Phone: 412-624-8375

Fax: 412-624-8397

E-mail: cbsg@pitt.edu

Publications

To contact us:

Selected publications co-authored by students or postdoctoral fellows:

 

In Press

 

* I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M. F. Wheeler, and I. Yotov. Convergence of a symmetric mpfa method on quadrilateral grids. To appear in Computational Geosciences.

* V. 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.

* 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.

* 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.

* Y. Epshteyn and B. Riviere. Analysis of hp discontinuous Galekin methods for incompressible twophase flow. SIAM Journal on Numerical Analysis, 2007. Submitted.

* V. Girault and B. Riviere. DG approximation of coupled Navier-Stokes and Darcy equations by Beaver-Joseph-Saffman interface condition. SIAM Journal on Numerical Analysis, 2007. Submitted.

* S. Zenker, J. Rubin, and G. Clermont. Towards a model based medicine: a clinically meaningful approach to ill-posed inverse problems in quantitative physiology. 2007. Submitted.

 

2007

 

* Q. Mi, B. Riviere, S. Cetin, Y. Vodovotz, and D. Hackam. One-dimensional elastic continuum model of enterocyte layer migration. Biophys. J. 93:3745-3752, 2007.

* Y. Biton, D. Swigon, and B.D. Coleman. On bifurcations of equilibria of intrinsically curved, electrically charged, rod-like structures that model dna molecules in solution. J. Elasticity., 87:187-210, 2007.

* T. Arbogast, G. Pencheva, M. F. Wheeler, and I. Yotov. A multiscale mortar mixed finite element method. SIAM J. Multiscale Modeling and Simulation, 6(1):319–346, 2007.

* Y. Epshteyn and B. Riviere. Fully implicit discontinuous finite element methods for two-phase flow. Applied Numerical Mathematics, 57:383–401, 2007.

* M. Grabe, H.C. Lai, M. Jain, Y.N. Jan, and L. Yeh. Structure prediction for the down state of a potassium channel voltage sensor. Nature, 445:550–553, 2007.

* B. Hancioglu, D. Swigon, and G. Clermont. A dynamical model of human immune response to influenza a virus infection. J. Theor. Biol., 246(1):70–86, 2007.

* T.F. Russell, M.F. Wheeler, and I. Yotov. Superconvergence for control-volume mixed finite element methods on rectangular grids. SIAM J. Numer. Anal., 45(1):223–235, 2007.

* J. S. Upperman, V. Camerini, B. Lugo, I. Yotov, J. Sullivan, J. Rubin, G. Clermont, R. Zamora, G. B. Ermentrout, H. R. Ford, and Y. Vodovotz. Mathematical modeling in Necrotizing Enterocotitis a new look at an ongoing problem. Journal of Pediatric Surgery, 42(3):445–453, 2007.

 

2006

 

* E. Z. Bagci, Y. Vodovotz, T. R. Billiar, G. B. Ermentrout, and I. Bahar. Bistability in apoptosis: Roles of Bax, Bcl-2, and mitochondrial permeability transition pores. Biophys. J., 90(5):1546–1559, 2006.

* L. Czapla, D. Swigon, and W.K. Olson. Sequence-dependent effects in the cyclization of short dna. J. Chem. Theory Comput., 2:685–695, 2006.

* J. D. Drover and G. B. Ermentrout. Phase boundaries as electrically induced phosphenes. Siam J. On Appl. Dynamical Systems, 5(4):529–551, 2006.

* Y. Epshteyn and B. Riviere. Estimation of penalty parameters for symmetric interior penalty Galerkin methods. Journal of Computational and Applied Mathematics, 2006. doi:10.1016/j.cam.2006.08.029.

* Y. Epshteyn and B. Riviere. On the solution of incompressible two-phase flow by a p-version discontinuous Galerkin method. Communications in Numerical Methods in Engineering, 22:741–751, 2006.

* R. F. Galan, G. B. Ermentrout, and N. N. Urban. Predicting synchronized neural assemblies from experimentally estimated phase-resetting curves. Neurocomputing, 69(10-12):1112–1115, 2006.

* R. F. Galan, G. B. Ermentrout, and N. N. Urban. Reliability, discriminability and stochastic synchronization of olfactory neurons. Sensors Actuators B-chemical, 116(1-2):168–173, 2006.

