Algebraic Systems Biology: A Case Study for the Wnt Pathway

Steady state analysis of dynamical systems for biological networks give rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here the variety is described by a polynomial system in 19 unknowns and 36 parameters. Current methods from computational algebraic geometry and combinatorics are applied to analyze this model.Comment: 24 pages, 2 figure

Autonomous control procedures for shuttle rendezvous proximity operations

The results are presented of a study which uses fuzzy sets to model a Space Shuttle pilot's reasoning and actions while performing rendezvous proximity operation maneuvers. In this model fuzzy sets are used to simulate smooth and continuous actions as would be expected from an experienced pilot and to simulate common sense reasoning in the decision process. The present model assumes visual information available to the Shuttle pilot from the Shuttle Crew Optical Alignment Sighting (COAS) device and the overhead window and rendezvous radar sensor information available to him from an onboard display. This model will be used in a flight analysis simulator to perform studies requiring a large number of runs, each of which currently needs an engineer in the loop to supply the piloting decisions. This work has much broader implications in control of robots such as the Flight Telerobotic Servicer, in automated pilot control and attitude control, and in advisory and evaluation functions that could be used for flight data monitoring or for testing of various rule sets in flight preparation

Simple models suffice for the single dot quantum shuttle

A quantum shuttle is an archetypical nanoelectromechanical device, where the mechanical degree of freedom is quantized. Using a full-scale numerical solution of the generalized master equation describing the shuttle, we have recently shown [Novotn\'{y} {\it et al.}, Phys. Rev. Lett. {\bf 92}, 248302 (2004)] that for certain limits of the shuttle parameters one can distinguish three distinct charge transport mechanisms: (i) an incoherent tunneling regime, (ii) a shuttling regime, where the charge transport is synchronous with the mechanical motion, and (iii) a coexistence regime, where the device switches between the tunneling and shuttling regimes. While a study of the cross-over between these three regimes requires the full numerics, we show here that by identifying the appropriate time-scales it is possible to derive vastly simpler equations for each of the three regimes. The simplified equations allow a clear physical interpretation, are easily solved, and are in good agreement with the full numerics in their respective domains of validity.Comment: 23 pages, 14 figures, invited paper for the Focus issue of the New Journal of Physics on Nano-electromechanical system