We derive some symmetrization and anti-symmetrization properties of parabolic equations. First, we deduce from a result by Jones (1983) a quantitative estimate of how far the level sets of solutions ...are from being spherical. Next, using this property, we derive a criterion providing solutions whose level sets do not converge to spheres for a class of equations including linear equations and Fisher-KPP reaction-diffusion equations.
ABSTRACT
We have implemented prescriptions for modelling pulsars in the rapid binary population synthesis code Compact Object Mergers: Population Astrophysics and Statistics. We perform a detailed ...analysis of the double neutron star (DNS) population, accounting for radio survey selection effects. The surface magnetic field decay time-scale (∼1000 Myr) and mass-scale (∼0.02 M⊙) are the dominant uncertainties in our model. Mass accretion during common envelope evolution plays a non-trivial role in recycling pulsars. We find a best-fitting model that is in broad agreement with the observed Galactic DNS population. Though the pulsar parameters (period and period derivative) are strongly biased by radio selection effects, the observed orbital parameters (orbital period and eccentricity) closely represent the intrinsic distributions. The number of radio observable DNSs in the Milky Way at present is about 2500 in our model, corresponding to approximately 10 per cent of the predicted total number of DNSs in the Galaxy. Using our model calibrated to the Galactic DNS population, we make predictions for DNS mergers observed in gravitational waves. The DNS chirp mass distribution varies from 1.1 to 2.1 M⊙ and the median is found to be 1.14 M⊙. The expected effective spin χeff for isolated DNSs is ≲0.03 from our model. We predict that 34 per cent of the current Galactic isolated DNSs will merge within a Hubble time, and have a median total mass of 2.7 M⊙. Finally, we discuss implications for fast radio bursts and post-merger remnant gravitational waves.
Social media represent an important source of news for many users. They are, however, affected by misinformation and they might be playing a role in the growth of political polarization. In this ...paper, we create an agent based model to investigate how policing content and backlash on social media (i.e. conflict) can lead to an increase in polarization for both users and news sources. Our model is an advancement over previously proposed models because it allows us to study the polarization of both users and news sources, the evolution of the audience connections between users and sources, and it makes more realistic assumptions about the starting conditions of the system. We find that the tendency of users and sources to avoid policing, backlash and conflict in general can increase polarization online. Specifically polarization comes from the ease of sharing political posts, intolerance for opposing points of view causing backlash and policing, and volatility in changing one's opinion when faced with new information. On the other hand, it seems that the integrity of a news source in trying to resist the backlash and policing has little effect.
Motivated by the rapid spread of coronavirus disease 2019 (COVID-19) in mainland China, we use a global metapopulation disease transmission model to project the impact of travel limitations on the ...national and international spread of the epidemic. The model is calibrated on the basis of internationally reported cases and shows that, at the start of the travel ban from Wuhan on 23 January 2020, most Chinese cities had already received many infected travelers. The travel quarantine of Wuhan delayed the overall epidemic progression by only 3 to 5 days in mainland China but had a more marked effect on the international scale, where case importations were reduced by nearly 80% until mid-February. Modeling results also indicate that sustained 90% travel restrictions to and from mainland China only modestly affect the epidemic trajectory unless combined with a 50% or higher reduction of transmission in the community.
In this paper, we develop a novel backtrackless aligned-spatial graph convolutional network (BASGCN) model to learn effective features for graph classification. Our idea is to transform ...arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed BASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based graph convolutional network (GCN) models, but also bridges the theoretical gap between traditional convolutional neural network (CNN) models and spatially-based GCN models. Furthermore, the proposed BASGCN model can both adaptively discriminate the importance between specified vertices during the convolution process and reduce the notorious tottering problem of existing spatially-based GCNs related to the Weisfeiler-Lehman algorithm, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.
Vehicles’ trajectory prediction is a topic with growing interest in recent years, as there are applications in several domains ranging from autonomous driving to traffic congestion prediction and ...urban planning. Predicting trajectories starting from Floating Car Data (FCD) is a complex task that comes with different challenges, namely Vehicle to Infrastructure (V2I) interaction, Vehicle to Vehicle (V2V) interaction, multimodality, and generalizability. These challenges, especially, have not been completely explored by state-of-the-art works. In particular, multimodality and generalizability have been neglected the most, and this work attempts to fill this gap by proposing and defining new datasets, metrics, and methods to help understand and predict vehicle trajectories. We propose and compare Deep Learning models based on Long Short-Term Memory and Generative Adversarial Network architectures; in particular, our GAN-3 model can be used to generate multiple predictions in multimodal scenarios. These approaches are evaluated with our newly proposed error metrics N-ADE and N-FDE, which normalize some biases in the standard Average Displacement Error (ADE) and Final Displacement Error (FDE) metrics. Experiments have been conducted using newly collected datasets in four large Italian cities (Rome, Milan, Naples, and Turin), considering different trajectory lengths to analyze error growth over a larger number of time-steps. The results prove that, although LSTM-based models are superior in unimodal scenarios, generative models perform best in those where the effects of multimodality are higher. Space-time and geographical analysis are performed, to prove the suitability of the proposed methodology for real cases and management services.
