Bernoulli numbers and solitons

We present a new formula for the Bernoulli numbers as the following integral $$B_{2m} =\frac{(-1)^{m-1}}{2^{2m+1}} \int_{-\infty}^{+\infty} (\frac{d^{m-1}}{dx^{m-1}} {sech}^2 x)^2dx.$$ This formula is motivated by the results of Fairlie and Veselov, who discovered the relation of Bernoulli polynomials with soliton theory.Comment: 5 page

Addressing Comorbidities in People with Parkinson’s Disease: Considerations From An Expert Panel

In the UK, guidance exists to aid clinicians and patients deciding when treatment for Parkinson’s disease (PD) should be initiated and which therapies to consider. National Institute for Health and Care Excellence (NICE) guidance recommends that before starting PD treatment clinicians should discuss the following: the patient’s individual clinical circumstances; lifestyle; preferences; needs and goals; as well as the potential benefits and harms of the different drug classes. Individualization of medicines and management in PD significantly improves patients’ outcomes and quality of life. This article aims to provide simple and practical guidance to help clinicians address common, but often overlooked, co-morbidities. A multi-disciplinary group of PD experts discussed areas where clinical care can be improved by addressing commonly found co-morbidities in people with Parkinson’s (PwP) based on clinical experience and existing literature, in a roundtable meeting organized and funded by Bial Pharma UK Ltd. The experts identified four core areas (bone health, cardiovascular risk, anticholinergic burden, and sleep quality) that, if further standardized may improve treatment outcomes for PwP patients. Focusing on anticholinergic burden, cardiac risk, sleep, and bone health could offer a significant contribution to personalizing regimes for PwP and improving overall patient outcomes. Within this opinion-based paper, the experts offer a list of guiding factors to help practitioners in the management of PwP

Olfaction in Parkin single and compound heterozygotes in a cohort of young onset Parkinson's disease patients

Background Parkin related Parkinson's disease (PD) is differentiated from idiopathic PD by absent or sparse Lewy bodies, and preserved olfaction. The significance of single Parkin mutations in the pathogenesis of PD is debated. Objectives To assess olfaction results according to Parkin mutation status. To compare the prevalence of Parkin single heterozygous mutations in patients diagnosed with PD to the rate in healthy controls in order to establish whether these single mutations could be a risk factor for developing PD. Methods Parkin gene mutation testing was performed in young onset PD (diagnosed <50 years old) to identify three groups: Parkin homozygous or compound heterozygote mutation carriers, Parkin single heterozygote mutation carriers, and non-carriers of Parkin mutations. Olfaction was tested using the 40-item British version of the University of Pennsylvania smell identification test (UPSIT). Results Of 344 young onset PD cases tested, 8 (2.3%) were Parkin compound heterozygotes and 13 (3.8%) were Parkin single heterozygotes. Olfaction results were available in 282 cases (eight compound heterozygotes, nine single heterozygotes, and 265 non-carriers). In Parkin compound heterozygotes, the median UPSIT score was 33, interquartile range (IQR) 28.5–36.5, which was significantly better than in single Parkin heterozygotes (median 19, IQR 18–28) and non-carriers (median score 22, IQR 16–28) (ANOVA P < 0.001). These differences persisted after adjusting for age, disease duration, gender, and smoking (P < 0.001). There was no significant difference in UPSIT scores between single heterozygotes and non-carriers (P = 0.90). Conclusions Patients with Parkin compound heterozygous mutations have relatively preserved olfaction compared to Parkin single heterozygotes and non-carriers. The prevalence of Parkin single heterozygosity is similar to the 3.7% rate reported in healthy controls

Comparison of the ‘Denver regimen’ against acute tuberculosis in the mouse and guinea pig

Objectives: In this study, we sought to compare the sterilizing activity of human-equivalent doses of the ‘Denver regimen ’ against acute tuberculosis (TB) infection in the standard mouse model and in the guinea pig. Methods: Pharmacokinetic studies in guinea pigs were used to establish human-equivalent doses for rifampicin, isoniazid and pyrazinamide. Guinea pigs and mice were aerosol-infected with Mycobacterium tuberculosis CDC1551 and treatment was started 2 weeks later with rifampicin/isoniazid/pyrazinamide for up to 6 months. For the first 2 weeks of therapy, the dosing frequency was 5 days/week, and for the remaining period, twice weekly. Treatment was discontinued in groups of 30 mice and 10 guinea pigs at 5 months and at 6 months, and these animals were held for a further 3 months in order to assess relapse rates. Results: Guinea pig lungs became culture-negative after 3 months of predominantly twice-weekly treatment and relapse rates were 0 % (0/10) both after 5 months and after 6 months of treatment. In contrast, all mice remained culture-positive despite 6 months of the same treatment, and 93 % (28/30) and 69 % (20/29) of mice relapsed after treatment for 5 and 6 months, respectively. Conclusions: Treatment with rifampicin/isoniazid/pyrazinamide administered at human-equivalent doses is much more potent against acute TB infection in guinea pigs than in mice. Our findings have importan

