Weighted Sobolev spaces of radially symmetric functions

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.Comment: 38 page

Genome Wide Assessment of Young Onset Parkinson's Disease from Finland

In the current study we undertook a series of experiments to test the hypothesis that a monogenic cause of disease may be detectable within a cohort of Finnish young onset Parkinson’s disease patients. In the first instance we performed standard genome wide association analyses, and subsequent risk profile analysis. In addition we performed a series of analyses that involved testing measures of global relatedness within the cases compared to controls, searching for excess homozygosity in the cases, and examining the cases for signs of excess local genomic relatedness using a sliding window approach. This work suggested that the previously identified common, low risk alleles, and the risk models associated with these alleles, were generalizable to the Finnish Parkinson’s disease population. However, we found no evidence that would suggest a single common high penetrance mutation exists in this cohort of young onset patients

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

OBJECTIVE: The purpose of this study was to examine the relationship between vascular disease (and vascular risk factors), cognition and motor phenotype in Parkinson's disease (PD). METHODS: Recently diagnosed PD cases were enrolled in a multicenter prospective observational longitudinal cohort study. Montreal cognitive assessment (normal >23, mild cognitive impairment 22 to 23 or lower but without functional impairment, and dementia 21 or less with functional impairment) and Movement Disorder Society Unified PD Rating Scale part 3 (UPDRS 3) scores were analyzed in relation to a history of vascular events and risk factors. RESULTS: In 1759 PD cases, mean age 67.5 (standard deviation 9.3) years, mean disease duration 1.3 (standard deviation 0.9) years, 65.2% were men, 4.7% had a history of prior stroke or transient ischemic attack, and 12.5% had cardiac disease (angina, myocardial infarction, heart failure). In cases without a history of vascular disease, hypertension was recorded in 30.4%, high cholesterol 27.3%, obesity 20.7%, diabetes 7.2%, and cigarette smoking in 4.6%. Patients with prior stroke or transient ischemic attack were more likely to have cognitive impairment (42% vs 25%) and postural instability gait difficulty (53.5% vs 39.5%), but these findings were not significant after adjustment for age, sex, and disease duration (P = .075). The presence of more than 2 vascular risks was associated with worse UPDRS 3 motor scores (beta coefficient 4.05, 95% confidence interval 1.48, 6.61, p = .002) and with cognitive impairment (ordinal odds ratio 2.24, 95% confidence interval 1.34, 3.74, p = .002). In 842 patients (47.8%) with structural brain imaging, white matter leukoaraiosis, but not lacunar or territorial infarction, was associated with impaired cognition (p = .006) and postural instability gait difficulty (p = .010). CONCLUSION: Vascular comorbidity is significantly associated with cognitive and gait impairment in patients with early PD, which may have prognostic and treatment implications. © 2016 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society

Pathogenic Parkinson's disease mutations across the functional domains of LRRK2 alter the autophagic/lysosomal response to starvation

LRRK2 is one of the most important genetic contributors to Parkinson's disease (PD). Point mutations in this gene cause an autosomal dominant form of PD, but to date no cellular phenotype has been consistently linked with mutations in each of the functional domains (ROC, COR and Kinase) of the protein product of this gene. In this study, primary fibroblasts from individuals carrying pathogenic mutations in the three central domains of LRRK2 were assessed for alterations in the autophagy/lysosomal pathway using a combination of biochemical and cellular approaches. Mutations in all three domains resulted in alterations in markers for autophagy/lysosomal function compared to wild type cells. These data highlight the autophagy and lysosomal pathways as read outs for pathogenic LRRK2 function and as a marker for disease, and provide insight into the mechanisms linking LRRK2 function and mutations

Next-generation sequencing reveals substantial genetic contribution to dementia with Lewy bodies

Dementia with Lewy bodies (DLB) is the second most common neurodegenerative dementia after Alzheimer's disease. Although an increasing number of genetic factors have been connected to this debilitating condition, the proportion of cases that can be attributed to distinct genetic defects is unknown. To provide a comprehensive analysis of the frequency and spectrum of pathogenic missense mutations and coding risk variants in nine genes previously implicated in DLB, we performed exome sequencing in 111 pathologically confirmed DLB patients. All patients were Caucasian individuals from North America. Allele frequencies of identified missense mutations were compared to 222 control exomes. Remarkably, ~ 25% of cases were found to carry a pathogenic mutation or risk variant in APP, GBA or PSEN1, highlighting that genetic defects play a central role in the pathogenesis of this common neurodegenerative disorder. In total, 13% of our cohort carried a pathogenic mutation in GBA, 10% of cases carried a risk variant or mutation in PSEN1, and 2% were found to carry an APP mutation. The APOE ε4 risk allele was significantly overrepresented in DLB patients (p-value < 0.001). Our results conclusively show that mutations in GBA, PSEN1, and APP are common in DLB and consideration should be given to offer genetic testing to patients diagnosed with Lewy body dementia

