Factorizations of skew braces

We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang-Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of It\^{o}'s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang-Baxter equation. Finally, we classify skew braces that contain no non-trivial proper ideals.Comment: 12 page

Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

A longitudinal analysis of the vaginal microbiota and vaginal immune mediators in women from sub-Saharan Africa

In cross-sectional studies increased vaginal bacterial diversity has been associated with vaginal inflammation which can be detrimental for health. We describe longitudinal changes at 5 visits over 8 weeks in vaginal microbiota and immune mediators in African women. Women (N = 40) with a normal Nugent score at all visits had a stable lactobacilli dominated microbiota with prevailing Lactobacillus iners. Presence of prostate-specific antigen (proxy for recent sex) and being amenorrhoeic (due to progestin-injectable use), but not recent vaginal cleansing, were significantly associated with microbiota diversity and inflammation (controlled for menstrual cycle and other confounders). Women (N = 40) with incident bacterial vaginosis (Nugent 7-10) had significantly lower concentrations of lactobacilli and higher concentrations of Gardnerella vaginalis, Atopobium vaginae, and Prevotella bivia, at the incident visit and when concentrations of proinflammatory cytokines (IL-1β, IL-12p70) were increased and IP-10 and elafin were decreased. A higher 'composite-qPCR vaginal-health-score' was directly associated with decreased concentrations of proinflammatory cytokines (IL-1α, IL-8, IL-12(p70)) and increased IP-10. This longitudinal study confirms the inflammatory nature of vaginal dysbiosis and its association with recent vaginal sex and progestin-injectable use. A potential role for proinflammatory mediators and IP-10 in combination with the vaginal-health-score as predictive biomarkers for vaginal dysbiosis merits further investigation

Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation

We study relations between different notions of nilpotency in the context of skew braces and applications to the structure of solutions to the Yang-Baxter equation. In particular, we consider annihilator nilpotent skew braces, an important class that turns out to be a brace-theoretic analog to the class of nilpotent groups. In this vein, several well-known theorems in group theory are proved in the more general setting of skew braces.Comment: 18 pages. Postprint versio

Factorizations of skew braces

We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals.Fil: Jespers, E.. Vrije Unviversiteit Brussel; BélgicaFil: Kubat, L.. Vrije Unviversiteit Brussel; BélgicaFil: Van Antwerpen, A.. Vrije Unviversiteit Brussel; BélgicaFil: Vendramin, Claudio Leandro. Institute of Mathematical Sciences at NYU Shanghai; China. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Performance of swabs, lavage, and diluents to quantify biomarkers of female genital tract soluble mucosal mediators

Background: Measurement of immune mediators and antimicrobial activity in female genital tract secretions may provide biomarkers predictive of risk for HIV-1 acquisition and surrogate markers of microbicide safety. However, optimal methods for sample collection do not exist. This study compared collection methods. Methods: Secretions were collected from 48 women (24 with bacterial vaginosis [BV]) using vaginal and endocervical Dacron and flocked swabs. Cervicovaginal lavage (CVL) was collected with 10 mL of Normosol-R (n = 20), saline (n = 14), or water (n = 14). The concentration of gluconate in Normosol-R CVL was determined to estimate the dilution factor. Cytokine and antimicrobial mediators were measured by Luminex or ELISA and corrected for protein content. Endogenous anti-HIV-1 and anti-E. coli activity were measured by TZM-bl assay or E. coli growth. Results: Higher concentrations of protein were recovered by CVL, despite a 10-fold dilution of secretions, as compared to swab eluents. After protein correction, endocervical swabs recovered the highest mediator levels regardless of BV status. Endocervical and vaginal flocked swabs recovered significantly higher levels of anti-HIV-1 and anti-E. coli activity than Dacron swabs (P<0.001). BV had a significant effect on CVL mediator recovery. Normosol-R tended to recover higher levels of most mediators among women with BV, whereas saline or water tended to recover higher levels among women without BV. Saline recovered the highest levels of anti-HIV-1 activity regardless of BV status. Conclusions: Endocervical swabs and CVL collected with saline provide the best recovery of most mediators and would be the optimal sampling method(s) for clinical trials. © 2011 Dezzutti et al

Contraceptive rings promote vaginal lactobacilli in a high bacterial vaginosis prevalence population: A randomised, open-label longitudinal study in Rwandan women

Background Hormonal contraception has been associated with a reduced risk of vaginal dysbiosis, which in turn has been associated with reduced prevalence of sexually transmitted infections (STIs), including HIV. Vaginal rings are used or developed as delivery systems for contraceptive hormones and antimicrobial drugs for STI and HIV prevention or treatment. We hypothesized that a contraceptive vaginal ring (CVR) containing oestrogen enhances a lactobacilli-dominated vaginal microbial community despite biomass accumulation on the CVR's surface. Methods We enrolled 120 women for 12 weeks in an open-label NuvaRing® study at Rinda Ubuzima, Kigali, Rwanda. Vaginal and ring microbiota were assessed at baseline and each ring removal visit by Gram stain Nugent scoring (vaginal only), quantitative PCR for Lactobacillus species, Gardnerella vaginalis and Atopobium vaginae, and fluorescent in situ hybridization to visualize cell-adherent bacteria. Ring biomass was measured by crystal violet staining. Results Bacterial vaginosis (BV) prevalence was 48% at baseline. The mean Nugent score decreased significantly with ring use. The presence and mean log10 concentrations of Lactobacillus species in vaginal secretions increased significantly whereas those of G. vaginalis and presence of A. vaginae decreased significantly. Biomass accumulated on the CVRs with a species composition mirroring the vaginal microbiota. This ring biomass composition and optical density after crystal violet staining did not change significantly over time. Conclusions NuvaRing® promoted lactobacilli-dominated vaginal microbial communities in a population with high baseline BV prevalence despite the fact that biomass accumulated on the rings

Toward assay-aware bioactivity model(er)s: getting a grip on biological context

Medicinal Chemistr

Mechanics of cutting manoeuvres by ostriches ('Struthio camelus')

We studied the strategies used by cursorial bipeds (ostriches) to maneuver during running. Eight ostriches were induced to run along a trackway and execute turns. Ground reaction forces and three-dimensional kinematics of the body and leg joints were simultaneously recorded, allowing calculation of joint angles and quasi-static net joint torques. Sidesteps, where the leg on the outside of the turn changes the movement direction, and crossovers using the inside leg, occurred with nearly equal frequency. Ostriches executed maneuvers using a simple control strategy that required minimal changes to leg kinematics or net torque production at individual joints. Although ostriches did use acceleration or braking forces to control body rotation, their morphology allowed for both crossovers and sidesteps to be accomplished with minimal net acceleratory/braking force production. Moreover, body roll and ab/adduction of the leg shifted the foot position away from the turn direction, reducing the acceleratory/braking forces required to prevent under-or over-rotation and aligning the leg with the ground reaction force