## 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

## Mathematical Neuroscience and Cell Biology

I am a Professor of Mathematics in the Department of Mathematics at the University of Utah, where I am a faculty member of the Mathematical Biology Group and the Brain Institute. I am also a Visiting Professor at the Mathematical Institute, University of Oxford and INRIA, Sophia-Antipolis.

My main research interests lie in the areas of mathematical neuroscience and cell biology, with a particular focus on stochastic processes. My work draws upon a wide range of techniques in applied mathematics and theoretical physics such as non-equilibrium statistical physics, partial differential equations, pattern formation and nonlinear wave theory, dynamical systems theory, and the theory of self-organizing systems. Current research topics include the following:

Continuum neural field models of binocular rivalry waves

Stochastic neural field theory

Large deviations and metastability in stochastic hybrid systems, with applications to ion channels, chemical reaction networks, and neuronal population dynamics

Stochastic active transport models of cell polarization

Molecular motor models of axonal length control and polarization

Stochastic models of vesicular transport and delivery

**NEW!** Paul C. Bressloff Stochastic Processes in Cell Biology *Interdisciplinary Applied Mathematics (Springer)* Due: Summer (2014)

Paul C. Bressloff Waves in Neural Media: From Single Neurons to Neural Fields *Lecture Notes on Mathematical Modelling 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)

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

Notes and corrections
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).

### Stochastic hybrid systems and metastability

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. Keeener. 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 models of intracellular transport

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

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. Directed intermittent search for a hidden target on a dendritic tree. *Phys. Rev. E* **80** 021913 (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. Modeling the role of lateral
membrane diffusion on AMPA receptor trafficking along a spiny dendrite.
*J. Comput. Neurosci. * **25** 366-389 (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).

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

### Stochastic neural fields

P. C. Bressloff. From invasion to extinction in heterogeneous neural fields. *J. Math. Neurosci.* **2** 6 (2012).

M. A. Webber and P. C. Bressloff. The effects of noise on binocular rivalry waves: a stochastic neural field model. *J. Stat. Mech.* (2012).

P. C. Bressloff and M. A. Webber. Front Propagation in stochastic neural fields *SIAM J. Appl. Dyn. Syst. * **11** 708-740 (2012).

Notes and corrections
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).

### Adaptive neural fields and binocular rivalry

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 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. Spatially structured oscillations in a 2D excitatory neuronal network with synaptic depression. *J. Comput. Neurosci.* **239** 1048-1060 (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).

### Waves propagation in continuum neural fields

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, 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).

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

### Neural pattern formation and development

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

P. C. Bressloff and A. M. Oster. A theory for the alignment of cortical feature maps during development. *Phys. Rev. E* **82** 021920 (2010).

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

P. C. Bressloff and J. D. Cowan, The visual cortex as a crystal. *Physica D ***173 **:226-258 (2002).

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).

### Models of 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).

### 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).

Ethan Levien (Utah)
*TBA* (1st year)

Sam Carroll (Utah)
*Neural field theory* (2nd year)

Bhargav Karamched (Utah)
*Axonal transport* (3rd year)

Bin Xu (Utah)
*Cell polarization* (3rd year)

Heather Brooks (Utah)
*Stochastic hybrid systems* (3rd 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

Jay Newby (2010-2012)

Berton Earnshaw (2007-2009)

Lars Schwabe (2005-2006)

Steve Coombes (1996-1998)

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