# Department of Mathematical Sciences

# UCID 'horacio' has a private entry

**Academic Interests: ** mathematical biology, computational neuroscience, dynamical systems

# About Me

The research of Horacio G. Rotstein focuses mainly on the study of the biophysical and dynamic mechanisms underlying the generation of rhythmic oscillatory activity in the brain, particularly in the hippocampus and entorhinal cortex. Rhythmic oscillations at theta (8 - 12 Hz) and gamma (30 - 80 Hz) frequencies in these areas of the brain have been correlated with various forms of learning and memory. In addition, alteration in particular sorts of brain rhythmic oscillations have been shown to correlate with the existence and progression of a variety of neuropsychiatric conditions, including schizophrenia and dementia. Rhythms differ not only in their frequency range, but also in the underlying biophysical mechanisms by which they are generated. These mechanisms usually vary in different brain areas, and may operate at a single cell level or may involve the coherent activity of many cells and cell types in a network. The primary goal of my research is to uncover and understand the underlying biophysical and dynamic principles that govern the generation of rhythmic activity in the brain. As secondary goals I hope to understand the functional implications for brain functioning of the previous results, the relation between disruption of rhythmic activity and diseases of the nervous system, and the effects that changes at a subcellular level have on rhythms observed at the single cell and network levels.

# Education

- PhD, Applied Mathematics, TECHNION - Israel Institute of Technology (1998).
- MSc, Applied Mathematics, TECHNION - Israel Institute of Technology (1994).
- BSc, Chemistry, Universidad Nacional del Sur, Argentina (1989).

# Courses Taught

- Math 430 & Math635 - Analytical and Computational Neuroscience
- Math 112 - Calculus II
- Mathematical Biology Seminar

# Classes Taught

# Research Interests

- Mathematical biology
- Computational neuroscience
- Pattern formation in chemical and biological systems: Oscillatory chemical reactions and evolution of fronts
- Dynamical Systems

# Selected Publications

- H. G. Rotstein, T. Oppermann, J. A. White, N. Kopell (2006). The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells. To be published in the J. Comp. Neurosci.
- D. D. Pervouchine, T. I. Netoff, H. G. Rotstein, J. A. White, M. O. Cunningham, M. A. Whittington, N. Kopell (2006). Low-dimensional maps encoding dynamics in the entorhinal cortex and the hippocampus. Neural Computation 18:2617-2650.
- H. G. Rotstein, R. Kuske (2006). Localized and asynchronous patterns via canards in coupled calcium oscillators. Physica D. 215:46-61.
- H. G. Rotstein, D. D. Pervouchine, C. D. Acker, M. J. Gillies, J. A. White, E. H. Buhl, M. A. Whittington, N. Kopell (2005). Slow and fast inhibition and an h-current interact to create a theta rhythm in a model of CA1 interneuron network. J. Neurophysiol. 94:1509-1518.
- T. Gloveli, T. Dugladze, H. G. Rotstein, R. D. Traub, H. Monyer, U. Heinemann, M. Whittington, N. Kopell (2005). Orthogonal arrangement of rhythm-generating microcircuits in the hippocampus. PNAS 102:13295-13300.
- H. G. Rotstein, N. Kopell, A. M. Zhabotinsky, I. R. Epstein (2003). Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback. J. Chem. Phys. 119:8824-8832.
- H. G. Rotstein, N. Kopell, A. M. Zhabotinsky, I. R. Epstein (2003). A canard mechanism for localization in systems of globally coupled oscillators. SIAM J. Appl. Math., 63:1098-2019.

# Book Chapters

Polymer-metal nanocluster composites. Invited contribution to ``Advances in Nanophase Materials and Nanotechnology (Vol. Functionalization and Surface Treatment of Nanoparticles) edited by Marie-Isabelle Baraton, American Scientific Publishers, 2002. .*R. Tannenbaum, H. G. Rotstein.*

