Selected Publications - Under Construction

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, 1021701, 1312508, 1516288, 1612913 as well as the National Institutes of Health/NINDS under Grant No. 1R01NS070865-01A1. 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 these funding agencies.

Preprints - contact me if you're interested!

  • R. Bertram and J.E. Rubin, "Multi-timescale systems and fast-slow analysis", Math. Biosci., accepted. Access online.
  • J.E. Rubin, "Computational models of basal ganglia dysfunction: the dynamics is in the details", Curr. Opin. Neurobiology, under review.
  • B. Letson, J.E. Rubin, and T. Vo, "Analysis of interacting local oscillation mechanisms in three-timescale systems", SIAM J. Appl. Math., under review.
  • D.E. Burstein and J.E. Rubin, "Degree switching and partitioning for enumerating graphs to arbitrary orders of accuracy", under review.
  • D. Swigon, S.R. Stanhope and J.E. Rubin, "Parameter estimation for ensemble ODE models", under review.
  • J.E. Rubin, B. Krauskopf and H.M. Osinga, "Quantitative modeling and analysis of bifurcation-induced bursting", under review.
  • J.E. Rubin, J. Signerska-Rynkowska, J.D. Touboul, and A. Vidal, "Wild oscillations in a nonlinear neuron model with resets: (I) bursting, spike adding and chaos", under review.
  • J.E. Rubin, J. Signerska-Rynkowska, J.D. Touboul, and A. Vidal, "Wild oscillations in a nonlinear model with resets: (II) mixed-mode oscillations", under review.
  • G. Young, M. Demir, H. Salman, G.B. Ermentrout, and J.E. Rubin, "Interactions of solitary pulses of E. coli in a one-dimensional nutrient gradient", PLoS Comp. Biol., under review.
  • Y. Wang and J.E. Rubin, "Timescales and mechanisms of sigh-like bursting and spiking in models of rhythmic respiratory neurons", J. Math. Neurosci,, under review.
  • S. Stanhope, J.E. Rubin, and D. Swigon, "Robustness of solutions of the inverse problem for linear dynamical systems with uncertain data", SIAM J. Uncert. Quant., accepted.

    Refereed and Review Articles

    2017

  • D. Burstein and J. Rubin, "Sufficient conditions for graphicality of bidegree sequences", SIAM. J. Discrete Math., 31:50-62, 2017.
  • R. Rosenbaum, M.A. Smith, A. Kohn, J.E. Rubin, and B. Doiron, "The spatial structure of correlated neuronal variability", Nat. Neurosci., 20:107-114, 2017.
  • Y.I. Molkov*, J.E. Rubin*, I.A. Rybak*, and J.C. Smith*, "Computational models of the neural control of breathing", WIREs Syst. Biol. Med. 2017, e1371, doi:10.1002/wsbm.1371. Access online.

    2016

  • Y. Wang and J.E. Rubin, "Multiple timescale mixed bursting dynamics in a respiratory neuron model", J. Comp. Neurosci., 41:245-268, 2016.
  • V.L. Corbit*, T.C. Whalen*, K.T. Zitelli, S.Y. Crilly, J.E. Rubin**, A.H. Gittis**, "Pallidostriatal projections promote beta oscillations in a dopamine-depleted biophysical network model", J. Neurosci., 36: 5556-5571, 2016.
  • B. Bacak, T. Kim, J.C. Smith, J.E. Rubin, and I.A. Rybak, "Mixed-mode oscillations and population bursting in the pre-Botzinger complex", eLife, 5 (2016): e13403. Access online.
  • M. Duanmu, N. Whitaker, P.G. Kevrekidis, A. Vainchtein, and J. Rubin, "Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators", Physica D, doi:10.1016/j.physd.2016.02.001, 2016.

    2015

  • R.G. Kumar, J.E. Rubin, R.P. Berger, P.M. Kochanek, A.K. Wagner, "Principal components derived from CSF inflammatory profiles predict outcome in survivors after severe traumatic brain injury", Brain Behav. Immun., doi:10.1016/j.bbi.2015.12.008, 2015.
  • K.L. Roberts, J.E. Rubin, and M. Wechselberger, "Averaging, folded singularities, and torus canards: explaining transitions between bursting and spiking in a coupled neuron model, SIAM J. Appl. Dyn. Syst., 14:1808-1844, 2015.
  • P. Nan, Y. Wang, V. Kirk, and J.E. Rubin, "Understanding and distinguishing three-time-scale oscillations: a case study in a coupled Morris-Lecar system", SIAM J. Appl. Dyn. Syst., 14:1518-1557, 2015.
  • G. Young, B. Ermentrout, and J.E. Rubin, "A boundary value approach to optimization with an application to Salmonella competition", Bull. Math. Biol., 77:1327-1348, 2015.
  • A.C. Snyder and J.E. Rubin, "Conditions for multi-functionality in a rhythm generating network inspired by turtle scratching", J. Math. Neurosci., doi10.1186/s13408-015-0026-5, 2015.
  • A. Bose and J.E. Rubin, "Strategies to maximize burst lengths in rhythmic anti-phase activity of networks with reciprocal inhibition", Int. J. Bif. Chaos, 25:1540004, doi:10.1142/s0218127415400040, 2015.
  • W. Wei, J.E. Rubin, and X.-J. Wang, "Role of the indirect pathway of the basal ganglia in perceptual decision making", J. Neurosci., 35:4052-4064, 2015.

