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In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for wave propagation phenomena described as port-Hamiltonian systems. The strategy relies on finite element exterior calculus and a domain decomposition to interconnect two systems with different causalities. The spatial domain is split into two parts by introducing an arbitrary interface. Each subdomain is discretized with a mixed finite element formulation that introduces a uniform boundary condition in a natural way as the input. In each subdomain the spaces are selected from a finite element subcomplex to obtain a stable discretization. The two systems are then interconnected together by making use of a feedback interconnection. This is achieved by discretizing the boundary inputs using appropriate spaces that couple the two formulations. The final systems includes all boundary conditions explicitly and does not contain any Lagrange multiplier. Each subdomain is integrated using an implicit midpoint scheme in an uncoupled way from the other by means of a leapfrog scheme. The proposed strategy is tested on three different examples: the Euler-Bernoulli beam, the wave equation and the Maxwell equations. Numerical tests assess the conservation properties of the scheme and the effectiveness of the methodology.

In the framework of a mixed finite element method, a structure-preserving formulation for incompressible MHD equations with general boundary conditions is proposed. A leapfrog-type temporal scheme fully decouples the fluid part from the Maxwell part by means of staggered discrete time sequences and, in doing so, partially linearizes the system. Conservation and dissipation properties of the formulation before and after the decoupling are analyzed. We demonstrate optimal spatial and second-order temporal error convergence and conservation and dissipation properties of the proposed method using manufactured solutions, and apply it to the benchmark Orszag-Tang and lid-driven cavity test cases.

The digital age provides new challenges as information travels more quickly in a system of increasing complexity. But it also offers new opportunities, as we can track and study the system more efficiently. Several studies individually addressed different digital tracks, focusing on specific aspects like disinformation production or content-sharing dynamics. In this work, we propose to study the news ecosystem as an information market by analysing three main metrics: Supply, Demand, and Diffusion of information. Working on a dataset relative to Italy from December 2019 to August 2020, we validate the choice of the metrics, proving their static and dynamic relations, and their potential in describing the whole system. We demonstrate that these metrics have specific equilibrium relative levels. We reveal the strategic role of Demand in leading a non-trivial network of causal relations. We show how disinformation news Supply and Diffusion seem to cluster among different social media platforms. Disinformation also appears to be closer to information Demand than the general news Supply and Diffusion, implying a potential danger to the health of the public debate. Finally, we prove that the share of disinformation in the Supply and Diffusion of news has a significant linear relation with the gap between Demand and Supply/Diffusion of news from all sources. This finding allows for a real-time assessment of disinformation share in the system. It also gives a glimpse of the potential future developments in the modelisation of the news ecosystem as an information market studied through its main drivers.

In the hypertrophic and uncharted information world, recommender systems are gatekeepers of knowledge. The evolution of these algorithms is usually an opaque process, but in February 2023, the recommender system of X, formerly Twitter, was altered by its chairman (Elon Musk) transparently, offering a unique study opportunity. This paper analyses the cross-platform impact of adjusting the platform's recommender system on public discourse. We focus on the account of Elon Musk and, for comparison, the account of the President of the United States (Joe Biden). Our results highlight how algorithm adjustments can boost content visibility, user engagement, and community involvement without increasing the engagement or involvement probabilities. We find that higher visibility can increase the influence on social dialogue but also backfire, triggering negative community reactions. Finally, our analysis offers insights to detect future less transparent changes to recommender systems.

The increasing pervasiveness of fruitless disagreement poses a considerable risk to social cohesion and constructive public discourse. While polarised discussions can exhibit significant distrust in the news, it is still largely unclear whether disagreement is somehow linked to misinformation. In this work, we exploit the results of `Cartesio', an online experiment to rate the trustworthiness of Italian news articles annotated for reliability by expert evaluators. We developed a metric for disagreement that allows for correct comparisons between news with different mean trust values. Our findings indicate that, though misinformation receives lower trust ratings than accurate information, it does not appear to be more controversial. Additionally, we examined the relationship between these findings and Facebook user engagement with news articles. Our results show that disagreement correlates with an increased likelihood of commenting, probably linked to inconclusive and long discussions. The emerging scenario is one in which fighting disinformation seems ineffective in countering polarisation. Disagreement focuses more on the divergence of opinions, trust, and their effects on social cohesion. This study offers a foundation for unsupervised news item analysis independent of expert annotation. Incorporating similar principles into the design of news distribution platforms and social media systems can enhance online interactions and foster the development of a less divisive news ecosystem.

