Root Cover Pebbling on Graphs

Consider a graph, G, with pebbles on its vertices. A pebbling move is defined to be the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The cover pebbling number of a graph, γ(G), is the minimum number of pebbles such that, given any configuration of γ(G) pebbles on the vertices of G, pebbling moves can be used to place one pebble on each vertex of G. We define the root vertex of a graph and fix an initial configuration of pebbles on G where we place all pebbles on the root vertex of G. We define the root cover pebbling number, R(G), of a graph to be the minimum number of pebbles needed so that, if R(G) pebbles are placed on the root vertex, pebbling moves can be used to place one pebble on each vertex. We obtain formulas for root cover pebbling numbers of two types of graphs. We use these formulas to compare the cover pebbling number with the root cover pebbling number of paths, stars and fuses. We also determine ways to minimize the root cover pebbling number of a graph

End of life care of hospitalized patients with Parkinson disease: a retrospective analysis and brief review

BackgroundTowards the end of life (EOL), persons with parkinsonism (PwP) have complex needs and can present with unique palliative care (PC) challenges. There are no widely accepted guidelines to aid neurologists, hospitalists, or PC clinicians in managing the symptoms of PwP at EOL. We examined a population of PwP at EOL, aiming to describe trends of in-hospital management and utilization of PC services.MethodsAll PwP admitted to two hospitals during 2018 (N = 727) were examined retrospectively, assessing those who died in hospital or were discharged with hospice (EOL group, N = 35) and comparing them to the main cohort. Their demographics, clinical data, engagement of multidisciplinary and palliative services, code status changes, invasive care, frequency of admissions, and medication administration were assessed.ResultsAmong the EOL group, 8 expired in hospital, and 27 were discharged to hospice. Forty-six percent of EOL patients received a PC consultation during their admission. The median interval from admission to death was 37 days. Seventy-seven percent had a full code status on admission. Compared to hospice patients, those who expired in hospital had higher rates of invasive procedures and intensive care unit transfers (41% vs. 75%, in both variables), and lower rates of PC involvement (52% vs. 25%). The transition of code status change for the EOL group from Full code to Do Not Resuscitate (DNR) occurred at a median 4–5 days from admission. For patients that passed in the hospital, the median days from transition of code status to death was 0(IQR 0–1). Levodopa dose deviations were frequent in both EOL and non-EOL group, but contraindicated medications were infrequently administered (11% in EOL group vs. 9% in non-EOL group).ConclusionOur data suggest a low utilization of PC services and delayed discussions of goals of care. More work is needed to raise awareness of inpatient teams managing PwP regarding the unique but common challenges facing PwP with advanced disease. A brief narrative review summarizing the suggested management of symptoms common to hospitalized PwP near EOL is provided

Longitudinal neurobehavioral profiles in children and young adults with PTEN hamartoma tumor syndrome and reliable methods for assessing neurobehavioral change

Abstract Background Individuals with PTEN hamartoma tumor syndrome (PHTS) demonstrate a distinct neurobehavioral profile suggesting primary disruption of frontal lobe symptoms, with more severe cognitive deficits in those with associated autism spectrum disorder (ASD) that extend to other areas of neurobehavioral function as well (e.g., adaptive behavior, sensory deficits). The current study sought to characterize longitudinal neurobehavioral profiles in individuals with PHTS who completed serial assessments (2–3 evaluations) over a 2-year time period. Methods Comprehensive neurobehavioral evaluations were conducted on 92 participants (age range 6–21) with PHTS and/or ASD. Spaghetti plots and linear mixed effects models were used to visualize the individual patient profiles and group trends and examine the group differences in cognitive/behavioral test scores over time. Practice-adjusted reliable change indices (RCIs) and standardized regression-based change scores (SRBs) were calculated for those measures in the battery with adequate sample sizes and test–retest reliabilities for future use in assessing neurobehavioral change in children and young adults with PHTS. Results Wide individual differences were observed at baseline across all measures. Encouragingly, baseline differences between patient groups persisted at the same magnitude over a 2-year time period with no differences in longitudinal neurobehavioral profiles within any one group. Test–retest reliabilities were generally high, ranging from 0.62 to 0.97, and group mean change from baseline to 12 months was small (range − 3.8 to 3.7). A Microsoft Excel calculator was created that clinicians and researchers can use to automatically calculate RCI and SRB thresholds at both 80% and 90% confidence intervals using test scores from a given child or young adult with PHTS. Conclusions Our results suggest that the neurobehavioral phenotypes observed in individuals with PHTS remain relatively stable over time, even in those with ASD. The RCIs and SRBs provided can be used in future research to examine patient outcomes at the individual level as well as to detect negative deviations from the expected trajectory that can be used to inform intervention strategies

Global trends of whole-genome duplications revealed by the ciliate Paramecium tetraurelia.

The duplication of entire genomes has long been recognized as having great potential for evolutionary novelties, but the mechanisms underlying their resolution through gene loss are poorly understood. Here we show that in the unicellular eukaryote Paramecium tetraurelia, a ciliate, most of the nearly 40,000 genes arose through at least three successive whole-genome duplications. Phylogenetic analysis indicates that the most recent duplication coincides with an explosion of speciation events that gave rise to the P. aurelia complex of 15 sibling species. We observed that gene loss occurs over a long timescale, not as an initial massive event. Genes from the same metabolic pathway or protein complex have common patterns of gene loss, and highly expressed genes are over-retained after all duplications. The conclusion of this analysis is that many genes are maintained after whole-genome duplication not because of functional innovation but because of gene dosage constraints