C∗-algebren mit geordneten ideal folge

AbstractLet K be a separable infinite-dimensional Hilbert space and let J be a countable totally ordered set. Every decomposition of J, J = {i ϵ J ¦i < j} ∪ {i ϵ J ¦i ⩾ j} induces a factorisation of the incomplete tensorproduct H of K over J, H = Hj ⊗ Hj. Let K(H) denote the algebra of all compact operators on H. Then AJ is the C∗-algebra of operators on H generated by 1⊗H(Hj). All ideals of AJ are primitive and form a chain. They correspond to certain cuts in J. In particular, AJ has a maximal (minimal) ideal iff J has a largest (smallest) element. Thus AJ is antiliminal iff J has no smallest element, and AJ is postliminal iff J is well ordered. In particular, Az is antiliminal and all proper quotients of Az are isomorphic postliminal C∗-algebras. The example AN has been considered previously by J. Dixmier

L1-determined ideals in group algebras of exponential Lie groups

A locally compact group $G$ is said to be $\ast$-regular if the natural map \Psi:\Prim C^\ast(G)\to\Prim_{\ast} L^1(G) is a homeomorphism with respect to the Jacobson topologies on the primitive ideal spaces \Prim C^\ast(G) and \Prim_{\ast} L^1(G). In 1980 J. Boidol characterized the $\ast$-regular ones among all exponential Lie groups by a purely algebraic condition. In this article we introduce the notion of $L^1$-determined ideals in order to discuss the weaker property of primitive $\ast$-regularity. We give two sufficient criteria for closed ideals $I$ of $C^\ast(G)$ to be $L^1$-determined. Herefrom we deduce a strategy to prove that a given exponential Lie group is primitive $\ast$-regular. The author proved in his thesis that all exponential Lie groups of dimension $\le 7$ have this property. So far no counter-example is known. Here we discuss the example $G=B_5$, the only critical one in dimension $\le 5$

A Small Genomic Region Containing Several Loci Required for Gastrulation in Drosophila

Genetic screens in Drosophila designed to search for loci involved in gastrulation have identified four regions of the genome that are required zygotically for the formation of the ventral furrow. For three of these, the genes responsible for the mutant phenotypes have been found. We now describe a genetic characterization of the fourth region, which encompasses the cytogenetic interval 24C3-25B, and the mapping of genes involved in gastrulation in this region. We have determined the precise breakpoints of several existing deficiencies and have generated new deficiencies. Our results show that the region contains at least three different loci associated with gastrulation effects. One maternal effect gene involved in ventral furrow formation maps at 24F but could not be identified. For a second maternal effect gene which is required for germ band extension, we identify a candidate gene, CG31660, which encodes a G protein coupled receptor. Finally, one gene acts zygotically in ventral furrow formation and we identify it as Traf4

Semi-supervised learning for the identification of syn-expressed genes from fused microarray and in situ image data

Background: Gene expression measurements during the development of the fly Drosophila melanogaster are routinely used to find functional modules of temporally co-expressed genes. Complimentary large data sets of in situ RNA hybridization images for different stages of the fly embryo elucidate the spatial expression patterns. Results: Using a semi-supervised approach, constrained clustering with mixture models, we can find clusters of genes exhibiting spatio-temporal similarities in expression, or syn-expression. The temporal gene expression measurements are taken as primary data for which pairwise constraints are computed in an automated fashion from raw in situ images without the need for manual annotation. We investigate the influence of these pairwise constraints in the clustering and discuss the biological relevance of our results. Conclusion: Spatial information contributes to a detailed, biological meaningful analysis of temporal gene expression data. Semi-supervised learning provides a flexible, robust and efficient framework for integrating data sources of differing quality and abundance

