Average consensus on arbitrary strongly connected digraphs with dynamic topologies
Why this work is in the frame
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Bibliographic record
Abstract
We have recently proposed a “surplus-based” algorithm which solves the multi-agent average consensus problem on general strongly connected and static digraphs. The essence of that algorithm is to employ an additional variable to keep track of the state changes of each agent, thereby achieving averaging even though the state sum is not preserved. In this paper, we extend this approach to the more challenging case of dynamic digraphs, and consider both deterministic and randomized (of the gossip type) time-varying scenarios. For each scenario, we design an extended surplus-based algorithm and derive a necessary and sufficient graphical condition which guarantees state averaging. In the deterministic time-varying case, the digraphs should be strongly connected in a joint sense; and in the randomized gossip case, the digraphs in the mean should be strongly connected. In particular, these conditions do not impose “balanced” or “symmetric” requirements on the network topology, and are therefore more general than those previously reported in the literature.
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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 | 0.001 | 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 it