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•How 2.3 Facebook users consumed different information.•Qualitatively different information is consumed in a similar way.•Users more prone to interact with false claims are usually ...exposed to conspiracy rumors.
In this work we study, on a sample of 2.3million individuals, how Facebook users consumed different information at the edge of political discussion and news during the last Italian electoral competition. Pages are categorized, according to their topics and the communities of interests they pertain to, in (a) alternative information sources (diffusing topics that are neglected by science and main stream media); (b) online political activism; and (c) main stream media. We show that attention patterns are similar despite the different qualitative nature of the information, meaning that unsubstantiated claims (mainly conspiracy theories) reverberate for as long as other information. Finally, we classify users according to their interaction patterns among the different topics and measure how they responded to the injection of 2788 false information. Our analysis reveals that users which are prominently interacting with conspiracists information sources are more prone to interact with intentional false claims.
Many organic micropollutants present in wastewater, such as pharmaceuticals and pesticides, are poorly removed in conventional wastewater treatment plants (WWTPs). To reduce the release of these ...substances into the aquatic environment, advanced wastewater treatments are necessary. In this context, two large-scale pilot advanced treatments were tested in parallel over more than one year at the municipal WWTP of Lausanne, Switzerland. The treatments were: i) oxidation by ozone followed by sand filtration (SF) and ii) powdered activated carbon (PAC) adsorption followed by either ultrafiltration (UF) or sand filtration. More than 70 potentially problematic substances (pharmaceuticals, pesticides, endocrine disruptors, drug metabolites and other common chemicals) were regularly measured at different stages of treatment. Additionally, several ecotoxicological tests such as the Yeast Estrogen Screen, a combined algae bioassay and a fish early life stage test were performed to evaluate effluent toxicity. Both treatments significantly improved the effluent quality. Micropollutants were removed on average over 80% compared with raw wastewater, with an average ozone dose of 5.7mgO3l−1 or a PAC dose between 10 and 20mgl−1. Depending on the chemical properties of the substances (presence of electron-rich moieties, charge and hydrophobicity), either ozone or PAC performed better. Both advanced treatments led to a clear reduction in toxicity of the effluents, with PAC-UF performing slightly better overall. As both treatments had, on average, relatively similar efficiency, further criteria relevant to their implementation were considered, including local constraints (e.g., safety, sludge disposal, disinfection), operational feasibility and cost. For sensitive receiving waters (drinking water resources or recreational waters), the PAC-UF treatment, despite its current higher cost, was considered to be the most suitable option, enabling good removal of most micropollutants and macropollutants without forming problematic by-products, the strongest decrease in toxicity and a total disinfection of the effluent.
•Micropollutants are efficiently removed by both ozone and powdered activated carbon.•Specific substances were removed more efficiently by ozone.•Powdered activated carbon effectively removed a wider range of pollutants.•Both treatments significantly reduced the toxicity of WWTP effluent.•Both treatments are feasible for use in municipal WWTPs.
Multiplex social networks are characterized by a common set of actors connected through multiple types of relations. The multinet package provides a set of R functions to analyze multiplex social ...networks within the more general framework of multilayer networks, where each type of relation is represented as a layer in the network. The package contains functions to import/export, create and manipulate multilayer networks, implementations of several state-of-the-art multiplex network analysis algorithms, e.g., for centrality measures, layer comparison, community detection and visualization. Internally, the package is mainly written in native C++ and integrated with R using the Rcpp package.
This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are ...the standard traveling fronts, but the class of transition fronts is much larger and the dynamics of the solutions of such equations is very rich. In the paper, we describe the class of transition fronts and we study their qualitative dynamical properties. In particular, we characterize the set of their admissible asymptotic past and future speeds and their asymptotic profiles and we show that the transition fronts can only accelerate. We also classify the transition fronts in the class of measurable superpositions of standard traveling fronts.
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