Quantum tops as examples of commuting differential operators

We study the quantum analogs of tops on Lie algebras $so(4)$ and $e(3)$ represented by differential operators.Comment: 24 p

Variation in Recent Onset Parkinson's Disease : Implications for Prodromal Detection

The research was funded by Parkinson’s UK and supported by the National Institute for Health Research (NIHR) DeNDRoN network, the NIHR Newcastle Biomedical Research Unit based at Newcastle upon Tyne Hospitals NHS Foundation Trust and Newcastle University, and the NIHR funded Biomedical Research Centre in Cambridge.Peer reviewedPublisher PD

Rifampicin and clarithromycin (extended release) versus rifampicin and streptomycin for limited Buruli ulcer lesions: a randomised, open-label, non-inferiority phase 3 trial.

BACKGROUND: Buruli ulcer is a neglected tropical disease caused by Mycobacterium ulcerans infection that damages the skin and subcutis. It is most prevalent in western and central Africa and Australia. Standard antimicrobial treatment with oral rifampicin 10 mg/kg plus intramuscular streptomycin 15 mg/kg once daily for 8 weeks (RS8) is highly effective, but streptomycin injections are painful and potentially harmful. We aimed to compare the efficacy and tolerability of fully oral rifampicin 10 mg/kg plus clarithromycin 15 mg/kg extended release once daily for 8 weeks (RC8) with that of RS8 for treatment of early Buruli ulcer lesions. METHODS: We did an open-label, non-inferiority, randomised (1:1 with blocks of six), multicentre, phase 3 clinical trial comparing fully oral RC8 with RS8 in patients with early, limited Buruli ulcer lesions. There were four trial sites in hospitals in Ghana (Agogo, Tepa, Nkawie, Dunkwa) and one in Benin (Pobè). Participants were included if they were aged 5 years or older and had typical Buruli ulcer with no more than one lesion (caterories I and II) no larger than 10 cm in diameter. The trial was open label, and neither the investigators who took measurements of the lesions nor the attending doctors were masked to treatment assignment. The primary clinical endpoint was lesion healing (ie, full epithelialisation or stable scar) without recurrence at 52 weeks after start of antimicrobial therapy. The primary endpoint and safety were assessed in the intention-to-treat population. A sample size of 332 participants was calculated to detect inferiority of RC8 by a margin of 12%. This study was registered with ClinicalTrials.gov, NCT01659437. FINDINGS: Between Jan 1, 2013, and Dec 31, 2017, participants were recruited to the trial. We stopped recruitment after 310 participants. Median age of participants was 14 years (IQR 10-29) and 153 (52%) were female. 297 patients had PCR-confirmed Buruli ulcer; 151 (51%) were assigned to RS8 treatment, and 146 (49%) received oral RC8 treatment. In the RS8 group, lesions healed in 144 (95%, 95% CI 91 to 98) of 151 patients, whereas lesions healed in 140 (96%, 91 to 99) of 146 patients in the RC8 group. The difference in proportion, -0·5% (-5·2 to 4·2), was not significantly greater than zero (p=0·59), showing that RC8 treatment is non-inferior to RS8 treatment for lesion healing at 52 weeks. Treatment-related adverse events were recorded in 20 (13%) patients receiving RS8 and in nine (7%) patients receiving RC8. Most adverse events were grade 1-2, but one (1%) patient receiving RS8 developed serious ototoxicity and ended treatment after 6 weeks. No patients needed surgical resection. Four patients (two in each study group) had skin grafts. INTERPRETATION: Fully oral RC8 regimen was non-inferior to RS8 for treatment of early, limited Buruli ulcer and was associated with fewer adverse events. Therefore, we propose that fully oral RC8 should be the preferred therapy for early, limited lesions of Buruli ulcer. FUNDING: WHO with additional support from MAP International, American Leprosy Missions, Fondation Raoul Follereau France, Buruli ulcer Groningen Foundation, Sanofi-Pasteur, and BuruliVac