There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator

Höhn S, Hallmann A. There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator. BMC Biology. 2011;9(1): 89.Background: Epithelial folding is a common morphogenetic process during the development of multicellular organisms. In metazoans, the biological and biomechanical processes that underlie such three-dimensional (3D) developmental events are usually complex and difficult to investigate. Spheroidal green algae of the genus Volvox are uniquely suited as model systems for studying the basic principles of epithelial folding. Volvox embryos begin life inside out and then must turn their spherical cell monolayer outside in to achieve their adult configuration; this process is called 'inversion.' There are two fundamentally different sequences of inversion processes in Volvocaceae: type A and type B. Type A inversion is well studied, but not much is known about type B inversion. How does the embryo of a typical type B inverter, V. globator, turn itself inside out? Results: In this study, we investigated the type B inversion of V. globator embryos and focused on the major movement patterns of the cellular monolayer, cell shape changes and changes in the localization of cytoplasmic bridges (CBs) connecting the cells. Isolated intact, sectioned and fragmented embryos were analyzed throughout the inversion process using light microscopy, confocal laser scanning microscopy, scanning electron microscopy and transmission electron microscopy techniques. We generated 3D models of the identified cell shapes, including the localizations of CBs. We show how concerted cell-shape changes and concerted changes in the position of cells relative to the CB system cause cell layer movements and turn the spherical cell monolayer inside out. The type B inversion of V. globator is compared to the type A inversion in V. carteri. Conclusions: Concerted, spatially and temporally coordinated changes in cellular shapes in conjunction with concerted migration of cells relative to the CB system are the causes of type B inversion in V. globator. Despite significant similarities between type A and type B inverters, differences exist in almost all details of the inversion process, suggesting analogous inversion processes that arose through parallel evolution. Based on our results and due to the cellular biomechanical implications of the involved tensile and compressive forces, we developed a global mechanistic scenario that predicts epithelial folding during embryonic inversion in V. globator

Specification of Drosophila Corpora Cardiaca Neuroendocrine Cells from Mesoderm Is Regulated by Notch Signaling

Drosophila neuroendocrine cells comprising the corpora cardiaca (CC) are essential for systemic glucose regulation and represent functional orthologues of vertebrate pancreatic α-cells. Although Drosophila CC cells have been regarded as developmental orthologues of pituitary gland, the genetic regulation of CC development is poorly understood. From a genetic screen, we identified multiple novel regulators of CC development, including Notch signaling factors. Our studies demonstrate that the disruption of Notch signaling can lead to the expansion of CC cells. Live imaging demonstrates localized emergence of extra precursor cells as the basis of CC expansion in Notch mutants. Contrary to a recent report, we unexpectedly found that CC cells originate from head mesoderm. We show that Tinman expression in head mesoderm is regulated by Notch signaling and that the combination of Daughterless and Tinman is sufficient for ectopic CC specification in mesoderm. Understanding the cellular, genetic, signaling, and transcriptional basis of CC cell specification and expansion should accelerate discovery of molecular mechanisms regulating ontogeny of organs that control metabolism

A Modifier Screen for Bazooka/PAR-3 Interacting Genes in the Drosophila Embryo Epithelium

The development and homeostasis of multicellular organisms depends on sheets of epithelial cells. Bazooka (Baz; PAR-3) localizes to the apical circumference of epithelial cells and is a key hub in the protein interaction network regulating epithelial structure. We sought to identify additional proteins that function with Baz to regulate epithelial structure in the Drosophila embryo.The baz zygotic mutant cuticle phenotype could be dominantly enhanced by loss of known interaction partners. To identify additional enhancers, we screened molecularly defined chromosome 2 and 3 deficiencies. 37 deficiencies acted as strong dominant enhancers. Using deficiency mapping, bioinformatics, and available single gene mutations, we identified 17 interacting genes encoding known and predicted polarity, cytoskeletal, transmembrane, trafficking and signaling proteins. For each gene, their loss of function enhanced adherens junction defects in zygotic baz mutants during early embryogenesis. To further evaluate involvement in epithelial polarity, we generated GFP fusion proteins for 15 of the genes which had not been found to localize to the apical domain previously. We found that GFP fusion proteins for Drosophila ASAP, Arf79F, CG11210, Septin 5 and Sds22 could be recruited to the apical circumference of epithelial cells. Nine of the other proteins showed various intracellular distributions, and one was not detected.Our enhancer screen identified 17 genes that function with Baz to regulate epithelial structure in the Drosophila embryo. Our secondary localization screen indicated that some of the proteins may affect epithelial cell polarity by acting at the apical cell cortex while others may act through intracellular processes. For 13 of the 17 genes, this is the first report of a link to baz or the regulation of epithelial structure

A Polarised Population of Dynamic Microtubules Mediates Homeostatic Length Control in Animal Cells

An analysis of cells grown on micro-patterned lines, and of cells during zebrafish development, identifies a population of microtubules that align along the long axis of cells to mediate homeostatic length control