A shooting algorithm for problems with singular arcs

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated to the perturbed problem. We present numerical tests that validate our method.Comment: No. RR-7763 (2011); Journal of Optimization, Theory and Applications, published as 'Online first', January 201

Measuring the representational space of music with fMRI: a case study with Sting

Functional brain imaging has revealed much about the neuroanatomical substrates of higher cognition, including music, language, learning, and memory. The technique lends itself to studying of groups of individuals. In contrast, the nature of expert performance is typically studied through the examination of exceptional individuals using behavioral case studies and retrospective biography. Here, we combined fMRI and the study of an individual who is a world-class expert musician and composer in order to better understand the neural underpinnings of his music perception and cognition, in particular, his mental representations for music [...

The neurochemistry of music: Evidence for health outcomes

Children with autism spectrum disorders (ASD) frequently display unusual reactions to sound, ranging from idiosyncratic responses to avoidances. This atypical sensitivity often decreases over time, but little is known about how early avoidance of sounds might affect later enjoyment of auditory stimuli such as music. We surveyed children and adolescents with ASD, and an age-matched group of typically developing (TD) adolescents and the parents of both groups about early auditory sensitivities and musical experience, preferences, and enjoyment in later childhood and adolescence using an adaptation of the Queen’s University Music Questionnaire and the Salk and McGill Musical Inventory (SAMMI) [...

Musicality correlates with sociability and emotionality in Williams Syndrome

Williams syndrome (WS) is a neurogenetic developmental disorder characterized by peaks and valleys of cognitive abilities. One peak that has been understudied is the affinity that many individuals with WS have with music. It remains unknown whether their high levels of musical interest, skill, and expressivity are related to their sociable personality or their verbal intelligence. We examined the relationships between musicality (musical interest, creativity, and expressivity), sociability (social-emotionality, social approach), and language comprehension in WS and typically developing (TD) controls [...

Trait anhedonia is associated with reduced reactivity and connectivity of mesolimbic and paralimbic reward pathways

Anhedonia is the inability to experience pleasure from normally pleasant stimuli. Although anhedonia is a prominent feature of many psychiatric disorders, trait anhedonia is also observed dimensionally in healthy individuals. Currently, the neurobiological basis of anhedonia is poorly understood because it has been mainly investigated in patients with psychiatric disorders. Thus, previous studies have not been able to adequately disentangle the neural correlates of anhedonia from other clinical symptoms. In this study, trait anhedonia was assessed in well-characterized healthy participants with no history of Axis I psychiatric illness. Functional magnetic resonance imaging with musical stimuli was used to examine brain responses and effective connectivity in relation to individual differences in anhedonia [...

Processing of musical structure by highfunctioning adolescents with autism spectrum disorders

Enhanced pitch perception and memory have been cited as evidence of a local processing bias in autism spectrum disorders (ASD). This bias is argued to account for enhanced perceptual functioning ( Mottron & Burack, 2001 ; Mottron, Dawson, Soulières, Hubert, & Burack, 2006 ) and central coherence theories of ASD ( Frith, 1989 ; Happé & Frith, 2006 ). A local processing bias confers a different cognitive style to individuals with ASD ( Happé, 1999 ), which accounts in part for their good visuospatial and visuoconstructive skills. Here, we present analogues in the auditory domain, audiotemporal or audioconstructive processing, which we assess using a novel experimental task: a musical puzzle [...

Multivariate Activation and Connectivity Patterns Discriminate Speech Intelligibility in Wernicke’s, Broca’s, and Geschwind’s Areas

The brain network underlying speech comprehension is usually described as encompassing fronto–temporal–parietal regions while neuroimaging studies of speech intelligibility have focused on a more spatially restricted network dominated by the superior temporal cortex. Here we use functional magnetic resonance imaging with a novel whole-brain multivariate pattern analysis (MVPA) to more fully characterize neural responses and connectivity to intelligible speech. Consistent with previous univariate findings, intelligible speech elicited greater activity in bilateral superior temporal cortex relative to unintelligible speech. However, MVPA identified a more extensive network that discriminated between intelligible and unintelligible speech, including left-hemisphere middle temporal gyrus, angular gyrus, inferior temporal cortex, and inferior frontal gyrus pars triangularis [...