Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},00$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.Comment: 12 pages, LaTe

Genome-Wide Maps of Circulating miRNA Biomarkers for Ulcerative Colitis

Inflammatory Bowel Disease – comprised of Crohn's Disease and Ulcerative Colitis (UC) - is a complex, multi-factorial inflammatory disorder of the gastrointestinal tract. In this study we have explored the utility of naturally occurring circulating miRNAs as potential blood-based biomarkers for non-invasive prediction of UC incidences. Whole genome maps of circulating miRNAs in micro-vesicles, Peripheral Blood Mononuclear Cells and platelets have been constructed from a cohort of 20 UC patients and 20 normal individuals. Through Significance Analysis of Microarrays, a signature of 31 differentially expressed platelet-derived miRNAs has been identified and biomarker performance estimated through a non-probabilistic binary linear classification using Support Vector Machines. Through this approach, classifier measurements reveal a predictive score of 92.8% accuracy, 96.2% specificity and 89.5% sensitivity in distinguishing UC patients from normal individuals. Additionally, the platelet-derived biomarker signature can be validated at 88% accuracy through qPCR assays, and a majority of the miRNAs in this panel can be demonstrated to sub-stratify into 4 highly correlated intensity based clusters. Analysis of predicted targets of these biomarkers reveal an enrichment of pathways associated with cytoskeleton assembly, transport, membrane permeability and regulation of transcription factors engaged in a variety of regulatory cascades that are consistent with a cell-mediated immune response model of intestinal inflammation. Interestingly, comparison of the miRNA biomarker panel and genetic loci implicated in IBD through genome-wide association studies identifies a physical linkage between hsa-miR-941 and a UC susceptibility loci located on Chr 20. Taken together, analysis of these expression maps outlines a promising catalog of novel platelet-derived miRNA biomarkers of clinical utility and provides insight into the potential biological function of these candidates in disease pathogenesis

Inherited determinants of Crohn's disease and ulcerative colitis phenotypes: a genetic association study

Crohn's disease and ulcerative colitis are the two major forms of inflammatory bowel disease; treatment strategies have historically been determined by this binary categorisation. Genetic studies have identified 163 susceptibility loci for inflammatory bowel disease, mostly shared between Crohn's disease and ulcerative colitis. We undertook the largest genotype association study, to date, in widely used clinical subphenotypes of inflammatory bowel disease with the goal of further understanding the biological relations between diseases

Generation of some first-order autoregressive Markovian sequences of positive random variables with given marginal distributions

Methods for simulating dependent sequences of continuous positive-valued random variables with exponential uniform, Gamma, and mixed exponential marginal distributions are given. In most cases the sequences are first-order, linear autoregressive, Markovian processes. A very broad two-parameter family of this type, GNEAR(1), with exponential marginals and both positive and negative correlation is defined and its transformation to a similar multiplicative process with uniform marginals is given. It is shown that for a subclass of this two-parameter family extension to mixed exponential marginals is possible, giving a model of broad applicability for analyzing data and modelling stochastic systems, although negative correlation is more difficult to obtain than in the exponential case. Finally, two schemes for autoregressive sequences with Gamma distributed marginals are outlined. Efficient simulation of some of these schemes is discussed. (Author)Naval Postgraduate School, Monterey, CAhttp://archive.org/details/generationofsome00lawrNAApproved for public release; distribution is unlimited

Bivariate semi α-Laplace distribution and processes

Autoregressive process, Geometric compound, Functional equation, Linnik/α-Laplace distribution, Semi α-Laplace distribution, Semi stable distribution,