# Meet the Researchers

Mark Bodner is Co-founder and President of Research at the MIND Research Institute. He is an adjunct professor of mathematics at the University of Pittsburgh and visiting professor at the Institute of Cognitive Neuroscience at the East China Normal University. He formerly held faculty appointments at the Johns Hopkins University’s Department of Neurosurgery, and joint faculty appointments at UCLA’s Neuropsychiatric Institute, and UC Irvine’s Department of Physics. His research focus is computational neuroscience and mathematical biology. Recent work has focused on understanding the patterns and mechanisms of activity in networks of neurons, and working memory, and how seizures arise in cortical networks in epilepsy and how they may be terminated through specific brain stimulation. Other work focuses on the application of knot theory and group theory in modeling the structure and function of DNA.

Mark has received several national and international awards including the J.J. Sakuri prize; the Ettore Majorana award at the Majorana School of Subnuclear Physics in Erice, Italy; and the Halliday and Resnick Award in physics for solving the liquid crystal structure of particular cholestoral esters linked to cardiovascular disease. He has been a grant recipient from the National Science Foundation for demonstrating the feasibility of elucidating cognitive function in awake behaving primates using optical and infrared imaging methods. Mark received his Ph.D. and master’s degrees in theoretical high-energy and mathematical physics from UCLA and bachelor’s degree in both physics and chemistry from the University of Pittsburgh. He received a fellowship from the National Institute of Mental Health for postdoctoral work in Neuroscience at UCLA. Mark has over 100 papers and abstracts published in neuroscience, physics and mathematics.

Select publications:

**Reduction of Seizure occurrence from exposure to auditory stimulation in individuals with neurological handicaps: A randomized controlled trial.**

Bodner, M., Turner, RP, Schwacke, J., Bowers, C., Norment, C. (2012).

PLoS ONE doi:10.1371/journal.pone.0045303.

**Affine reflection groups for tiling applications: Knot theory and DNA.**

Bodner, M., Patera, J., Peterson, M. (2012).

J. Math. Phys. 53 013516.

**Persistent neuronal firing in SI cortex during instructed delays between haptic stimuli in the absence of working-memory requirement.**

Wang, L., Li, X., Hsiao, S., Bodner, M., Lenz, F. and Zhou Y-D. (2012).

Journal of Cognitive Neuroscience 24: 664-676.

**Modeling neuropathologies as disruption of normal sequence generation in working memory networks.**

Verduzco, S., Ermentrout, B., Bodner, M. (2012).

Neural Networks. DOI: 10.1016/j.neunet.2011.09.007.

**Behavioral choice-related neuronal activity in monkey primary somatosensory cortex in a haptic delay task.**

Wang, L., Li, X., Hsiao, S., Bodner, M., Lenz, F., and Zhou, Y-D. (2012).

Journal of cognitive neuroscience; 24(7):1634-44.

**A model for complex sequence learning and reproduction in neural populations.**

Verduzco, S., Bodner, M., Ermentrout, B. (2012).

J. Comput. Neurosci.; 32: 403-423.

**Sequential Neural Processes in Abacus Mental Addition: An EEG and fMRI Case Study.**

Ku, Y., Hong, B., Zhou, W., Bodner, M., Zhou, Y. (2012).

PLoS ONE 7(5): e36410.doi:10.1371/journal.pone.0036410.

**From working memory to epilepsy: Dynamics of facilitation and inhibition in a cortical network.**

Verduzco, S., Ermentrout, B., Bodner, M. (2009).

Chaos; 19:015115.

**Working memory cell’s behavior may be explained by cross-regional networks with synaptic facilitation.**

Verduzco, S., Bodner, M., Ermentrout, B., Fuster, J.M., Zhou, Y-D. (2009).

PLoS ONE 4(8): e6399.

**Variability in neuronal activity in primate cortex during working memory tasks.**

Shafi, M., Zhou, Y-D., Quintana, J., Chow, C., Fuster, J.M., Bodner, M. (2007).

Neuroscience; 146: 1082-1108.

**Patterned firing of parietal cells in a haptic working memory task.**

Bodner, M., Shafi, M., Zhou, Y-D., Fuster, J.M. (2005).

Eur. J. Neurosci.; 21: 2538-2546.

