Revisiting Garg's 2-Approximation Algorithm for the k-MST Problem in Graphs

This paper revisits the 2-approximation algorithm for $k$-MST presented by Garg in light of a recent paper of Paul et al.. In the $k$-MST problem, the goal is to return a tree spanning $k$ vertices of minimum total edge cost. Paul et al. extend Garg's primal-dual subroutine to improve the approximation ratios for the budgeted prize-collecting traveling salesman and minimum spanning tree problems. We follow their algorithm and analysis to provide a cleaner version of Garg's result. Additionally, we introduce the novel concept of a kernel which allows an easier visualization of the stages of the algorithm and a clearer understanding of the pruning phase. Other notable updates include presenting a linear programming formulation of the $k$-MST problem, including pseudocode, replacing the coloring scheme used by Garg with the simpler concept of neutral sets, and providing an explicit potential function.Comment: Proceedings of SIAM Symposium on Simplicity in Algorithms (SOSA) 202

Hypothalamic volume loss is associated with reduced melatonin output in Parkinson's disease.

BACKGROUND: Recent studies have suggested that melatonin-a hormone produced by the pineal gland under circadian control-contributes to PD-related sleep dysfunction. We hypothesized that degenerative changes to the neural structures controlling pineal function (especially the suprachiasmatic nuclei of the anterior hypothalamus) may be responsible for reduced melatonin output in these patients. We compared hypothalamic volumes in PD patients with matched controls and determined whether volume loss correlated with reduced melatonin output in the PD group. METHODS: A total of 12 PD patients and 12 matched controls underwent magnetic resonance imaging to determine hypothalamic volume. In addition, PD patients underwent 24-hour blood sampling in a controlled environment to determine serum melatonin concentrations using enzyme-linked immunosorbent assays. RESULTS: PD patients had significantly reduced hypothalamic gray matter volume when compared with matched controls. Melatonin levels were significantly associated with hypothalamic gray matter volume and disease severity in PD patients. CONCLUSION: Melatonin levels are associated with hypothalamic gray matter volume loss and disease severity in PD patients. This provides anatomical and physiological support for an intrinsic sleep and circadian phenotype in PD. © 2016 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society.The authors would like to acknowledge the study funders: the Big Lottery Fund (C498A738) and Parkinson’s UK (J-0802). The research was supported by a National Institute of Health Research Biomedical Research Award (to Addenbrooke’s Hospital/University of Cambridge), the Wellcome Trust (103838, 100333/Z/12/Z) and a Raymond and Beverly Sackler Studentship (to DPB). We would like to thank staff at the Wellcome Trust Clinical Research Facility in Addenbrooke’s Hospital, Cambridge for performing the melatonin blood sampling.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1002/mds.2659

Cerebrospinal Fluid Cytokines and Neurodegeneration-Associated Proteins in Parkinson's Disease.

INTRODUCTION: Immune markers are altered in Parkinson's disease (PD), but relationships between cerebrospinal fluid (CSF) and plasma cytokines and associations with neurodegeneration-associated proteins remain unclear. METHODS: CSF and plasma samples and demographic/clinical measures were obtained from 35 PD patients. CSF samples were analyzed for cytokines (together with plasma) and for α-synuclein, amyloid β(1-42) peptide, total tau, and phospho(Thr231)-tau. RESULTS: There were no CSF-plasma cytokine correlations. Interleukin (IL)-8 was higher and interferon-γ, IL-10, and tumor necrosis factor-α were lower in CSF versus plasma. In CSF, total tau correlated positively with IL-8 and IL-1β, whereas α-synuclein correlated positively with amyloid β(1-42) and negatively with semantic fluency (a known marker of PD dementia risk). DISCUSSION: CSF and peripheral cytokine profiles in PD are not closely related. Associations between CSF IL-8 and IL-1β and tau suggest that CSF inflammatory changes may relate to tau pathology within PD. CSF α-synuclein/amyloid β may reflect the risk of developing PD dementia. © 2020 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society.Funding for this work was provided by the Rosetrees Trust (M369-F1), Addenbrooke’s Charitable Trust (PF15/CWG) and the NIHR Cambridge Biomedical Research Centre Dementia and Neurodegeneration Theme (146281). RSW was supported by a Fellowship from Addenbrooke’s Charitable Trust (RG77199). SFM was supported by the Transeuro EU FP7 grant (242003) and is now an NIHR Academic Clinical Fellow (ACF-2015-23-501). DPB is supported by a Wellcome Trust Clinical Research Career Development Fellowship. RAB is an NIHR Senior Investigator (NF-SI-0616-10011) and is supported by the Wellcome Trust-MRC Cambridge Stem Cell Institute. CHWG holds a RCUK/UKRI Research Innovation Fellowship awarded by the Medical Research Council (MR/R007446/1) and receives support from the Cambridge Centre for Parkinson-Plus

