Class 2025-26 :
Computational methods and data modeling in basic and clinical neuroscience
Instructors :
D. Holcman (École Normale Supérieure)
T. Lagache (Institut Pasteur)
J. Reingruber (INSERM)
Course Duration :
Academic Year : 2025-2026
Schedule : Thursdays, 17:00 - 19:00
Dates : To be announced.
Location :
Salle Conference.
École Normale Supérieure (ENS)
46 Rue d’Ulm, 75005 Paris
Affiliated Universities and Programs :
Sorbonne University, PSL, ENS
Applicable Fields : Applied Mathematics, Computational Medicine, Data science, Computational Biology
Course Overview : This course explores mathematical modeling and computational approaches to be used in basic and clinical neuroscience, particularly at the cellular and network level. Drawing from Holcman’s group research, students will study how synaptic transmission integrates across brain scales. Methods are stochastic modeling, rare event dynamics, signal processing and clinical applications including anesthesia, and brain representation.
Part I : Modeling and Asymptotic Analysis for data analysis
Introduction to Computational Neuroscience : Overview of basic neuroscience : synapses, networks, diffusion, and dynamics. Role of modeling in modern neuroscience
- Summary of stochastic processes : Ornstein-Uhlenbeck, Fokker-Planck equations, and Mean First Passage Time (MFPT)
- Extreme statistics and redundancy principles for rare event analysis, involving asymptotic methods, path-integral techniques, and hybrid stochastic simulations
- Spectral decomposition and parameter estimation : Spectrogram and wavelet transport theory for artifact correction.
- Mean-field models for neuronal networks : Models based on short-term synaptic plasticity and stochastic dynamical systems, with phase-space analysis and membrane voltage predictions. Including after-hyperpolarization (AHP). effects and modeling the thalamo-cortical loop during anesthesia.
- Modeling alpha Spindles. Statistics, Passage time distributions.
Reconstruction and Neuronal network modeling :
- Neuron-glial interaction modeling
- Graph reconstruction and statistical analysis : Functional connectivity in neurons and astrocytes.
Spatial statistics and deep learning for image processing :
- Analysis of cellular organization during development, including Level Set methods, Ripley functions, adaptive DBSCAN, and clustering/deviations from random distributions
- Theory of random Clustering.
Real-Time Statistical Analysis, Parameter Estimation, and Classification in Clinical Neuroscience
- EEG signal statistics : FOOF decomposition, wavelet-based artifact removal, state-chart decomposition, segmentation, empirical mode decomposition, and alpha band modeling
- Predictive algorithm design for anesthesia
- Classification algorithms for coma prognosis : Methods to predict comaoutcomes using database-driven approaches
- Differentiating Parkinson’s disease from essential tremor : Using regression techniques for classification
- Adaptive real-time control for closed-loop neuromodulation.
Evaluation : small projects
— only for Master students— (40h, 2 pages report, 20 minutes oral presentations).
References :
Basics :
– D. Holcman Z. Schuss, Stochastic Narrow Escape : theory and
applications, Springer 2015
– D. Holcman, Z. Schuss, Asymptotics of Singular Perturbations and Mixed Boundary Value Problems for Elliptic Partial Differential Equations, and their applications, Springer 2018
– Schuss, Z., Theory and Applications of Stochastic Processes (Hardback, 2009) Springer ; 1st Edition. (December 21, 2009)
Advanced :
– Zonca, L., Dossi, E., Rouach, N., & Holcman, D. (2024). Computational Methods and Algorithms to Segment and Model Recurrent Bursting Events in Long-Time Series Springer Nature Book about Neuromethods. In New Aspects in Analyzing the Synaptic Organization of the Brain (pp. 323-370). New York, NY : Springer US.
– Dora, M, S Jaffard, and D Holcman. "The WQN algorithm for EEG artifact removal in the absence of scale invariance." IEEE Transactions on Signal Processing (2024).
– Z Schuss, K Basnayake, D Holcman, Redundancy principle and the role of extreme statistics in molecular and cellular biology, Physics of life reviews 28, 52-79 (2019)
– N Rouach, KD Duc, J Sibille, D. Holcman, ionic fluxes regulated neurons and astrocytes. Dynamics of ion fluxes between neurons, astrocytes and the extracellular space during neurotransmission, Opera
Medica et Physiologica 4 (1), 1-18, 2018.
– L Zonca, FC Bellier, G Milior, P Aymard, J Visser, A Rancillac, N Rouach, D. Holcman, Unveiling the Functional Connectivity of Astrocytic Networks with AstroNet, a Graph Reconstruction Algorithm Coupled to Image Processing, 2025.
– Loison, V., Yuliya Voskobiynyk, Britta Lindquist, Deanna Necula, Dan Longrois, J. Paz, and David Holcman. "Mapping general anesthesia states based on electro-encephalogram transition phases." NeuroImage
285 (2024) : 120498.