The Herglotz variational problem on spheres and its optimal control approach

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.

Optimization of a multielectrode array (MEA)-based approach to study the impact of Aβ on the SH-SY5Y cell line

The human brain stores, integrates, and transmits information recurring to millions of neurons, interconnected by countless synapses. Though neurons communicate through chemical signaling, information is coded and conducted in the form of electrical signals. Neuroelectrophysiology focus on the study of this type of signaling. Both intra and extracellular approaches are used in research, but none holds as much potential in high-throughput screening and drug discovery, as extracellular recordings using multielectrode arrays (MEAs). MEAs measure neuronal activity, both in vitro and in vivo. Their key advantage is the capability to record electrical activity at multiple sites simultaneously. Alzheimer’s disease (AD) is the most common neurodegenerative disease and one of the leading causes of death worldwide. It is characterized by neurofibrillar tangles and aggregates of amyloid-β (Aβ) peptides, which lead to the loss of synapses and ultimately neuronal death. Currently, there is no cure and the drugs available can only delay its progression. In vitro MEA assays enable rapid screening of neuroprotective and neuroharming compounds. Therefore, MEA recordings are of great use in both AD basic and clinical research. The main aim of this thesis was to optimize the formation of SH-SY5Y neuronal networks on MEAs. These can be extremely useful for facilities that do not have access to primary neuronal cultures, but can also save resources and facilitate obtaining faster high-throughput results to those that do. Adhesion-mediating compounds proved to impact cell morphology, viability and exhibition of spontaneous electrical activity. Moreover, SH-SY5Y cells were successfully differentiated and demonstrated acute effects on neuronal function after Aβ addition. This effect on electrical signaling was dependent on Aβ oligomers concentration. The results here presented allow us to conclude that the SH-SY5Y cell line can be successfully differentiated in properly coated MEAs and be used for assessing acute Aβ effects on neuronal signaling.

Change-point detection in environmental time series based on the informational approach

In this study, the Schwarz Information Criterion (SIC) is applied in order to detect change-points in the time series of surface water quality variables. The application of change-point analysis allowed detecting change-points in both the mean and the variance in series under study. Time variations in environmental data are complex and they can hinder the identification of the so-called change-points when traditional models are applied to this type of problems. The assumptions of normality and uncorrelation are not present in some time series, and so, a simulation study is carried out in order to evaluate the methodology’s performance when applied to non-normal data and/or with time correlation.