Welcome to Neuronal Cascades’s documentation!

Neuronal Cascades is a python package for simulating spreading processes, such as Watts-Thresholds model [1,2] or Simplicial Threshold model [3] on networks. For example, for STM cascades, a vertex \(v_{i}\) becomes active only when the activity across its simplicial neighbors surpasses a threshold \(T_{i}\). See the paper [3] for details.

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[1] - Watts, Duncan J. A simple model of global cascades on random networks, PNAS, 99, 9, 2002, 10.1073/pnas.082090499.

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[2] - Taylor, D., Klimm, F., Harrington, H. et al. Topological data analysis of contagion maps for examining spreading processes on networks. Nature Communications, 6, 7723 (2015). https://doi.org/10.1038/ncomms8723

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[3] - Kilic, B.Ü., Taylor, D. Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes. Communications Physics, 5, 278 (2022). https://doi.org/10.1038/s42005-022-01062-3

Contents:

• Introduction
  • Geometric and Noisy Geometric Ring complexes
  • Simplicial Threshold Model
  • Neuronal Subtypes
• Tutorial
  • Initiate a Geometric_Brain_Network object
  • Inheriting neuron objects
  • Run a single example cascade
  • Running experiments without changing the network connectivity
  • Running simplicial cascades
  • Neurons with memory and refractory period
  • Running stochastic models
  • Looking at the cascade size
  • Run a full scale experiment
  • Persistence diagrams
• Semantics of Neuronal Cascades

Indices and tables

• Index

• Module Index

• Search Page