Memory Evolutive Systems Research Articles

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”.

A Memory Evolutive System-Model of Immunocompetence with Applications to SARS-CoV-2 Immunity

The immune system of higher vertebrates is one of the most complex biological networks known and undoubtedly plays a determining role in the survival of our species in the face of continuous pressure from pathogenic microorganisms to which we are exposed. The adequate immune response, known as immunological fitness or immunocompetence, is a central concept in immunology, but its use, although widespread, does not have a formal operational definition. In the present work, A qualitative mathematical model of the notion of immunocompetence is developed, based on the formalism of Memory Evolutive Systems (MES), from which, immune fitness is defined as an emergent structure of a higher order arising from the signal networks that are established between effector cells and molecules of the immune response in the presence of an antigen. In addition, a mechanism is proposed, which may explain how immunocompetence is achieved in an organism endowed with innate and adaptive components of its immune system. Finally, a practical method to measure the immunocompetence status was established, using elements of the theory of small random graphs and considering the characteristics of the immune networks, established through transcriptional studies, of patients with severe COVID-19 and healthy patients, assuming that both types of patients were vaccinated with an effective biological against SARS-CoV-2.

MES: A Mathematical Model for the Revival of Natural Philosophy

The different kinds of knowledge which were connected in Natural Philosophy (NP) have been later separated. The real separation came when Physics took its individuality and developed specific mathematical models, such as dynamic systems. These models are not adapted to an integral study of living systems, by which we mean evolutionary multi-level, multi-agent, and multi-temporality self-organized systems, such as biological, social, or cognitive systems. For them, the physical models can only be applied to the local dynamic of each co-regulator agent, but not to the global dynamic intertwining these partial dynamics. To ‘revive’ NP, we present the Memory Evolutive Systems (MES) methodology which is based on a ‘dynamic’ Category Theory; it proposes an info-computational model for living systems. Among the main results: (i) a mathematical translation of the part–whole problem (using the categorical operation colimit) which shows how the different interpretations of the problem support diverging philosophical positions, from reductionism to emergentism and holism; (ii) an explanation of the emergence, over time, of structures and processes of increasing complexity order, through successive ‘complexification processes’. We conclude that MES provides an emergentist-reductionism model and we discuss the different meanings of the concept of emergence depending on the context and the observer, as well as its relations with anticipation and creativity.

Towards a first implementation of the WLIMES approach in living system studies advancing the diagnostics and therapy in augmented personalized medicine

The goal of this paper is to advance an extensible theory of living systems using an approach to biomathematics and biocomputation that suitably addresses self-organized, self-referential and anticipatory systems with multi-temporal multi-agents. Our first step is to provide foundations for modelling of emergent and evolving dynamic multi-level organic complexes and their sustentative processes in artificial and natural life systems. Main applications are in life sciences, medicine, ecology and astrobiology, as well as robotics, industrial automation, man-machine interface and creative design. Since 2011 over 100 scientists from a number of disciplines have been exploring a substantial set of theoretical frameworks for a comprehensive theory of life known as Integral Biomathics. That effort identified the need for a robust core model of organisms as dynamic wholes, using advanced and adequately computable mathematics. The work described here for that core combines the advantages of a situation and context aware multivalent computational logic for active self-organizing networks, Wandering Logic Intelligence (WLI), and a multi-scale dynamic category theory, Memory Evolutive Systems (MES), hence WLIMES. This is presented to the modeller via a formal augmented reality language as a first step towards practical modelling and simulation of multi-level living systems. Initial work focuses on the design and implementation of this visual language and calculus (VLC) and its graphical user interface. The results will be integrated within the current methodology and practices of theoretical biology and (personalized) medicine to deepen and to enhance the holistic understanding of life.

