An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Sequencing of a 17.6 kb segment on the right arm of yeast chromosome VII reveals 12 ORFs, including CCT, ADE3 and TR-I genes, homologues of the yeast PMT and EF1G genes, of the human and bacterial electron-transferring flavoproteins (beta-chain) and of the Escherichia coli phosphoserine phosphohydrolase, and five new ORFs.

A 17.6 kb DNA fragment from the right arm of chromosome VII of Saccharomyces cerevisiae has been sequenced and analysed. The sequence contains twelve open reading frames (ORFs) longer than 100 amino acids. Three genes had already been cloned and sequenced: CCT, ADE3 and TR-I. Two ORFs are similar to other yeast genes: G7722 with the YAL023 (PMT2) and PMT1 genes, encoding two integral membrane proteins, and G7727 with the first half of the genes encoding elongation factors 1gamma, TEF3 and TEF4. Two other ORFs, G7742 and G7744, are most probably yeast orthologues of the human and Paracoccus denitrificans electron-transferring flavoproteins (beta chain) and of the Escherichia coli phosphoserine phosphohydrolase. The five remaining identified ORFs do not show detectable homology with other protein sequences deposited in data banks. The sequence has been deposited in the EMBL data library under Accession Number Z49133.