Orbit closures in flag varieties for the centralizer of an order-two nilpotent element : normality and resolutions for types A, B, D

Let G be a reductive algebraic group in classical types A, B, D and e be an element of its Lie algebra with Z its centraliser in G for the adjoint action. We suppose that e identifies with an nilpotent matrix of order two, which guarantees the number of Z-orbits in the flag variety of G is finite. For types B, D in characteristic two, we also suppose the image of e is totally isotropic. We show that any closure Y of such orbit is normal. We also prove that Y is Cohen-Macaulay with rational singularities provided that the base field is of characteristic zero, and that Cohen-Macaulayness remains in any characteristic for type A. We exhibit a birational, rational morphism onto Y involving Schubert varieties. Our work generalizes a result by N. Perrin and E. Smirnov on Springer fibers ([PS12])

Interindividual variability in the dimensions of goaldirected behaviour and their neural correlates

Goal-directed behaviour is an instrumental action performed to control our environment in order to provide a satisfactory outcome. It has been shown that these actions do not solely depend on action-outcome contingencies, but are also strongly influenced by personality traits or psychiatric disorders. Personality aspects such as sensitivity to rewards and impulsivity, as well as schizophrenia, have been identified as prominent factors, though the exact relation still remains unclear. Therefore, the goal of this dissertation is to provide an additional specification of interindividual differences in goal-directed behaviour on a neural level. Using functional imaging, we employed 2 different paradigms to probe reward-related as well as inhibition-related neural activation in healthy subjects and patients with schizophrenia. Study I investigated the neural response during a monetary incentive delay task in 23 healthy subjects, relating the observed activations with psychometric assessed traits of behavioural approach/inhibition. We found that the tendency to approach reward-related situations leads to an elevated neural response to positive outcomes, and an attenuated response to omissions. Additionally, a high behavioural inhibition tendency led to an attenuated response to rewards. Study II applied the monetary incentive delay task on a group of 15 patients with schizophrenia, demonstrating a negative relation between striatal activation during the expectation of reward and the symptom of apathy, as well as negative relation between orbitofrontal activation during the receipt of a reward and the symptom of depression. Study III investigated the relation between the personality trait of impulsivity and brain activation during the inhibition of inappropriate responses. Results showed that impulsivity is positively related to activations of bilateral ventroprefrontal regions. The results illustrate the importance of frontal-subcortical networks in goal-directed behaviour in clinical and non-clinical populations. An orbitofrontal/striatal network is specifically related to behavioural approach and inhibition tendencies, whereas impairments in the ventral striatum can lead to symptoms of apathy and depression in patients with schizophrenia. Additionally, activity in ventrolateral prefrontal regions is related to motor inhibition during successful inhibition of unwanted responses. Providing exact definitions of the specific functions and dependencies of frontal-subcortical circuits can inform our understanding of cognitive and emotional functions, and support research dealing with psychiatric disorders

Cosmic Ray Nuclei (CRN) detector investigation

The Cosmic Ray Nuclei (CRN) detector was designed to measure elemental composition and energy spectra of cosmic radiation nuclei ranging from lithium to iron. CRN was flown as part of Spacelab 2 in 1985, and consisted of three basic components: a gas Cerenkov counter, a transition radiation detector, and plastic scintillators. The results of the experiment indicate that the relative abundance of elements in this range, traveling at near relativistic velocities, is similar to those reported at lower energy

Synthetic studies towards an organometallic rotaxane

The synthesis of interlocking molecules such as rotaxanes and catenanes is a branch of supramolecular chemistry of particular current interest. The aim of this work was to assess the viability of the synthesis of an organometallic rotaxane in which the transition metal is covalently bonded to a carbon atom of an alkyl group. The formation of a rotaxane using the host cyclophane, cyclobis (paraquat-pphenylene), formed by a template effect, has been investigated using our chiral organometallic polyether