Describing semigroups with defining relations of the form xy=yz xy and yx=zy and connections with knot theory

We introduce a knot semigroup as a cancellative semigroup whose defining relations are produced from crossings on a knot diagram in a way similar to the Wirtinger presentation of the knot group; to be more precise, a knot semigroup as we define it is closely related to such tools of knot theory as the twofold branched cyclic cover space of a knot and the involutory quandle of a knot. We describe knot semigroups of several standard classes of knot diagrams, including torus knots and torus links T(2, n) and twist knots. The description includes a solution of the word problem. To produce this description, we introduce alternating sum semigroups as certain naturally defined factor semigroups of free semigroups over cyclic groups. We formulate several conjectures for future research

Identities of the kauffman monoid K4 and of the Jones Monoid J4

Kauffman monoids Kn and Jones monoids Jn, n=2,3,…, are two families of monoids relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman monoids K3 and K4 satisfy exactly the same identities. This leads to a polynomial time algorithm to check whether a given identity holds in K4. As a byproduct, we also find a polynomial time algorithm for checking identities in the Jones monoid J4. © Springer Nature Switzerland AG 2020.M. V. Volkov—Supported by Ural Mathematical Center under agreement No. 075-02-2020-1537/1 with the Ministry of Science and Higher Education of the Russian Federation

Association of surfactant protein A polymorphisms with otitis media in infants at risk for asthma

BACKGROUND: Otitis media is one of the most common infections of early childhood. Surfactant protein A functions as part of the innate immune response, which plays an important role in preventing infections early in life. This prospective study utilized a candidate gene approach to evaluate the association between polymorphisms in loci encoding SP-A and risk of otitis media during the first year of life among a cohort of infants at risk for developing asthma. METHODS: Between September 1996 and December 1998, women were invited to participate if they had at least one other child with physician-diagnosed asthma. Each mother was given a standardized questionnaire within 4 months of her infant's birth. Infant respiratory symptoms were collected during quarterly telephone interviews at 6, 9 and 12 months of age. Genotyping was done on 355 infants for whom whole blood and complete otitis media data were available. RESULTS: Polymorphisms at codons 19, 62, and 133 in SP-A1, and 223 in SP-A2 were associated with race/ethnicity. In logistic regression models incorporating estimates of uncertainty in haplotype assignment, the 6A(4)/1A(5)haplotype was protective for otitis media among white infants in our study population (OR 0.23; 95% CI 0.07,0.73). CONCLUSION: These results indicate that polymorphisms within SP-A loci may be associated with otitis media in white infants. Larger confirmatory studies in all ethnic groups are warranted

Burden of acute otitis media in primary care pediatrics in Italy: A secondary data analysis from the Pedianet database

Background: The incidence of acute otitis media (AOM) vary from country to country. Geographical variations together with differences in study designs, reporting and settings play a role. We assessed the incidence of AOM in Italian children seen by primary care paediatricians (PCPs), and described the methods used to diagnose the disease.Methods: This secondary data analysis from the Pedianet database considered children aged 0 - 6 years between 01/2003 and 12/2007. The AOM episodes were identified and validated by means of patient diaries. Incidence rates/100 person-years (PY) were calculated for total AOM and for single or recurrent AOM.Results: The 92,373 children (52.1% males) were followed up for a total of 227,361 PY: 23,039 (24.9%) presented 38,241 episodes of AOM (94.6% single episodes and 5.4% recurrent episodes). The total incidence rate of AOM in the 5-year period was 16.8 episodes per 100 PY (95% CI: 16.7-16.9), including single AOM (15.9 episodes per 100 PY; 95% CI: 15.7-16.1) and recurrent AOM (0.9 episodes per 100 PY; 95% CI: 0.9-0.9). There was a slight and continuously negative trend decrease over time (annual percent change -4.6%; 95%CI: -5.3, -3.9%). The AOM incidence rate varied with age, peaking in children aged 3 to 4 years (22.2 episodes per 100 PY; 95% CI 21.8-22.7). The vast majority of the AOM episodes (36,842/38,241, 96.3%) were diagnosed using a static otoscope; a pneumatic otoscope was used in only 3.7%.Conclusions: Our data fill a gap in our knowledge of the incidence of AOM in Italy, and indicate that AOM represents a considerable burden for the Italian PCP system. Educational programmes concerning the diagnosis of AOM are needed, as are further studies to monitor the incidence in relation to the introduction of wider pneumococcal conjugate vaccines

