On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang--Baxter equation

Given a finite bijective non-degenerate set-theoretic solution $(X,r)$ of the Yang--Baxter equation we characterize when its structure monoid $M(X,r)$ is Malcev nilpotent. Applying this characterization to solutions coming from racks, we rediscover some results obtained recently by Lebed and Mortier, and by Lebed and Vendramin on the description of finite abelian racks and quandles. We also investigate bijective non-degenerate multipermutation (not necessarily finite) solutions $(X,r)$ and show, for example, that this property is equivalent to the solution associated to the structure monoid $M(X,r)$ (respectively structure group $G(X,r)$) being a multipermuation solution and that $G=G(X,r)$ is solvable of derived length not exceeding the multipermutation level of $(X,r)$ enlarged by one, generalizing results of Gateva-Ivanova and Cameron obtained in the involutive case. Moreover, we also prove that if $X$ is finite and $G=G(X,r)$ is nilpotent, then the torsion part of the group $G$ is finite, it coincides with the commutator subgroup $[G,G]_+$ of the additive structure of the skew left brace $G$ and $G/[G,G]_+$ is a trivial left brace.Comment: 35 page

The significance of Lactobacillus crispatus and L. vaginalis for vaginal health and the negative effect of recent sex: a cross-sectional descriptive study across groups of African women

Background: Women in sub-Saharan Africa are vulnerable to acquiring HIV infection and reproductive tract infections. Bacterial vaginosis (BV), a disruption of the vaginal microbiota, has been shown to be strongly associated with HIV infection. Risk factors related to potentially protective or harmful microbiota species are not known. Methods: We present cross-sectional quantitative polymerase chain reaction data of the Lactobacillus genus, five Lactobacillus species, and three BV-related bacteria (Gardnerella vaginalis, Atopobium vaginae, and Prevotella bivia) together with Escherichia coli and Candida albicans in 426 African women across different groups at risk for HIV. We selected a reference group of adult HIV-negative women at average risk for HIV acquisition and compared species variations in subgroups of adolescents, HIV-negative pregnant women, women engaging in traditional vaginal practices, sex workers and a group of HIV-positive women on combination antiretroviral therapy. We explored the associations between presence and quantity of the bacteria with BV by Nugent score, in relation to several factors of known or theoretical importance. Results: The presence of species across Kenyan, South African and Rwandan women was remarkably similar and few differences were seen between the two groups of reference women in Kenya and South Africa. The Rwandan sex workers and HIV-positive women had the highest Gardnerella vaginalis presence (p = 0.006). Pregnant women had a higher Lactobacillus genus mean log (7.01 genome equivalents (geq)/ml) compared to the reference women (6.08 geq/ml). L. vaginalis (43%) was second to L. iners (81.9%) highly present in women with a normal Nugent score. Recent sexual exposure negatively affected the presence of Lactobacillus crispatus (<0.001), L. vaginalis (p = 0.001), and Lactobacillus genus (p < 0.001). Having more than one sexual partner in the last three months was associated with an increased prevalence of Gardnerella vaginalis (p = 0.044) and L. iners (p = 0.001). Conclusions: Although the composition of species across the studied African countries was similar, the presence of protective species i.e. Lactobacillus crispatus and L. vaginalis in women with a normal Nugent score appeared lower compared to non-African studies. Furthermore, Lactobacillus species were negatively affected by sexual behavioural. Strategies to support protective Lactobacillus species are urgently needed

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

Non-Sexual Transmission of Trichomonas vaginalis in Adolescent Girls Attending School in Ndola, Zambia

