The cyclic insertion conjecture of Borwein, Bradley, Broadhurst and Lisoněk states that inserting all cyclic shifts of some fixed blocks of 2's into the multiple zeta value ζ(1, 3, . . . , 1, 3) gives an explicit rational multiple of a power of π. In this paper we use motivic multiple zeta values to establish a non-explicit symmetric insertion result: inserting all possible permutations of some fixed blocks of 2's into ζ (1, 3, . . . , 1, 3) gives some rational multiple of a power of π.

Summary Background Hidradenitis suppurativa (HS) is a debilitating and distressing chronic inflammatory skin disease. There is also evolving evidence supporting the association between HS and cardiovascular risk factors, including smoking, obesity, hyperlipidaemia and metabolic syndrome. Notably, these are clinical features and risk factors that are closely associated with type 2 diabetes mellitus (DM). Aims We performed a pooled adjusted meta‐analysis of comparative studies to investigate the relationship between HS and DM. Methods A systematic review and meta‐analysis was performed according to recommended Preferred Reporting Items for Systematic Reviews and Meta‐Analyses guidelines. OR was used as the summary effect size. Results From pooled analysis of unadjusted data from 12 studies, we found a significantly higher proportion of DM in HS cases compared with non‐HS healthy controls (16.1% vs. 15.7%; OR = 2.17; 95% CI 1.85–2.55; P < 0.001). Adjusted effect sizes from five studies were also pooled. A significantly higher proportion of DM was found for HS compared with healthy controls, although the effect size was attenuated compared with unadjusted analyses (OR 1.69; 95% CI 1.50–1.91; P < 0.001). Conclusions To our knowledge, our systematic review and meta‐analysis is the first to pool adjusted effect sizes. We found that HS was associated with a 1.69‐fold increased odds of diabetes; however, the absolute risk difference was small (16.1% vs. 15.7%) and is probably not clinically relevant. Treating clinicians should be aware of this association, but there may not be an urgent need to perform screening for impaired glucose tolerance or diabetes.

Background/Objective There have been a number of case reports and small clinical series reporting the potential association between dipeptidyl peptidase‐4 inhibitors (DPPIs) for diabetes and the onset of bullous pemphigoid (BP). The aim of this study was to assess the association between DPPI use and BP, and whether this varied according to DPPI type. Methods We performed a systematic review and meta‐analysis according to PRISMA guidelines. We identified five studies with cases and controls. We performed unadjusted and adjusted meta‐analyses to assess the potential association. Results Adjusted meta‐analysis revealed significant association between DPPI use and BP (OR 2.13, 95% CI 1.59–2.86, I2 = 46%, P < 0.00001). This association was stronger between vildagliptin and BP (OR 5.08, 95% CI 1.70–15.19, P = 0.004) compared to linagliptin (OR 2.87, 95%CI 1.06–7.79, P = 0.04), and no association was found between sitagliptin and BP (OR 1.29, 95%CI 0.79–2.08, P = 0.31). Subgroup analysis demonstrated that the association between DPPI use and BP remained significant in males (OR 2.35, 95% CI 1.46–3.78, P = 0.0005) and females (OR 1.88, 95%CI 1.10–3.22, P = 0.02). Conclusions Limitations were that studies reviewed were retrospective by design which are susceptible to bias and lack of randomisation. Our adjusted analysis supports a significant association between DPPI use and onset of bullous pemphigoid. Vildagliptin had the highest odds of BP. These findings have clinical implications for dermatologists and the management of patients with diabetes and being treated with DPPI agents.

Background: There is a significant variation in the reported prevalence of hidradenitis suppurativa (HS), ranging from 0.03-4%. We hypothesized that this significant variation may be due to different prevalence rates of HS according to geographical location as well as sex. Objective: We aimed to perform a meta-analysis to determine pooled overall prevalence of HS, prevalence stratified according to geographical region and sex. Materials and methods: A systematic review was performed by searching Ovid Medline, PubMed, Cochrane Library, DARE, and Embase, from inception to August 2018. A systematic review and meta-analysis was performed according to PRISMA guidelines. A meta-analysis of proportions was performed to determined pooled prevalence rates, with meta-regression based on geographic region. Prevalence in males versus females was also performed according to region. Results: The overall pooled prevalence rate was 0.3% (0.2-0.6%) based on 118,760,093 HS cases available. Subgroup analysis demonstrated prevalence differences, with the highest being in Europe 0.8% (0.5-1.3%), compared to the USA 0.2% (0.1-0.4%), Asia-Pacific 0.2% (0.01-2.2%), and South America 0.2% (0.01-0.9%). Prevalence in males was lower compared to females in the USA (OR 0.403, 95% CI 0.37-0.439, P < 0.001) as well as in Europe (OR 0.635, 95% CI 0.397-1.015, P = 0.08) but not in the Asia-Pacific region (OR 0.936, 95% CI 0.319-2.751, P = 0.78). Conclusion: Prevalence of HS varies significantly according to the geographical population. This variation is likely attributed to different ethnicity distributions amongst different continents.

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Background Hidradenitis suppurativa (HS) is a debilitating and distressing chronic systemic inflammatory skin disease. There have been several prior observational studies which reported a possibility link between HS and metabolic syndrome, however the current evidence is not definitive. It is unclear in HS whether this possible relationship is independent or driven by underlying risk factors and comorbidities. Objective To determine whether HS is independently associated with metabolic syndrome via adjusted meta‐analysis of case‐control studies. Methods A systematic review and meta‐analysis was performed according to PRISMA guidelines. Electronic searches were performed using six electronic databases (Ovid Medline, PubMed, CCTR, CDSR, ACP Journal Club, and DARE) from their inception until September 2018. Data were extracted and analyzed according to predefined clinical endpoints. Results We identified six case‐control studies included for meta‐analysis. Based on unadjusted analysis, we found a significant association between adult cases of HS and metabolic syndrome (OR 1.95, 95% CI 1.31–2.89, P = 0.001). Adjusted meta‐analysis, after adjustment for age, sex, other cardiovascular risk factors, and comorbidities, found a significant association (OR 2.19, 95% CI 1.70–2.81, I2 = 32%, P < 0.00001). Limitations Studies reviewed were observational by design which are susceptible to bias, and there was lack of randomization. The quality of the current systematic review is also limited by the quality of available evidence which was predominantly observational in nature. Conclusions This pooled analysis of existing case‐control studies supports an association between HS and metabolic syndrome. Clinicians treating patients with HS should be aware of this potential association.

Balanitis xerotica obliterans (BXO), or penile lichen sclerosus, is a progressive sclerosing inflammatory dermatosis of the glans penis and foreskin. It is associated with significant morbidity and may result in impaired urinary and sexual function. It was initially described by Stuhmer in 1928, named after its pathological features, and is considered the male equivalent of vulvar lichen sclerosis (LS).3,40 The etiology of BXO is uncertain; however, autoimmune disease, local trauma, and genetic and infective causes have been proposed. BXO occurs most commonly on the prepuce and glans penis. It is considered to have premalignant potential to transform into squamous neoplasia. This postulation rests on retrospective studies and parallels drawn with vulvar LS and squamous cell carcinoma (SCC) development. Histologically, BXO and vulvar LS are considered the same disease.41 There is a paucity of evidence‐based guidelines to assist with appropriate follow‐up for patients with BXO.