[Glymphatic dysfunction and sleep disorders: indirect effects on Alzheimer's disease]. / Glimfaticheskaya disfunktsiya i narusheniya sna: oposredovannoe vliyanie na bolezn' Al'tsgeimera.

Modern research raises the question of the potentially significant role of glymphatic dysfunction in the development of neurodegeneration and pathological aging. The exact molecular mechanisms are not yet fully understood, but there is ample evidence of a link between sleep deprivation and decreased clearance of ß-amyloid and other neurotoxin proteins that are associated with the development of neurodegenerative diseases, particularly Alzheimer's disease. The review analyzes current scientific information in this area of research, describes the latest scientific discoveries of the features of the glymphatic system, and also illustrates studies of markers that presumably indicate a deterioration in the glymphatic system. The relationship between sleep deprivation and pathophysiological mechanisms associated with neurodegenerative diseases is considered, and potential targets that can be used to treat or delay the development of these disorders are noted.

Dynamics of advectively coupled Van der Pol equations chain.

A ring chain of the coupled Van der Pol equations with two types of unidirectional advective couplings is considered. It is assumed that the number of elements in the chain is sufficiently large. The transition to a distributed model with a continuous spatial variable is realized. We study the local-in the equilibrium neighborhood-dynamics of such a model. It is shown that the critical cases in the problem of the zero solution stability have infinite dimension. As the main result, the special nonlinear partial differential equations are constructed that do not contain small and large parameters, which are the equations of the first approximation: their solutions determine the main part of the asymptotic behavior of the original model solutions. Thereby, the nonlocal dynamics of the constructed equations describes the local structure of the Van der Pol chain solutions. The asymptotic behavior of the solutions is carried out. Differences were revealed when using various unidirectional couplings. It is shown that these differences can be significant. In some of the most interesting cases, the obtained equations of the first approximation contain two spatial variables; therefore, it is natural to expect the appearance of complex dynamic effects. The studies are methodologically based on the method for constructing quasinormal forms developed by the author.