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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: 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: Abdul Hanif Abdul Halim
Publisher: Springer Nature
ISBN: 3031740130
Category :
Languages : en
Pages : 330
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Book Description
Author: Ronald W. Shonkwiler
Publisher: Springer Science & Business Media
ISBN: 0387878378
Category : Mathematics
Languages : en
Pages : 249
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Book Description
Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.
Author: Jerry Burkhart
Publisher: Taylor & Francis
ISBN: 1000500152
Category : Education
Languages : en
Pages : 273
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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
Author: Dr. Raja Sarath Kumar Boddu
Publisher: Xoffencerpublication
ISBN: 9394707239
Category : Computers
Languages : en
Pages : 254
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Book Description
Over the course of the last decade, the amount of data with which one must deal has skyrocketed to levels that are difficult to fathom, while at the same time, the cost of storing data has steadily decreased. Private firms and research organizations collect terabytes of data about their customers' interactions, commerce, and social media, as well as sensors from devices such as mobile phones and vehicles. This data is used for a variety of purposes, including marketing and advertising. Figuring out how to make sense of all this data is one of the most difficult challenges of our day. The analysis of large amounts of data comes into play at this point. Big Data Analytics entails, for the most part, the gathering of data from a variety of sources, the management of this data in such a manner that it can be utilized by analysts, and the delivery of data products that are beneficial to the organization's business.
Author: M. R. Mickey
Publisher:
ISBN:
Category : Mines and mineral resources
Languages : en
Pages : 80
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Book Description
Author: Rajendra Prasath
Publisher: Springer
ISBN: 3319038443
Category : Computers
Languages : en
Pages : 862
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Book Description
This book constitutes the proceedings of the First International Conference on Mining Intelligence and Knowledge Exploration, MIKE 2013, held in Tamil Nadu, India on December 2013. The 82 papers presented were carefully reviewed and selected from 334 submissions. The papers cover the topics such as feature selection, classification, clustering, image processing, network security, speech processing, machine learning, information retrieval, recommender systems, natural language processing, language, cognition and computation and other certain problems in dynamical systems.
Author: Jia'en Lin
Publisher: Springer Nature
ISBN: 981137127X
Category : Technology & Engineering
Languages : en
Pages : 2063
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Book Description
This book gathers selected papers from the 8th International Field Exploration and Development Conference (IFEDC 2018) and addresses a broad range of topics, including: Reservoir Surveillance and Management, Reservoir Evaluation and Dynamic Description, Reservoir Production Stimulation and EOR, Ultra-Tight Reservoirs, Unconventional Oil and Gas Resources Technology, Oil and Gas Well Production Testing, and Geomechanics. In brief, the papers introduce readers to upstream technologies used in oil & gas development, the main principles of the process, and various related design technologies. The conference not only provided a platform to exchange experiences, but also promoted the advancement of scientific research in oil & gas exploration and production. The book is chiefly intended for industry experts, professors, researchers, senior engineers, and enterprise managers.
Author: Lev Knoring
Publisher: Elsevier
ISBN: 0080517846
Category : Science
Languages : en
Pages : 337
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Book Description
Here is a valuable guide to appraise and develop petroleum resources. Geology largely determines exploration policy. This book analyzes the strategic connection between the two and shows how to improve decision making on appraising and developing petroleum resources. It examines and describes the internal patterns in finding oil and gas deposits and outlines a process to evaluate the resources. The book also provides a means for long-term reserve accrual forecasting and evaluation. It uses mathematical modeling as a method to evaluate the initial potential of an oil and gas region as well as a way to forecast future reserves. These models improve the reliability and validity of exploration forecasts and estimates. Strategies for Optimizing Petroleum Exploration helps petroleum engineers and explorationists focus and improve their reserve assessment and decision making. This book shows how to develop and appraise petroleum resources.