In this paper we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such as velocity and rate-of-strain, as intensive vector-valued forms while kinetics variables, such as stress and momentum, as extensive covector-valued pseudo-forms. We treat the spatial, material and convective representations of the motion and show how to geometrically convert from one representation to the other. Furthermore, we show the equivalence of our exterior calculus formulation to standard formulations in the literature based on tensor calculus. In addition, we highlight two types of structures underlying the theory. First, the principle bundle structure relating the space of embeddings to the space of Riemannian metrics on the body, and how the latter represents an intrinsic space of deformations. Second, the de Rham complex structure relating the spaces of bundle-valued forms to each other.

In this paper we prove that a large class of linear evolution PDEs defines a Stokes-Dirac structure over Hilbert spaces. To do so, the theory of boundary control system is employed. This definition encompasses problems from mechanics, that cannot be handled by the seminal geometric setting given in [van der Schaft and Maschke, Hamiltonian formulation of distributed-parameter systems with boundary energy flow, 2002 ]. Many worked-out examples stemming from continuum mechanics and physics are presented in detail, and a particular focus is given on the functional spaces in duality at the boundary of the geometrical domain. For each example, the connection between the differential operators and the associated Hilbert complexes is illustrated.

In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al., Hybridization and postprocessing in finite element exterior calculus, 2023 ] to port-Hamiltonian systems describing linear wave propagation phenomena. To this aim, a dual field mixed Galerkin discretization is introduced, in which one variable is approximated via conforming finite element spaces, whereas the second is completely local. This scheme is equivalent to the second order mixed Galerkin formulation and retains a discrete power balance and discrete conservation laws. The mixed formulation is also equivalent to the hybrid formulation. The hybrid system can be efficiently solved using a static condensation procedure in discrete time. The size reduction achieved thanks to the hybridization is greater than the one obtained for the Hodge Laplacian as one field is completely discarded. Numerical experiments on the 3D wave and Maxwell equations show the convergence of the method and the size reduction achieved by the hybridization., Comment: 24 pages, 10 figures

One of the most pressing challenges in the digital media landscape is understanding the impact of biases on the news sources that people rely on for information. Biased news can have significant and far-reaching consequences, influencing our perspectives and shaping the decisions we make, potentially endangering the public and individual well-being. With the advent of the Internet and social media, discussions have moved online, making it easier to disseminate both accurate and inaccurate information. To combat mis- and dis-information, many have begun to evaluate the reliability of news sources, but these assessments often only examine the validity of the news (narrative bias) and neglect other types of biases, such as the deliberate selection of events to favor certain perspectives (selection bias). This paper aims to investigate these biases in various news sources and their correlation with third-party evaluations of reliability, engagement, and online audiences. Using machine learning to classify content, we build a six-year dataset on the Italian vaccine debate and adopt a Bayesian latent space model to identify narrative and selection biases. Our results show that the source classification provided by third-party organizations closely follows the narrative bias dimension, while it is much less accurate in identifying the selection bias. Moreover, we found a nonlinear relationship between biases and engagement, with higher engagement for extreme positions. Lastly, analysis of news consumption on Twitter reveals common audiences among news outlets with similar ideological positions.

The Covid-19 pandemic has sparked renewed attention on the prevalence of misinformation online, whether intentional or not, underscoring the potential risks posed to individuals' quality of life associated with the dissemination of misconceptions and enduring myths on health-related subjects. In this study, we analyze 6 years (2016-2021) of Italian vaccine debate across diverse social media platforms (Facebook, Instagram, Twitter, YouTube), encompassing all major news sources - both questionable and reliable. We first use the symbolic transfer entropy analysis of news production time-series to dynamically determine which category of sources, questionable or reliable, causally drives the agenda on vaccines. Then, leveraging deep learning models capable to accurately classify vaccine-related content based on the conveyed stance and discussed topic, respectively, we evaluate the focus on various topics by news sources promoting opposing views and compare the resulting user engagement. Aside from providing valuable resources for further investigation of vaccine-related misinformation, particularly in a language (Italian) that receives less attention in scientific research compared to languages like English, our study uncovers misinformation not as a parasite of the news ecosystem that merely opposes the perspectives offered by mainstream media, but as an autonomous force capable of even overwhelming the production of vaccine-related content from the latter. While the pervasiveness of misinformation is evident in the significantly higher engagement of questionable sources compared to reliable ones, our findings underscore the importance of consistent and thorough pro-vax coverage. This is especially crucial in addressing the most sensitive topics where the risk of misinformation spreading and potentially exacerbating negative attitudes toward vaccines among the users involved is higher.

