Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy

It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings encapsulates nothing but a fundamental theorem of ancient Greek geometry. Thus, it is demonstrated that the connection with Menelaus' theorem and, more generally, Clifford configurations renders the dSKP equation a natural object of inversive geometry on the plane. The geometric and algebraic integrability of dSKP lattices and their reductions to lattices of Menelaus-Darboux, Schwarzian KdV, Schwarzian Boussinesq and Schramm type is discussed. The dSKP and discrete Schwarzian Boussinesq equations are shown to represent discretizations of families of quasi-conformal mappings.Comment: 26 pages, 9 figure

Delay in referral of oropharyngeal squamous cell carcinoma to secondary care correlates with a more advanced stage at presentation, and is associated with poorer survival

Squamous carcinoma of the oropharynx presents with symptoms common to many benign diseases, and this can cause delay in referral to secondary care. We investigate delay in referral, defining this as the time from symptom-onset to date of general practitioners referral letter to secondary care, and the effect of that delay, using a retrospective case notes based study of patients presenting at our institution with oropharyngeal squamous carcinoma between 1995 and 2005. Using correlation analysis and ordinal regression, we examined the relationship between increased referral delay from primary care, clinical stage at presentation, and survival. Increasing time from symptom onset to referral to secondary care was positively correlated with more advanced disease stage at presentation (rs=+0.346, P=0.004). This was confirmed with ordinal regression modelling (delay estimate=0.045, P=0.042). Patients with delay of less than 6 weeks had significantly improved survival compared to those with a delay of greater than 6 weeks (P=0.032). For every 1 week of delay in referral, we estimate that the stage of presentation will progress by 0.045 of ‘a stage'

Sialadenosis in Patients with Advanced Liver Disease

Sialadenosis (sialosis) has been associated most often with alcoholic liver disease and alcoholic cirrhosis, but a number of nutritional deficiencies, diabetes, and bulimia have also been reported to result in sialadenosis. The aim of this study was to determine the prevalence of sialadenosis in patients with advanced liver disease. Patients in the study group consisted of 300 candidates for liver transplantation. Types of liver disease in subjects with clinical evidence of sialadenosis were compared with diagnoses in cases who had no manifestations of sialadenosis. The data were analyzed for significant association. Sialadenosis was found in 28 of the 300 subjects (9.3%). Among these 28 cases, 11 (39.3%) had alcoholic cirrhosis. The remaining 17 (60.7%) had eight other types of liver disease. There was no significant association between sialadenosis and alcoholic cirrhosis (P = 0.389). These findings suggest that both alcoholic and non-alcoholic cirrhosis may lead to the development of sialadenosis. Advanced liver disease is accompanied by multiple nutritional deficiencies which may be exacerbated by alcohol. Similar metabolic abnormalities may occur in patients with diabetes or bulimia. Malnutrition has been associated with autonomic neuropathy, the pathogenic mechanism that has been proposed for sialadenosis

Periodontitis is associated with significant hepatic fibrosis in patients with non-alcoholic fatty liver disease

This work was funded by the Diabetes Research and Wellness Fund. WA is in receipt of an MRC New Investigator Award

Diabetes mellitus and oral lichen planus: A systematic review and meta-analysis

Objective: To undertake a meta-analysis of the association of Oral Lichen Planus (OLP) with diabetes, two diseases with an important impact on public health and the economy, but the evidence of which about their association is inconsistent. Methods: Relevant studies were localized by searching MEDLINE, EMBASE, Conference Proceedings, and other databases from inception to October 2020, without restrictions. The reference lists of included studies and of related reviews were also inspected. Global pooled odds ratios were calculated, and predefined subgroup analyses were performed. The heterogeneity between studies and publication bias was assessed and sensitivity analysis was carried out. Results: Thirty-two studies were included in the meta-analysis. Pooled ORs showed a moderate association between diabetes and OLP [OR: 1.87 (95%CI: 1.57, 2.34)]. The association is limited to studies carried out on adults only [OR: 2.12 (95%CI: 1.75, 2.57)] and is observed in all study designs. Globally, the heterogeneity was low to moderate. Studies carried out in European populations show a stronger association of diabetes and OLP than Asiatic studies [OR: 2.49 (95%CI: 1.87, 3.32) and 1.60 (95%CI: 1.25, 2.03), respectively]. Conclusions: Diabetes and OLP are moderately associated. Systematic diagnosis of diabetes in OLP patients could prove usefulS

Determinants of DNA yield and purity collected with buccal cell samples

Buccal cells are an important source of DNA in epidemiological studies, but little is known about factors that influence amount and purity of DNA. We assessed these factors in a self-administered buccal cell collection procedure, obtained with three cotton swabs. In 2,451 patients DNA yield and in 1,033 patients DNA purity was assessed. Total DNA yield ranged from 0.08 to 1078.0 μg (median 54.3 μg; mean 82.2 μg ± SD 92.6). The median UV 260:280 ratio, was 1.95. Samples from men yielded significantly more DNA (median 58.7 μg) than those from women (median 44.2 μg). Diuretic drug users had significantly lower purity (median 1.92) compared to other antihypertensive drug users (1.95). One technician obtained significantly lower DNA yields. Older age was associated with lower DNA purity. In conclusion, DNA yield from buccal swabs was higher in men and DNA purity was associated with age and the use of diuretics