Selected Publications
Please feel free to contact me at rubin@math.pitt.edu for reprints/preprints.
Note that some of the material below is based upon work supported by
the National Science Foundation under Grants No. 0108857, 0414023, and
0716936.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Preprints
S. Daun, J. Rubin, I. Rybak, "Control of oscillation periods and phase durations in half-center central pattern generators: a comparative mechanistic analysis", submitted. Download pdf preprint.
J. Day, J. Rubin, C. Chow, "Competition between transients in the rate of approach to a fixed point", submitted. Download pdf preprint (about 4 MB).
S. Daun, J. Rubin, G. Clermont, "Equation-based models of dynamic biological systems", J. Crit. Care., accepted.
Refereed Articles
S. Daun, J. Rubin, Y. Vodovotz, A. Roy, R. Parker, G. Clermont, "An ensemble of models of the acute inflammatory response: results from parameter reduction", J. Theor. Biol., Articles in Press
doi:10.1016/j.jtbi.2008.04.033.
J. Rubin, M. Wechselberger, "The selection of mixed mode oscillations in a Hodgkin-Huxley model with multiple timescalesChaos, 18: 015105-1--015105-12, 2008.
Download pdf file.
Y. Guo, J. Rubin, C. McIntyre, J. Vitek, and D. Terman, "Thalamocortical relay fidelity varies across subthalamic nucleus deep brain
stimulation protocols in a data-driven computational model", J. Neurophysiol., 99: 1477-1492, 2008.
Download pdf file.
S. Zenker, J. Rubin, and G. Clermont, "Towards a model based medicine: a clinically meaningful approach to ill-posed inverse problems in quantitative
physiology", PLoS Comp. Biol., 3: 2072-2086, 2007.
Downlead pdf file.
Available as Pitt
Department of Mathematics Technical Report 07-04.
J. Upperman et al., "Mathematical modeling in necrotizing enterocolitis -
a new look at an ongoing problem", J. Ped. Surg., 42: 445-453, 2007. Download pdf file.
J. Rubin and M. Wechselberger, "Giant squid - hidden canard: the
3D geometry of the Hodgkin-Huxley model", Biological Cybernetics,
97: 5-32, 2007.
Download pdf file.
J. Rubin and K. Josic, "The firing of an excitable neuron in the
presence of stochastic trains of strong inputs", Neural Comp.,
19: 1251-1294, 2007.
Download pdf file.
J. Rubin and A. Bose, "The geometry of neuronal recruitment",
Physica D, 221: 37-57, 2006 (DOI 10.1016/j.physd.2006.07.012).
J. Rubin, "Bursting induced by excitatory synaptic coupling in
non-identical conditional relaxation oscillators or square-wave bursters",
Phys. Rev. E, 74, 021917, 2006.
Download pdf file or link online.
J.M. Prince et al., "In silico and in vivo approach to elucidate the
inflammatory complexity of CD-14 deficient mice," Mol. Medicine, 12: 88-96, 2006.
A. Reynolds, J. Rubin, G. Clermont, J. Day, Y. Vodovotz, and B. Ermentrout, "A reduced mathematical model for the acute inflammatory response. I. Derivation of model and analysis of anti-inflammation", J. Theor. Biol., 242: 220-236, 2006.
Download pdf file or link online.
J. Day, J. Rubin, Y. Vodovotz, C. Chow, A. Reynolds, and G. Clermont, "A reduced mathematical model for the acute inflammatory response. II. Capturing scenarios of repeated endotoxin administrations", J. Theor. Biol., 242: 237-256, 2006.
Download pdf file or link online.
J. Best, A. Borisyuk, J. Rubin, D. Terman and M. Wechselberger,
"The dynamic range of bursting in a model respiratory pacemaker network,"
SIAM J. Appl. Dyn. Syst., 4: 1107-1139, 2005.
Download pdf file.
Jonathan Rubin, "Surprising effects of synaptic excitation", J. Comp. Neurosci., 18: 333-342, 2005.
Download pdf file.
Guo-Qiang Bi and Jonathan Rubin, "Timing in synaptic plasticity: from detection to integration", Trends in Neuroscience, 28: 222-228, 2005.
Donload pdf file.
