Critical Point Theory and the Number of Solutions of a Nonlinear Dirichlet Problem

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Fake News Detection on Twitter Using Propagation Structures

The growth of social media has revolutionized the way people access information. Although platforms like Facebook and Twitter allow for a quicker, wider and less restricted access to information, they also consist of a breeding ground for the dissemination of fake news. Most of the existing literature on fake news detection on social media proposes user-based or content-based approaches. However, recent research revealed that real and fake news also propagate significantly differently on Twitter. Nonetheless, only a few articles so far have explored the use of propagation features in their detection. Additionally, most of them have based their analysis on a narrow tweet retrieval methodology that only considers tweets to be propagating a news piece if they explicitly contain an URL link to an online news article. By basing our analysis on a broader tweet retrieval methodology that also allows tweets without an URL link to be considered as propagating a news piece, we contribute to fill this research gap and further confirm the potential of using propagation features to detect fake news on Twitter. We firstly show that real news are significantly bigger in size, are spread by users with more followers and less followings, and are actively spread on Twitter for a longer period of time than fake news. Secondly, we achieve an 87% accuracy using a Random Forest Classifier solely trained on propagation features. Lastly, we design a Geometric Deep Learning approach to the problem by building a graph neural network that directly learns on the propagation graphs and achieve an accuracy of 73.3%

On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations

We study boundary blow-up solutions of semilinear elliptic equations $Lu=u_+^p$ with $p>1$, or $Lu=e^{au}$ with $a>0$, where $L$ is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence theorem are obtained.Comment: To appear in Comm. Partial Differential Equations; 10 page

Validation of Dunbar's number in Twitter conversations

Modern society's increasing dependency on online tools for both work and recreation opens up unique opportunities for the study of social interactions. A large survey of online exchanges or conversations on Twitter, collected across six months involving 1.7 million individuals is presented here. We test the theoretical cognitive limit on the number of stable social relationships known as Dunbar's number. We find that users can entertain a maximum of 100-200 stable relationships in support for Dunbar's prediction. The "economy of attention" is limited in the online world by cognitive and biological constraints as predicted by Dunbar's theory. Inspired by this empirical evidence we propose a simple dynamical mechanism, based on finite priority queuing and time resources, that reproduces the observed social behavior.Comment: 8 pages, 6 figure

Mobile Communication Signatures of Unemployment

The mapping of populations socio-economic well-being is highly constrained by the logistics of censuses and surveys. Consequently, spatially detailed changes across scales of days, weeks, or months, or even year to year, are difficult to assess; thus the speed of which policies can be designed and evaluated is limited. However, recent studies have shown the value of mobile phone data as an enabling methodology for demographic modeling and measurement. In this work, we investigate whether indicators extracted from mobile phone usage can reveal information about the socio-economical status of microregions such as districts (i.e., average spatial resolution < 2.7km). For this we examine anonymized mobile phone metadata combined with beneficiaries records from unemployment benefit program. We find that aggregated activity, social, and mobility patterns strongly correlate with unemployment. Furthermore, we construct a simple model to produce accurate reconstruction of district level unemployment from their mobile communication patterns alone. Our results suggest that reliable and cost-effective economical indicators could be built based on passively collected and anonymized mobile phone data. With similar data being collected every day by telecommunication services across the world, survey-based methods of measuring community socioeconomic status could potentially be augmented or replaced by such passive sensing methods in the future

Emergence of good conduct, scaling and Zipf laws in human behavioral sequences in an online world

We study behavioral action sequences of players in a massive multiplayer online game. In their virtual life players use eight basic actions which allow them to interact with each other. These actions are communication, trade, establishing or breaking friendships and enmities, attack, and punishment. We measure the probabilities for these actions conditional on previous taken and received actions and find a dramatic increase of negative behavior immediately after receiving negative actions. Similarly, positive behavior is intensified by receiving positive actions. We observe a tendency towards anti-persistence in communication sequences. Classifying actions as positive (good) and negative (bad) allows us to define binary 'world lines' of lives of individuals. Positive and negative actions are persistent and occur in clusters, indicated by large scaling exponents alpha~0.87 of the mean square displacement of the world lines. For all eight action types we find strong signs for high levels of repetitiveness, especially for negative actions. We partition behavioral sequences into segments of length n (behavioral `words' and 'motifs') and study their statistical properties. We find two approximate power laws in the word ranking distribution, one with an exponent of kappa-1 for the ranks up to 100, and another with a lower exponent for higher ranks. The Shannon n-tuple redundancy yields large values and increases in terms of word length, further underscoring the non-trivial statistical properties of behavioral sequences. On the collective, societal level the timeseries of particular actions per day can be understood by a simple mean-reverting log-normal model.Comment: 6 pages, 5 figure

Does \u2018bigger\u2019mean \u2018better\u2019? Pitfalls and shortcuts associated with big data for social research

\u2018Big data is here to stay.\u2019 This key statement has a double value: is an assumption as well as the reason why a theoretical reflection is needed. Furthermore, Big data is something that is gaining visibility and success in social sciences even, overcoming the division between humanities and computer sciences. In this contribution some considerations on the presence and the certain persistence of Big data as a socio-technical assemblage will be outlined. Therefore, the intriguing opportunities for social research linked to such interaction between practices and technological development will be developed. However, despite a promissory rhetoric, fostered by several scholars since the birth of Big data as a labelled concept, some risks are just around the corner. The claims for the methodological power of bigger and bigger datasets, as well as increasing speed in analysis and data collection, are creating a real hype in social research. Peculiar attention is needed in order to avoid some pitfalls. These risks will be analysed for what concerns the validity of the research results \u2018obtained through Big data. After a pars distruens, this contribution will conclude with a pars construens; assuming the previous critiques, a mixed methods research design approach will be described as a general proposal with the objective of stimulating a debate on the integration of Big data in complex research projecting