Professor Paul C Bressloff

Contact details
Department of Mathematics
University of Utah
155 South 1400 East
Salt Lake City
Utah 84112
Tel.: 801 585 1633
Fax.: 801 581 4148
Email: bressloff@math.utah.edu


News
New! Congratulations to Dr. Sam Carroll, who successfully defended his thesis on Mar 6th 2018.
New! Congratulations to Dr. Ethan Levien, who successfully defended his thesis on Feb 28th 2018. Ethan has been appointed as a postdoctoral fellow, SEAS Harvard
New! Congratulations to Dr. Heather Brooks, who successfully defended her thesis on Feb 23rd 2018. Heather has been appointed as a postdoctoral fellow, Department of Mathematics, UCLA
New! Congratulations to Dr. James MacLaurin, who has been appointed as an assistant professor, New Jersey Institute of Technology.
New! Congratulations to alumnus Dr. Jay Newby, who has been appointed as an assistant professor, University of Alberta.
PCB awarded a Distinguished Scholar and Creative Researcher Award, University of Utah (2017).
Dr. Bin Xu successfully defended her thesis on Mar 3rd 2017. Bin is currently a postdoctoral fellow in the Department of Applied Mathematics, Notre Dame.
Dr. Bhargav Karamched successfully defended his thesis on Feb 27th 2017. Bhargav is currently a postdoctoral fellow in the Department of Mathematics, University of Houston.
Dr. James Maclaurin joined our group as a 3year postdoctoral fellow in July 2017. This position is jointly funded by the NSF and the Department of Mathematics.
PCB elected a Fellow of the Society for Industrial and Applied Mathematics (2016)
PCB appointed Associate Editor of the SIAM Journal of Applied Mathematics (2015)
PCB invited as a plenary speaker: SIAM Conference on Nonlinear waves and Coherent Structures (2014)
PCB published two books for Springer (2014): Stochastic Processes in Cell Biology, Waves in Neural Media
Biophysics and Stochastic Processes
A major goal of this research is to understand the fundamental biophysical mechanisms underlying cellular function in health and disease, with a particular emphasis on molecular and cellular neuroscience. This includes both single cells and multicellular systems. Our work draws upon a wide variety of methods in applied mathematics and theoretical physics including stochastic processes, statistical physics, nonlinear PDEs, and dynamical systems theory. We are also developing new mathematical and numerical methods for analyzing complex and stochastic nonlinear systems. Current research topics include the following:
Biological processes in switching environments: intracellular diffusion in domains with stochastically gated boundaries; intercellular diffusion via stochastic gap junctions; diffusionlimited biochemical reactions in cells; bacterial persistence in switching environments
Stochastic models of axonal and dendritic transport: PDE models of motorbased vesicular transport; synaptic democracy and vesicular transport; exclusion processes; aggregation models of intracellular transport; random intermittent search processes.
Cell polarization: Microtubule regulation in growth cone steering; active transport in budding yeast; symmetry unbreaking in fission yeast.
Intracellular pattern formation: Synaptogenesis in C elegans; Turing mechanism and active transport; intracellular waves and chemical signaling.
Cellular length control: axonal length sensing; axonal regeneration; intraflagellar transport in bacteria
Stochastic hybrid systems: stochastic ion channels and voltage fluctuations; large deviations and pathintegrals; stochastic neural oscillators; genetic switches and oscillators; stochastic neural networks.
Bacterial quorum sensing: parallel signaling pathways in Vibrio; contraction mappings and mean field theory; coupled PDEODE systems; stochastic models
Morphogenesis: cytonememediated morphogen gradients; robustness
Neural Field Theory and Vision
Our research in this area focuses on the spatiotemporal dynamics of continuum neural fields. Neural fields model the largescale dynamics of spatially structured biological neural networks in terms of nonlinear integrodifferential equations, whose associated integral kernels represent the spatial distribution of neuronal synaptic connections. They provide an important example of spatially extended excitable systems with nonlocal interactions, and exhibit a wide range of spatially coherent dynamics, including traveling waves, oscillations and Turinglike patterns. Current research topics include the following:
Neural field models of cortex: binocular rivalry waves; pattern formation, symmetric bifurcation theory and visual hallucinations; laminar neural fields.
