Publications

2012

• S. Jayasuriya & Z.P. Kilpatrick, Effects of Time-Dependent 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 Excitatory-Inhibitory Neural Fields, Phys. Rev. Lett., accepted (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. 535-543.
• 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 self-coupled 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 1019-1060.
• J. R. Dunmyre & J. E. Rubin, Optimal Intrinsic Dynamics for Bursting in a Three-Cell Network, SIAM J. Appl. Dyn. Syst., 9 (2010), pp. 154-187.
• 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 Feedback-Mediated Dynamics in Three Coupled Nephrons. SIURO 2(1): 1-25, 2009.
• B. Riviere, Y. Epshteyn, D. Swigon, & Y. Vodovotz, A Mathematical Model of Signaling Resulting from the Binding of Lipopolysaccharide with Toll-like Receptors Demonstrates Inherent Preconditioning Behavior, Math. Biosciences 217: 19-26, 2009.
• S. Bayram, T.L. Stepien, E.B. Pitman. TGF-Mediated Dynamics in a System of Many Coupled Nephrons. Bull. Math. Biol. 71: 1482-1506, 2009.
• 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.
• 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
• Ermentrout B, Ko TW, Delays and weakly coupled neuronal oscillators, Philosophical Transactions of the Royal Society A – Mathematical Physical and Engineeering Sciences, 367:1097-1115,2009
• Ko TW, Ermentrout GB, Phase-response 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: 1-10, 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 oxygen-dependent ATP release by red blood cells and conducted responses in metabolic regulation of blood flow. Am J Physiol. Heart. Circ. Physiol. 295:H1562-H1571, 2008.
• Carlson, B.E., Arciero, J.C., Secomb, T.W. Relative influence of myogenic, shear-dependent, and conducted responses on vascular autoregulation. Am. J. Physiol. Heart. Circ. 367:1097-1115 2009
• Ko TW, Ermentrout GB, Bistability between synchrony and incoherence in limit-cycle 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 half-center 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., 253:843-853, 2008.
• G. B. Ermentrout, R.F. Galan, and N. N. Urban. Reliability, synchrony and noise. Trends in Neuroscience, 31:428-434, 2008.
• R.F. Galan, G.B. Ermentrout, and N.N. Urban. Optimal time scale for spike-time reliability: Theory, simulations and experiments. J. of Neurophysiol., 99(1):277-283, 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 data-driven computational model. J. Neurophysiol., 99:1477-1492, 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):491-509, 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 limit-cycle 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 patient-specific 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. Class-II neurons display a higher degree of stochastic synchronization than class-I neurons. Physical Review E, 77(4):041918, 2008.
• Q. Mi, B. Riviere, G. Clermont, D.L. Steed, and Y. Vodovotz. Agent-based modeling of inflammation and wound healing: insights into diabetic foot ulcer pathology and the role of transforming growth factor-beta 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, 22:84-85, 2008.
• 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.