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

Effectiveness of Hindman's theorem for bounded sums

We consider the strength and effective content of restricted versions of Hindman's Theorem in which the number of colors is specified and the length of the sums has a specified finite bound. Let $\mathsf{HT}^{\leq n}_k$ denote the assertion that for each $k$-coloring $c$ of $\mathbb{N}$ there is an infinite set $X \subseteq \mathbb{N}$ such that all sums $\sum_{x \in F} x$ for $F \subseteq X$ and $0 < |F| \leq n$ have the same color. We prove that there is a computable $2$-coloring $c$ of $\mathbb{N}$ such that there is no infinite computable set $X$ such that all nonempty sums of at most $2$ elements of $X$ have the same color. It follows that $\mathsf{HT}^{\leq 2}_2$ is not provable in $\mathsf{RCA}_0$ and in fact we show that it implies $\mathsf{SRT}^2_2$ in $\mathsf{RCA}_0$. We also show that there is a computable instance of $\mathsf{HT}^{\leq 3}_3$ with all solutions computing $0'$. The proof of this result shows that $\mathsf{HT}^{\leq 3}_3$ implies $\mathsf{ACA}_0$ in $\mathsf{RCA}_0$

Rtt107/Esc4 binds silent chromatin and DNA repair proteins using different BRCT motifs

BACKGROUND: By screening a plasmid library for proteins that could cause silencing when targeted to the HMR locus in Saccharomyces cerevisiae, we previously reported the identification of Rtt107/Esc4 based on its ability to establish silent chromatin. In this study we aimed to determine the mechanism of Rtt107/Esc4 targeted silencing and also learn more about its biological functions. RESULTS: Targeted silencing by Rtt107/Esc4 was dependent on the SIR genes, which encode obligatory structural and enzymatic components of yeast silent chromatin. Based on its sequence, Rtt107/Esc4 was predicted to contain six BRCT motifs. This motif, originally identified in the human breast tumor suppressor gene BRCA1, is a protein interaction domain. The targeted silencing activity of Rtt107/Esc4 resided within the C-terminal two BRCT motifs, and this region of the protein bound to Sir3 in two-hybrid tests. Deletion of RTT107/ESC4 caused sensitivity to the DNA damaging agent MMS as well as to hydroxyurea. A two-hybrid screen showed that the N-terminal BRCT motifs of Rtt107/Esc4 bound to Slx4, a protein previously shown to be involved in DNA repair and required for viability in a strain lacking the DNA helicase Sgs1. Like SLX genes, RTT107ESC4 interacted genetically with SGS1; esc4Δ sgs1Δ mutants were viable, but exhibited a slow-growth phenotype and also a synergistic DNA repair defect. CONCLUSION: Rtt107/Esc4 binds to the silencing protein Sir3 and the DNA repair protein Slx4 via different BRCT motifs, thus providing a bridge linking silent chromatin to DNA repair enzymes

Some Combinatorial Properties of Schubert Polynomials

Schubert polynomials were introduced by Bernstein et al. and Demazure, and were extensively developed by Lascoux, Schützenberger, Macdonald, and others. We give an explicit combinatorial interpretation of the Schubert polynomial in terms of the reduced decompositions of the permutation w . Using this result, a variation of Schensted's correspondence due to Edelman and Greene allows one to associate in a natural way a certain set of tableaux with w , each tableau contributing a single term to . This correspondence leads to many problems and conjectures, whose interrelation is investigated. In Section 2 we consider permutations with no decreasing subsequence of length three (or 321-avoiding permutations). We show for such permutations that is a flag skew Schur function . In Section 3 we use this result to obtain some interesting properties of the rational function , where denotes a skew Schur function.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46173/1/10801_2004_Article_415600.pd

Supramolecular photocatalysis: insights into cucurbit[8]uril catalyzed photodimerization of 6-methylcoumarin

Guest induced shape change of the cucurbit[8]uril cavity is likely rate limiting in the supramolecular photocatalytic cycle for CB8 mediated photodimerization of 6-methylcoumarin

A polychromatic Ramsey theory for ordinals

The Ramsey degree of an ordinal α is the least number n such that any colouring of the edges of the complete graph on α using finitely many colours contains an n-chromatic clique of order type α. The Ramsey degree exists for any ordinal α < ω ω . We provide an explicit expression for computing the Ramsey degree given α. We further establish a version of this result for automatic structures. In this version the ordinal and the colouring are presentable by finite automata and the clique is additionally required to be regular. The corresponding automatic Ramsey degree turns out to be greater than the set theoretic Ramsey degree. Finally, we demonstrate that a version for computable structures fails

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