How large dimension guarantees a given angle

Abstract We study the following two problems: (1) Given n ≥ 2 and α, how large Hausdorff dimension can a compact set A ⊂ R n have if A does not contain three points that form an angle α? (2) Given α and δ, how large Hausdorff dimension can a compact subset A of a Euclidean space have if A does not contain three points that form an angle in the δ-neighborhood of α? Some angles (0, 60 • ) turn out to behave differently than other α ∈ [0, 180 • ]

Cutaneous hypersensitivity reactions to freshwater cyanobacteria – human volunteer studies

BACKGROUND: Pruritic skin rashes associated with exposure to freshwater cyanobacteria are infrequently reported in the medical and scientific literature, mostly as anecdotal and case reports. Diagnostic dermatological investigations in humans are also infrequently described. We sought to conduct a pilot volunteer study to explore the potential for cyanobacteria to elicit hypersensitivity reactions. METHODS: A consecutive series of adult patients presenting for diagnostic skin patch testing at a hospital outpatient clinic were invited to participate. A convenience sample of volunteers matched for age and sex was also enrolled. Patches containing aqueous suspensions of various cyanobacteria at three concentrations were applied for 48 hours; dermatological assessment was made 48 hours and 96 hours after application. RESULTS: 20 outpatients and 19 reference subjects were recruited into the study. A single outpatient produced unequivocal reactions to several cyanobacteria suspensions; this subject was also the only one of the outpatient group with a diagnosis of atopic dermatitis. No subjects in the reference group developed clinically detectable skin reactions to cyanobacteria. CONCLUSION: This preliminary clinical study demonstrates that hypersensitivity reactions to cyanobacteria appear to be infrequent in both the general and dermatological outpatient populations. As cyanobacteria are widely distributed in aquatic environments, a better appreciation of risk factors, particularly with respect to allergic predisposition, may help to refine health advice given to people engaging in recreational activities where nuisance cyanobacteria are a problem

The integrated analysis of metabolic and protein interaction networks reveals novel molecular organizing principles

Background: The study of biological interaction networks is a central theme of systems biology. Here, we investigate the relationships between two distinct types of interaction networks: the metabolic pathway map and the protein-protein interaction network (PIN). It has long been established that successive enzymatic steps are often catalyzed by physically interacting proteins forming permanent or transient multi-enzymes complexes. Inspecting high-throughput PIN data, it was shown recently that, indeed, enzymes involved in successive reactions are generally more likely to interact than other protein pairs. In our study, we expanded this line of research to include comparisons of the underlying respective network topologies as well as to investigate whether the spatial organization of enzyme interactions correlates with metabolic efficiency. Results: Analyzing yeast data, we detected long-range correlations between shortest paths between proteins in both network types suggesting a mutual correspondence of both network architectures. We discovered that the organizing principles of physical interactions between metabolic enzymes differ from the general PIN of all proteins. While physical interactions between proteins are generally dissortative, enzyme interactions were observed to be assortative. Thus, enzymes frequently interact with other enzymes of similar rather than different degree. Enzymes carrying high flux loads are more likely to physically interact than enzymes with lower metabolic throughput. In particular, enzymes associated with catabolic pathways as well as enzymes involved in the biosynthesis of complex molecules were found to exhibit high degrees of physical clustering. Single proteins were identified that connect major components of the cellular metabolism and may thus be essential for the structural integrity of several biosynthetic systems. Conclusion: Our results reveal topological equivalences between the protein interaction network and the metabolic pathway network. Evolved protein interactions may contribute significantly towards increasing the efficiency of metabolic processes by permitting higher metabolic fluxes. Thus, our results shed further light on the unifying principles shaping the evolution of both the functional (metabolic) as well as the physical interaction network

