Venue: The University of Tokyo, Komaba I Campus, KOMCEE (Komaba Center for Educational Excellence) west (map), Lecture hall
Date: October 22nd, 2024
Time: 15:00-18:00 (JST)
Schedule:
15:00-16:15 Ben Fulcher (55 min presentation + 20 min Q&A)
16:15-16:30 Break
16:30-17:10 Itsushi Sakata (30 min presentation + 10 min Q&A)
17:10-17:20 Break
17:20-18:00 Daiki Sekizawa (30 min presentation + 10 min Q&A)
Short Bio:
Dr Ben Fulcher is a Senior Lecturer in The School of Physics at The University of Sydney. His research uses physical modeling, dynamical systems, genetics, and statistical machine-learning approaches to understand organizational principles of complex systems, including the brain.
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Ben Fulcher: Quantifying non-stationary dynamical structure in complex neural systems
Like many systems in the world around us, the brain is a non-stationary physical system with intricate neural activity patterns that evolve through space and time. As scientists, we now have access to detailed recordings of brain dynamics captured with unprecedented resolution, but which quantitative representations of them best capture the key underlying mechanisms? In this talk I will argue that many important problems in neuroscience require us to develop new methods that can properly address the challenges of complex, non-stationary signals. I will describe the analysis methods that we have developed for phenotyping dynamical structure, and how we've used it to track non-stationary dynamics (including in sleep), infer hierarchical variation of near-critical dynamics in noisy mouse-brain recordings, and estimate dynamical biomarkers of psychiatric disease.
Refs:
1. Owen and Fulcher (2024). Parameter inference from a non-stationary unknown process. arXiv: http://arxiv.org/abs/2407.08987
2. Harris et al. (2024). Tracking the Distance to Criticality in Systems with Unknown Noise. Phys Rev X. https://link.aps.org/doi/10.1103/PhysRevX.14.031021
3. Bryant et al. (2024). Extracting interpretable signatures of whole-brain dynamics through systematic comparison. bioRxiv. https://www.biorxiv.org/content/10.1101/2024.01.10.573372v1
Itsushi Sakata: Spectral Analysis in Nonlinear Dynamics Using Pseudoeigenfunctions of the Continuous Spectrum
Complex behavior analysis in empirical data presents challenges across scientific disciplines. Dynamic Mode Decomposition (DMD) reveals spectral features of nonlinear systems, but struggles with continuous spectra from chaos and noise. We propose a clustering method for analyzing dynamics using pseudoeigenfunctions associated with continuous spectra, employing Residual DMD (ResDMD) to approximate spectral properties. Our approach uses subspace-based algorithms to compare pseudoeigenfunctions. We demonstrate its effectiveness by analyzing thermal noise-affected 1D signals and 2D time-series of coupled chaotic systems, revealing previously obscured dynamic patterns and insights into coupled chaos complexities.
Refs:
1. Sakata, I., & Kawahara, Y. (2024). Enhancing spectral analysis in nonlinear dynamics with pseudoeigenfunctions from continuous spectra. Scientific Reports. https://www.nature.com/articles/s41598-024-69837-y
2. Colbrook, M. J., & Townsend, A. (2024). Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems. Communications on Pure and Applied Mathematics. https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.22125
Daiki Sekizawa: Decomposing Thermodynamic Dissipation of Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics
Recent developments in stochastic thermodynamics have elucidated various relations between the entropy production rate (thermodynamic dissipation) and the physical limits of information processing. These findings have been actively utilized and have opened new perspectives in the analysis of real biological systems, including the brain. However, the relationship between entropy production rate and oscillations, which are prevalent in many biological systems, is unclear. Here, we derive a novel decomposition of the entropy production rate of linear Langevin systems, using a methods similar to Dynamic Mode Decomposition (DMD). Our decomposition enables us to calculate the contribution of oscillatory modes to the entropy production rate. To demonstrate the utility of our decomposition, we applied our decomposition to an electrocorticography (ECoG) dataset recorded during awake and anesthetized conditions in monkeys, wherein the properties of oscillations change drastically. We show that the contribution of oscillatory modes from the delta band are larger in the anesthetized condition than in the awake condition, while those from the higher-frequency bands, such as the theta band, are smaller. These results may allow us to interpret the change in neural oscillation in terms of stochastic thermodynamics and the physical limit of information processing. Finally, we discuss a future perspective on how to extend our framework to nonlinear Langevin systems using the Koopman operator method.
Refs:
1. Sekizawa, D., Ito, S., & Oizumi, M. (2024). Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics. Physical Review X. https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.041003
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Host: Masafumi Oizumi (The University of Tokyo)