On the separable quotient problem for Banach spaces

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the results presented are consequence of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces c_0 and l_p, for 1 <= p <= \infty. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica

Bounded resolutions for spaces Cp(X) and a characterization in terms of X

An internal characterization of the Arkhangel’ski˘ı-Calbrixmain theorem from [4] is obtained by showing that the space Cp(X) of continuous real-valued functions on a Tychonoff space X is K-analytic framed in RX if and only if X admits a nice framing. This applies to show that a metrizable (or cosmic) space X is σ -compact if and only if X has a nice framing. We analyse a few concepts which are useful while studying nice framings. For example, a class of Tychonoff spaces X containing strictly Lindelöf Cˇ ech-complete spaces is introduced for which a variant of Arkhangel’ski˘ı-Calbrix theorem for σ-boundedness of X is shown

Orthogonal sequences in non-archmedean locally convex spaces

AbstractThe problem of the existence of (orthogonal) bases and basic sequences in non-archimedean locally convex spaces is studied. To this end we derive a characterization of compactoidity in terms of orthogonal sequences (Theorem 2.2)

cis sequence effects on gene expression

<p>Abstract</p> <p>Background</p> <p>Sequence and transcriptional variability within and between individuals are typically studied independently. The joint analysis of sequence and gene expression variation (genetical genomics) provides insight into the role of linked sequence variation in the regulation of gene expression. We investigated the role of sequence variation in <it>cis </it>on gene expression (<it>cis </it>sequence effects) in a group of genes commonly studied in cancer research in lymphoblastoid cell lines. We estimated the proportion of genes exhibiting <it>cis </it>sequence effects and the proportion of gene expression variation explained by <it>cis </it>sequence effects using three different analytical approaches, and compared our results to the literature.</p> <p>Results</p> <p>We generated gene expression profiling data at N = 697 candidate genes from N = 30 lymphoblastoid cell lines for this study and used available candidate gene resequencing data at N = 552 candidate genes to identify N = 30 candidate genes with sufficient variance in both datasets for the investigation of <it>cis </it>sequence effects. We used two additive models and the haplotype phylogeny scanning approach of Templeton (Tree Scanning) to evaluate association between individual SNPs, all SNPs at a gene, and diplotypes, with log-transformed gene expression. SNPs and diplotypes at eight candidate genes exhibited statistically significant (p < 0.05) association with gene expression. Using the literature as a "gold standard" to compare 14 genes with data from both this study and the literature, we observed 80% and 85% concordance for genes exhibiting and not exhibiting significant <it>cis </it>sequence effects in our study, respectively.</p> <p>Conclusion</p> <p>Based on analysis of our results and the extant literature, one in four genes exhibits significant <it>cis </it>sequence effects, and for these genes, about 30% of gene expression variation is accounted for by <it>cis </it>sequence variation. Despite diverse experimental approaches, the presence or absence of significant <it>cis </it>sequence effects is largely supported by previously published studies.</p

Unordered Baire-like spaces without local convexity

The aim of the present paper is to study the class of tvs which we define by ommiting the word “increasing” in the definition of $\ast$-suprabarrelled spaces. We prove that the product of Baire tvs is $\ast$-UBL ant hence the class of $\ast$-UBL spaces is strictly larger than the class of Baire spaces

CS-barrelled spaces

This note contains a proof of the following result: Let $E$ be a locally convex space. Every absorbing absolutely convex CS-closed subset of $E$ is a neighbourhood of zero in $E$ if and only if every sequentially closed linear map from $E$ into an arbitrary Banach space is continuous. Some consequences and remarks are also given

Noncollinear Ordering of the Orbital Magnetic Moments in Magnetite

The magnitude of the orbital magnetic moment and its role as a trigger of the Verwey transition in the prototypical Mott insulator, magnetite, remain contentious. Using 1s2p resonant inelastic x-ray scattering angle distribution (RIXS-AD), we prove the existence of noncollinear orbital magnetic ordering and infer the presence of dynamical distortion creating a polaronic precursor for the metal to insulator transition. These conclusions are based on a subtle angular shift of the RIXS-AD spectral intensity as a function of the magnetic field orientation. Theoretical simulations show that these results are only consistent with noncollinear magnetic orbital ordering. To further support these claims we perform Fe K-edge x-ray magnetic circular dichroism in order to quantify the Fe average orbital magnetic moment