Paul C. Bressloff and J. Newby. Stochastic models of intracellular transport *Rev. Mod. Phys. * **85** 135-196 (2013)

Paul C. Bressloff. Spatiotemporal Dynamics of Continuum Neural Fields J. Phys. A **45 **(2012) 033001

P. C. Bressloff. Lectures in Mathematical Neuroscience *In: Mathematical Biology, IAS/Park City Mathematical Series.(M. A. Lewis, M. A. J. Chaplain, J. P. Keener and P. K. Maini (eds)* **14** 293-398 (American Mathematical Society, 2009).

P. C. Bressloff. Pattern formation in visual cortex. *Les Houches Lectures in Neurophysics* (2005).

P. C. Bressloff and S. Coombes. Physics of the extended neuron. * Int. J.
Mod. Phys. B* **11**:2343-2393 (1997).

**Biological processes in switching environments**

E. Levien and P. C. Bressloff. A stochastic hybrid framework for obtaining statistics of many random walkers in a switching environment. *Submitted* (2016).

P. C. Bressloff. Diffusion in cells with stochastically-gated gap junctions. *Submitted* (2016).

P. C. Bressloff and S. D. Lawley. Diffusion on a tree with stochastically-gated nodes. *J. Phys. A* In press (2016).

P. C. Bressloff and S. D. Lawley. Stochastically-gated diffusion-limited 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. *Multi-scale Model. Simul.* **13** 1420-1445 (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).

**Self-organization in biological cells**

H. A. Brooks and P. C. Bressloff. A mechanism for Turing pattern formation with active and passive transport. *Submitted* (2016).

Bin Xu and P. C. Bressloff. A PDE-DDE model for cell polarization in fission yeast *Submitted* (2016).

Bin Xu and P. C. Bressloff. Model of growth cone membrane polarization via microtubule length regulation. *Biophys. J.* **109** 2203-2214 (2015).

P. C. Bressloff and B. Xu. Stochastic active-transport model of cell polarization. *SIAM J. Appl. Appl. Math.* **75** 652-678 (2015).

P. C. Bressloff and B. Karamched. A frequency-dependent 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** 2408-2419 (2015).

V. M. Burlakov, N. Emptage, A. Goriely and P. C. Bressloff. Synaptic bistability due to nucleation and evaporation of receptor clusters. *Phys. Rev. Lett.* **108**
028101 (2012).

**Stochastic models of intracellular transport**

P. C. Bressloff and B. Karamched. Model of reversible vesicular transport with exclusion *Submitted* (2016).

P. C. Bressloff. Aggregation-fragmentation model of vesicular transport in neurons. *J. Phys. A* ** 49 ** 145601 (2016).

E. Levien and P. C. Bressloff. Quasi-steady-state analysis of flashing ratchets. *Phys. Rev. E* **92** 042129 (2015).

P. C. Bressloff and E. Levien. Synaptic democracy and active intracellular transport in axons. *Phys. Rev. Lett.* **114** 168101 (2015).

P. C. Bressloff and J. M. Newby. Filling of a Poisson trap by a population of random intermittent searchers. *Phys. Rev. E* **85** 031909 (2012).

P. C. Bressloff and J. Newby. Quasi-steady state analysis of motor-driven transport on a two-dimensional microtubular network. *Phys. Rev. E* **83** 061139 (2011).

J. Newby and P. C. Bressloff. Local synaptic signalling enhances the stochastic transport of motor-driven cargo in neurons. *Phys. Biol.* **7** 036004 (2010).

J. Newby and P. C. Bressloff. Random intermittent search and the tug-of-war model of motor-driven transport. *J. Stat. Mech.* **P04014** (2010).

J. Newby and P. C. Bressloff. Quasi-steady state reduction of molecular-based models of directed intermittent search. *Bull. Math. Biol.* **72** 1840-1866 (2010).

J. Newby and P. C. Bressloff. Directed intermittent search for a hidden target on a dendritic tree. *Phys. Rev. E* **80** 021913 (2009).

B. A. Earnshaw and P. C. Bressloff. A dynamical corral model of protein trafficking in spines.
*Biophys. J. * **96** 1789-1802 (2009).