Stochastic neural fields: stochastic traveling waves; variational methods and large deviations; homogenization of heterogeneous neural media
Recurrent network models of visual cortex: contextual image processing and the role of extrastriate feedback
Paul C. Bressloff Stochastic Processes in Cell Biology Interdisciplinary Applied Mathematics (Springer) August (2014)
Supplementary material
Paul C. Bressloff Waves in Neural Media: From Single Neurons to Neural Fields Lecture Notes on Mathematical Modeling in the Life Sciences (Springer) Published (2014)
Stephen Coombes and Paul C. Bressloff(eds.) Bursting: the Genesis of Rhythm in the Nervous System World Scientific (2005)
P. C. Bressloff and J. M. Maclaurin. Stochastic hybrid systems in cellular neuroscience Submitted (2018)
P. C. Bressloff. Stochastic switching in biology: from genotype to phenotype (Topical Review) J. Phys. A 50 133001 (2017)
A. Angelucci, M. Bijanzadeh, L. Nurminen, F. Federer, S. Merlin and P. C. Bressloff. Circuits and mechanisms for surround modulation in visual cortex. Ann. Rev. Neurosci. 40 425451 (2017).
P. C. Bressloff and J. M. Newby. Stochastic models of intracellular transport (Review) Rev. Mod. Phys. 85 135196 (2013)
P C. Bressloff. Spatiotemporal Dynamics of Continuum Neural Fields (Review) J. Phys. A 45 (2012) 033001
Stochastic hybrid systems
P. C. Bressloff and J. Maclaurin. A variational method for analyzing limit cycle oscillations in stochastic hybrid systems. Submitted (2018).
P. C. Bressloff and J. Maclaurin. A variational method for analyzing stochastic limit cycle oscillators Submitted (2018).
P. C. Bressloff and S. D. Lawley. Mean first passage times for piecewise deterministic Markov processes and the effects of critical points. J. Stat. Mech. 063202 (2017).
P. C. Bressloff and O. Faugeras. On the Hamiltonian structure of large deviations in stochastic hybrid systems. J. Stat. Mech. 033206 (2017).
P. C. Bressloff. FeynmanKac formula for stochastic hybrid systems. Phys. Rev. E 95 012138 (2017).
P. C. Bressloff. Stochastic Liouville equation for particles driven by dichotomous environmental noise. Phys. Rev. E 95 012124 (2017).
P. C. Bressloff. Pathintegral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks. J. Math. Neurosci 5 33pp. (2015).
P. C. Bressloff and J. M. Newby. Pathintegrals and large deviations in stochastic hybrid systems. Phys. Rev. E 89 042701 (2014).
P. C. Bressloff and J. M. Newby. Stochastic hybrid model of spontaneous dendritic NMDA spikes. Phys. Biol. 11 016006 (13pp) (2014).
J. M. Newby, P. C. Bressloff and J. P. Keener. The effect of Potassium channels on spontaneous action potential initiation by stochastic ion channels. Phys. Rev. Lett. 111 128101 (2013).
P. C. Bressloff and J. M. Newby. Metastability in a stochastic neural network modeled as a jump velocity Markov process. SIAM J. Appl. Dyn. Syst. 12 13941435 (2013).
Stochastic models of intracellular transport
P. C. Bressloff, S. D. Lawley and P. Murphy. Diffusion in an agestructured randomly switching environment Submitted (2018).
P. C. Bressloff, B. M. Karamched, S. D. Lawley and E. Levien. Diffusive transport in the presence of stochastically gated absorption. Phys. Rev. E 96 022102 (2017).
P. C. Bressloff and S. D. Lawley. Hybrid colored noise process with spacedependent switching rates. Phys. Rev. E 96 012129 (2017).
P. C. Bressloff and S. D. Lawley. Temporal disorder as a mechanism for spatially heterogeneous diffusion. Phys. Rev. E 95 060101(R) (2017).
P. C. Bressloff and S. D. Lawley. Dynamically active compartments coupled by a stochasticallygated gap junction. J. Nonlin. Sci. 27 1487–1512 (2017)
P. C. Bressloff and S. D. Lawley. Residence times of a Brownian particle with temporal heterogeneity. J. Phys. A 50 195001 (2017).
P. C. Bressloff. Stochasticallygated local and occupation times of a Brownian particle. Phys. Rev. E 95 012130 (2017).
B. Karamched and P. C. Bressloff. Effects of geometry on reversible vesicular transport. J. Phys. A 50 055601 (2017).
P. C. Bressloff. Stochastic FokkerPlanck equation in random environments. Phys. Rev. E 94 042129 (2016).
E. Levien and P. C. Bressloff. A stochastic hybrid framework for obtaining statistics of many random walkers in a switching environment. Multiscale Model. Simul. 14 14171433 (2016).
P. C. Bressloff. Diffusion in cells with stochasticallygated gap junctions. SIAM J. Appl. Math. 76 16581682 (2016).
P. C. Bressloff and S. D. Lawley. Diffusion on a tree with stochasticallygated nodes. J. Phys. A 49 245601 (2016).
P. C. Bressloff and B. Karamched. Model of reversible vesicular transport with exclusion J. Phys. A 49 345602 (2016).
P. C. Bressloff. Aggregationfragmentation model of vesicular transport in neurons. J. Phys. A 49 145601 (2016).
P. C. Bressloff and E. Levien. Synaptic democracy and active intracellular transport in axons. Phys. Rev. Lett. 114 168101 (2015).
