Abstract We characterize colour-preserving automorphism vertex transitivity and vertex transitivity of the Cayley graphs of all semigroups in a class of pseudo-unitary homogeneous semigroups.

Irritable bowel syndrome (IBS) is a gut‐brain disorder in which symptoms are shaped by serotonin acting centrally and peripherally. The serotonin transporter gene SLC6A4 has been implicated in IBS pathophysiology, but the underlying genetic mechanisms remain unclear. We sequenced the alternative P2 promoter driving intestinal SLC6A4 expression and identified single nucleotide polymorphisms (SNPs) that were associated with IBS in a discovery sample. Identified SNPs built different haplotypes, and the tagging SNP rs2020938 seems to associate with constipation‐predominant IBS (IBS‐C) in females. rs2020938 validation was performed in 1978 additional IBS patients and 6,038 controls from eight countries. Meta‐analysis on data from 2,175 IBS patients and 6,128 controls confirmed the association with female IBS‐C. Expression analyses revealed that the P2 promoter drives SLC6A4 expression primarily in the small intestine. Gene reporter assays showed a functional impact of SNPs in the P2 region. In silico analysis of the polymorphic promoter indicated differential expression regulation. Further follow‐up revealed that the major allele of the tagging SNP rs2020938 correlates with differential SLC6A4 expression in the jejunum and with stool consistency, indicating functional relevance. Our data consolidate rs2020938 as a functional SNP associated with IBS‐C risk in females, underlining the relevance of SLC6A4 in IBS pathogenesis.

Hepatic steatosis is a disorder with high prevalence among obese people. Traditional imaging modalities are more common in hepatic steatosis diagnosis, but they are not suitable for monitoring or treatment evaluation. This study aims at developing a new technique suitable for electromagnetic (EM) tool in the microwave band to differentiate steatotic from nonsteatotic liver. A differential permittivity estimation method for hepatic steatosis detection is proposed. First, the effective permittivity of the right side of the torso is estimated based on the phase difference of EM waves traveling along symmetric paths within the torso. Then, permittivity modeling and statistical frequency selection are performed to model the estimated values and to extract reliable frequency samples. Finally, the percentage of the difference between the permittivity of the left and right sides of the torso is calculated over the selected samples. The effectiveness of the proposed method is validated using simulated signals and phantom measurements. The analyzed results reveal higher contrast between the average permittivity of the left and right sides of the torso for cases with hepatic steatosis (average contrast of 29.2%) compared to those with healthy liver (average contrast of 7.9%). The proposed method can differentiate between steatotic and nonsteatotic liver. It is suitable for clinical applications due to its robustness to unwanted noise and interferences, as well as errors in placement of sensors. The results verify the potential of EM devices, which could overcome shortcomings of traditional imaging techniques by being safe, cost-effective, and portable.