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.

We study an XY-rotor model on regular one dimensional lattices by varying the number of neighbours. The parameter 2 ≥ γ ≥ 1 is defined. γ = 2 corresponds to mean field and γ = 1 to nearest neighbours coupling. We find that for γ < 1.5 the system does not exhibit a phase transition, while for γ > 1.5 the mean field second order transition is recovered. For the critical value γ = γc = 1.5, the systems can be in a non trivial fluctuating phase for which the magnetisation shows important fluctuations in a given temperature range, implying an infinite susceptibilty. For all values of γ the magnetisation is computed analytically in the low temperatures range and the magnetised versus non-magnetised state which depends on the value of γ is recovered, confirming the critical value γc = 1.5.

Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are Lévy flights, where the walkers are allowed to perform jumps, the "flights", that can eventually be very long as their length distribution is asymptotically power-law distributed. In our work, we present a model in which walkers are allowed to perform, on a 1D lattice, "cascades" of n unitary steps instead of one jump of a randomly generated length, as in the Lévy case, where n is drawn from a cascade distribution pn. We show that this local mechanism may give rise to superdiffusion or normal diffusion when pn is distributed as a power law. We also introduce waiting times that are power-law distributed as well and therefore the probability distribution scaling is steered by the two PDF's power-law exponents. As a perspective, our approach may engender a possible generalization of anomalous diffusion in context where distances are difficult to define, as in the case of complex networks, and also provide an interesting model for diffusion in temporal networks.

The influence of networks topology on collective properties of dynamical systems defined upon it is studied in the thermodynamic limit. A network model construction scheme is proposed where the number of links, the average eccentricity and the clustering coefficient are controlled. This is done by rewiring links of a regular one dimensional chain according to a probability $p$ within a specific range $r$, that can depend on the number of vertices $N$. We compute the thermodynamic behavior of a system defined on the network, the $XY-$rotors model, and monitor how it is affected by the topological changes. We identify the network dimension $d$ as a crucial parameter: topologies with $d\textless{}2$ exhibit no phase transitions while ones with $d\textgreater{}2$ display a second order phase transition. Topologies with $d=2$ exhibit states characterized by infinite susceptibility and macroscopic chaotic/turbulent dynamical behavior. These features are also captured by $d$ in the finite size context

Many dynamical processes on real world networks display complex temporal patterns as, for instance, a fat-tailed distribution of inter-events times, leading to heterogeneous waiting times between events. In this work, we focus on distributions whose average inter-event time diverges, and study its impact on the dynamics of random walkers on networks. The process can naturally be described, in the long time limit, in terms of Riemann-Liouville fractional derivatives. We show that all the dynamical modes possess, in the asymptotic regime, the same power law relaxation, which implies that the dynamics does not exhibit time-scale separation between modes, and that no mode can be neglected versus another one, even for long times. Our results are then confirmed by numerical simulations.

In order to investigate the stances of high school students and researchers toward STEM subjects, we introduce the methodology of forma mentis networks -- free association networks enriched with affective attributes that represent how people conceptually perceive and structure their stance toward a given topic. In this paper, we constructed separate forma mentis networks for ($N_s=159$) Italian high school students and ($N_r=59$) interdisciplinary professionals and researchers in order to investigate how these groups differed in their mental associations and emotional perceptions of STEM subjects. At the global scale, STEM concepts occupied central positions in students' forma mentis network, suggesting that students understood the general importance of such topics in science. At a microscopic scale, although the concept of "science'' was positively perceived in both the students' and professionals' forma mentis networks, students not only perceived STEM concepts such as "physics'' and "mathematics'' as negative but also associated them with other negative STEM-related concepts. This aura of negative emotional associations towards quantitative STEM subjects was absent in professionals. Cross-validation with external datasets suggested that the negative emotional aura in the forma mentis network of students might be attributed to science anxiety. Further consideration of the semantic associates of maths and physics indicated that their negative aura may originate from a negative, dry perception of the technical methodology and quantitative tools frequently taught in these subjects (e.g., "function'', "integral'').Whereas students associated mathematics and physics with quantitative tools, professionals linked the same disciplines to more general and creative aspects of science and displayed a positive stance towards these concepts. Overall, our results underline the crucial importance of emphasising nontechnical and applied aspects in the teaching of quantitative disciplines, highlighting the necessity of establishing interdisciplinary links between science, the complexity of the real-world and creativity in order to enhance the impact of STEM education and outreach activities.