Measuring and Understanding Complex Phenomena: Indicators and Their Analysis in Different Scientific Fields, Bruggemann Rainer, Carlsen Lars, Beycan Tugce
Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.
The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.
Автор: Dineen Sean Название: Analysis: A Gateway to Understanding Mathematics ISBN: 9811208751 ISBN-13(EAN): 9789811208751 Издательство: World Scientific Publishing Рейтинг: Цена: 10483.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book shows that it is possible to provide a fully rigorous treatment of calculus for those planning a career in an area that uses mathematics regularly (e.g., statistics, mathematics, economics, finance, engineering, etc.). It reveals to students on the ways to approach and understand mathematics. It covers efficiently and rigorously the differential and integral calculus, and its foundations in mathematical analysis. It also aims at a comprehensive, efficient, and rigorous treatment by introducing all the concepts succinctly. Experience has shown that this approach, which treats understanding on par with technical ability, has long term benefits for students.
Описание: Offers information for researchers in complex analysis, differential geometry and mathematical physics. This book contains various developments and trends in the studies on constructions of holomorphic Cliffordian functions; and, the swelling constructions of minimal surfaces with higher genus in flat tori.
This volume contains papers by the main participants in the meeting of the 6th International Colloquium on Differential Geometry and its Related Fields (ICDG2018).
The volume consists of papers devoted to the study of recent topics in geometric structures on manifolds -- which are related to complex analysis, symmetric spaces and surface theory -- and also in discrete mathematics.
Thus, it presents a broad overview of differential geometry and provides up-to-date information to researchers and young scientists in this field, and also to those working in the wide spectrum of mathematics.
Автор: Skillicorn Название: Understanding Complex Datasets ISBN: 1584888326 ISBN-13(EAN): 9781584888321 Издательство: Taylor&Francis Рейтинг: Цена: 13779.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Focusing on data mining mechanics and applications, this book explores some of the most common matrix decompositions, including singular value, semidiscrete, independent component analysis, non-negative matrix factorization, and tensors. It also discusses several important theoretical and algorithmic problems of matrix decompositions.
Описание: Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music. remove
Описание: This volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014).
Описание: 'This book is epic in the sense that it covers so much ground that one is left somewhat dizzy. And yet, it all makes sense once one realizes how it is possible for something that is complex, for example a flower, to evolve via natural processes from humble beginnings. After all, starting with single-cell creatures such as amoebae we follow a complicated but rational evolutionary path to arrive at the most complex organizations that we know of - ourselves. So, if you follow the logic of this book, starting with the basic concepts of thermodynamics, symmetry, quantum theory and so on, you will be treated to many many thought-provoking ideas, which will likely challenge your own preconceptions and leave you thirsting for more.' (From the Foreword by Prof. A. M. Glazer, University of Oxford) Science is all about trying to understand natural phenomena under the strict discipline imposed by the celebrated scientific method. Practically all the systems we encounter in Nature are dynamical systems, meaning that they evolve with time. Among them there are the 'simple' or 'simplifiable' systems, which can be handled by traditional, reductionistic science; and then there are 'complex' systems, for which nonreductionistic approaches have to be attempted for understanding their evolution. In this book the author makes a case that a good way to understand a large number of natural phenomena, both simple and complex, is to focus on their self-organization and emergence aspects. Self-organization and emergence are rampant in Nature and, given enough time, their cumulative effects can be so mind-boggling that many people have great difficulty believing that there is no designer involved in the emergence of all the structure and order we see around us. But it is really quite simple to understand how and why we get so much 'order for free'. It all happens because, as ordained by the infallible second law of thermodynamics, all 'thermodynamically open' systems in our ever-expanding and cooling (and therefore gradient-creating) universe constantly tend to move towards equilibrium and stability, often ending up in ordered configurations. In other words, order emerges because Nature tends to find efficient ways to annul gradients of all types. This book will help you acquire a good understanding of the essential features of many natural phenomena, via the complexity-science route. It has four parts: (1) Complexity Basics; (2) Pre-Human Evolution of Complexity; (3) Humans and the Evolution of Complexity; and (4) Appendices. The author gives centrestage to the second law of thermodynamics for 'open' systems, which he describes as 'the mother of all organizing principles'. He also highlights a somewhat unconventional statement of this law: 'Nature abhors gradients'. The book is written at two levels, one of which hardly uses any mathematical equations; the mathematical treatment of some relevant topics has been pushed to the last part of the book, in the form of ten appendices. Therefore the book should be accessible to a large readership. It is a general-science book written in a reader-friendly language, but without any dumbing down of the narrative.