P. C. Bressloff, B. A. Earnshaw and M. J. Ward. Diffusion of
protein receptors on a cylindrical dendritic membrane with partially
absorbing traps. *SIAM J. Appl. Math*. **68** 1223-1246 (2008).

B. A. Earnshaw and P. C. Bressloff. A biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD. *J. Neurosci.* ** 26 ** 12362-12373 (2006).

P. C. Bressloff. A stochastic model of intraflagellar transport. *Phys. Rev. E* ** 73 ** 061916 (2006).

P. C. Bressloff, A stochastic model of protein receptor trafficking prior to synaptogenesis. *Phys. Rev. E* ** 74 ** 031910 (2006).

**Stochastic hybrid systems, ion channels and large deviations**

P. C. Bressloff and O. Faugeras. On the Hamiltonian structure of large deviations in stochastic hybrid systems with applications to ion channels. *Submitted * (2016).

P. C. Bressloff Path-integral 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. Path-integrals 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** 1394-1435 (2013).

**Stochastic neural fields**

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** 305-334 (2015).

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. 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** 708-740 (2012).

P. C. Bressloff. Metastable states and quasicycles in a stochastic Wilson-Cowan model of neural population dynamics. *Phys. Rev. E* **82** 051903 (2010).

P. C. Bressloff. Stochastic neural field theory and the system-size expansion. *SIAM J. Appl. Math* **70** 1488-1521 (2009).

**Waves in neural media**

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** 8-17 (2014).

P. C. Bressloff and S. M. Carroll. Spatio-temporal dynamics of neural fields on product spaces. * SIAM J. Appl. Dyns. Syst.* **13** 1620-1653 (2014).

P. C. Bressloff. Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. *J. Math. Biol. * **66** 1499-1525 (2013).

P. C. Bressloff and M. A. Webber. Neural field model of binocular rivalry waves. *J. Comput. Neurosci.* **32** 233-252 (2012).

Z. P. Kilpatrick and P. C. Bressloff. Binocular rivalry in a competitive neural network with synaptic depression. *SIAM J. Appl. Dyn. Syst.* **9** 1303-1347 (2010).

Z. P. Kilpatrick and P. C. Bressloff. Stability of bumps in piecewise smooth neural fields with nonlinear adaptation. *Physica D* **239** 1048-1060 (2010).

Z. P. Kilpatrick and P. C. Bressloff. Spatially structured oscillations in a 2D excitatory neuronal network with synaptic depression. *J. Comput. Neurosci.* **239** 1048-1060 (2010).

Z. P. Kilpatrick, S. E. Folias and P. C. Bressloff. Traveling
pulses and wave propagation failure in an inhomogeneous neural network.
*SIAM J. Appl. Dyn. Syst. * **7** 161-185 (2008).

S. E. Folias and P. C. Bressloff, Breathers in two-dimensional excitable neural media. *Phys. Rev. Lett. * **95**: 208107(2005).

S. E. Folias and P. C. Bressloff, Stimulus-locked waves and breathers in an excitatory neural network. *SIAM J. Appl. Math* **65**:2067-2092 (2005).

S. E. Folias and P. C. Bressloff, Breathing pulses in an excitatory neural network. *SIAM J. Appl. Dyn. Syst. * **3,**: 378-407(2004).

P. C. Bressloff and S. E. Folias, Front bifurcations in an excitatory neural network. *SIAM J. Appl. Math. * **65**: 131-151 (2004).

S. Coombes and P. C. Bressloff. Saltatory waves in the spike-diffuse-spike model of active dendrites. *Phys. Rev. Lett.* **91**:028102 (2003).

P. C. Bressloff, Traveling fronts and wave propagation failure in an inhomogeneous neural network. *Physica D * **155 **:83-100 (2001).

**Neural pattern formation and models of primary visual cortex**

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** 60-83 (2016).

M. Galtier, O. Faugeras and P. C. Bressloff. Hebbian learning of recurrent connections: a geometrical perspective. *Neural Comput.* **24** 2346-2383 (2012).

