Coupled Spatio-Temporal Dynamics and Nonlocality in Advanced Mathematical Models for the Analysis of Complex Neurodegenerative Disease Pathologies
Bibliographic record
Abstract
One in six of the world’s population has to deal with neurodegenerative disorders, and while medical devices exist to detect, prevent, and treat such disorders, some fundamentals of the progression of associated diseases remain ambiguous. In this contribution, we focus on Alzheimer’s disease (AD), where amyloid-beta (Aβ) and tau proteins are among the main contributors to the development or propagation of AD. The Aβ proteins clump together to form plaques and disrupt cell functions. Moreover, the abnormal chemical change in the brain helps to build sticky tau tangles that block the neuron’s transport system. Astrocytes generally maintain a healthy balance in the brain by clearing the Aβ toxic plaques. Even so, over-activated astrocytes release chemokines and cytokines and also react to pro-inflammatory cytokines, further increasing the production of Aβ. We have provided details of a novel coupled mathematical model that can capture astrocytes’ dual behaviour, emphasizing the importance of spatio-temporal coupling and nonlocality. We have demonstrated that the disease propagation depends on memory effects, that is the disease’s earlier status, which involves non-Markovian processes. We have explained how to integrate brain connectome data in the network model and to study this effect, as well as the dual role of astrocytes as a coupled phenomenon. Depending on toxic loads in the brain, we have also discussed details of the analysis of the neuronal damage in the brain. We have explained how the memory effect can slow down the propagation of toxic proteins in the brain, decreasing the rate of neuronal damage. Representative numerical examples have been given, and special attention has been paid to nonequilibrium considerations and stochastic modelling frameworks in the study of neurodegenerative diseases.
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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".