Macro and micro-sleep dysfunctions as translational biomarkers for Parkinson's disease.

Sleep disturbances are highly prevalent among patients with Parkinson's disease (PD) and often appear from the early-phase disease or prodromal stages. In this chapter, we will discuss the current evidence addressing the links between sleep dysfunctions in PD, focusing most closely on those data from animal and mathematical/computational models, as well as in human-based studies that explore the electrophysiological and molecular mechanisms by which PD and sleep may be intertwined, whether as predictors or consequences of the disease. It is possible to clearly state that leucine-rich repeat kinase 2 gene (LRRK2) is significantly related to alterations in sleep architecture, particularly affecting rapid eye movement (REM) sleep and non-REM sleep, thus impacting sleep quality. Also, decreases in gamma power, observed after dopaminergic lesions, correlates negatively with the degree of injury, which brings other levels of understanding the impacts of the disease. Besides, abnormal synchronized oscillations among basal ganglia nuclei can be detrimental for information processing considering both motor and sleep-related processes. Altogether, despite clear advances in the field, it is still difficult to definitely establish a comprehensive understanding of causality among all the sleep dysfunctions with the disease itself. Although, certainly, the search for biomarkers is helping in shortening this road towards a better and faster diagnosis, as well as looking for more efficient treatments.

Generalized statistics: Applications to data inverse problems with outlier-resistance.

The conventional approach to data-driven inversion framework is based on Gaussian statistics that presents serious difficulties, especially in the presence of outliers in the measurements. In this work, we present maximum likelihood estimators associated with generalized Gaussian distributions in the context of Rényi, Tsallis and Kaniadakis statistics. In this regard, we analytically analyze the outlier-resistance of each proposal through the so-called influence function. In this way, we formulate inverse problems by constructing objective functions linked to the maximum likelihood estimators. To demonstrate the robustness of the generalized methodologies, we consider an important geophysical inverse problem with high noisy data with spikes. The results reveal that the best data inversion performance occurs when the entropic index from each generalized statistic is associated with objective functions proportional to the inverse of the error amplitude. We argue that in such a limit the three approaches are resistant to outliers and are also equivalent, which suggests a lower computational cost for the inversion process due to the reduction of numerical simulations to be performed and the fast convergence of the optimization process.