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A minimal model of cognition based on oscillatory and reinforcement processes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0002-8745-4480
(Nordic Institute for Theoretical Physics)ORCID iD: 0000-0002-3872-3971
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Artificial Intelligence.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Building mathematical models of brains is difficult because of the sheer complexity of the problem. One potential approach is to start by identifying models of basal cognition, which give an abstract representation of a range organisms without central nervous systems, including fungi, slime moulds and bacteria. We propose one such model, demonstrating how a combination of oscillatory and current-based reinforcement processes can be used to couple resources in an efficient manner. We first show that our model connects resources in an efficient manner when the environment is constant. We then show that in an oscillatory environment our model builds efficient solutions, provided the environmental oscillations are sufficiently out of phase. We show that amplitude differences can promote efficient solutions and that the system is robust to frequency differences. We identify connections between our model and basal cognition in biological systems and slime moulds, in particular, showing how oscillatory and problem-solving properties of these systems are captured by our model.

National Category
Other Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-523413OAI: oai:DiVA.org:uu-523413DiVA, id: diva2:1838668
Available from: 2024-02-18 Created: 2024-02-18 Last updated: 2024-02-21
In thesis
1. The Art of Modelling Oscillations and Feedback across Biological Scales
Open this publication in new window or tab >>The Art of Modelling Oscillations and Feedback across Biological Scales
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four papers in the field of mathematical biology. All papers aim to advance our understanding of biological systems through the development and application of innovative mathematical models. These models cover a diverse range of biological scales, from the nuclei of unicellular organisms to the collective behaviours of animal populations, showcasing the broad applicability and potential of mathematical approaches in biology. While the first three papers study mathematical models of very different applications and at various scales, all models contribute to the understanding of how oscillations and/or feedback mechanisms on the individual level give rise to complex emergent patterns on the collective level. In Paper I, we propose a mathematical model of basal cognition, inspired by the true slime mould, Physarum polycephalum. The model demonstrates how a combination of oscillatory and current-based reinforcement processes can be used to couple resources in an efficient manner. In Paper II, we propose a model of social burst-and-glide motion in pairs of swimming fish by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. Our model, in which visual stimuli of the position of the other fish affect the internal burst or glide state of the fish, captures a rich set of swimming dynamics found in many species of fish. In Paper III, we study a class of spatially explicit individual-based models with contest competition. Based on measures of the spatial statistics, we develop two new approximate descriptions of the spatial population dynamics. Paper IV takes a reflective turn, advocating from a philosophical perspective the importance of developing new mathematical models in the face of current scientific challenges.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2024. p. 48
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 135
Keywords
mathematical biology, mathematical modelling, oscillations, feedback mechanisms, dynamical systems, individual-based models, complex systems
National Category
Mathematics
Research subject
Applied Mathematics and Statistics
Identifiers
urn:nbn:se:uu:diva-523639 (URN)978-91-506-3039-8 (ISBN)
Public defence
2024-04-12, Sonja Lyttkens (101121), Ångströmlaboratoriet, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2024-03-19 Created: 2024-02-21 Last updated: 2024-03-19

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Gyllingberg, Linnéa

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CiteExportLink to record
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Citation style
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