Institut de Biologie de l'École Normale Supérieure ENS . CNRS UMR8197 . Inserm U1024 Directeur : Pierre Paoletti

Multiscale Modeling for Data Classification and Algorithm Design in Basic and Clinical Neuroscience

Instructors :
D. Holcman (École Normale Supérieure)
T. Lagache (Institut Pasteur)
J. Reingruber (INSERM)

Course Duration :
Academic Year : 2024-2025
Schedule : Thursdays, 17:00 - 19:00
Dates : Starting Thursday, November 7, 2024, through February 2025

Location :
Room 316, Third Floor Teaching Unit
École Normale Supérieure (ENS)
46 Rue d’Ulm, 75005 Paris

Affiliated Universities and Programs :
Sorbonne University, PSL, ENS
Applicable Fields : Applied Mathematics, Statistical Physics, Computer
Science, Computational Biology

Attendance : Open to all
Format : On-site Classes
General Overview : This class offers a comprehensive approach to modern data-modeling, statistical methodologies, and algorithm design, particularly suited for applications in basic and clinical neuroscience. Emphasis is placed on analyzing brain function and predicting neural behavior in
real-time.

The course begins with stochastic mean-field models covering neural and cellular elements such as neurons, synapses, and glial cells, including topics like calcium dynamics, learning, and memory extraction from time series data. It progresses into reverse engineering methods to reconstruct graphs from time series. The final part introduces Model-Machine-learning techniques aimed at classifying cells using levelset assisted by Deep-learning and predicting brain activity from EEG data, with practical applications in coma and anesthesia analysis.

Objectives The class aims to teach modeling techniques, stochastic analysis, and
signal processing and classification methodologies focused on
extracting predictive features from physiological data, making it
ideal for students and professionals in applied mathematics, physics,
theoretical chemistry, or computer science.

Online Resources :
Supplementary lectures are accessible on Holcman’s YouTube channel.
www.bionewmetrics.org
Contact : david.holcman chez ens.fr

Syllabus
The course is organized into three primary parts :

Part I : Modeling and Asymptotic Analysis for Data

1. Stochastic processes : Ornstein-Uhlenbeck, Fokker-Planck equations, and Mean First Passage Time (MFPT)
2. Extreme statistics and redundancy principles for rare event analysis, involving asymptotic methods, path-integral techniques, and hybrid stochastic simulations
3. Electro-diffusion modeling and applications in cellular processes
4. Spectral decomposition and parameter estimation : Spectrogram and wavelet transport theory for artifact correction

Part II : Data Modeling from Cellular to Neuronal Networks

1. Mean-field models for neuronal networks : Models based on short-term ynaptic plasticity and stochastic dynamical systems, with phase-space analysis and membrane voltage predictions
2. Neuronal network modeling : Including after-hyperpolarization (AHP)
3. effects and modeling the thalamo-cortical loop during anesthesia
4. Neuron-glial interaction modeling
5. Graph reconstruction and statistical analysis : Functional connectivity
6. from correlated events in time series, focusing on neuronal and astrocytic networks
7. Morphogenetic gradient modeling : Brain wiring, neuronal migration, and combinatorial puzzle-solving
8. Spatial statistics and deep learning for image processing : Techniques to analyze cellular organization during development, including Level Set methods, Ripley functions, adaptive DBSCAN, and clustering/deviations from random distributions

Part III : Real-Time Statistical Analysis, Parameter Estimation, and
Classification in Clinical Neuroscience

1. EEG signal statistics : FOOF decomposition, wavelet-based artifact removal, state-chart decomposition, segmentation, empirical mode decomposition, and alpha band modeling
2. Predictive algorithm design for anesthesia
3. Classification algorithms for coma prognosis : Methods to predict comaoutcomes using database-driven approaches
4. Differentiating Parkinson’s disease from essential tremor : Using deep-learning techniques for classification

Evaluation : small projects—only for Master students— (40h, 2 pages
report, 20 minutes oral presentations).

References :
– 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.
– U Dobramysl, D Holcman, Computational methods and diffusion theory in triangulation sensing to model neuronal navigation, Reports on Progress in Physics 85 (10), 104601 (2022)
– 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).
– D. Holcman Z. Schuss, 100 years after Smoluchowski : stochastic processes in cell biology, J. Phys. A (2016).
– 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, bioRxiv, 2024.10. 15.618423
– 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.