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

Experimental study of the microwave emission from electrons in air

We searched for the emission of microwave radiation in the Ku band generated by a 95 keV electron beam in air. We unequivocally detected the radiation, and measured its yield and angular dependence. Both the emitted power and its angular pattern are well described by a model, where microwave photons are generated via bremsstrahlung in the free-electron atomic-nucleus collisions, during the slowdown of the electrons. As a consequence, the radiation is not isotropic but peaked in the forward direction. The emission yield scales proportionally with the number of electrons. This contrasts a previous claim that the yield scales with the number squared, due to coherence. With a Monte Carlo simulation we extrapolate our results to the Ultra High Energy Cosmic Ray energy range.Comment: 5 pages, 4 figures. Accepted for publication in Phys.Rev.

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