Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

The Status of Dosage Compensation in the Multiple X Chromosomes of the Platypus

Dosage compensation has been thought to be a ubiquitous property of sex chromosomes that are represented differently in males and females. The expression of most X-borne genes is equalized between XX females and XY males in therian mammals (marsupials and “placentals”) by inactivating one X chromosome in female somatic cells. However, compensation seems not to be strictly required to equalize the expression of most Z-borne genes between ZZ male and ZW female birds. Whether dosage compensation operates in the third mammal lineage, the egg-laying monotremes, is of considerable interest, since the platypus has a complex sex chromosome system in which five X and five Y chromosomes share considerable genetic homology with the chicken ZW sex chromosome pair, but not with therian XY chromosomes. The assignment of genes to four platypus X chromosomes allowed us to examine X dosage compensation in this unique species. Quantitative PCR showed a range of compensation, but SNP analysis of several X-borne genes showed that both alleles are transcribed in a heterozygous female. Transcription of 14 BACs representing 19 X-borne genes was examined by RNA-FISH in female and male fibroblasts. An autosomal control gene was expressed from both alleles in nearly all nuclei, and four pseudoautosomal BACs were usually expressed from both alleles in male as well as female nuclei, showing that their Y loci are active. However, nine X-specific BACs were usually transcribed from only one allele. This suggests that while some genes on the platypus X are not dosage compensated, other genes do show some form of compensation via stochastic transcriptional inhibition, perhaps representing an ancestral system that evolved to be more tightly controlled in placental mammals such as human and mouse