Projects Summary (by topic)
(Updated June 2012)
http://www.math.utah.edu/~borisyuk/research.html

My research focuses on mathematical analysis of neuronal models. It is of particular interest to me how dynamics of neural activity is shaped by low-level processes such as single cell properties, network architecture, plasticity of connections between cells, etc.

Currently, my main focus is on questions of temporal processing in the auditory system, odor coding in the olfactory system, and on properties of stochastic neuronal models.

A more detailed list of current and recent projects can be found here.

Auditory
- Mechanisms of slow rise time selectivity in frog midbrain (Presentation, Manuscript is in preparation)
- Reconstructing input conductances from current clamp recordings: stochastic approach
* S.E.Odom, A.Borisyuk. Estimating three synaptic conductances in a stochastic neural model. J. Comput Neurosci 33, 191-205, 2012 (pdf, Supplementary material )
- Sound localization: moving sources
* A. Borisyuk, M. N. Semple, J. Rinzel. Adaptation and inhibition underlie responses to time-varying interaural phase cues in a model of inferior colliculus neurons. J. Neurophysiol. 88: 2134-2146, 2002 (pdf)
* A. Borisyuk, M. N. Semple, J. Rinzel.Computational model for the dynamic aspects of sound processing in the auditory midbrain. Neurocomputing 38: 1127-1134, 2001 (pdf)
- Sound localization: cochlear implants (ongoing)
- Transmission of spike-timing precision (ongoing)

Olfaction
- Mechanisms of learning-induced oscillations in the antennal lobe (Presentation, see Model II)
- Activation patterns in honeybee antennal lobe: correlates of behavior
* A. Borisyuk, B. H. Smith. Odor interactions and learning in a model of the insect antennal lobe. Neurocomputing 58-60: 1041-1047, 2004 (pdf)
- Transient synchrony: reduction to a discrete model
* S.Ahn, B.H. Smith, A. Borisyuk, D. Terman. Analyzing Neuronal Networks Using Discrete-Time Dynamics, Physica D: Nonlinear phenomena 239(9): 515-528, 2010 (pdf)
- Glomerular processing of olfactory inputs (ongoing)

Synchrony and phase-locking in neuronal networks
- Noise-driven rhythmogenesis
* W.H. Nesse, A. Borisyuk, P.C. Bressloff. Fluctuation-Driven rhythmogenesis in an excitatory network with slow adaptation, J Comp Neurosci. 25(2): 317-33, 2008 (pdf)
- Contribution of dendritic channels (Presentation)
- Decorrelation: separating frequencies
* A. Borisyuk, J. Best, D. Terman. Frequency separation by an excitatory-inhibitory network. J. Comp. Neurosci. 34(2), 231-243 (2013) (reprint)
- Phase-locking to noisy periodic drive
* T. Broicher, P. Malerba, A. Dorval, A. Borisyuk, F. Fernandez, and J. White. Spike Phase Locking in CA1 Pyramidal Neurons depends on Background Conductance and Firing Rate. Journal of Neuroscience, 32(41), 14374-14388 (2012) (preprint)
- From spectrum to dynamics in stochastic circle maps
* A. Borisyuk, F. Rassoul-Agha. Quasiperiodicity and Phase Locking in Stochastic Circle Maps: a Spectral Approach. Submitted. (preprint)

Control of breathing (Pre-Botzinger complex)
- Noise-induced increase of dynamic range (see Nesse et al. above)
- Dynamic regimes in a synaptically coupled network
* J. Best, A. Borisyuk, J. Rubin, D. Terman, M. Wechselberger. The dynamic range of bursting in a network of synaptically coupled square-wave bursting respiratory pacemaker cells, SIAM J. of Appl. Dyn. Syst. 4: 1107-1139, 2005 (pdf)

General: Book chapters
* A. Borisyuk. Physiology and mathematical modeling of the auditory system. In: Tutorials in Mathematical Bio- sciences I. Mathematical Neurosciences, Lecture Notes in Mathematics, Vol. 1860, Springer, Berlin Heidelberg New York, 2005 (book link , preprint)
* A. Borisyuk, J. Rinzel. Understanding neuronal dynamics by geometrical dissection of minimal models. In: Methods and Models in Neurophysics, Les Houches Summer School, Session LXXX, C. Chow, B. Gutkin, D. Hansel and C. Meunier (eds). Elsevier, 2005 (book link , preprint)