Lexicographic cones and the ordered projective tensor product

We introduce lexicographic cones, a method of assigning an ordered vector space \Lex(S) to a poset $S$, generalising the standard lexicographic cone. These lexicographic cones are then used to prove that the projective tensor cone of two arbitrary cones is a cone, and to find a new characterisation of finite-dimensional vector lattices.Comment: 8 page

Interpolation and harmonic majorants in big Hardy-Orlicz spaces

Free interpolation in Hardy spaces is caracterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces $H^p$, $p>0$. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class). Since the Smirnov class can be regarded as the union over all Hardy-Orlicz spaces associated with a so-called strongly convex function, it is natural to ask how the condition changes from the Carleson condition in classical Hardy spaces to harmonic majorants in the Smirnov class. The aim of this paper is to narrow down this gap from the Smirnov class to ``big'' Hardy-Orlicz spaces. More precisely, we characterize interpolating sequences for a class of Hardy-Orlicz spaces that carry an algebraic structure and that are strictly bigger than $\bigcup_{p>0} H^p$. It turns out that the interpolating sequences are again characterized by the existence of quasi-bounded majorants, but now the weights of the majorants have to be in suitable Orlicz spaces. The existence of harmonic majorants in such Orlicz spaces will also be discussed in the general situation. We finish the paper with an example of a separated Blaschke sequence that is interpolating for certain Hardy-Orlicz spaces without being interpolating for slightly smaller ones.Comment: 19 pages, 2 figure

Price of anarchy on heterogeneous traffic-flow networks

The efficiency of routing traffic through a network, comprising nodes connected by links whose cost of traversal is either fixed or varies in proportion to volume of usage, can be measured by the `price of anarchy'. This is the ratio of the cost incurred by agents who act to minimise their individual expenditure to the optimal cost borne by the entire system. As the total traffic load and the network variability - parameterised by the proportion of variable-cost links in the network - changes, the behaviours that the system presents can be understood with the introduction of a network of simpler structure. This is constructed from classes of non-overlapping paths connecting source to destination nodes that are characterised by the number of variable-cost edges they contain. It is shown that localised peaks in the price of anarchy occur at critical traffic volumes at which it becomes beneficial to exploit ostensibly more expensive paths as the network becomes more congested. Simulation results verifying these findings are presented for the variation of the price of anarchy with the network's size, aspect-ratio, variability and traffic load

Identification of potential non-invasive biomarkers in diastrophic dysplasia.

Diastrophic dysplasia (DTD) is a recessive chondrodysplasia caused by pathogenic variants in the SLC26A2 gene encoding for a cell membrane sulfate/chloride antiporter crucial for sulfate uptake and glycosaminoglycan (GAG) sulfation. Research on a DTD animal model has suggested possible pharmacological treatment approaches. In view of future clinical trials, the identification of non-invasive biomarkers is crucial to assess the efficacy of treatments. Urinary GAG composition has been analyzed in several metabolic disorders including mucopolysaccharidoses. Moreover, the N-terminal fragment of collagen X, known as collagen X marker (CXM), is considered a real-time marker of endochondral ossification and growth velocity and was studied in individuals with achondroplasia and osteogenesis imperfecta. In this work, urinary GAG sulfation and blood CXM levels were investigated as potential biomarkers for individuals affected by DTD. Chondroitin sulfate disaccharide analysis was performed on GAGs isolated from urine by HPLC after GAG digestion with chondroitinase ABC and ACII, while CXM was assessed in dried blood spots. Results from DTD patients were compared with an age-matched control population. Undersulfation of urinary GAGs was observed in DTD patients with some relationship to the clinical severity and underlying SLC26A2 variants. Lower than normal CXM levels were observed in most patients, even if the marker did not show a clear pattern in our small patient cohort because CXM values are highly dependent on age, gender and growth velocity. In summary, both non-invasive biomarkers are promising assays targeting various aspects of the disorder including overall metabolism of sulfated GAGs and endochondral ossification

Zircon ages in granulite facies rocks: decoupling from geochemistry above 850 °C?

