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Multistationarity in molecular systems underlies switch-like responses in cellular decision making. Determining whether and when a system displays multistationarity is in general a difficult problem. In this work we completely determine the set of kinetic parameters that enable multistationarity in a ubiquitous motif involved in cell signaling, namely a dual phosphorylation cycle. In addition we show that the regions of multistationarity and monostationarity are both path connected. We model the dynamics of the concentrations of the proteins over time by means of a parametrized polynomial ordinary differential equation (ODE) system arising from the mass-action assumption. Since this system has three linear first integrals defined by the total amounts of the substrate and the two enzymes, we study for what parameter values the ODE system has at least two positive steady states after suitably choosing the total amounts. We employ a suite of techniques from (real) algebraic geometry, which in particular concern the study of the signs of a multivariate polynomial over the positive orthant and sums of nonnegative circuit polynomials.

We prove the higher-dimensional analogue of Wolff's local smoothing estimate (Geom. Funct. Anal. 2001) for large p. As in the 2+1-dimensional case, the estimate is sharp for any given value of p, but it is likely that the range of p can be improved., Comment: 25 pages

A general definition of Mission Planning is given. The definition covers the full scope of an end-to-end mission planning system. Noting the mission-specific nature of most mission planning systems, a classification of autonomous spacecraft missions is made into Observatory, Survey, multi-instrument science, and Telecommunications missions. The mission planning approach for one mission in each category is examined critically. The following missions were chosen: ISO (Infrared Space Observatory); ERS-1 (European Remote Sensing Satellite); and Eureca (European Retrievable Carrier). The paper gives a summary of lessons learned from these missions suggesting improvements in areas such as requirements analysis, testing, user interfacing, rules, and constraints handling. The paper will also examine commonalities in functions, which could constitute a basis for identification of generic mission planning support tools.