Neuronal Dynamics: Mathematical Modeling of Neural Activity
Mathematical Methods in Neural Systems: A comprehensive exploration of quantitative tools for analyzing brain dynamics and information processing.
Mathematical Methods in Neural Systems: A comprehensive exploration of quantitative tools for analyzing brain dynamics and information processing.
Dive into the fascinating world of theoretical and computational neuroscience with this advanced course on neuronal dynamics. Learn how to use sophisticated mathematical tools such as differential equations, phase plane analysis, and stochastic processes to model and understand the behavior of single neurons and neural networks. Explore how neurons encode information through electrical pulses (spikes) and decode complex stimuli. This course provides a solid foundation in computational neuroscience, bridging the gap between biology and mathematics to unravel the mysteries of neural information processing.
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What you'll learn
Apply differential equations to model neuronal behavior and dynamics
Use phase plane analysis to understand complex neuronal systems
Analyze spike train variability and its implications for neural coding
Develop and interpret Hodgkin-Huxley models for realistic neuron simulations
Apply stochastic processes to model noise in neuronal systems
Understand the principles of neural coding and decoding
Skills you'll gain
This course includes:
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Graded assignments, exams
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Module Description
This course offers a comprehensive introduction to theoretical and computational neuroscience, focusing on models of single neurons. Students will learn how to use advanced mathematical tools to understand and model neuronal dynamics and neural coding. The curriculum covers a wide range of topics, from simple neuron models to complex biophysical representations. Key areas of study include Hodgkin-Huxley models, two-dimensional models with phase plane analysis, dendritic computation, and the analysis of spike train variability. The course also delves into noise models and their impact on neural coding, as well as techniques for estimating neuron models for coding and decoding. Throughout the course, students will gain hands-on experience in applying mathematical concepts to real neuroscience problems, bridging the gap between theoretical frameworks and biological observations.
Fee Structure
Instructor
2 Courses
Pioneer in Computational Neuroscience and Neural Networks
Wulfram Gerstner is a Full Professor at École polytechnique fédérale de Lausanne (EPFL), holding a joint appointment in Computer Science and Life Sciences since 2006. After studying physics at Tübingen and Munich, followed by research at UC Berkeley, he earned his Ph.D. in theoretical physics from TU Munich in 1993, focusing on associative memory in networks of spiking neurons. Since joining EPFL in 1996, he has directed the Laboratory of Computational Neuroscience, making significant contributions to understanding neural networks, spike-timing dependent plasticity, and reward-based learning in spiking neurons. His research bridges theoretical neuroscience with practical applications, influencing fields from artificial intelligence to neurobiology. Gerstner has served on editorial boards of prestigious journals including Science and the Journal of Computational Neuroscience, and received the Valentino Braitenberg Award for Computational Neuroscience in 2018. His work continues to shape our understanding of neural computation and learning mechanisms in biological and artificial systems.
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