Features of GBA-associated Parkinson’s disease at presentation in the UK Tracking Parkinson’s study

Objectives: To examine the influence of the glucocerebrosidase (GBA) mutation carrier state on age at onset of Parkinson’s disease (PD), the motor phenotype and cognitive function at baseline assessment in a large cohort of UK patients. We also analysed the prevalence of mood and behavioural problems that may confound the assessment of cognitive function. Methods: We prospectively recruited patients with PD in the Tracking Parkinson’s study. We fully sequenced the GBA gene in all recently diagnosed patients (≤3.5 years). We examined cognitive (Montreal Cognitive Assessment) and motor (Movement Disorder Society Unified Parkinson’s Disease Rating Scale part 3) function at a baseline assessment, at an average of 1.3 years after diagnosis. We used logistic regression to determine predictors of PD with mild cognitive impairment and PD with dementia. Results: We studied 1893 patients with PD: 48 (2.5%) were heterozygous carriers for known Gaucher’s disease (GD) causing pathogenic mutations; 117 (6.2%) had non-synonymous variants, previously associated with PD, and 28 (1.5%) patients carried variants of unknown significance in the GBA gene. L444P was the most common pathogenic GBA mutation. Patients with pathogenic GBA mutations were on average 5 years younger at disease onset compared with non-carriers (P=0.02). PD patients with GD-causing mutations did not have an increased family risk of PD. Patients with GBA mutations were more likely to present with the postural instability gait difficulty phenotype compared with non-carriers (P=0.02). Patients carrying pathogenic mutations in GBA had more advanced Hoehn and Yahr stage after adjustment for age and disease duration compared with non-carriers (P=0.005). There were no differences in cognitive function between GBA mutation carriers and non-carriers at this early disease stage. Conclusions: Our study confirms the influence of GBA mutations on the age of onset, disease severity and motor phenotype in patients with PD. Cognition did not differ between GBA mutation carriers and non-carriers at baseline, implying that cognitive impairment/dementia, reported in other studies at a later disease stage, is not present in recently diagnosed cases. This offers an important window of opportunity for potential disease-modifying therapy that may protect against the development of dementia in GBA-PD. Clinical trial registration: NCT02881099; Results

A Systematic Review of Online Sex Addiction and Clinical Treatments Using CONSORT Evaluation

Researchers have suggested that the advances of the Internet over the past two decades have gradually eliminated traditional offline methods of obtaining sexual material. Additionally, research on cybersex and/or online sex addictions has increased alongside the development of online technology. The present study extended the findings from Griffiths’ (2012) systematic empirical review of online sex addiction by additionally investigating empirical studies that implemented and/or documented clinical treatments for online sex addiction in adults. A total of nine studies were identified and then each underwent a CONSORT evaluation. The main findings of the present review provide some evidence to suggest that some treatments (both psychological and/or pharmacological) provide positive outcomes among those experiencing difficulties with online sex addiction. Similar to Griffiths’ original review, this study recommends that further research is warranted to establish the efficacy of empirically driven treatments for online sex addiction

Entropic Uncertainty Relations in Quantum Physics

Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the R\'enyi and the Shannon entropies. The advantages of these entropic uncertainty relations are pointed out and their more direct connection to the observed phenomena is emphasized. Several remaining open problems are mentionedComment: 35 pages, review pape

Rare variants analysis of cutaneous malignant melanoma genes in Parkinson's disease

A shared genetic susceptibility between cutaneous malignant melanoma (CMM) and Parkinson's disease (PD) has been suggested. We investigated this by assessing the contribution of rare variants in genes involved in CMM to PD risk. We studied rare variation across 29 CMM risk genes using high-quality genotype data in 6875 PD cases and 6065 controls and sought to replicate findings using whole-exome sequencing data from a second independent cohort totaling 1255 PD cases and 473 controls. No statistically significant enrichment of rare variants across all genes, per gene, or for any individual variant was detected in either cohort. There were nonsignificant trends toward different carrier frequencies between PD cases and controls, under different inheritance models, in the following CMM risk genes: BAP1, DCC, ERBB4, KIT, MAPK2, MITF, PTEN, and TP53. The very rare TYR p.V275F variant, which is a pathogenic allele for recessive albinism, was more common in PD cases than controls in 3 independent cohorts. Tyrosinase, encoded by TYR, is the rate-limiting enzyme for the production of neuromelanin, and has a role in the production of dopamine. These results suggest a possible role for another gene in the dopamine-biosynthetic pathway in susceptibility to neurodegenerative Parkinsonism, but further studies in larger PD cohorts are needed to accurately determine the role of these genes/variants in disease pathogenesis