Jonathan Rubin, Richard Gerkin, Guo-Qiang Bi, and Carson Chow, "Calcium time course as a signal for spike-timing dependent plasticity", J. Neurophys., 93: 2600-2613, 2005.
Download pdf file.
Kresimir Josic and Jonathan Rubin, "Deriving information about architecture from activity patterns in coupled cell systems", SIAM Journal of
Applied Dynamical Systems, 4: 53-77, 2005.
Download pdf file.
This is also University of
Pittsburgh Department of Mathematics Technical Report 04-04.
Jonathan Rubin and Amitabha Bose, "Localized activity patterns in excitatory neuronal networks",
Network: Comp. Neural Sys., 15: 133-158, 2004.
Available online.
Download pdf file or
gzipped postscript file.
This is also University of Pittsburgh Department of Mathematics Technical Report 04-01.
Jonathan Drover, Jonathan Rubin, Jianzhong Su, and Bard Ermentrout,
"Analysis of a canard mechanism by which excitatory synaptic coupling can
synchronize neurons at low firing frequencies," SIAM J. Appl.
Math., 65: 69-92, 2004.
Available online at SIAM Journal on Applied Mathematics website or download pdf file here.
Jonathan Rubin and David Terman, "High frequency stimulation of the subthalamic
nucleus eliminates pathological rhythmicity in a computational model," J.
Comp. Neurosci., 16: 211-235, 2004.
Download pdf file.
Jonathan Rubin and Bill Troy, "Sustained spatial patterns of activity in neuronal
populations without recurrent excitation," SIAM J. Appl. Math., 64: 1609-1635, 2004.
Download
pdf file.
Jianzhong Su, Jonathan Rubin, and David Terman, "Effects of noise on
elliptic bursters," Nonlinearity, 17: 133-157, 2004.
Available online at Nonlinearity website.
Note that this is University of Pittsburgh Technical Report TR 03-01.
Remus Osan, Rodica Curtu, Jonathan Rubin, and Bard Ermentrout, "Multiple-spike
waves in a one-dimensional integrate-and-fire neural network," J. Math. Biol. , 48: 243-274, 2004.
Download
gzipped postscript file or
pdf file
Jonathan Rubin, "A nonlocal eigenvalue problem for the stability of a traveling
wave in a neuronal medium," Disc. Cont. Dyn.
Sys. - A, 4: 925-940, 2004. Download pdf file or gzipped
postscript file.
Jonathan Rubin and David Terman, "Synchronized bursts and loss of synchrony
among heterogeneous conditional oscillators," SIAM J. Appl. Dyn.
Sys. , 1: 146-174, 2002.
View article online.
Download pdf file.
D. Terman, J.E. Rubin, A.C. Yew and C.J. Wilson, "Activity patterns in a model
for the Subthalamopallidal Network of the Basal Ganglia," J. Neurosci., 22: 2963-2976, 2002.
Download pdf file.
Remus Osan, Jonathan Rubin, and Bard Ermentrout, "Regular traveling waves
in a one-dimensional network of theta neurons," SIAM J. Appl.
Math., 62: 1197-1221, 2002.
Download pdf file.
Jonathan Rubin, David Terman, and Carson Chow, "Localized bumps
of activity sustained by inhibition in a two-layer thalamic network",
J. Comp. Neurosci., 10: 313-331, 2001.
Download pdf file
Jonathan Rubin, "Steady states in an iterative model for multiplicative
spike-timing dependent plasticity", Network: Comp. Neural Sys., 12(2): 131-140, 2001.
Download pdf file
Jonathan Rubin, Daniel D. Lee, and Haim Sompolinsky,
"Equilibrium properties of temporally asymmetric Hebbian plasticity",
Phys. Rev. Lett., 86(2): 364-367, 2001.
Download pdf file
Jonathan Rubin and David Terman, "Analysis of clustered firing
patterns in synaptically coupled networks of oscillators",
J. Math. Biol., 41(6): 513-545, 2000.
Download zipped postscript file
or pdf file
J.E. Rubin and D. Terman, "Geometric analysis of population rhythms
in synaptically coupled neuronal networks," Neural Comput., 12(3): 597-645, 2000.
Download pdf file.
Todd Kapitula and Jonathan Rubin, "Existence and stability of
hole solutions to complex Ginzburg-Landau equations,"
Nonlinearity,, 13(1): 77-112, 2000.
