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The brain produces rhythms in a variety of frequency bands. Some are likely by-products of neuronal processes; others are thought to be top-down. Produced entirely naturally, these rhythms have clearly recognizable beats, but they are very far from periodic in the sense of mathematics. The signals are broad-band, episodic, wandering in amplitude and frequency; the rhythm comes and goes, degrading and regenerating. Gamma rhythms, in particular, have been studied by many authors in computational neuroscience, using reduced models as well as networks of hundreds to thousands of integrate-and-fire neurons. All of these models captured successfully the oscillatory nature of gamma rhythms, but the irregular character of gamma in reduced models has not been investigated thoroughly. In this article, we tackle the mathematical question of whether signals with the properties of brain rhythms can be generated from low dimensional dynamical systems. We found that while adding white noise to single periodic cycles can to some degree simulate gamma dynamics, such models tend to be limited in their ability to capture the range of behaviors observed. Using an ODE with two variables inspired by the FitzHugh-Nagumo and Leslie-Gower models, with stochastically varying coefficients designed to control independently amplitude, frequency, and degree of degeneracy, we were able to replicate the qualitative characteristics of natural brain rhythms. To demonstrate model versatility, we simulate the power spectral densities of gamma rhythms in various brain states recorded in experiments.
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This content will become publicly available on September 1, 2026
Reflections on Simplicity and Complexity in Computational Neuroscience
Abstract This double interview with two distinguished researchers in computational neuroscience, Kanaka Rajan and Alessandro Treves, aims to capture a part of their talks and discussions that emerged during a workshop on physical modelling of thought, held in Berlin in January 2023. The topic is the fascinating all-round intersection of physics and neuroscience through the perspectives of the interviewees. The dialogue traverses the complex terrain of modelling thought processes, shedding light on the trade-off between simplicity and complexity that defines the field of computational neuroscience. From the early days of physics-inspired brain models to the cutting-edge advancements in large language models, the interviewees share their journey, challenges, and insights into the modelling of physical and biological systems; they recount their experience with computational neuroscience, explore the impact of large language models on our understanding of human language and cognition, and speculate on the future directions of physics-inspired computational neuroscience, emphasising the importance of interdisciplinary collaboration and a deeper integration of complexity and detail in modelling the brain and its functions.
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- PAR ID:
- 10658219
- Publisher / Repository:
- Human Arenas
- Date Published:
- Journal Name:
- Human Arenas
- Volume:
- 8
- Issue:
- 3
- ISSN:
- 2522-5790
- Page Range / eLocation ID:
- 741 to 749
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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