Insulin Concentration Modulates Hepatic Lipid Accumulation in Mice in Part via Transcriptional Regulation of Fatty Acid Transport Proteins

Fatty liver disease (FLD) is commonly associated with insulin resistance and obesity, but interestingly it is also observed at low insulin states, such as prolonged fasting. Thus, we asked whether insulin is an independent modulator of hepatic lipid accumulation.In mice we induced, hypo- and hyperinsulinemia associated FLD by diet induced obesity and streptozotocin treatment, respectively. The mechanism of free fatty acid induced steatosis was studied in cell culture with mouse liver cells under different insulin concentrations, pharmacological phosphoinositol-3-kinase (PI3K) inhibition and siRNA targeted gene knock-down. We found with in vivo and in vitro models that lipid storage is increased, as expected, in both hypo- and hyperinsulinemic states, and that it is mediated by signaling through either insulin receptor substrate (IRS) 1 or 2. As previously reported, IRS-1 was up-regulated at high insulin concentrations, while IRS-2 was increased at low levels of insulin concentration. Relative increase in either of these insulin substrates, was associated with an increase in liver-specific fatty acid transport proteins (FATP) 2&5, and increased lipid storage. Furthermore, utilizing pharmacological PI3K inhibition we found that the IRS-PI3K pathway was necessary for lipogenesis, while FATP responses were mediated via IRS signaling. Data from additional siRNA experiments showed that knock-down of IRSs impacted FATP levels.States of perturbed insulin signaling (low-insulin or high-insulin) both lead to increased hepatic lipid storage via FATP and IRS signaling. These novel findings offer a common mechanism of FLD pathogenesis in states of both inadequate (prolonged fasting) and ineffective (obesity) insulin signaling

The Functional Hearing Gain with an Active Transcutaneous Bone Conduction Implant Does Not Correlate with the Subjective Hearing Performance

The functional hearing outcome with hearing implants does not always properly reflect the subjective benefit in everyday listening situations. In this study, the functional hearing gain and the impact on the subjective hearing ability and quality of life were assessed in patients with a Bonebridge. A chart review was performed on 45 patients with a Bonebridge who were provided with questionnaires regarding the hearing quality and health-related quality of life during their last clinical visit. The questionnaires consisted of the Speech, Spatial and Qualities (SSQ) and the Health Utility Index Mark 3 (HUI3). Eleven patients had to be excluded due to missing data. A total of 34 patients (37 ears) were included in the study. Aided hearing thresholds were significantly lower compared with the unaided condition, with a mean functional gain of 26.87 dB for patients with mixed/conductive hearing loss (MHL/CHL). Although patients with single-sided deafness (SSD) scored slightly lower on the SSQ compared with patients with MHL/CHL, all included patients reported improved subjective hearing quality with the BB compared with the hearing situation before implantation. No correlation was found between the functional hearing gain and the subdomains of the SSQ. SSD patients scored the HUI3 subdomain “hearing” slightly lower compared with MHL/CHL patients. Although not significant, a relationship was found between the functional gain and the “hearing” subdomain. No correlation was found for the other subdomains of the HUI3. Audiological measurements showed significantly improved hearing thresholds with the Bonebridge. Most importantly, the subjective benefit achieved in everyday listening situations was superior compared with the previous hearing condition. The lack of correlation between subjective questionnaire results and the functional hearing gain shows the importance of assessing both audiological and subjective hearing quality parameters in clinical routine