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Symmetries of Discrete Systems
In this series of lectures, we review the application of Lie point symmetries, and their generalizations, to the study of difference equations. The...
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Discrete Painlevé Equations: A Review
We present a review of what is current knowledge about discrete Painlevé equations. We start with a historical introduction which explains how the...
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Sato Theory and Transformation Groups. A Unified Approach to Integrable Systems
More than 20 years ago, it was discovered that the solutions of the Kadomtsev-Petviashvili (KP) hierarchy constitute an infinite-dimensional...
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Ultradiscrete Systems (Cellular Automata)
Ultradiscretization is a limiting procedure which allows one to obtain a cellular automaton (CA) from continuous equations. Using this method, we can...
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Time in Science: Reversibility vs. Irreversibility
To discuss properly the question of irreversibility one needs to make a careful distinction between reversibility of the equations of motion and the...
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A. Proof of Thm. 4.34
Abstract not available
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Topological Concepts in Gauge Theories
In these lecture notes, an introduction to topological concepts and methods in studies of gauge field theories is presented. The three paradigms of...
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5 Managing the Unexpected: Complexity as Distributed Sensemaking
In 1998 the Centers for Disease Control (CDC) published a statement of their strategy entitled “Preventing Emerging Infectious Diseases: A Strategy...
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10 An Introduction to the Mathematics and Meaning of Chaos
It is a pleasure for me to be here, both to talk and to listen. I thank Curt Lindberg and the other organizers for this opportunity. It has been a...
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11 The Social Construction of Uncertainty in Healthcare Delivery
We explore the following question: How would healthcare delivery be different if uncertainty were widely recognized, accurately diagnosed, and...
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18 Uncertainty and Surprise: Ideas from the Open Discussion
Approximately one hundred participants met for three days at a conference entitled “Uncertainty and Surprise: Questions on Working with the...
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15 The Fundamental Uncertainty of Business: Real Options
The purpose of this paper is to discuss the manner in which uncertainty is currently evaluated in business, with an emphasis on economic measures. In...
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Forces from Connes’ Geometry
Einstein derived general relativity from Riemannian geometry. Connes extends this derivation to noncommutative geometry and obtains electro–magnetic,...
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Exact solutions of nonlinear partial differential equations by singularity analysis
Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with...
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Hirota bilinear method for nonlinear evolution equations
The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples...
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References
Abstract not available
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Discrete Lagrangian Models
These lectures are devoted to discrete integrable Lagrangian models. A large collection of integrable models is presented in the Lagrangian fashion,...