arXiv subjects

Jacob Carroll

Publications and source records attributed to Jacob Carroll.

3 recordsLinked to original sources

arXiv2018

The effects of inhibitory and excitatory neurons on the dynamics and control of avalanching neural networks

The statistical analysis of the collective neural activity known as avalanches provides insight into the proper behavior of brains across many species. We consider a neural network model based on the work of Lombardi, Herrmann, De Arcangelis et al. that captures the relevant dynamics of neural avalanches, and we show how tuning the fraction of inhibitory neurons in this model alters the connectivity of the network over time, removes exponential cut-offs present in the distributions of avalanche strength and duration, and transitions the power spectral density of the network into an `epileptic' regime. We propose that the brain operates away from this power law regime of low inhibitory fraction to protect itself from the dominating avalanches present in these extended distributions. We present control strategies that curtail these power law distributions through either random or, more effectively, targeted disabling of excitatory neurons.

cond-mat.dis-nn↗

arXiv2017

Phase Transitions in Image Denoising via Sparsely Coding Convolutional Neural Networks

Neural networks are analogous in many ways to spin glasses, systems which are known for their rich set of dynamics and equally complex phase diagrams. We apply well-known techniques in the study of spin glasses to a convolutional sparsely encoding neural network and observe power law finite-size scaling behavior in the sparsity and reconstruction error as the network denoises 32$\times$32 RGB CIFAR-10 images. This finite-size scaling indicates the presence of a continuous phase transition at a critical value of this sparsity. By using the power law scaling relations inherent to finite-size scaling, we can determine the optimal value of sparsity for any network size by tuning the system to the critical point and operate the system at the minimum denoising error.

cs.NE↗

arXiv2016

Ligand-receptor binding kinetics in surface plasmon resonance cells: A Monte Carlo analysis

Surface plasmon resonance (SPR) chips are widely used to measure association and dissociation rates for the binding kinetics between two species of chemicals, e.g., cell receptors and ligands. It is commonly assumed that ligands are spatially well mixed in the SPR region, and hence a mean-field rate equation description is appropriate. This approximation however ignores the spatial fluctuations as well as temporal correlations induced by multiple local rebinding events, which become prominent for slow diffusion rates and high binding affinities. We report detailed Monte Carlo simulations of ligand binding kinetics in an SPR cell subject to laminar flow. We extract the binding and dissociation rates by means of the techniques frequently employed in experimental analysis that are motivated by the mean-field approximation. We find major discrepancies in a wide parameter regime between the thus extracted rates and the known input simulation values. These results underscore the crucial quantitative importance of spatio-temporal correlations in binary reaction kinetics in SPR cell geometries, and demonstrate the failure of a mean-field analysis of SPR cells in the regime of high Damk\"ohler number Da > 0.1, where the spatio-temporal correlations due to diffusive transport and ligand-receptor rebinding events dominate the dynamics of SPR systems.

q-bio.QM↗