Fractional reaction-diffusion equations

In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for reaction-diffusion systems with L\'evy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.Comment: LaTeX, 17 pages, corrected typo

Overlap of Genetic Risk between Interstitial Lung Abnormalities and Idiopathic Pulmonary Fibrosis

Rationale: Interstitial lung abnormalities (ILAs) are associated with the highest genetic risk locus for idiopathic pulmonary fibrosis (IPF); however, the extent to which there are unique associations among individuals with ILAs or additional overlap with IPF is not known.Objectives: To perform a genome-wide association study (GWAS) of ILAs.Methods: ILAs and a subpleural-predominant subtype were assessed on chest computed tomography (CT) scans in the AGES (Age Gene/Environment Susceptibility), COPDGene (Genetic Epidemiology of Chronic Obstructive Pulmonary Disease [COPD]), Framingham Heart, ECLIPSE (Evaluation of COPD Longitudinally to Identify Predictive Surrogate End-points), MESA (Multi-Ethnic Study of Atherosclerosis), and SPIROMICS (Subpopulations and Intermediate Outcome Measures in COPD Study) studies. We performed a GWAS of ILAs in each cohort and combined the results using a meta-analysis. We assessed for overlapping associations in independent GWASs of IPF.Measurements and Main Results: Genome-wide genotyping data were available for 1,699 individuals with ILAs and 10,274 control subjects. The MUC5B (mucin 5B) promoter variant rs35705950 was significantly associated with both ILAs (P = 2.6 × 10-27) and subpleural ILAs (P = 1.6 × 10-29). We discovered novel genome-wide associations near IPO11 (rs6886640, P = 3.8 × 10-8) and FCF1P3 (rs73199442, P = 4.8 × 10-8) with ILAs, and near HTRE1 (rs7744971, P = 4.2 × 10-8) with subpleural-predominant ILAs. These novel associations were not associated with IPF. Among 12 previously reported IPF GWAS loci, five (DPP9, DSP, FAM13A, IVD, and MUC5B) were significantly associated (P < 0.05/12) with ILAs.Conclusions: In a GWAS of ILAs in six studies, we confirmed the association with a MUC5B promoter variant and found strong evidence for an effect of previously described IPF loci; however, novel ILA associations were not associated with IPF. These findings highlight common genetically driven biologic pathways between ILAs and IPF, and also suggest distinct ones

Regulation and manipulation of body reserves along the lactation cycle

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