BV solutions to a hyperbolic system of balance laws with logistic growth

We study BV solutions for a $2\times2$ system of hyperbolic balance laws. We show that when initial data have small total variation on $(-\infty,\infty)$ and small amplitude, and decay sufficiently fast to a constant equilibrium state as $|x|\rightarrow\infty$, a Cauchy problem (with generic data) has a unique admissible BV solution defined globally in time. Here the solution is admissible in the sense that its shock waves satisfy the Lax entropy condition. We also study asymptotic behavior of solutions. In particular, we obtain a time decay rate for the total variation of the solution, and a convergence rate of the solution to its time asymptotic solution. Our system is a modification of a Keller-Segel type chemotaxis model. Its flux function possesses new features when comparing to the well-known model of Euler equations with damping. This may help to shed light on how to extend the study to a general system of hyperbolic balance laws in the future

Counting derangements with signed right-to-left minima and excedances

Recently Alexandersson and Getachew proved some multivariate generalizations of a formula for enumerating signed excedances in derangements. In this paper we first relate their work to a recent continued fraction for permutations and confirm some of their observations. Our second main result is two refinements of their multivariate identities, which clearly explain the meaning of each term in their main formulas. We also explore some similar formulas for permutations of type B.Comment: Advances in Applied Mathematics 152, 10259

Research on One Novel Logging Interpretation Method of CBM Reservoir

Coalbed methane (CBM) is a kind of natural gas which is stored in the micropores and fractures of the “coal seam” and has not been transported out of the source rock. Conventional logging technology plays an important role in coalbed methane exploration and development. By analyzing the response characteristics of conventional logging of coalbed methane, coal bearing strata are accurately determined. Two methods of statistical model and volume model are established to analyze and calculate industrial components. Based on the study of adsorption isotherm and correlation between logging parameters and coal core gas content, the calculation method of coal seam gas content is determined In practices, the calculation accuracy of industrial components and gas content of coal seam has been significantly improved. Abstract: coalbed methane (CBM) is a kind of natural gas which is stored in the micropores and fractures of “coal seam” and has not been transported out of the source rock. Conventional logging technology plays an important role in coalbed methane exploration and development. By analyzing the response characteristics of conventional logging of coalbed methane, coal bearing strata are accurately determined. Two methods of statistical model and volume model are established to analyze and calculate industrial components. Based on the study of adsorption isotherm and correlation between logging parameters and coal core gas content, the calculation method of coal seam gas content is determined In practice, the calculation accuracy of industrial components and gas content of coal seam has been significantly improved

Linking protein to phenotype with Mendelian Randomization detects 38 proteins with causal roles in human diseases and traits

To efficiently transform genetic associations into drug targets requires evidence that a particular gene, and its encoded protein, contribute causally to a disease. To achieve this, we employ a three-step proteome-by-phenome Mendelian Randomization (MR) approach. In step one, 154 protein quantitative trait loci (pQTLs) were identified and independently replicated. From these pQTLs, 64 replicated locally-acting variants were used as instrumental variables for proteome-by-phenome MR across 846 traits (step two). When its assumptions are met, proteome-by-phenome MR, is equivalent to simultaneously running many randomized controlled trials. Step 2 yielded 38 proteins that significantly predicted variation in traits and diseases in 509 instances. Step 3 revealed that amongst the 271 instances from GeneAtlas (UK Biobank), 77 showed little evidence of pleiotropy (HEIDI), and 92 evidence of colocalization (eCAVIAR). Results were wide ranging: including, for example, new evidence for a causal role of tyrosine-protein phosphatase non-receptor type substrate 1 (SHPS1; SIRPA) in schizophrenia, and a new finding that intestinal fatty acid binding protein (FABP2) abundance contributes to the pathogenesis of cardiovascular disease. We also demonstrated confirmatory evidence for the causal role of four further proteins (FGF5, IL6R, LPL, LTA) in cardiovascular disease risk

Lifestyle and Genetic Factors Modify Parent-of-Origin Effects on the Human Methylome

