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Resolving a noted open problem, we show that the Undi-rected Feedback Vertex Set problem, parameterized by the size of the solution set of vertices, is in the parameterized complexity class P oly(k), that is, polynomial-time pre-processing is sufficient to reduce an initial problem instance (G, k) to a decision-equivalent simplified instance (G , k) where k(More)
Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and(More)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. When the heat equation and wave equation are approximated by ut =(More)
We analyze the governing partial differential equations of a model of pole-to-pole oscillations of the MinD protein in a bacterial cell. The sensitivity to extrinsic noise in the parameters of the model is explored. Our analysis shows that overall, the oscillations are robust to extrinsic perturbations in the sense that small perturbations in reaction(More)
The role of mathematical models of signaling networks is showcased by examples from Drosophila development. Three models of consecutive stages in dorsoventral patterning are presented. We begin with a compartmental model of intracellular reactions that generates a gradient of nuclear-localized Dorsal, exhibiting constant shape and dynamic amplitude. A(More)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. Many systems of equations fit naturally in the form du/dt = A(u) +(More)