I graduated in June 2014 and am now a Swartz Postdoc Fellow at Center for Brain Science, Harvard University.

Yu Hu

Department of Applied Mathematics, University of Washington

Email: huyu (at) uw.edu or hu03 (at) fas.harvard.edu

Address: Lewis Hall #322, Box 353925

Seattle, WA 98195 USA

Curriculum vitae

I am a PhD student (gratuating in Spring 2014) in Applied Mathematics studying Theoretical Neuroscience (advisor Eric Shea-Brown).

Neurons in a brain area are highly interconnected. Moreover, recent experiments found that certain connectivity patterns, or motifs, in biological neural networks occur at markedly different frequencies than what would be expected if the neurons were randomly connected. Thus motivated, I study how connectivity motif structures will influence dynamics (correlation between the activity (spikes) of pairs of neurons) and simple functions (filtering of a temporal signal) of neural networks.

We find that the overall correlation in a network is determineddetermined by the statistical prevalence of two families of motifs: chain and diverging motifs. We show this by developing a series expression of the correlation that shows contributions of each motif in order. The critical step is to quantify the prevalence of a motif, not “naively” by its number of occurrence in a network, but by a new graphical statistic we call the motif cumulant. Importantly, in practical examples motif cumulants fall off quickly with size of the motif. The consequence is that measurements of prevalence of motifs involving only a few cells (therefore are local connecivity features!), when assembled through our series expression, are often enough to predict the overall correlation of a network.

Recently, we combine the graph statistics tools developed ealier with control theory to study how connectivity motifs changes or sustain how a recurrent network process temporal signals.

Research

- Signal filtering properties in recurrent networks with connecivity motif statistics
- Population coding with optimal noise correlations under fixed mean responses

- Connectivity motif statistics and spike correlations in neuronal networks
- Linear response theory for spiking neurons

Publications

Y. Hu, J. Trousdale, K. Josić and E. Shea-Brown. Local paths to global coherence: cutting networks down to size. Physical Review E. 89(3):032802. doi:10.1103/PhysRevE.89.032802, (2014)

Y. Hu, J. Zylberberg, and E. Shea-Brown. The sign rule and beyond: Boundary effects, flexibility, and optimal noise correlations in neural population codes. PLoS Computational Biology. 10(2):e100346. doi:10.1371/journal.pcbi.1003469, (2014)

J. Trousdale, Y. Hu, E. Shea-Brown, and K. Josić. A generative spike train model with time-structured higher order correlations. Frontiers Comp. Neuroscience 7:84. doi: 10.3389/fncom.2013.00084, (2013)

Y. Hu, J. Trousdale, K. Josić, and E. Shea-Brown. Motif Statistics and Spike Correlations in Neuronal Networks. J. Stat. Mech. P03012. (2013)

J. Trousdale, Y. Hu, E. Shea-Brown, and K. Josić. Impact of Network Structure and Cellular Response on Spike Time Correlations. PLoS Computational Biology. 8(3):e1002408. doi:10.1371/journal.pcbi.1002408.t001 (2012)

Teaching

I have been teaching assistant for AMATH 383 Introduction to Continuous Mathematical Modeling in Fall 2009, 2011, AMATH 353 Fourier Analysis and Partial Differential Equations Spring 2011, and calculus sequences MATH 124 Winter 2011, MATH 125 Winter 2009.

Links

Eric Shea-Brown's neural dynamics group

Department of Applied Mathematics, University of Washington

My collaborators:

James Trousdale

Kreso Josić

Joel Zylberberg

Steve Brunton

Nathan Kutz