A note on the component structure in random intersection graphs with tunable clustering

We study the component structure in random intersection graphs with tunable clustering, and show that the average degree works as a threshold for a phase transition for the size of the largest component. That is, if the expected degree is less than one, the size of the largest component is a.a.s. of logarithmic order, but if the average degree is greater than one, a.a.s. a single large component of linear order emerges, and the size of the second largest component is at most of logarithmic order.Comment: 8 pages, Published at http://www.combinatorics.org/Volume_15/PDF/v15i1n10.pdf by the Electronic Journal of Combinatorics (http://www.combinatorics.org

A Discussion of Discrimination and Fairness in Insurance Pricing

Indirect discrimination is an issue of major concern in algorithmic models. This is particularly the case in insurance pricing where protected policyholder characteristics are not allowed to be used for insurance pricing. Simply disregarding protected policyholder information is not an appropriate solution because this still allows for the possibility of inferring the protected characteristics from the non-protected ones. This leads to so-called proxy or indirect discrimination. Though proxy discrimination is qualitatively different from the group fairness concepts in machine learning, these group fairness concepts are proposed to 'smooth out' the impact of protected characteristics in the calculation of insurance prices. The purpose of this note is to share some thoughts about group fairness concepts in the light of insurance pricing and to discuss their implications. We present a statistical model that is free of proxy discrimination, thus, unproblematic from an insurance pricing point of view. However, we find that the canonical price in this statistical model does not satisfy any of the three most popular group fairness axioms. This seems puzzling and we welcome feedback on our example and on the usefulness of these group fairness axioms for non-discriminatory insurance pricing.Comment: 14 page

Effects of a male meiotic driver on male and female transcriptomes in the house mouse

Not all genetic loci follow Mendel's rules, and the evolutionary consequences of this are not yet fully known. Genomic conflict involving multiple loci is a likely outcome, as restoration of Mendelian inheritance patterns will be selected for, and sexual conflict may also arise when sexes are differentially affected. Here, we investigate effects of the t haplotype, an autosomal male meiotic driver in house mice, on genome-wide gene expression patterns in males and females. We analysed gonads, liver and brain in adult same-sex sibling pairs differing in genotype, allowing us to identify t-associated differences in gene regulation. In testes, only 40% of differentially expressed genes mapped to the approximately 708 annotated genes comprising the t haplotype. Thus, much of the activity of the t haplotype occurs in trans, and as upregulation. Sperm maturation functions were enriched among both cis and trans acting t haplotype genes. Within the t haplotype, we observed more downregulation and differential exon usage. In ovaries, liver and brain, the majority of expression differences mapped to the t haplotype, and were largely independent of the differences seen in the testis. Overall, we found widespread transcriptional effects of this male meiotic driver in the house mouse genome

Structural Encoding of Static Single Assignment Form

AbstractStatic Single Assignment (SSA) form is often used as an intermediate representation during code optimization in Java Virtual Machines. Recently, SSA has successfully been used for bytecode verification. However, constructing SSA at the code consumer is costly. SSA-based mobile code transport formats have been shown to eliminate this cost by shifting SSA creation to the code producer. These new formats, however, are not backward compatible with the established Java class-file format. We propose a novel approach to transport SSA information implicitly through structural code properties of standard Java bytecode. While the resulting bytecode sequence can still be directly executed by traditional Virtual Machines, our novel VM can infer SSA form and confirm its safety with virtually no overhead

Fairness: plurality, causality, and insurability

This article summarizes the main topics, findings, and avenues for future work from the workshop Fairness with a view towards insurance held August 2023 in Copenhagen, Denmark

The baculum affects paternity success of first but not second males in house mouse sperm competition

The vast variation observed in genital morphology is a longstanding puzzle in evolutionary biology. Studies showing that the morphology of the mammalian baculum (penis bone) can covary with a male’s paternity success indicate a potential impact of baculum morphology on male fitness, likely through influencing sperm competition outcomes. We therefore measured the size (measurements of length and width) and shape (geometric morphometric measurements) of the bacula of male house mice used in previously published sperm competition experiments, in which two males mated successively with the same female in staged matings. This enabled us to correlate baculum morphology with sperm competition success, incorporating potential explanatory variables related to copulatory plugs, male mating behavior and a selfish genetic element that influences sperm motility. We found that a wider baculum shaft increased a male’s paternity share when mating first, but not when mating second with a multiply-mating female. Geometric morphometric shape measurements were not clearly associated with fertilization success for either male. We found limited evidence that the effect of baculum morphology on male fertilization success was altered by experimental removal of the copulatory plug. Furthermore, neither genetic differences in sperm motility, nor covariation with male mating behavior mediated the effect of baculum morphology on male fertilization success. Taken together with previous findings, the mating-order effects we found here suggest that baculum-mediated stimulation by the first male might be particularly important for fertilization