Extending a perfect matching to a Hamiltonian cycle

Graph TheoryInternational audienceRuskey and Savage conjectured that in the d-dimensional hypercube, every matching M can be extended to a Hamiltonian cycle. Fink verified this for every perfect matching M, remarkably even if M contains external edges. We prove that this property also holds for sparse spanning regular subgraphs of the cubes: for every d ≥7 and every k, where 7 ≤k ≤d, the d-dimensional hypercube contains a k-regular spanning subgraph such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle. We do not know if this result can be extended to k=4,5,6. It cannot be extended to k=3. Indeed, there are only three 3-regular graphs such that every perfect matching (possibly with external edges) can be extended to a Hamiltonian cycle, namely the complete graph on 4 vertices, the complete bipartite 3-regular graph on 6 vertices and the 3-cube on 8 vertices. Also, we do not know if there are graphs of girth at least 5 with this matching-extendability property

Using digital image analysis to accurately determine the thousand kernel weight of randomly distributed barley, malt and wheat samples

Rapid, accurate and non-subjective grain tests help growers and processors agree on a fair price and ensure that the grain is used for the most appropriate purpose. Common tests include protein, moisture, test (hectolitre) weight, screenings and dockages for pests, disease and foreign matter (Vicgrain, 2000). Each test contributes to a more comprehensive assessment of the grain. The tests assist breeders when selecting promising new cultivars. Plant breeders and maltsters also use the thousand kernel weight (TKW) test, which provides additional information on seed morphology. The test indicates the average kernel weight, with the units expressed as grams per thousand seeds. TKWs are valuable to maltsters and millers as high TKW kernels are plumper, malt and/or mill more evenly and have a higher proportion of endosperm than small kernels. The high TKW grains also produce more attractive malt (Stuart, 1998). TKWs assist breeders in selecting large kernel cultivars and permit growers to calculate their optimum sowing rates (Schwarz and Horsley, 1995).E

Continuous subcutaneous foslevodopa/foscarbidopa infusion for the treatment of motor fluctuations in Parkinson's disease:Considerations for initiation and maintenance

Background:As Parkinson's disease (PD) advances, management is challenged by an increasingly variable and inconsistent response to oral dopaminergic therapy, requiring special considerations by the provider. Continuous 24 h/day subcutaneous infusion of foslevodopa/foscarbidopa (LDp/CDp) provides steady dopaminergic stimulation that can reduce symptom fluctuation. Objective: Our aim is to review the initiation, optimization, and maintenance of LDp/CDp therapy, identify possible challenges, and share potential mitigations.Methods: Review available LDp/CDp clinical trial data for practical considerations regarding the management of patients during LDp/CDp therapy initiation, optimization, and maintenance based on investigator clinical trial experience. Results: LDp/CDp initiation, optimization, and maintenance can be done without hospitalization in the clinic setting. Continuous 24 h/day LDp/CDp infusion can offer more precise symptom control than oral medications, showing improvements in motor fluctuations during both daytime and nighttime hours. Challenges include infusion-site adverse events for which early detection and prompt management may be required, as well as systemic adverse events (eg, hallucinations) that may require adjustment of the infusion rate or other interventions. A learning curve should be anticipated with initiation of therapy, and expectation setting with patients and care partners is key to successful initiation and maintenance of therapy. Conclusion: Continuous subcutaneous infusion of LDp/CDp represents a promising therapeutic option for individuals with PD. Individualized dose optimization during both daytime and nighttime hours, coupled with patient education, and early recognition of certain adverse events (plus their appropriate management) are required for the success of this minimally invasive and highly efficacious therapy.</p

Omics‐based molecular analyses of adhesion by aquatic invertebrates

Many aquatic invertebrates are associated with surfaces, using adhesives to attach to the substratum for locomotion, prey capture, reproduction, building or defence. Their intriguing and sophisticated biological glues have been the focus of study for decades. In all but a couple of specific taxa, however, the precise mechanisms by which the bioadhesives stick to surfaces underwater and (in many cases) harden have proved to be elusive. Since the bulk components are known to be based on proteins in most organisms, the opportunities provided by advancing ‘omics technologies have revolutionised bioadhesion research. Time‐consuming isolation and analysis of single molecules has been either replaced or augmented by the generation of massive data sets that describe the organism's translated genes and proteins. While these new approaches have provided resources and opportunities that have enabled physiological insights and taxonomic comparisons that were not previously possible, they do not provide the complete picture and continued multi‐disciplinarity is essential. This review covers the various ways in which ‘omics have contributed to our understanding of adhesion by aquatic invertebrates, with new data to illustrate key points. The associated challenges are highlighted and priorities are suggested for future research

