A confidence ellipse analysis for stochastic dynamics model of Alzheimer’s disease
Bibliographic record
Abstract
Abstract The Alzheimer’s disease (AD) is a neurodegenerative disease, which is caused by the aggregation of beta-amyloid peptide (Aβ) in the patient’s brain and the disorder of Ca2+ homeostasis in neurons. Caluwé and Dupont [1] proposed a deterministic AD model to explore the effect of Ca2+ on AD. They demonstrated the positive feedback loop between Aβ and Ca2+ and the occurrence of bistability. Based on their results, we further discuss the bistable behaviors. We present two periodically feasible drug strategies to alleviate the AD and screen out more effective one. In this paper, we also formulate a stochastic AD model, analyze the existence and uniqueness of global positive solutions and establish sufficient conditions for the existence of ergodic stationary distribution. Furthermore, the confidence ellipses describing the configurational arrangement of stochastic coexistence equilibria are constructed by stochastic sensitivity function technique, and tipping threshold is estimated as well. Noise-induced stochastic switching between two coexistence equilibria is observed in bistability region. Our results provide a new idea to control noise to alleviate AD through physical therapy and drug therapy.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".