    2014

  • S. Stanhope, J.E. Rubin, and D. Swigon, "Identifiability of linear and linear-in-parameters dynamical systems from a single trajectory", SIAM J. Appl. Dyn. Syst., 13:1792-1815, 2014.
  • Y.I. Molkov, N.A. Shevtsova, C. Park, A. Ben-Tal, J.C. Smith, J.E. Rubin, and I.A. Rybak, "A closed-loop model of the respiratory system: focus on hypercapnia and active expiration", PLoS One, 9:e109894, 2014.
  • R. Rosenbaum, A. Zimnik, F. Zheng, R.S. Turner, C. Alzheimer, B. Doiron, and J.E. Rubin, "Axonal and synaptic failure suppress the transmission of firing rate oscillations, synchrony, and information during high frequency deep brain stimulation", Neurobiol. Disease, 62:86-99, 2014. Available online.

    2013

  • D. Terman, J.E. Rubin, and C. Diekman, "Irregular activity arises as a natural consequence of synaptic inhibition", Chaos, 23:4, 046110 (doi:10.1063/1.4831752) Available online.
  • J.J. Rubin, J.E. Rubin, G.B. Ermentrout, "Analysis of synchronization in a slowly changing environment: how slow coupling becomes fast weak coupling", Phys. Rev. Lett., 110: 204101, 2013.
  • S.E. Folias, S. Yu, A. Snyder, D. Nikolic, and J.E. Rubin, "Synchronisation hubs in the visual cortex may arise from strong rhythmic inhibition during gamma oscillations", Eur. J. Neurosci., 38:2864-2883, 2013.
  • N.D. Jimenez, S. Mihalas, R. Brown, E. Niebur, and J. Rubin, "Locally contractive dynamics in generalized integrate-and-fire neurons", SIAM J. Appl. Dyn. Syst., 12:1474-1514, 2013.
  • J. Arciero, G.B. Ermentrout, R. Siggers, A. Afrazi, D. Hackam, Y. Vodovotz, and J. Rubin, "Modeling the interactions of bacteria and Toll-like receptor-mediated inflammation in necrotizing enterocolitis", J. Theor. Biol., 321:83-99, 2013. Available online.
  • R. Rosenbaum, J.E. Rubin, and B. Doiron, "Short term synaptic depression and stochastic vesicle dynamics reduce and reshape neuronal correlations", J. Neurophysiol., 109:475-484, 2013.
  • D.R. Cleary, A.M. Raslan, J.E. Rubin, D. Baghat, A. Viswanathan, M.M. Heinricher, and K.J. Burchiel, "Deep brain stimulation entrains local neuronal firing in human globus pallidus internus", J. Neurophysiol., 109: 978-987, 2013.
  • C. Park and J.E. Rubin, "Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Botzinger complex neurons", J. Comp. Neurosci., 34:345-366, 2013.

    2012

  • R. Rosenbaum, J. Rubin, and B. Doiron, "Short term synaptic depression imposes a frequency dependent filter on synaptic information transfer", PLoS Comp. Biol., 8: e1002557, 2012.
  • J. Rubin and D. Terman, "Explicit maps to predict activation order in multiphase rhythms of a coupled cell network", J. Math. Neurosci., 2:4, DOI 10.1186/2190-8567-2-4, 2012.
  • 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", Eur. J. Neurosci., 36, 2213-2228, 2012. Check out a related video interview on the EJN site!

    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, J. Su, H. Perez Gonzalez, and J. Rubin, "A reliability study of square wave bursting beta-cells with noise", Discrete Cont. Dyn. Syst. Series B, 16, 569-588, 2011.
  • 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. Download pdf file.
  • 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. Download pdf file.
  • 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, encyclopedia/book chapters, and others

  • J.E. Rubin and J. Rinzel, "Neurons and neuronal networks as dynamical systems", From Neuron to Cognition via Computational Neuroscience, edited by M.A. Arbib and J.J. Bonaiuto, The MIT Press, Cambridge, MA, 2016.
  • C.C. McIntyre and J.E. Rubin, "Computational models of deep brain stimulation (DBS)", Springer Encyclopedia of Computational Neuroscience, 2015.
  • J.E. Rubin, "Basal ganglia: Overview", Springer Encyclopedia of Computational Neuroscience, 2015.
  • J.E. Rubin, "Comparative analysis of half-center central pattern generators (CPGs)", Springer Encyclopedia of Computational Neuroscience, 2015.
  • 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.E. Kass, J.E. Rubin, S. Zenker, Comment on "Parameter estimation for differential equations: a generalized smoothing approach" by J.O. Ramsay, G. Hooker, D. Campbell, and J. Cao, J. Royal Stat. Soc. B, 69: 741-770, 2007.
  • 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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