Angel Cobo - Böcker

A unique, applied approach to problem solving in linear algebra Departing from the standard methods of analysis, this unique book presents methodologies and algorithms based on the concept of orthogonality and demonstrates their application to both standard and novel problems in linear algebra. Covering basic theory of linear systems, linear inequalities, and linear programming, it focuses on elegant, computationally simple solutions to real-world physical, economic, and engineering problems. The authors clearly explain the reasons behind the analysis of different structures and concepts and use numerous illustrative examples to correlate the mathematical models to the reality they represent. Readers are given precise guidelines for:* Checking the equivalence of two systems* Solving a system in certain selected variables* Modifying systems of equations* Solving linear systems of inequalities* Using the new exterior point method* Modifying a linear programming problem With few prerequisites, but with plenty of figures and tables, end-of-chapter exercises as well as Java and Mathematica programs available from the authors' Web site, this is an invaluable text/reference for mathematicians, engineers, applied scientists, and graduate students in mathematics.

This book introduces 'functional networks', a novel neural-based paradigm, and shows that functional network architectures can be efficiently applied to solve many interesting practical problems. Included is an introduction to neural networks, a description of functional networks, examples of applications, and computer programs in Mathematica and Java languages implementing the various algorithms and methodologies. Special emphasis is given to applications in several areas such as: Box-Jenkins AR(p), MA(q), ARMA(p,q), and ARIMA (p,d,q) models with application to real-life economic problems such as the consumer price index, electric power consumption and international airlines' passenger data. Random time series and chaotic series are considered in relation to the Henon, Lozi, Holmes and Burger maps, as well as the problems of noise reduction and information masking. Learning differential equations from data and deriving the corresponding equivalent difference and functional equations. Examples of a mass supported by two springs and a viscous damper or dashpot, and a loaded beam, are used to illustrate the concepts.The problem of obtaining the most general family of implicit, explicit and parametric surfaces as used in Computer Aided Design (CAD). Applications of functional networks to obtain general nonlinear regression models are given and compared with standard techniques. Functional Networks with Applications: A Neural-Based Paradigm will be of interest to individuals who work in computer science, physics, engineering, applied mathematics, statistics, economics, and other neural networks and data analysis related fields.

Artificial neural networks have been recognized as a powerful tool to learn and reproduce systems in various fields of applications. Neural net­ works are inspired by the brain behavior and consist of one or several layers of neurons, or computing units, connected by links. Each artificial neuron receives an input value from the input layer or the neurons in the previ­ ous layer. Then it computes a scalar output from a linear combination of the received inputs using a given scalar function (the activation function), which is assumed the same for all neurons. One of the main properties of neural networks is their ability to learn from data. There are two types of learning: structural and parametric. Structural learning consists of learning the topology of the network, that is, the number of layers, the number of neurons in each layer, and what neurons are connected. This process is done by trial and error until a good fit to the data is obtained. Parametric learning consists of learning the weight values for a given topology of the network. Since the neural functions are given, this learning process is achieved by estimating the connection weights based on the given information. To this aim, an error function is minimized using several well known learning methods, such as the backpropagation algorithm. Unfortunately, for these methods: (a) The function resulting from the learning process has no physical or engineering interpretation. Thus, neural networks are seen as black boxes.

The book Soft Computing for Business Intelligence is the remarkable output of a program based on the idea of joint trans-disciplinary research as supported by the Eureka Iberoamerica Network and the University of Oldenburg.It contains twenty-seven papers allocated to three sections: Soft Computing, Business Intelligence and Knowledge Discovery, and Knowledge Management and Decision Making. Although the contents touch different domains they are similar in so far as they follow the BI principle “Observation and Analysis” while keeping a practical oriented theoretical eye on sound methodologies, like Fuzzy Logic, Compensatory Fuzzy Logic (CFL), Rough Sets and other soft computing elements.The book tears down the traditional focus on business, and extends Business Intelligence techniques in an impressive way to a broad range of fields like medicine, environment, wind farming, social collaboration and interaction, car sharing and sustainability.