Open sets satisfying systems of congruences

A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A,B,C such that A is congruent to B (i.e., there is an isometry of the sphere which sends A to B), B is congruent to C, and A is congruent to (B union C); this result was the precursor of the Banach-Tarski paradox. Later, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the (entire) sphere with rotations witnessing the congruences. The pieces involved were nonmeasurable. In the present paper, we consider the problem of which systems of congruences can be satisfied using open subsets of the sphere (or related spaces); of course, these open sets cannot form a partition of the sphere, but they can be required to cover "most of" the sphere in the sense that their union is dense. Various versions of the problem arise, depending on whether one uses all isometries of the sphere or restricts oneself to a free group of rotations (the latter version generalizes to many other suitable spaces), or whether one omits the requirement that the open sets have dense union, and so on. While some cases of these problems are solved by simple geometrical dissections, others involve complicated iterative constructions and/or results from the theory of free groups. Many interesting questions remain open.Comment: 44 page

Peptidomic and glycomic profiling of commercial dairy products: identification, quantification and potential bioactivities.

Peptidomics and glycomics are recently established disciplines enabling researchers to characterize functional characteristics of foods at a molecular level. Milk-derived bioactive peptides and oligosaccharides have garnered both scientific and commercial interest because they possess unique functional properties, such as anti-hypertensive, immunomodulatory and prebiotic activities; therefore, the objective of this work was to employ peptidomic and glycomic tools to identify and measure relative and absolute quantities of peptides and oligosaccharides in widely consumed dairy products. Specifically, we identified up to 2117 unique peptides in 10 commercial dairy products, which together represent the most comprehensive peptidomic profiling of dairy milk in the literature to date. The quantity of peptides, measured by ion-exchange chromatography, varied between 60 and 130 mg/L among the same set of dairy products, which the majority originated from caseins, and the remaining from whey proteins. A recently published bioactive peptide database was used to identify 66 unique bioactive peptides in the dataset. In addition, 24 unique oligosaccharide compositions were identified in all the samples by nano LC Chip QTOF. Neutral oligosaccharides were the most abundant class in all samples (66-91.3%), followed by acidic (8.6-33.7%), and fucosylated oligosaccharides (0-4.6%). Variation of total oligosaccharide concentration ranged from a high of 65.78 to a low of 24.82 mg/L. Importantly, characterizing bioactive peptides and oligosaccharides in a wider number of dairy products may lead to innovations that go beyond the traditional vision of dairy components used for nutritional purposes but that will rather focus on improving human health

Responses of plant species diversity and soil physical-chemical-microbial properties to Phragmites australis invasion along a density gradient

Abstract The invasion of ecosystems by strongly colonising plants such as Phragmites australis is viewed as one of the greatest threats to plant diversity and soil properties. This study compared a range of diversity measures including soil properties and mycorrhizal potential under different degrees of Phragmites density among three populations in coastal wetland, Victoria, Australia. Species richness, evenness and Shanon-Wiener index had significantly higher values in low degree of Phragmites density in all populations. Higher densities had the lowest diversity, with Shannon-Wiener index = 0 and Simpson’s index = 1 indicating its mono-specificity. Significant alterations in soil properties associated with different degrees of Phragmites density were noticed. These had interactive effects (population × density) on water content, dehydrogenase activity, microbial biomass (C, N and P) but not on pH, electrical conductivity, phenolics, organic carbon, and spore density. Furthermore, the study elucidated decrease of competitive abilities of native plants, by interfering with formation of mycorrhizal associations and biomass. Overall, our results suggest that significant ecological alterations in vegetation and soil variables (including mycorrhizal potential) were strongly dependent on Phragmites density. Such changes may lead to an important role in process of Phragmites invasion through disruption of functional relationships amongst those variables

Smooth Sailing or Stormy Seas? Atlantic Canadian Physical Educators on the State and Future of Physical Education

This article summarizes results from a recently completed study that focused upon the current state and possible future of physical education within Canada’s four Atlantic provinces. Data from both large-scale surveys and eight follow-up focus group interviews are shared as they relate to the state and future of physical education, possible reforms in physical education, and two elements of NASPE’s PE2020 framework (physical education teacher education [PETE], curriculum). Results suggest physical educators within Atlantic Canada are largely satisfied with the state of physical education, with few (external) negative observations. Moreover, there is little-to-no perceived need for internal reform within the discipline. Physical educators also provided insightful informationrelated to their beliefs and practices regarding PETE and curriculum. Results might be of particular interest to those similarly engaged in “futures” inquiry within physical education. More specifically, this research attends to the call for physical educator-informed reform efforts

A genome-wide association study reveals specific transferases as candidate loci for bovine milk oligosaccharides synthesis.

