The Minimum Shared Edges Problem on Grid-like Graphs

We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can be decided on bounded (i.e. finite) grids in linear time when both dimensions are either small or large compared to the number $p$ of paths. On the contrary, we show that MSE remains NP-hard on subgraphs of bounded grids. Finally, we study MSE from a parametrised complexity point of view. It is known that MSE is fixed-parameter tractable with respect to the number $p$ of paths. We show that, under standard complexity-theoretical assumptions, the problem parametrised by the combined parameter $k$, $p$, maximum degree, diameter, and treewidth does not admit a polynomial-size problem kernel, even when restricted to planar graphs

The Complexity of Routing with Few Collisions

We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph $G$ with two distinct terminal vertices and two positive integers $p$ and $k$, the question is whether one can connect the terminals by at least $p$ routes (e.g. paths) such that at most $k$ edges are time-wise shared among them. We study three types of routes: traverse each vertex at most once (paths), each edge at most once (trails), or no such restrictions (walks). We prove that for paths and trails the problem is NP-complete on undirected and directed graphs even if $k$ is constant or the maximum vertex degree in the input graph is constant. For walks, however, it is solvable in polynomial time on undirected graphs for arbitrary $k$ and on directed graphs if $k$ is constant. We additionally study for all route types a variant of the problem where the maximum length of a route is restricted by some given upper bound. We prove that this length-restricted variant has the same complexity classification with respect to paths and trails, but for walks it becomes NP-complete on undirected graphs

Calculation of health expectancies with administrative data for North Rhine-Westphalia, a Federal State of Germany, 1999–2005

Pinheiro JP, Krämer A. Calculation of health expectancies with administrative data for North Rhine-Westphalia, a Federal State of Germany, 1999-2005. Population Health Metrics. 2009;7(1):4.OBJECTIVES: The main objectives of this study were to prove the feasibility of health expectancy analyses with regional administrative health statistics and to explore the utility of the calculated health expectancies in describing the health state of the population living in North Rhine-Westphalia, a Federal State of Germany. MATERIALS AND METHODS: Administrative population and mortality data as well as health data on disability and long-term care provided by public services were used to calculate: a) the life expectancy and b) the health expectancies Severe-Disability-Free Life Expectancy (SDFLE) and Long-Term-Care-Free Life Expectancy (LTCFLE) from 1999 to 2005. Calculations were done using the Sullivan method. RESULTS: SDFLE at birth was 69.9 years (males 66.2 and females 73.2 years) in 1999 and it increased to 71.7 years (males 68.6 and females 74.7 years) in 2005. The proportion of the SDFLE on the total life expectancy at birth was 89.8% (males 88.6 and females 90.8%) in 1999 and 90.7% (males 89.8 and females 91.4%) in 2005.LTCFLE at birth was 75.3 years (males 73.1 and females 77.5 years) in 1999 and it increased to 76.6 years (males 74.7 and females 78.6 years) in 2005. The proportion of the LTCFLE on the total life expectancy at birth was 96.8% (males 97.8 and females 96.1%) in 1999 and 96.8% (males 97.8 and females 96.2%) in 2005. DISCUSSION AND CONCLUSION: Both health expectancies indicate an improvement in the quantity as well as in the quality of healthy life for the population living in North Rhine Westphalia and therefore suggest a compression of morbidity from 1999 to 2005. The findings however have several limitations in their sensitivity, since we applied dichotomous valuations to the health states. In addition, the results are restricted to comparisons over time because the morbidity concepts do not allow for comparisons with populations other than the German one. Refined calculations with other summary measures of population health and with health data on other morbidity concepts are therefore reasonable