* R. F. Galan, N. Fourcaud-Trocme, G. B. Ermentrout, and N. N. Urban. Correlation-induced synchronization of oscillations in olfactory bulb neurons. J. Neuroscience, 26(14):3646–3655, 2006.

* D. Golomb, A. Shedmi, R. Curtu, and G. B. Ermentrout. Persistent synchronized bursting activity in cortical tissues with low magnesium concentration: A modeling study. J. Neurophysiology, 95(2):1049–1067, 2006.

* F. G. Kazanci and B. Ermentrout. Pattern formation in an array of oscillators with electrical and chemical coupling. Siam J. On Appl. Mathematics, 67(2):512–529, 2006.

* W. Klieber and B. Riviere. Adaptive simulations of two-phase flow by discontinuous Galerkin methods. Computer Methods in Applied Mechanics and Engineering, 196:404–419, 2006.

* S. B. Moldakarimov, J. L. McClelland, and G. B. Ermentrout. A homeostatic rule for inhibitory synapses promotes temporal sharpening and cortical reorganization. Proc. National Acad. Sciences United States Am., 103(44):16526–16531, 2006.

* A. Reynolds, J. Rubin, G. Clermont, J. Day, YY. Vodovotz, and B. Ermentrout. A reduced mathematical model for the acute inflammatory response. I. Derivation of model and analysis of antiinflammation. J. Theor. Biol., 242:220–236, 2006.

* A. Reynolds, J. Rubin, G. Clermont, J. Day, YY. Vodovotz, and B. Ermentrout. A reduced mathematical model for the acute inflammatory response. II. Capturing scenarios of repeated endotoxin administrations. J. Theor. Biol., 242:237–256, 2006.

* B. Riviere and V. Girault. Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces. Computer Methods in Applied Mechanics and Engineering, 195:3274–3292, 2006.

* J. Sullivan and I. Yotov. Mathematical and numerical modeling of inflammation. In Electronic proceedings of Undergraduate Mathematics Day, University of Dayton, Ohio, Vol. 2, http://academic.udayton.edu/EPUMD, 2006.

* D. Swigon, B.D. Coleman, and W.K. Olson. Modeling the lac repressor-operator assembly: I. the influence of dna looping on lac repressor conformation. Proc. Natl. Acad. Sci. USA, 103:9879–9884, 2006.

* M. F. Wheeler, G. Pencheva, S. G. Thomas, and I. Yotov. Multiscale mortar mixed finite elements for multiphase flow in porous media. In 10th European Conference on the Mathematics of Oil Recovery, Amsterdam, 2006.

* M.F. Wheeler and I. Yotov. A cell-centered finite difference method on quadrilaterals. In Compatible spatial discretizations, volume 142 of IMA Vol. Math. Appl., pages 189–207. Springer, New York, 2006.

* M.F. Wheeler and I. Yotov. A multipoint flux mixed finite element method. SIAM J. Numer. Anal., 44(5):2082–2106, 2006.

 

2005

 

* M. Berndt, K. Lipnikov, M. Shashkov, M. F. Wheeler, and I. Yotov. A mortar mimetic finite difference method on non-matching grids. Numer. Math., 102(2):203–230, 2005.

* M. Berndt, K. Lipnikov, M. Shashkov, M. F.Wheeler, and I. Yotov. Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals. SIAM J. Numer. Anal., 43(4):1728–1749, 2005.

* G-Q. Bi and J. Rubin. Timing in synaptic plasticity: from detection to integration. Trends in Neurosci., 28:222–228, 2005.

* R. F. Galan, G. B. Ermentrout, and N. N. Urban. Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. Phys. Rev. Lett., 94(15), 2005.

* V. Girault, B. Riviere, and M. Wheeler. A discontinuous Galerkin method with non-overlapping domain decomposition for the Stokes and Navier-Stokes problems. Mathematics of Computation, 74:53–84, 2005.

* V. Girault, B. Riviere, and M. Wheeler. A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations. Mathematical Modelling and Numerical Analysis, 39(6):1115–1148, 2005.

* O. Jensen, P. Goel, N. Kopell, M. Pohja, R. Hari, and B. Ermentrout. On the human sensorimotorcortex beta rhythm: sources and modeling. Neuroimage, 26(2):347–355, Jun 2005. Clinical Trial.

* S. Kaya and B. Riviere. A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations. SIAM Journal on Numerical Analysis, 43(4):1572–1595, 2005.

