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Skew left braces arise naturally from the study of non-degenerate set-theoretic solutions of the Yang–Baxter equation. To understand the algebraic structure of skew left braces, a study of the decomposition into minimal substructures is relevant. We introduce chief series and prove a strengthened form of the Jordan–Hölder theorem for finite skew left braces. A characterization of right nilpotency and an application to multipermutation solutions are also given.

The algebraic structure of skew left brace has proved to be useful as a source of set-theoretic solutions of the Yang–Baxter equation. We study in this paper the connections between left and right $$\pi $$ -nilpotency and the structure of finite skew left braces. We also study factorisations of skew left braces and their impact on the skew left brace structure. As a consequence of our study, we define a Fitting-like ideal of a left brace. Our approach depends strongly on a description of a skew left brace in terms of a triply factorised group obtained from the action of the multiplicative group of the skew left brace on its additive group.

We propose an extension of coherent control using laser-synthesized free-electron matter waves. In contrast to coherent control schemes exploiting optical coherences to steer the dynamics of matter waves, we analyze the opposite and investigate the control of quantum light emission driven by laser-sculpted coherent free-electron matter waves. We apply this concept to the control of entangled photon-pair emission in electron-atom collisions, in which the incident electron wave packet, colliding with a target atom $B$, is engineered by interferometric resonantly-enhanced multiphoton ionization of a parent atom $A$. Each ionization pathway leads to electron wave packets that coherently interfere during temporal evolution in the continuum. Their mutual coherence can be controlled by adjusting the relative phases or time delays of the frequency components of the ionizing field contributing to the interfering pathways. We report coherent control of entangled photon-pair generation in radiative photo-cascade emission upon decay of the target atom after inelastic excitation triggered by the collision with the synthesized electron wave packet., 12 pages, 4 figures

This letter presents the theoretical and experimental analysis of a magnetic field sensor based on the interaction of a conical frustum of magnetostrictive composite with an embedded fiber Bragg grating (FBG) along its axis. The possibility of tailoring a nonuniform-induced strain along the FBG through magnetostriction enables the inference of the magnetic field with both wavelength shift and optical power measurements. Strain coupling interaction and power reflectance of the FBG were modeled and showed a very good agreement with experimental data.

Background & Aims: Hepatocellular carcinoma (HCC) may develop in patients with chronic hepatitis (CHB) even after 5 years of oral therapy and cannot be easily predicted. We assessed predictors of HCC development and the need for HCC surveillance in this setting. Methods: Of 1,951 adult Caucasians with CHB included in the PAGE-B cohort, 1,427 (73%) had completed >5 years of follow-up under therapy without developing HCC by year 5. Median follow-up was 8.4 years from treatment onset. Points-based risk scores were developed to predict HCC risk after year 5. Results: In years 5–12, HCC was diagnosed in 33/1,427 (2.3%) patients with cumulative incidences of 2.4%, 3.2% and 3.8% at 8, 10 and 12 years, respectively. Older age or age >50 years, baseline cirrhosis and liver stiffness (LSM) ≥12 kPa at year 5 were independently associated with increased HCC risk. The HCC incidence was lower in non-cirrhotics than cirrhotics at baseline with year-5 LSM

