Systems Computational Neuroscience (Math 636)
Please note: The copyrights to the publications below are held by the corresponding publishers. The files below are provided only for educational purposes. They may not
be used for any other purpose without the express permission of the appropriate publishers. This webpage is password protected.
One- and two-dimensional neural systems
Chemical and electrical synapses / Synaptic transmission
Membrane potential (sub-threshold) and firing frequency (supra-threshold) resonance
B. Hutcheon & Y. Yarom (2000), 'Resonance, oscillation and the intrinsic frequency preferences of neurons', Trends Neurosci., 23:216-222
T. A. Engel, L. Schimansky-Geier, A. V. M. Herz, S. Schreiber and I. Erchova (2008), 'Subthreshold Membrane-Potential Resonances Shape Spike-Train Patterns in the Entorhinal Cortex', J. Neurophysiol. 100:1576-1589
M. J. E. Richardson, N. Brunel, V. Hakim (2003), 'From Subthreshold to Firing-Rate Resonance', J. Neurophysiol. 89:2538-2554
Z. F. Mainen & T. J. Sejnowski (1995), 'Reliability of spike timing in neocortical neurons', Science, 268:1503-1506
S. Schreiber, I. Samengo & A. V. M. Herz (2009), 'Two distinct mechanism shape the reliability of neural responses', J. Neurophysiol 101:2239-2251
G. Mato & I. Samengo (2008), 'Type I and type II neuron models are selectively driven by differential stimulus features' Neural Computation' 20:2418-2440.
.
Phase Response Curves / Spike Time Response Curves
D. Terman & B. Ermentrout. Computational Neuroscience. Chapter 8.
C. C. Canavier (2006), 'Phase response curve', Scholarpedia, 1(12):1332.
C. Acker, J. A. White & N. Kopell (2003), 'Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics', J. Comp. Neurosci., 15:71-90.
D. D. Pervouchine, T. I. Netoff, H. G. Rotstein, J. A. White, M. O. Cunningham, M. A. Whittington, N. J. Kopell (2006), 'Low-dimensional maps encoding dynamics in entorhinal cortex and hippocampus'
.
Central Pattern Generators
E. Marder & R. L. Calabrese (1996), 'Principles of Rhythmic Motor Pattern Generation', Physiological Reviews, 687-717
R. M. Ghigliazza & P. Holmes (2004), 'A minimal model of a central pattern generator and motoneurons for insect locomotion', SIAM J Applied Dynamical Systems, 3:671-700
C. Soto-Trevino, P. Rabbah, E. Marder & F. Nadim (2005), 'Computational Model of Electrically Coupled, Intrinsically Distinct Pacemaker Neurons', J Neurophysiol 94:590-604
J.-M. Ramirez, A. K. Tryba, F. Pena (2004), 'Pacemaker neurons and neuronal networks: an integrative view', Current Opinion in Neurobiology, 14:665-674
A. Taylor, G. W. Cotrell, W. B. Kristan (2000),'A model of the leech segmental swim central pattern generator', Neurocomputing 32-33:573-584
.
Data Analysis
(Jaime de la Rocha)
Networks
D. Terman & B. Ermentrout. Computational Neuroscience. Chapter 9.
B. Ermentrout (1998)
'Phase-Plane Analysis of Neural Nets'
F. K. Skinner, N. Kopell, E. Marder (1994),
'Mechanisms for Oscillation and Frequency Control in Reciprocally Inhibitory Model Neural Networks'
J. Comp. Neurosci., 1:69-87
D. Terman, N. Kopell & A. Bose (1998), 'Dynamics of two mutually coupled slow inhibitory neurons', Physica D 117:241-275.
N. Kopell & D. Somers (1995), 'Anti-phase solutions in relaxation oscillators coupled through excitatory interactions', J. Math. Bio. 33:261-280
C. van Vreeswijk, L. F. Abbott, G. B. Ermentrout (1994),
'When Inhibition not Excitation Synchronizes Neural Firing', J. Comp. Neurosci., 1:313:321.
K. Senn, J. C. Jorge-Rivera, E. Marder, L. F. Abbott (1996),
'Decoding Synapses', J. Neurosci., 16:6307-6318.
F. Nadim, Y. Manor, N. Kopell, E. Marder(1999),
'Synaptic depression creates a switch that controls the frequency of an oscillatory input', PNAS, 96:8206-8211.
.
Waves
B. Ermentrout & D. Pinto (2007), 'Neurophysiology and waves', SIAM News, Vol 40
D. Golomb, X.-J. Wang, J. Rinzel (1996), 'Propagation of spindle waves in a thalamic slice model', J. Neurophysiol, 75:750-769
A. Devor & Y. Yarom (2002), 'Generation and Propagation of Subthreshold Waves in
a Network of Inferior Olivary Neurons', J Neurophysiol 87:3059-3069
O. Feinerman, M. Segal & e. Moses (2005), 'Signal Propagation Along Unidimensional Neuronal Networks', J Neurophysiol, 94:3406-3416
D. J. Pinto, S. L. Patrick, W. C. Huang & B. W. Connors, 'Initiation, Propagation, and Termination of Epileptiform
Activity in Rodent Neocortex In Vitro Involve
Distinct Mechanisms', J. Neurosci. 25:8131-8140
X. Huang, W. C. Troy, Q. Yang, H. Ma, C. R. Laing, S. J. Schiff & J.-Y. Wu (2004), 'Spiral Waves in Disinhibited Mammalian Neocortex', J. Neurosci 24:9897:9902
R. Osan & B. Ermentrout (2002), 'The evolution of synaptically generated waves
in one- and two-dimensional domains', Physica D 163:217-235
R. Osan, J. Rubin & B. Ermentrout (2002), 'Regular traveling waves in a one-dimensional network of theta neurons', SIAM J Appl. Math 62:1197-1221
.
.
Rate Equations
(.ode)
.
Matlab - Basics (D. Kim & J. Yi)
T&E
:
"Mathematical Foundations of Neuroscience", by G. B. Ermentrout & D. H. Terman - Springer (2010), 1st edition. ISBN 978-0-387-87707-5.
J&W
:
"Foundations of Cellular Neurophysiology", by Daniel Johnston and Samuel M.-S.
Wu. The MIT Press, 1995. ISBN 0-262-10053-3.
I
:
"Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting",
by Eugene M. Izhikevich. The MIT Press, 2007. ISBN 0-262-09043-8
K
:
"Biophysics of Computation - Information processing in single neurons", by
Christof Koch. Oxford University Press, 1999. ISBN 0-19-510491-9.
D&A
:
"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
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Department of Mathematical Sciences(DMS).
New Jersey Institute of Technology (NJIT).
Horacio
Last modified: Fri Apr 30 17:40:33 EDT 2010