A Spatio-temporal Investigation of Dynamics of a Two-dimensional Multi-scale Fitz-Hugh Nagumo Neuronal Network
Bibliographic record
Abstract
Abstract The multi scale architecture by Breakspear and Stam [2] introduces a framework to consider the dynamical processes specific to a nested hierarchy of spatial scales, from neuronal masses to cortical columns and functional brain regions. They hypothesize that the neural dynamics is a function of the structural properties of the neural system at a certain scale as well as the emergent behaviour of the smaller scale activities. In this paper, we adopt the multi scale framework to investigate a generalized version of the stochastic Fitz-Hugh Nagumo (FHN) neuronal system within the small scale process and their emergent large scale synchronization effects leading to the formation of travelling waves in the large scale system. We extend the multi scale framework to incorporate the nonlinear biological synaptic connectivity at the neuronal mass scale. The modified multi scale scheme utilizes the two-dimensional wavelet decomposition in the plane of dynamical interconnected neurons. In addition, we consider the large-scale spatio-temporal system of FHN reaction-diffusion partial differential equations and evaluate the formation of travelling waves in the simplified context of a cellular neural network (CNN) model. Numerical examples are given to illustrate the response and the isolated influence of the strength of neural connectivity on the travelling wave formation modes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".