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Author: Gregory F. Lawler
Publisher: American Mathematical Society
ISBN: 1470467666
Category : Mathematics
Languages : en
Pages : 215
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Book Description
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: Gregory F. Lawler
Publisher: American Mathematical Society
ISBN: 1470467666
Category : Mathematics
Languages : en
Pages : 215
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Book Description
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: Martin Gogolla
Publisher: Springer Science & Business Media
ISBN: 3642217672
Category : Computers
Languages : en
Pages : 215
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Book Description
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: Burkhart Wolff
Publisher: Springer
ISBN: 3642245803
Category : Computers
Languages : en
Pages : 235
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Book Description
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: Melanie Mitchell
Publisher: Oxford University Press
ISBN: 0199741026
Category : Science
Languages : en
Pages : 367
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Book Description
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: Bruce Hajek
Publisher: Cambridge University Press
ISBN: 1316241246
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
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: Gautam Shroff
Publisher: OUP Oxford
ISBN: 0191664626
Category : Computers
Languages : en
Pages : 346
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Book Description
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: James Wei
Publisher: Oxford University Press
ISBN: 0190289341
Category : Technology & Engineering
Languages : en
Pages : 390
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Book Description
The current chemical engineering curriculum concentrates on process: the efficient manufacturing in quantity of traditional chemical products such as ammonia and benzene. However, many chemical companies now invent and manufacture specialty products with particular properties such as pharmaceuticals, cosmetics, and electronic coatings, and their employees need to know how to design the products as well as manufacture them. James Wei, a famous chemical engineer, is writing this book to provide theories and case studies in product engineering the design of new, useful products with desired properties. The first section relates historical case studies of successful product invention and development by individuals and companies. The second part of the book describes the toolbox of molecular structure-property relations. A desired product needs to have certain properties (for example, phase transition or thermal properties) and the chemist must find or design a molecular structure with the required properties This section will instruct chemists in the analysis of structure and property information. The third section is concerned with the next stage: product research and design. It will discuss improving the desired product by additives and blending, among other strategies. It will also cover future challenges in product engineering.
Author: Khaled El-Fakih
Publisher: Springer
ISBN: 3319259458
Category : Computers
Languages : en
Pages : 271
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Book Description
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: Rodrigo Quian Quiroga
Publisher: CRC Press
ISBN: 1439853304
Category : Medical
Languages : en
Pages : 643
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Book Description
Understanding how populations of neurons encode information is the challenge faced by researchers in the field of neural coding. Focusing on the many mysteries and marvels of the mind has prompted a prominent team of experts in the field to put their heads together and fire up a book on the subject. Simply titled Principles of Neural Coding, this book covers the complexities of this discipline. It centers on some of the major developments in this area and presents a complete assessment of how neurons in the brain encode information. The book collaborators contribute various chapters that describe results in different systems (visual, auditory, somatosensory perception, etc.) and different species (monkeys, rats, humans, etc). Concentrating on the recording and analysis of the firing of single and multiple neurons, and the analysis and recording of other integrative measures of network activity and network states—such as local field potentials or current source densities—is the basis of the introductory chapters. Provides a comprehensive and interdisciplinary approach Describes topics of interest to a wide range of researchers The book then moves forward with the description of the principles of neural coding for different functions and in different species and concludes with theoretical and modeling works describing how information processing functions are implemented. The text not only contains the most important experimental findings, but gives an overview of the main methodological aspects for studying neural coding. In addition, the book describes alternative approaches based on simulations with neural networks and in silico modeling in this highly interdisciplinary topic. It can serve as an important reference to students and professionals.
Author: Jerry Burkhart
Publisher: Routledge
ISBN: 1000493067
Category : Education
Languages : en
Pages : 256
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Book Description
Stretch your students' mathematical imaginations to their limits as they solve challenging real-world and mathematical problems that extend concepts from the Common Core State Standards for Mathematics in Advanced Common Core Math Explorations: Probability and Statistics. Students will learn powerful mathematical ideas about data and chance as they make sense of real-world situations from science, sports, and everyday life. Each activity comes with extensive teacher support, including student handouts, discussion guides, detailed solutions, and suggestions for extending the investigations. Grades 5-8
