Zachary Kilpatrick
Assistant Professor
Applied Mathematics

Research Interests:

  • Mathematical neuroscience
  • Spatiotemporal pattern formation
  • Stochastic dynamics of neural activity
  • Evidence accumulation and decision making

*undergraduate; †graduate student; ‡post-doc; ⧫equal contribution

N Krishnan*, DB Poll†, and ZP Kilpatrick.ÌýÌýsubmitted (2017)

ZP Kilpatrick.ÌýÌýsubmitted (2017)

ZP Kilpatrick and DB Poll†.ÌýÌýPhys. Rev. EÌý(2017) in press.

DB Poll† and ZP Kilpatrick.ÌýVelocity integration in a multilayer neural field model of spatial working memoryÌýSIAM J Appl. Dyn. Syst.Ìý16 (2017) pp.Ìý1197-1234.

AE Radillo, A Veliz-Cuba, K Josic⧫, and ZP Kilpatrick⧫.ÌýEvidence accumulation and change rate inference in dynamic environmentsÌýNeural Comput. 29 (2017) pp. 1561-1610.

AÌýJacot-Guillarmod⧫, YÌýWang⧫, CÌýPedroza, HÌýOgmen, ZPÌýKilpatrick⧫, andÌýKÌýJosic⧫.ÌýExtending Levelt’s Propositions to perceptual multistability involving interocular groupingÌýVision Res. 133 (2017) pp. 37-46.

DB Poll† and ZP Kilpatrick.ÌýPersistent search in single and multiple confined domains: a velocity-jump process modelÌýJ Stat. Mech. (2016) 053201.

ZT McCleney* and ZP Kilpatrick.ÌýEntrainment in up and down states of neural populations: non-smooth and stochastic modelsÌýJ Math. Biol. 73 (2016) pp.Ìý1131-1160.

DB Poll†, K Nguyen*, and ZP Kilpatrick.ÌýSensory feedback in a bump attractor model of path integrationÌýJ Comput. Neurosci. 40 (2016) pp. 137-155.

ZP Kilpatrick.ÌýGhosts of bump attractors in stochastic neural fields: Bottlenecks and extinctionÌýDiscrete Contin. Dyn. Syst. Ser. B 21 (2016) p. 2211-2231.

A Veliz-Cuba‡, ZP Kilpatrick⧫, K Josic⧫.ÌýStochastic models of evidence accumulation in changing environmentsÌýSIAM Rev. 58 (2016) pp. 264–289.

A Veliz-Cuba‡, HZ Shouval, K Josic⧫, ZP Kilpatrick⧫.ÌýNetworks that learn the precise timing of event sequences.ÌýJ Comput. Neurosci. 39 (2015) pp. 235-254.

DB Poll† and ZP Kilpatrick.ÌýStochastic motion of bumps in planar neural fields.ÌýSIAM J Appl. Math. 75 (2015) pp. 1553-1577.

ZP Kilpatrick.ÌýStochastic synchronization of neural activity waves.ÌýPhys. Rev. E 91 (2015) 040701(R).

PC Bressloff and ZP Kilpatrick.ÌýNonlinear Langevin equations for wandering patterns in stochastic neural fields.ÌýSIAM J Appl. Dyn. Syst. 14 (2015) pp. 305-334.

ZP Kilpatrick.ÌýDelay stabilizes stochastic motion of bumps in layered neural fields.ÌýPhysica D 295 (2015) pp. 30-45.

ZP Kilpatrick and G Faye.ÌýPulse bifurcations in stochastic neural fields.ÌýSIAM J Appl. Dyn. Syst. 13 (2014) pp. 830-860.

JK Kim‡, ZP Kilpatrick, MR Bennett, K Josic.ÌýMolecular mechanisms that regulate the coupled period of the mammalian circadian clock.ÌýBiophys. J 106 (2014) pp. 2071-2081. (Ìýby S.R. Taylor)

ZP Kilpatrick.ÌýCoupling layers regularizes wave propagation in stochastic neural fields.ÌýPhys. Rev. E, 89 (2014) 022706.

ZP Kilpatrick.ÌýWilson-Cowan model.ÌýÌý(2014) Ed. D Jaeger and R Jung, Springer-Verlag.

S Carroll*, K Josic, and ZP Kilpatrick.ÌýEncoding certainty in bump attractors.ÌýJ Comput. Neurosci., 37 (2014) pp. 29-48.

B Ermentrout, SE Folias, and ZP Kilpatrick.ÌýSpatiotemporal pattern formation in neural fields with linear adaptation.ÌýÌý(2014) Ed. S Coombes, P beim Graben, R Potthast, and JJ Wright, Springer Verlag.

ZP Kilpatrick.ÌýInterareal coupling reduces encoding variability in multi-area models of spatial working memory.ÌýFront. Comput. Neurosci., 7 (2013) 82.

ZP Kilpatrick, B Ermentrout, and B Doiron.ÌýOptimizing working memory with heterogeneity of recurrent cortical excitation.ÌýJ Neurosci., 33 (2013) pp. 18999-19011.

ZP Kilpatrick, B Ermentrout.ÌýWandering bumps in stochastic neural fields.ÌýSIAM J. Appl. Dyn. Syst., 12 (2013), pp. 61-94.

ZP Kilpatrick.ÌýShort term synaptic depression improves information transfer in perceptual multistability.ÌýFront. Comput. Neurosci., 7 (2013) 85.

SM Jayasuriya*, ZP Kilpatrick.ÌýEffects of time-dependent stimuli on a competitive neural network model of perceptual rivalry.ÌýBull. Math. Biol., 6 (2012) pp. 1396-1426.

ZP Kilpatrick, B Ermentrout.ÌýResponse of traveling waves to transient inputs in neural fields.ÌýPhys. Rev. E, 85 (2012) 021910.

ZP Kilpatrick, GB Ermentrout.ÌýHallucinogen persisting perception disorder in neuronal networks with adaptation.ÌýJ Comput. Neurosci., 32 (2012) pp. 25-53.

ZP Kilpatrick, B Ermentrout.ÌýSparse gamma rhythms arising through clustering in adapting neuronal networks.ÌýPLoS Comput. Biol., 7 (2011) e1002281.

PC Bressloff, ZP Kilpatrick.ÌýTwo-dimensional bumps in piecewise smooth neural fields with synaptic depression.ÌýSIAM J. Appl. Math., 71 (2011) pp. 379-408.

ZP Kilpatrick, PC Bressloff.ÌýBinocular rivalry in a competitive neural network model with synaptic depression.ÌýSIAM J. Appl. Dyn. Syst., 9 (2010) pp. 1303-1347.

ZP Kilpatrick, PC Bressloff.ÌýStability of bumps in piecewise smooth neural fields with nonlinear adaptation.ÌýPhysica D, 239 (2010) pp. 1048-1060.

ZP Kilpatrick, PC Bressloff.ÌýSpatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression.ÌýJ. Comput. Neurosci., 28 (2010) pp. 193-209.

ZP Kilpatrick, PC Bressloff.ÌýEffects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network.ÌýPhysica D, 239 (2010) pp. 547-560.

PC Bressloff, ZP Kilpatrick.ÌýNonlocal Ginzburg-Landau equation for cortical pattern formation.ÌýPhys. Rev. E, 78 (2008), 041916.

ZP Kilpatrick, SE Folias, and PC Bressloff.ÌýTraveling pulses and wave propagation failure in inhomogeneous neural media.ÌýSIAM J. Appl. Dyn. Syst., 7 (2008), pp. 161-185.