Analytical Computational Neuroscience (Math 635)
All Students should be aware that the Department of Mathematical Sciences
takes the NJIT
Academic Honor Code
very seriously and enforces it strictly. This means
there must not be any forms of plagiarism, i.e., copying of homework, class
projects, or lab assignments, or any form of cheating in quizzes and exams.
Under the Honor Code, students are obligated to report any such activities
to the Instructor.
Please re-read Article III of the
Academic Honor Code,
which describes conducts that are considered unacceptable (cheating, violating
the US Copyright law, etc).
E-mail:
horacio at njit edu (preferred)
Tel:
(973) 596-5306
Course Description:
A mathematical and computational introduction to the biophysical mechanisms that underlie physiological functions of single neurons and synapses. Topics include voltage-dependent channel gating mechanisms, the Hodgkin-Huxley model for membrane excitability, repetitive and burst firing, nerve impulse propagation in axons and dendrites, single- and multi-compartmental modeling, synaptic transmission, calcium handling dynamics and calcium dependent currents and processes.
Textbooks:
"Mathematical Foundations of Neuroscience", by G. B. Ermentrout & D. H. Terman - Springer (2010), 1st edition. ISBN 978-0-387-87707-5.
"Foundations of Cellular Neurophysiology", by Daniel Johnston and Samuel M.-S.
Wu. The MIT Press, 1995. ISBN 0-262-10053-3.
Recommended Books:
"Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting",
by Eugene M. Izhikevich. The MIT Press, 2007. ISBN 0-262-09043-8
"Biophysics of Computation - Information processing in single neurons", by
Christof Koch. Oxford University Press, 1999. ISBN 0-19-510491-9.
"Theoretical Neuroscience: Computational and Mathematical Modeling of Neural
Systems", by Peter Dayan and Larry F. Abbott. The MIT Press,2001.
ISBN 0-262-04199-5
Class meets:
Tue: 08:30 - 09:55, KUPF-203
Fri: 10:00 - 11:25, KUPF-203
Office hours:
Tue 10:00-11:30
Grading Policy:
Homework & Quizzes: .........
40%
Student Presentations: .......
30%
Final Exam: .......................
30%
.
Please note that the University Drop Date
November 1, 2010 deadline will be
strictly enforced
Homework Policy
Homework will consist of modeling and simulations exercises on the topics discussed in class. Homework assignments will be posted on the course website.
A number of assignments will be given out during the semester
Assignments will be collected one week after they are given out
Only hard copies of the assignments will be accepted
(NO electronic submissions)
The source code used in your calculations MUST accompany the submitted homework
Class Policies:
Attendance and Participation:
Students must attend all classes. Absences from class will inhibit your
ability to fully participate in class discussions and problem solving sessions
and, therefore, affect your grade. Tardiness to class is very disruptive to
the instructor and students and will not be tolerated.
Makeup Exam Policy:
There will be no makeup exams, except in rare and extenuating situations where
the student has a legitimate reason for missing an exam. The
student must notify the NJIT Math office and the Instructor that he/she will
miss an exam. In all cases, the student must present written verifiable
proof of the reason for missing the exam, e.g., a doctor's note, police
report, court notice, etc., clearly stating the date AND times of the
mitigating problem.
Cellular Phones:
All cellular phones and beepers must be switched off during class and exam
times.
|
Class |
Date |
Topic of the Class |
Notes |
|
1
|
Aug 31
|
Introduction
Introduction to Computational Neuroscience and neural dynamics I
|
LN-01
LN-02
|
|
2
|
Sep 3
|
Introduction to Computational Neuroscience and neural dynamics II
Passive membrane properties - The passive membrane equation
|
LN-02
LN-03
|
|
3
|
Sep 7
|
How to solve ordinary differential equations (ODEs) - Review of analytical methods
|
LN-04
|
|
4
|
Sep 10
|
Introduction to XPP for ODEs
Introduction to Matlab for ODEs
|
LN-05
.
|
|
5
|
Sep 14
|
Dynamics of the passive membrane equation I
|
LN-06
|
|
6
|
Sep 17
|
Dynamics of the passive membrane equation II
|
"
|
|
7
|
Sep 21
|
Integrate-and-fire models
|
LN-07
|
|
8
|
Sep 24
|
Thd Hodgkin-Huxley model I
|
LN-08
|
|
9
|
Sep 28
|
Thd Hodgkin-Huxley model II
|
"
|
|
10
|
Oct 1
|
The cable equation I
|
LN-09
|
|
11
|
Oct 5
|
The cable equation II
|
"
|
|
12
|
Oct 8
|
Discussion on modeling and simulatins issues
|
|
|
13
|
Oct 12
|
Introduction to dynamical systems methods for neural models
|
LN-10
|
|
14
|
Oct 15
|
Reduced one- and two-dimensional neural models
|
"
|
|
15
|
Oct 19
|
One-dimensional neural models: Phase-space analysis I
|
LN-11
|
|
16
|
Oct 22
|
One-dimensional neural models: Phase-space analysis II
|
"
|
|
17
|
Oct 26
|
Two-dimensional neural models: Phase-space analysis I
|
LN-12
|
|
18
|
Oct 29
|
Two-dimensional neural models: Phase-space analysis II
|
|
|
19
|
Nov 2
|
Two-dimensional neural models: Phase-space analysis III
|
|
|
20
|
Nov 5
|
Two-dimensional neural models: Phase-space analysis IV
|
|
|
21
|
Nov 9
|
Subthreshold oscillations: Two- and three-dimensional models
|
|
|
22
|
Nov 12
|
Subthreshold oscillations: The canard phenomenon
|
|
|
23
|
Nov 16
|
Bursting I
|
|
|
24
|
Nov 19
|
Bursting II
|
|
|
25
|
Nov 23
|
Student Presentations: Douglass, Rambert & Xavier
|
|
|
.
|
Nov 26
|
Thanksgiving Recess (no class)
|
|
|
26
|
Nov 30
|
Student presentations: Cardie, Pavan & Motolani
|
|
|
27
|
Dec 3
|
Student presentations: Dun, Zeynep & Stephanie
|
|
|
.
|
Dec 7
|
Classes follow a Thursday schedule (no class)
|
|
|
.
|
Dec 8
|
Student Presentations: Gokhan & Ali (Classes follow a Friday schedule)
|
|
|
--
|
|
Final Exam Period
|
|
.
.
.
.
Department of Mathematical Sciences(DMS).
New Jersey Institute of Technology (NJIT).
Horacio
Last modified: Sun Oct 31 13:16:02 EDT 2010