Research and Publications: Zachary Kilpatrick

This work has been funded by NSF DMS-1615737 (2016-), NSF DMS-1517629 (2015-), NSF DMS-1311755 (2013-2017), and NSF DMS-1004422 (2010-2012).

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

1. G Faye and ZP Kilpatrick. Threshold of front propagation in neural fields: An interface dynamics approach submitted (2018)
2. ZP Kilpatrick. Synaptic mechanisms of interference in working memory submitted (2017)
3. N Krishnan*, DB Poll†, and ZP Kilpatrick. Synaptic efficacy shapes resource limitations in working memory J Comput. Neurosci. (2018) in press
4. ZP Kilpatrick and DB Poll†. Neural field model of memory-guided search Phys. Rev. E 96 (2017) 062411.
5. DB Poll† and ZP Kilpatrick. Velocity integration in a multilayer neural field model of spatial working memory SIAM J Appl. Dyn. Syst. 16 (2017) pp. 1197-1234.
6. AE Radillo, A Veliz-Cuba, K Josic⧫, and ZP Kilpatrick⧫. Evidence accumulation and change rate inference in dynamic environments Neural Comput. 29 (2017) pp. 1561-1610.
7. A Jacot-Guillarmod⧫, Y Wang⧫, C Pedroza, H Ogmen, ZP Kilpatrick⧫, and K Josic⧫. Extending Levelt’s Propositions to perceptual multistability involving interocular grouping Vision Res. 133 (2017) pp. 37-46.
8. DB Poll† and ZP Kilpatrick. Persistent search in single and multiple confined domains: a velocity-jump process model J Stat. Mech. (2016) 053201.
9. ZT McCleney* and ZP Kilpatrick. Entrainment in up and down states of neural populations: non-smooth and stochastic models J Math. Biol. 73 (2016) pp. 1131-1160.
10. DB Poll†, K Nguyen*, and ZP Kilpatrick. Sensory feedback in a bump attractor model of path integration J Comput. Neurosci. 40 (2016) pp. 137-155.
11. ZP Kilpatrick. Ghosts of bump attractors in stochastic neural fields: Bottlenecks and extinction Discrete Contin. Dyn. Syst. Ser. B 21 (2016) p. 2211-2231.
12. A Veliz-Cuba‡, ZP Kilpatrick⧫, K Josic⧫. Stochastic models of evidence accumulation in changing environments SIAM Rev. 58 (2016) pp. 264–289.
13. A Veliz-Cuba‡, HZ Shouval, K Josic⧫, ZP Kilpatrick⧫. Networks that learn the precise timing of event sequences. J Comput. Neurosci. 39 (2015) pp. 235-254.
14. DB Poll† and ZP Kilpatrick. Stochastic motion of bumps in planar neural fields. SIAM J Appl. Math. 75 (2015) pp. 1553-1577.
15. ZP Kilpatrick. Stochastic synchronization of neural activity waves. Phys. Rev. E 91 (2015) 040701(R).
16. PC Bressloff and ZP Kilpatrick. Nonlinear Langevin equations for wandering patterns in stochastic neural fields. SIAM J Appl. Dyn. Syst. 14 (2015) pp. 305-334.
17. ZP Kilpatrick. Delay stabilizes stochastic motion of bumps in layered neural fields. Physica D 295 (2015) pp. 30-45.
18. ZP Kilpatrick and G Faye. Pulse bifurcations in stochastic neural fields. SIAM J Appl. Dyn. Syst. 13 (2014) pp. 830-860.
19. JK Kim‡, ZP Kilpatrick, MR Bennett, K Josic. Molecular mechanisms that regulate the coupled period of the mammalian circadian clock. Biophys. J 106 (2014) pp. 2071-2081. (New and Notable by S.R. Taylor)
20. ZP Kilpatrick. Coupling layers regularizes wave propagation in stochastic neural fields. Phys. Rev. E, 89 (2014) 022706.
21. ZP Kilpatrick. Wilson-Cowan model. Encyclopedia of Computational Neuroscience (2014) Ed. D Jaeger and R Jung, Springer-Verlag.
22. S Carroll*, K Josic, and ZP Kilpatrick. Encoding certainty in bump attractors. J Comput. Neurosci., 37 (2014) pp. 29-48.
23. B Ermentrout, SE Folias, and ZP Kilpatrick. Spatiotemporal pattern formation in neural fields with linear adaptation. Neural Fields (2014) Ed. S Coombes, P beim Graben, R Potthast, and JJ Wright, Springer Verlag.
24. ZP Kilpatrick. Interareal coupling reduces encoding variability in multi-area models of spatial working memory. Front. Comput. Neurosci., 7 (2013) 82.
25. ZP Kilpatrick, B Ermentrout, and B Doiron. Optimizing working memory with heterogeneity of recurrent cortical excitation. J Neurosci., 33 (2013) pp. 18999-19011.
26. ZP Kilpatrick, B Ermentrout. Wandering bumps in stochastic neural fields. SIAM J. Appl. Dyn. Syst., 12 (2013), pp. 61-94.
27. ZP Kilpatrick. Short term synaptic depression improves information transfer in perceptual multistability. Front. Comput. Neurosci., 7 (2013) 85.
28. SM Jayasuriya*, ZP Kilpatrick. Effects of time-dependent stimuli on a competitive neural network model of perceptual rivalry. Bull. Math. Biol., 6 (2012) pp. 1396-1426.
29. ZP Kilpatrick, B Ermentrout. Response of traveling waves to transient inputs in neural fields. Phys. Rev. E, 85 (2012) 021910.
30. ZP Kilpatrick, GB Ermentrout. Hallucinogen persisting perception disorder in neuronal networks with adaptation. J Comput. Neurosci., 32 (2012) pp. 25-53.
31. ZP Kilpatrick, B Ermentrout. Sparse gamma rhythms arising through clustering in adapting neuronal networks. PLoS Comput. Biol., 7 (2011) e1002281.
32. PC Bressloff, ZP Kilpatrick. Two-dimensional bumps in piecewise smooth neural fields with synaptic depression. SIAM J. Appl. Math., 71 (2011) pp. 379-408.
33. ZP Kilpatrick, PC Bressloff. Binocular rivalry in a competitive neural network model with synaptic depression. SIAM J. Appl. Dyn. Syst., 9 (2010) pp. 1303-1347.
34. ZP Kilpatrick, PC Bressloff. Stability of bumps in piecewise smooth neural fields with nonlinear adaptation. Physica D, 239 (2010) pp. 1048-1060.
35. ZP Kilpatrick, PC Bressloff. Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression. J. Comput. Neurosci., 28 (2010) pp. 193-209.
36. ZP Kilpatrick, PC Bressloff. Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network. Physica D, 239 (2010) pp. 547-560.
37. PC Bressloff, ZP Kilpatrick. Nonlocal Ginzburg-Landau equation for cortical pattern formation. Phys. Rev. E, 78 (2008), 041916.
38. ZP Kilpatrick, SE Folias, and PC Bressloff. Traveling pulses and wave propagation failure in inhomogeneous neural media. SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 161-185.

Dissertation 
ZP Kilpatrick. Spatially structured waves and oscillations in neuronal networks with synaptic depression and adaptation. PhD Dissertation. University of Utah, Salt Lake City UT, 2010.