Title PageAbbreviated title (50 character max): SfN Mock ArticleAuthor Names and Affiliations: Pete D. Nicholson\(^1\), Alberto Pepe\(^1\)\(^1\): Authorea, Brooklyn, NY 11249Number of pages: 6Number of figures: 2Number of WordsAbstract: 147Introduction: 27Discussion: 504Conflict of interest statement: The authors declare no competing financial interests.Acknowledgements: None
General Remarks and Definitions:Def: Chaos A deterministic system exhibits aperiodic behavior that depends sensitively on the initial conditions. thereby rendering long-term predictions impossible.Dynamical system typesDifferential equations: They describe the system evolution in continuous timeIterated maps: They describe the system evolution in discrete timeDifferential equations
Lynn & Bassett (2019): The physics of brain network structure, function and controlNetwork models of structural connections in the brain:Random networks: Can be generated by the Erdös-Renyi model wherein each pair of nodes is connected independently with a fixed probability.Community structure: Characterized by dense intra-community coupling and sparse inter-community coupling. Can be generated via the stochastic block model, where the coupling probabilities depend on the community assignments of the to-be-coupled nodes Small world structure: Characterized by a high clustering coefficient and average path lengths that are shorter than expected in random networks. Can be generated by the Watts-Strogatz model which is an interpolation of a circular nearest neighbor network and a random network.Hub structure: Characterized by high-degree hubs that form a densely interconnected structural core. Can be identified by a heavy-tailed degree distribution, such as observed in scale-free networks. Can be generated by the Barabasi-Albert model that adds nodes sequentially to a network and connects them to existing network nodes with a probability proportional to the degree of the node.
Montbrio et al. (2015) Macroscopic Description for Networks of Spiking NeuronsSummaryIn this paper( https://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.021028), Montbrio and colleagues derive a mathematically exact description of the macroscopic dynamics of a globally coupled network of quadratic integrate and fire neurons (QIFs). They start out with the membrane potential evolution of a single QIF neuron: