In order to investigate how high school students and researchers perceive science-related (STEM) subjects, we introduce forma mentis networks. This framework models how people conceptually structure their stance, mindset or forma mentis toward a given topic. In this study, we build forma mentis networks revolving around STEM and based on psycholinguistic data, namely free associations of STEM concepts (i.e., which words are elicited first and associated by students/researchers reading “science”?) and their valence ratings concepts (i.e., is “science” perceived as positive, negative or neutral by students/researchers?). We construct separate networks for (Ns = 159) Italian high school students and (Nr = 59) interdisciplinary professionals and researchers in order to investigate how these groups differ in their conceptual knowledge and emotional perception of STEM. Our analysis of forma mentis networks at various scales indicate that, like researchers, students perceived “science” as a strongly positive entity. However, differently from researchers, students identified STEM subjects like “physics” and “mathematics” as negative and associated them with other negative STEM-related concepts. We call this surrounding of negative associations a negative emotional aura. Cross-validation with external datasets indicated that the negative emotional auras of physics, maths and statistics in the students’ forma mentis network related to science anxiety. Furthermore, considering the semantic associates of “mathematics” and “physics” revealed that negative auras may originate from a bleak, dry perception of the technical methodology and mnemonic tools taught in these subjects (e.g., calculus rules). Overall, our results underline the crucial importance of emphasizing nontechnical and applied aspects of STEM disciplines, beyond purely methodological teaching. The quantitative insights achieved through forma mentis networks highlight the necessity of establishing novel pedagogic and interdisciplinary links between science, its real-world complexity, and creativity in science learning in order to enhance the impact of STEM education, learning and outreach activities.

Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called mean-field XY model and by the ϕ^{4} lattice model, respectively. For both models the relationship between phase transitions and the topological properties of certain submanifolds of configuration space are exactly known. It turns out that these a priori known facts are clearly retrieved by persistent homology analysis of dynamically sampled submanifolds of configuration space.

We study the XY rotors model on small networks whose number of links scales with the system size N(links)~N(γ), where 1≤γ≤2. We first focus on regular one-dimensional rings in the microcanonical ensemble. For γ<1.5 the model behaves like a short-range one and no phase transition occurs. For γ>1.5, the system equilibrium properties are found to be identical to the mean field, which displays a second-order phase transition at a critical energy density ε=E/N,ε(c)=0.75. Moreover, for γ(c)~/=1.5 we find that a nontrivial state emerges, characterized by an infinite susceptibility. We then consider small-world networks, using the Watts-Strogatz mechanism on the regular networks parametrized by γ. We first analyze the topology and find that the small-world regime appears for rewiring probabilities which scale as p(SW)[proportionality]1/N(γ). Then considering the XY-rotors model on these networks, we find that a second-order phase transition occurs at a critical energy ε(c) which logarithmically depends on the topological parameters p and γ. We also define a critical probability p(MF), corresponding to the probability beyond which the mean field is quantitatively recovered, and we analyze its dependence on γ.