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

Exploratory study of the use of community treatment orders with clients of an Ontario ACT team

Community Treatment Orders (CTOs) have raised questions about coercion, lack of autonomy, and effectiveness in reducing hospitalizations and improving service users’ quality of life. This study examined the experiences of clients and clinicians when CTOs are used in combination with Assertive Community Treatment (ACT) in a recovery oriented approach. Eleven clients who were or had previously been on a CTO and eight ACT clinicians were interviewed. Although most clients had negative feelings about CTOs, some acknowledged their lives had improved. Clinicians reported that the decision to employ a CTO is sometimes debated within the team but they agreed that combining CTOs and ACT resulted in regular access to mental health supports, fewer hospitalizations and overall improvement of quality of life for their clients

Neuropathology of dementia in patients with Parkinson’s disease: a systematic review of autopsy studies

Background: Dementia is a common, debilitating feature of late Parkinson’s disease (PD). PD dementia (PDD) is associated with α-synuclein propagation, but coexistent Alzheimer’s disease (AD) pathology may coexist. Other pathologies (cerebrovascular, transactive response DNA-binding protein 43 (TDP-43)) may also influence cognition. We aimed to describe the neuropathology underlying dementia in PD. Methods: Systematic review of autopsy studies published in English involving PD cases with dementia. Comparison groups included PD without dementia, AD, dementia with Lewy bodies (DLB) and healthy controls. Results: 44 reports involving 2002 cases, 57.2% with dementia, met inclusion criteria. While limbic and neocortical α-synuclein pathology had the strongest association with dementia, between a fifth and a third of all PD cases in the largest studies had comorbid AD. In PD cases with dementia, tau pathology was moderate or severe in around a third, and amyloid-β pathology was moderate or severe in over half. Amyloid-β was associated with a more rapid cognitive decline and earlier mortality, and in the striatum, distinguished PDD from DLB. Positive correlations between multiple measures of α-synuclein, tau and amyloid-β were found. Cerebrovascular and TDP-43 pathologies did not generally contribute to dementia in PD. TDP-43 and amyloid angiopathy correlated with coexistent Alzheimer pathology. Conclusions: While significant α-synuclein pathology is the main substrate of dementia in PD, coexistent pathologies are common. In particular, tau and amyloid-β pathologies independently contribute to the development and pattern of cognitive decline in PD. Their presence should be assessed in future clinical trials where dementia is a key outcome measure

Utility of the new Movement Disorder Society clinical diagnostic criteria for Parkinson's disease applied retrospectively in a large cohort study of recent onset cases

Objective: To examine the utility of the new Movement Disorder Society (MDS) diagnostic criteria in a large cohort of Parkinson's disease (PD) patients. Methods: Recently diagnosed (<3.5 years) PD cases fulfilling United Kingdom (UK) brain bank criteria in Tracking Parkinson's, a UK multicenter prospective natural history study were assessed by retrospective application of the MDS criteria. Results: In 2000 cases, 1835 (91.7%) met MDS criteria for PD, either clinically established (n = 1261, 63.1%) or clinically probable (n = 574, 28.7%), leaving 165 (8.3%) not fulfilling criteria. Clinically established cases were significantly more likely to have limb rest tremor (89.3%), a good l-dopa response (79.5%), and olfactory loss (71.1%), than clinically probable cases (60.6%, 44.4%, and 34.5% respectively), but differences between probable PD and ‘not PD’ cases were less evident. In cases not fulfilling criteria, the mean MDS UPDRS3 score (25.1, SD 13.2) was significantly higher than in probable PD (22.3, SD 12.7, p = 0.016) but not established PD (22.9, SD 12.0, p = 0.066). The l-dopa equivalent daily dose of 341 mg (SD 261) in non-PD cases was significantly higher than in probable PD (250 mg, SD 214, p < 0.001) and established PD (308 mg, SD 199, p = 0.025). After 30 months' follow-up, 89.5% of clinically established cases at baseline remained as PD (established/probable), and 86.9% of those categorized as clinically probable at baseline remained as PD (established/probable). Cases not fulfilling PD criteria had more severe parkinsonism, in particular relating to postural instability, gait problems, and cognitive impairment. Conclusion: Over 90% of cases clinically diagnosed as early PD fulfilled the MDS criteria for PD. Those not fulfilling criteria may have an atypical parkinsonian disorder or secondary parkinsonism that is not correctly identified by the UK Brain Bank criteria, but possibly by the new criteria

Vascular disease and vascular risk factors in relation to motor features and cognition in early Parkinson's disease

Funded by Parkinson's UK National Institute for Health Research (NIHR) DeNDRoN network NIHR Newcastle Biomedical Research Unit Newcastle University NIHR funded Biomedical Research Centre in CambridgePeer reviewedPublisher PD

Conserving indigenous crayfish: stock assessment and habitat requirements in the threatened Austropotamobius italicus.

International audienceAs part of the Austropotamobius pallipes species complex, the crayfish Austropotamobius italicus is a species of community interest whose preservation requires the designation of Special Areas of Conservation (SACs) (Annex II, EU Habitats Directive). This study aimed at (1) assessing the conservation status of this threatened indigenous species by stock assessment in central Italy and (2) identifying some aspects of its elective habitat

Motor complications in Parkinson’s disease:results from 3,343 patients followed for up to 12 years

Background: Motor complications are well recognised in Parkinson’s disease (PD), but their reported prevalence varies and functional impact has not been well studied. Objectives: To quantify the presence, severity, impact and associated factors for motor complications in PD.Methods: Analysis of 3 large prospective cohort studies of recent-onset PD patients followed for up to 12 years. The MDS-UPDRS part 4 assessed motor complications and multivariable logistic regression tested for associations. Genetic risk score (GRS) for Parkinson’s was calculated from 79 single nucleotide polymorphisms. Results: 3,343 cases were included (64.7% male). Off periods affected 35.0% (95% CI 33.0, 37.0) at 4-6 years and 59.0% (55.6, 62.3) at 8-10 years. Dyskinesia affected 18.5% (95% CI 16.9, 20.2) at 4-6 years and 42.1% (38.7, 45.5) at 8-10 years. Dystonia affected 13.4% (12.1, 14.9) at 4-6 years and 22.8% (20.1, 25.9) at 8-10 years. Off periods consistently caused greater functional impact than dyskinesia. Motor complications were more common among those with higher drug doses, younger age at diagnosis, female gender, and greater dopaminergic responsiveness (in challenge tests), with associations emerging 2 to 4 years post-diagnosis. Higher Parkinson’s GRS was associated with early dyskinesia (0.026 ≤ P ≤ 0.050 from 2 to 6 years).Conclusions: Off periods are more common and cause greater functional impairment than dyskinesia. We confirm previously reported associations between motor 4 complications with several demographic and medication factors. Greater dopaminergic responsiveness and a higher genetic risk score are two novel and significant independent risk factors for the development of motor complications