Download pdf file
Jonathan Rubin, "Stability, bifurcations, and edge oscillations for
standing pulse solutions to an inhomogeneous reaction-diffusion system,"
Proc. Roy. Soc. Edinb., Ser. A, 129: 1033-1079, 1999.
Christopher K.R.T. Jones and Jonathan E. Rubin, "Existence of
standing pulse solutions to an inhomogeneous reaction-diffusion
system," J. Dyn. Diff. Eq., 10(1): 1-35, 1998.
Jonathan E. Rubin and Christopher K.R.T. Jones, "Bifurcations and
edge oscillations in the semiconductor Fabry-Perot interferometer,"
Optics Comm., 140: 93-98, 1997.
Download pdf file
J. Rubin, C.K.R.T. Jones, and M. Maxey, "Settling and Asymptotics
of Aerosol Particles in a Cellular Flow Field," J. Nonlinear Sci.
5: 337-358, 1995.
Andre C.M. Ran, Leiba Rodman, and Jonathan E. Rubin, "Direct
Complements of Invariant Lagrangian Subspaces and Minimal Factorizations
of Skew-Symmetric Rational Matrix Functions," Lin. Alg.
Appl., 180: 61-94, 1993.
Conference Papers
Y. Vodovotz et al., "In silico models of acute inflammation in
animals," to appear in Shock.
Y. Vodovotz et al., "Mathematical simulations of sepsis and trauma", Proceedings of the 11th Congress of the
European Shock Society, 2005.
B. Siegler, M. Ritchey, and J. Rubin, "Spike-timing dependent plasticity
as a mechanism for ocular dominance shift," Neurocomputing , 65-66: 181-188, 2005.
G. Hernandez, J. Rubin, and P. Munro, "The effect of spike redistribution in a reciprocally
connected pair of neurons with spike timing-dependent plasticity,"
Neurocomputing , 52-54: 347-353, 2003. Download pdf file.
R. Osan, J. Rubin, R. Curtu, and B. Ermentrout, "Traveling waves in a one-dimensional integrate-and-fire neural network with finite support connectivity," Neurocomputing , 52-54: 869-875, 2003. Download pdf file.
G. Hernandez, P. Munro, and J. Rubin, "Mapping from the spike domain ot the rate-based domain," 2003 International Conference on Neural Information
Processing (ICONIP)
D. Terman, J.E. Rubin, A.C. Yew and C.J. Wilson, "Synchronous
parkinsonian rhythms in a model for the indirect pathway of the
basal ganglia," Neurocomputing, 38-40: 973-982, 2001.
Download zipped postscript file.
Jonathan Rubin and David Terman, "Geometric analysis of neuronal firing
patterns in network models with fast inhibitory synapses,"
Neurocomputing, 26-27: 491-498, 1999.
Others
Jonathan E. Rubin (2007) Burst
synchronization. Scholarpedia,
2(10):1666
J. Rubin, "Emergent bursting in small networks of model conditional
pacemaker cells in the pre-Botzinger complex",
in M. Poulin and R. Wilson, editors, Integration in Respiratory Control: From Genes to Systems, Springer Advances in Experimental Medicine and Biology, Volume 605, 2008.
Download pdf file.
R. Butera, J. Rubin, D. Terman, and J. Smith, "Oscillatory bursting
mechanisms in respiratory pacemaker neurons," in
S. Coombes and P. Bressloff, editors, Bursting: The Genesis of Rhythm in the Nervous System, World Scientific Press, 2005.
G. Clermont, Y. Vodovotz, and J. Rubin, "Equation-based models of
dynamic biological systems," to appear in W.C. Aird, editor, Comprehensive Treatise on Endothelial Biomedicine,
Cambridge University Press.
Jonathan Rubin, "Catch the Buzz: Staging an Integration Bee," MAA Focus, Vol. 22, Number 9, December, 2002.
Jonathan Rubin and David Terman, "Geometric Singular Perturbation
Analysis of Neuronal Dynamics," in B. Fiedler, editor, Handbook of Dynamical
Systems, Vol. 2, Elsevier, 2002.
C.K.R.T. Jones, G. Haller, P.D. Miller, and J. Rubin, "Settling and
Mixing in Oceanic Flows: The Role of Heteroclinic Orbits," Naval
Research Reviews XLVII(1): 17-28, 1995.