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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
Get Book Here
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: 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: Jesús A. López
Publisher: Springer
ISBN: 3540304789
Category : Computers
Languages : en
Pages : 258
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Book Description
This volume of the Springer Lecture Notes in Computer Science series contains the contributions presented at the International Symposium on Knowledge Exploration in Life Science Informatics (KELSI 2004) held in Milan, Italy, 25-26 November 2004. The two main objectives of the symposium were: • To explore the symbiosis between information and knowledge technologies and v- ious life science disciplines, such as biochemistry, biology, neuroscience, medical research, social sciences, and so on. • To investigate the synergy among different life science informatics areas, including cheminformatics,bioinformatics,neuroinformatics,medical informatics,systems - ology, socionics, and others. Modern life sciences investigate phenomena and systems at the level of molecules, cells, tissues, organisms, and populations. Typical areas of interest include natural e- lution, development,disease, behavior,cognition,and consciousness.This quest is g- eratinganoverwhelmingandfast-growingamountofdata,information,andknowledge, re?ecting living systems at different levels of organization. Future progress of the life sciences will depend on effective and ef?cient management, sharing, and exploitation of these resources by computational means.
Author: Ray L. Sengbush
Publisher: Springer Science & Business Media
ISBN: 9401163979
Category : Science
Languages : en
Pages : 299
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Book Description
This book describes the seismic methods used in geophys ical exploration for oil and gas in a comprehensive, non rigorous, mathematical manner. I have used it and its predecessors as a manual for short courses in seismic methods, and it has been extensively revised time and again to include the latest advances in our truly remark able science. I once called it, "Advanced Seismic Inter pretation," but the geophysicists who attended the courses always wondered when I was going to start dis cussing interpretation. They discovered at the end that I never did discuss interpretation as they knew it. No men tion was made of reflection picking, posting times, map ping, contouring, and things they already knew perfectly well. Instead, I discussed Fourier transforms, sampling theory, impulse responses, distortion operators, Wiener filters, noise in f-k space, velocity spectra, wave-equation migration, and direct detection of hydrocarbons as each of these topics appeared on the seismic scene. I wanted the geophysicists to think beyond the routine ofinterpre tation, to develop a better understanding of why seismic sections look as they do, to have a better feel for what digital processing is doing, for good or evil, to the seismic data. I attempted to stretch their minds. Whitehead said it best: "A mind once stretched by a new idea can never shrink to its former dimension. " May this book be a suc cessful mind-stretcher. R. L.
Author: James V Lambers
Publisher: World Scientific
ISBN: 9811227950
Category : Mathematics
Languages : en
Pages : 691
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Book Description
This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.
Author: John Logsdon
Publisher: Penguin
ISBN: 1101993499
Category : Technology & Engineering
Languages : en
Pages : 402
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Book Description
The fascinating story of how NASA sent humans to explore outer space, told through a treasure trove of historical documents--publishing in celebration of NASA's 60th anniversary and with a foreword by Bill Nye "An extremely useful and thought provoking documentary journey through the maze of space history. There is no wiser or more experienced navigator through the twists and turns and ups and downs than John Logsdon." -James Hansen, New York Times bestselling author of First Man, now a feature film starring Ryan Gosling and Claire Foy Among all the technological accomplishments of the last century, none has captured our imagination more deeply than the movement of humans into outer space. From Sputnik to SpaceX, the story of that journey--including the inside history of our voyages to the moon depicted in First Man--is told as never before in The Penguin Book of Outer Space Exploration. Renowned space historian John Logsdon traces the greatest moments in human spaceflight by weaving together essential, fascinating documents from NASA's history with his expert narrative guidance. Beginning with rocket genius Wernher von Braun's vision for voyaging to Mars, and closing with Elon Musk's contemporary plan to get there, this volume traces major events like the founding of NASA, the first American astronauts in space, the Apollo moon landings, the Challenger disaster, the daring Hubble Telescope repairs, and more. In these pages, we such gems as Eisenhower's reactions to Sputnik, the original NASA astronaut application, John Glenn's reflections on zero gravity, Kennedy's directives to go to the moon, discussions on what Neil Armstrong's first famous first words should be, firsthands accounts of spaceflight, and so much more.
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.
