Selected Publications

Please feel free to contact me at jonrubin@pitt.edu for reprints/preprints. Note that some of the material below is based upon work supported by the National Science Foundation under Division of Mathematical Sciences Grants No. 0108857, 0414023, 0716936, and 1021701. 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 - contact me if you're interested!

  • J. Rubin and D. Terman, "Explicit maps to predict activation order in multiphase rhythms of a coupled cell network".
  • J.E. Rubin, C.C. McIntyre, R.S. Turner and T. Wichmann, "Basal ganglia activity patterns in parkinsonism and computational modeling of their downstream effects".
  • S. Zenker, G. Clermont, and J. Rubin, "Ratio approximation Markov Chain Monte Carlo (RAMC): Towards a tuning-free, efficient Markov Chain Monte Carlo algorithm".
  • A. Roy et al., "A mathematical model of acute inflammatory response to endotoxin challenge".

    Refereed and Review Articles

    2011

  • R. Curtu and J. Rubin, "Interaction of canard and singular Hopf mechanisms in a neural model", SIAM J. Appl. Dyn Syst., 10: 1443-1479, 2011.
  • P. Reitsma, B. Doiron, and J. Rubin, "Correlation transfer from basal ganglia to thalamus in Parkinson's disease", Frontiers Comp. Neurosci., 5: doi10.3389/fncom.2011.00058, 2011.
  • L.E. Spardy, S.N. Markin, N.A. Shevtsova, B.I. Prilutsky, I.A. Rybak, and J.E. Rubin, "A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: I. Rhythm generation", J. Neural Eng., 8: 065003, 2011.
  • L.E. Spardy, S.N. Markin, N.A. Shevtsova, B.I. Prilutsky, I.A. Rybak, and J.E. Rubin, "A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: II. Phase asymmetry", J. Neural Eng., 8: 065004, 2011.
  • Z. Hao, L.E. Spardy, E.B.L. Nguyen, J.E. Rubin, and A. Berkowitz, "Strong interactions between spinal cord networks for locomotion and scratching", J. Neurophysiol., 106: 1766-1781, 2011.
  • D.J. Bourbeau, J.A. Hokanson, J.E. Rubin, and D.J. Weber, "A computational model for estimating recruitment of primary afferent fibers by intraneural stimulation in the dorsal root ganglia", J. Neural Eng., 8: 056009, 2011.
  • S. Kubota and J.E. Rubin, "NMDA-induced burst firing in a model subthalamic nucleus neuron", J. Neurophysiol., 106: 527-537, 2011.
  • J. Dunmyre, C.A. Del Negro, and J.E. Rubin, "Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct busting regimes in a model of respiratory neurons", J. Comp. Neurosci., 31:305-328, DOI: 10.1007/s10827-010-0311-y, 2011.
  • C. Gaiteri and J.E. Rubin, "The interaction of intrinsic dynamics and network topology in determining network burst synchrony", Frontiers Comp. Neurosci., 5, doi:10.3389/fncom.2011.00010, 2011. Free open access.
  • J. Wang, W. Costello, and J.E. Rubin, "Tailoring inputs to achieve maximal neuronal firing", J. Math. Neurosci., 1, doi:10.1186/2190-8567-1-3, 2011. Free open access.
  • Y. Guo and J.E. Rubin, "Multi-site stimulation of subthalamic nucleus diminishes thalamocortical relay errors in a biophysical network model", Neural Networks, 24: 602-616, 2011.
  • H.F. Parks, B. Ermentrout, and J.E. Rubin, "The dynamics of a forced coupled network of active elements", Physica D, 240: 554-567, 2011.
  • J.E. Rubin, B.J. Bacak, Y.I. Molkov, N.A. Shevtsova, J.C. Smith, and I.A. Rybak, "Interacting oscillations in neural control of breathing: modeling and qualitative analysis", J. Comp. Neurosci., 30:607-632, 2011 (DOI: 10.1007/s10827-010-0281-0).

