The Mathematics Of The Uncertain
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The Mathematics Of The Uncertain
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Author : Eduardo Gil
language : en
Publisher: Springer
Release Date : 2018-02-28
The Mathematics Of The Uncertain written by Eduardo Gil and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-28 with Technology & Engineering categories.
This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlighted twenty years ago, there are several well-known mathematical branches for this purpose, including Mathematics of chance (Probability and Statistics), Mathematics of communication (Information Theory), and Mathematics of imprecision (Fuzzy Sets Theory and others). These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications. The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.
Mathematics Of Uncertainty
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Author : Hans Bandemer
language : en
Publisher: Springer
Release Date : 2008-01-25
Mathematics Of Uncertainty written by Hans Bandemer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-25 with Technology & Engineering categories.
"Mathematics of Uncertainty" provides the basic ideas and foundations of uncertainty, covering the fields of mathematics in which uncertainty, variability, imprecision and fuzziness of data are of importance. This introductory book describes the basic ideas of the mathematical fields of uncertainty from simple interpolation to wavelets, from error propagation to fuzzy sets and neural networks. The book presents the treatment of problems of interpolation and approximation, as well as observation fuzziness which can essentially influence the preciseness and reliability of statements on functional relationships. The notions of randomness and probability are examined as a model for the variability of observation and measurement results. Besides these basic ideas the book also presents methods of qualitative data analysis such as cluster analysis and classification, and of evaluation of functional relationships such as regression analysis and quantitative fuzzy data analysis.
Mathematics Of Uncertainty Modeling In The Analysis Of Engineering And Science Problems
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Author : Chakraverty, S.
language : en
Publisher: IGI Global
Release Date : 2014-01-31
Mathematics Of Uncertainty Modeling In The Analysis Of Engineering And Science Problems written by Chakraverty, S. and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-31 with Mathematics categories.
"This book provides the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications"--Provided by publisher.
Linear Models In The Mathematics Of Uncertainty
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Author : Carol Jones
language : en
Publisher: Springer
Release Date : 2013-02-01
Linear Models In The Mathematics Of Uncertainty written by Carol Jones and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-01 with Technology & Engineering categories.
The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data is difficult to measure and an assumption of randomness and/or statistical validity is questionable. We apply our methods to real world issues in international relations such as nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and failed states. Finally, issues involving deaf and hard of hearing children are explored.
Perspectives On Practice And Meaning In Mathematics And Science Classrooms
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Author : D. Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03-31
Perspectives On Practice And Meaning In Mathematics And Science Classrooms written by D. Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-31 with Education categories.
This is a variegated picture of science and mathematics classrooms that challenges a research tradition that converges on the truth. The reader is surrounded with different images of the classroom and will find his beliefs confirmed or challenged. The book is for educational researchers, research students, and practitioners with an interest in optimizing the effectiveness of classrooms as environments for learning.
Measurement Uncertainty
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Author : Simona Salicone
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-04
Measurement Uncertainty written by Simona Salicone and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-04 with Mathematics categories.
It is widely recognized, by the scienti?c and technical community that m- surements are the bridge between the empiric world and that of the abstract concepts and knowledge. In fact, measurements provide us the quantitative knowledge about things and phenomena. It is also widely recognized that the measurement result is capable of p- viding only incomplete information about the actual value of the measurand, that is, the quantity being measured. Therefore, a measurement result - comes useful, in any practicalsituation, only if a way is de?ned for estimating how incomplete is this information. The more recentdevelopment of measurement science has identi?ed in the uncertainty concept the most suitable way to quantify how incomplete is the information provided by a measurement result. However, the problem of how torepresentameasurementresulttogetherwithitsuncertaintyandpropagate measurementuncertaintyisstillanopentopicinthe?eldofmetrology,despite many contributions that have been published in the literature over the years. Many problems are in fact still unsolved, starting from the identi?cation of the best mathematical approach for representing incomplete knowledge. Currently, measurement uncertainty is treated in a purely probabilistic way, because the Theory of Probability has been considered the only available mathematical theory capable of handling incomplete information. However, this approach has the main drawback of requiring full compensation of any systematic e?ect that a?ects the measurement process. However, especially in many practical application, the identi?cation and compensation of all s- tematic e?ects is not always possible or cost e?ective.
Decisions Uncertainty And The Brain
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Author : Paul W. Glimcher
language : en
Publisher: MIT Press
Release Date : 2004-09-17
Decisions Uncertainty And The Brain written by Paul W. Glimcher and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-17 with Medical categories.
