English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Complex systems can fail through different routes, often progressing througha series of (rate-limiting) steps and modified by environmental exposures. Theonset of disease, cancer in particular, is no different. Multi-stage modelsprovide a simple but very general mathematical framework for studying thefailure of complex systems, or equivalently, the onset of disease. They includethe Armitage Doll multi-stage cancer model as a particular case, and havepotential to provide new insights into how failures and disease, arise andprogress. A method described by E.T. Jaynes is developed to provide ananalytical solution for a large class of these models, and highlightsconnections between the convolution of Laplace transforms, sums of randomvariables, and Schwinger/Feynman parameterisations. Examples include: exactsolutions to the Armitage-Doll model, the sum of Gamma-distributed variableswith integer-valued shape parameters, a clonal-growth cancer model, and a modelfor cascading disasters. Applications and limitations of the approach arediscussed in the context of recent cancer research. The model is sufficientlygeneral to be used in many contexts, such as engineering, project management,disease progression, and disaster risk for example, allowing the estimation offailure rates in complex systems and projects. The intended result is amathematical toolkit for applying multi-stage models to the study of failurerates in complex systems and to the onset of disease, cancer in particular.

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease