Compact Hilbert Indices for Multi-Dimensional Data
Bibliographic record
Abstract
Space-filling curves, particularly Hilbert curves, have proven to be a powerful paradigm for maintaining spatial groupings of multi-dimensional data in a variety of application areas including database systems,data structures and distributed information systems. One significant limitation in the standard definition of Hilbert curves is the requirement that the grid size (i.e. the cardinality) in each dimension be the same. In the real world, not all dimensions are of equal size and the work-around of padding all dimensions to the size of the largest dimension wastes memory and disk space, while increasing the time spent manipulating and communicating these "inflated" values. In this paper we define a new compact Hilbert index which, maintains all the advantages of the standard Hilbert curve and permits dimension cardinalities of varying sizes. This index can be used in any application that would have previously relied on Hilbert curves but, in the case of unequal side lengths, provides a more memory efficient representation. This is particularly important in distributed applications (parallel, P2P and grid), in which not only is memory space saved but communication volume reduced
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".