Applied Math Seminar: Zoltan Toroczkai


Location: 127 Hayes-Healy

Zoltan Toroczkai
Department of Physics

4:00 PM*
127 Hayes-Healy

*This seminar will be held 30 minutes later than the regular seminar time.

The Brain in Space

Recent advances in neuroscience have raised interest in large-scale brain networks. Using a consistent database of cortico-cortical connectivity, generated from hemisphere-wide, retrograde tracing experiments in the macaque, we analyzed interareal connection weights and axonal projection distances to reveal an important organizational principle of brain connectivity. Using appropriate graph theoretical measures, we show that although very dense (66%), the interareal network has strong structural specificity. Connection weights exhibit a heavy-tailed lognormal distribution spanning five orders of magnitude and conform to a distance rule reflecting exponential decay with interareal separation. Based on this rule, we introduce a single-parameter random graph model, the EDR model, which predicts all local and global features of the cortical network: (1) the existence of a network core and the distribution of cliques, (2) global and local binary properties, (3) global and local weight-based communication efficiencies modeled as network conductance, and (4) overall wire-length minimization. Finally, using data provided by the Paul Allen Institute in the mouse brain and University of South California, we show that that the EDR model describes the mouse cortical network as well (using the corresponding decay rate of connection probability in the mouse and the intearareal distance matrix from direct measurements). These findings underscore the importance of distance and weight-based heterogeneity in cortical architecture and processing and provides a way to quantify the large-scale cortical network through the mammalian evolutionary tree.


















List of Speakers:

Apr. 23 Jason MacLean - Department of Neurobiology, University of Chicago
Apr. 16 Daniel Molzahn - Dow Sustainability Fellow, University of Michigan
Apr. 9 Zoltan Toroczkai - Physics
Apr. 2 Martina Bukač - Applied and Computational Mathematics and Statistics
Mar. 19 Daniel Brake - Applied and Computational Mathematics and Statistics
Feb. 19 Dhagash Mehta - Applied and Computational Mathematics and Statistics
Feb. 12 Holly Goodson - Chemistry and Biochemistry
Feb. 5 Joseph Powers - Aerospace and Mechanical Engineering
Jan. 27 Yunhua Xue - Nankai University and University of Dartmouth, Massachusetts
Jan. 22, 2015 Ava Mauro - Applied and Computational Mathematics and Statistics
Dec. 10 Nicolas Brunel - Department of Statistics and Neurobiology, University of Chicago
Dec. 3 Amy Buchmann - Applied and Computational Mathematics and Statistics
Nov. 19 Pinar Zorlutuna - Aerospace and Mechanical Engineering
Nov. 12 Ling Xu - Applied and Computational Mathematics and Statistics
Oct. 29 Joel Boerckel - Aerospace and Mechanical Engineering
Oct. 15 Zhangli Peng -  Aerospace and Mechanical Engineering
Oct. 8 Tim Weninger - Computer Science and Engineering
Oct. 1, 2014 Dervis Can Vural - Physics