The stochastic order of probability measures on ordered metric spaces

The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of probability measures on ordered Banach spaces, we introduce and study a stochastic order on the space of probability measures $\mathcal{P}(X)$, where $X$ is a metric space equipped with a closed partial order, and derive several useful equivalent versions of the definition. We establish the antisymmetry and closedness of the stochastic order (and hence that it is a closed partial order) for the case of a partial order on a Banach space induced by a closed normal cone with interior. We also consider order-completeness of the stochastic order for a cone of a finite-dimensional Banach space and derive a version of the arithmetic-geometric-harmonic mean inequalities in the setting of the associated probability space on positive matrices.Comment: 25 page

Functional enrichment of lineage specific expanding gene families for GO slim terms.

<p>Each cell represents a GO slim term from the biological process, molecular function or cellular component ontology. The positioning of the cells is determined by a term overlap metric so that more similar terms are positioned close together. Cells are shaded if one or more expanding gene family shows enrichment for that term. The intensity of the shading represents the number of gene families showing enrichment for that term. The most intense colour shows 10 families are enriched. Each panel represents a species from the Génolevures data set: <i>Y. lipolytica</i> (A), <i>D. hansenii</i> (B), <i>E. gossypii</i> (C), <i>K. lactis</i> (D), <i>S. kluyveri</i> (E), <i>K. thermotolerans</i> (F), <i>Z. rouxii</i> (G), <i>S. cerevisiae</i> (H) and <i>C. glabrata</i> (I). Lists of enriched terms in expanding families are available in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099480#pone.0099480.s003" target="_blank">File S3</a></p

Lineage specific gene family expansions in the Génolevures data.

<p>Lineage specific gene family expansions in the Génolevures data.</p

The rate of family evolution in the Génolevures data estimated by DupliPHY-ML as the mean posterior rate with gamma-distributed rates across families.

<p>Here a high estimated rate indicates a family that is evolving quickly and has undergone many duplication and loss events in its history. The average rate is 1.</p

The rate of family evolution in the Génolevures data estimated by DupliPHY-ML as the mean posterior rate with gamma-distributed rates across families.

<p>Here a high estimated rate indicates a family that is evolving quickly and has undergone many duplication and loss events in its history. The average rate is 1.</p

The distribution of average family sizes in the Génolevures data.

<p>The distribution of average family sizes in the Génolevures data.</p

Additional file 6 of LinkImputeR: user-guided genotype calling and imputation for non-model organisms

Full cannabis results. (DOCX 13 kb

Additional file 3: Figure S1. of Genomic ancestry estimation quantifies use of wild species in grape breeding

Distance (kb) between filtered SNPs used for ancestry estimation. (PDF 96 kb

Additional file 1: Table S1. of Genomic ancestry estimation quantifies use of wild species in grape breeding

A list of the 78 cultivars used in this study as well as location and institute. Sample information is also provided for the additional 16 samples which were discarded during the genotyping analysis pipeline and they are highlighted in yellow. (XLSX 27 kb

Additional file 2: Table S2. of Genomic ancestry estimation quantifies use of wild species in grape breeding

Matrix of genome-wide average IBS values for 64 hybrids. (XLSX 82 kb