Computational methods of EEG signals analysis for Alzheimer's disease classification.

Computational analysis of electroencephalographic (EEG) signals have shown promising results in detecting brain disorders, such as Alzheimer's disease (AD). AD is a progressive neurological illness that causes neuron cells degeneration, resulting in cognitive impairment. While there is no cure for AD, early diagnosis is critical to improving the quality of life of affected individuals. Here, we apply six computational time-series analysis methods (wavelet coherence, fractal dimension, quadratic entropy, wavelet energy, quantile graphs and visibility graphs) to EEG records from 160 AD patients and 24 healthy controls. Results from raw and wavelet-filtered (alpha, beta, theta and delta bands) EEG signals show that some of the time-series analysis methods tested here, such as wavelet coherence and quantile graphs, can robustly discriminate between AD patients from elderly healthy subjects. They represent a promising non-invasive and low-cost approach to the AD detection in elderly patients.

Application of Optimal Control of Infectious Diseases in a Model-Free Scenario.

Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin's maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method.

Quantile graphs for EEG-based diagnosis of Alzheimer's disease.

Known as a degenerative and progressive dementia, Alzheimer's disease (AD) affects about 25 million elderly people around the world. This illness results in a decrease in the productivity of people and places limits on their daily lives. Electroencephalography (EEG), in which the electrical brain activity is recorded in the form of time series and analyzed using signal processing techniques, is a well-known neurophysiological AD biomarker. EEG is noninvasive, low-cost, has a high temporal resolution, and provides valuable information about brain dynamics in AD. Here, we present an original approach based on the use of quantile graphs (QGs) for classifying EEG data. QGs map frequency, amplitude, and correlation characteristics of a time series (such as the EEG data of an AD patient) into the topological features of a network. The five topological network metrics used here-clustering coefficient, mean jump length, betweenness centrality, modularity, and Laplacian Estrada index-showed that the QG model can distinguish healthy subjects from AD patients, with open or closed eyes. The QG method also indicates which channels (corresponding to 19 different locations on the patients' scalp) provide the best discriminating power. Furthermore, the joint analysis of delta, theta, alpha, and beta wave results indicate that all AD patients under study display clear symptoms of the disease and may have it in its late stage, a diagnosis known a priori and supported by our study. Results presented here attest to the usefulness of the QG method in analyzing complex, nonlinear signals such as those generated from AD patients by EEGs.

Duality between time series and networks.

Studying the interaction between a system's components and the temporal evolution of the system are two common ways to uncover and characterize its internal workings. Recently, several maps from a time series to a network have been proposed with the intent of using network metrics to characterize time series. Although these maps demonstrate that different time series result in networks with distinct topological properties, it remains unclear how these topological properties relate to the original time series. Here, we propose a map from a time series to a network with an approximate inverse operation, making it possible to use network statistics to characterize time series and time series statistics to characterize networks. As a proof of concept, we generate an ensemble of time series ranging from periodic to random and confirm that application of the proposed map retains much of the information encoded in the original time series (or networks) after application of the map (or its inverse). Our results suggest that network analysis can be used to distinguish different dynamic regimes in time series and, perhaps more importantly, time series analysis can provide a powerful set of tools that augment the traditional network analysis toolkit to quantify networks in new and useful ways.

On universality in human correspondence activity.

The identification and modeling of patterns of human activity have important ramifications for applications ranging from predicting disease spread to optimizing resource allocation. Because of its relevance and availability, written correspondence provides a powerful proxy for studying human activity. One school of thought is that human correspondence is driven by responses to received correspondence, a view that requires a distinct response mechanism to explain e-mail and letter correspondence observations. We demonstrate that, like e-mail correspondence, the letter correspondence patterns of 16 writers, performers, politicians, and scientists are well described by the circadian cycle, task repetition, and changing communication needs. We confirm the universality of these mechanisms by rescaling letter and e-mail correspondence statistics to reveal their underlying similarity.