Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia
Bibliographic record
Abstract
Periodic chronic myelogenous leukemia and cyclical neutropenia are two hematological diseases that display oscillations in circulating cell numbers with a period far in excess of what one might expect based on the stem cell cycle duration. Motivated by this observation and a desire to understand how long period oscillations can arise, we analytically prove the existence and stability of long period oscillations in a $G_{0}$ phase cell cycle model described by a nonlinear differential delay equation. This periodic oscillation $p_{\infty }$ can be analytically constructed when the proliferative control is of a "bang-bang" type (the Hill coefficient involved in the nonlinear feedback is infinite). We further obtain a contractive return map (for the semiflow generated by the functional differential equation) in a closed and convex cone containing $p_{\infty }$ when the proliferative control is smooth (the Hill coefficient is large but finite). The fixed point of this contractive map gives the long period oscillation previously observed both numerically and experimentally.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".