Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity
Bibliographic record
Abstract
We propose a method to search for signs of causal structure in spatiotemporal data making minimal a priori assumptions about the underlying dynamics. To this end, we generalize the elementary concept of recurrence for a point process in time to recurrent events in space and time. An event is defined to be a recurrence of any previous event if it is closer to it in space than all the intervening events. As such, each sequence of recurrences for a given event is a record breaking process. This definition provides a strictly data driven technique to search for structure. Defining events to be nodes, and linking each event to its recurrences, generates a network of recurrent events. Significant deviations in statistical properties of that network compared to networks arising from (acausal) random processes allows one to infer attributes of the causal dynamics that generate observable correlations in the patterns. We derive analytically a number of properties for the network of recurrent events composed by a random process in space and time. We extend the theory of records to treat not only the variable where records happen, but also time as continuous. In this way, we construct a fully symmetric theory of records leading to a number of results. Those analytic results are compared in detail to the properties of a network synthesized from time series of epicenter locations for earthquakes in Southern California. Significant disparities from the ensemble of acausal networks that can be plausibly attributed to the causal structure of seismicity are as follows. (1) Invariance of network statistics with the time span of the events considered. (2) The appearance of a fundamental length scale for recurrences, independent of the time span of the catalog, which is consistent with observations of the "rupture length." (3) Hierarchy in the distances and times of subsequent recurrences. As expected, almost all of the statistical properties of a network constructed from a surrogate in which the original magnitudes and locations of earthquake epicenters are randomly "shuffled" are completely consistent with predictions from the acausal null model.
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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) | 0.000 | 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 | 0.000 |
| 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".