Researchers in the natural sciences are faced with problems that require a novel approach to improve the quality of forecasts of processes that are sensitive to environmental conditions. Nonlinearity of a system may significantly complicate the predictability of future states: a small variation of parameters can dramatically change the dynamics, while sensitive dependence of the initial state may severely limit the predictability horizon. Uncertainties also play a role. This volume addresses such problems by using tools from chaos theory and systems theory, adapted for the analysis of problems in the environmental sciences. Sensitive dependence on the initial state (chaos) and the parameters are analyzed using methods such as Lyapunov exponents and Monte Carlo simulation. Uncertainty in the structure and the values of parameters of a model is studied in relation to processes that depend on the environmental conditions. These methods also apply to biology and economics. For research workers at universities and (semi)governmental institutes for the environment, agriculture, ecology, meteorology and water management, and theoretical economists.

Resilience has emerged as a recurrent notion to explain how territorial socio-economic systems adapt successfully (or not) to negative events. In this book, the authors use resilience as a bridging notion to connect different types of theoretical and empirical approaches to help understand the impacts of economic turbulence at the system and actor levels. The book provides a unique overview of the financial crisis and the important dimension of innovation dynamics for regional resilience. It also offers an engaging debate as to how regional resilience can be improved and explores the social aspects of vulnerability, resilience and innovation.

This book argues that complexity theory offers new departures for (spatial-) economic modelling. It offers a broad overview of recent advances in non-linear dynamics (catastrophe theory, chaos theory, evolutionary theory and so forth) and illustrates the relevance of this new paradigm on the basis of several illustrations in the area of space-economy. The empirical limitations - inherent in the use of non-linear dynamic systems approaches - are also addressed. Next, the application potential of biocomputing (in particular, neural networks and evolutionary algorithms) is stressed, while various empirical model results are presented. The book concludes with an agenda for further research.

In the past decades several researchers have developed statistical models for the prediction of corporate bankruptcy, e. g. Altman (1968) and Bilderbeek (1983). A model for predicting corporate bankruptcy aims to describe the relation between bankruptcy and a number of explanatory financial ratios. These ratios can be calculated from the information contained in a company's annual report. The is to obtain a method for timely prediction of bankruptcy, a so ultimate purpose called "early warning" system. More recently, this subject has attracted the attention of researchers in the area of machine learning, e. g. Shaw and Gentry (1990), Fletcher and Goss (1993), and Tam and Kiang (1992). This research is usually directed at the comparison of machine learning methods, such as induction of classification trees and neural networks, with the "standard" statistical methods of linear discriminant analysis and logistic regression. In earlier research, Feelders et al. (1994) performed a similar comparative analysis. The methods used were linear discriminant analysis, decision trees and neural networks. We used a data set which contained 139 annual reports of Dutch industrial and trading companies. The experiments showed that the estimated prediction error of both the decision tree and neural network were below the estimated error of the linear discriminant. Thus it seems that we can gain by replacing the "traditionally" used linear discriminant by a more flexible classification method to predict corporate bankruptcy. The data set used in these experiments was very small however.

Policy-makers and the public, it has famously been said, are more interested in the possibility of non-linear dislocations and surprises in the behaviour of the environment than in smooth extrapolations of current trends. The International Task Force in Forecasting Environmental Change (1993-1998) dedicated its work to developing procedures of model building capable of addressing our palpable concerns for substantial change in the future. This volume discusses the immense challenges that such structural change presents - that the behaviour of the environment may become radically different from that observed in the past - and investigates the potentially profound implications for model development. Drawing upon case histories from the Great Lakes, acidic atmospheric deposition and, among others, the urban ozone problem, this discourse responds to a new agenda of questions. For example: "What system of 'radar' might we design to detect threats to the environment lying just beyond the 'horizon'?" and "Are the seeds of structural change identifiable within the record of the recent past?" Meticulously researched by leading environmental modellers, this milestone volume engages vigorously with its subject and offers an animated account of how models can begin to take into consideration the significant threats and uncertainties posed by structural change.