Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60

Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

Asymptotic and structural properties of special cases of the Wright function arising in probability theory

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function 1Ψ1(ρ, k; ρ, 0; x) = X∞ n=0 Γ(k + ρn) Γ(ρn) x n n! (|x| < ∞) when the parameter ρ ∈ (−1, 0)∪(0, ∞) and the argument x is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter k is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of ρ. The asymptotics of 1Ψ1(ρ, k; ρ, 0; x) are obtained under numerous assumptions on the behavior of the arguments k and x when the parameter ρ is both positive and negative. We also provide some integral representations and structural properties involving the ‘reduced’ Wright function 0Ψ1(−−; ρ, 0; x) with ρ ∈ (−1, 0) ∪ (0, ∞), which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions 0Ψ1(−−;±ρ, 0; ·) and certain Bessel functions. Several asymptotic relationships for both particular cases of this function are also given. A few of these follow under additional constraints from probability theory results which, although previously available, were unknown to analysts.

On Hankel Transform of Generalized Mathieu Series

Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20

Evolutionary genomics of the Fox genes: origin of gene families and the ancestry of gene clusters

Over the past decade genomic approaches have begun to revolutionise the study of animal diversity. In particular, genome sequencing programmes have spread beyond the traditional model species to encompass an increasing diversity of animals from many different phyla, as well as unicellular eukaryotes that are closely related to the animals. Whole genome sequences allow researchers to establish, with reasonable confidence, the full complement of any particular family of genes in a genome. Comparison of gene complements from appropriate genomes can reveal the evolutionary history of gene families, indicating when both gene diversification and gene loss have occurred. More than that, however, assembled genomes allow the genomic environment in which individual genes are found to be analysed and compared between species. This can reveal how gene diversification occurred. Here, we focus on the Fox genes, drawing from multiple animal genomes to develop an evolutionary framework explaining the timing and mechanism of origin of the diversity of animal Fox genes. Ancient linkages between genes are a prominent feature of the Fox genes, depicting a history of gene clusters, some of which may be relevant to understanding Fox gene function.

Renewal Processes of Mittag-Leffler and Wright Type

2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.

Generalization of the Modified Bessel Function and Its Generating Function

2000 Mathematics Subject Classification: 33C10, 33-02, 60K25

Krätzel Function as a Function of Hypergeometric Type

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15

Matrix-Variate Statistical Distributions and Fractional Calculus

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday

Integration of genome-wide association studies with biological knowledge identifies six novel genes related to kidney function.

In conducting genome-wide association studies (GWAS), analytical approaches leveraging biological information may further understanding of the pathophysiology of clinical traits. To discover novel associations with estimated glomerular filtration rate (eGFR), a measure of kidney function, we developed a strategy for integrating prior biological knowledge into the existing GWAS data for eGFR from the CKDGen Consortium. Our strategy focuses on single nucleotide polymorphism (SNPs) in genes that are connected by functional evidence, determined by literature mining and gene ontology (GO) hierarchies, to genes near previously validated eGFR associations. It then requires association thresholds consistent with multiple testing, and finally evaluates novel candidates by independent replication. Among the samples of European ancestry, we identified a genome-wide significant SNP in FBXL20 (P = 5.6 × 10(-9)) in meta-analysis of all available data, and additional SNPs at the INHBC, LRP2, PLEKHA1, SLC3A2 and SLC7A6 genes meeting multiple-testing corrected significance for replication and overall P-values of 4.5 × 10(-4)-2.2 × 10(-7). Neither the novel PLEKHA1 nor FBXL20 associations, both further supported by association with eGFR among African Americans and with transcript abundance, would have been implicated by eGFR candidate gene approaches. LRP2, encoding the megalin receptor, was identified through connection with the previously known eGFR gene DAB2 and extends understanding of the megalin system in kidney function. These findings highlight integration of existing genome-wide association data with independent biological knowledge to uncover novel candidate eGFR associations, including candidates lacking known connections to kidney-specific pathways. The strategy may also be applicable to other clinical phenotypes, although more testing will be needed to assess its potential for discovery in general.