Cyanobacterial lipopolysaccharides and human health – a review

Cyanobacterial lipopolysaccharide/s (LPS) are frequently cited in the cyanobacteria literature as toxins responsible for a variety of heath effects in humans, from skin rashes to gastrointestinal, respiratory and allergic reactions. The attribution of toxic properties to cyanobacterial LPS dates from the 1970s, when it was thought that lipid A, the toxic moiety of LPS, was structurally and functionally conserved across all Gram-negative bacteria. However, more recent research has shown that this is not the case, and lipid A structures are now known to be very different, expressing properties ranging from LPS agonists, through weak endotoxicity to LPS antagonists. Although cyanobacterial LPS is widely cited as a putative toxin, most of the small number of formal research reports describe cyanobacterial LPS as weakly toxic compared to LPS from the Enterobacteriaceae. We systematically reviewed the literature on cyanobacterial LPS, and also examined the much lager body of literature relating to heterotrophic bacterial LPS and the atypical lipid A structures of some photosynthetic bacteria. While the literature on the biological activity of heterotrophic bacterial LPS is overwhelmingly large and therefore difficult to review for the purposes of exclusion, we were unable to find a convincing body of evidence to suggest that heterotrophic bacterial LPS, in the absence of other virulence factors, is responsible for acute gastrointestinal, dermatological or allergic reactions via natural exposure routes in humans. There is a danger that initial speculation about cyanobacterial LPS may evolve into orthodoxy without basis in research findings. No cyanobacterial lipid A structures have been described and published to date, so a recommendation is made that cyanobacteriologists should not continue to attribute such a diverse range of clinical symptoms to cyanobacterial LPS without research confirmation

Distance sets, orthogonal projections, and passing to weak tangents

The author is supported by a Leverhulme Trust Research Fellowship (RF-2016-500).We consider the Assouad dimension analogues of two important problems in geometric measure theory. These problems are tied together by the common theme of ‘passing to weak tangents’. First, we solve the analogue of Falconer’s distance set problem for Assouad dimension in the plane: if a planar set has Assouad dimension greater than 1, then its distance set has Assouad dimension 1. We also obtain partial results in higher dimensions. Second, we consider how Assouad dimension behaves under orthogonal projection. We extend the planar projection theorem of Fraser and Orponen to higher dimensions, provide estimates on the (Hausdorff) dimension of the exceptional set of projections, and provide a recipe for obtaining results about restricted families of projections. We provide several illustrative examples throughout.PostprintPeer reviewe

Comparative analyses imply that the enigmatic sigma factor 54 is a central controller of the bacterial exterior

Contains fulltext : 95738.pdf (publisher's version ) (Open Access)BACKGROUND: Sigma-54 is a central regulator in many pathogenic bacteria and has been linked to a multitude of cellular processes like nitrogen assimilation and important functional traits such as motility, virulence, and biofilm formation. Until now it has remained obscure whether these phenomena and the control by Sigma-54 share an underlying theme. RESULTS: We have uncovered the commonality by performing a range of comparative genome analyses. A) The presence of Sigma-54 and its associated activators was determined for all sequenced prokaryotes. We observed a phylum-dependent distribution that is suggestive of an evolutionary relationship between Sigma-54 and lipopolysaccharide and flagellar biosynthesis. B) All Sigma-54 activators were identified and annotated. The relation with phosphotransfer-mediated signaling (TCS and PTS) and the transport and assimilation of carboxylates and nitrogen containing metabolites was substantiated. C) The function annotations, that were represented within the genomic context of all genes encoding Sigma-54, its activators and its promoters, were analyzed for intra-phylum representation and inter-phylum conservation. Promoters were localized using a straightforward scoring strategy that was formulated to identify similar motifs. We found clear highly-represented and conserved genetic associations with genes that concern the transport and biosynthesis of the metabolic intermediates of exopolysaccharides, flagella, lipids, lipopolysaccharides, lipoproteins and peptidoglycan. CONCLUSION: Our analyses directly implicate Sigma-54 as a central player in the control over the processes that involve the physical interaction of an organism with its environment like in the colonization of a host (virulence) or the formation of biofilm