Granulite facies rocks frequently show a large spread in their zircon ages, the interpretation of which raises questions: Has the isotopic system been disturbed? By what process(es) and conditions did the alteration occur? Can the dates be regarded as real ages, reflecting several growth episodes? Furthermore, under some circumstances of (ultra-)high-temperature metamorphism, decoupling of zircon U–Pb dates from their trace element geochemistry has been reported. Understanding these processes is crucial to help interpret such dates in the context of the P–T history. Our study presents evidence for decoupling in zircon from the highest grade metapelites (> 850 °C) taken along a continuous high-temperature metamorphic field gradient in the Ivrea Zone (NW Italy). These rocks represent a well-characterised segment of Permian lower continental crust with a protracted high-temperature history. Cathodoluminescence images reveal that zircons in the mid-amphibolite facies preserve mainly detrital cores with narrow overgrowths. In the upper amphibolite and granulite facies, preserved detrital cores decrease and metamorphic zircon increases in quantity. Across all samples we document a sequence of four rim generations based on textures. U–Pb dates, Th/U ratios and Ti-in-zircon concentrations show an essentially continuous evolution with increasing metamorphic grade, except in the samples from the granulite facies, which display significant scatter in age and chemistry. We associate the observed decoupling of zircon systematics in high-grade non-metamict zircon with disturbance processes related to differences in behaviour of non-formula elements (i.e. Pb, Th, U, Ti) at high-temperature conditions, notably differences in compatibility within the crystal structure

The impact of urea-induced unfolding on the redox process of immobilised cytochrome c

We have studied the effect of urea-induced unfolding on the electron transfer process of yeast iso-1-cytochrome c and its mutant K72AK73AK79A adsorbed on electrodes coated by mixed 11-mercapto-1-undecanoic acid/11-mercapto-1-undecanol self-assembled monolayers. Electrochemical measurements, complemented by surface enhanced resonance Raman studies, indicate two distinct states of the adsorbed proteins that mainly differ with respect to the ligation pattern of the haem. The native state, in which the haem is axially coordinated by Met80 and His18, displays a reduction potential that slightly shifts to negative values with increasing urea concentration. At urea concentrations higher than 6 M, a second state prevails in which the Met80 ligand is replaced by an additional histidine residue. This structural change in the haem pocket is associated with an approximately 0.4 V shift of the reduction potential to negative values. These two states were found for both the wild-type protein and the mutant in which lysine residues 72, 73 and 79 had been substituted by alanines. The analysis of the reduction potentials, the reaction enthalpies and entropies as well as the rate constants indicates that these three lysine residues have an important effect on stabilising the protein structure in the adsorbed state and facilitating the electron transfer dynamics

Early Childhood Caries among a Bedouin community residing in the eastern outskirts of Jerusalem

<p>Abstract</p> <p>Background</p> <p>ECC is commonly prevalent among underprivileged populations. The Jahalin Bedouin are a severely deprived, previously nomadic tribe, dwelling on the eastern outskirts of Jerusalem. The aim of this study was to assess ECC prevalence and potentially associated variables.</p> <p>Methods</p> <p>102 children aged 12–36 months were visually examined for caries, mothers' anterior dentition was visually subjectively appraised, demographic and health behavior data were collected by interview.</p> <p>Results</p> <p>Among children, 17.6% demonstrated ECC, among mothers, 37.3% revealed "fairly bad" anterior teeth. Among children drinking bottles there was about twice the level of ECC (20.3%) than those breast-fed (13.2%). ECC was found only among children aged more than one year (p < 0.001); more prevalent ECC (55.6%) was found among large (10–13 children) families than among smaller families (1–5 children: 13.5%, 6–9 children: 15.6%) (p = 0.009); ECC was more prevalent among children of less educated mothers (p = 0.037); ECC was more prevalent among mothers with "fairly poor" anterior dentition (p = 0.04). Oral hygiene practices were poor.</p> <p>Conclusion</p> <p>ECC levels in this community were not very high but neither low. This changing population might be on the verge of a wider dental disease "epidemic". Public health efforts clearly need to be invested towards the oral health and general welfare of this community.</p