Mathematical Neuroscience Tutorials
September 2002 - August 2003
A Crash Course: Introduction to Biology (by Brian Smith) and Introduction to Dynamical Systems (by David Terman) (August 26-30, 2002)
The course introduced the postdocs and other interested students and faculty to basic concepts in biology (cells, neurons, etc.) and to elementary concepts and tools in dynamical systems.
August 26: Brian lectures 9-10am, 10:30-11:30am; David mentors 2-3pm
August 27: Brian lectures 9-10am, 10:30-11:30am; David mentors 2-3pm
August 28: Brian lectures 9-10am, 10:30-11:30am; David lectures 2-3pm
August 29: David lectures 9-10am, 10:30-11:30am; David mentors 2-3pm
August 30: David lectures 9-10am, 10:30-11:30am; David mentors 2-3pm
Tutorial on Neuronal Dynamics (September 5-12, 2002)
The program began with a tutorial introducing post-docs and interested faculty to neuronal dynamics at all levels: from the sub-cellular to the network, as well as system level modeling.
The tutorial considered modeling, analytic and computatinal aspects of neuronal systems. They discussed the Hodgkin-Huxley model for electrical activity in a nerve axon, simple models for chemical synapses, and properties of larger networks. Mathematical topics included coupled oscillators, averaging, geometric singular perturbation theory, synchronization and other types of pattern formation such as propagating waves and bursting oscillations. Finally, they demonstrated how numerical software such as XPPAUT can be used to analyze the neuronal models.
September 5-6: John Rinzel, 9:00-10:00am, 10:30-11:30am
September 9-10: David Terman, 9:00-10:00am, 10:30-11:30am
September 11-12: Bard Ermentrout, 9:00-10:00am, 10:30-11:30am
Tutorial on neurophysiology and neural encoding (January 9-10, 2003)
Topics Included: information theory and analysis of massive multi-spike data streams.
This two-day tutorial introduced postdocs and interested faculty and students to the study of neural coding. The workshop on neural coding took place during February 10-14. On the first day, John Miller focused on neurophysiological and experimental issues. On the second day, Alex Dimitrov focused on theoretical and analytical issues, and will summarize techniques from information theory and multivariate statistics that have been productive in recent studies of neural coding. As well as providing background for the workshops, the "tutors" defined some of the major conceptual and technical barriers to our understanding of neural computation and representation, and presented a few recently developed approaches that show promise for getting around these barriers. The tutors also "hung out" with any interested MBI attendees in the afternoon hours following the tutorial lectures, to address any questions that may arise during the lectures, and to design some effective supplemental tutorials to be given by other visiting workshop participants during the afternoon hours of Workshop 3.
January 9: John Miller: Tutorial lectures on neurophysiology and neural encoding: 9:00-10:00, 10:30-12:00. Discussion and "office hours": 2:00-5:00.
January 10: Alex Dimitrov: Tutorial lectures on statistical analysis of neural data: 9:00-10:00, 10:30-12:00. Discussion and "office hours": 2:00-5:00.
The tutors identified two books that would be of considerable benefit to workshop participants, and were discussed at the tutorials and workshop. The books are as follows:
- Arathorn, D. (2002). Map-seeking circuits in visual cognition: A computational mechanism for biological and machine vision. Stanford, CA: Stanford University Press. ISBN: 0-8047-4277-4.
- Eliasmith, C., & Anderson, C.H. (2002). Neural Engineering: Computation, representation, and dynamics in neurobiological systems. Cambridge, MA: MIT Press. ISBN: 0-262-05071-4.
Tutorial on Olfaction, Audition and the Sensory-Motor System (March 31 - April 2, 2003)
Topics included anatomy and physiology of each neuronal system, introduction to neuronal modeling.
March 31: David Terman: 9:00AM-10:30AM, Informal discussion: 2:00PM-3:30PM
April 1: Brian Smith: 9:00AM-10:30AM, Informal discussion: 2:00PM-3:30PM
April 2: Catherine Carr: 8:30AM-10:30AM, Mike Reed: 1:00PM-2:30PM
A review background information (with a handout) on the auditory system, starting with inner ear function followed by central auditory physiology and anatomy. We will also review modern views on neural substrates for communication, speech & language.
These lectures focus on mathematical and computational modeling of neurons within the basal ganglia, a group of nuclei that play an important role in the generation of movement. Dysfunction of the basal ganglia is associated with movement disorders such as Parkinson's disease and Huntington's chorea. Structures within the basal ganglia have in fact been the target of recent therapeutic surgical procedures including deep brain stimulation. Numerous experiments have demonstrated that neurons within the basal ganglia display a variety of dynamic behaviors; moreover, patterns of neuronal activity differ between normal and pathological states. Neither the origins of these neural firing patterns nor the neuronal mechanisms that underlie the patterns are understood. As experiments continue to demonstrate the importance of temporal dynamics, the need for more realistic, biophysically based models is becoming increasingly clear.