P. C. Bressloff and S. D. Lawley. Stochasticallygated diffusionlimited reactions for a small target in a bounded domain. Phys. Rev. E 92 062117 (2015).
P. C. Bressloff and S. D. Lawley. Escape from subcellular domains with randomly switching boundaries. Multiscale Model. Simul. 13 14201445 (2015).
P. C. Bressloff and S. D. Lawley. Escape from a potential well with a switching boundary. J. Phys. A 48 225001 (2015).
P. C. Bressloff and S. D. Lawley. Moment equations for a piecewise deterministic PDE. J. Phys. A 48 105001 (2015).
Selforganization in cellular and developmental biology
G. Fan and P. C. Bressloff. Modeling the role of feedback in the adaptive response of bacterial quorum sensing Submitted (2018)
H. Kim and P. C. Bressloff. Direct vs. synaptic contacts in a mathematical model of cytonemebased morphogen gradient formation Submitted (2018).
P. C. Bressloff and H. Kim. Bidirectional transport model of morphogen gradient formation via cytonemes Phys. Biol. 15 026010 (2018).
P. C. Bressloff and B. Karamched. A doubly stochastic Poisson model of flagellar length control. SIAM J. Appl. Math 78 719741 (2018).
G. Fan and P. C. Bressloff. Population model of quorum sensing with multiple parallel pathways Bull. Math. Biol. 79 25992626 (2017)
Bin Xu and P. C. Bressloff. A theory of synchrony for active compartments with delays coupled through bulk diffusion Physica D 341 4559 (2017).
H. A. Brooks and P. C. Bressloff. Turing mechanism for homeostatic control of synaptic density in C. elegans. Phys. Rev. E 96 012413 (2017).
H. A. Brooks and P. C. Bressloff. A mechanism for Turing pattern formation with active and passive transport. SIAM J. Appl. Dyn. Syst. 15 18231843 (2016).
P. C. Bressloff. Ultrasensitivity and noise amplification in a model of V. harveyi quorum sensing. Phys. Rev. E 93 062418 (2016).
Bin Xu and P. C. Bressloff. A PDEDDE model for cell polarization in fission yeast SIAM J. Appl. Math 76 18441870 (2016).
Bin Xu and P. C. Bressloff. Model of growth cone membrane polarization via microtubule length regulation. Biophys. J. 109 22032214 (2015).
P. C. Bressloff and B. Xu. Stochastic activetransport model of cell polarization. SIAM J. Appl. Appl. Math. 75 652678 (2015).
P. C. Bressloff and B. Karamched. A frequencydependent decoding mechanism for axonal length sensing. Front. Cellular Neurosci. 9 281 (2015).
B. Karamched and P. C. Bressloff. A delayed feedback model of axonal length sensing. Biophys. J 108 24082419 (2015).
Biochemical reaction networks
P. C. Bressloff and E. Levien. Propagation of extrinsic fluctuations in biochemical birthdeath processes. Submitted (2018).
E. Levien and P. C. Bressloff. Robustness of stochastic chemical reaction networks to extrinsic noise: the role of deficiency. Multiscale Model. Simul. In press (2018).
E. Levien and P. C. Bressloff. Reversibility and stationary distributions in hybrid chemical reaction networks. J. Phys. A 50 475004 (2017).
E. Levien and P. C. Bressloff. Coupling sample paths to the thermodynamic limit in Monte Carlo estimators with applications to gene expression. J. Comp. Phys. 346 113 (2017).
Neural field theory and vision
S. Carroll and P. C. Bressloff. Symmetric Bifurcations in a Neural Field Model for encoding the direction of spatial contrast gradients. SIAM J. Appl. Dyn. Syst. 17 151 (2018).
S. Carroll and P. C. Bressloff. Phase equation for patterns of orientation selectivity in a neural field model of visual cortex. SIAM J. Appl. Dan. Syst. 15 6083 (2016).
P. C. Bressloff and Z. P. Kilpatrick. Nonlinear Langevin equations for the wandering of fronts in stochastic neural fields. SIAM J. Appl. Dyn. Syst. 14 305334 (2015).
P. C. Bressloff and S. Carroll. Laminar neural field model of laterally propagating waves of orientation selectivity. PLoS Comput. Biol. 11 e1004545 (2015).
S. Carroll and P. C. Bressloff. Binocular rivalry waves in directionally selective neural field models. Physica D 285 817 (2014).
