Quantifying the potentiality for polarization in opinion networks

Polarization in debates and social networks is a phenomenon clearly present in modern societies that strongly modifies the way we relate as communities. Regardless of the importance of this phenomenon, there is not a clear explanation yet for its emergence or a suitable parameter to quantify it. Here, we present a methodology based on the Turing instability, a frequent mechanism in Nature which explains differentiation processes, that maps the conditions needed for a given network to undergo polarization of opinions. From this mapping, we measure the likelihood of the system's nodes to differentiate each other or, in other terms, the degree of polarization of the networkWe gratefully acknowledge financial support by the Spanish Ministerio de Economía y Competitividad and European Regional Development Fund under contract RTI2018-097063-B-I00 AEI/FEDER, UE, and by Xunta de Galicia under Research Grant No. 2021-PG036. All these programs are co-funded by FEDER (UE). A. Carballosa acknowledges financial support from Xunta de Galicia. The simulations were run in the Supercomputer Center of Galicia (CESGA) and we acknowledge their supportS

Incorporating social opinion in the evolution of an epidemic spread

The evolution of the COVID19 pandemic worldwide has shown that the most common and effective strategy to control it used worldwide involve imposing mobility constrains to the population. A determinant factor in the success of such policies is the cooperation of the population involved but this is something, at least, difficult to measure. In this manuscript, we propose a method to incorporate in epidemic models empirical data accounting for the society predisposition to cooperate with the mobility restriction policiesThis research is supported by the Spanish Ministerio de Economía y Competitividad and European Regional Development Fund, research grant No. COV20/00617 and RTI2018-097063-B-I00 AEI/FEDER, UE; by Xunta de Galicia, Research Grant No. 2018-PG082, and the CRETUS Strategic Partnership, AGRUP2015/02, supported by Xunta de Galicia. All these programs are co-funded by FEDER (UE). We also acknowledge support from the Portuguese Foundation for Science and Technology (FCT) within the Project n. 147S

Bimodal Kuramoto Model with Higher Order Interactions

We have examined the synchronization and de-synchronization transitions observable in the Kuramoto model with a standard pair-wise first harmonic interaction plus a higher order (triadic) symmetric interaction for unimodal and bimodal Gaussian distributions of the natural frequencies. These transitions have been accurately characterized thanks to a self-consistent mean-field approach joined to accurate numerical simulations. The higher-oder interactions favour the formation of two cluster states, which emerge from the incoherent regime via continuous (discontinuos) transitions for unimodal (bimodal) distributions. Fully synchronized initial states give rise to two symmetric equally populated clusters at a angular distance $\gamma$, which increases for decreasing pair-wise couplings until it reaches $\gamma=\pi$ (corresponding to an anti-phase configuration) where the cluster state disappears via a saddle-node bifurcation and reforms immediately after with a smaller angle $\gamma$. For bimodal distributions we have obtained detailed phase diagrams involving all the possible dynamical states in terms of standard and novel order parameters. In particular, the clustering order parameter, here introduced, appears quite suitable to characterize the two cluster regime. As a general aspect, hysteretic (non hysteretic) synchronization transitions, mostly mediated by the emergence of standing waves, are observable for attractive (repulsive) higher-order interactions.Comment: 18 pages, 15 figure

Assessing the risk of pandemic outbreaks across municipalities with mathematical descriptors based on age and mobility restrictions

By March 14th 2022, Spain is suffering the sixth wave of the COVID-19 pandemic. All the previous waves have been intimately related to the degree of imposed mobility restrictions and its consequent release. Certain factors explain the incidence of the virus across regions revealing the weak locations that probably require some medical reinforcements. The most relevant ones relate with mobility restrictions by age and administrative competence, i.e., spatial constrains. In this work, we aim to find a mathematical descriptor that could identify the critical communities that are more likely to suffer pandemic outbreaks and, at the same time, to estimate the impact of different mobility restrictions. We analyze the incidence of the virus in combination with mobility flows during the so-called second wave (roughly from August 1st to November 30th, 2020) using a SEIR compartmental model. After that, we derive a mathematical descriptor based on linear stability theory that quantifies the potential impact of becoming a hotspot. Once the model is validated, we consider different confinement scenarios and containment protocols aimed to control the virus spreading. The main findings from our simulations suggest that the confinement of the economically non-active individuals may result in a significant reduction of risk, whose effects are equivalent to the confinement of the total population. This study is conducted across the totality of municipalities in SpainS

Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal

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.publishe

Emergent dynamics in complex networks: Synchronization, polarization and epidemics

From the collective behavior of many coupled units results the spontaneous emergence of certain dynamic properties that tend to increase the order in the system, such as coherent oscillations, structured pattern formations and biological waves. In this thesis, we revolve around the idea that the communication among the elements of a system transforms them into parts of something greater. Using numerical models, theoretical analysis and experimental setups, here we study the interplay between complexity at the interactio

Incorporating social opinion in the evolution of an epidemic spread

Attempts to control the epidemic spread of COVID19 in the different countries often involve imposing restrictions to the mobility of citizens. Recent examples demonstrate that the effectiveness of these policies strongly depends on the willingness of the population to adhere them. And this is a parameter that it is difficult to measure and control. We demonstrate in this manuscript a systematic way to check the ‘mood’ of a society and a way to incorporate it into dynamical models of epidemic propagation. We exemplify the process considering the case of Spain although the results and methodology can be directly extrapolated to other countries

Intermittency regimes of poorly-mixed chemical oscillators

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 spaceS

Microstructural modifications of the expansive hydrates formed under different curing and restraining conditions in expansive concretes

Trabajo presentado al 15th International Congress on the Chemistry of Cement (ICCC), celebrado en Praga (República Checa) del 16 al 20 de septiembre de 2019.The application of expansive concretes to construction projects is gradually becoming popular for both new construction and refurbishment. Expansive concretes are mainly made by using expansive agents with different chemical compositions that result in the increase of certain hydrates contents within the concrete matrix. The most usual agents promote the formation of ettringite (type-K) or portlandite (type-G). Many parameters influence the efficacy of the expansive agents and the performance of the corresponding expansive concretes such as curing, restraining conditions or concrete composition. These parameters affect the content, chemical composition and morphology of the expansive hydrates, and the resulting expansion is closely related to these modifications in the hydrates characteristics. Therefore, different concrete mixes were designed in this work, most of them selfcompacting concretes, in order to evaluate these effects. Two expansive agents, two supplementary cementitious materials, two expansion conditions and two curing conditions were considered. The microstructure of the concretes was evaluated by BSEM and XRD. The results obtained indicate that restraining conditions influence the morphology and the chemical composition of the expansive hydrates formed. An eminently amorphous ettringite type was identified as responsible for the expansion when using type-K agent. Regarding the concretes with type-G agent, denser portlandite plates better integrated in the cement paste matrix were formed in the concretes cured in more restrained conditions. Curing conditions and concrete composition also influence the reactivity of the expansive agents.Authors gratefully acknowledge the Spanish Ministry of Economy and Competitiveness for the financial support given to this research in BIA2015-64363-R project