Date of Submission

Spring 2015

Academic Programs and Concentrations

Mathematics; Mind, Brain, and Behavior

Project Advisor 1

Csilla Szabo

Project Advisor 2

Arseny Khakhalin

Abstract/Artist's Statement

We investigate the connectivity of neural networks in the Xenopus tadpole as the organism is confronted with various visual stimuli. We begin with techniques for processing calcium imaging data. An existing deconvolution algorithm is applied to the fluorescence data to get spike trains that indicate when a neuron is firing. The goal is to find connectivity of the neurons based on their spike trains. We cross correlate the spike trains of every pair of neurons in our network to infer when a signal propagates from one neuron to another. We quantify two neurons as being connected based on their measure of cross correlation. If their cross correlation value is above some threshold, we consider the two connected. We then test whether the degree distribution of our data is consistent with that of a random network, which follows a Poisson distribution. To do so, we use a chi-squared goodness-of-fit test. The test is repeated for varying threshold values to find the value that produces the maximum test statistic. Once we have a threshold, the matrix of cross correlation values is converted into an adjacency matrix that represents all directed connections between neurons. The degree distribution of our optimized network is then fit with a power law distribution. This indicates if our network has properties of a scale-free network, meaning that most neurons have only a few links while a small number of neurons act as hubs with many links. We find that the data does follow a power law, but that the parameters that govern this fit are atypical of a scale-free network. Finally, we compare metrics, namely network density and power law parameters, between networks derived from the varying visual stimuli. We find that the different stimuli produce very similar networks, both in the density of the networks and in the parameters of their power law models.

Open Access Agreement

On-Campus only

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.