Variational Inequalities and Network Equilibrium Problems

Variational Inequalities and Network Equilibrium Problems
Author: F. Giannessi
Publisher: Springer Science & Business Media
Total Pages: 304
Release: 2013-06-29
Genre: Social Science
ISBN: 1489913580

This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

Uncertainty in Artificial Intelligence

Uncertainty in Artificial Intelligence
Author: Laveen N. Kanal
Publisher: North Holland
Total Pages: 509
Release: 1986
Genre: Artificial intelligence
ISBN: 9780444700582

Hardbound. How to deal with uncertainty is a subject of much controversy in Artificial Intelligence. This volume brings together a wide range of perspectives on uncertainty, many of the contributors being the principal proponents in the controversy.Some of the notable issues which emerge from these papers revolve around an interval-based calculus of uncertainty, the Dempster-Shafer Theory, and probability as the best numeric model for uncertainty. There remain strong dissenting opinions not only about probability but even about the utility of any numeric method in this context.

Introduction to Soergel Bimodules

Introduction to Soergel Bimodules
Author: Ben Elias
Publisher: Springer Nature
Total Pages: 588
Release: 2020-09-26
Genre: Mathematics
ISBN: 3030488268

This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are fairly elementary objects and explicit calculations are possible. On the other, they have deep connections to Lie theory and geometry. Taking these two aspects together, they offer a wonderful primer on geometric representation theory. In this book the reader is introduced to the theory through a series of lectures, which range from the basics, all the way to the latest frontiers of research. This book serves both as an introduction and as a reference guide to the theory of Soergel bimodules. Thus it is intended for anyone who wants to learn about this exciting field, from graduate students to experienced researchers.

Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval

Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval
Author: David Ruelle
Publisher: American Mathematical Soc.
Total Pages: 76
Release: 1994
Genre: Mathematics
ISBN: 9780821836019

With a general introduction to the subject, this title presents a detailed study of the zeta functions associated with piecewise monotone maps of the interval $ 0,1]$. In particular, it gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of $\zeta (z)$ and the eigenvalues of the transfer operator.

The Alignment Problem: Machine Learning and Human Values

The Alignment Problem: Machine Learning and Human Values
Author: Brian Christian
Publisher: W. W. Norton & Company
Total Pages: 459
Release: 2020-10-06
Genre: Science
ISBN: 039363583X

A jaw-dropping exploration of everything that goes wrong when we build AI systems and the movement to fix them. Today’s “machine-learning” systems, trained by data, are so effective that we’ve invited them to see and hear for us—and to make decisions on our behalf. But alarm bells are ringing. Recent years have seen an eruption of concern as the field of machine learning advances. When the systems we attempt to teach will not, in the end, do what we want or what we expect, ethical and potentially existential risks emerge. Researchers call this the alignment problem. Systems cull résumés until, years later, we discover that they have inherent gender biases. Algorithms decide bail and parole—and appear to assess Black and White defendants differently. We can no longer assume that our mortgage application, or even our medical tests, will be seen by human eyes. And as autonomous vehicles share our streets, we are increasingly putting our lives in their hands. The mathematical and computational models driving these changes range in complexity from something that can fit on a spreadsheet to a complex system that might credibly be called “artificial intelligence.” They are steadily replacing both human judgment and explicitly programmed software. In best-selling author Brian Christian’s riveting account, we meet the alignment problem’s “first-responders,” and learn their ambitious plan to solve it before our hands are completely off the wheel. In a masterful blend of history and on-the ground reporting, Christian traces the explosive growth in the field of machine learning and surveys its current, sprawling frontier. Readers encounter a discipline finding its legs amid exhilarating and sometimes terrifying progress. Whether they—and we—succeed or fail in solving the alignment problem will be a defining human story. The Alignment Problem offers an unflinching reckoning with humanity’s biases and blind spots, our own unstated assumptions and often contradictory goals. A dazzlingly interdisciplinary work, it takes a hard look not only at our technology but at our culture—and finds a story by turns harrowing and hopeful.

Introductory Lectures on Convex Optimization

Introductory Lectures on Convex Optimization
Author: Y. Nesterov
Publisher: Springer Science & Business Media
Total Pages: 253
Release: 2013-12-01
Genre: Mathematics
ISBN: 144198853X

It was in the middle of the 1980s, when the seminal paper by Kar markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear op timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical pre diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direc tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly develop ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].

Complex Variables

Complex Variables
Author: Joseph L. Taylor
Publisher: American Mathematical Soc.
Total Pages: 319
Release: 2011
Genre: Mathematics
ISBN: 0821869019

"The text covers a broad spectrum between basic and advanced complex variables on the one hand and between theoretical and applied or computational material on the other hand. With careful selection of the emphasis put on the various sections, examples, and exercises, the book can be used in a one- or two-semester course for undergraduate mathematics majors, a one-semester course for engineering or physics majors, or a one-semester course for first-year mathematics graduate students. It has been tested in all three settings at the University of Utah. The exposition is clear, concise, and lively. There is a clean and modern approach to Cauchy's theorems and Taylor series expansions, with rigorous proofs but no long and tedious arguments. This is followed by the rich harvest of easy consequences of the existence of power series expansions. Through the central portion of the text, there is a careful and extensive treatment of residue theory and its application to computation of integrals, conformal mapping and its applications to applied problems, analytic continuation, and the proofs of the Picard theorems. Chapter 8 covers material on infinite products and zeroes of entire functions. This leads to the final chapter which is devoted to the Riemann zeta function, the Riemann Hypothesis, and a proof of the Prime Number Theorem." -- Publisher.

Function Theory of One Complex Variable

Function Theory of One Complex Variable
Author: Robert Everist Greene
Publisher: American Mathematical Soc.
Total Pages: 536
Release: 2006
Genre: Mathematics
ISBN: 9780821839621

Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

Multiple Criteria Decision Aiding

Multiple Criteria Decision Aiding
Author: Constantin Zopounidis
Publisher:
Total Pages: 0
Release: 2012
Genre: Decision making
ISBN: 9781621007531

The changes in the technological and business environment have complicated the nature of the decision-making process in real-world problems, thus motivating the development of new operations research (OR) methodologies. The traditional OR context is usually based on a single objective approach using profit (cost) maximisation (minimisation) criteria. However, it is now widely acknowledged that such an approach overlooks additional factors which are also highly relevant in a decision-making context. This book presents the recent advances to the theory of multicriteria analysis, covering all its major aspects in a unique edited volume.