Описание: This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume I — covers everything that a researcher may want to know about memristors but is too afraid to ask.Volume II — shows that memristors can be either volatile or non-volatile, and effectively proving that synapses are non-volatile memristors, while action potentials are generated by locally-active memristors.Volume III — presents an overview of the fascinating phenomenon called chaos, while immersing the audience with the sights and sound of chaos from the Chua Circuit, invented in 1984 by Leon Chua, and has now become the standard textbook example of chaos exhibited by a real nonlinear electronic circuit, and not by computer simulations.Volume IV — surprises the audience with a new law of nature — dubbed the local activity principle, as discovered and proved mathematically in 1996 by Leon Chua. In particular, a Corollary of Chua's local activity theorem, dubbed the edge of chaos, is shown via insightful examples to be the originator of most complex phenomena, including intelligence, creativity, and deep learning. The edge of chaos is Mother Nature's tool for overcoming the tyranny of the second law of thermodynamics by providing an escape hatch for entropy to decrease over time. Indeed, the local activity principle which is profusely illustrated in the final volume, is widely recognized as a new law of thermodynamics, and is identified as the sine qua non of all complex phenomena, including life itself.Exclusive Access to the accompanying Video and Audio materials comes with the purchase of this book.
Steadily growing applications of game theory in modern science (including psychology, biology and economics) require sources to provide rapid access in both classical tools and recent developments to readers with diverse backgrounds. This book on game theory, its applications and mathematical methods, is written with this objective in mind.
The book gives a concise but wide-ranging introduction to games including older (pre-game theory) party games and more recent topics like elections and evolutionary games and is generously spiced with excursions into philosophy, history, literature and politics. A distinguished feature is the clear separation of the text into two parts: elementary and advanced, which makes the book ideal for study at various levels.
Part I displays basic ideas using no more than four arithmetic operations and requiring from the reader only some inclination to logical thinking. It can be used in a university degree course without any (or minimal) prerequisite in mathematics (say, in economics, business, systems biology), as well as for self-study by school teachers, social and natural scientists, businessmen or laymen. Part II is a rapid introduction to the mathematical methods of game theory, suitable for a mathematics degree course of various levels.
To stimulate the mathematical and scientific imagination, graphics by a world-renowned mathematician and mathematics imaging artist, A T Fomenko, are used. The carefully selected works of this artist fit remarkably into the many ideas expressed in the book.
This new edition has been updated and enlarged. In particular, two new chapters were added on statistical limit of games with many agents and on quantum games, reflecting possibly the two most stunning trends in the game theory of the 21st century.
Описание: In medical and health care the scientific method is little used, and statistical software programs are experienced as black box programs producing lots of p-values, but little answers to scientific questions. The pocket calculator analyses appears to be, particularly, appreciated, because they enable medical and health professionals and students for the first time to understand the scientific methods of statistical reasoning and hypothesis testing. So much so, that it can start something like a new dimension in their professional world. In addition, a number of statistical methods like power calculations and required sample size calculations can be performed more easily on a pocket calculator, than using a software program. Also, there are some specific advantages of the pocket calculator method. You better understand what you are doing. The pocket calculator works faster, because far less steps have to be taken, averages can be used. The current nonmathematical book is complementary to the nonmathematical "SPSS for Starters and 2nd Levelers" (Springer Heidelberg Germany 2015, from the same authors), and can very well be used as its daily companion.