In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation laws and cope with mixed open boundary conditions using a single computational mesh. The possibility of including open boundary conditions allows for modular composition of complex multi-physical systems whereas the exterior calculus formulation provides a coordinate-free treatment. Our approach relies on a dual-field representation of the physical system that is redundant at the continuous level but eliminates the need of mimicking the Hodge star operator at the discrete level. By considering the Stokes-Dirac structure representing the system together with its adjoint, which embeds the metric information directly in the codifferential, the need for an explicit discrete Hodge star is avoided altogether. By imposing the boundary conditions in a strong manner, the power balance characterizing the Stokes-Dirac structure is then retrieved at the discrete level via symplectic Runge-Kutta integrators based on Gauss-Legendre collocation points. Numerical experiments validate the convergence of the method and the conservation properties in terms of energy balance both for the wave and Maxwell equations in a three dimensional domain. For the latter example, the magnetic and electric fields preserve their divergence free nature at the discrete level., Comment: 44 pages, 15 figures

The media attention to the personal sphere of famous and important individuals has become a key element of the gender narrative. Here we combine lexical, syntactic and sentiment analysis to investigate the role of gender in the personalization of a wide range of political office holders in Italy during the period 2017-2020. On the basis of a score for words that is introduced to account for gender unbalance in both representative and news coverage, we show that the political personalization in Italy is more detrimental for women than men, with the persistence of entrenched stereotypes including a masculine connotation of leadership, the resulting women's unsuitability to hold political functions, and a greater deal of focus on their attractiveness and body parts. In addition, women politicians are covered with a more negative tone than their men counterpart when personal details are reported. Further, the major contribution to the observed gender differences comes from online news rather than print news, suggesting that the expression of certain stereotypes may be better conveyed when click baiting and personal targeting have a major impact.

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly we introduce the ongoing project SCRIMP (Simulation and ContRol of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available., Comment: 33 pages

Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and port-Hamiltonian systems has been carried out. In this paper we demonstrate how existing methods can be employed to discretize dynamical plate problems in a structure-preserving way. Based on convergence results of existing schemes, new error estimates are conjectured; numerical simulations confirm the expected behaviors.

We develop a minimalist compartmental model to study the impact of mobility restrictions in Italy during the Covid-19 outbreak. We show that an early lockdown shifts the epidemic in time, while that beyond a critical value of the lockdown strength, the epidemic tend to restart after lifting the restrictions. As a consequence, specific mitigation strategies must be introduced. We characterize the relative importance of different broad strategies by accounting for two fundamental sources of heterogeneity, i.e. geography and demography. First, we consider Italian regions as separate administrative entities, in which social interactions between age classs occur. Due to the sparsity of the inter-regional mobility matrix, once started the epidemics tend to develop independently across areas, justifying the adoption of solutions specific to individual regions or to clusters of regions. Second, we show that social contacts between age classes play a fundamental role and that measures which take into account the age structure of the population can provide a significant contribution to mitigate the rebound effects. Our model is general, and while it does not analyze specific mitigation strategies, it highlights the relevance of some key parameters on non-pharmaceutical mitigation mechanisms for the epidemics.

We address the diffusion of information about the COVID-19 with a massive data analysis on Twitter, Instagram, YouTube, Reddit and Gab. We analyze engagement and interest in the COVID-19 topic and provide a differential assessment on the evolution of the discourse on a global scale for each platform and their users. We fit information spreading with epidemic models characterizing the basic reproduction numbers $R_0$ for each social media platform. Moreover, we characterize information spreading from questionable sources, finding different volumes of misinformation in each platform. However, information from both reliable and questionable sources do not present different spreading patterns. Finally, we provide platform-dependent numerical estimates of rumors' amplification.