Colimits in free categories

The problem of characterizing colimits in graphs (i.e., in free categories) has arisen in connection with the modelisation of natural systems such as biological or neural systems. Indeed, in a series of papers with J.-P. Vanbremeersch since 1986, we have developed a model based on category theory, where the emergence of complex objects is modelled by a completion process. The present results show that this process cannot be done in the sole framework of graphs, since they imply that the completion of a free category is not free. This vindicates our recourse to (general) categories, instead of considering only graphs as some people have advocated.http://www.numdam.org/item/DIA_1997__37__3_0

Approach to a model of the aging phenomenon

Numerous physiological theories of aging have been proposed; most of them approach the problem in an essentially local manner, stressing the role of a particular factor intervening at a certain level and the resulting pathological consequences. But they do not allow for a combination of the different phenomena observed in the aging process. This paper proposes a more unified and global approach to this process. It is presented in the frame of a mathematical model for complex systems with a hierarchy of internal regulation centers (CR), developed by the authors in preceding papers; the dynamics of such a system depends on a dialectics between these CRs due to their different complexity level and different timescales. Aging for an organism is described as a consequence of this dialectics, that progressively triggers a "cascade of de/resynchronizations" between the CRs, resulting from the reduction in stability of complex components (increase in turnover or acceleration of degradation) and the increase in transmission delays for functioning and repair. This temporal imbalance comes from the interplay between external stochastic disturbances and more or less predetermined sub-systems with limited capacities for repair

How to model consciousness in Memory Evolutive Systems?

Memory Evolutive Systems (MES) represent a mathematical model, based on Category Theory, to study natural open autonomous systems such as biological, neural or social systems. It has been progressively developed by the authors in a series of papers since 1986. In this model the dynamics is modulated by the competitive interactions between a net of internal more or less complex organs of regulation, called CoRegulators (CR), with a differential access to a central hierarchical Memory. This article attempts to model the notions of Semantics and Consciousness in such a MES A Semantics will emerge through the detection of specific invariances by the CRs that leads to classify objects according to their main attributes, and record the invariance classes. The model explains how it relies on a hierarchical 2 steps process: first a pragmatically 'acted' classification at the level of specific attributes (such as colors), then this classification is 'reflected' and analyzed at a higher level, and a new formal unit, called a 'concept', is formed to represent the invariance class (e.g., the color 'blue'). The introduction of more and more abstract concepts gives more flexibility to the comportment. It is essential for the development of some kind of 'consciousness'. A 'conscious' CR is characterized by the capacity to respond to a new event or to a fracture by an increase in awareness, which permits: (i) to extend its actual 'landscape' (formed by the information it can gather) retrospectively to past lower levels; (ii) to operate an abduction process in this extended landscape to find possible causes of the fracture; (iii) and finally to planify a strategy for several steps ahead, through the formation of internal 'virtual' landscapes in which strategies can be tried without energy costs. Thus consciousness would amount to an internalization of Semantics and Time, giving a selective advantage. In the second Part of the paper, a MES modeling a neural system is explicitly described and it is shown how the various processes described above are in agreement with present neurophysiological knowledge. Finally the general ideas are illustrated on a concrete example

A Mathematical Framework for Enriching Human–Machine Interactions

This paper presents a conceptual mathematical framework for developing rich human–machine interactions in order to improve decision-making in a social organisation, S. The idea is to model how S can create a “multi-level artificial cognitive system”, called a data analyser (DA), to collaborate with humans in collecting and learning how to analyse data, to anticipate situations, and to develop new responses, thus improving decision-making. In this model, the DA is “processed” to not only gather data and extend existing knowledge, but also to learn how to act autonomously with its own specific procedures or even to create new ones. An application is given in cases where such rich human–machine interactions are expected to allow the DA+S partnership to acquire deep anticipation capabilities for possible future changes, e.g., to prevent risks or seize opportunities. The way the social organization S operates over time, including the construction of DA, is described using the conceptual framework comprising “memory evolutive systems” (MES), a mathematical theoretical approach introduced by Ehresmann and Vanbremeersch for evolutionary multi-scale, multi-agent and multi-temporality systems. This leads to the definition of a “data analyser–MES”