Geometric Deep Lean Learning: Evaluation Using a Twitter Social Network

The goal of this work is to evaluate a deep learning algorithm that has been designed to predict the topological evolution of dynamic complex non-Euclidean graphs in discrete–time in which links are labeled with communicative messages. This type of graph can represent, for example, social networks or complex organisations such as the networks associated with Industry 4.0. In this paper, we first introduce the formal geometric deep lean learning algorithm in its essential form. We then propose a methodology to systematically mine the data generated in social media Twitter, which resembles these complex topologies. Finally, we present the evaluation of a geometric deep lean learning algorithm that allows for link prediction within such databases. The evaluation results show that this algorithm can provide high accuracy in the link prediction of a retweet social network.

Normal approximation for statistics of Gibbsian input in geometric probability

This paper concerns the asymptotic behavior of a random variableWλresulting from the summation of the functionals of a Gibbsian spatial point process over windowsQλ↑ℝd. We establish conditions ensuring thatWλhas volume order fluctuations, i.e. they coincide with the fluctuations of functionals of Poisson spatial point processes. We combine this result with Stein's method to deduce rates of a normal approximation forWλas λ → ∞. Our general results establish variance asymptotics and central limit theorems for statistics of random geometric and related Euclidean graphs on Gibbsian input. We also establish a similar limit theory for claim sizes of insurance models with Gibbsian input, the number of maximal points of a Gibbsian sample, and the size of spatial birth-growth models with Gibbsian input.

Normal approximation for statistics of Gibbsian input in geometric probability

This paper concerns the asymptotic behavior of a random variable Wλ resulting from the summation of the functionals of a Gibbsian spatial point process over windows Qλ ↑ ℝd. We establish conditions ensuring that Wλ has volume order fluctuations, i.e. they coincide with the fluctuations of functionals of Poisson spatial point processes. We combine this result with Stein's method to deduce rates of a normal approximation for Wλ as λ → ∞. Our general results establish variance asymptotics and central limit theorems for statistics of random geometric and related Euclidean graphs on Gibbsian input. We also establish a similar limit theory for claim sizes of insurance models with Gibbsian input, the number of maximal points of a Gibbsian sample, and the size of spatial birth-growth models with Gibbsian input.