Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property

Intersectin associates with synapsin and regulates its nanoscale localization and function.

Neurotransmission is mediated by the exocytic release of neurotransmitters from readily releasable synaptic vesicles (SVs) at the active zone. To sustain neurotransmission during periods of elevated activity, release-ready vesicles need to be replenished from the reserve pool of SVs. The SV-associated synapsins are crucial for maintaining this reserve pool and regulate the mobilization of reserve pool SVs. How replenishment of release-ready SVs from the reserve pool is regulated and which other factors cooperate with synapsins in this process is unknown. Here we identify the endocytic multidomain scaffold protein intersectin as an important regulator of SV replenishment at hippocampal synapses. We found that intersectin directly associates with synapsin I through its Src-homology 3 A domain, and this association is regulated by an intramolecular switch within intersectin 1. Deletion of intersectin 1/2 in mice alters the presynaptic nanoscale distribution of synapsin I and causes defects in sustained neurotransmission due to defective SV replenishment. These phenotypes were rescued by wild-type intersectin 1 but not by a locked mutant of intersectin 1. Our data reveal intersectin as an autoinhibited scaffold that serves as a molecular linker between the synapsin-dependent reserve pool and the presynaptic endocytosis machinery

Synaptic vesicle recycling is unaffected in the Ts65Dn mouse model of Down syndrome

Down syndrome (DS) is the most common genetic cause of intellectual disability, and arises from trisomy of human chromosome 21. Accumulating evidence from studies of both DS patient tissue and mouse models has suggested that synaptic dysfunction is a key factor in the disorder. The presence of several genes within the DS trisomy that are either directly or indirectly linked to synaptic vesicle (SV) endocytosis suggested that presynaptic dysfunction could underlie some of these synaptic defects. Therefore we determined whether SV recycling was altered in neurons from the Ts65Dn mouse, the best characterised model of DS to date. We found that SV exocytosis, the size of the SV recycling pool, clathrin-mediated endocytosis, activity-dependent bulk endocytosis and SV generation from bulk endosomes were all unaffected by the presence of the Ts65Dn trisomy. These results were obtained using battery of complementary assays employing genetically-encoded fluorescent reporters of SV cargo trafficking, and fluorescent and morphological assays of fluid-phase uptake in primary neuronal culture. The absence of presynaptic dysfunction in central nerve terminals of the Ts65Dn mouse suggests that future research should focus on the established alterations in excitatory / inhibitory balance as a potential route for future pharmacotherapy