“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Web-based access to mouse models of human cancers: the Mouse Tumor Biology (MTB) Database

The Mouse Tumor Biology (MTB) Database serves as a curated, integrated resource for information about tumor genetics and pathology in genetically defined strains of mice (i.e., inbred, transgenic and targeted mutation strains). Sources of information for the database include the published scientific literature and direct data submissions by the scientific community. Researchers access MTB using Web-based query forms and can use the database to answer such questions as ‘What tumors have been reported in transgenic mice created on a C57BL/6J background?’, ‘What tumors in mice are associated with mutations in the Trp53 gene?’ and ‘What pathology images are available for tumors of the mammary gland regardless of genetic background?’. MTB has been available on the Web since 1998 from the Mouse Genome Informatics web site (http://www.informatics.jax.org). We have recently implemented a number of enhancements to MTB including new query options, redesigned query forms and results pages for pathology and genetic data, and the addition of an electronic data submission and annotation tool for pathology data.