Topology and Uniqueness of Optimal Plans for Multi-marginal and Stratified Mass Transport Problems
Bibliographic record
Abstract
This thesis is based on the papers [3] and [4], which were produced during the period of research. Mohammad Ali Ahmadpoor Jadehkenary 2024First and foremost, I would like to express my heartfelt gratitude to Professor Abbas Moameni, my supervisor, who has guided me in both scientific and everyday aspects of life.His undivided attention, continuous encouragement, and, above all, his passion as a supervisor have been the motivating factors behind my journey in academia.It goes without saying that his extensive knowledge and meticulous guidance, coupled with the way he articulates complex problems, have been remarkably inspiring and have made researching in this field an immensely pleasurable experience.My time in the PhD program under Professor Momeni's supervision will always hold a special place in my heart.I wish to express my genuine appreciation to the members of the examination committee for their effort in reviewing and offering valuable insights on this dissertation.Additionally, my sincere gratitude goes out to the faculty and supportive staff of the School of Mathematics and Statistics at Carleton University.Their assistance have been indispensable throughout my doctoral studies.Finally, I owe an immeasurable debt of gratitude to my family, whose belief and encouragement have been the cornerstone of my academic journey in mathematics.Their unwavering support and boundless love have been instrumental in shaping my path and driving me to continually strive for personal growth.To them, I extend my deepest appreciation for being my greatest source of support.B r (x) ball centered at x with radius
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| 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 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".