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

Properties and Immune Function of Cardiac Fibroblasts.

This chapter will discuss the role of cardiac fibroblasts as a target of various immunological inputs as well as an immunomodulatory hub of the heart through interaction with immune cell types and chemokine or cytokine signaling. While the purpose of this chapter is to explore the immunomodulatory properties of cardiac fibroblasts, it is important to note that cardiac fibroblasts are not a homogeneous cell type, but have a unique embryological origin and molecular identity. Specific properties of cardiac fibroblasts may influence the way they interact with the heart microenvironment to promote healthy homeostatic function or respond to pathological insults. Therefore, we will briefly discuss these aspects of cardiac fibroblast biology and then focus on their immunomodulatory role in the heart. Adv Exp Med Biol 2017; 1003:35-70