The poly-omics of ageing through individual-based metabolic modelling

Abstract Background Ageing can be classified in two different ways, chronological ageing and biological ageing. While chronological age is a measure of the time that has passed since birth, biological (also known as transcriptomic) ageing is defined by how time and the environment affect an individual in comparison to other individuals of the same chronological age. Recent research studies have shown that transcriptomic age is associated with certain genes, and that each of those genes has an effect size. Using these effect sizes we can calculate the transcriptomic age of an individual from their age-associated gene expression levels. The limitation of this approach is that it does not consider how these changes in gene expression affect the metabolism of individuals and hence their observable cellular phenotype. Results We propose a method based on poly-omic constraint-based models and machine learning in order to further the understanding of transcriptomic ageing. We use normalised CD4 T-cell gene expression data from peripheral blood mononuclear cells in 499 healthy individuals to create individual metabolic models. These models are then combined with a transcriptomic age predictor and chronological age to provide new insights into the differences between transcriptomic and chronological ageing. As a result, we propose a novel metabolic age predictor. Conclusions We show that our poly-omic predictors provide a more detailed analysis of transcriptomic ageing compared to gene-based approaches, and represent a basis for furthering our knowledge of the ageing mechanisms in human cells

Nephronophthisis

Nephronophthisis (NPH) is an autosomal recessive disease characterized by a chronic tubulointerstitial nephritis that progress to terminal renal failure during the second decade (juvenile form) or before the age of 5 years (infantile form). In the juvenile form, a urine concentration defect starts during the first decade, and a progressive deterioration of renal function is observed in the following years. Kidney size may be normal, but loss of corticomedullary differentiation is often observed, and cysts occur usually after patients have progressed to end-stage renal failure. Histologic lesions are characterized by tubular basement membrane anomalies, tubular atrophy, and interstitial fibrosis. The infantile form is characterized by cortical microcysts and progression to end-stage renal failure before 5 years of age. Some children present with extrarenal symptoms: retinitis pigmentosa (Senior-Løken syndrome), mental retardation, cerebellar ataxia, bone anomalies, or liver fibrosis. Positional cloning and candidate gene approaches led to the identification of eight causative genes (NPHP1, 3, 4, 5, 6, 7, 8, and 9) responsible for the juvenile NPH and one gene NPHP2 for the infantile form. NPH and associated disorders are considered as ciliopathies, as all NPHP gene products are expressed in the primary cilia, similarly to the polycystic kidney disease (PKD) proteins

The dynamic cilium in human diseases

Cilia are specialized organelles protruding from the cell surface of almost all mammalian cells. They consist of a basal body, composed of two centrioles, and a protruding body, named the axoneme. Although the basic structure of all cilia is the same, numerous differences emerge in different cell types, suggesting diverse functions. In recent years many studies have elucidated the function of 9+0 primary cilia. The primary cilium acts as an antenna for the cell, and several important pathways such as Hedgehog, Wnt and planar cell polarity (PCP) are transduced through it. Many studies on animal models have revealed that during embryogenesis the primary cilium has an essential role in defining the correct patterning of the body. Cilia are composed of hundreds of proteins and the impairment or dysfunction of one protein alone can cause complete loss of cilia or the formation of abnormal cilia. Mutations in ciliary proteins cause ciliopathies which can affect many organs at different levels of severity and are characterized by a wide spectrum of phenotypes. Ciliary proteins can be mutated in more than one ciliopathy, suggesting an interaction between proteins. To date, little is known about the role of primary cilia in adult life and it is tempting to speculate about their role in the maintenance of adult organs. The state of the art in primary cilia studies reveals a very intricate role. Analysis of cilia-related pathways and of the different clinical phenotypes of ciliopathies helps to shed light on the function of these sophisticated organelles. The aim of this review is to evaluate the recent advances in cilia function and the molecular mechanisms at the basis of their activity