A. M. Oster and P. C. Bressloff, A developmental model of ocular dominance formation on a growing cortex *Bull. Math. Biol. * **68 ** 73-98 (2006).

P. C. Bressloff, Spontaneous symmetry breaking in self-organizing neural fields. *Biol. Cybern.* **93**: 256-274 (2005).

P. C. Bressloff, Euclidean shift-twist symmetry in population models of self-aligning objects. *SIAM J. Appl. Math.* **64**:1668-1690 (2004).

P. C. Bressloff, Spatially periodic modulation of cortical patterns by long-range horizontal connections. * Physica D * **185**:131-157 (2003).

P. C. Bressloff and J. D. Cowan, Spherical model of orientation and spatial frequency tuning in a cortical hypercolumn. * Phil. Trans. Roy. Soc. B * **358**:1643-1667 (2003).

P. C. Bressloff, Bloch waves, periodic feature maps and cortical pattern formation. *Phys. Rev. Lett.* **89 **: 088101 (2002).

P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas and M.
Wiener, Geometric visual hallucinations, Euclidean symmetry and the
functional architecture of striate cortex * Phil. Trans. Roy. Soc. B ***40 **:299-330
(2001).

**Contextual effects in primary visual cortex**

Shushruth, P. Mangapathy, J. M. Ichida, P. C. Bressloff, L. Schwabe and A. Angelucci. Strong recurrent networks compute the orientation-tuning of surround modulation in primate V1. * J. Neurosci.* ** 32 ** 308-321 (2012).

J. Icheda, L. Schwabe, P. C. Bressloff and A. Angelucci. Response
facilitation from the ``suppressive'' surround of V1 neurons. *J. Neurophysiol. * ** 98 ** 2168-2181 (2007).

A. Angelucci and P. C. Bressloff. The contribution of feedforward, lateral and feedback
connections to the classical receptive field center and extra-classical receptive field surround
of primate V1 neurons * Prog. Brain Res.* ** 154 ** 93-121 (2006).

L. Schwabe, K. Obermayer, A. Angelucci and P. C. Bressloff. The
role of feedback in shaping the extra-classical receptive field of
cortical neurons: a recurrent network model * J. Neurosci.* ** 26 ** 9117-9129 (2006).

J. S. Lund, A. Angelucci and P. C. Bressloff, Anatomical
substrates for the functional column in macaque primary visual cortex. *Cerebral Cortex* **12**:15-24 (2003).

P. C. Bressloff and J. D. Cowan, An amplitude equation approach to contextual effects in primary visual cortex. *Neural Comput. * **14 **:493-525 (2002).

**Stochastic population oscillators and noise-induced synchronization**

P. C. Bressloff and Yi Ming Lai. Dispersal and noise: Various modes of synchrony in ecological oscillators. *J. Math. Biol.*
**67** 1669-1690 (2013).

Y-M Lai, J. Newby and P. C. Bressloff. Effects of demographic noise on the synchronization of metacommunities by a fluctuating environment. *Phys. Rev. Lett* **107** 118102 (2011).

P. C. Bressloff and Y-M Lai. Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. *J. Math. Neurosci.* **1** 2 (2011).

**Dynamics of integrate-and-fire networks**

P. C. Bressloff, Traveling waves and pulses in a one-dimensional
network of integrate-and-fire neurons. * J. Math. Biol. ***40 **:169-183
(2000).

P. C. Bressloff and S. Coombes, Dynamical theory of spike train
dynamics in networks of integrate-and-fire oscillators. * SIAM J. Appl. Math. * **60**:828-841 (2000).

S. Coombes and P. C. Bressloff, Solitary waves in a model of dendritic
cable with active spines. * SIAM J. Appl. Math. * **61**:432-453 (2000).

P. C. Bressloff and S. Coombes, Dynamics of strongly coupled spiking
neurons. *Neural Comput. * **12 **:91-129 (2000).

P. C. Bressloff, Synaptically generated wave propagation in excitable
neural media. *Phys. Rev. Lett. * **82**:2979-2982 (1999).

P. C. Bressloff and S. Coombes, Symmetry and phase-locking in a ring of
pulse-coupled oscillators with distributed delays. * Physica D * **126 **:99-122
(1999).

