
Publications
2013
 J.J. Rubin, J.E. Rubin & G.B. Ermentrout Analysis of synchronization in a slowly changing environment: how slow coupling becomes weak coupling, Phys. Rev. Lett., 110(20): 204101 (2013).
 Rosenbaum, R., Rubin, J. E., & Doiron, B. Shortterm synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations, J. Neurophysiol., 109(2): 475484 (2013).
 Reich, S. & Rosenbaum, R., The impact of short term synaptic depression and stochastic vesicle dynamics on neuronal variability, J. Comp. Neurosci., accepted (2013).
2012
 C.J. Miller, G.B. Ermentrout & L.A. Davidson, Rotational model for actin filament alignment by myosin, J. Theor. Biol., 300:344359 (2012).
 K. Penner, B. Ermentrout & D. Swigon, Pattern formation in a model of acute inflammation, SIAM J. Appl. Dyn. Syst., 11: 629660 (2012).
 J. Arciero, G.B. Ermentrout, R. Siggers, A. Afrazi, D. Hackam, Y. Vodovotz, & J. Rubin, Modeling the interactions of bacteria and inflammation in necrotizing enterocolitis, J. Theor. Biol., accepted (2012).

S. Jayasuriya & Z.P. Kilpatrick, Effects of TimeDependent Stimuli in a Competitive Neural Network Model of Perceptual Rivalry,
Bull. Math. Biol., accepted (2012).

S.E. Folias & G.B. Ermentrout, Bifurcations of Stationary Solutions in an Interacting Pair of E–I Neural Fields,
SIAM J. Appl. Dyn. Syst., accepted (2012).
2011

S.E. Folias & G.B. Ermentrout, New Patterns of Activity in a
Pair of Interacting ExcitatoryInhibitory Neural Fields,
Phys. Rev. Lett., 107:228103 (2011).

S.E. Folias, Nonlinear Analysis of Breathing Pulses in a Synaptically Coupled Neural Network,
SIAM J. Appl. Dyn. Syst., 10 (2011) pp. 744–787.

J.C. Arciero, Q. Mi, M.F. Branca, D. Hackam, &
D. Swigon, Continuum Model of Collective Cell Migration in Wound
Healing and Colony Expansion, Biophys. J., 100 (2011) pp. 535543.

J. R. Dunmyre, C. A. Del Negro, & J. E. Rubin, Interactions of the CAN and persistent
sodium current within a model respiratory neuron yield dynamically distinct bursting
regimes, J. Comput. Neurosci. (accepted)

J. R. Dunmyre, Qualitative validation of the reduction from two reciprocally coupled
neurons to one selfcoupled neuron in a respiratory network model, J. Biol. Phys. (accepted)

H.F. Parks, G.B. Ermentrout & J.E. Rubin, The dynamics of a forced coupled network of active elements, Physica D, (in press)
2010

S.E. Folias & G.B. Ermentrout, Spatially localized synchronous oscillations in
synaptically coupled neuronal networks: conductance–based models and discrete maps,
SIAM J. Appl. Dyn. Syst., 9 (2010), pp 10191060.

J. R. Dunmyre & J. E. Rubin, Optimal Intrinsic Dynamics for Bursting in a ThreeCell
Network, SIAM J. Appl. Dyn. Syst., 9 (2010), pp. 154187.

S. Lim, Y. Kim, & D. Swigon, Dynamics of an electrostatically charged rod in fluid, Proc. Roy Soc. A, online publication doi: 10.1098/rspa.2010.0174, 2010.

Arciero, J.C., Ermentrout, G.B., Upperman, J.S., Vodovotz, Y., & Rubin, J.E. (2010) Using a Mathematical Model to Analyze the Role of Probiotics and Inflammation in Necrotizing Enterocolitis. PLoS ONE 5(4): e10066. doi:10.1371/journal.pone.0010066
2009

T.L. Stepien. Tubuloglomerular FeedbackMediated Dynamics in Three
Coupled Nephrons. SIURO 2(1): 125, 2009.

B. Riviere, Y. Epshteyn, D. Swigon, & Y. Vodovotz, A Mathematical Model of Signaling Resulting from the Binding of Lipopolysaccharide with Tolllike Receptors Demonstrates Inherent Preconditioning Behavior, Math. Biosciences 217: 1926, 2009.

S. Bayram, T.L. Stepien, E.B. Pitman. TGFMediated Dynamics in a
System of Many Coupled Nephrons. Bull. Math. Biol. 71: 14821506, 2009.

