Stochastic Modeling in Life Sciences

Topics

Mathematical problems in neuroscience

Recent advances in neuroscience provide theoretical neuroscientists with a vast wealth of new data and open questions related to information theory, high-dimensional geometry of representation and computation, and dynamics in the brain. The groups of Ila Fiete, Ngoc Mai Tran and Thibaud Taillefumier study these questions from analytical and numerical perspectives. Fiete and Tran have recently studied the learning capacity of neural networks (see “A binary Hopfield network with 1/\log(n) information rate and applications to grid cell decoding“, “ Robust exponential memory in Hopfield networks“, and “ Associative content-addressable networks with exponentially many robust stable states“).

Optimization of DNA sequencing

High throughput DNA sequencing technology has greatly increased the speed and reduced the cost of genome sequencing. The process is divided into to two steps: generating a library of short reads and reassembling those reads into the original genome. Eliza O’Reilly, François Baccelli, Gustavo de Veciana, and Haris Vikalo have worked on modeling this process using stochastic geometry and queueing theory in order to optimize the output of correct reads and the probability of successful reassembly (see End-to-End Optimization of High Throughput DNA Sequencing).

Synchrony in stochastic spiking neural networks

Neural systems propagate information via neuronal networks that transform sensory input into distributed spiking patterns, and dynamically process these patterns to generate behaviorally relevant responses. The presence of noise at every stage of neural processing imposes serious limitation on the coding strategies of these networks. In particular, coding information via spike timings, which presumably achieves the highest information transmission rate, requires neural assemblies to exhibit high level of synchrony. Thibaud Taillefumier and collaborators are interested in understanding how synchronous activity emerges in modeled populations of spiking neurons, focusing on the interplay between driving inputs and network structure. Their approach relies on methods from Markov chain, point processes, and diffusion processes theories, in combination with exact event-driven simulation techniques. The ultimate goal is two-fold: 1) to identify the input/structure relations that optimize information transmission capabilities and 2) to characterize the “physical signature’’ of such putative optimal tunings in recorded spiking activity.

Members

Thibaud Taillefumier

Department of Mathematics and Department of Neuroscience
taillef@math.utexas.edu
512 475 8145
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Ila Fiete

Department of Neuroscience
ilafiete@mail.clm.utexas.edu
512 232 8439
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Eliza O’Reilly

Department of Mathematics, UT Austin
eoreilly@math.utexas.edu
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Ngoc Mai Tran

Department of Mathematics, UT Austin
ntran@math.utexas.edu
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Sriram Vishwanath

Department of Electrical and Computer Engineering, UT Austin
sriram@ece.utexas.edu
512 471 1190
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Gustavo de Veciana

Department of Electrical and Computer Engineering, UT Austin
gustavo@ece.utexas.edu
512 471 1573
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François Baccelli

Department of Mathematics and Deparment of Electrical and Computer Engineering, UT Austin
baccelli@math.utexas.edu
512 471 17 54
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Publications

2017_1000869 2016_1000586

End-to-End Optimization of High Throughput DNA Sequencing

Eliza O'Reilly, Francois Baccelli, Gustavo de Veciana, Haris Vikalo Journal of Computational Biology 2016
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2014-07-22_1000381

A binary Hopfield network with 1/\log(n) information rate and applications to grid cell decoding

Ila Fiete, David J. Schwab and Ngoc M Tran 2nd Workshop on Biological Distributed Algorithms 2014
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