Comments and information appearing on the internet and on different social media sway opinion concerning potential remedies for diagnosing and curing diseases. In many cases, this has an impact on citizens’ health and affects medical professionals, who find themselves having to defend their diagnoses as well as the treatments they propose against ill-informed patients. The propagation of these opinions follows the same pattern as the dissemination of fake news about other important topics, such as the environment, via social media networks, which we use as a testing ground for checking our procedure. In this article, we present an algorithm to analyse the behaviour of users of Twitter, the most important social network with respect to this issue, as well as a dynamic knowledge graph construction method based on information gathered from Twitter and other open data sources such as web pages. To show our methodology, we present a concrete example of how the associated graph structure of the tweets related to World Environment Day 2019 is used to develop a heuristic analysis of the validity of the information. The proposed analytical scheme is based on the interaction between the computer tool—a database implemented with Neo4j—and the analyst, who must ask the right questions to the tool, allowing to follow the line of any doubtful data. We also show how this method can be used. We also present some methodological guidelines on how our system could allow, in the future, an automation of the procedures for the construction of an autonomous algorithm for the detection of false news on the internet related to health.

We develop a new topological structure for the construction of a reinforcement learning model in the framework of financial markets. It is based on Lipschitz type extension of reward functions defined in metric spaces. Using some known states of a dynamical system that represents the evolution of a financial market, we use our technique to simulate new states, that we call "dreams". These new states are used to feed a learning algorithm designed to improve the investment strategy.

Consider a directed tree $${\mathcal {U}}$$ U and the space of all finite walks on it endowed with a quasi-pseudo-metric—the space of the strategies $${\mathcal {S}}$$ S on the graph,—which represent the possible changes in the evolution of a dynamical system over time. Consider a reward function acting in a subset $${\mathcal {S}}_0 \subset {\mathcal {S}}$$ S 0 ⊂ S which measures the success. Using well-known facts of the theory of semi-Lipschitz functions in quasi-pseudo-metric spaces, we extend the reward function to the whole space $${\mathcal {S}}.$$ S . We obtain in this way an oracle function, which gives a forecast of the reward function for the elements of $${\mathcal {S}}$$ S , that is, an estimate of the degree of success for any given strategy. After explaining the fundamental properties of a specific quasi-pseudo-metric that we define for the (graph) trees (the bifurcation quasi-pseudo-metric), we focus our attention on analyzing how this structure can be used to represent dynamical systems on graphs. We begin the explanation of the method with a simple example, which is proposed as a reference point for which some variants and successive generalizations are consecutively shown. The main objective is to explain the role of the lack of symmetry of quasi-metrics in our proposal: the irreversibility of dynamical processes is reflected in the asymmetry of their definition.

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A new model for the control of financial processes based on metric graphs is presented. Our motivation has its roots in the current interest in finding effective algorithms to detect and classify relations among elements of a social network. For example, the analysis of a set of companies working for a given public administration or other figures in which automatic fraud detection systems are needed. Given a set [Formula: see text] and a proximity function [Formula: see text], we define a new metric for [Formula: see text] by considering a path distance in [Formula: see text] that is considered as a graph. We analyze the properties of such a distance, and several procedures for defining the initial proximity matrix [Formula: see text]. Using this formalism, we state our main idea regarding fraud detection: financial fraud can be detected because it produces a meaningful local change of density in the metric space defined in this way.