Outcomes Impacting Quality of Life in Advanced Parkinson's Disease Patients Treated with Levodopa-Carbidopa Intestinal Gel

BACKGROUND: It is believed that motor symptoms, including dyskinesia, and non-motor symptoms impact health-related quality of life (HRQoL) in patients with Parkinson’s disease (PD), and that improvements in these metrics are correlated. OBJECTIVE: Investigate the relationship between HRQoL and measures of PD severity and treatment efficacy, including motor and non-motor symptoms. METHODS: This was a planned investigation of an international, prospective, single-arm, post-marketing observational study of the long-term effectiveness of levodopa-carbidopa intestinal gel (LCIG) in patients with advanced PD. Pearson correlation coefficients (PCC) were calculated for baseline and change from baseline at 12 months between HRQoL and motor and non-motor symptoms. RESULTS: A total of 195 patients were included. At baseline, HRQoL was moderately positively correlated with Activities of Daily Living (UPDRS II, PCC = 0.44), non-motor symptoms (0.48), and measures of sleep (0.50 and 0.40); all p < 0.001. After 12 months of treatment with LCIG, improvements in HRQoL were moderately positively correlated with improvement from baseline in non-motor symptoms (PCC = 0.42), sleep (0.54), and daytime sleepiness (0.40; all p < 0.001), and weakly correlated with improvement in dyskinesia signs and symptoms (PCC = 0.23; p = 0.011). Improvement in HRQoL was not correlated with improvements in OFF time or dyskinesia time. CONCLUSION: Both at baseline and for change from baseline at 12 months, HRQoL was correlated with baseline and change from baseline in dyskinesia, Activities of Daily Living, and non-motor symptoms, including sleep; but not with baseline or change in OFF time

A Genotype-First Approach for the Molecular and Clinical Characterization of Uncommon De Novo Microdeletion of 20q13.33

Background: Subtelomeric deletions of the long arm of chromosome 20 are rare, with only 11 described in the literature. Clinical features of individuals with these microdeletions include severe limb malformations, skeletal abnormalities, growth retardation, developmental and speech delay, mental retardation, seizures and mild, non-specific dysmorphic features. Methodology/Principal Findings: We characterized microdeletions at 20q13.33 in six individuals referred for genetic evaluation of developmental delay, mental retardation, and/or congenital anomalies. A comparison to previously reported cases of 20q13.33 microdeletion shows phenotypic overlap, with clinical features that include mental retardation, developmental delay, speech and language deficits, seizures, and behavior problems such as autistic spectrum disorder. There does not appear to be a clinically recognizable constellation of dysmorphic features among individuals with subtelomeric 20q microdeletions. Conclusions/Significance: Based on genotype-phenotype correlation among individuals in this and previous studies, we discuss several possible candidate genes for specific clinical features, including ARFGAP1, CHRNA4 and KCNQ2 and neurodevelopmental deficits. Deletion of this region may play an important role in cognitive development

Determination of Beta-Defensin Genomic Copy Number in Different Populations: A Comparison of Three Methods

There have been conflicting reports in the literature on association of gene copy number with disease, including CCL3L1 and HIV susceptibility, and β-defensins and Crohn's disease. Quantification of precise gene copy numbers is important in order to define any association of gene copy number with disease. At present, real-time quantitative PCR (QPCR) is the most commonly used method to determine gene copy number, however the Paralogue Ratio Test (PRT) is being used in more and more laboratories.In this study we compare a Pyrosequencing-based Paralogue Ratio Test (PPRT) for determining beta-defensin gene copy number with two currently used methods for gene copy number determination, QPCR and triplex PRT by typing five different cohorts (UK, Danish, Portuguese, Ghanaian and Czech) of DNA from a total of 576 healthy individuals. We found a systematic measurement bias between DNA cohorts revealed by QPCR, but not by the PRT-based methods. Using PRT, copy number ranged from 2 to 9 copies, with a modal copy number of 4 in all populations.QPCR is very sensitive to quality of the template DNA, generating systematic biases that could produce false-positive or negative disease associations. Both triplex PRT and PPRT do not show this systematic bias, and type copy number within the correct range, although triplex PRT appears to be a more precise and accurate method to type beta-defensin copy number