Ciliopathies: an expanding disease spectrum

Ciliopathies comprise a group of disorders associated with genetic mutations encoding defective proteins, which result in either abnormal formation or function of cilia. As cilia are a component of almost all vertebrate cells, cilia dysfunction can manifest as a constellation of features that include characteristically, retinal degeneration, renal disease and cerebral anomalies. Additional manifestations include congenital fibrocystic diseases of the liver, diabetes, obesity and skeletal dysplasias. Ciliopathic features have been associated with mutations in over 40 genes to date. However, with over 1,000 polypeptides currently identified within the ciliary proteome, several other disorders associated with this constellation of clinical features will likely be ascribed to mutations in other ciliary genes. The mechanisms underlying many of the disease phenotypes associated with ciliary dysfunction have yet to be fully elucidated. Several elegant studies have crucially demonstrated the dynamic ciliary localisation of components of the Hedgehog and Wnt signalling pathways during signal transduction. Given the critical role of the cilium in transducing “outside-in” signals, it is not surprising therefore, that the disease phenotypes consequent to ciliary dysfunction are a manifestation of aberrant signal transduction. Further investigation is now needed to explore the developmental and physiological roles of aberrant signal transduction in the manifestation of ciliopathy phenotypes. Utilisation of conditional and inducible murine models to delete or overexpress individual ciliary genes in a spatiotemporal and organ/cell-specific manner should help clarify some of the functional roles of ciliary proteins in the manifestation of phenotypic features

Guidelines for diagnosis and management of the cobalamin-related remethylation disorders cblC, cblD, cblE, cblF, cblG, cblJ and MTHFR deficiency

BACKGROUND: Remethylation defects are rare inherited disorders in which impaired remethylation of homocysteine to methionine leads to accumulation of homocysteine and perturbation of numerous methylation reactions. OBJECTIVE: To summarise clinical and biochemical characteristics of these severe disorders and to provide guidelines on diagnosis and management. DATA SOURCES: Review, evaluation and discussion of the medical literature (Medline, Cochrane databases) by a panel of experts on these rare diseases following the GRADE approach. KEY RECOMMENDATIONS: We strongly recommend measuring plasma total homocysteine in any patient presenting with the combination of neurological and/or visual and/or haematological symptoms, subacute spinal cord degeneration, atypical haemolytic uraemic syndrome or unexplained vascular thrombosis. We strongly recommend to initiate treatment with parenteral hydroxocobalamin without delay in any suspected remethylation disorder; it significantly improves survival and incidence of severe complications. We strongly recommend betaine treatment in individuals with MTHFR deficiency; it improves the outcome and prevents disease when given early

Twelve-month observational study of children with cancer in 41 countries during the COVID-19 pandemic

Introduction Childhood cancer is a leading cause of death. It is unclear whether the COVID-19 pandemic has impacted childhood cancer mortality. In this study, we aimed to establish all-cause mortality rates for childhood cancers during the COVID-19 pandemic and determine the factors associated with mortality. Methods Prospective cohort study in 109 institutions in 41 countries. Inclusion criteria: children <18 years who were newly diagnosed with or undergoing active treatment for acute lymphoblastic leukaemia, non-Hodgkin's lymphoma, Hodgkin lymphoma, retinoblastoma, Wilms tumour, glioma, osteosarcoma, Ewing sarcoma, rhabdomyosarcoma, medulloblastoma and neuroblastoma. Of 2327 cases, 2118 patients were included in the study. The primary outcome measure was all-cause mortality at 30 days, 90 days and 12 months. Results All-cause mortality was 3.4% (n=71/2084) at 30-day follow-up, 5.7% (n=113/1969) at 90-day follow-up and 13.0% (n=206/1581) at 12-month follow-up. The median time from diagnosis to multidisciplinary team (MDT) plan was longest in low-income countries (7 days, IQR 3-11). Multivariable analysis revealed several factors associated with 12-month mortality, including low-income (OR 6.99 (95% CI 2.49 to 19.68); p<0.001), lower middle income (OR 3.32 (95% CI 1.96 to 5.61); p<0.001) and upper middle income (OR 3.49 (95% CI 2.02 to 6.03); p<0.001) country status and chemotherapy (OR 0.55 (95% CI 0.36 to 0.86); p=0.008) and immunotherapy (OR 0.27 (95% CI 0.08 to 0.91); p=0.035) within 30 days from MDT plan. Multivariable analysis revealed laboratory-confirmed SARS-CoV-2 infection (OR 5.33 (95% CI 1.19 to 23.84); p=0.029) was associated with 30-day mortality. Conclusions Children with cancer are more likely to die within 30 days if infected with SARS-CoV-2. However, timely treatment reduced odds of death. This report provides crucial information to balance the benefits of providing anticancer therapy against the risks of SARS-CoV-2 infection in children with cancer