P. C. Bressloff and S. Coombes, Travelling waves in a chain of pulse-coupled
integrate-and-fire oscillators with distributed delays.
*Physica D*** 130**:232-254 (1999).

P. C. Bressloff and S. Coombes, Travelling waves in chain of pulse-coupled
oscillators. * Phys. Rev. Lett. * **80**:4815-4818 (1998).

P. C. Bressloff and S. Coombes, Desynchronization, mode-locking and
bursting in strongly-coupled integrate-and-fire oscillators. * Phys. Rev. Lett. * **81**:2168-2171 (1998).

P. C. Bressloff and S. Coombes, Spike train dynamics underlying pattern
formation in an integrate-and-fire oscillator network. * Phys. Rev. Lett. * **81**:2384-2387 (1998).

P. C. Bressloff and S. Coombes, Synchrony in an array of integrate-and-fire
neurons with dendritic structure.* Phys. Rev. Lett. *** 78**:4665-4668 (1997).

P. C. Bressloff, S. Coombes and B. De Souza, Dynamics of a ring of
pulse-coupled oscillators: Group theoretic approach. * Phys. Rev. Lett.*** 79**:2791-2794 (1997).

**Miscellaneous**

P. C. Bressloff and G. Rowlands, Exact travelling wave solutions of an
"integrable" discrete reaction-diffusion equation. *Physica D ***106**:255-269
(1997).

P. C. Bressloff, A self-organizing network in the weak coupling limit.
*Physica D ***110**:195-208 (1997).

P. C. Bressloff, A new Green's function method for solving linear PDE's
in two variables. * J. Math. Anal. Appl. ***210**:390-415 (1997).

P. C. Bressloff, V. M. Dwyer and M. J. Kearney, Classical diffusion and
percolation in random environments on trees. * Phys. Rev. E*** 55**:6765-6775
(1997).

P. C. Bressloff, C. V. Wood and P. A. Howarth, Nonlinear shunting model
of the pupil light reflex. * Proc. Roy. Soc. B ***263**:953-960 (1996).

Ethan Levien (Utah)
*Biological processes in switching environments* (2nd year)

Sam Carroll (Utah)
*Neural field theory* (3rd year)

Jenna Noll (Utah)
*Cellular length control* (4th year)

Bhargav Karamched (Utah)
*Axonal transport* (4th year)

Bin Xu (Utah)
*Cell polarization* (4th year)

Heather Brooks (Utah)
*Intracellular pattern formation* (4th year)

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 motor-based 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)
*Stimulus-induced 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 *Noise-induced effects in neural systems * (Ph. D 1998)

**Postdocs**

Sean Lawley (2014-2016)

Jay Newby (2010-2012)

Berton Earnshaw (2007-2009)

Lars Schwabe (2005-2006)

Steve Coombes (1996-1998)

Spatially Distributed Stochastic Dynamical Systems in Biology Isaac Newton Institute, Cambridge, UK, June 20-24, 2016

The First International Conference on Mathematical NeuroScience (ICMNS), Antibes, Juan-Les-Pins, France, June 8-10, 2015

Axonal Transport and Neuronal Mechanics, Mathematical Biosciences Institute, Ohio State, November 3-7, 2014

SIAM Conference on Nonlinear Waves and Coherent Structures, University of Cambridge, August 11-14, 2014

Stochastic Network Models of Neocortex (a Festschrift for Jack Cowan), Banff International research station, July 13-18, 2014

Nonlinear dynamics and stochastic methods: from neuroscience to other biological applications (Bard Ermentrout’s 60th) University of Pittsburgh, March 10-12, 2014

Oxford Conference on Challenges in Applied Mathematics University of Oxford, July 1-5, 2013

Stochastic Modeling of Biological Processes, IMA, University of Minnesota, May 13-17, 2013

Random models in neuroscience Université Pierre et Marie Curie, July 2-6, 2012

Stochastic Modelling in Biological Systems, University of Oxford, March 18-23, 2012

Spatio-Temporal Evolution Equations and Neural Fields, CIRM, Marseilles, October 24-28, 2011