Author: Stefano Zambelli Publisher: John Wiley & Sons ISBN: 1118300432 Category : Business & Economics Languages : en Pages : 352
Book Description
Nonlinearity, Complexity and Randomness in Economics presents a variety of papers by leading economists, scientists, and philosophers who focus on different aspects of nonlinearity, complexity and randomness, and their implications for economics. A theme of the book is that economics should be based on algorithmic, computable mathematical foundations. Features an interdisciplinary collection of papers by economists, scientists, and philosophers Presents new approaches to macroeconomic modelling, agent-based modelling, financial markets, and emergent complexity Reveals how economics today must be based on algorithmic, computable mathematical foundations
Author: K. Vela Velupillai Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
In this paper I make an attempt to describe, discuss and extend a few aspects of the rich mathematical tapestry that can be woven with rigorous notions of non-linear dynamics, complexity and randomness, in terms of"algorithmic mathematics. It is a tapestry that I try to weave with economic analysis, economic theory and economic modelling in mind. All three notions - that is, non-linear dynamics, complexity and randomness - have a rich conceptual, modelling or analytic tradition in core areas of economic theory, both at the micro and macro levels. It is the algorithmic foundation I try to provide for them that could be considered the novel contribution in this paper. Once the algorithmic foundations are in place, it is, for example, almost natural to consider the famed difficulties of obtaining closed form solutions for non-linear, complex or random dynamic models in economics almost a trivial vestige of a pre-simulation era in mathematical modelling.
Author: Bernard Chazelle Publisher: Cambridge University Press ISBN: 9780521003575 Category : Computers Languages : en Pages : 500
Book Description
The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal to students and researchers in computer science, operations research, pure and applied mathematics, and engineering.
Author: A. Shen Publisher: American Mathematical Society ISBN: 1470470640 Category : Mathematics Languages : en Pages : 511
Book Description
Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.
Author: Yaneer Bar-yam Publisher: CRC Press ISBN: 0429717598 Category : Mathematics Languages : en Pages : 866
Book Description
This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.
Author: Dimitri Volchenkov Publisher: Springer Nature ISBN: 9811590346 Category : Mathematics Languages : en Pages : 198
Book Description
This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe a complex nexus of dependences in multi-level complex systems and to effectively engineer their important functions. The collection of works devoted to the memory of Professor Valentin Afraimovich introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in physics, machine learning, brain and urban dynamics. The book can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, urban planners, and even musicians (with some mathematical background).
Author: Ashok Sengupta Publisher: Springer Science & Business Media ISBN: 3540317562 Category : Computers Languages : en Pages : 373
Book Description
This book explores non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems, drawing on relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It offers a self-contained theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.
Author: Stefano Zambelli
Author: Stefano Zambelli
Author: Stefano Zambelli
Author: K. Vela Velupillai
Author: Bernard Chazelle
Author: A. Shen
Author: Yaneer Bar-yam
Author: Dimitri Volchenkov
Author: Ashok Sengupta
Author: Norbert Wiener