Fundamental interactions in self-organised critical dynamics on higher order networks
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Bibliographic record
Abstract
Abstract In functionally complex systems, higher order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organised criticality, a specific type of non-equilibrium collective behaviour associated with an attractor of internal dynamics with long-range correlations and scale invariance, which ensures the robust functioning of complex systems, such as the brain. Here, we highlight the intertwining of features of higher order geometry and self-organised critical dynamics as a plausible mechanism for the emergence of new properties on a larger scale, representing the central paradigm of the physical notion of complexity. Considering the time-scale of the structural evolution with the known separation of the time-scale in self-organised criticality, i.e., internal dynamics and external driving, we distinguish three classes of geometries that can shape the self-organised dynamics on them differently. We provide an overview of current trends in the study of collective dynamics phenomena, such as the synchronisation of phase oscillators and discrete spin dynamics with higher order couplings embedded in the faces of simplicial complexes. For a representative example of self-organised critical behaviour induced by higher order structures, we present a more detailed analysis of the dynamics of field-driven spin reversal on the hysteresis loops in simplicial complexes composed of triangles. These numerical results suggest that two fundamental interactions representing the edge-embedded and triangle-embedded couplings must be taken into account in theoretical models to describe the influence of higher order geometry on critical dynamics. Graphical abstract
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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 it