Eugene Fink – författare

Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion generalizes standard convexity and several types of nontraditional convexity. We explore the properties of this generalized convexity in multidimensional Euclidean space, describes restricted-orientation analogs of lines, hyperplanes, flats, and halfspaces, and identify major properties of standard convex sets that also hold for restricted-orientation convexity. We then introduce the notion of strong restricted-orientation convexity, which is an alternative generalization of convexity, and show that its properties are also similar to those of standard convexity.

Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion generalizes standard convexity and several types of nontraditional convexity. We explore the properties of this generalized convexity in multidimensional Euclidean space, describes restricted-orientation analogs of lines, hyperplanes, flats, and halfspaces, and identify major properties of standard convex sets that also hold for restricted-orientation convexity. We then introduce the notion of strong restricted-orientation convexity, which is an alternative generalization of convexity, and show that its properties are also similar to those of standard convexity.

The performance of all reasoning systems crucially depends on problem representation: the same problem may be easy or difficult, depending on the way we describe it. Researchers in psychology and artificial intelligence have accumulated much evidence on the importance of appropriate representations for both human and artificial intelligence systems. The book proposes techniques for automatic improvement of problem representation, which are based on integration of multiple learning and problem-solving algorithms. It gives theoretical foundations of the proposed techniques, describes their implementation, and discusses empirical evidence of their utility.

The purpose of our research is to enhance the efficiency of AI problem solvers by automating representation changes. We have developed a system that improves the description of input problems and selects an appropriate search algorithm for each given problem. Motivation. Researchers have accumulated much evidence on the impor­ tance of appropriate representations for the efficiency of AI systems. The same problem may be easy or difficult, depending on the way we describe it and on the search algorithm we use. Previous work on the automatic im­ provement of problem descriptions has mostly been limited to the design of individual learning algorithms. The user has traditionally been responsible for the choice of algorithms appropriate for a given problem. We present a system that integrates multiple description-changing and problem-solving algorithms. The purpose of the reported work is to formalize the concept of representation and to confirm the following hypothesis: An effective representation-changing system can be built from three parts: • a library of problem-solving algorithms; • a library of algorithms that improve problem descriptions; • a control module that selects algorithms for each given problem.