Sleep and Circadian Rhythm Regulation in Early Parkinson Disease

Importance: Sleep disturbances are recognized as a common nonmotor complaint in Parkinson disease but their etiology is poorly understood. Objective: To define the sleep and circadian phenotype of patients with early-stage Parkinson disease. Design, Setting, and Participants: Initial assessment of sleep characteristics in a large population-representative incident Parkinson disease cohort (N=239) at the University of Cambridge, England, followed by further comprehensive case-control sleep assessments in a subgroup of these patients (n=30) and matched controls (n=15). Main Outcomes and Measures: Sleep diagnoses and sleep architecture based on polysomnography studies, actigraphy assessment, and 24-hour analyses of serum cortisol, melatonin, and peripheral clock gene expression (Bmal1, Per2, and Rev-Erbα). Results: Subjective sleep complaints were present in almost half of newly diagnosed patients and correlated significantly with poorer quality of life. Patients with Parkinson disease exhibited increased sleep latency (P = .04), reduced sleep efficiency (P = .008), and reduced rapid eye movement sleep (P = .02). In addition, there was a sustained elevation of serum cortisol levels, reduced circulating melatonin levels, and altered Bmal1 expression in patients with Parkinson disease compared with controls. Conclusions and Relevance: Sleep dysfunction seen in early Parkinson disease may reflect a more fundamental pathology in the molecular clock underlying circadian rhythms

The Cerebrospinal Fluid Profile of Cholesterol Metabolites in Parkinson’s Disease and Their Association With Disease State and Clinical Features

Disordered cholesterol metabolism is linked to neurodegeneration. In this study we investigated the profile of cholesterol metabolites found in the cerebrospinal fluid (CSF) of Parkinson’s disease (PD) patients. When adjustments were made for confounding variables of age and sex, 7α,(25R)26-dihydroxycholesterol and a second oxysterol 7α,x,y-trihydroxycholest-4-en-3-one (7α,x,y-triHCO), whose exact structure is unknown, were found to be significantly elevated in PD CSF. The likely location of the additional hydroxy groups on the second oxysterol are on the sterol side-chain. We found that CSF 7α-hydroxycholesterol levels correlated positively with depression in PD patients, while two presumptively identified cholestenoic acids correlated negatively with depression

Cognitive decline and quality of life in incident Parkinson's disease: The role of attention.

INTRODUCTION: Parkinson's disease dementia (PDD) is associated with poorer quality of life (QoL). Prior to the onset of PDD, many patients experience progressive cognitive impairment. There is a paucity of longitudinal studies investigating the effects of cognitive decline on QoL. This study aimed to determine the longitudinal impact of cognitive change on QoL in an incident PD cohort. METHODS: Recently diagnosed patients with PD (n = 212) completed a schedule of neuropsychological assessments and QoL measures; these were repeated after 18 (n = 190) and 36 months (n = 158). Mild cognitive impairment (PD-MCI) was classified with reference to the Movement Disorder Society criteria. Principal component analysis was used to reduce 10 neuropsychological tests to three cognitive factors: attention, memory/executive function, and global cognition. RESULTS: Baseline PD-MCI was a significant contributor to QoL (β = 0.2, p < 0.01). For those subjects (9%) who developed dementia, cognitive function had a much greater impact on QoL (β = 10.3, p < 0.05). Multivariate modelling showed attentional deficits had the strongest predictive power (β = -2.3, p < 0.01); brief global tests only modestly predicted decline in QoL (β = -0.4, p < 0.01). CONCLUSIONS: PD-MCI was associated with poorer QoL over three years follow up. Cognitive impairment had a greater impact on QoL in individuals who developed dementia over follow-up. Impaired attention was a significant determinant of QoL in PD. Interventions which improve concentration and attention in those with PD could potentially improve QoL