A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors

Benchmarking of Whole Exome Sequencing and Ad Hoc Designed Panels for Genetic Testing of Hereditary Cancer

Next generation sequencing panels have been developed for hereditary cancer, although there is some debate about their cost-effectiveness compared to exome sequencing. The performance of two panels is compared to exome sequencing. Twenty-four patients were selected: ten with identified mutations (control set) and fourteen suspicious of hereditary cancer but with no mutation (discovery set). TruSight Cancer (94 genes) and a custom panel (122 genes) were assessed alongside exome sequencing. Eightythree genes were targeted by the two panels and exome sequencing. More than 99% of bases had a read depth of over 30x in the panels, whereas exome sequencing covered 94%. Variant calling with standard settings identified the 10 mutations in the control set, with the exception of MSH6 c.255dupC using TruSight Cancer. In the discovery set, 240 unique non-silent coding and canonic splice-site variants were identified in the panel genes, 7 of them putatively pathogenic (in ATM, BARD1, CHEK2, ERCC3, FANCL, FANCM, MSH2). The three approaches identified a similar number of variants in the shared genes. Exomes were more expensive than panels but provided additional data. In terms of cost and depth, panels are a suitable option for genetic diagnostics, although exomes also identify variants in non-targeted genes

Tail probabilities of St. Petersburg sums, trimmed sums, and their limit

We provide exact asymptotics for the tail probabilities $\mathbb{P} \{S_{n,r} > x\}$ as $x \to \infty$, for fix $n$, where $S_{n,r}$ is the $r$-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that although the St. Petersburg distribution is only O-subexponential, the subexponential property almost holds. We also determine the exact tail behavior of the $r$-trimmed limits.Comment: 24 pages, 2 figure

A whole-genome sequence and transcriptome perspective on HER2-positive breast cancers

HER2-positive breast cancer has long proven to be a clinically distinct class of breast cancers for which several targeted therapies are now available. However, resistance to the treatment associated with specific gene expressions or mutations has been observed, revealing the underlying diversity of these cancers. Therefore, understanding the full extent of the HER2-positive disease heterogeneity still remains challenging. Here we carry out an in-depth genomic characterization of 64 HER2-positive breast tumour genomes that exhibit four subgroups, based on the expression data, with distinctive genomic features in terms of somatic mutations, copy-number changes or structural variations. The results suggest that, despite being clinically defined by a specific gene amplification, HER2-positive tumours melt into the whole luminal-basal breast cancer spectrum rather than standing apart. The results also lead to a refined ERBB2 amplicon of 106 kb and show that several cases of amplifications are compatible with a breakage-fusion-bridge mechanism

Transcriptome characterization by RNA sequencing identifies a major molecular and clinical subdivision in chronic lymphocytic leukemia

Chronic lymphocytic leukemia (CLL) has heterogeneous clinical and biological behavior. Whole-genome and -exome sequencing has contributed to the characterization of the mutational spectrum of the disease, but the underlying transcriptional profile is still poorly understood. We have performed deep RNA sequencing in different subpopulations of normal B-lymphocytes and CLL cells from a cohort of 98 patients, and characterized the CLL transcriptional landscape with unprecedented resolution. We detected thousands of transcriptional elements differentially expressed between the CLL and normal B cells, including protein-coding genes, noncoding RNAs, and pseudogenes. Transposable elements are globally derepressed in CLL cells. In addition, two thousand genes-most of which are not differentially expressed-exhibit CLL-specific splicing patterns. Genes involved in metabolic pathways showed higher expression in CLL, while genes related to spliceosome, proteasome, and ribosome were among the most down-regulated in CLL. Clustering of the CLL samples according to RNA-seq derived gene expression levels unveiled two robust molecular subgroups, C1 and C2. C1/C2 subgroups and the mutational status of the immunoglobulin heavy variable (IGHV) region were the only independent variables in predicting time to treatment in a multivariate analysis with main clinico-biological features. This subdivision was validated in an independent cohort of patients monitored through DNA microarrays. Further analysis shows that B-cell receptor (BCR) activation in the microenvironment of the lymph node may be at the origin of the C1/C2 differences

