Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

The Architecture of Home in Cairo: Socio-Spatial Practice of the Hawari's Everyday Life

The hawari of Cairo - narrow non-straight alleyways - are the basic urban units that have formed the medieval city since its foundation back in 969 AD. Until early in the C20th, they made up the primary urban divisions of the city and were residential in nature. Contemporary hawari, by contrast, are increasingly dominated by commercial and industrial activity. This medieval urban maze of extremely short, broken, zigzag streets and dead ends are defensible territories, powerful institutions, and important social systems. While the hawari have been studied as an exemplar for urban structure of medieval Islamic urbanism, and as individual building typologies, this book is the first to examine in detail the socio-spatial practice of the architecture of home in the city. It investigates how people live, communicate and relate to each other within their houses or shared spaces of the alleys, and in doing so, to uncover several new socio-spatial dimensions and meanings in this architectural form.

In an attempt to re-establish the link between architecture past and present, and to understand the changing social needs of communities, this book uncovers the notion of home as central to understand architecture in such a city with long history as Cairo. It firstly describes the historical development of the domestic spaces (indoor and outdoor), and provides an inclusive analysis of spaces of everyday activities in the hawari of old Cairo. It then broadens its analysis to other parts of the city, highlighting different customs and representations of home in the city at large. Cairo, in the context of this book, is represented as the most sophisticated urban centre in the Middle East with different and sometimes contrasting approaches to the architecture of home, as a practice and spatial system.

In order to analyse the complexity and interconnectedness of the components and elements of the hawari as a 'collective home', it layers its narratives of architectural and social developments as a domestic environment over the past two hundred years, and in doing so, explores the in-depth social meaning and performance of spaces, both private and public.

The maximal C*-algebra of quotients as an operator bimodule

We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product of A with itself labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved.

On the Distribution of Signal Phase in Body Area Networks

In this letter, we investigate the distribution of the phase component of the complex received signal observed in practical experiments using body area networks. Two phase distributions, the recently proposed kappa-mu and eta-mu probability densities, which together encompass the most widely used fading models, namely Semi-Gaussian, Rayleigh, Hoyt, Rice, and Nakagami-m, have been compared with measurement data. The kappa-mu distribution has been found to provide the best fit over a range of on-body links, while the user was mobile. The experiments were carried out in two dissimilar indoor environments at opposite ends of the multipath spectrum. It has also been found that the uniform phase distribution has not arisen in anyone of the experiments.

Cold-induced silencing by long antisense transcripts of an Arabidopsis Polycomb target.

Transcription in eukaryotic genomes generates an extensive array of non-protein-coding RNA, the functional significance of which is mostly unknown. We are investigating the link between non-coding RNA and chromatin regulation through analysis of FLC - a regulator of flowering time in Arabidopsis and a target of several chromatin pathways. Here we use an unbiased strategy to characterize non-coding transcripts of FLC and show that sense/antisense transcript levels correlate in a range of mutants and treatments, but change independently in cold-treated plants. Prolonged cold epigenetically silences FLC in a Polycomb-mediated process called vernalization. Our data indicate that upregulation of long non-coding antisense transcripts covering the entire FLC locus may be part of the cold-sensing mechanism. Induction of these antisense transcripts occurs earlier than, and is independent of, other vernalization markers and coincides with a reduction in sense transcription. We show that addition of the FLC antisense promoter sequences to a reporter gene is sufficient to confer cold-induced silencing of the reporter. Our data indicate that cold-induced FLC antisense transcripts have an early role in the epigenetic silencing of FLC, acting to silence FLC transcription transiently. Recruitment of the Polycomb machinery then confers the epigenetic memory. Antisense transcription events originating from 3' ends of genes might be a general mechanism to regulate the corresponding sense transcription in a condition/stage-dependent manner.

A molecular model for drug binding to tandem repeats of telomeric G-quadruplexes.

The extreme 3'-ends of human telomeres consist of 150–250 nucleotides of single-stranded DNA sequence together with associated proteins. Small-molecule ligands can compete with these proteins and induce a conformational change in the DNA to a four-stranded quadruplex arrangement, which is also no longer a substrate for the telomerase enzyme. The modified telomere ends provide signals to the DNA-damage-response system and trigger senescence and apoptosis. Experimental structural data are available on such quadruplex complexes comprising up to four telomeric DNA repeats, but not on longer systems that are more directly relevant to the single-stranded overhang in human cells. The present paper reports on a molecular modelling study that uses Molecular Dynamics simulation methods to build dimer and tetramer quadruplex repeats. These incorporate ligand-binding sites and are models for overhang–ligand complexes.

