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Singularly perturbed dynamics of the tippedisk.

ABSTRACT: The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disc, being reminiscent of (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global analysis of the reduced system is pursued using the framework of singular perturbation theory. It is shown how the presence of friction leads to slow-fast dynamics and the creation of a two-dimensional slow manifold. Furthermore, it is revealed that a bifurcation scenario involving a homoclinic bifurcation and a Hopf bifurcation leads to an explanation of the inversion phenomenon. In particular, a closed-form condition for the critical spinning speed for the inversion phenomenon is derived. Hence, the tippedisk forms an excellent mathematical-mechanical problem for the analysis of global bifurcations in singularly perturbed dynamics.

SUBMITTER: Sailer S

PROVIDER: S-EPMC8652273 | biostudies-literature | 2021 Dec

REPOSITORIES: biostudies-literature

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Singularly perturbed dynamics of the tippedisk.

Sailer Simon S Leine Remco I RI

Proceedings. Mathematical, physical, and engineering sciences 20211208 2256

The <i>tippedisk</i> is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disc, being reminiscent of (but different from) the well-known inversion of the tippetop. A reduced model of the tippedisk, in the form of a three-dimensional ordinary differential equation, has been derived recently, followed by a preliminary local stability analysis of stationary spinning solutions. In the current paper, a global ...[more]

PMID: 35153604

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Project description:BackgroundOne of the current directions of precision medicine is the use of computational methods to aid in the diagnosis, prognosis, and treatment of disease based on data driven approaches. For instance, in oncology, there has been a particular focus on development of algorithms and biomarkers that can be used for pre-clinical and clinical applications. In particular large-scale omics-based models to predict drug sensitivity in in vitro cancer cell line panels have been used to explore the utility and aid in the development of these models as clinical tools. Additionally, a number of web-based interfaces have been constructed for researchers to explore the potential of drug perturbed gene expression as biomarkers including the NCI Transcriptional Pharmacodynamic Workbench. In this paper we explore the influence of drug perturbed gene dynamics of the NCI Transcriptional Pharmacodynamics Workbench in computational models to predict in vitro drug sensitivity for 15 drugs on the NCI60 cell line panel.ResultsThis work presents three main findings. First, our models show that gene expression profiles that capture changes in gene expression after 24 h of exposure to a high concentration of drug generates the most accurate predictive models compared to the expression profiles under different dosing conditions. Second, signatures of 100 genes are developed for different gene expression profiles; furthermore, when the gene signatures are applied across gene expression profiles model performance is substantially decreased when gene signatures developed using changes in gene expression are applied to non-drugged gene expression. Lastly, we show that the gene interaction networks developed on these signatures show different network topologies and can be used to inform selection of cancer relevant genes.ConclusionOur models suggest that perturbed gene signatures are predictive of drug response, but cannot be applied to predict drug response using unperturbed gene expression. Furthermore, additional drug perturbed gene expression measurements in in vitro cell lines could generate more predictive models; but, more importantly be used in conjunction with computational methods to discover important drug disease relationships.

Dataset Information

Singularly perturbed dynamics of the tippedisk.

Publications

Singularly perturbed dynamics of the tippedisk.

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