IV JORNADES
D'INTRODUCCIÓ ALS SISTEMES DINÀMICS (JISD2005)
(4th
DAYS OF INTRODUCTION TO DYNAMICAL SYSTEMS)
Barcelona,
June 27- July
1,
2005
The fourth edition
of the JORNADES D'INTRODUCCIÓ ALS SISTEMES DINÀMICS
(JISD2005), will be held from June 27 to July 1, 2005, at the Universitat Politècnica de Catalunya
(UPC),
in Barcelona.
The JISD2005
will be devoted to courses on computational and
mathematical neuroscience given by:
- Prof. John Rinzel,
Professor of Neural Science and Mathematics, Courant
Institute and Center for Neural Science, New York University;
- Prof. David Terman,
Professor of Mathematics, Ohio
State University,
in the Doctorate
Programme in
Applied Mathematics (course number 5.17, entitled "Simulation
methods") inside the Graduate studies
at UPC, under the supervision of Prof. Antoni Guillamon,
coordinator
of the Dynamical Systems branch of the Programme. The courses will be
delivered from June 27 to July 1,
and will consist of 5 hours of lectures every day.
The JISD2005,
as well as the Doctoral Programme in Applied Mathematics, is supported
by a Spanish grant
Mención de calidad en programas de doctorado.
John
Rinzel. "Understanding
neuronal dynamics by geometrical dissection of minimal models"
Notes
for the course, see
also: [Borisyuk A, Rinzel J. "Understanding neuronal dynamics by
geometrical dissection of minimal models". In: Chow C, Gutkin B, Hansel
D, Meunier C, Dalibard J, eds. Models
and Methods in Neurophysics, Proc Les Houches Summer School 2003,
(Session LXXX), Elsevier, 2005: 19-72.]
1. Introduction to cellular
neurophysiology
2. The Hodgkin-Huxley story; fast/slow analysis
3. The Morris-Lecar model and phase plane analysis; firing properties
and
bifurcation treatment
4. Bursting oscillations; cellular and network
5. Cable properties of dendrites (Rall’s model; active properties;
reduced
models)
6. Axonal impulse propagation; dispersion relations; kinematics;
heterogeneities
7. Synaptic dynamics and synchronization of cells.
All the files will be posted only
until July 8th, 2005
David Terman. "Neuronal Dynamics: use of dynamical systems
methods to analyze models of neuronal firing patterns"
Notes
for the course
1. Introduction to dynamical systems.
1.A. One dimensional equations:
geometric approach, bifurcations, bistability and hysteresis.
1.B. Two dimensional systems: phase plane, oscillations, local and
global bifurcations, geometric singular perturbation theory.
2. Single neurons.
2.A. Some biology.
2.B. Hodgkin-Huxley equations
2.C. Reduced models
2.D. Bursting oscillations
2.E. Travelling wave solutions
3. Two mutually coupled cells.
3.A. Synaptic coupling
3.B. Geometric approach
3.C. Synchrony with
excitatory synapses
3.D. Desynchrony with inhibitory synapses
4. Larger
networks and applications: thalamic sleep rhythms,
Parkinsonian rhythms and the basal ganglia.
4.A. Thalamic sleep rhythms
4.B. Parkinsonian rhythms and the basal ganglia
All the files will be posted only
until July 8th, 2005
|
Monday
27th
|
Tuesday
28th
|
Wednesday
29th
|
Thursday
30th
|
Friday
1st
|
9:00 - 11:00
|
J. Rinzel. "Understanding
neuronal dynamics by geometrical dissection of minimal models"
|
D. Terman. "Neuronal Dynamics: use
of dynamical systems
methods to analyze models of neuronal firing patterns" |
J. Rinzel. "Understanding
neuronal dynamics by geometrical dissection of minimal models" |
D. Terman. "Neuronal Dynamics: use
of dynamical systems
methods to analyze models of neuronal firing patterns" |
J. Rinzel. "Understanding
neuronal dynamics by geometrical dissection of minimal models" |
11:00 - 11:30
|
Coffee
break
|
Coffee
break |
Coffee
break |
Coffee
break |
Coffee
break |
11:30-13:30
|
D. Terman. "Neuronal Dynamics: use
of dynamical systems
methods to analyze models of neuronal firing patterns" |
J. Rinzel.
XPP tutorial class,
Aula PC2, FME (computer room at the right wing of the ground floor)
|
D. Terman. "Neuronal Dynamics: use
of dynamical systems
methods to analyze models of neuronal firing patterns" |
J. Rinzel. "Understanding
neuronal dynamics by geometrical dissection of minimal models" |
D. Terman. "Neuronal Dynamics: use
of dynamical systems
methods to analyze models of neuronal firing patterns" |
All the courses
will be held in "Aula 005"
of the FME
building (Facultat de
Matemàtiques i
Estadistica), at C/ Pau Gargallo, n. 5 Barcelona, 08028.
- Financial
support: There
are limited funds for the attendants to help covering lodging or
travelling expenses.
Previous registration in the corresponding UPC doctorate course will be
required. Please contact Antoni Guillamon
--antoni.guillamon@(upc.edu)--. Applications received by May 15th will
have preference. For those
who have applied for grants: you will be informed as soon as we receive
news from the sponsors. Thanks for the patience
- Registration:
Formal registrations will be done during the course. However,
we would like to know the number of attendants in advance; please, send an
email to antoni.guillamon
upc.edu
before June 21st if you want to attend and you are not in this list
of attendants.
- Lodging:
The attendants should book
the lodging themselves. There is a residence in the UPC that can be
specially convenient (see here
and the links therein).
- Transportation:
The FME at UPC is close to the subway (Metro)
station of Palau Reial
(on the green line). See http://www.tmb.net/en_US/home.jsp
for more information of public transportation. If you arrive by train
to Sants-Estació, take
the green line (Línia 3)
towards Zona Universitària.
From the airport, there is a train to Sants-Estació.
For more
information, please contact antoni.guillamonupc.edu
Last update: June 30th, 2005, 17:08
Lecture
4.1 (3,6 Mb)