-Generic Computability, Turing Reducibility and Asymptotic Density

Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has density 1 and which agrees with the characteristic function of A on its domain. A set A is coarsely computable if there is a computable set C such that the symmetric difference of A and C has density 0. We prove that there is a c.e. set which is generically computable but not coarsely computable and vice versa. We show that every nonzero Turing degree contains a set which is not coarsely computable. We prove that there is a c.e. set of density 1 which has no computable subset of density 1. As a corollary, there is a generically computable set A such that no generic algorithm for A has computable domain. We define a general notion of generic reducibility in the spirt of Turing reducibility and show that there is a natural order-preserving embedding of the Turing degrees into the generic degrees which is not surjective

Oxygen pressure measurement using singlet oxygen emission

Pressure sensitive paint (PSP) provides a visualization of two-dimensional pressure distributions on airfoil and model automobile surfaces. One type of PSP utilizes platinum tetra(pentafluorophenyl)porphine (PtTFPP) dissolved in a fluoro-polymer film. Since the intense 650 nm triplet emission of PtTFPP is quenched by ground state oxygen, it is possible to measure two-dimensional oxygen concentration from the 650 nm emission intensity using a Stern-Volmer-type relationship. This article reports an alternative luminescence method to measure oxygen concentration based on the porphyrin-sensitized 1270 nm singlet oxygen emission, which can be imaged with an InGaAs near infrared camera. This direct measurement of oxygen emission complements and further validates the oxygen measurement based on PtTFPP phosphorescence quenching. Initial success at obtaining a negative correlation between the 650nm PtTFPP emission and the 1270 nm O_2 emission in solution led us to additional two-dimensional film studies using surfaces coated with PtTFPP, MgTFPP, and H_2TFPP in polymers in a pressure and temperature controlled chamber

Modulating Photochemical Properties to Enhance the Stability of Electronically Dimmable Eye Protection Devices

The study evaluates compatibility of stabilizers with dye doped liquid crystal (LC) scaffolds that are used in electronically dimmable materials. The photodegradation of the materials was investigated and suitable stabilizers were evaluated to slow the degradation process. Various types of benzotriazole-based stabilizers were evaluated for stabilizing the liquid crystals. Based on spin trapping experiments, radicals generated upon UV exposure is likely responsible for the degradation of the system. The radical generation is competitively inhibited by the addition of stabilizers. Abbreviations: LC, liquid crystal; STB, stabilizers

The lower and upper bound problems for cubical polytopes

We construct a family of cubical polytypes which shows that the upper bound on the number of facets of a cubical polytope (given a fixed number of vertices) is higher than previously suspected. We also formulate a lower bound conjecture for cubical polytopes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41359/1/454_2005_Article_BF02189315.pd

Actin: its cumbersome pilgrimage through cellular compartments

In this article, we follow the history of one of the most abundant, most intensely studied proteins of the eukaryotic cells: actin. We report on hallmarks of its discovery, its structural and functional characterization and localization over time, and point to present days’ knowledge on its position as a member of a large family. We focus on the rather puzzling number of diverse functions as proposed for actin as a dual compartment protein. Finally, we venture on some speculations as to its origin

Distinct Molecular Evolutionary Mechanisms Underlie the Functional Diversification of the Wnt and TGFβ Signaling Pathways

The canonical Wnt pathway is one of the oldest and most functionally diverse of animal intercellular signaling pathways. Though much is known about loss-of-function phenotypes for Wnt pathway components in several model organisms, the question of how this pathway achieved its current repertoire of functions has not been addressed. Our phylogenetic analyses of 11 multigene families from five species belonging to distinct phyla, as well as additional analyses employing the 12 Drosophila genomes, suggest frequent gene duplications affecting ligands and receptors as well as co-evolution of new ligand–receptor pairs likely facilitated the expansion of this pathway’s capabilities. Further, several examples of recent gene loss are visible in Drosophila when compared to family members in other phyla. By comparison the TGFβ signaling pathway is characterized by ancient gene duplications of ligands, receptors, and signal transducers with recent duplication events restricted to the vertebrate lineage. Overall, the data suggest that two distinct molecular evolutionary mechanisms can create a functionally diverse developmental signaling pathway. These are the recent dynamic generation of new genes and ligand–receptor interactions as seen in the Wnt pathway and the conservative adaptation of ancient pre-existing genes to new roles as seen in the TGFβ pathway. From a practical perspective, the former mechanism limits the investigator’s ability to transfer knowledge of specific pathway functions across species while the latter facilitates knowledge transfer

Calcineurin Selectively Docks with the Dynamin Ixb Splice Variant to Regulate Activity-dependent Bulk Endocytosis

Depolarization of nerve terminals stimulates rapid dephosphorylation of two isoforms of dynamin I (dynI), mediated by the calcium-dependent phosphatase calcineurin (CaN). Dephosphorylation at the major phosphorylation sites Ser-774/778 promotes a dynI-syndapin I interaction for a specific mode of synaptic vesicle endocytosis called activity-dependent bulk endocytosis (ADBE). DynI has two main splice variants at its extreme C terminus, long or short (dynIxa and dynIxb) varying only by 20 (xa) or 7 (xb) residues. Recombinant GST fusion proteins of dynIxa and dynIxb proline-rich domains (PRDs) were used to pull down interacting proteins from rat brain nerve terminals. Both bound equally to syndapin, but dynIxb PRD exclusively bound to the catalytic subunit of CaNA, which recruited CaNB. Binding of CaN was increased in the presence of calcium and was accompanied by further recruitment of calmodulin. Point mutations showed that the entire C terminus of dynIxb is a CaN docking site related to a conserved CaN docking motif (PXIXI(T/S)). This sequence is unique to dynIxb among all other dynamin variants or genes. Peptide mimetics of the dynIxb tail blocked CaN binding in vitro and selectively inhibited depolarization-evoked dynI dephosphorylation in nerve terminals but not of other dephosphins. Therefore, docking to dynIxb is required for the regulation of both dynI splice variants, yet it does not regulate the phosphorylation cycle of other dephosphins. The peptide blocked ADBE, but not clathrin-mediated endocytosis of synaptic vesicles. Our results indicate that Ca(2+) influx regulates assembly of a fully active CaN-calmodulin complex selectively on the tail of dynIxb and that the complex is recruited to sites of ADBE in nerve terminals