Modeling overlapping structures
Bibliographic record
Abstract
The problem of overlapping structures has long been familiar to the structured document community. In a poem, for example, the verse and line structures overlap, and having them both available simultaneously is convenient, and sometimes necessary (for example for automatic analyses). However, only structures that embed nicely can be represented directly in XML. Proposals to address this problem include XML solutions (based essentially on a layer of semantics) and non-XML ones. Among the latter is TexMecs HS2003 , a markup language that allows overlap (and many other features). XML documents, when viewed as graphs, correspond to trees. Marcoux M2008 characterized overlap-only TexMecs documents by showing that they correspond exactly to completion-acyclic node-ordered directed acyclic graphs . In this paper, we elaborate on that result in two ways. First, we cast it in the setting of a strictly larger class of graphs, child-arc-ordered directed graphs , that includes multi-graphs and non-acyclic graphs, and show that — somewhat surprisingly — it does not hold in general for graphs with multiple roots. Second, we formulate a stronger condition, full-completion-acyclicity , that guarantees correspondence with an overlap-only document, even for graphs that have multiple roots. The definition of fully-completion-acyclic graph does not in itself suggest an efficient algorithm for checking the condition, nor for computing a corresponding overlap-only document when the condition is satisfied. We present basic polynomial-time upper bounds on the complexity of accomplishing those tasks.
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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 | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".