The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to “normal life” and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.

The Belousov–Zhabotinsky (BZ) reaction has long been a paradigmatic system for studying chemical oscillations. Here, we experimentally studied the synchronization control within photochemically coupled star networks of BZ oscillators. Experiments were carried out in wells performed in soda-lime glass constructed using novel laser technologies. Utilizing the inherent oscillatory nature of the BZ reaction, we engineered a star network of oscillators interconnected through photochemical inhibitory coupling. Furthermore, the experimental setup presented here could be extrapolated to more complex network architectures with both excitatory and inhibitory couplings, contributing to the fundamental understanding of synchronization in complex systems.

Social networks constitute an almost endless source of social behavior information. In fact, sometimes the amount of information is so large that the task to extract meaningful information becomes impossible due to temporal constrictions. We developed an artificial-intelligence-based method that reduces the calculation time several orders of magnitude when conveniently trained. We exemplify the problem by extracting data freely available in a commonly used social network, Twitter, building up a complex network that describes the online activity patterns of society. These networks are composed of a huge number of nodes and an even larger number of connections, making extremely difficult to extract meaningful data that summarizes and/or describes behaviors. Each network is then rendered into an image and later analyzed using an AI method based on Convolutional Neural Networks to extract the structural information.

Perfect mixing or interaction between oscillators is almost never achieved under experimental conditions and, nevertheless, it might be crucial in understanding the observed phenomena. We propose a mathematical model that directly introduces the degree of mixing and analyze the consequences on the synchronization patterns observed. For that we considered catalyst-loaded chemical oscillators as they represent a paradigm for synchronization phenomena from the experimental and numerical point of view. In this study we explore a modified 3-variable Oregonator model where the active surrounding solution is discretized as oscillators themselves and a discrete radius of chemical exchange is introduced to account for spatial distribution and movement dynamics. We found that for low-to none levels of mixing in the system, a series of irregular states appear on the edge of phase transitions among dynamical regimes, and that several novel non-fully synchronized behaviors appear for a small window in the parameter space.

Background: The relevance of spontaneous activity has been unlocked thanks to recent large scale recordings that revealed, via Shared Variance Component Analysis (SVCA), the high-dimensional nature of the ongoing activity. A fundamental problem is how the dimension modifies when more neurons are included in the analysis. Contradictory results have been reported on this subject based on SVCA and Principal Component Analysis (PCA). New Method: We investigate pro et contra of SVCA and PCA for the identification of reliable responses encoding underlying state variables. We focus on common features of the spectra of the reliable variances (RVs) and on their dimensionality. The analysis is demonstrated on previously published Ca2 ⁺ data from the visual and the dorsal cortex in head fixed mice during spontaneous behavior. Results: RVs grow proportionally to the number N of neurons and show a power-law decay k ^{− α} with the k -th SVC dimension over a range bounded by a maximal dimension k _c , initially diverging as N ^{1 /α} and then saturating at sufficiently large N . The reliable dimensionality, estimated with different methodologies, also shows a clear saturation to an asymptotic value for large N . Furthermore, its value decreases when α becomes larger, as demonstrated by employing experimental data as well as theoretical predictions. Conclusion: We have shown that SVCA is an extremely effective tool to extract reliable features from the neural signals, and that the exponent α represents a biomarker able to reveal the level of correlation of the neurons as well as the dimensionality of the reliable space. Highlights: Advantages and drawbacks of Shared Variance Component Analysis to extract reliable signals from neural data Comparison of different methods to estimate reliable neural dimensionality associated to spontaneous activity Analytical expressions of embedding dimensionality for power-law decaying reliable variances Bounded growth of the dimensionality with the number of neurons