P. C. Bressloff and S. M. Carroll. Spatiotemporal dynamics of neural fields on product spaces. SIAM J. Appl. Dyns. Syst. 13 16201653 (2014).
M. A. Webber and P. C. Bressloff. The effects of noise on binocular rivalry waves: a stochastic neural field model. J. Stat. Mech. 3 P03001 (2013).
P. C. Bressloff and M. A. Webber. Neural field model of binocular rivalry waves. J. Comput. Neurosci. 32 233252 (2012).
P. C. Bressloff. From invasion to extinction in heterogeneous neural fields. J. Math. Neurosci. 2 6 (2012).
P. C. Bressloff and M. A. Webber. Front Propagation in stochastic neural fields. SIAM J. Appl. Dyn. Syst. 11 708740 (2012).
Shushruth, P. Mangapathy, J. M. Ichida, P. C. Bressloff, L. Schwabe and A. Angelucci. Strong recurrent networks compute the orientationtuning of surround modulation in primate V1. J. Neurosci. 32 308321 (2012).
Hyunjoong Kim (Utah)
Cytonmemebased morphogenesis (3rd year)
Bridget Fan (Utah)
Quorum sensing (4th year)
Patrick Murphy (Utah)
Diffusion in agestructured switching environments (4th year)
Ethan Levien (Utah)
Noise propagation in biochemical reaction networks: multi scale and populationlevel perspectives (Ph. D 2018)
Sam Carroll (Utah)
Spatiotemporal dynamics of orientationselective neural populations in the visual cortex (Ph. D 2018)
Heather Brooks (Utah)
Dynamics and structure: from microtubule networks to population networks (Ph. D 2018)
Bin Xu (Utah)
Mathematical models of cell polarization (Ph. D 2017)
Bhargav Karamched (Utah)
Mathematical models of motorbased intracellular transport (Ph. D 2017)
Matthew Webber (Oxford)
Stochastic neural field models of binocular rivalry waves (D. Phil. 2013)
Yi Ming Lai (Oxford) Stochastic population oscillators in ecology and neuroscience (D. Phil. 2013)
Jay Newby (Utah)
Molecular motorbased models of random intermittent search in dendrites (Ph. D 2010)
Zachary Kilpatrick (Utah)
Spatially structured waves and oscillations in neuronal networks with synaptic depression and adaptation (Ph. D 2010)
William Nesse (Utah)
Random fluctuations in dynamical neural networks. (Ph. D 2008)
Berton Earnshaw (Utah)
Biophysical models of AMPA receptor trafficking and synaptic plasticity (Ph. D 2007)
Andrew M. Oster (Utah)
Models of cortical development (Ph. D 2006)
Stefanos E. Folias (Utah)
Stimulusinduced waves and breathers in excitable neural media (Ph. D 2005)
Matthew James
Oscillations and waves in IF networks (Ph. D 2002)
Barry de Souza Dynamics of neuronal networks with dendritic interactions (Ph. D 2000)
Peter Roper Noiseinduced effects in neural systems (Ph. D 1998)
Postdocs
James Maclaurin (2017)
Sean Lawley (20142016)
Jay Newby (20102012)
Berton Earnshaw (20072009)
Lars Schwabe (20052006)
Steve Coombes (19961998)
The Third International Conference on Mathematical NeuroScience (ICMNS), University of Colorado Boulder, May 30June 2, 2017
The Second International Conference on Mathematical NeuroScience (ICMNS), Antibes, JuanLesPins, France, May 30  June 1, 2016
Spatially Distributed Stochastic Dynamical Systems in Biology Isaac Newton Institute, Cambridge, UK, June 2024, 2016
The First International Conference on Mathematical NeuroScience (ICMNS), Antibes, JuanLesPins, France, June 810, 2015
Axonal Transport and Neuronal Mechanics, Mathematical Biosciences Institute, Ohio State, November 37, 2014
SIAM Conference on Nonlinear Waves and Coherent Structures, University of Cambridge, August 1114, 2014
Stochastic Network Models of Neocortex (a Festschrift for Jack Cowan), Banff International research station, July 1318, 2014
Nonlinear dynamics and stochastic methods: from neuroscience to other biological applications (Bard Ermentrout’s 60th) University of Pittsburgh, March 1012, 2014
Oxford Conference on Challenges in Applied Mathematics University of Oxford, July 15, 2013
Stochastic Modeling of Biological Processes, IMA, University of Minnesota, May 1317, 2013
Random models in neuroscience Université Pierre et Marie Curie, July 26, 2012
Stochastic Modelling in Biological Systems, University of Oxford, March 1823, 2012
SpatioTemporal Evolution Equations and Neural Fields, CIRM, Marseilles, October 2428, 2011
Utah

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