Four Dimensional Orbit Spaces of Compact Coregular Linear Groups

All four dimensional orbit spaces of compact coregular linear groups have been determined. The results are obtained through the integration of a universal differential equation, that only requires as input the number of elements of an integrity basis of the ideal of polynomial invariants of the linear group. Our results are relevant and lead to universality properties in the physics of spontaneous symmetry breaking at the classical level.Comment: 23 pages, plain LaTeX, a review that has not distributed regularl

Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing in J. Phys. A: Math. Ge

The charm of structural neuroimaging in insanity evaluations. guidelines to avoid misinterpretation of the findings

Despite the popularity of structural neuroimaging techniques in twenty-first-century research, its results have had limited translational impact in real-world settings, where inferences need to be made at the individual level. Structural neuroimaging methods are now introduced frequently to aid in assessing defendants for insanity in criminal forensic evaluations, with the aim of providing “convergence” of evidence on the mens rea of the defendant. This approach may provide pivotal support for judges’ decisions. Although neuroimaging aims to reduce uncertainty and controversies in legal settings and to increase the objectivity of criminal rulings, the application of structural neuroimaging in forensic settings is hampered by cognitive biases in the evaluation of evidence that lead to misinterpretation of the imaging results. It is thus increasingly important to have clear guidelines on the correct ways to apply and interpret neuroimaging evidence. In the current paper, we review the literature concerning structural neuroimaging in court settings with the aim of identifying rules for its correct application and interpretation. These rules, which aim to decrease the risk of biases, focus on the importance of (i) descriptive diagnoses, (ii) anatomo-clinical correlation, (iii) brain plasticity and (iv) avoiding logical fallacies, such as reverse inference. In addition, through the analysis of real forensic cases, we describe errors frequently observed due to incorrect interpretations of imaging. Clear guidelines for both the correct circumstances for introducing neuroimaging and its eventual interpretation are defined

Minding the gap(s): public perceptions of AI and socio-technical imaginaries

Deepening and digging into the social side of AI is a novel but emerging requirement within the AI community. Future research should invest in an “AI for people”, going beyond the undoubtedly much-needed efforts into ethics, explainability and responsible AI. The article addresses this challenge by problematizing the discussion around AI shifting the attention to individuals and their awareness, knowledge and emotional response to AI. First, we outline our main argument relative to the need for a socio-technical perspective in the study of AI social implications. Then, we illustrate the main existing narratives of hopes and fears associated with AI and robots. As building blocks of broader “sociotechnical imaginaries”, narratives are powerful tools that shape how society sees, interprets and organizes technology. An original empirical study within the University of Bologna collects the data to examine the levels of awareness, knowledge and emotional response towards AI, revealing interesting insights to be carried on in future research. Replete with exaggerations, both utopian and dystopian narratives are analysed with respect to some relevant socio-demographic variables (gender, generation and competence). Lastly, focusing on two issues – the state of AI anxiety and the point of view of non-experts – opens the floor to problematizing the discourse around AI, sustaining the need for a sociological perspective in the field of AI and discussing future comparative research