J. Rubin, N. Shevtsova, B. Ermentrout, J. Smith, I. Rybak. Multiple rhythmic states in a model of the respiratory CPG. J. Neurophysiol. 101: 21462165, 2009.

J. Rubin, J. Hayes, J. Mendenhall, C. Del Negro.
Calciumactivated nonspecific cation current and synaptic depression promote networkdependent burst oscillations. Proc. Natl. Acad. Sci. USA 106: 29392944, 2009
 Ermentrout B, Ko TW, Delays and weakly coupled neuronal oscillators,
Philosophical Transactions of the Royal Society A – Mathematical Physical and Engineeering Sciences, 367:10971115,2009
 Ko TW, Ermentrout GB, Phaseresponse curves of coupled oscillators
Phys Rev E:79: 016211, 2009

Y. Vodovotz, G. Constantine, J. Rubin, M. Csete, E. Voit, G. An, Mechanistic simulations of inflammation: Current state and future prospects, Math. Biosci., 217: 110, 2009
2008

I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M. F. Wheeler, and I. Yotov. Convergence of a symmetric mpfa method on quadrilateral grids. Computational Geosciences. (accepted)

Arciero, J.C., Carlson, B.E., Secomb, T.W. Roles of oxygendependent ATP release by red blood cells and conducted responses in metabolic regulation of blood flow. Am J Physiol. Heart. Circ. Physiol. 295:H1562H1571, 2008.

Carlson, B.E., Arciero, J.C., Secomb, T.W. Relative influence of myogenic, sheardependent, and conducted responses on vascular autoregulation. Am. J. Physiol. Heart. Circ. 367:10971115 2009
 Ko TW, Ermentrout GB, Bistability between synchrony and incoherence in limitcycle oscillators with coupling strength inhomogeneity, Phys Rev E 78: 026210, 2008

S. Daun, J. Rubin, I. Rybak. Control of oscillation periods and phase durations in halfcenter central pattern generators: a comparative mechanistic analysis. J. Comp. Neurosci., accepted.

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., 253:843853, 2008.

G. B. Ermentrout, R.F. Galan, and N. N. Urban. Reliability, synchrony and noise. Trends in Neuroscience, 31:428434, 2008.

R.F. Galan, G.B. Ermentrout, and N.N. Urban. Optimal time scale for spiketime reliability: Theory, simulations and experiments. J. of Neurophysiol., 99(1):277283, 2008.

U. Girault, S. Sun, M. F. Wheeler, and I. Yotov. Coupling discontinuous galerkin and mixed finite element discretizations using mortar finite elements. Submitted to SIAM J. Numer. Anal.

Y. Guo, J. Rubin, C. McIntyre, J. Vitek, and D. Terman. Thalamocortical relay fidelity varies across subthalamic nucleus deep brain stimulation protocols in a datadriven computational model. J. Neurophysiol., 99:14771492, 2008.

F.G. Kazanci, and G.B. Ermentrout. Wave formation through the interactions between clustered states and local coupling in arrays of neural oscillators. SIAM J. Appl. Dyn. Syst., 7(2):491509, 2008.

T.W. Ko, and G.B. Ermentrout. Partially locked states in coupled oscillators due to inhomogeneous coupling. Physical Review E, 78(1):016203, 2008.

T.W. Ko, and G.B. Ermentrout. Bistability between synchrony and incoherence in limitcycle oscillators with coupling strength inhomogeneity. Physical Review E, 78;026210, 2008.

N. Li, K. Verdolini, G. Clermont, Q. Mi, P. Hebda, and Y. Vodovotz. A patientspecific in silico model of inflammation and healing tested in acute vocal fold injury. Submitted.

K. Lipnikov, M. Shashkov, and I. Yotov. Local flux mimetic finite difference methods. Submitted to Numer. Math.

S. Marella, and G.B. Ermentrout. ClassII neurons display a higher degree of stochastic synchronization than classI neurons. Physical Review E, 77(4):041918, 2008.

Q. Mi, B. Riviere, G. Clermont, D.L. Steed, and Y. Vodovotz. Agentbased modeling of inflammation and wound healing: insights into diabetic foot ulcer pathology and the role of transforming growth factorbeta 1. Wound Repair and Regeneration, To appear.

A. Reynolds, G. Clermont, J. Rubin, et al. A mathematical model of acute inflammation which accounts for blood and tissue ineractions. Shock, 22:8485, 2008.

J. Rubin, M. Wechselberger. The selection of mixed mode oscillations in a HodgkinHuxley model with multiple timescales. Chaos, 18:015105101510512, 2008.
