Part I : NZ – German School of Computational Intelligence at KES2004 -- Basics of Engineering The Intelligent Hybrid Systems - Not Industrial Applications Only -- Basics of Machine Learning by Support Vector Machines -- Supporting Deep Learning in an Open-ended Domain -- Data Driven Fuzzy Modelling with Neural Networks -- Hybrid Computational Intelligence Systems for Real World Applications -…
Topology and Calculus -- Limits and Topology -- Differentiability -- Inverse and Implicit Functions -- Integration -- The Fundamental Theorem of Calculus and Fubini’s Theorem -- Vector Fields -- Fixpoints -- Main Theorem of ODEs -- Third Advanced Topic -- Selected Higher Subjects -- Categories -- Splines -- Fourier Theory -- Wavelets -- Fractals -- Neural Networks -- Probability Theory -- Lam…
Uncertainty and Surprise: An Introduction -- Understanding Social and Economic Systems as Evolutionary Complex Systems -- Managing the Unexpected -- Surprises in Half of a Century -- An Integrated View of Uncertainty and Surprise -- Fundamental 'Uncertainty' in Science -- The Complementary Nature of Coordination Dynamics: Self-Organization and the Creation of Information -- The tyranny of Many …
Equations with One Dependent Function -- Systems of Equations -- Method of the Degenerate Hodograph -- Method of Differential Constraints -- Invariant and Partially Invariant Solutions -- Symmetries of Equations with Nonlocal Operators -- Symbolic Computer Calculations.Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Each so…
Basic quantities and definitions -- The Boltzmann equation and its properties -- The Chapman-Enskog method -- Moment equations -- Grad’s moment method -- Regularization of Grad equations -- Order of magnitude approach -- Macroscopic transport equations for rarefied gas flows -- Stability and dispersion -- Shock structures -- Boundary value problems.The well known transport laws of Navier-Stok…
Hybrid Estimation at a Glance -- Probabilistic Hybrid Automata -- Hybrid Estimation -- Case Studies -- Conclusion.This monograph provides a tool-set for hybrid estimation that can successfully monitor the behavior of complex artifacts with a large number of possible operational and failure modes such as production plants, automotive or aeronautic systems, and autonomous robots. For this purpose…
From Genetic Variation to Probabilistic Modeling -- Probabilistic Model-Building Genetic Algorithms -- Bayesian Optimization Algorithm -- Scalability Analysis -- The Challenge of Hierarchical Difficulty -- Hierarchical Bayesian Optimization Algorithm -- Hierarchical BOA in the Real World.This book provides a framework for the design of competent optimization techniques by combining advanced evo…
Introduction to Fuzzy Sets and Fuzzy Logic -- Algebras with Fuzzy Equalities -- Fuzzy Equational Logic -- Fuzzy Horn Logic.The book deals with similarity relations defined on a set with functions. The functions are required to map similar elements to similar ones. The book presents basic mathematical properties of structures consisting of similarity-preserving functions and logics for reasoning…
Mathematical Aspects -- Theory and Applications of Fractal Tops -- Splines, Fractal Functions, and Besov and Triebel-Lizorkin Spaces -- Hölderian random functions -- Fractal Stationary Density in Coupled Maps -- Physics -- A Network of Fractal Force Chains and Their Effect in Granular Materials under Compression -- Percolation and permeability of three dimensional fracture networks with a powe…
Section 1 – Rule Discovery. Population Dynamics of Genetic Algorithms. Approximating Value Functions in Classifier Systems. Two Simple Learning Classifier Systems. Computational Complexity of the XCS Classifier System. An Analysis of Continuous-Valued Representations for Learning Classifier Systems -- Section 2 – Credit Assignment. Reinforcement Learning: a Brief Overview. A Mathematical Fr…