Functional Networks with Applications - Antonio Gutierrez, Jose

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Résumé :
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. br/ 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. br/ Special emphasis is given to applications in several areas such as: ul liBox-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 H?non, Lozi, Holmes and Burger maps, as well as the problems of noise reduction and information masking. /li liLearning 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. /li liThe problem of obtaining the most general family of implicit, explicit and parametric surfaces as used in Computer Aided Design (CAD). /li liApplications of functional networks to obtain general nonlinear regression models are given and compared with standard techniques./li /ul br/ emFunctional Networks with Applications: A Neural-Based Paradigm/em 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.

Sommaire:
I Neural Networks.- 1 Introduction to Neural Networks.- II Functional Networks.- 2 Introduction to Functional Networks.- 3 Functional Equations.- 4 Some Functional Network Models.- 5 Model Selection.- III Applications.- 6 Applications to Time Series.- 7 Applications to Differential Equations.- 8 Applications to CAD.- 9 Applications to Regression.- IV Computer Programs.- 10 Mathematica Programs.- 11 A Java Applet.- Notation.- References.