BACKGROUND: parent-of-origin effects (POE) play important roles in complex disease and thus understanding their regulation and associated molecular and phenotypic variation are warranted. Previous studies mainly focused on the detection of genomic regions or phenotypes regulated by POE. Understanding whether POE may be modified by environmental or genetic exposures is important for understanding of the source of POE-associated variation, but only a few case studies addressing modifiable POE exist. METHODS: in order to understand this high order of POE regulation, we screened 101 genetic and environmental factors such as ‘predicted mRNA expression levels’ of DNA methylation/imprinting machinery genes and environmental exposures. POE-mQTL-modifier interaction models were proposed to test the potential of these factors to modify POE at DNA methylation using data from Generation Scotland: The Scottish Family Health Study(N=2315). FINDINGS: a set of vulnerable/modifiable POE-CpGs were identified (modifiable-POE-regulated CpGs, N=3). Four factors, ‘lifetime smoking status’ and ‘predicted mRNA expression levels’ of TET2, SIRT1 and KDM1A, were found to significantly modify the POE on the three CpGs in both discovery and replication datasets. We further identified plasma protein and health-related phenotypes associated with the methylation level of one of the identified CpGs. INTERPRETATION: the modifiable POE identified here revealed an important yet indirect path through which genetic background and environmental exposures introduce their effect on DNA methylation, motivating future comprehensive evaluation of the role of these modifiers in complex diseases. FUNDING: NSFC (81971270),H2020-MSCA-ITN(721815), Wellcome (204979/Z/16/Z,104036/Z/14/Z), MRC (MC_UU_00007/10, MC_PC_U127592696), CSO (CZD/16/6,CZB/4/276, CZB/4/710), SFC (HR03006), EUROSPAN (LSHG-CT-2006-018947), BBSRC (BBS/E/D/30002276), SYSU, Arthritis Research UK, NHLBI, NIH

Haplotype-based association analysis of general cognitive ability in Generation Scotland, the English Longitudinal Study of Ageing, and UK Biobank

Background: Cognitive ability is a heritable trait with a polygenic architecture, for which several associated variants have been identified using genotype-based and candidate gene approaches. Haplotype-based analyses are a complementary technique that take phased genotype data into account, and potentially provide greater statistical power to detect lower frequency variants. Methods: In the present analysis, three cohort studies (ntotal = 48,002) were utilised: Generation Scotland: Scottish Family Health Study (GS:SFHS), the English Longitudinal Study of Ageing (ELSA), and the UK Biobank. A genome-wide haplotype-based meta-analysis of cognitive ability was performed, as well as a targeted meta-analysis of several gene coding regions. Results: None of the assessed haplotypes provided evidence of a statistically significant association with cognitive ability in either the individual cohorts or the meta-analysis. Within the meta-analysis, the haplotype with the lowest observed P-value overlapped with the D-amino acid oxidase activator (DAOA) gene coding region. This coding region has previously been associated with bipolar disorder, schizophrenia and Alzheimer’s disease, which have all been shown to impact upon cognitive ability. Another potentially interesting region highlighted within the current genome-wide association analysis (GS:SFHS: P = 4.09 x 10-7), was the butyrylcholinesterase (BCHE) gene coding region. The protein encoded by BCHE has been shown to influence the progression of Alzheimer’s disease and its role in cognitive ability merits further investigation. Conclusions: Although no evidence was found for any haplotypes with a statistically significant association with cognitive ability, our results did provide further evidence that the genetic variants contributing to the variance of cognitive ability are likely to be of small effect

Assessing the role of genome-wide DNA methylation between smoking and risk of lung cancer using repeated measurements: the HUNT Study

Background - It is unclear if smoking-related DNA methylation represents a causal pathway between smoking and risk of lung cancer. We sought to identify novel smoking-related DNA methylation sites in blood, with repeated measurements, and to appraise the putative role of DNA methylation in the pathway between smoking and lung cancer development. Methods - We derived a nested case-control study from the Trøndelag Health Study (HUNT), including 140 incident patients who developed lung cancer during 2009–13 and 140 controls. We profiled 850 K DNA methylation sites (Illumina Infinium EPIC array) in DNA extracted from blood that was collected in HUNT2 (1995–97) and HUNT3 (2006–08) for the same individuals. Epigenome-wide association studies (EWAS) were performed for a detailed smoking phenotype and for lung cancer. Two-step Mendelian randomization (MR) analyses were performed to assess the potential causal effect of smoking on DNA methylation as well as of DNA methylation (13 sites as putative mediators) on risk of lung cancer. Results - The EWAS for smoking in HUNT2 identified associations at 76 DNA methylation sites (P –8), including 16 novel sites. Smoking was associated with DNA hypomethylation in a dose-response relationship among 83% of the 76 sites, which was confirmed by analyses using repeated measurements from blood that was collected at 11 years apart for the same individuals. Two-step MR analyses showed evidence for a causal effect of smoking on DNA methylation but no evidence for a causal link between DNA methylation and the risk of lung cancer. Conclusions - DNA methylation modifications in blood did not seem to represent a causal pathway linking smoking and the lung cancer risk