Relationship between the Mandelbrot Algorithm and the Platonic Solids

This paper focuses on the dynamics of the eight tridimensional principal slices of the tricomplex Mandelbrot set for the power 2: the Tetrabrot, the Arrowheadbrot, the Mousebrot, the Turtlebrot, the Hourglassbrot, the Metabrot, the Airbrot (octahedron) and the Firebrot (tetrahedron). In particular, we establish a geometrical classification of these 3D slices using the properties of some specific sets that correspond to projections of the bicomplex Mandelbrot set on various two-dimensional vector subspaces, and we prove that the Firebrot is a regular tetrahedron. Finally, we construct the so-called "Stella octangula" as a tricomplex dynamical system composed of the union of the Firebrot and its dual, and after defining the idempotent 3D slices of $\mathcal{M}_{3}$, we show that one of them corresponds to a third Platonic solid: the cube

Un modèle à criticalité auto-régulée de la magnétosphère terrestre

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Impact of social anxiety on social cognition and functioning in patients with recent-onset schizophrenia spectrum disorders

Schizophrenia patients display important rates of comorbid social anxiety disorder (SAD) but few studies have directly examined how SAD affects the presentation of schizophrenia, notably social cognition deficits and functioning. Aims : To compare social cognition performance of schizophrenia patients who meet the diagnostic criteria for a comorbid SAD (SZ +) relative to patients without such comorbidity (SZ −) and to determine if the impact of social cognition performance on functioning is moderated by that comorbidity. Method : Social cognition performance (emotion recognition, social knowledge, and mentalizing), a control non-social reasoning task, as well as clinical symptoms and functioning were assessed in 26 patients with comorbid SAD (SZ +), 29 SZ − and 84 healthy controls. Results : Patient groups significantly differed from each other on social knowledge performance, but not in levels of symptoms or overall functioning. Relative to healthy controls, SZ + were impaired uniquely on mentalizing, whereas SZ − showed a more encompassing social cognition deficit that included mentalizing, social knowledge and non-social reasoning impairments. Mentalizing was the best predictor of functioning across both patient groups. Importantly, non-social reasoning negatively influenced mentalizing and in turn functioning only in the SZ − group. Conclusions : The overall pattern of results indicates common mentalizing deficits in SZ + and SZ −; however, these deficits appear linked to different underlying deficits and different pathways to functional impact in the two patient subgroups. This study highlights some distinctive characteristics of schizophrenia patients with comorbid SAD and signals a need for further investigations into the sources of the mentalizing and functioning impairments in SZ + patients

F-region ionosphere effects on the mapping accuracy of SuperDARN HF radar echoes

Structured particle precipitation in the cusp is an important source for the generation of F-region ionospheric irregularities. The equatorward boundaries of broad Doppler spectral width in Super Dual Auroral Radar Network (SuperDARN) data and the concurrent OI 630.0 nm auroral emission are good empirical proxies for the dayside open-closed field line boundary (OCB). However, SuperDARN currently employs a simple virtual model to determine the location of its echoes, instead of a direct calculation of the radio wave path. The varying ionospheric conditions could influence the final mapping accuracy of SuperDARN echoes. A statistical comparison of the offsets between the SuperDARN Finland radar spectral width boundary (SWB) and the OI 630.0 nm auroral emission boundary (AEB) from a meridian-scanning photometer (MSP) on Svalbard is performed in this paper. By restricting the location of the 630.0 nm data to be near local zenith where the MSP has the highest spatial resolution, the optical mapping errors were significantly reduced. The variation of the SWB – AEB offset confirms that there is a close relationship between the mapping accuracy of the HF radar echoes and solar activity. The asymmetric variation of the SWB – AEB offset versus magnetic local time suggests that the intake of high density solar extreme ultraviolet ionized plasma from post-noon at sub-auroral latitudes could result in a stronger refraction of the HF radar signals in the noon sector. While changing the HF radar operating frequency also has a refraction effect that contributes to the final location of the HF radar echoes

Effective ion speeds at ~200–250 km from comet 67P/Churyumov–Gerasimenko near perihelion

In 2015 August, comet 67P/Churyumov–Gerasimenko, the target comet of the ESA Rosetta mission, reached its perihelion at ~1.24 au. Here, we estimate for a three-day period near perihelion, effective ion speeds at distances ~200–250 km from the nucleus. We utilize two different methods combining measurements from the Rosetta Plasma Consortium (RPC)/Mutual Impedance Probe with measurements either from the RPC/Langmuir Probe or from the Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA)/Comet Pressure Sensor (COPS) (the latter method can only be applied to estimate the effective ion drift speed). The obtained ion speeds, typically in the range 2–8 km s⁻¹, are markedly higher than the expected neutral outflow velocity of ~1 km s⁻¹. This indicates that the ions were de-coupled from the neutrals before reaching the spacecraft location and that they had undergone acceleration along electric fields, not necessarily limited to acceleration along ambipolar electric fields in the radial direction. For the limited time period studied, we see indications that at increasing distances from the nucleus, the fraction of the ions’ kinetic energy associated with radial drift motion is decreasing

Situation du placement des finissants, finissantes du secteur professionnel du collège André-Laurendeau : promotion -- /

1989 /Gratuit (1993

Characterization of frequency effect in SuperDARN spectral width distributions

International audienceThis study investigates the frequency dependence of spectral width distributions observed by the SuperDARN HF radars. The evolution of spectral width values with range is shown to be dependent on the operating radar frequency. First, this evolution is clearly pointed out using a multifrequency scanning mode. This study is then generalized and this effect is shown to affect the whole SuperDARN spectral width data set. Several studies are performed in order to determine the dependence of this effect upon season, beam orientation and mean radar orientation