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Dynamics of the Box-Ball System with Random Initial Conditions via Pitman’s Transformation
The box-ball system (BBS), introduced by Takahashi and Satsuma in 1990, is a cellular automaton that exhibits solitonic behaviour. In
this article, we study the BBS when started from a random two-sided infinite particle configuration. For such a model, Ferrari et al.
recently showed the invariance in distribution of Bernoulli product measures with density strictly less than
eBook
Ergodicity of Markov Processes via Nonstandard Analysis
The Markov chain ergodic theorem is well-understood if either the time-line or the state space is discrete. However, there does not
exist a very clear result for general state space continuous-time Markov processes. Using methods from mathematical logic and
nonstandard analysis, we introduce a class of hyperfinite Markov processes-namely, general Markov processes which behave like finite
state space discrete-time Markov processes. We show that, under moderate conditions, the transition probability of hyperfinite Markov
processes align with the transition probability of standard Markov processes. The Markov chain ergodic theorem for hyperfinite Markov
processes will then imply the Markov chain ergodic theorem for general state space continuous-time Markov processes.
eBook
Body Composition in Sport, Exercise and Health
The analysis of body composition (fat, bone and muscle) is an important process throughout the biomedical sciences. This is the first book to offer a clear and detailed introduction to the key methods and techniques in body composition analysis and to explain the importance of body composition data in the context of sport, exercise and health.
With contributions from some of the world's leading body composition specialists, the book goes further than any other in demonstrating the practical and applied value of body composition analysis in areas such as performance sport and weight control in clinical populations. The book pays particular attention to the important concept of change in body composition, and includes discussion of ethical issues in the collection, interpretation and presentation of data, and considerations when working with special populations.
Bridging the gap between research methods and practical application, this book is important reading for advanced students and practitioners working in sport and exercise science, health science, anatomy, nutrition, physical therapy or ergonomics.
eBook
A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria
We analyze a class of nonlinear partial differential equations (PDEs) defined on
eBook
Stability of heat kernel estimates for symmetric non-local Dirichlet forms
In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition,
and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent
characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In
particular, we establish stability of heat kernel estimates for
eBook