Author: Chong Ho Alex Yu
Publisher: CRC Press
ISBN: 1000777790
Category : Business & Economics
Languages : en
Pages : 290
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Book Description
This book introduces both conceptual and procedural aspects of cutting-edge data science methods, such as dynamic data visualization, artificial neural networks, ensemble methods, and text mining. There are at least two unique elements that can set the book apart from its rivals. First, most students in social sciences, engineering, and business took at least one class in introductory statistics before learning data science. However, usually these courses do not discuss the similarities and differences between traditional statistics and modern data science; as a result learners are disoriented by this seemingly drastic paradigm shift. In reaction, some traditionalists reject data science altogether while some beginning data analysts employ data mining tools as a “black box”, without a comprehensive view of the foundational differences between traditional and modern methods (e.g., dichotomous thinking vs. pattern recognition, confirmation vs. exploration, single method vs. triangulation, single sample vs. cross-validation etc.). This book delineates the transition between classical methods and data science (e.g. from p value to Log Worth, from resampling to ensemble methods, from content analysis to text mining etc.). Second, this book aims to widen the learner's horizon by covering a plethora of software tools. When a technician has a hammer, every problem seems to be a nail. By the same token, many textbooks focus on a single software package only, and consequently the learner tends to fit the problem with the tool, but not the other way around. To rectify the situation, a competent analyst should be equipped with a tool set, rather than a single tool. For example, when the analyst works with crucial data in a highly regulated industry, such as pharmaceutical and banking, commercial software modules (e.g., SAS) are indispensable. For a mid-size and small company, open-source packages such as Python would come in handy. If the research goal is to create an executive summary quickly, the logical choice is rapid model comparison. If the analyst would like to explore the data by asking what-if questions, then dynamic graphing in JMP Pro is a better option. This book uses concrete examples to explain the pros and cons of various software applications.
Author: Michael Walker
Publisher: Packt Publishing Ltd
ISBN: 1803245913
Category : Computers
Languages : en
Pages : 542
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Book Description
Explore supercharged machine learning techniques to take care of your data laundry loads Key FeaturesLearn how to prepare data for machine learning processesUnderstand which algorithms are based on prediction objectives and the properties of the dataExplore how to interpret and evaluate the results from machine learningBook Description Many individuals who know how to run machine learning algorithms do not have a good sense of the statistical assumptions they make and how to match the properties of the data to the algorithm for the best results. As you start with this book, models are carefully chosen to help you grasp the underlying data, including in-feature importance and correlation, and the distribution of features and targets. The first two parts of the book introduce you to techniques for preparing data for ML algorithms, without being bashful about using some ML techniques for data cleaning, including anomaly detection and feature selection. The book then helps you apply that knowledge to a wide variety of ML tasks. You'll gain an understanding of popular supervised and unsupervised algorithms, how to prepare data for them, and how to evaluate them. Next, you'll build models and understand the relationships in your data, as well as perform cleaning and exploration tasks with that data. You'll make quick progress in studying the distribution of variables, identifying anomalies, and examining bivariate relationships, as you focus more on the accuracy of predictions in this book. By the end of this book, you'll be able to deal with complex data problems using unsupervised ML algorithms like principal component analysis and k-means clustering. What you will learnExplore essential data cleaning and exploration techniques to be used before running the most popular machine learning algorithmsUnderstand how to perform preprocessing and feature selection, and how to set up the data for testing and validationModel continuous targets with supervised learning algorithmsModel binary and multiclass targets with supervised learning algorithmsExecute clustering and dimension reduction with unsupervised learning algorithmsUnderstand how to use regression trees to model a continuous targetWho this book is for This book is for professional data scientists, particularly those in the first few years of their career, or more experienced analysts who are relatively new to machine learning. Readers should have prior knowledge of concepts in statistics typically taught in an undergraduate introductory course as well as beginner-level experience in manipulating data programmatically.
Author: S. M. Gandhi
Publisher: Elsevier
ISBN: 0128053321
Category : Science
Languages : en
Pages : 422
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Book Description
Essentials of Mineral Exploration and Evaluation offers a thorough overview of methods used in mineral exploration campaigns, evaluation, reporting and economic assessment processes. Fully illustrated to cover the state-of-the-art exploration techniques and evaluation of mineral assets being practiced globally, this up-to-date reference offers balanced coverage of the latest knowledge and current global trends in successful mineral exploration and evaluation. From mineral deposits, to remote sensing, to sampling and analysis, Essentials of Mineral Exploration and Evaluation offers an extensive look at this rapidly changing field. Covers the complete spectrum of all aspects of ore deposits and mining them, providing a "one-stop shop" for experts and students Presents the most up-to-date information on developments and methods in all areas of mineral exploration Includes chapters on application of GIS, statistics, and geostatistics in mineral exploration and evaluation Includes case studies to enhance practical application of concepts
