Analytical Computational Neuroscience

            Math 635 / Math 430 - Fall 2016

    NJIT HONOR CODE:

    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).

    TA: Taku Ito

      E-mail: takuya.ito@rutgers.edu

    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, dynamical systems tools for the analysis of mechanisms of neural activity.

    Textbook:

      "Mathematical Foundations of Neuroscience", by G. B. Ermentrout & D. H. Terman - Springer (2010), 1st edition. ISBN 978-0-387-87707-5.

    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

      "Foundations of Cellular Neurophysiology", by Daniel Johnston and Samuel M.-S. Wu. The MIT Press, 1995. ISBN 0-262-10053-3.
      "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:

      Mon & Thu: 2:30 - 4:00 CKB217

    Office hours:

      Mon & Wed: 1:00 - 2:30 (HGR)

      Tue: 4:00 - 5:30 (TI)

    Grading Policy:

      Math635 (Graduate):

      Homework, quizzes & class participation: .................. 40%

      Projects / Presentations: .............................................. 30%

      Midterm exam: ............................................................. 30%

      Math430 (Undergraduate):

      Homework, quizzes & class participation: .................. 40%

      Midterm exam: .............................................................. 30%

      Final Exam: .................................................................. 30%

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      Please note that the University Drop Date November 7, 201 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 this course website (see below).

      A number of assignments will be given out during the semester

      Assignments will be collected on the published due date

      Late homework will not be accepted

      Only hard copies of the assignments will be accepted (NO electronic submissions)

      The source code used in your calculations MUST accompany the submitted homework

      Upon request, students must be able to explain their results and codes

    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, beepers and other electronic devices must be switched off during class and exam times (except when specifically allowed by the instructor).

      Chatting in class using electronic devices will not be tolerated.

    Course Outline:


Week Topics of the Class Notes
1

Introduction to the course

Introduction to Computational Neuroscience and neural dynamics

Passive membrane properties - The passive membrane equation

LN-01

LN-02

LN-03

2

Ordinary differential equations (ODEs) - Review of analytical methods

Ordinary differential equations (ODEs) - Review of numerical methods

LN-04

3

Dynamics of the passive membrane equation LN-05
4

Integrate-and-fire models

Thd Hodgkin-Huxley model I

LN-06

LN-07

5

Thd Hodgkin-Huxley model II

The cable equation I

LN-07

LN-08

6

The cable equation II

Introduction to dynamical systems methods for neural models

Reduced one- and two-dimensional neural models

LN-08

LN-09

7

One-dimensional neural models: Phase-space analysis I LN-12
8

Two-dimensional neural models: Phase-space analysis I LN-11
9

Two-dimensional neural models: Phase-space analysis II LN-11
10

Subthreshold oscillations: Two- and three-dimensional models

and

Subthreshold and suprathreshold resonance

LN-12

LN-13

11

Bursting: three-dimensional models LN-14
12

Synaptic Dynamics

Network Dynamics

LN-15

LN-16

13

Project Presentations
14

Project Presentations


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Department of Mathematical Sciences(DMS).

New Jersey Institute of Technology (NJIT).

Horacio
Last modified: Sun Oct 31 13:16:02 EDT 2010