BACKGROUND Atopic dermatitis is the most common chronic skin disease affecting the pediatric population. Probiotics have been proposed to be effective in preventing the development of pediatric atopic dermatitis. Although studies show promise for the use of probiotics, the evidence is still inconclusive due to significant heterogeneity and imprecision. OBJECTIVE To determine the comparative effectiveness of the different types of probiotic strains in preventing the development of atopic dermatitis among pediatric patients. METHODOLOGY A systematic search of Cochrane Library, MEDLINE, TRIP Database, and Centre for Research and Dissemination was conducted. Manual search of the reference lists and search for unpublished articles were also done. All randomized controlled trials available from inception until April 12, 2020, on the use of probiotics in the prevention of atopic dermatitis among children were included. The comparator groups considered are other probiotic strains and placebo. The primary outcome of interest was the development of atopic dermatitis. Two authors independently searched for articles, screened the articles for inclusion, appraised the articles using the Cochrane risk of bias tool version 2, and extracted the data. In case of disagreement, the two authors discussed the source of disagreement until consensus was reached. If consensus was not reached, an independent third party reviewer was consulted. Frequentist network meta-analysis was conducted using STATA 14 software. The ranking probabilities and surface under the cumulative ranking curve (SUCRA) values were obtained to determine ranking of the different probiotic strains based on efficacy and safety data. RESULTS We included 21 original studies represented by 35 records and a total of 5406 children with atopic dermatitis as diagnosed by clinicians or fulfillment of validated diagnostic criteria. All studies were randomized placebo-controlled trials. The top 3 probiotic preparations in terms of efficacy in reducing the risk of atopic dermatitis are Mix8 (Lactobacillus paracasei ST11, Bifidobacterium longum BL999), LP (Lactobacillus paracasei ssp paracasei F19) and Mix3 (Lactobacillus rhamnosus GG, Bifidobacterium animalis ssp lactis Bb-12). Mix8 compared with placebo probably reduces the risk of atopic dermatitis based on low-quality evidence (RR = 0.46, 95% CI 0.25-0.85). Mix3 compared with placebo also probably reduces the risk of atopic dermatitis based on low-quality evidence (RR = 0.50, 95% CI 0.27-0.94). It is uncertain whether LP compared with placebo reduces the risk of atopic dermatitis due to very-low-quality certainty of evidence (RR = 0.49, 95% CI 0.20-1.19). In terms of adverse events, LGG may slightly lead to less adverse events compared with placebo based on low-quality evidence (RR = 0.70, 95% CI 0.32-1.52). Mix4 may slightly lead to more adverse events compared with placebo based on low-quality evidence (RR = 1.06, 95% CI 0.02-51.88). Based on subgroup analysis of studies involving infants, Mix3 compared with placebo probably reduces the risk of atopic dermatitis based on low-quality evidence (RR = 0.46, 95% CI 0.22-0.97). In the subgroup analysis of studies where probiotics were administered to pregnant women and to infants, LRH compared with placebo probably reduces the risk of atopic dermatitis based on moderate-quality evidence (RR = 0.54, 95% CI 0.26-1.11). CONCLUSION Certain probiotic preparations demonstrate efficacy in reducing the risk of developing atopic dermatitis when administered to pregnant women, infants, or both.

A subgroup X of a group G is said to satisfy the weak subnormalizer condition if $$N_G(Y)\le N_G(X)$$ for each non-normal subgroup Y of G such that $$X\le Y\le N_G(X)$$ . The behaviour of generalized soluble groups whose (cyclic) subgroups satisfy the weak subnormalizer condition is investigated.

Background & Aims Little is known about substitutions that mediate resistance of hepatitis C virus (HCV) to direct-acting antivirals (DAAs), due to the small number of patients with treatment failure in approval studies. It is important to identify resistance patterns to select effective salvage treatments. Methods We performed a comprehensive analysis for resistance-associated substitutions (RASs) in HCV genes (nonstructural protein [NS]3, NS5A, NS5B) targeted by DAAs. We compared NS3, NS5A, and NS5B sequences from 626 patients in Europe with DAA failure with sequences from 2322 DAA-naive patients, infected with HCV genotypes 1 to 4. We considered RASs to be relevant if they were associated with DAA failure in patients or conferred a greater than twofold change in susceptibility compared with a reference strain in in vitro replicon assays. Data were collected on pretreatment status, DAA regimen, the treatment initiation date and duration, and virologic response. Patients who received at least 4 weeks of antiviral treatment were included in the analysis. Results RASs in NS3 associated with simeprevir or paritaprevir failure include R155K and D168E/V. In addition, several RASs were specifically associated with failure of simeprevir (Q80K/R in patients with genotype 1a or 4) or paritaprevir (Y56H in combination with D168V in patients with genotype 1b). Y93H in NS5A was the RAS most frequently associated with failure of daclatasvir, ledipasvir, or ombitasvir in patients with genotype 1b infection, and L31M was associated with failure of daclatasvir or ledipasvir, but not ombitasvir. RASs in NS5A were heterogeneous among patients with HCV genotype 1a or genotype 4 infections. In patients with HCV genotype 3, Y93H was associated with resistance to daclatasvir, but no RASs were associated with ledipasvir failure, pointing to a limited efficacy of ledipasvir in patients with genotype 3. Among patients failed by sofosbuvir-containing regimens, L159F was enriched in patients with genotype 1b (together with C316N) or genotype 3 infection, whereas the RAS S282T was rarely observed. Conclusions We compared RASs in NS3, NS5A, and NS5B among patients failed by DAA therapy. Theses varied with the HCV genotype and subtype, and the different drug classes. These findings might be used to select salvage therapies.