Ergodicity and Conservativity of products of infinite transformations and their inverses

We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\times T$ of the transformation with itself is ergodic, but the product $T\times T^{-1}$ of the transformation with its inverse is not ergodic. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.Comment: Added references and revised some arguments; removed old section 6; main results unchange

Causal Estimation of Position Bias in Recommender Systems Using Marketplace Instruments

Information retrieval systems, such as online marketplaces, news feeds, and search engines, are ubiquitous in today's digital society. They facilitate information discovery by ranking retrieved items on predicted relevance, i.e. likelihood of interaction (click, share) between users and items. Typically modeled using past interactions, such rankings have a major drawback: interaction depends on the attention items receive. A highly-relevant item placed outside a user's attention could receive little interaction. This discrepancy between observed interaction and true relevance is termed the position bias. Position bias degrades relevance estimation and when it compounds over time, it can silo users into false relevant items, causing marketplace inefficiencies. Position bias may be identified with randomized experiments, but such an approach can be prohibitive in cost and feasibility. Past research has also suggested propensity score methods, which do not adequately address unobserved confounding; and regression discontinuity designs, which have poor external validity. In this work, we address these concerns by leveraging the abundance of A/B tests in ranking evaluations as instrumental variables. Historical A/B tests allow us to access exogenous variation in rankings without manually introducing them, harming user experience and platform revenue. We demonstrate our methodology in two distinct applications at LinkedIn - feed ads and the People-You-May-Know (PYMK) recommender. The marketplaces comprise users and campaigns on the ads side, and invite senders and recipients on PYMK. By leveraging prior experimentation, we obtain quasi-experimental variation in item rankings that is orthogonal to user relevance. Our method provides robust position effect estimates that handle unobserved confounding well, greater generalizability, and easily extends to other information retrieval systems.Comment: 13 pages, 2 figure

Prevalence and risk factors for sexual assault among class 6 female students in unplanned settlements of Nairobi, Kenya: Baseline analysis from the IMPower & Sources of Strength cluster randomized controlled trial.

BackgroundGender-based violence (GBV) is a crucial global health problem among all age groups, including adolescents. This study describes incidences of GBV, as well as factors associated with sexual assault, among female adolescents in class six living in urban informal settlements in Nairobi, Kenya.MethodsStudy participants were interviewed using a structured survey instrument focusing on experiences of GBV, including emotional, physical, and sexual violence, and corresponding perpetrators, as well as gender attitudes, alcohol use, self-efficacy, and previous sexual experiences. Summary statistics and clustered bootstrap confidence intervals were calculated for social behaviors and violence rates. Stepwise logistic regression identified variables associated with an adolescent's experience of sexual assault.FindingsIn this population 7·2% of adolescent girls reported being raped in the prior twelve months, with 11·1% of these rape victims reporting over five experiences. Among the 21·3% who report having had a boyfriend, 38·1% reported emotional, physical, and/or sexual intimate partner violence (IPV). Boyfriends were identified most often as perpetrators, accounting for 46·3% of reported lifetime rapes. Previous experience of physical (p = InterpretationSexual assault and GBV are major challenges in this highly-disadvantaged population. Novel prevention efforts are needed for this age group, as prevention is often targeted at older adolescents. Prevention efforts should focus on assaults by perpetrators known to adolescents, especially boyfriends, and may need to account for the adolescents' previous experience of, and exposure to, violence

Submitochondrial Distribution of Three Key Steroidogenic Proteins (Steroidogenic Acute Regulatory Protein and Cytochrome P450 scc and 3β-Hydroxysteroid Dehydrogenase Isomerase Enzymes) upon Stimulation by Intracellular Calcium in Adrenal Glomerulosa Cells

International audienceIn adrenal glomerulosa cells, angiotensin II (Ang II) and potassium stimulate aldosterone synthesis through activation of the calcium messenger system. The rate-limiting step in steroidogenesis is the transfer of cholesterol to the inner mitochondrial membrane. This transfer is believed to depend upon the presence of the steroidogenic acute regulatory (StAR) protein. The aim of this study was 1) to examine the effect of changes in cytosolic free calcium concentration and of Ang II on intramitochondrial cholesterol and 2) to study the distribution of StAR protein in submitochondrial fractions during activation by Ca2+ and Ang II. To this end, freshly prepared bovine zona glomerulosa cells were submitted to a high cytosolic Ca2+ clamp (600 nM) or stimulated with Ang II (10 nM) for 2 h. Mitochondria were isolated and subfractionated into outer membranes, inner membranes (IM), and contact sites (CS). Stimulation of intact cells with Ca2+ or Ang II led to a marked, cycloheximide-sensitive increase in cholesterol in CS (to 143 +/- 3. 2 and 151.1 +/- 18.1% of controls, respectively) and in IM (to 119 +/- 5.1 and 124.5 +/- 6.5% of controls, respectively). Western blot analysis revealed a cycloheximide-sensitive increase in StAR protein in mitochondrial extracts of Ca2+-clamped glomerulosa cells (to 159 +/- 23% of controls). In submitochondrial fractions, there was a selective accumulation of StAR protein in IM following stimulation with Ca2+ (228 +/- 50%). Similarly, Ang II increased StAR protein in IM, and this effect was prevented by cycloheximide. In contrast, neither Ca2+ nor Ang II had any effect on the submitochondrial distribution of cytochrome P450scc and 3beta-hydroxysteroid dehydrogenase isomerase. The intramitochondrial presence of the latter enzyme was further confirmed by immunogold staining in rat adrenal fasciculata cells and by immunoblot analysis in MA-10 mouse testicular Leydig cells. These findings demonstrate that under acute stimulation with Ca2+-mobilizing agents, newly synthesized StAR protein accumulates in IM after transiting through CS. Moreover, our results suggest that the import of StAR protein into IM may be associated with cholesterol transfer, thus promoting precursor supply to the two first enzymes of the steroidogenic cascade within the mitochondria and thereby activating mineralocorticoid synthesis