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Humanity's most basic intellectual quest to decipher nature and master it has led to numerous efforts to build machines that simulate the world or communi­ cate with it [Bus70, Tur36, MP43, Sha48, vN56, Sha41, Rub89, NK91, Nyc92]. The computational power and dynamic behavior of such machines is a central question for mathematicians, computer scientists, and occasionally, physicists. Our interest is in computers called artificial neural networks. In their most general framework, neural networks consist of assemblies of simple processors, or'neurons,'each of which computes a scalar activation function of its input. This activation function is nonlinear, and is typically a monotonic function with bounded range, much like neural responses to input stimuli. The scalar value produced by a neuron affects other neurons, which then calculate a new scalar value of their own. This describes the dynamical behavior of parallel updates. Some of the signals originate from outside the network and act as inputs to the system, while other signals are communicated back to the environment and are thus used to encode the end result of the computation.

The Group Method of Data Handling (GMDH) is a typical inductive modeling method that is built on principles of self-organization for modeling complex systems. However, it is known to often under-perform on non-parametric regression tasks, while time series modeling GMDH exhibits a tendency to find very complex polynomials that cannot model well future, unseen oscillations of the series. In order to alleviate these problems, GMDH has been recently hybridized with some computational intelligence (CI) techniques resulting in more robust and flexible hybrid intelligent systems for solving complex, real-world problems. The central theme of this book is to present in a very clear manner hybrids of some computational intelligence techniques and GMDH approach. The hybrids discussed in the book include GP-GMDH (Genetic Programming-GMDH) algorithm, GA-GMDH (Genetic Algorithm-GMDH) algorithm, DE-GMDH (Differential Evolution-GMDH) algorithm, and PSO-GMDH (Particle Swarm Optimization) algorithm. Also included is the description of the recently introduced GAME (Group Adaptive Models Evolution algorithm. The hybrid character of models and their self-organizing ability give these hybrid self-organizing modeling systems an advantage over standard data mining models. The modeling and data mining solutions of several real-life problems in the areas of engineering, bioinformatics, finance, and economics are presented in the chapters. The book will benefit amongst others, people who are working in the areas of neural networks, machine learning, artificial intelligence, complex system modeling and analysis, and optimization.

A paradigmatic perspective for modeling and control of physical systems has been used since a long time ago: The input/output approach. Although quite natural for our human experience, this perspective imposes a cause/effect framework to the system under study although such system may not have necessarily such cause/effect structure. Actually, from a general point of view, a system interacts with its environment by exchange of mass and energy which should imply the use of bidirectional arrows in a block diagram rather than using unidirectional ones. Another perspective arose when a new variable showed up in systems and control theory: the state (Kalman). Thus, the input/state/output approach was born. Although the concept of state is cornerstone, qualitative characteristics of a system (stability, controllability and observability) have to be defined in terms of a representation of the system, i.e., such characteristics become representation dependent. In contrast, the relatively new Behavioral Approach for systems and control (Jan C. Willems) deals directly with the solution of the differential equations which represent the system. This set of allowed solutions is referred to as the behavior of the system. Thus, the key is the behavior and not the representation. This fact makes this perspective a representation free approach. This book reviews known topics of the Behavioral Approach and offers new theoretic results with the advantage of including control algorithms implemented numerically in the computer. In addition, issues of numerical analysis are also included. The programs and algorithms are MATLAB based.