Extrapolation theory for the real interpolation method

We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega

The geographical concentration of industry across Spanish Regions, 1856-1995

New economic geography models show that there may be a strong relationship between economic integration and the geographical concentration of industries. Nevertheless, this relationship is neither unique nor stable, and may follow a ?-shaped pattern in the long term. The aim of the present paper is to analyze the evolution of the geographical concentration of manufacturing across Spanish regions during the period 1856-1995. We construct several geographical concentration indices for different points in time over these 140 years. The analysis is carried out at two levels of aggregation, in regions corresponding to the NUTS-II and NUTS-III classifications. We confirm that the process of economic integration stimulated the geographical concentration of industrial activity. Nevertheless, the localization coefficients only started to fall after the beginning of the integration of the Spanish Economy into the international markets in the mid-70s, and this new path was not interrupted by Spain¿s entry in the European Union some years later

A peroxisomal glutathione transferase of Saccharomyces cerevisiae is functionally related to sulfur amino acid metabolism

Saccharomyces cerevisiae cells contain three omega-class glutathione transferases with glutaredoxin activity (Gto1, Gto2, and Gto3), in addition to two glutathione transferases (Gtt1 and Gtt2) not classifiable into standard classes. Gto1 is located at the peroxisomes, where it is targeted through a PTS1-type sequence, whereas Gto2 and Gto3 are in the cytosol. Among the GTO genes, GTO2 shows the strongest induction of expression by agents such as diamide, 1-chloro-2,4-dinitrobenzene, tert-butyl hydroperoxide or cadmium, in a manner that is dependent on transcriptional factors Yap1 and/or Msn2/4. Diamide and 1-chloro-2,4-dinitrobenzene (causing depletion of reduced glutathione) also induce expression of GTO1 over basal levels. Phenotypic analyses with single and multiple mutants in the S. cerevisiae glutathione transferase genes show that, in the absence of Gto1 and the two Gtt proteins, cells display increased sensitivity to cadmium. A gto1-null mutant also shows growth defects on oleic acid-based medium, which is indicative of abnormal peroxisomal functions, and altered expression of genes related to sulfur amino acid metabolism. As a consequence, growth of the gto1 mutant is delayed in growth medium without lysine, serine, or threonine, and the mutant cells have low levels of reduced glutathione. The role of Gto1 at the S. cerevisiae peroxisomes could be related to the redox regulation of the Str3 cystathionine -lyase protein. This protein is also located at the peroxisomes in S. cerevisiae, where it is involved in transulfuration of cysteine into homocysteine, and requires a conserved cysteine residue for its biological activity.

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Divergent evolution and purifying selection of the flaA gene sequences in Aeromonas

BACKGROUND: The bacterial flagellum is the most important organelle of motility in bacteria and plays a key role in many bacterial lifestyles, including virulence. The flagellum also provides a paradigm of how hierarchical gene regulation, intricate protein-protein interactions and controlled protein secretion can result in the assembly of a complex multi-protein structure tightly orchestrated in time and space. As if to stress its importance, plants and animals produce receptors specifically dedicated to the recognition of flagella. Aside from motility, the flagellum also moonlights as an adhesion and has been adapted by humans as a tool for peptide display. Flagellar sequence variation constitutes a marker with widespread potential uses for studies of population genetics and phylogeny of bacterial species. RESULTS: We sequenced the complete flagellin gene (flaA) in 18 different species and subspecies of Aeromonas. Sequences ranged in size from 870 (A. allosaccharophila) to 921 nucleotides (A. popoffii). The multiple alignment displayed 924 sites, 66 of which presented alignment gaps. The phylogenetic tree revealed the existence of two groups of species exhibiting different FlaA flagellins (FlaA1 and FlaA2). Maximum likelihood models of codon substitution were used to analyze flaA sequences. Likelihood ratio tests suggested a low variation in selective pressure among lineages, with an omega ratio of less than 1 indicating the presence of purifying selection in almost all cases. Only one site under potential diversifying selection was identified (isoleucine in position 179). However, 17 amino acid positions were inferred as sites that are likely to be under positive selection using the branch-site model. Ancestral reconstruction revealed that these 17 amino acids were among the amino acid changes detected in the ancestral sequence. CONCLUSION: The models applied to our set of sequences allowed us to determine the possible evolutionary pathway followed by the flaA gene in Aeromonas, suggesting that this gene have probably been evolving independently in the two groups of Aeromonas species since the divergence of a distant common ancestor after one or several episodes of positive selection. REVIEWERS: This article was reviewed by Alexey Kondrashov, John Logsdon and Olivier Tenaillon (nominated by Laurence D Hurst).

Intravitreal docosahexaenoic acid in a rabbit model: preclinical safety assessment

Purpose The purpose of the present study was to evaluate the retinal toxicity of a single dose of intravitreal docosahexaenoic acid (DHA) in rabbit eyes over a short-term period. Methods Sixteen New Zealand albino rabbits were selected for this pre-clinical study. Six concentrations of DHA (Brudy Laboratories, Barcelona, Spain) were prepared: 10 mg/50 µl, 5 mg/50 µl, 2'5 mg/50 µl, 50 µg/50 µl, 25 µg/50 µl, and 5 µg/50 µl. Each concentration was injected intravitreally in the right eye of two rabbits. As a control, the vehicle solution was injected in one eye of four animals. Retinal safety was studied by slit-lamp examination, and electroretinography. All the rabbits were euthanized one week after the intravitreal injection of DHA and the eyeballs were processed to morphologic and morphometric histological examination by light microscopy. At the same time aqueous and vitreous humor samples were taken to quantify the concentration of omega-3 acids by gas chromatography. Statistical analysis was performed by SPSS 21.0. Results Slit-lamp examination revealed an important inflammatory reaction on the anterior chamber of the rabbits injected with the higher concentrations of DHA (10 mg/50 µl, 5 mg/50 µl, 2'5 mg/50 µ) Lower concentrations showed no inflammation. Electroretinography and histological studies showed no significant difference between control and DHA-injected groups except for the group injected with 50 µg/50 µl. Conclusions Our results indicate that administration of intravitreal DHA is safe in the albino rabbit model up to the maximum tolerated dose of 25 µg/50 µl. Further studies should be performed in order to evaluate the effect of intravitreal injection of DHA as a treatment, alone or in combination, of different retinal diseases.