Journal ArticleDOI
Landscapes of change: Catastrophe theory and biological processes
TLDR
In this paper, the catastrophe manifold is used as an illustrative metaphor for the local description of biological development, and it replaces earlier theories of development that utilized paths on an ad hoc epigenetic landscape, for example, with one that generates trajectories on a well-defined hypersurface.Abstract:
Elementary catastrophe theory provides a method for the qualitative description of systems with associated potential energy functions. It can serve at least as an illustrative metaphor for the local description of biological development. It replaces earlier theories of development that utilized paths on an ad hoc epigenetic landscape, for example, with one that generates trajectories on a well-defined hypersurface, the catastrophe manifold. While the elementary theory does provide a much richer mathematical language than the earlier geometric theories, it suffers from several drawbacks, outlined in this paper, which prevent it from being a conclusive theory for biological development.read more
Citations
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The epigenetic landscape in the course of time: Conrad Hal Waddington's methodological impact on the life sciences.
TL;DR: This paper argues that Waddington's legacy is much broader than is usually recognized--it is widespread across the life sciences (e.g. stem cell biology, developmental psychology and cultural anthropology) and shows that there exist as yet unrecognized heuristic roles, especially in model building and theory formation, which WaddINGTON's images play within his work.
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A butterfly catastrophe model of motivation in organization: Academic performance.
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Stochastic catastrophe theory in computer performance modeling
TL;DR: Deterministic Catastrophe theory is introduced first and it is shown how the theory can be applied in a stochastic framework, which is useful for understanding computer system performance models.
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Catastrophe theory in ecology: a critical review and an example of the butterfly catastrophe
TL;DR: In this article, the validity and usefulness of catastrophe theory applications in ecology was explored, expanding on an early review by Kempf, who concluded that catastrophe theory is a useful qualitative tool, but that some care must be exercised in its use.
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A cusp catastrophe model for adolescent alcohol use: An empirical test.
TL;DR: In this paper, a cusp catastrophe model was used to predict adolescent alcohol use in the context of a study with a large number of dependent variables, such as dispositions as a normal parameter and situational pressure as splitting parameter.
References
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Book
On Growth and Form
TL;DR: This book is an application of some of the concepts of physical science and sundry mathematical methods to the study of organic form and is like one of Darwin's books, well-considered, patiently wrought-out, learned, and cautious.
Journal ArticleDOI
Positional information and the spatial pattern of cellular differentiation
TL;DR: These concepts provide a unifying framework within which a wide variety of patterns formed from fields may be discussed, and give new meaning to classical concepts such as induction, dominance and field.