A categorical approach to neurodynamical modelling of musical tonality

Music gives rise to some of the strongest emotional experiences in our lives. Both musicological and music-psychological evidence converge on the theory that music achieves this by a sophisticated play with our expectancies [1]. The extent to which a pitch/chord is expected in the context of a musical sequence is closely related to its perceived and also to how much it apparently attracts other pitches/chords in the sequence (see [2] and the references thereof). The phenomenon wherein more stable pitches attract the less stable ones is called tonality. Over the eons, virtually every musical culture has created its own set of musical scales. Generally, each scale imposes a hierarchy of stability on all pitches sounded in its context [3]. We call such a hierarchy a tonal hierarchy. In [4] a formula for computing tonal stability of arbitrary pitch in a given context was proposed based on a network of neural oscillators. Even though high correlations with tonal hierarchies obtained experimentally were achieved by tuning the single parameter of the formula, there were some notable discrepancies between predictions of the formula and the psychological data. These might be explained by drastic approximations made on the way from the complete neurodynamical model to the formula which were necessitated by the complexity of the model. For instance, all interactions within the network were neglected. Nevertheless, this line of research clearly demonstrates the potential of neurodynamics to serve as a basis for derivation of a general theory of tonality applicable even to contemporary art music which is our main interest. Indeed, the neurodynamical model from [4] makes no assumptions whatsoever regarding its inputs. What is currently missing is a model of a suitable form so that such a theory can be derived from it without drastic approximations. We aim to fill this gap. It has become a standard in neuroscience community to approach neurodynamics from a dynamical perspective. Unfortunately, none of the approaches to analytical treatment of oscillatory dynamical we have reviewed proved suitable for our purposes. Consequently, inspired by the so-called memory evolutive neural systems [5], we are currently developing a neurodynamical model based on category theory. More specifically, we model the neural rhythms present in the auditory system during stimulation with a tone/chord as a category with objects representing the rhythms and morphisms representing the resonant interactions among them. Response to a sequence of stimuli is modelled using partial functors between such categories. The preliminary results are quite promising: from a very simple model we managed to derive a formula which predicts the ordering of pitches according to tonal stability within a major scale almost perfectly. Moreover, due to its nature, our model yields an almost mechanistic explanation of tonality. This, in our opinion, is as important a feature of any model as a good fit to data.

D-MES: Conceptualizing the Working Designers

Domain-independent design theories grounded on formal frameworks are of interest for a wide spectrum of professionals including in design education. While much attention has been paid to the modeling of the specification process of an entity, less attention has been paid to the modeling of the creative social interactions involved in the process of designing. There is still a need for conceptual approach that could further integrate the creative, social, cognitive and mental aspects of design. This paper aims to develop such an integrative view by relying on Memory Evolutive Systems (MES) (Ehresmann and Vanbremeersch 2007). Based on a conceptual mathematical domain named “Category Theory”, a MES provides a relational approach for an evolutionary, multi-scale, multi-temporality and self-organized system. Using the MES approach, we develop a conceptual framework which encompasses the various phases of a design process and considers how it is directed by the multiple mental and social interactions between different actors. Our approach, named D-MES, extends prior research by providing a formal account of how various intentional entities can operate in parallel to form creative combinations of new shared objects and processes of different levels of complexity throughout the design process. An illustration is provided in the case of garden design.

Geiringer theorems: from population genetics to computational intelligence, memory evolutive systems and Hebbian learning

The classical Geiringer theorem addresses the limiting frequency of occurrence of various alleles after repeated application of crossover. It has been adopted to the setting of evolutionary algorithms and, a lot more recently, reinforcement learning and Monte-Carlo tree search methodology to cope with a rather challenging question of action evaluation at the chance nodes. The theorem motivates novel dynamic parallel algorithms that are explicitly described in the current paper for the first time. The algorithms involve independent agents traversing a dynamically constructed directed graph that possibly has loops. A rather elegant and profound category-theoretic model of cognition in biological neural networks developed by a well-known French mathematician, professor Andree Ehresmann jointly with a neurosurgeon, Jan Paul Vanbremeersch over the last thirty years provides a hint at the connection between such algorithms and Hebbian learning.

MENS, an Info-Computational Model for (Neuro-)cognitive Systems Capable of Creativity

MENS is a bio-inspired model for higher level cognitive systems; it is an application of the Memory Evolutive Systems developed with Vanbremeersch to model complex multi-scale, multi-agent self-organized systems, such as biological or social systems. Its development resorts to an info-computationalism: first we characterize the properties of the human brain/mind at the origin of higher order cognitive processes up to consciousness and creativity, then we ‘abstract’ them in a MENS mathematical model for natural or artificial cognitive systems. The model, based on a ‘dynamic’ Category Theory incorporating Time, emphasizes the computability problems which are raised.

Some Comments on the Reviews

We comment on the preceding reviews of our book “Memory Evolutive Systems”, discussing the improvements proposed by some of the reviewers and answering to critics of others, in particular on the use of category theory for modeling living systems.

