TI - Teses de Doutoramento (defendidas no estrangeiro com bolsa de doutoramento financiada pela Fundação para a Ciência e a Tecnologia (FCT))
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- Neuroimaging studies on familiarity of music in children with autism spectrum disorderPublication . De Barros Freitas, Carina PatríciaThe field of music neuroscience allows us to use music to investigate human cognition in vivo. Examining how brain processes familiar and unfamiliar music can elucidate underlying neural mechanisms of several cognitive processes. To date, familiarity in music listening and its neural correlates in typical adults have been investigated using a variety of neuroimaging techniques, yet the results are inconsistent. In addition, these correlates and respective functional connectivity related to music familiarity in typically developing (TD) children and children with autism spectrum disorder (ASD) are unknown. The present work consists of two studies. The first one reviews and qualitatively synthesizes relevant literature on the neural correlates of music familiarity, in healthy adult populations, using different neuroimaging methods. Then it estimates the brain areas most active when listening to familiar and unfamiliar musical excerpts using a coordinate-based meta-analyses technique of neuroimaging data. We established that motor brain structures were consistently active during familiar music listening. The activation of these motor-related areas could reflect audio-motor synchronization to elements of the music, such as rhythm and melody, so that one can tap, dance and “covert” sing along with a known song. Results from this research guided our second study. This work investigated the familiarity effect in music listening in both TD and ASD children, using magnetoencephalography (MEG). This technique enabled us to study brain connectivity and characterize the networks and frequency bands involved while listening to familiar and unfamiliar songs. TD children recruited a similar brain network as those in typical adults during familiar music listening, in the gamma frequency band. Compared to TD, children with ASD showed relatively intact processing of familiar songs but atypical processing of unfamiliar songs in theta and beta-bands. Atypical functional connectivity of other unfamiliar stimuli has been reported in ASD. Our findings reinforced that processing novelty is a challenge. Overall, this work contributes to the advancement of both fields of music neuroscience and brain connectivity in ASD.
- Geometric and Numerical analysis of nonholonomic systemsPublication . Simões, AlexandreGeometric mechanics is a fairly recent field of mathematics lying in the intersection of at least four different scientific fields: differential geometry, physics, numerical analysis and dynamical systems. Its starting point is to shed light on the underlying geometry behind mechanics and use it to obtain new results which frequently reach a variety of different mathematical fields. One of the practical applications that was made possible by using geometric techniques was the ability to construct \textit{variational integrators}, which are numerical methods reproducing the geometry of the original mechanical system such as symplecticity, conservation of momentum and energy. These methods are often computationally cheaper than standard ones while demonstrating an adequate qualitative behaviour even at low order. However, not all mechanical systems may be approximated using variational integrators. Nonholonomic mechanics is one of such cases, where we lack a variational principle, symplecticity and conservation of momentum, in general. Hence, the investigation of the geometric structure of nonholonomic mechanics must be carried out having into account its non-symplectic and non-variational nature. In this thesis, we will deduce new geometric and analytical properties of nonholonomic systems which hopefully will provide a new insight to the subject. Our main definition, which we will meet across all sections, is the nonholonomic exponential map. This map is a generalization of the well-known Riemannian exponential map and we will see that it plays a role in the description of nonholonomic trajectories as well as on the applications to numerical analysis. After introducing this new object, the thesis may be divided into two parts. In the first part, we take advantage of the nonholonomic exponential map to present new geometric properties of mechanical nonholonomic systems such as the existence of a constrained Riemannian manifold containing radial nonholonomic trajectories with fixed starting point and on which they are geodesics. This is a new and surprising result because it opens the possibility of applying variational techniques to nonholonomic dynamics, which is commonly seen to be non-variational in nature. Also, introduce the notion of a nonholonomic Jacobi field and provide a nonholonomic Jacobi equation. In the second part, which is more applied, we use the nonholonomic exponential map to characterize the exact discrete trajectory of nonholonomic systems. Then we propose a numerical method which is able to generate the exact trajectory. On the last chapter, we discuss contact systems and apply the nonholonomic exponential map to construct an exact discrete Lagrangian function for these systems.