OBJECTIVES: To identify risk factors for trichomoniasis among young women in Ndola, Zambia. METHOD: The study was a cross-sectional study among adolescent girls aged 13-16 years in Ndola, Zambia. Study participants were recruited from schools in selected administrative areas that represented the different socio-economic strata in town. Consenting participants were interviewed about their socio-demographic characteristics; sexual behaviour; and hygiene practices. Self-administered vaginal swabs were tested for Trichomonas vaginalis. HSV-2 antibodies were determined on serum to validate the self-reported sexual activity. RESULTS: A total of 460 girls participated in the study. The overall prevalence of trichomoniasis was 27.1%, 33.9% among girls who reported that they had ever had sex and 24.7% among virgins. In multivariate analysis the only statistically significant risk factor for trichomoniasis was inconsistent use of soap. For the virgins, none of the risk factors was significantly associated with trichomoniasis, but the association with use of soap (not always versus always) and type of toilet used (pit latrine/bush versus flush toilet) was of borderline significance. CONCLUSION: We found a high prevalence of trichomoniasis in girls in Ndola who reported that they had never had sex. We postulate that the high prevalence of trichomoniasis in virgins in Ndola is due to non-sexual transmission of trichomoniasis via shared bathing water and inconsistent use of soap

Prevalence and correlates of bacterial vaginosis in different sub-populations of women in Sub-Saharan Africa: a cross-sectional study

Background: Clinical development of vaginally applied products aimed at reducing the transmission of HIV and other sexually transmitted infections, has highlighted the need for a better characterisation of the vaginal environment. We set out to characterise the vaginal environment in women in different settings in sub-Saharan Africa. Methods: A longitudinal study was conducted in Kenya, Rwanda and South-Africa. Women were recruited into pre-defined study groups including adult, non-pregnant, HIV-negative women; pregnant women; adolescent girls; HIV-negative women engaging in vaginal practices; female sex workers; and HIV-positive women. Consenting women were interviewed and underwent a pelvic exam. Samples of vaginal fluid and a blood sample were taken and tested for bacterial vaginosis (BV), HIV and other reproductive tract infections (RTIs). This paper presents the cross-sectional analyses of BV Nugent scores and RTI prevalence and correlates at the screening and the enrolment visit. Results: At the screening visit 38% of women had BV defined as a Nugent score of 7-10, and 64% had more than one RTI (N. gonorrhoea, C. trachomatis, T. vaginalis, syphilis) and/or Candida. At screening the likelihood of BV was lower in women using progestin-only contraception and higher in women with more than one RTI. At enrolment, BV scores were significantly associated with the presence of prostate specific antigen (PSA) in the vaginal fluid and with being a self-acknowledged sex worker. Further, sex workers were more likely to have incident BV by Nugent score at enrolment. Conclusions: Our study confirmed some of the correlates of BV that have been previously reported but the most salient finding was the association between BV and the presence of PSA in the vaginal fluid which is suggestive of recent unprotected sexual intercourse

New Binding Mode to TNF-Alpha Revealed by Ubiquitin-Based Artificial Binding Protein

A variety of approaches have been employed to generate binding proteins from non-antibody scaffolds. Utilizing a beta-sheet of the human ubiquitin for paratope creation we obtained binding proteins against tumor necrosis factor (TNF)-alpha. The bioactive form of this validated pharmacological target protein is a non-covalently linked homo-trimer. This structural feature leads to the observation of a certain heterogeneity concerning the binding mode of TNF-alpha binding molecules, for instance in terms of monomer/trimer specificity. We analyzed a ubiquitin-based TNF-alpha binder, selected by ribosome display, with a particular focus on its mode of interaction. Using enzyme-linked immunosorbent assays, specific binding to TNF-alpha with nanomolar affinity was observed. In isothermal titration calorimetry we obtained comparable results regarding the affinity and detected an exothermic reaction with one ubiquitin-derived binding molecule binding one TNF-alpha trimer. Using NMR spectroscopy and other analytical methods the 1∶3 stoichiometry could be confirmed. Detailed binding analysis showed that the interaction is affected by the detergent Tween-20. Previously, this phenomenon was reported only for one other type of alternative scaffold-derived binding proteins – designed ankyrin repeat proteins – without further investigation. As demonstrated by size exclusion chromatography and NMR spectroscopy, the presence of the detergent increases the association rate significantly. Since the special architecture of TNF-alpha is known to be modulated by detergents, the access to the recognized epitope is indicated to be restricted by conformational transitions within the target protein. Our results suggest that the ubiquitin-derived binding protein targets a new epitope on TNF-alpha, which differs from the epitopes recognized by TNF-alpha neutralizing antibodies