Topics in Stochastics, Symbolic Dynamics and Neural Networks

摘要

Research was supported in inverse application areas of probability, ergodictheory and dynamical systems (including neural networks). Theorems on rates of learning in unsupervised Neural Networks, relating to the sampling method for available environmental data were obtained. Results on the consistency and effectiveness of estimators for correlation dimension were derived, together with advanced percolation structures useful in mammalian lung development models. Ways of using 'continued fractions' to construct highly mixing stochastic processes were expounded.