Iterative forcing and hyperimmunity in reverse mathematics

The separation between two theorems in reverse mathematics is usually done by constructing a Turing ideal satisfying a theorem P and avoiding the solutions to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a forcing technique for iterating a computable non-reducibility in order to separate theorems over omega-models. In this paper, we present a modularized version of their framework in terms of preservation of hyperimmunity and show that it is powerful enough to obtain the same separations results as Wang did with his notion of preservation of definitions.Comment: 15 page

Partitioning the triangles of the cross polytope into surfaces

We present a constructive proof that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope $\beta^k$ into closed surfaces of genus $g \leq 1$, each with a transitive automorphism group given by the vertex transitive $\mathbb{Z}_{2k}$-action on $\beta^k$. Furthermore we show that for each $k \equiv 1,5(6)$ the 2-skeleton of the (k-1)-simplex is a union of highly symmetric tori and M\"obius strips.Comment: 13 pages, 1 figure. Minor update. Journal-ref: Beitr. Algebra Geom. / Contributions to Algebra and Geometry, 53(2):473-486, 201

On a triangulation of the 3-ball and the solid torus

AbstractWe show that neither the 3-ball nor the solid torus admits a triangulation in which (i) every vertex is on the boundary, and (ii) every tetrahedron has exactly one triangle on the boundary. Such triangulations are relevant to an unresolved conjecture of Perles

Amplification of the Index of Refraction of Aqueous Immersion Fluids by Ionic Surfactants

In order to find new immersion liquids to improve the resolution of 193 nm immersion photolithography, we have attempted to discover aqueous system possessing an index of refraction greater than that of water using aqueous surfactant systems. The index of refraction (RI) of both cationic and anionic surfactant systems were examined in the presence of wide range of inorganic salts, and parameters such as size of surfactants, concentrations, and temperature were varied. The refractive index (RI) was found to be increased in the presence of both anionic and cationic surfactants compared to those of water and also increased as a function of surfactant concentration. However the refractive index tends to increase much more strongly as a function of salt concentration. In our study, a maximum RI enhancement was observed from 6.5 M CdCl2 in 8.2 mM aqueous SDS solution. The effect of micellar properties such as the critical micelle concentration (cmc) and degree of ionization were systematically studied for aqueous SDS system in the presence of CdCl2. The correlation on index of refraction between empirical data and theoretical prediction were performed using the concept of molar refraction. Wavelength dependence of RI from theoretical prediction based on empirical equation was examined for various concentration of CdCl2 system and the results are reported in the paper

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

On FPL configurations with four sets of nested arches

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function adde

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

Neuronal Profilin Isoforms Are Addressed by Different Signalling Pathways

Profilins are prominent regulators of actin dynamics. While most mammalian cells express only one profilin, two isoforms, PFN1 and PFN2a are present in the CNS. To challenge the hypothesis that the expression of two profilin isoforms is linked to the complex shape of neurons and to the activity-dependent structural plasticity, we analysed how PFN1 and PFN2a respond to changes of neuronal activity. Simultaneous labelling of rodent embryonic neurons with isoform-specific monoclonal antibodies revealed both isoforms in the same synapse. Immunoelectron microscopy on brain sections demonstrated both profilins in synapses of the mature rodent cortex, hippocampus and cerebellum. Both isoforms were significantly more abundant in postsynaptic than in presynaptic structures. Immunofluorescence showed PFN2a associated with gephyrin clusters of the postsynaptic active zone in inhibitory synapses of embryonic neurons. When cultures were stimulated in order to change their activity level, active synapses that were identified by the uptake of synaptotagmin antibodies, displayed significantly higher amounts of both isoforms than non-stimulated controls. Specific inhibition of NMDA receptors by the antagonist APV in cultured rat hippocampal neurons resulted in a decrease of PFN2a but left PFN1 unaffected. Stimulation by the brain derived neurotrophic factor (BDNF), on the other hand, led to a significant increase in both synaptic PFN1 and PFN2a. Analogous results were obtained for neuronal nuclei: both isoforms were localized in the same nucleus, and their levels rose significantly in response to KCl stimulation, whereas BDNF caused here a higher increase in PFN1 than in PFN2a. Our results strongly support the notion of an isoform specific role for profilins as regulators of actin dynamics in different signalling pathways, in excitatory as well as in inhibitory synapses. Furthermore, they suggest a functional role for both profilins in neuronal nuclei

Coevolution between MHC class I and antigen-processing genes in salamanders

Animal sciencesNaturali

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