Probability and Computing

Probability and Computing
Author: Michael Mitzenmacher
Publisher: Cambridge University Press
Total Pages: 372
Release: 2005-01-31
Genre: Computers
ISBN: 9780521835404

Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.

Abstraction, Refinement and Proof for Probabilistic Systems

Abstraction, Refinement and Proof for Probabilistic Systems
Author: Annabelle McIver
Publisher: Springer Science & Business Media
Total Pages: 412
Release: 2005
Genre: Computers
ISBN: 9780387401157

Provides an integrated coverage of random/probabilistic algorithms, assertion-based program reasoning, and refinement programming models, providing a focused survey on probabilistic program semantics. This book illustrates, by examples, the typical steps necessary to build a mathematical model of any programming paradigm.

The Probabilistic Method

The Probabilistic Method
Author: Noga Alon
Publisher: John Wiley & Sons
Total Pages: 396
Release: 2015-11-02
Genre: Mathematics
ISBN: 1119062071

Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.

Process Algebra and Probabilistic Methods: Performance Modeling and Verification

Process Algebra and Probabilistic Methods: Performance Modeling and Verification
Author: Holger Hermanns
Publisher: Springer
Total Pages: 225
Release: 2003-08-02
Genre: Mathematics
ISBN: 3540456058

This volume contains the proceedings of the second joint PAPM-PROBMIV Workshop, held at the University of Copenhagen, Denmark, July 25–26, 2002 as part of the Federated Logic Conference (FLoC 2002). The PAPM-PROBMIV workshop results from the combination of two wo- shops: PAPM (Process Algebras and Performance Modeling) and PROBMIV (Probabilistic Methods in Veri?cation). The aim of the joint workshop is to bring together the researchers working across the whole spectrum of techniques for the modeling, speci?cation, analysis, and veri?cation of probabilistic systems. Probability is widely used in the design and analysis of software and hardware systems, as a means to derive e?cient algorithms (e.g. randomization), as a model for unreliable or unpredictable behavior (as in the study of fault-tolerant systems and computer networks), and as a tool to study performance and - pendability properties. The topics of the workshop include speci?cation, m- els, and semantics of probabilistic systems, analysis and veri?cation techniques, probabilistic methods for the veri?cation of non-probabilistic systems, and tools and case studies. The ?rst PAPM workshop was held in Edinburgh in 1993; the following ones were held in Regensberg (1994), Edinburgh (1995), Turin (1996), Enschede (1997), Nice (1998), Zaragoza (1999), and Geneva (2000). The ?rst PROBMIV workshop was held in Indianapolis, Indiana (1998); the next one took place in Eindhoven (1999). In 2000, PROBMIV was replaced by a Dagstuhl seminar on Probabilistic Methods in Veri?cation.

Process Algebra and Probabilistic Methods. Performance Modelling and Verification

Process Algebra and Probabilistic Methods. Performance Modelling and Verification
Author: Luca de Alfaro
Publisher: Springer Science & Business Media
Total Pages: 228
Release: 2001-08-29
Genre: Mathematics
ISBN: 354042556X

This book constitutes the refereed proceedings of the Joint Workshop on Process Algebra and Performance Modeling and Probabilistic Methods in Verification, PAPM-PROBMIV 2001, held in Aachen, Germany in September 2001. The 12 revised full papers presented together with one invited paper were carefully reviewed and selected from 23 submissions. Among the topics addressed are model representation, model checking, probabilistic systems analysis, refinement, Markov chains, random variables, stochastic timed systems, Max-Plus algebra, process algebra, system modeling, and the Mobius modeling framework.

Graph Searching Games and Probabilistic Methods

Graph Searching Games and Probabilistic Methods
Author: Anthony Bonato
Publisher: CRC Press
Total Pages: 346
Release: 2017-11-28
Genre: Mathematics
ISBN: 135181477X

Graph Searching Games and Probabilistic Methods is the first book that focuses on the intersection of graph searching games and probabilistic methods. The book explores various applications of these powerful mathematical tools to games and processes such as Cops and Robbers, Zombie and Survivors, and Firefighting. Written in an engaging style, the book is accessible to a wide audience including mathematicians and computer scientists. Readers will find that the book provides state-of-the-art results, techniques, and directions in graph searching games, especially from the point of view of probabilistic methods. The authors describe three directions while providing numerous examples, which include: • Playing a deterministic game on a random board. • Players making random moves. • Probabilistic methods used to analyze a deterministic game.

Applying Integration Techniques and Methods in Distributed Systems and Technologies

Applying Integration Techniques and Methods in Distributed Systems and Technologies
Author: Kecskemeti, Gabor
Publisher: IGI Global
Total Pages: 368
Release: 2019-04-12
Genre: Computers
ISBN: 1522582967

Distributed systems intertwine with our everyday lives. The benefits and current shortcomings of the underpinning technologies are experienced by a wide range of people and their smart devices. With the rise of large-scale IoT and similar distributed systems, cloud bursting technologies, and partial outsourcing solutions, private entities are encouraged to increase their efficiency and offer unparalleled availability and reliability to their users. Applying Integration Techniques and Methods in Distributed Systems is a critical scholarly publication that defines the current state of distributed systems, determines further goals, and presents architectures and service frameworks to achieve highly integrated distributed systems and presents solutions to integration and efficient management challenges faced by current and future distributed systems. Highlighting topics such as multimedia, programming languages, and smart environments, this book is ideal for system administrators, integrators, designers, developers, researchers, and academicians.

