Название: Qualitative Theory of ODEs: An Introduction to Dynamical Systems Theory
Автор: Henryk Żoladek, Raul Murillo
Издательство: World Scientific Publishing
Год: 2023
Страниц: 283
Язык: английский
Формат: pdf (true)
Размер: 16.4 MB

The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods.

Название: Spatiotemporal Analytics
Автор: Jay Lee
Издательство: CRC Press
Год: 2023
Страниц: 267
Язык: английский
Формат: pdf (true)
Размер: 20.0 MB

This book introduces readers to spatiotemporal analytics that are extended from spatial statistics. Spatiotemporal analytics help analysts to quantitatively recognize and evaluate the spatial patterns and their temporal trends of a set of geographic events or objects. Spatiotemporal analyses are very important in geography, environmental sciences, economy, and many other domains. Spatiotemporal Analytics explains in very simple terms the concepts of spatiotemporal data and statistics, theories, and methods used. Each chapter introduces a case study as an example application for an in-depth learning process. The software used and the codes provided enable readers not only to learn statistics but also to use them effectively in their projects.

Название: Quantum-like Networks: An Approach to Neural Behavior through their Mathematics and Logic
Автор: Stephen A Selesnick
Издательство: World Scientific Publishing
Год: 2023
Страниц: 354
Язык: английский
Формат: pdf (true), epub
Размер: 30.1 MB

Do brains compute? If they do, what do they compute and how do they do it? The first part of the book introduces the development of a model that simulates actual biological neurons more closely than do current standard models of neural networks, as well as the deduction of its physics-like and computational properties from first principles. The second part presents a collection of applications of the model to memory formation and loss, a general syntax for memory retrieval, language itself, and certain forms of aphasia. A linear development of the discussion with proofs in situ is employed by the author, making the book essentially self-contained. A pair of helpful appendices are provided to acquaint the reader with necessary fundamentals of topics in logic and mathematics. Quantum-like Networks: An Approach to Neural Behavior through their Mathematics and Logic will show you an entirely new approach to an ancient subject. Readership: Researchers and graduate students in Neuroscience, Biomathematics, Biophysics, Mathematics, Computer Science, and related fields.

Название: Data Science and Human-Environment Systems
Автор: Steven M. Manson
Издательство: Cambridge University Press
Год: 2023
Страниц: 279
Язык: английский
Формат: pdf
Размер: 10.0 MB

Transformation of the Earth's social and ecological systems is occurring at a rate and magnitude unparalleled in human experience. Data Science is a revolutionary new way to understand human-environment relationships at the heart of pressing challenges like climate change and sustainable development. However, data science faces serious shortcomings when it comes to human-environment research. There are challenges with social and environmental data, the methods that manipulate and analyze the information, and the theory underlying the data science itself; as well as significant legal, ethical and policy concerns. This timely book offers a comprehensive, balanced, and accessible account of the promise and problems of this work in terms of data, methods, theory, and policy. It demonstrates the need for data scientists to work with human-environment scholars to tackle pressing real-world problems, making it ideal for researchers and graduate students in Earth and environmental science, data science and the environmental social sciences. Data Science and cognate fields like Big Data and Artificial Intelligence hold great promise for studying human-environment systems.

Название: The Mystery of Time: Asymmetry of Time and Irreversibility in the Natural Processes
Автор: A.L. Kuzemsky
Издательство: World Scientific Publishing
Год: 2023
Страниц: 484
Язык: английский
Формат: pdf (true), epub
Размер: 10.0 MB

The book focuses on the study of the temporal behavior of complex many-particle systems. The phenomenon of time and its role in the temporal evolution of complex systems is a remaining mystery. The book presents the necessity of the interdisciplinary point of view regarding on the phenomenon of time. The aim of the present study is to summarize and formulate in a concise but clear form the trends and approaches to the concept of time from a broad interdisciplinary perspective exposing tersely the complementary approaches and theories of time in the context of thermodynamics, statistical physics, cosmology, theory of information, biology and biophysics, including the problem of time and aging. Various approaches to the problem show that time is an extraordinarily interdisciplinary and multifaceted underlying notion which plays an extremely important role in various natural complex processes.

Название: A Bridge to Advanced Mathematics: From Natural to Complex Numbers
Автор: Sebastian M. Cioaba, Werner Linde
Издательство: American Mathematical Society
Год: 2023
Страниц: 544
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

Most introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties. Understanding the properties of these systems is necessary throughout higher mathematics. The book is an ideal introduction to mathematical reasoning and proof techniques, building on familiar content to ensure comprehension of more advanced topics in abstract algebra and real analysis with over 700 exercises as well as many examples throughout. Readers will learn and practice writing proofs related to new abstract concepts while learning new mathematical content. The first task is analogous to practicing soccer while the second is akin to playing soccer in a real match. The authors believe that all students should practice and play mathematics. The book is written for students who already have some familiarity with formal proof writing but would like to have some extra preparation before taking higher mathematics courses like abstract algebra and real analysis.

Название: Занимательная байесовская статистика. Манга
Автор: Такахаси Макото, Уэдзу Юхо
Издательство: ДМК Пресс
Год: 2021
Cтраниц: 228
Формат: pdf
Размер: 31 мб
Язык: русский

Простой, последовательный, наглядный и необременительный путь изучения байесовской статистики! Нанами Конно предстоит использовать байесовскую статистику в своей работе - с этой целью она записывается на университетский курс. Вместе со своим однокурсником Ямабуки она узнает, чем байесовская статистика отличается от традиционной, как в ней понимается вероятность, что такое функция правдоподобия и как формулируется теорема Байеса. В заключительных главах рассматриваются методы Монте-Карло для марковских цепей. Вниманию читателя предлагается множество практических задач с подробным объяснением решений. Манга будет полезна студентам, программистам и всем, кто интересуется математическим анализом и расчётом вероятности событий.

Название: Anisotropy Across Fields and Scales
Автор: Özarslan E., Schultz T., Zhang E., Fuster A.
Издательство:Springer
Год: 2021
Формат: PDF
Страниц:290
Размер: 10,7 МБ
Язык: English

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain.

Название: Principles of Probability Theory and its Applications
Автор: Eyvazian M., Mehrpour M.R.
Издательство:Independently published
Год:2022
Формат:PDF
Страниц:548
Размер: 10,4 МБ
Язык: English

Probability theory is a branch of mathematics that investigates the probabilities associated with a random phenomenon. A random phenomenon can have several outcomes. Probability theory describes the chance of occurrence of a particular outcome by using certain formal concepts.

Название: Synergies in Analysis, Discrete Mathematics, Soft Computing and Modelling
Автор: P.V. Subrahmanyam, V. Antony Vijesh, Balasubramaniam Jayaram, Prakash Veeraraghavan
Издательство: Springer
Серия: Forum for Interdisciplinary Mathematics
Год: 2023
Страниц: 225
Язык: английский
Формат: pdf (true), epub
Размер: 35.3 MB

In real-life situations, we come across problems that comprise imprecise or uncertain, simple or complex information that needs to be analyzed for various requirements. To tackle this situation, Zadeh in 1965 formulated the concept of a fuzzy set, which in an imprecise environment that captured the inexactness present in a system. Later, Zadeh elucidated the concept of linguistic variables to handle situations that involved less preciseness in humanistic systems. This was further studied by several researchers using appropriate quantification of fuzziness on kinds of fuzzy numbers. To process and analyze the features connected with entities in such a scenario, fuzzy information systems were studied in the literature.