# Scienctific (Peer Reviewed) Journals

- Y. Boubendir, V. Mendez, H. G. Rotstein. Dynamics of one- and two-dimensional fronts in a bistable equation with delayed global coupling: localization and control (2008) Submitted.
J. Jalics, M. Krupa, H. G. Rotstein. A novel mechanism for mixed-mode oscillations in a neural model. (2007) Submitted. H. G. Rotstein, M. Wechselberger, N. Kopell Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model (2007) In Press. To be published in SIADS (Siam Journal on Applied Dynamical Systems). M. Brons, T. J. Kaper, H. G. Rotstein Introduction to Focus Issue: Mixed Mode Oscillations: Experiment, Computation, and Analysis (2008) Chaos 18:015101, Focus Issue on Mixed-Mode Oscillations. M. Krupa, N. Popovic, N. Kopell, H. G. Rotstein Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron (2008) Chaos 18:015106, Focus Issue on Mixed-Mode Oscillations. H. G. Rotstein, F. Nadim. Neurons and neural networks: Computational models. (2007) In: Encyclopedia of Life Sciences. John Wiley & Sons, Ltd: Chichester http://www.els.net/ [DOI: 10.1002/9780470015902.a0000089.pub2] A. B. L. Tort, H. G. Rotsein, T. Dugladze, T. Gloveli, N. Kopell. Formation of gamma coherent cell assemblies by oriens lacunosum-moleculare interneurons in the hippocampus: a modeling study. (2007) PNAS 104:13490-13495. Supplementary material (Table 1), Supplementary material (Table 2). N. Kopell, D. Pervouchine, H. G. Rotstein, T. Netoff, M. Whittington, T. Gloveli. Multiple rhythms and switches in the nervous system (2006) Proceedings of the Second International Symposium on the Frontier of Applied Mathematics in honor of Prof. C. C. Lin. H. G. Rotstein, T. Oppermann, J. A. White, N. Kopell. The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells. (2006) J. Comp. Neurosci., 21:271-292. D. D. Pervouchine, T. I. Netoff, H. G. Rotstein, J. A. White, M. O. Cunningham, M. A. Whittington, N. Kopell. Low-dimensional maps encoding dynamics in the entorhinal cortex and the hippocampus. (2006) Neural Computation, 18:2617-2650. H. G. Rotstein, R. Kuske. Localized and asynchronous patterns via canards in coupled calcium oscillators. (2006) Physica D. 215:46-61. H. G. Rotstein, A. M. Zhabotinsky, I. R. Epstein. Localized structures in a nonlinear wave equation stabilized by negative global feedback: one-dimensional and quasi-two-dimensional kinks (2006) Phys. Rev. E., 74:016612 T. Gloveli, T. Dugladze, H. G. Rotstein, R. D. Traub, H. Monyer, U. Heinemann, M. Whittington, N. Kopell. Orthogonal arrangement of rhythm-generating microcircuits in the hippocampus (2005) PNAS 102:13295-13300. Supplementary material H. G. Rotstein, D. D. Pervouchine, C. D. Acker, M. J. Gillies, J. A. White, E. H. Buhl, M. A. Whittington, N. Kopell. Slow and fast inhibition and an h-current interact to create a theta rhythm in a model of CA1 interneuron network. (2005) J. Neurophysiol. 94:1509-1518. R. Clewley, H. G. Rotstein, N. Kopell. A computational tool for the reduction of nonlinear ODE systems possesing multiple scales. (2005) SIAM J. on Multiscale Modeling and Simulations 4:732-759. H. G. Rotstein, N. Kopell, A. M. Zhabotinsky, I. R. Epstein. Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback. (2003) J. Chem. Phys. 119:8824-8832. H. G. Rotstein, N. Kopell, A. M. Zhabotinsky, I. R. Epstein. A canard mechanism for localization in systems of globally coupled oscillators. (2003) SIAM J. Appl. Math., 63:1098-2019. V. Mendez, J. Fort, H. G. Rotstein, S. Fedotov. Speed of reaction-diffusion fronts in spatially heterogeneous media. (2003) Phys. Rev. E. 68:041105. M. E. Sola, H. G. Rotstein, J. C. Bazan. The Ag/AgI/Graphite solid cell as iodine sensor: speed of response and use of Cs-doped AgI as electrolyte. (2002) J. Solid State Electrochemistry, 6:279-283. H. G. Rotstein, R. Tannenbaum. Cluster coagulation and growth limited by surface interactions with polymers. (2002) J. Phys. Chem. B, 106:146-151. H. G. Rotstein, I. Mitkov, A. M. Zhabotinsky, I. R. Epstein. Dynamics of Kinks in One- and Two- Dimensional Hyperbolic Models with Quasi-discrete Nonlinearities. (2001) Phys. Rev. E, 63:066613. H. G. Rotstein, A. M. Zhabotinsky, I. R. Epstein. Dynamics of one- and two-dimensional kinks in reaction diffusion equations of Allen-Cahn type with a quasi-discrete source of reaction. (2001) Chaos, 11:833-842. H. G. Rotstein, S. Brandon, A. Novick-Cohen, A. A. Nepomnyashchy. Phase field equations with memory: the hyperbolic case. (2001) SIAM J. Appl. Math, 62:264-282. M. Grasselli, H. G. Rotstein. Hyperbolic phase-field dynamics with memory. (2001) J.Math. Anal. Appl., 261:205-230. B. Malomed, H. G. Rotstein. Ramped-induced states in the parametrically driven Ginzburg-Landau model . (2001) Physics Letters A, 283:327-334. H. G. Rotstein, A. I. Domoshnitsky, A. A. Nepomnyashchy. Front motion for phase transitions in systems wity memory. (2000) Physica D, 146:137-149. B. Malomed, H. G. Rotstein. A quasicrystallic domain wall in nonlinear dissipative systems. (2000) Physica Scripta, 62:164-168. H. G. Rotstein, A. A. Nepomnyashchy. Dynamics of kinks in two dimensional hyperbolic models. (2000) Physica D, 136:245-265. H. G. Rotstein, A. I. Domoshnitsky, A. A. Nepomnyashchy. Phase transition dynamics with memory Functional Differential Equations (1998), 5:439-451. H. G. Rotstein, A. A. Nepomyashchy, A. Novick-Cohen. Hyperbolic non-conserved phase field equations. (1999) Journal of Crystal Growth, Proceedings of the ICCG12, 198-199:1262-1266. H. G. Rotstein, S. Brandon, A. Novick-Cohen. Hyperbolic flow by mean curvature. (1999) Journal of Crystal Growth, Proceedings of the ICCG12, 198-199:1256-1261. H. G. Rotstein, A. Novick-Cohen, R. Tannenbaum. Gelation and cluster growth with cluster-wall interactions (1998) J. Stat. Phys, 90-1/2.

# Teaching Material

- T. Saadon, H. G. Rotstein. Exercise notes in Partial Differential Equations. (Problems and solutions - in hebrew). Technion - Israel Institute of Technology, Department of Mathematics.