Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

The Edinburgh Social Cognition Test (ESCoT):Examining the effects of age on a new measure of theory of mind and social norm understanding

<div><p>Current measures of social cognition have shown inconsistent findings regarding the effects of healthy aging. Moreover, no tests are currently available that allow clinicians and researchers to examine cognitive and affective theory of mind (ToM) and understanding of social norms within the same test. To address these limitations, we present the Edinburgh Social Cognition Test (ESCoT) which assesses cognitive and affective ToM and inter- and intrapersonal understanding of social norms. We examined the effects of age, measures of intelligence and the Broader Autism Phenotype (BAP) on the ESCoT and established tests of social cognition. Additionally, we investigated the convergent validity of the ESCoT based on traditional social cognition measures. The ESCoT was administered alongside Reading the Mind in Films (RMF), Reading the Mind in Eyes (RME), Judgement of Preference and Social Norm Questionnaire to 91 participants (30 aged 18–35 years, 30 aged 45–60 years and 31 aged 65–85 years). Poorer performance on the cognitive and affective ToM ESCoT subtests were predicted by increasing age. The affective ToM ESCoT subtest and RMF were predicted by gender, where being female predicted better performance. Unlike the ESCoT, better performance on the RMF was predicted by higher verbal comprehension and perceptual reasoning abilities, while better performance on the RME was predicted by higher verbal comprehension scores. Lower scores on inter-and intrapersonal understanding of social norms were both predicted by the presence of more autism-like traits while poorer interpersonal understanding of social norms performance was predicted by increasing age. These findings show that the ESCoT is a useful measure of social cognition and, unlike established tests of social cognition, performance is not predicted by measures of verbal comprehension and perceptual reasoning. This is particularly valuable to obtain an accurate assessment of the influence of age on our social cognitive abilities.</p></div

Mixed emotions: The contribution of alexithymia to the emotional symptoms of autism

It is widely accepted that autism is associated with disordered emotion processing, and in particular, with deficits of emotional reciprocity such as impaired emotion recognition and reduced empathy. However, a close examination of the literature reveals wide heterogeneity within the autistic population with respect to emotional competence. Here we argue that, where observed, emotional impairments are due to alexithymia - a condition that frequently co-occurs with autism - rather than a feature of autism per se. Alexithymia is a condition characterized by a reduced ability to identify and describe one’s own emotion, but which results in reduced empathy and an impaired ability to recognize the emotions of others. We briefly review studies of emotion processing in alexithymia, and in autism, before describing a recent series of studies directly testing this ‘alexithymia hypothesis’. If found to be correct, the alexithymia hypothesis has wide-reaching implications for the study of autism, and how we might best support sub-groups of autistic individuals with, and without, accompanying alexithymia. Finally, we note the presence of elevated rates of alexithymia, and inconsistent reports of emotional impairments, in eating disorders, schizophrenia, substance abuse, Parkinson’s Disease, Multiple Sclerosis, and anxiety disorders. We speculate that examining the contribution of alexithymia to the emotional symptoms of these disorders may bear fruit in the same way that it is starting to do in autism

The feeling of me feeling for you: Interoception, alexithymia and empathy in autism.

Following recent evidence for a link between interoception, emotion and empathy, we investigated relationships between these factors in Autism Spectrum Disorder (ASD). 26 adults with ASD and 26 healthy participants completed tasks measuring interoception, alexithymia and empathy. ASD participants with alexithymia demonstrated lower cognitive and affective empathy than ASD participants without alexithymia. ASD participants showed reduced interoceptive sensitivity (IS), and also reduced interoceptive awareness (IA). IA was correlated with empathy and alexithymia, but IS was related to neither. Alexithymia fulfilled a mediating role between IA and empathy. Our findings are suggestive of an alexithymic subgroup in ASD, with distinct interoceptive processing abilities, and have implications for diagnosis and interventions

Symmetry theorems for the Newtonian 4- and 5-body problems with equal masses

International audienceWe present a new proof of the algebraic part of a symmetry theorem for the central configurations of the newtonian planar 4-body problem with equal masses, using Gröbner bases. This approach is used to obtain a new symmetry theorem for the central configurations of the newtonian spatial 5-body problem with equal masses in the convex case. In fact we prove a more general statement of the theorem, valid for a class of potentials defined by functions with increasing and concave derivatives