Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case

Given a d-dimensional random vector X = (X 1, . . ., X d ), if the standard uniform vector U obtained by the component-wise probability integral transform (PIT) of X has the same distribution of its point reflection through the center of the unit hypercube, then X is said to have copula radial symmetry. We generalize to higher dimensions the bivariate test introduced in [11], using three different possibilities for estimating copula derivatives under the null. In a comprehensive simulation study, we assess the finite-sample properties of the resulting tests, comparing them with the finite-sample performance of the multivariate competitors introduced in [17] and [1].

The Distance learning in the teacher qualification system in Morocco

The spread of the Coronavirus has led to close the teacher training centers and triggered distance learning (DL). This situation constitutes a point reflection regarding the DL role in the qualification process of teachers in Morocco. Meta-analysis of official documents has been applied to characterize the DL infrastructures already in place. Results reveal a considerable gap between expectations and achievements. This alternative training can contribute to the qualification. However, its status reflects a very low level of recognition and the curricula remain incompatible with the desirable.

The Three Reflections Theorem Revisited

It is well-known that, in a Euclidean plane, the product of three reflections is again a reflection, iff their axes pass through a common point. For this ``Three reflections Theorem'' (3RT) also non-Euclidean versions exist, see e.g. [4]. This article presents affine versions of it, considering a triplet of skew reflections with axes through a common point. It turns out that the essence of all those cases of 3RT is that the three pairs (axis, reflection direction) of the given (skew) reflections can be observed as an involutoric projectivity. For the Euclidean case and its non-Euclidean counterparts this property is automatically fulfilled. From the projective geometry point of view a (skew) reflection is nothing but a harmonic homology. In the affine situation a reflection is an indirect involutoric transformation, while ``direct'' or ``indirect'' makes no sense in projective planes. A harmonic homology allows an interpretation both, as an axial reflection and as a point reflection. Nevertheless, one might study products of three harmonic homologies, which result in a harmonic homology again. Some special mutual positions of axes and centres of the given homologies lead to elations or even to the identity, too. A consequence of the presented results are further generalisations of the 3RT, e.g. in planes with Minkowski metric, affine or projective 3-space, or in circle geometries.

Development and Current State of Smart Grids: A Review

Smart grids are an important component of the modernization of the power industry worldwide. Many researchers have contributed to their development. At this point, reflection on whether smart grids are being used as was expected and where further investigation is necessary to make them more applicable to the future power industry is warranted. The aim of this paper is to introduce the state of research and path of development of smart grids worldwide. In this investigation, the primary objectives of smart grids, from their inception to the present with changes along the way, are also presented. In addition, difficulties and barriers in their development and implementation and whether these issues are being solved are discussed. Finally, the future and accompanying challenges of smart grids are presented. It should be noted that the current state and development of smart grids is a very deep topic, and it is not possible to mention all the relevant points in a single article. The present review paper attempts to address a limited portion of these to provide an essential understanding of smart grids. Regarding the communication base of a smart grid, only smart meters, some developed communication techniques and smart grid models are presented.

Why do galactic spins flip in the cosmic web? A Theory of Tidal Torques near saddles

Filaments of the cosmic web drive spin acquisition of disc galaxies. The point process of filament-type saddle represent best this environment and can be used to revisit the Tidal Torque Theory in the context of an anisotropic peak (saddle) background split. The constrained misalignment between the tidal tensor and the Hessian of the density field generated in the vicinity of filament saddle points simply explains the corresponding transverse and longitudinal point-reflection symmetric geometry of spin distribution. It predicts in particular an azimuthal orientation of the spins of more massive galaxies and spin alignment with the filament for less massive galaxies. Its scale dependence also allows us to relate the transition mass corresponding to the alignment of dark matter halos' spin relative to the direction of their neighboring filament to this geometry, and to predict accordingly it's scaling with the mass of non linearity, as was measured in simulations.

Nonthermal filamentary radio features within 20 pc of the Galactic center

Deep imaging of the Sgr A complex at 6 cm wavelength with the B and C configurations of the Karl G. Jansky VLA† has revealed a new population of faint radio filaments. Like their brighter counterparts that have been observed throughout the Galactic center on larger scales, these filaments can extend up to ∼10 parsecs, and in most cases are strikingly uniform in brightness and curvature. Comparison with a survey of Paschen-α emission reveals that some of the filaments are emitting thermally, but most of these structures are nonthermal: local magnetic flux tubes illuminated by synchrotron emission. The new image reveals considerable filamentary substructure in previously known nonthermal filaments (NTFs). Unlike NTFs previously observed on larger scales, which tend to show a predominant orientation roughly perpendicular to the Galactic plane, the NTFs in the vicinity of the Sgr A complex are relatively randomly oriented. Two well-known radio sources to the south of Sgr A – sources E and F – consist of numerous quasi-parallel filaments that now appear to be particularly bright portions of a much larger, strongly curved, continuous, nonthermal radio structure that we refer to as the “Southern Curl”. It is therefore unlikely that sources E and F are Hii regions or pulsar wind nebulae. The Southern Curl has a smaller counterpart on the opposite side of the Galactic center – the Northern Curl – that, except for its smaller scale and smaller distance from the center, is roughly point-reflection symmetric with respect to the Southern Curl. The curl features indicate that some field lines are strongly distorted, presumably by mass flows. The point symmetry about the center then suggests that the flows originate near the center and are somewhat collimated.