This article introduces finitist set theory (FST) and shows how it can be applied in modeling finite nested structures. Mereology is a straightforward foundation for transitive chains of part-whole relations between individuals but is incapable of modeling antitransitive chains. Traditional set theories are capable of modeling transitive and antitransitive chains of relations, but due to their function as foundations of mathematics they come with features that make them unnecessarily difficult in modeling finite structures. FST has been designed to function as (...) a practical tool in modeling transitive and antitransitive chains of relations without suffering from difficulties of traditional set theories, and a major portion of the functionality of discrete mereology can be incorporated in FST. This makes FST a viable collection theory in ontological modeling. (shrink)

A fundamental question in visual neuroscience is: Why are the response properties of visual neurons as they are? A modern approach to this problem emphasizes the importance of adaptation to ecologically valid input, and it proceeds by modeling statistical regularities in ecologically valid visual input (natural images). A seminal model was linear sparse coding, which is equivalent to independent component analysis (ICA), and provided a very good description of the receptive fields of simple cells. Further models based on modeling residual (...) dependencies of the ‘‘independent” components have later been introduced. These models lead to emergence of further properties of visual neurons: the complex cell receptive fields, the spatial organization of the cells, and some surround suppression and Gestalt effects. So far, these models have concentrated on the response properties of neurons, but they hold great potential to model various forms of inference and learning. (shrink)