AI Article Synopsis
- The brain is a complex system primarily made up of interconnected nodes called neurons, and understanding its structural connectivity can reveal its functional properties.
- The paper focuses on analyzing the connectome of the nematode Caenorhabditis elegans, which has a relatively simple network of 302 neurons, using mathematical tools like the Laplacian Matrix to investigate patterns in its neural connections.
- The study examines characteristics such as small-world properties and eigenfunction localization, comparing these results against random networks and fractals to propose new algorithms for generating similar graphs.
Article Abstract
The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron "giant component" of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been "rewired" to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.
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|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3465333 | PMC |
| http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0040483 | PLOS |
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