Andrée Charles Ehresmann

Université de Picardie Jules Verne | UPJV · LAMFA - Laboratoire amiénois de mathématique fondamentale et appliquée - CNRS

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 d...

L’apport de la littératie des futurs à l’anticipation se rapproche de celui de l’écriture à la parole. La langue parlée tout comme l’anticipation relèvent de capacités innées à l’espèce humaine. Il nous est possible de renforcer et de déployer l’étendue de ces capacités grâce à des compétences socialement et historiquement construites : l’écriture...

In this paper, we evolve from sparsity, a key concept in robust statistics, to concepts and theoretical results of what we call the mathematics of resilience, at the interface between category theory, the theory of dynamical systems, statistical signal processing and biology. We first summarize a recent result on dynamical systems [Beurier, Pastor,...

This paper is a corrected version of the original conference paper presented at ACT 2019, with same title and authors

Motivated by the concept of degeneracy in biology (Edelman, Gally 2001), we establish a first connection between the Multiplicity Principle (Ehresmann, Vanbremeersch 2007) and mathematical statistics. Specifically, we exhibit two families of statistical tests that satisfy this principle to achieve the detection of a signal in noise.

Klumpenhouwer networks (K-nets) and their recent categorical generalization, poly-Klumpenhouwer networks (PK-nets), are network structures allowing both the analysis of musical objects through the study of the transformations between their constituents, and the comparison of these objects between them. In this work, we propose a groupoid-based appr...

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,...

In the field of transformational music theory, which emphasizes the possible transformations between musical objects, Klumpenhouwer networks (K-nets) constitute a useful framework with connections in both group theory and graph theory. Recent attempts at formalizing K-nets in their most general form have evidenced a deeper connection with category...

"Futures Literacy" (FL), as defined by Riel Miller (2018), is a human capacity generally developed through human interactions only. Here we propose to enrich FL by developing a conceptual framework of Human-Machine Interaction allowing to generate richer anticipatory assumptions to "use-the-future" and . "collective intelligence knowledge creation...

OPEN ACCESS: https://www.taylorfrancis.com/books/e/9781351047999 Anticipation is a fundamental building block of this universe. It is a key to turning complexity from a liability into an asset. Yet few have thought about the anticipatory systems and processes that not only surround us but are critical ingredients of the actions everyone, from a bab...

Transformational music theory, pioneered by the work of Lewin, shifts the music-theoretical and analytical focus from the "object-oriented" musical content to an operational musical process, in which transformations between musical elements are emphasized. In the original framework of Lewin, the set of transformations often form a group, with a cor...

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 org...

Forty-two years ago, Capra published "The Tao of Physics" (Capra, 1975). In this book (page 17) he writes: "The exploration of the atomic and subatomic world in the twentieth century has …. necessitated a radical revision of many of our basic concepts" and that, unlike 'classical' physics, the sub-atomic and quantum "modern physics" shows resonance...

Use of the Memory Evolutive Systems methodology (Ehresmann & Vanbremeersch) for better monitoring and prevention of geriatric risk factors in a high-risk population such as the residents of a nursing-home for elderly dependent persons (EHPAD in French). The idea is to design a high-tech multi-level Data Analyser able to: (i) continuously collect me...

Some recalls and reflexions on the Memory Evolutive Systems methodology and its applications (developed by Ehresmann and Vanbremeersch since 1987) leading to new questions about the ’nature’ of MES and new ways to develop it.

The aim of this chapter is to study anticipation in autonomous adaptive systems, such as biological and social systems, which have a multilevel multi-agent organization and develop a robust though flexible long-term memory. The problem is to find the characteristics allowing the system, through some of its agent(s), (i) to enhance its comprehension...

In the field of transformational music theory, which emphasizes the possible transformations between musical objects, Klumpenhouwer networks (K-Nets) constitute a useful framework with connections in both group theory and graph theory. Recent attempts at formalizing K-Nets in their most general form have evidenced a deeper connection with category...

The aim is to describe a Memory Evolutive System (Ehresmann and Vanbremeersch 2007), called I-MES, which models the Immune System with its global multi-scale organization.

L’analyse musicale a développé des outils théoriques qui touchent à plusieurs domaines des mathématiques. En particulier, la théorie transformationnelle de la musique proposée par David Lewin dans les années 1980 est basée sur la théorie des actions de groupes sur des ensembles d’objets musicaux. Les relations entre éléments musicaux sont décrites...

The Glass Bead platform aims at “navigating between heterogeneous and increasingly specialized epistemic sites” and constructing “the conditions for universal transits that transform the sites between which they operate.” It borrows its name from the Glass Bead Game (GBG) presented in the book Magister Ludi by Hermann Hesse1 (1943) as embodying “th...

Domain-independent design theories grounded on formal frameworks are of interest for a wide spectrum of professional and academic fields, including design education, design management and innovation strategy. While much attention has been paid to the modeling of the specification process of an artifact, less attention has been paid to the modeling...

The paper discusses how neural and mental processes correlate for developing cognitive abilities like memory or spatial representation and allowing the emergence of higher cognitive processes up to embodied cognition, consciousness and creativity. It is done via the presentation of MENS (for Memory Evolutive Neural System), a mathematical methodolo...

This article proposes a functorial framework for generalizing some constructions of transformational theory. We focus on Klumpenhouwer Networks for which we propose a categorical generalization via the concept of set-valued poly-K-nets (henceforth PK-nets). After explaining why K-nets are special cases of these category-based transformational netwo...