Symposium on the Scottish labour market

In the post-war period, up to the late 1960s, Britain enjoyed a modicum of unemployment and government policies which were geared to producing Full Employment were considered a success. It was simple - boost demand and more people would find work. But the mid 1970s the economic regency enjoyed by those advocating demand sided policies fell into disrepute as the OPEC nations raised prices dramatically and brought in a new era of both rising prices and unemployment. The laws of economics, which previously had viewed policy decisions as the choice between lower unemployment and higher inflation were now redundant. Both unemployment and inflation were moving in the same direction. The era of stagflation had begun

Genomic adaptations to aquatic and aerial life in mayflies and the origin of insect wings

The evolution of winged insects revolutionized terrestrial ecosystems and led to the largest animal radiation on Earth. However, we still have an incomplete picture of the genomic changes that underlay this diversification. Mayflies, as one of the sister groups of all other winged insects, are key to understanding this radiation. Here, we describe the genome of the mayfly Cloeon dipterum and its gene expression throughout its aquatic and aerial life cycle and specific organs. We discover an expansion of odorant-binding-protein genes, some expressed specifically in breathing gills of aquatic nymphs, suggesting a novel sensory role for this organ. In contrast, flying adults use an enlarged opsin set in a sexually dimorphic manner, with some expressed only in males. Finally, we identify a set of wing-associated genes deeply conserved in the pterygote insects and find transcriptomic similarities between gills and wings, suggesting a common genetic program. Globally, this comprehensive genomic and transcriptomic study uncovers the genetic basis of key evolutionary adaptations in mayflies and winged insects

Extreme genomic erosion after recurrent demographic bottlenecks in the highly endangered Iberian lynx

Background: Genomic studies of endangered species provide insights into their evolution and demographic history, reveal patterns of genomic erosion that might limit their viability, and offer tools for their effective conservation. The Iberian lynx (Lynx pardinus) is the most endangered felid and a unique example of a species on the brink of extinction. Results: We generate the first annotated draft of the Iberian lynx genome and carry out genome-based analyses of lynx demography, evolution, and population genetics. We identify a series of severe population bottlenecks in the history of the Iberian lynx that predate its known demographic decline during the 20th century and have greatly impacted its genome evolution. We observe drastically reduced rates of weak-to-strong substitutions associated with GC-biased gene conversion and increased rates of fixation of transposable elements. We also find multiple signatures of genetic erosion in the two remnant Iberian lynx populations, including a high frequency of potentially deleterious variants and substitutions, as well as the lowest genome-wide genetic diversity reported so far in any species. Conclusions: The genomic features observed in the Iberian lynx genome may hamper short- and long-term viability through reduced fitness and adaptive potential. The knowledge and resources developed in this study will boost the research on felid evolution and conservation genomics and will benefit the ongoing conservation and management of this emblematic species

Intercrops of grass with legumes as green manure for agroecological systems.

The stud article aimed to assess the accumulation and rates of nutrients in the biomass of the consortium of millet and leguminous plants for green fertilisation. The treatments were consortia of millet with four different leguminous plants: Cajanus cajan, Canavalia ensiformis, Mucuna aterrima, and Dolichos lablab. The treatments were distributed in a completely randomised design with four replications. The species of each consortium were planted in a line, at a distance of one metre apart. The aerial part of the plants was harvested after 90 days to determine the botanical composition, intercropping biomass, and the amount and accumulation of macronutrients in the biomass. The Millet mass did not differ among the consortia. However, among the legumes, M. aterrima has the highest mass (2806.31 kg/ha DM), which is reflected in the lower ratio of leguminous grasses in the millet consortium with M. aterrima (4.61). The consortia affected the rate and accumulation of P, B, and Fe. The biomass of the millet consortium with C. cajan presented the lowest rate. In addition, the accumulation of K, Mg, and Zn was low in this consortium. The biomass of millet intercrops with M. aterrima, D. lablab and C. ensiformis showed higher accumulations of K, Ca, and Mg. The highest accumulation of N was observed in the biomass of the consortium with M. aterrima (50.71 kg/ha). The rates and accumulations of Cu and Zn were higher in the consortium with M. aterrima. The consortium of millet with the leguminous plants is a sustainable alternative for fertilisation. The consortia with M. aterrima and D. lablab are the most promising ones, due to the higher proportion of plants