Molecular dynamics and principal components analysis of human telomeric quadruplex multimers.

Guanine-rich DNA repeat sequences located at the terminal ends of chromosomal DNA can fold in a sequence-dependent manner into G-quadruplex structures, notably the terminal 150–200 nucleotides at the 3' end, which occur as a single-stranded DNA overhang. The crystal structures of quadruplexes with two and four human telomeric repeats show an all-parallel-stranded topology that is readily capable of forming extended stacks of such quadruplex structures, with external TTA loops positioned to potentially interact with other macromolecules. This study reports on possible arrangements for these quadruplex dimers and tetramers, which can be formed from 8 or 16 telomeric DNA repeats, and on a methodology for modeling their interactions with small molecules. A series of computational methods including molecular dynamics, free energy calculations, and principal components analysis have been used to characterize the properties of these higher-order G-quadruplex dimers and tetramers with parallel-stranded topology. The results confirm the stability of the central G-tetrads, the individual quadruplexes, and the resulting multimers. Principal components analysis has been carried out to highlight the dominant motions in these G-quadruplex dimer and multimer structures. The TTA loop is the most flexible part of the model and the overall multimer quadruplex becoming more stable with the addition of further G-tetrads. The addition of a ligand to the model confirms the hypothesis that flat planar chromophores stabilize G-quadruplex structures by making them less flexible.

Genetic organization of the O7-specific lipopolysaccharide biosynthesis cluster of Escherichia coli VW187 (O7:K1)

In previous studies the authors cloned and characterized the DNA sequence of the regions at both ends of the O7-specific lipopolysaccharide (LPS) biosynthesis cluster of Escherichia coli VW187 (O7:K1), and identified the biosynthetic genes for dTDP-rhamnose and GDP-mannose, as well as one of the candidate glycosyltransferases. In this work the complete DNA sequence of a 6.9 kb intervening region is presented. Seven new ORFs were identified. All the functions required for the synthesis and transfer of the O7 LPS were assigned on the basis of complementation experiments of transposon insertion mutants, and amino acid sequence homology to proteins involved in LPS synthesis of other bacteria. Of the seven ORFs, two encoded membrane proteins that were homologous to the O-antigen translocase (Wzx) and polymerase (Wxy), two were involved in the biosynthesis of dTDP-N-acetylviosamine, and the remaining three showed homologies to sugar transferases. The O antigen chain length regulator gene wzz was also identified in the vicinity of the O7 polysaccharide cluster. O7-specific DNA primers were designed and tested for serotyping of O7 E. coli strains.

Altered cofactor binding affects stability and activity of human UDP-galactose 4′-epimerase: Implications for type III galactosemia

Deficiency of UDP-galactose 4'-epimerase is implicated in type III galactosemia. Two variants, p.K161N-hGALE and p.D175N-hGALE, have been previously found in combination with other alleles in patients with a mild form of the disease. Both variants were studied in vivo and in vitro and showed different levels of impairment. p.K161N-hGALE was severely impaired with substantially reduced enzymatic activity, increased thermal stability, reduced cofactor binding and no ability to rescue the galactose-sensitivity of gal10-null yeast. Interestingly p.K161N-hGALE showed less impairment of activity with UDP-N-acetylgalactosamine in comparison to UDP-galactose. Differential scanning fluorimetry revealed that p.K161N-hGALE was more stable than the wild-type protein and only changed stability in the presence of UDP-N-acetylglucosamine and NAD(+). p.D175N-hGALE essentially rescued the galactose-sensitivity of gal10-null yeast, was less stable than the wild-type protein but showed increased stability in the presence of substrates and cofactor. We postulate that p.K161N-hGALE causes its effects by abolishing an important interaction between the protein and the cofactor, whereas p.D175N-hGALE is predicted to remove a stabilizing salt bridge between the ends of two a-helices that contain residues that interact with NAD(+). These results suggest that the cofactor binding is dynamic and that its loss results in significant structural changes that may be important in disease causation.