Bayesian Methods for Hackers

Bayesian Methods for Hackers
Author: Cameron Davidson-Pilon
Publisher: Addison-Wesley Professional
Total Pages: 551
Release: 2015-09-30
Genre: Computers
ISBN: 0133902927

Master Bayesian Inference through Practical Examples and Computation–Without Advanced Mathematical Analysis Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples and intuitive explanations that have been refined after extensive user feedback. You’ll learn how to use the Markov Chain Monte Carlo algorithm, choose appropriate sample sizes and priors, work with loss functions, and apply Bayesian inference in domains ranging from finance to marketing. Once you’ve mastered these techniques, you’ll constantly turn to this guide for the working PyMC code you need to jumpstart future projects. Coverage includes • Learning the Bayesian “state of mind” and its practical implications • Understanding how computers perform Bayesian inference • Using the PyMC Python library to program Bayesian analyses • Building and debugging models with PyMC • Testing your model’s “goodness of fit” • Opening the “black box” of the Markov Chain Monte Carlo algorithm to see how and why it works • Leveraging the power of the “Law of Large Numbers” • Mastering key concepts, such as clustering, convergence, autocorrelation, and thinning • Using loss functions to measure an estimate’s weaknesses based on your goals and desired outcomes • Selecting appropriate priors and understanding how their influence changes with dataset size • Overcoming the “exploration versus exploitation” dilemma: deciding when “pretty good” is good enough • Using Bayesian inference to improve A/B testing • Solving data science problems when only small amounts of data are available Cameron Davidson-Pilon has worked in many areas of applied mathematics, from the evolutionary dynamics of genes and diseases to stochastic modeling of financial prices. His contributions to the open source community include lifelines, an implementation of survival analysis in Python. Educated at the University of Waterloo and at the Independent University of Moscow, he currently works with the online commerce leader Shopify.

Formal Methods for Distributed System Development

Formal Methods for Distributed System Development
Author: Tommaso Bolognesi
Publisher: Springer
Total Pages: 414
Release: 2013-03-20
Genre: Computers
ISBN: 0387355332

th The 20 anniversary of the IFIP WG6. 1 Joint International Conference on Fonna! Methods for Distributed Systems and Communication Protocols (FORTE XIII / PSTV XX) was celebrated by the year 2000 edition of the Conference, which was held for the first time in Italy, at Pisa, October 10-13, 2000. In devising the subtitle for this special edition --'Fonna! Methods Implementation Under Test' --we wanted to convey two main concepts that, in our opinion, are reflected in the contents of this book. First, the early, pioneering phases in the development of Formal Methods (FM's), with their conflicts between evangelistic and agnostic attitudes, with their over optimistic applications to toy examples and over-skeptical views about scalability to industrial cases, with their misconceptions and myths . . . , all this is essentially over. Many FM's have successfully reached their maturity, having been 'implemented' into concrete development practice: a number of papers in this book report about successful experiences in specifYing and verifYing real distributed systems and protocols. Second, one of the several myths about FM's - the fact that their adoption would eventually eliminate the need for testing - is still quite far from becoming a reality, and, again, this book indicates that testing theory and applications are still remarkably healthy. A total of 63 papers have been submitted to FORTEIPSTV 2000, out of which the Programme Committee has selected 22 for presentation at the Conference and inclusion in the Proceedings.

Probabilistic Methods Applied to Electric Power Systems

Probabilistic Methods Applied to Electric Power Systems
Author: Samy G. Krishnasamy
Publisher: Elsevier
Total Pages: 679
Release: 2013-10-22
Genre: Technology & Engineering
ISBN: 1483160742

Probabilistic Methods Applied to Electric Power Systems contains the proceedings of the First International Symposium held in Toronto, Ontario, Canada, on July 11-13, 1986. The papers explore significant technical advances that have been made in the application of probability methods to the design of electric power systems. This volume is comprised of 65 chapters divided into 10 sections and begins by discussing the probabilistic methodologies used in the assessment of power system reliability and structural design. The following chapters focus on the applications of probabilistic techniques to the analysis and design of transmission systems and structures; evaluation of design and reliability of distribution systems; system planning; and assessment of performance of transmission system components such as insulators, tower joints, and foundations. The probability-based procedures for dealing with data bases such as wind load and ice load are also considered, along with the effects of weather-induced loads on overhead power lines and the use of probability methods in upgrading existing power lines and components. The final section deals with applications of probability methods to power system problems not covered in other chapters. This book will be of value to engineers involved in uprating, designing, analyzing, and assessing reliability of transmission and distribution systems.