Formal inverse integrating factors and the nilpotent center problem

We are interested in deepening knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields X. As formal integrability is not enough to characterize such a centers we use a more general object, namely, formal inverse integrating factors V of X. Although by the existence of V is not possible to describe all nilpotent centers strata, we simplify, improve and also extend previous results on the relationship between these concepts. We use in the performed analysis the so-called Andreev number n N with n > 2 associated to X which is invariant under orbital conjugacy of X. Besides the leading terms in the (1,n)-quasihomogeneous expansions that V can have we also prove the following: (i) If n is even and there exists V then X has a center; (iii) If the existence of V characterizes all the centers; (iii) If there is a V with minimum ``vanishing multiplicity' at the singularity then, generically, X has a center.The author is partially supported by a MINECO grant number MTM2014-53703-P and by a CIRIT grant number 2014 SGR 1204

Differing views - can chimpanzees do level 2 perspective-taking?

We gratefully acknowledge financial support by the German National Academic Foundation.Although chimpanzees understand what others may see, it is unclear if they understand how others see things (Level 2 perspective-taking). We investigated whether chimpanzees can predict the behavior of a conspecific which is holding a mistaken perspective that differs from their own. The subject competed with a conspecific over two food sticks. While the subject could see that both were the same size, to the competitor one appeared bigger than the other. In a previously established game, the competitor chose one stick in private first and the subject chose thereafter, without knowing which of the sticks was gone. Chimpanzees and 6-year-old children chose the ‘riskier’ stick (that looked bigger to the competitor) significantly less in the game than in a nonsocial control. Children chose randomly in the control, thus showing Level 2 perspective-taking skills; in contrast, chimpanzees had a preference for the ‘riskier’ stick here, rendering it possible that they attributed their own preference to the competitor to predict her choice. We thus run a follow-up in which chimpanzees did not have a preference in the control. Now they also chose randomly in the game. We conclude that chimpanzees solved the task by attributing their own preference to the other, while children truly understood the other’s mistaken perspective.Publisher PDFPeer reviewe

Conscious perception of errors and its relation to the anterior insula

To detect erroneous action outcomes is necessary for flexible adjustments and therefore a prerequisite of adaptive, goal-directed behavior. While performance monitoring has been studied intensively over two decades and a vast amount of knowledge on its functional neuroanatomy has been gathered, much less is known about conscious error perception, often referred to as error awareness. Here, we review and discuss the conditions under which error awareness occurs, its neural correlates and underlying functional neuroanatomy. We focus specifically on the anterior insula, which has been shown to be (a) reliably activated during performance monitoring and (b) modulated by error awareness. Anterior insular activity appears to be closely related to autonomic responses associated with consciously perceived errors, although the causality and directions of these relationships still needs to be unraveled. We discuss the role of the anterior insula in generating versus perceiving autonomic responses and as a key player in balancing effortful task-related and resting-state activity. We suggest that errors elicit reactions highly reminiscent of an orienting response and may thus induce the autonomic arousal needed to recruit the required mental and physical resources. We discuss the role of norepinephrine activity in eliciting sufficiently strong central and autonomic nervous responses enabling the necessary adaptation as well as conscious error perception

Basic Abnormalities in Visual Processing Affect Face Processing at an Early Age in Autism Spectrum Disorder

Background: A detailed visual processing style has been noted in autism spectrum disorder (ASD); this contributes to problems in face processing and has been directly related to abnormal processing of spatial frequencies (SFs). Little is known about the early development of face processing in ASD and the relation with abnormal SF processing. We investigated whether young ASD children show abnormalities in low spatial frequency (LSF, global) and high spatial frequency (HSF, detailed) processing and explored whether these are crucially involved in the early development of face processing. Methods: Three-to 4-year-old children with ASD (n = 22) were compared with developmentally delayed children without ASD (n = 17). Spatial frequency processing was studied by recording visual evoked potentials from visual brain areas while children passively viewed gratings (HSF/LSF). In addition, children watched face stimuli with different expressions, filtered to include only HSF or LSF. Results: Enhanced activity in visual brain areas was found in response to HSF versus LSF information in children with ASD, in contrast to control subjects. Furthermore, facial-expression processing was also primarily driven by detail in ASD. Conclusions: Enhanced visual processing of detailed (HSF) information is present early in ASD and occurs for neutral (gratings), as well as for socially relevant stimuli (facial expressions). These data indicate that there is a general abnormality in visual SF processing in early ASD and are in agreement with suggestions that a fast LSF subcortical face processing route might be affected in ASD. This could suggest that abnormal visual processing is causative in the development of social problems in ASD