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

Interaction of chemical patterns in coupled layers

We investigate the interaction between reaction-diffusion systems coupled by diffusion. The photosensitive CDIMA (chorine dioxide–iodine–malonic acid) reaction allows us to study experimentally the mutual influence of two layers of Turing patterns coupled via a diffusive interaction. By illuminating each of the layers with different intensities of homogeneous external light, the chemical conditions in each layer can be shifted, allowing us to study the result of diffusive interaction between Turing patterns with different spatial configurations. Our experiments suggest a complex scenario for the interaction between different patterns, strongly dependent on the spatial characteristics of the interacting patterns. Numerical simulations are also reported in full agreement with experimental observationsThis work has been supported by the DGI (Spain) under Project No. FIS2010-21023 and Xunta de Galicia (Spain) under Project Nos. PGIDIT05PXIC20607PN and INCITE07PXI206131ES and by the NSF (USA). D.G.M. acknowledges a Ramon y Cajal Fellowship from the Ministry of Science and Technology of Spain and a Marie Curie International Reintegration Grant from the EU248346-NMSSBLS, as well as financial support from the CSIC-SPAIN (JAE-DOC

A spectrum of complexity uncovers Dunbar's number and other leaps in social structure

Social dynamics are shaped by each person's actions, as well as by collective trends that emerge when individuals are brought together. These latter kind of influences escape anyone's control. They are, instead, dominated by aggregate societal properties such as size, polarization, cohesion, or hierarchy. Such features add nuance and complexity to social structure, and might be present, or not, for societies of different sizes. How do societies become more complex? Are there specific scales at which they are reorganized into emergent entities? In this paper we introduce the {\em social complexity spectrum}, a methodological tool, inspired by theoretical considerations about dynamics on complex networks, that addresses these questions empirically. We use as a probe a sociolinguistic process that has unfolded over decades within the north-western Spanish region of Galicia, across populations of varied sizes. We estimate how societal complexity increases monotonously with population size; and how specific scales stand out, at which complexity would build up faster. These scales are noted as dips in our spectra, similarly to missing wavelengths in light spectroscopy. Also, `red-' and `blue-shifts' take place as the general population shifted from more rural to more urban settings. These shifts help us sharpen our observations. Besides specific results around social complexity build-up, our work introduces a powerful tool to be applied in further study cases.Comment: 13 pages, 4 figure

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

Emergence of a super-synchronized mobbing state in a large population of coupled chemical oscillators

Oscillatory phenomena are ubiquitous in Nature. The ability of a large population of coupled oscillators to synchronize constitutes an important mechanism to express information and establish communication among members. To understand such phenomena, models and experimental realizations of globally coupled oscillators have proven to be invaluable in settings as varied as chemical, biological and physical systems. A variety of rich dynamical behavior has been uncovered, although usually in the context of a single state of synchronization or lack thereof. Through the experimental and numerical study of a large population of discrete chemical oscillators, here we report on the unexpected discovery of a new phenomenon revealing the existence of dynamically distinct synchronized states reflecting different degrees of communication. Specifically, we discover a novel large-amplitude super-synchronized state separated from the conventionally reported synchronized and quiescent states through an unusual sharp jump transition when sampling the strong coupling limit. Our results assume significance for further elucidating globally coherent phenomena, such as in neuropathologies, bacterial cell colonies, social systems and semiconductor lasers

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