In this provocative book, Paul Glimcher argues that economic theory may provide an alternative to the classical Cartesian model of the brain and behavior. Glimcher argues that Cartesian dualism operates from the false premise that the reflex is able to describe behavior in the real world that animals inhabit. A mathematically rich cognitive theory, he claims, could solve the most difficult problems that any environment could present, eliminating the need for dualism by eliminating the need for a reflex theory. Such a mathematically rigorous description of the neural processes that connect sensation and action, he explains, will have its roots in microeconomic theory. Economic theory allows physiologists to define both the optimal course of action that an animal might select and a mathematical route by which that optimal solution can be derived. Glimcher outlines what an economics-based cognitive model might look like and how one would begin to test it empirically. Along the way, he presents a fascinating history of neuroscience. He also discusses related questions about determinism, free will, and the stochastic nature of complex behavior.
Mathematical Uncertainties And Their Applications
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Author : Illia Danilishyn
language : en
Publisher: Primedia eLaunch LLC
Release Date : 2025-05-30
Mathematical Uncertainties And Their Applications written by Illia Danilishyn and has been published by Primedia eLaunch LLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-30 with Mathematics categories.
The monograph first task: to understand hierarchy of energies in the Universe and the principles of functioning of living energy (living organism, in particular, human, subtle energies), and then using these principles to "construct" artificial living energies (let's call them pseudo-living energies). It is possible to significantly expand the horizons of science, in particular physics, by studying the subtle energies in the Universe. On the basis of mathematical uncertainties, new mathematical structures are formed, allowing us to describe processes and objects that are fundamentally not determined by conventional deterministic methods. Here is considered new mathematical uncertainties. Objective uncertainties in any case can mean manifestations of processes and objects that are fundamentally not determined by conventional deterministic methods. Many energies are indeterminate because they are based on uncertainties from the perspective of traditional science—large concentrations of specific energy in a chaotic state. The foundation of dynamic mathematics lies in working with uncertainties, which makes it possible to manipulate these indeterminate energies using direct-accumulative direct-parallel neural networks. The second task of the monograph is to construct a new mathematical apparatus for neural networks of a fundamentally new type: direct-parallel and direct-accumulative action. We construct models of singularities for singular work with them through neural networks - analogues of the human CNS. Ordinary regular work with them in ordinary science is fundamentally unable to realize their capabilities. Therefore, singular science realized on a neural network - an analogue of the human CNS - will be much more natural. Unfortunately, we do not have funding to perform the necessary experiments and the practical creation of a technical model of such a neural network. There is a need to develop an instrumental mathematical base for new technologies. The task of the work is to create new approaches for this by introducing new concepts and methods. Our mathematics is unusual for a mathematician, because here the fulcrum is the action, and not the result of the action as in classical mathematics. Therefore, our mathematics is adapted not only to obtain results, but also to directly control actions, which will certainly show its benefits on a fundamentally new type of neural networks with directly parallel calculations, for which it was created. Any action has much greater potential than its result. It is time for physicists to begin studying not only the manifestations of living energies, but also the living energies themselves, which are by no means expressed through objectivity and ordinary energies, although they are capable of manifesting themselves through a lower level - objectivity and ordinary energies. We, as mathematicians, offer a new corresponding apparatus for understanding nature and studying living energies. Significance of the article: in a new qualitatively different approach to the study of complex processes through new mathematical, hierarchical, dynamic structures, in particular those processes that are dealt with by Synergetics. The significance of our article is in the formation of the presumptive mathematical structure of subtle energies, this is being done for the first time in science, and the presumptive classification of the mathematical structures of subtle energies for the first time. The experiments of the 2022 Nobel laureates Asle Ahlen, John Clauser, Anton Zeilinger and the experiments in chemistry Nazhipa Valitov eloquently demonstrate that we are right and that these studies are necessary. Be that as it may, we created classes of new mathematical structures, new mathematical singularities, i.e., made a contribution to the development of mathematics.
The Geometry Of Uncertainty
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Author : Fabio Cuzzolin
language : en
Publisher: Springer Nature
Release Date : 2020-12-17
The Geometry Of Uncertainty written by Fabio Cuzzolin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Computers categories.
The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.
Elements For A Theory Of Decision In Uncertainty
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Author : Jaime Gil-Aluja
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elements For A Theory Of Decision In Uncertainty written by Jaime Gil-Aluja and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Business & Economics categories.
Decisions in uncertainty Scientific reaction to change During latter decades, the basic elements that have traditionally made up the society in wh ich economic activity develops, have been submitted to the effect of multiple aggressions as a consequence of the outcome of events motivated by the nature itself of the human being, always seeking a level of happiness that is never reached. In a very brief manner we are accustomed to mention these by using words such as revolution, profound changes, convulsions . . . . , the results of which are manifest through non-linear reactions that lead to a future charged with uncertainty. To get to know, explain and treat this new world constitutes one of the many objectives of those who desire a society in the service of man, and for those who aspire to the fact of the concept of mutuality transcending the use less limits of the printed word. But for this it will be necessary to overcome a whole realm of obstacles placed in the way by those comfortably embedded in old principles, decrepit ideas and are not willing to open the windows of their mind to receive the fresh air of a new era.