* H.C. Lai, M. Grabe, Y.N. Jan, and L.Y. Jan. The s4 voltage sensor packs against the pore domain in the kat1 voltage-gated potassium channel. Neuron, 47:395–406, 2005.

* D.J. Pinto, S.L. Patrick, W.C. Huang, and B.W. Connors. Initiation, propagation, and termination of epileptiform activity in rodent neocortex in vitro involve distinct mechanisms. J Neurosci, 25(36):8131–8140, Sep 2005. In Vitro.

* B. Riviere. Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems. Journal of Scientific Computing, 22(1):479–500, 2005.

* B. Rivi`ere and I. Yotov. Locally conservative coupling of Stokes and Darcy flows. SIAM J. Numer. Anal., 42(5):1959–1977, 2005.

* J. Rubin, R. Gerkin, G-Q. Bi, and C. Chow. Calcium time course as a signal for spike-timing dependent plasticity. J. Neurophysiol., 93:2600–2613, 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.

* M.F. Wheeler and I. Yotov. A posteriori error estimates for the mortar mixed finite element method. SIAM J. Numer. Anal., 43(3):1021–1042, 2005.

 

2004

 

* R. Curtu and B. Ermentrout. Pattern formation in a network of excitatory and inhibitory cells with adaptation. Siam J. On Appl. Dynamical Systems, 3(3):191–231, 2004.

* J. Drover, J. Rubin, J. H. Su, and B. Ermentrout. Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies. Siam J. On Appl. Mathematics, 65(1):69–92, 2004.

* M. Grabe, H. Lecar, Y.N. Jan, and L.Y. Jan. A quantitative assessment of models for voltagedependent gating of ion channels. Proc. Natl. Acad. Sci. USA, 101:17640–17645, 2004.

* X. Huang, W.C. Troy, Q. Yang, H. Ma, C.R. Laing, S.J. Schiff, and J-Y. Wu. Spiral waves in disinhibited mammalian neocortex. J Neurosci, 24(44):9897–9902, Nov 2004. In Vitro.

* J. Karbowski and G. B. Ermentrout. Model of the early development of thalamo-cortical connections and area patterning via signaling molecules. J. Computational Neuroscience, 17(3):347–363, 2004.

* R. Osan, R. Curtu, J. Rubin, and B. Ermentrout. Multiple-spike waves in a one-dimensional integrate-and-fire neural network. J. Math. Biol., 48(3):243–274, 2004.

* B. Riviere. Analysis of a multi-numerics/multi-physics problem. Numerical Mathematics and Advanced Applications, ENUMATH 2003, pages 726–735, 2004.

* J.E. Rubin and W.C. Troy. Sustained spatial patterns of activity in neuronal populations without recurrent excitation. SIAM J. Appl. Math, 64:1609–1635, 2004.

* K.M. Spencer, P.G. Nestor, R. Perlmutter, M.A. Niznikiewicz, M.C. Klump, M. Frumin, M.E. Shenton, and R.W. McCarley. Neural synchrony indexes disordered perception and cognition in schizophrenia. Proc Natl Acad Sci U S A, 101(49):17288–17293, Dec 2004.

* D. C.Whitcomb and G. B. Ermentrout. A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice. Pancreas, 29(2):E30–E40, 2004.

 

2003

 

* P. Bastian and B. Riviere. Superconvergence and H(div) projection for discontinuous Galerkin methods. International Journal for Numerical Methods in Fluids, 42:1043–1057, 2003.

* J. D. Drover and B. Ermentrout. Nonlinear coupling near a degenerate Hopf (Bautin) bifurcation. Siam J. On Appl. Mathematics, 63(5):1627–1647, 2003.

* 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.

* W.J. Layton, F. Schieweck, and I. Yotov. Coupling fluid flow with porous media flow. SIAM J. Numer. Anal., 40(6):2195–2218, 2003.

* H. Lecar, H.P. Larsson, and M. Grabe. Electrostatic model of s4 motion in voltage-gated ion channels. Biophys. J., 85:2584–2864, 2003.

* R. Osan and B. Ermentrout. Speed-up methods for simulations of traveling waves in integrate-andfire neural networks. Neurocomputing, 52-4:863–868, 2003.

* R. Osan, J. Rubin, R. Curtu, and B. Ermentrout. Traveling waves in a one-dimensional integrateand- fire neural network with finite support connectivity. Neurocomputing, 52-4:869–875, 2003.