BackgroundHuman milk oligosaccharides (OS) play a key role in brain and gut microbiota development of the neonate, but the underlying biosynthetic steps of OS in the mammary gland are still largely unknown. As bovine milk contains OS with somewhat similar structures and functionalities there is increased interest in further understanding the genetic basis underlying the OS content of milk for eventual extraction and generation of value-added ingredients for infant formulas and nutraceuticals. The present study is the first to report on genetic parameter estimation as well as on a genome wide association study (GWAS) from the largest bovine milk OS dataset analyzed to date.ResultsIn total 15 different bovine milk OS were monitored. Heritabilities ranged from 0 to 0.68 in Danish Holstein and from 0 to 0.92 in Danish Jersey. The GWAS identified in total 1770 SNPs (FDR < 0.10) for five different OS in Danish Holstein and 6913 SNPs (FDR < 0.10) for 11 OS in Danish Jersey. In Danish Holstein, a major overlapping QTL was identified on BTA1 for LNH and LNT explaining 24% of the variation in these OS. The most significant SNPs were associated with B3GNT5, a gene encoding a glycosyltransferase involved in glycan synthesis. In Danish Jersey, a very strong QTL was detected for the OS with composition 2 Hex 1 HexNAc (isomer 1) on BTA11. The most significant SNP had -log10(P-value) of 52.88 (BOVINEHD1100030300) and was assigned to ABO, a gene encoding ABO blood group glycosyltransferases. This SNP has been reported to be a missense mutation and explains 56% of the OS variation. Other candidate genes of interest identified for milk OS were ALG3, B3GALNT2, LOC520336, PIGV, MAN1C1, ST6GALNAC6, GLT6D1, GALNT14, GALNT17, COLGALT2, LFNG and SIGLEC.ConclusionTo our knowledge, this is the first study documenting a solid breeding potential for bovine milk OS and a strong indication of specific candidate genes related to OS synthesis underlying this genetic influence. This new information has the potential to guide breeding strategies to achieve production of milk with higher diversity and concentration of OS and ultimately facilitate large-scale extraction of bovine milk OS

Profiling of aminoxyTMT-labeled bovine milk oligosaccharides reveals substantial variation in oligosaccharide abundance between dairy cattle breeds.

Free milk oligosaccharides are bioactive molecules that function as prebiotics and prevent infections that commonly afflict developing infants. To date, few publications have examined the factors affecting bovine milk oligosaccharide production among cattle in the dairy industry. Here we have applied a high-throughput isobaric labeling technique to measure oligosaccharide abundances in milk collected from Danish Holstein-Friesian and Jersey dairy cattle by liquid chromatography-mass spectrometry. With a total of 634 milk samples, this collection represents the largest sample set used for milk oligosaccharide profiling in the current literature. This study is also the first to use isobaric labeling for the purpose of measuring free oligosaccharides in a real sample set. We have identified 13 oligosaccharides that vary significantly by breed, with most structures being more abundant in the milk of Jersey cattle. The abundances of several oligosaccharides were increased in second-parity cows, and correlations between the abundances of oligosaccharide pairs were identified, potentially indicating similarities in their synthetic pathways. Fucosylated oligosaccharide structures were widely identified among both breeds. Improving our understanding of oligosaccharide production will aid in developing strategies to recover these compounds from processing streams and may enable their use as a functional ingredient in foods for infants and adults

An anatomy of change : profiling cohort difference in beliefs and attitudes among Anglicans in England

Conservatism in theological belief, moral values and attitude toward ecclesiastical practices was measured in a sample of 5967 ordained and lay Anglicans in the Church of England. Average scores were compared between those who classed themselves as Anglo-catholic, broad church or evangelical, and by six different age cohorts. Overall, most measures of conservatism showed decline among more recent cohorts, but there were marked differences between traditions. Younger evangelicals showed little or no decline in theological or moral conservatism, and, in the case of Bible beliefs, were more conservative than their older counterparts. In ecclesiastical variables, however, Anglo-catholics were often more conservative and younger evangelicals showed less conservatism than other traditions or older evangelicals. The findings suggest that the divide between traditions is increasing among younger generations mainly because those in Anglo-catholic and broad-church traditions are becoming more liberal on theological or moral matters, whereas evangelicals are maintaining traditional conservative views of theology and morality but becoming less traditional in matters ecclesiastical