NEUR2110 Statistical Neuroscience
An introduction to the statistical modeling of neural dynamics in networks of neurons and large-scale brain networks with a focus on stochastic processes and random dynamical systems. Analysis of dynamical and statistical network properties: stationarity, directed transfer functions, stability and bifurcations, phase transitions. Related applications to prediction, control, low-dimensional representation, probabilistic neural population encoding and decoding are introduced as well. This is a course for senior undergraduate and graduate students with a background in systems/computational neuroscience and/or applied math/biomedical engineering. Lectures are accompanied by hands-on Python/Matlab-based applications to real and simulated neural data. Topics include (1) time and spectral domain models of network dynamics based on multivariate neural time series and point process observations with exogenous inputs; vector autoregressive processes, nonlinear Hawkes processes; stability, transfer functions; (2) identification of directed interactions in networks of neurons and brain inter-areal communication (Granger causality, transfer entropy, and related measures); (3) collective dynamics and low-dimensional representations of network dynamics; (4) Prediction, neural population encoding and decoding for brain-computer interfaces: Bayesian probabilistic approaches based on linear/nonlinear state-space models, machine learning; (5) data assimilation for modeling neural network dynamics. Example datasets include neuronal spike trains, local field potentials, ECoG/SEEG.
NEUR1930H Neurological Disorders: Neural Dynamics & Neurotechnology
This seminar course provides an introduction to neural dynamics in neurological and neuropsychiatric disorders, and an overview of current therapeutic approaches based on open-/closed-loop Brain-Computer Interfaces (BCIs) and adaptive neuromodulation, e.g. Deep Brain Stimulation (DBS). The lectures and discussion sections cover: (1) Disorders of consciousness: Primary and secondary generalized epileptic seizures; Multiscale neural dynamics in human epilepsy; Basics of open- and closed-loop neuromodulation and seizure prediction/control; Coma, medically induced coma and general anesthesia; Consciousness and integrated information theory; Consciousness neuromonitoring; (2) Sensory disorders: Auditory, visual and proprioceptive/somatosensory neuroprostheses; (3) Movement disorders: Paralysis and BCIs for restoring movement and communication; adaptive DBS for Parkinson’s disease and essential tremor. (4) Neuropsychiatric disorders: DBS for major depression and obsessive compulsive disorder. Computational approaches for tracking ongoing brain states/dynamics in BCIs and closed-loop neuromodulation/DBS will be reviewed. The course addresses concrete applications of mathematical and statistical approaches introduced in detail in the course NEUR2110, Statistical Neuroscience. Enrollment is capped at 20. Instructor permission required.