This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

Regular and Chaotic Dynamics

Dynamical systems: stability, symbolic dynamics and chaos

The Blackwell Guide to the Philosophy of Science

We develop a utilitarian framework to assess different decision rules for the European Council of Ministers. The proposals to be decided on are conceptualized as utility vectors and a probability distribution is assumed over the utilities. We first show what decision rules yield the highest expected utilities for different means of the probability distribution. For proposals with high mean utility, simple benchmark rules (such as majority voting with proportional weights) tend to outperform rules that have been proposed in the political arena. For proposals with low mean utility, it is the other way round. We then compare the expected utilities for smaller and larger countries and look for Pareto-dominance relations. Finally, we provide an extension of the model, discuss its restrictions, and compare our approach with assessments of decision rules that are based on the Penrose measure of voting power.

A Utilitarian Assessment of Alternative Decision Rules in the Council of Ministers

What Functions Explain: Having a Good

The new method of a gap recovery in symbol sequences is presented. A covering is combined from the suitable reasonably short strings of the parts of a sequence available for an observation. Two criteria are introduced to choose the best covering. It must yield the maximum of entropy of a frequency dictionary developed over the sequence obtained due to the recovery, if an overlapping combined from the copies of strings from the available parts of the sequence exists. The second criterion identifies the best covering in case when one has to use any string to cover the gap; here the best covering must yield the minimum of specific entropy of the frequency dictionary developed over the available parts of the sequence against that one developed over the entire sequence obtained due to the recovery. Kirdin kinetic machine that is the ideal fine-grained structureless computer has been used to resolve the problem of the reconstruction of a gap in symbol sequence.

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Data loss reparation due to indeterminate fine-grained parallel computation

The new method of a gap recovery in symbol sequences is presented. A covering is combined from the suitable reasonably short strings of the parts of a sequence available for observation. Two criteria are introduced to choose the best covering. It must yield the maximum of entropy of a frequency dictionary developed over the sequence obtained due to the recovery, if an overlapping combined from the copies of strings from the available parts of the sequence exists. The second criterion identifies the best covering in case when one has to use any string to cover the gap; here the best covering must yield the minimum of specific entropy of the frequency dictionary developed over the available parts of the sequence against the one developed over the entire sequence obtained due to the recovery. Kirdin kinetic machine which is the ideal fine-grained structureless computer has been used to resolve the problem of the reconstruction of a gap in symbol sequence.

Yuri V. Kondratenko

Papers

Data loss reparation due to indeterminate fine-grained parallel computation

Entropy Based Approach to Data Loss Reparation Through the Indeterminate Fine-Grained Parallel Computation