Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Map positions of third chromosomal female sterile and lethal mutations of Drosophila melanogaster

Chromosomal mutations induced by ethyl methanesulfonate (EMS) treatment can cause female sterility or maternal-effect lethality in Drosophila. EMS is particularly useful to researchers because it creates mutations independent of position effects. However, because researchers have little control over the chromosomal site of mutation, post-mutagenic genetic mapping is required to determine the cytological location of the mutation. To make a valuable set of mutants more useful to the research community, we have mapped the uncharacterized part of the female-sterile – maternal-effect lethal Tübingen collection. We mapped 49 female-sterile – maternal-effect lethal alleles and 72 lethal alleles to individual deficiency intervals on the third chromosome. In addition, we analyzed the phenotype of ovaries resulting from female sterile mutations. The observed phenotypes range from tumorous ovaries and early blocks in oogenesis, to later blocks, slow growth, blocks in stage 10, to apparently full development of the ovary. The mapping and phenotypic characterization of these 121 mutations provide the necessary information for the researcher to consider a specific mutant as a candidate for their gene of interest.Key words: Drosophila melanogaster, oogenesis, female sterile, maternal-effect lethal, EMS-induced mutations.

Psychomotor symptoms of schizophrenia map on the cerebral motor circuit

Schizophrenia is a devastating disorder thought to result mainly from cerebral pathology. Neuroimaging studies have provided a wealth of findings of brain dysfunction in schizophrenia. However, we are still far from understanding how particular symptoms can result from aberrant brain function. In this context, the high prevalence of motor symptoms in schizophrenia such as catatonia, neurological soft signs, parkinsonism, and abnormal involuntary movements is of particular interest. Here, the neuroimaging correlates of these motor symptoms are reviewed. For all investigated motor symptoms, neural correlates were found within the cerebral motor system. However, only a limited set of results exists for hypokinesia and neurological soft signs, while catatonia, abnormal involuntary movements and parkinsonian signs still remain understudied with neuroimaging methods. Soft signs have been associated with altered brain structure and function in cortical premotor and motor areas as well as cerebellum and thalamus. Hypokinesia is suggested to result from insufficient interaction of thalamocortical loops within the motor system. Future studies are needed to address the neural correlates of motor abnormalities in prodromal states, changes during the course of the illness, and the specific pathophysiology of catatonia, dyskinesia and parkinsonism in schizophrenia.