**Near-infrared spectroscopy (NIRS) in cognitive neuroscience of the primate brain.**

Fuster, J.M., Guiou, M., Ardestani, A., Cannestra, A., Sheth, S., Zhou, Y-D., Toga, A., Bodner. M. (2005).

NeuroImage; 26: 215-220.

**Cross-modal and cross-temporal association in neurons of frontal cortex.**

Fuster, J.M., Bodner, M., Kroger, J.K. (2000).

Nature; 405: 347-351.

Jiri Patera is Professor of Mathematics at the University of Montreal’s Department of Mathematics and Statistics, and a former visiting faculty member in the Department of Physics at the California Institute of Technology. Jiri’s recent work focuses on lattice-based special functions in multi-dimensional cases and their exploitation in Fourier analysis of digital data. He also focuses on application of Lie group and symmetry towards the modeling of biological and physical phenomena. Jiri received his Ph.D. in theoretical physics at the Czech Technical University in Prague, and performed postdoctoral work at Imperial College in London. He has been the recipient of the CRM-CAP Prize in Theoretical and Mathematical Physics for his outstanding contributions to Lie group and Lie algebra theory, with applications to elementary particle and nuclear physics and to quantum chemistry, and more recently for his significant contributions to the mathematical theory of quasicrystals, with applications to condensed matter physics and cryptography. Jiri’s work has had an impact on nuclear and elementary particle physics, quantum chemistry and solid state physics. His research on quasi-crystals even had implications in cryptography.

Select publications:

**On discretization of Tori of compact simple Lie Groups II.**

Hrivnak, J., Motlochova, L., Patera, J. (2012).

J. Phys. A. Math Theor.; 45 255201.

**Six Types of E-functions of the Lie groups O(5) and G(2).**

Hakova, L., Hrivnak, J., Patera, J. (2012).

J. Phys. A: Math. Theor.; 45 125201.

**Three-variable exponential functions of the alternating group.**

Hrivnak, J., Patera, J., Posta, S. (2012).

J. Phys. A: Math Theor.; 45 045201.

**Affine reflection groups for tiling applications: Knot theory and DNA.**

Bodner, M., Patera, J., Peterson, M. (2012).

J. Math. Phys.; 53 013516.

**Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations.**

Larouche, M., Lemire, F.W., Patera, J. (2011).

J. Phys. A: Math. Theor.; 44 415204, 25 pp. arXiv:1109.6917.

**Orthogonal polynomials of compact simple Lie groups.**

Nesterenko, M., Patera, P., Tereszkiewicz, A. (2011).

International Journal of Mathematics and Mathematical Sciences; Article ID 969424, 23 pages.

**On E-functions of semisimple Lie algebras.**

Hrivn´ak, J., Kashuba, I., Patera, J. (2011).

J. Phys. A: Math. Theor.; 44 325205; 16 pp.

**Branching rules for Weyl group orbits of simple Lie algebras Bn, Cn and Dn.**

Larouche, M., Patera, J. (2011).

J. Phys. A: Math. Theor.; 44 (37pp).

**Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups.**

Moody, R., Patera, J. (2011).

Advances of Applied Math; 47 509–535; arXiv:1005.2773v1 [math.FA].

**Orthogonal polynomials of compact simple Lie groups. The branching rules for polynomials.**

Nesterenko, M., Patera, J., Szajewska, M., Tereszkiewicz, A. (2010).

J. Phys. A: Math. Theor.; 43 495207 (20pp); arXiv:1007.4431v1.

**Two-dimensional symmetric and antisymmetric generalizations of sine functions.**

Hrivn´ak, J., Motlochov´a, L., Patera, J. (2010).

J. Math. Phys; 51 073509 (13pp); arXiv:0912.0241v1 [math-ph].

**On E–discretization of tori of compact simple Lie groups.**

Hrivn´ak, J., Patera, J. (2010).

J. Phys. A: Math. Theor.; 43 165206 (16pp); arXiv:0912.4194v1 [math-ph].

**Two dimensional symmetric and antisymmetric generalizations of exponential and cosine functions.**

Hrivn´ak, J., Patera, J. (2010).

J. Math. Phys.; 51, 023515; arXiv:0911.4209v1.