provides theories and case studies in product engineering - the design of new, useful products with desired properties.
Author | : Gautam Shroff |
Publisher | : OUP Oxford |
Total Pages | : 346 |
Release | : 2013-11-28 |
Genre | : Computers |
ISBN | : 0191664626 |
As we use the Web for social networking, shopping, and news, we leave a personal trail. These days, linger over a Web page selling lamps, and they will turn up at the advertising margins as you move around the Internet, reminding you, tempting you to make that purchase. Search engines such as Google can now look deep into the data on the Web to pull out instances of the words you are looking for. And there are pages that collect and assess information to give you a snapshot of changing political opinion. These are just basic examples of the growth of "Web intelligence", as increasingly sophisticated algorithms operate on the vast and growing amount of data on the Web, sifting, selecting, comparing, aggregating, correcting; following simple but powerful rules to decide what matters. While original optimism for Artificial Intelligence declined, this new kind of machine intelligence is emerging as the Web grows ever larger and more interconnected. Gautam Shroff takes us on a journey through the computer science of search, natural language, text mining, machine learning, swarm computing, and semantic reasoning, from Watson to self-driving cars. This machine intelligence may even mimic at a basic level what happens in the brain.
Author | : R. Russell Rhinehart |
Publisher | : John Wiley & Sons |
Total Pages | : 773 |
Release | : 2018-03-14 |
Genre | : Technology & Engineering |
ISBN | : 1118936310 |
An Application-Oriented Introduction to Essential Optimization Concepts and Best Practices Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the world grows increasingly reliant on complex systems, optimization has become both more important and more challenging than ever before. Engineering Optimization provides a practically-focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process. Although essential algorithms are explained in detail, the focus lies more in the human function: how to create an appropriate objective function, choose decision variables, identify and incorporate constraints, define convergence, and other critical issues that define the success or failure of an optimization project. Examples, exercises, and homework throughout reinforce the author’s “do, not study” approach to learning, underscoring the application-oriented discussion that provides a deep, generic understanding of the optimization process that can be applied to any field. Providing excellent reference for students or professionals, Engineering Optimization: Describes and develops a variety of algorithms, including gradient based (such as Newton’s, and Levenberg-Marquardt), direct search (such as Hooke-Jeeves, Leapfrogging, and Particle Swarm), along with surrogate functions for surface characterization Provides guidance on optimizer choice by application, and explains how to determine appropriate optimizer parameter values Details current best practices for critical stages of specifying an optimization procedure, including decision variables, defining constraints, and relationship modeling Provides access to software and Visual Basic macros for Excel on the companion website, along with solutions to examples presented in the book Clear explanations, explicit equation derivations, and practical examples make this book ideal for use as part of a class or self-study, assuming a basic understanding of statistics, calculus, computer programming, and engineering models. Anyone seeking best practices for “making the best choices” will find value in this introductory resource.
Author | : D. Jude Hemanth |
Publisher | : Springer Nature |
Total Pages | : 801 |
Release | : 2023-01-01 |
Genre | : Technology & Engineering |
ISBN | : 303109753X |
This book brings together the most recent, quality research papers accepted and presented in the 3rd International Conference on Artificial Intelligence and Applied Mathematics in Engineering (ICAIAME 2021) held in Antalya, Turkey between 1-3 October 2021. Objective of the content is to provide important and innovative research for developments-improvements within different engineering fields, which are highly interested in using artificial intelligence and applied mathematics. As a collection of the outputs from the ICAIAME 2021, the book is specifically considering research outcomes including advanced use of machine learning and careful problem designs on human-centred aspects. In this context, it aims to provide recent applications for real-world improvements making life easier and more sustainable for especially humans. The book targets the researchers, degree students, and practitioners from both academia and the industry.