Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Adrenergic and serotonergic function in dna synthesis during rat liver regeneration and in hepatocyte cultures

The adult mammalian liver is predominantly in a quiescent state with respect to cell division. This quiescent state changes dramatically, however, if the liver is injured by toxic, infectious or mechanic agents (Ponder, 1996). Partial hepatectomy (PH) which consists of surgical removal of two-thirds of the liver, has been used to stimulate hepatocyte proliferation (Higgins & Anderson 1931). This experimental model of liver regeneration has been the target of many studies to probe the mechanisms responsible for liver cell growth control (Michalopoulos, 1990; Taub, 1996). After PH most of the remaining cells in the renmant liver respond with co-ordinated waves of DNA synthesis and divide in a process called compensatory hyperplasia. Hence, liver regeneration is a model of relatively synchronous cell cycle progression in vivo. In contrast to hepatomas, cell division is terminated under some intrinsic control when the original cellular mass has been regained. This has made liver regeneration a useful model to dissect the biochemical and molecular mechanisms of cell division regulation. The liver is thus, one of the few adult organs that demonstrates a physiological growth rewonse (Fausto & Mead, 1989; Fausto & Webber, 1994). The regulation of liver cell proliferation involves circulating or intrahepatic factors that are involved in either the priming of hepatocytes to enter the cell cycle (Go to G1) or progression through the cell cycle. In order to understand the basis of liver regeneration it is mandatory to define the mechanisms which (a) trigger division, (b) allow the liver to concurrently grow and maintain dilferentiated fimction and (c) terminate cell proliferation once the liver has reached the appropriate mass. Studies on these aspects of liver regeneration will provide basic insight of cell growth and dilferentiation, liver diseases like viral hepatitis, toxic damage and liver transplant where regeneration of the liver is essential. In the present study, Go/G1/S transition of hepatocytes re-entering the cell cycle after PH was studied with special emphasis on the involvement of neurotransmitters, their receptors and second messenger function in the control of cell division during liver regeneration