🍩 Database of Original & Non-Theoretical Uses of Topology
(found 3 matches in 0.001585s)
The Growing Topology of the C. Elegans Connectome (2020)Alec Helm, Ann S. Blevins, Danielle S. Bassett
AbstractProbing the developing neural circuitry in Caenorhabditis elegans has enhanced our understanding of nervous systems. The C. elegans connectome, like those of other species, is characterized by a rich club of densely connected neurons embedded within a small-world architecture. This organization of neuronal connections, captured by quantitative network statistics, provides insight into the system's capacity to perform integrative computations. Yet these network measures are limited in their ability to detect weakly connected motifs, such as topological cavities, that may support the systems capacity to perform segregated computations. We address this limitation by using persistent homology to track the evolution of topological cavities in the growing C. elegans connectome throughout neural development, and assess the degree to which the growing connectomes topology is resistant to biological noise. We show that the developing connectome topology is both relatively robust to changes in neuron birth times and not captured by similar growth models. Additionally, we quantify the consequence of a neurons specific birth time and ask if this metric tracks other biological properties of neurons. Our results suggest that the connectomes growing topology is a robust feature of the developing connectome that is distinct from other network properties, and that the growing topology is particularly sensitive to the exact birth times of a small set of predominantly motor neurons. By utilizing novel measurements that track biological features, we anticipate that our study will be helpful in the construction of more accurate models of neuronal development in C. elegans
Cliques of Neurons Bound Into Cavities Provide a Missing Link Between Structure and Function (2017)Michael W. Reimann, Max Nolte, Martina Scolamiero, Katharine Turner, Rodrigo Perin, Giuseppe Chindemi, Paweł Dłotko, Ran Levi, Kathryn Hess, Henry Markram
AbstractThe lack of a formal link between neural network structure and its emergent function has hampered our understanding of how the brain processes information. We have now come closer to describing such a link by taking the direction of synaptic transmission into account, constructing graphs of a network that reflect the direction of information flow, and analyzing these directed graphs using algebraic topology. Applying this approach to a local network of neurons in the neocortex revealed a remarkably intricate and previously unseen topology of synaptic connectivity. The synaptic network contains an abundance of cliques of neurons bound into cavities that guide the emergence of correlated activity. In response to stimuli, correlated activity binds synaptically connected neurons into functional cliques and cavities that evolve in a stereotypical sequence towards peak complexity. We propose that the brain processes stimuli by forming increasingly complex functional cliques and cavities.