Extended Memory Evolutive Systems in a Hyperstructure Context

This paper is just a comment to the impressive work by A. C. Ehresmann and J.-P. Vanbremeersch on the theory of Memory Evolutive Systems (MES). MES are truly higher order systems. Hyperstructures represent a new concept which I introduced in order to capture the essence of what a higher order structure is—encompassing hierarchies and emergence. Hyperstructures are motivated by cobordism theory in topology and higher category theory. The morphism concept is replaced by the concept of a bond. In the paper I briefly introduce hyperstructures motivated geometrically and suggest further developments of the MESs along these lines, which could widen up new areas of applications.

Memory Evolutive Systems

This is a review of the book ‘Memory Evolutive Systems; Hierarchy, Emergence, Cognition’, by A. Ehresmann and J.P. Vanbremeersch. I welcome the use of category theory and the notion of colimit as a way of describing how complex hierarchical systems can be organised, and the notion of categories varying with time to give a notion of an evolving system. In this review I also point out the relation of the notion of colimit to ideas of communication; the necessity of communications to be symbolic representations; and the use of an analogy with mathematics to spell out some of the necessities of such a mode of communication to be powerful, robust and efficient.

Cohomological Emergence of Sense in Discourses (As Living Systems Following Ehresmann and Vanbremeersch)

As a significant extension of our previous calculus of logical differentials and moving logic, we propose here a mathematical diagram for specifying the emergence of novelty, through the construction of some “differentials” related to cohomological computations. Later we intend to examine how to use these “differentials” in the analysis of anticipation or evolution schemes. This proposal is given as a consequence of our comments on the Ehresmann–Vanbremeersch’s work on memory evolutive systems (MES), from the two points of view which are characterization of life and use of categorical modeling. It would not be possible to conceive of the “differentials” outside the frame of a MES (and specifically the description of the part played in a MES by the “co-regulators” and their “landscapes” for anticipation and emergence). Furthermore, we hope that this diagram will be useful to exhibit the “emergence of sense” in discourses, and this idea is supported here by a brief examination of how a discourse could be seen as a living system (and then could be studied as a MES).

Knowledge in Memory Evolutive Systems

Knowledge in Memory Evolutive Systems

The Memory Evolutive Systems as a Model of Rosen’s Organisms – (Metabolic, Replication) Systems

Robert Rosen has proposed several characteristics to distinguish “simple” physical systems (or “mechanisms”) from “complex” systems, such as living systems, which he calls “organisms”. The Memory Evolutive Systems (MES) introduced by the authors in preceding papers are shown to provide a mathematical model, based on category theory, which satisfies his characteristics of organisms, in particular the merger of the Aristotelian causes. Moreover they identify the condition for the emergence of objects and systems of increasing complexity. As an application, the cognitive system of an animal is modeled by the “MES of cat-neurons” obtained by successive complexifications of his neural system, in which the emergence of higher order cognitive processes gives support to Mario Bunge’s “emergentist monism.”

Hyperstructures and memory evolutive systems

The aim of the paper is to compare two different approaches to the modeling of complex natural systems, in particular of their hierarchical organization with higher-order structures and their emergence processes. These approaches are, respectively, the hyperstructures (HS) of Baas and the memory evolutive systems (MES) of Ehresmann and Vanbremeersch. The HS are “structural” while MES, based on category theory, take dynamics more into account. It is shown how the dynamical organization and mechanisms developed for MES rely on simple ideas of a philosophical nature, that might be disengaged from the categorical setting and extended to the general frame of HS.

Information processing and symmetry-breaking in memory evolutive systems

The aim of this paper is to evaluate the role of symmetry and symmetry-breaking processes on the complex information processing developed by hierarchical evolutionary natural systems, such as biological, neural, social or cultural systems. The study is conducted in the frame of the Memory Evolutive Systems, which give a mathematical model of these systems. The dynamics of a MES is modulated by the competition between a net of internal regulation centers, which act apart but encode overlapping strategies which have to be equilibrated. The main characteristics of these systems, at the root of their complexity and adaptability, is a symmetry-breaking in the passage from a higher (or macro) level to a lower (or micro) level: several disparate sub-systems with different comportments at the micro level can be undistinguishable at the higher macro level because of a similar macro behavior (Multiplicity Principle). It is responsible for the development of a dialectics between heterogeneous regulation centers, and for the emergence in time of more and more complex objects. An application to neural systems vindicates an emergentist dynamical reduction of mental states to physical states.

Multiplicity principle and emergence in memory evolutive systems

Multiplicity principle and emergence in memory evolutive systems