Common variants in mendelian kidney disease genes and their association with renal function.

Many common genetic variants identified by genome-wide association studies for complex traits map to genes previously linked to rare inherited Mendelian disorders. A systematic analysis of common single-nucleotide polymorphisms (SNPs) in genes responsible for Mendelian diseases with kidney phenotypes has not been performed. We thus developed a comprehensive database of genes for Mendelian kidney conditions and evaluated the association between common genetic variants within these genes and kidney function in the general population. Using the Online Mendelian Inheritance in Man database, we identified 731 unique disease entries related to specific renal search terms and confirmed a kidney phenotype in 218 of these entries, corresponding to mutations in 258 genes. We interrogated common SNPs (minor allele frequency >5%) within these genes for association with the estimated GFR in 74,354 European-ancestry participants from the CKDGen Consortium. However, the top four candidate SNPs (rs6433115 at LRP2, rs1050700 at TSC1, rs249942 at PALB2, and rs9827843 at ROBO2) did not achieve significance in a stage 2 meta-analysis performed in 56,246 additional independent individuals, indicating that these common SNPs are not associated with estimated GFR. The effect of less common or rare variants in these genes on kidney function in the general population and disease-specific cohorts requires further research.

Genome-wide association and functional follow-up reveals new loci for kidney function.

Chronic kidney disease (CKD) is an important public health problem with a genetic component. We performed genome-wide association studies in up to 130,600 European ancestry participants overall, and stratified for key CKD risk factors. We uncovered 6 new loci in association with estimated glomerular filtration rate (eGFR), the primary clinical measure of CKD, in or near MPPED2, DDX1, SLC47A1, CDK12, CASP9, and INO80. Morpholino knockdown of mpped2 and casp9 in zebrafish embryos revealed podocyte and tubular abnormalities with altered dextran clearance, suggesting a role for these genes in renal function. By providing new insights into genes that regulate renal function, these results could further our understanding of the pathogenesis of CKD.

Meta-analysis identifies multiple loci associated with kidney function-related traits in east Asian populations.

Chronic kidney disease (CKD), impairment of kidney function, is a serious public health problem, and the assessment of genetic factors influencing kidney function has substantial clinical relevance. Here, we report a meta-analysis of genome-wide association studies for kidney function-related traits, including 71,149 east Asian individuals from 18 studies in 11 population-, hospital- or family-based cohorts, conducted as part of the Asian Genetic Epidemiology Network (AGEN). Our meta-analysis identified 17 loci newly associated with kidney function-related traits, including the concentrations of blood urea nitrogen, uric acid and serum creatinine and estimated glomerular filtration rate based on serum creatinine levels (eGFRcrea) (P < 5.0 × 10(-8)). We further examined these loci with in silico replication in individuals of European ancestry from the KidneyGen, CKDGen and GUGC consortia, including a combined total of ∼110,347 individuals. We identify pleiotropic associations among these loci with kidney function-related traits and risk of CKD. These findings provide new insights into the genetics of kidney function.

Genetic associations at 53 loci highlight cell types and biological pathways relevant for kidney function.

Reduced glomerular filtration rate defines chronic kidney disease and is associated with cardiovascular and all-cause mortality. We conducted a meta-analysis of genome-wide association studies for estimated glomerular filtration rate (eGFR), combining data across 133,413 individuals with replication in up to 42,166 individuals. We identify 24 new and confirm 29 previously identified loci. Of these 53 loci, 19 associate with eGFR among individuals with diabetes. Using bioinformatics, we show that identified genes at eGFR loci are enriched for expression in kidney tissues and in pathways relevant for kidney development and transmembrane transporter activity, kidney structure, and regulation of glucose metabolism. Chromatin state mapping and DNase I hypersensitivity analyses across adult tissues demonstrate preferential mapping of associated variants to regulatory regions in kidney but not extra-renal tissues. These findings suggest that genetic determinants of eGFR are mediated largely through direct effects within the kidney and highlight important cell types and biological pathways.