* G. Pencheva and I. Yotov. Balancing domain decomposition for mortar mixed finite element methods. Numer. Linear Algebra Appl., 10(1-2):159–180, 2003.

 

2002

 

* P. Goel and B. Ermentrout. Synchrony, stability, and firing patterns in pulse-coupled oscillators. Physica D-nonlinear Phenomena, 163(3-4):191–216, 2002.

* J. Karbowski and G. B. Ermentrout. Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators. Phys. Rev. E, 65(3), 2002.

* J. Karbowski and G.B. Ermentrout. Synchrony arising from a balanced synaptic plasticity in a network of heterogenous neural oscillators. Phys. Rev. E, 65:031902, 2002.

* C.R. Laing, W.C. Troy, B. Gutkin, and G.B. Ermentrout. Multiple bumps in a neuronal model of working memory. SIAM J. Appl. Math., 63:62–97, 2002.

* R. Osan and B. Ermentrout. Development of joint ocular dominance and orientation selectivity maps in a correlation-based neural network model. Neurocomputing, 44:561–566, 2002.

* R. Osan and B. Ermentrout. The evolution of synaptically generated waves in one- and twodimensional domains. Physica D-nonlinear Phenomena, 163(3-4):217–235, 2002.

* R. Osan, J. Rubin, and B. Ermentrout. Regular traveling waves in a one-dimensional network of theta neurons. Siam J. On Appl. Mathematics, 62(4):1197–1221, 2002.

* B. Riviere and M. Wheeler. Coupling locally conservative methods for single phase flow. Computational Geosciences, 6(3):269–284, 2002.

* B. Riviere and M. Wheeler. Discontinuous Galerkin methods for flow and transport problems in porous media. Communications in Numerical Methods in Engineering, 18:63–68, 2002.

* J. Rubin and D. Terman. Geometric singular perturbation analysis of neuronal dynamics. In B. Fiedler, editor, Handbook of Dynamical Systems, vol. 2: Towards Applications. Elsevier, 2002.

* J. Rubin and D. Terman. Synchronized bursts and loss of synchrony among heterogeneous conditional oscillators. SIAM J. Appl. Dyn. Sys., 1:146–174, 2002.

* 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.

 

Pre 2002

 

* B.W. Connors, D.J. Pinto, and A.E. Telfeian. Local pathways of seizure propagation in neocortex. Int Rev Neurobiol, 45:527–546, 2001.

* D.J. Pinto and G.B. Ermentrout. Spatially structured activity in synaptically coupled neuronal networks: I. Traveling fronts and pulses. Siam J. On Appl. Mathematics, 62(1):206–225, 2001.

* B. Riviere, M. Wheeler, and V. Girault. A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM Journal on Numerical Analysis, 39(3):902–931, 2001.

* J.E. Rubin, D.D. Lee, and H. Sompolinsky. Equilibrium properties of temporally asymmetric Hebbian plasticity. Phys. Rev. Lett., 86:364–367, 2001.

* I. Yotov. A multilevel Newton-Krylov interface solver for multiphysics couplings of flow in porous media. Numer. Linear Algebra Appl., 8(8):551–570, 2001.

* T. Arbogast, L. C. Cowsar, M. F. Wheeler, and I. Yotov. Mixed finite element methods on nonmatching multiblock grids. SIAM J. Numer. Anal., 37:1295–1315, 2000.

* J. Rubin and D. Terman. Geometric analysis of population rhythms in synaptically coupled neuronal networks. Neural Comput., 12:597–645, 2000.

* M. F. Wheeler and I. Yotov. Multigrid on the interface for mortar mixed finite element methods for elliptic problems. Comput. Meth. Appl. Mech. Eng., 184:287–302, 2000.

* J.Y. Wu, L. Guan, and Y. Tsau. Propagating activation during oscillations and evoked responses in neocortical slices. J Neurosci, 19(12):5005–5015, Jun 1999.

* M. F. Wheeler and I. Yotov. Physical and computational domain decompositions for modeling subsurface flows. In Jan Mandel et al., editors, Tenth International Conference on Domain Decomposition Methods, Contemporary Mathematics, vol 218, pages 217–228. American Mathematical Society, 1998.

* T. Arbogast, M. F. Wheeler, and I. Yotov. Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences. SIAM J. Numer. Anal., 34(2):828–852, 1997.

Complex Biological Systems Group

Department of Mathematics, University of Pittsburgh