    2010

  • G.B. Ermentrout, J.Z. Jalics, and J.E. Rubin, "Stimulus-driven traveling solutions in continuum neuronal models with a general smooth firing rate function", SIAM J. Appl. Math., 70:3039-3064, 2010.
  • J. Day, J. Rubin, G. Clermont, "Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation", Mathematical Biosciences and Engineering, 7:739-763, 2010. Download pdf file.
  • E. Manica, G.S. Medvedev, and J.E. Rubin, "First return maps for the dynamics of synaptically coupled conditional bursters", Biological Cybernetics, 103:87-104, 2010. Download pdf file.
  • S. Kubota, J. Rubin, T. Kitajima, and T. Nakamura, "A variety of competitive properties arises from STDP incorporating metaplastic regulation", Artifical Life and Robotics, 15:185-188, 2010.
  • J.C. Arciero, G.B. Ermentrout, J.S. Upperman, Y. Vodovotz, and J.E. Rubin, "Using a mathematical model to analyze the role of probiotics and inflammation in necrotizing enterocolitis", PLoS ONE, 5(4), e10066, 2010, available online.
  • J. Dunmyre and J. Rubin, "Optimal intrinsic dynamics for bursting in a three-cell network", SIAM J. Appl. Dyn. Syst., 9:154-187, 2010. Download pdf file.

    2009

  • J. Day, J. Rubin, C. Chow, "Competition between transients in the rate of approach to a fixed point", SIAM J. Appl. Dyn. Syst., 8: 1523-1563, 2009. Download pdf file.
  • S. Daun, J. Rubin, I. Rybak, "Control of oscillation periods and phase durations in half-center central pattern generators: a comparative mechanistic analysis", J. Comp. Neurosci., doi:10.1007/s10827-0080-0124-4, 2009. Download pdf file.
  • S. Kubota, J. Rubin, and T. Kitajima, "Modulation of LTP/LTD balance in STDP by an activity-dependent feedback mechanism", Neural Networks, doi:10.1016/j.neunet.2009.06.012, 2009. Download pdf file.
  • J. Rubin, N. Shevtsova, B. Ermentrout, J. Smith, I. Rybak, "Multiple rhythmic states in a model of the respiratory CPG", J. Neurophysiol., 101:2146-2165, 2009. Download pdf file.
  • J. Rubin*, J. Hayes*, J. Mendenhall, C. Del Negro, "Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations", Proc. Natl. Acad. Sci. USA, 106: 2939-2944, 2009. Available online via OPEN ACCESS.
  • Y. Vodovotz, G. Constantine, J. Rubin, M. Csete, E. Voit, G. An, "Mechanistic simulations of inflammation: Current state and future prospects", Math. Biosci., 217: 1-10, 2009. Download pdf file. DOI: 10.1016/j.mbs.2008.07.013.

    2008

  • S. Daun, J. Rubin, Y. Vodovotz, and G. Clermont, "Equation-based models of dynamic biological systems", J. Crit. Care, 23: 585-594, 2008. Download pdf file.
  • 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., 253: 843-853, 2008. Download pdf file.
  • J. Rubin, M. Wechselberger, "The selection of mixed mode oscillations in a Hodgkin-Huxley model with multiple timescales", Chaos, 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.

    2007

  • 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.

    2006

  • 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.

    2005

  • 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. Download 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.

    2004

  • 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.

    2002 and earlier

  • 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 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.

    Books, book chapters, and others

  • R.C. Gerkin, G.-Q. Bi, and J.E. Rubin, "A phenomenological calcium-based model of STDP", in V. Cutsuridis et al., editors, Hippocampal microcircuits: A computational modeler's resource book, Springer Series in Computational Neuroscience, Volume 5, 2010.
  • Coherent behavior in neuronal networks, edited by K. Josic, J. Rubin, M. Matias, and R. Romo, Springer Series in Computational Neuroscience, Volume 3, 2009.
  • 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.

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