Characterizing self-organization and coevolution by ergodic invariants

In addition to the emergent complexity of patterns that appears when many agents come in interaction, it is also useful to characterize the dynamical processes that lead to their self-organization. A set of ergodic invariants is identified for this purpose, which is computed in several examples, namely a Bernoulli network with either global or nearest-neighbor coupling, a generalized Bak-Sneppen model and a continuous minority model.Comment: 21 pages Latex, 9 eps figure

Memory Organization for Invariant Object Recognition and Categorization

Using distributed representations of objects enables artificial systems to be more versatile regarding inter- and intra-category variability, improving the appearance-based modeling of visual object understanding. They are built on the hypothesis that object models are structured dynamically using relatively invariant patches of information arranged in visual dictionaries, which can be shared across objects from the same category. However, implementing distributed representations efficiently to support the complexity of invariant object recognition and categorization remains a research problem of outstanding significance for the biological, the psychological, and the computational approach to understanding visual perception. The present work focuses on solutions driven by top-down object knowledge. It is motivated by the idea that, equipped with sensors and processing mechanisms from the neural pathways serving visual perception, biological systems are able to define efficient measures of similarities between properties observed in objects and use these relationships to form natural clusters of object parts that share equivalent ones. Based on the comparison of stimulus-response signatures from these object-to-memory mappings, biological systems are able to identify objects and their kinds. The present work combines biologically inspired mathematical models to develop memory frameworks for artificial systems, where these invariant patches are represented with regular-shaped graphs, whose nodes are labeled with elementary features that capture texture information from object images. It also applies unsupervised clustering techniques to these graph image features to corroborate the existence of natural clusters within their data distribution and determine their composition. The properties of such computational theory include self-organization and intelligent matching of these graph image features based on the similarity and co-occurrence of their captured texture information. The performance to model invariant object recognition and categorization of feature-based artificial systems equipped with each of the developed memory frameworks is validated applying standard methodologies to well-known image libraries found in literature. Additionally, these artificial systems are cross-compared with state-of-the-art alternative solutions. In conclusion, the findings of the present work convey implications for strategies and experimental paradigms to analyze human object memory as well as technical applications for robotics and computer vision

How Does Our Visual System Achieve Shift and Size Invariance?

The question of shift and size invariance in the primate visual system is discussed. After a short review of the relevant neurobiology and psychophysics, a more detailed analysis of computational models is given. The two main types of networks considered are the dynamic routing circuit model and invariant feature networks, such as the neocognitron. Some specific open questions in context of these models are raised and possible solutions discussed

On Possible Implications of Self-Organization Processes through Transformation of Laws of Arithmetic into Laws of Space and Time

In the paper we present results based on the description of complex systems in terms of self-organization processes of prime integer relations. Realized through the unity of two equivalent forms, i.e., arithmetical and geometrical, the description allows to transform the laws of a complex system in terms of arithmetic into the laws of the system in terms of space and time. Possible implications of the results are discussed.Comment: 26 pages, 4 figure

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review