What characteristics should a social system have to become an Anticipation Literate Community ALC by integrating a net AN of (human or not) anticipators able to develop what Riel Miller [1] calls Futures Literacy FL?

This Open Peer Review proposes a mathematical approach to the framework developed in Dodig-Crnkovic’s target article. It points to an important property of natural computation, called the multiplicity principle (MP), which allows the development of increasingly complex cognitive processes and knowledge. While local dynamics are classically computab...

Application of the model MES introduced by A. Ehresmann and J.-P. Vanbremeersch for multi-scale self-organized systems to design.

It shows how the model MES which I developed with J.-P. Vanbremeersch relies on the a specifi categorical approach which was developed with Charles Ehresmann in the sixties which is recalled in the first part. The second part I stress it allows modeling the 'becoming' of a complex system by introduction of time and dynamics, in a setting which is s...

Monade, dyade et triade sont comme trois manières d’appréhender la relation comme chiffre intime de la réalité sous ses différentes modalités matérielles, organiques, culturelles et métaphysiques. Le parcours proposé est organisé autour de trois lieux qui ont trait à la théologique et à la métaphysique, aux sciences et philosophies des sciences, en...

Application of MES to anticipation problems

This article presents a first attempt at establishing a category-theoretical model of creative processes. The model, which is applied to musical creativity, discourse theory, and cognition, suggests the relevance of the notion of “colimit” as a unifying construction in the three domains as well as the central role played by the Yoneda lemma in the...

cote interne IRCAM: Andreatta13a

Purpose Future studies can be given several interpretations. The purpose of this paper is to develop a methodology for anticipation in a well delimited frame, that of multi‐scale complex systems with a dynamic directed by the cooperation/competition between a net of agents, the “co‐regulators”, each operating with its own rhythm and logic, with the...

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 hu...

This is the final outcome of the INBIOSA project which ends by the end of December 2011. A slighly different version including some appendices will be delivered to the EC later. We believe that this White Paper is a defining document that can be used to direct future research in Integral Biomathics. It can be the base for cooperation projects in th...

This paper compares two complementary theories, Simeonov’s Wandering Logic Intelligence and Ehresmann’s & Vanbremeersch’s Memory Evolutive Systems, in view of developing a common framework for the study of multi-scale complex systems such as living systems. It begins by a brief summary of WLI and MES, then analyzes their resemblances and difference...

How do higher mental processes, learning, intentions, thoughts, emotions, arise from the functioning of the brain? That is the question which, with Jean-Paul Vanbremeersch, we have attempted to approach in the model MENS (for Memory Evolutive Neural Systems), proposing a unified frame for the functioning of the neural, mental and cognitive systems....

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers.

This paper discusses the rebirth of the old quest for the principles of biology along the discourse line of machine-organism disanalogy and within the context of biocomputation from a modern perspective. It reviews some new attempts to revise the existing body of research and enhance it with new developments in some promising fields of mathematics...

Complex Event Processing is studied in the frame of Memory Evolutive Systems, a mathematical model, based on category theory, for evolutionary selforganized hierarchical systems such as biological, social or cognitive systems. Their self-organization depends on the interactions between a net of internal functional subsystems, each operating at its...

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.

The Memory Evolutive Systems (MES), introduced in a series of former papers, propose a mathematical model, based on Category theory, for open autonomous hierarchical systems such as biological, neural or social systems. Here the authors show that MES give a framework in which to study the formation, representation and interpretation of knowledge. I...

In the mid fifties, Charles Ehresmann defined Geometry as “the theory of more or less rich structures, in which algebraic and topological structures are generally intertwined”. In 1973 he defined it as the theory of differentiable categories, their actions and their prolongations. Here we explain how he progressively formed this conception, from ho...

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...

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 Vanbremeersc...

Evolution is marked by the emergence of new objects and interactions. Pursuing our preceding work on Memory Evolutive Systems (MES; cf. our Internet site), we propose a general mathematical model for this process, based on Category Theory. Its main characteristics is the Multiplicity Principle (MP) which asserts the existence of complex objects wit...

The notion of the root of the category, which is a minimal (in a precise sense) weakly coreflective subcategory, is introduced in view of defining ‘local’ solutions of universal problems: If U is a functor from C′ to C and c an object of C, the root of the comma-category c|U is called a U-universal root generated by c; when it exists, it is unique...

Natural autonomous systems, such as biological, neural, social or cultural systems, are open, self-organized systems with a more or less large hierarchy of interacting complexity levels; they are able to memorize their experiences and to adapt to various conditions through a change of behavior. These last fifteen years, the Authors have developed a...

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...

Memory Evolutive Systems, introduced in preceding papers [1, 2], propose a mathematical model, based on Category Theory, for self-organized hierarchical natural systems, such as biological, neural or social systems. Their dynamics is partially regulated by the coordinated and/or competitive interactions between a net of internal Centers of Regulati...

The notion of an evolutive hierarchical system proposed in this paper is a mathematical model for systems, like organisms, with more or less complex objects. This model, based on category theory, retains the following characteristics of natural systems: they have an internal organization consisting of components with interrelations; they maintain t...

The notion of an evolutive hierarchical system proposed here retains the following characteristics of some natural systems, like living organisms: they have an internal organization consisting of more or less complex components with interrelations; they maintain their organization in time although their components are changing; they may be studied...

Dernière partie des oeuvres de Charles Ehresmanna, éditée, avec commentaires et synopsis, par Andrée C. Ehresmann

Partie II-1 de "Charles Ehresmann : Oeuvres completes et commentees" : Strucutres locales; Edition, Synopsis and Comments by Andrée .C. Ehresmann