Greedy kernel methods for accelerating implicit integrators for parametric ODEs

We present a novel acceleration method for the solution of parametric ODEs by single-step implicit solvers by means of greedy kernel-based surrogate models. In an offline phase, a set of trajectories is precomputed with a high-accuracy ODE solver for a selected set of parameter samples, and used to train a kernel model which predicts the next point in the trajectory as a function of the last one. This model is cheap to evaluate, and it is used in an online phase for new parameter samples to provide a good initialization point for the nonlinear solver of the implicit integrator. The accuracy of the surrogate reflects into a reduction of the number of iterations until convergence of the solver, thus providing an overall speedup of the full simulation. Interestingly, in addition to providing an acceleration, the accuracy of the solution is maintained, since the ODE solver is still used to guarantee the required precision. Although the method can be applied to a large variety of solvers and different ODEs, we will present in details its use with the Implicit Euler method for the solution of the Burgers equation, which results to be a meaningful test case to demonstrate the method's features

First Assessment of Mountains on Northwestern Ellesmere Island, Nunavut, as Potential Astronomical Observing Sites

Ellesmere Island, at the most northerly tip of Canada, possesses the highest mountain peaks within 10 degrees of the pole. The highest is 2616 m, with many summits over 1000 m, high enough to place them above a stable low-elevation thermal inversion that persists through winter darkness. Our group has studied four mountains along the northwestern coast which have the additional benefit of smooth onshore airflow from the ice-locked Arctic Ocean. We deployed small robotic site testing stations at three sites, the highest of which is over 1600 m and within 8 degrees of the pole. Basic weather and sky clarity data for over three years beginning in 2006 are presented here, and compared with available nearby sea-level data and one manned mid-elevation site. Our results point to coastal mountain sites experiencing good weather: low median wind speed, high clear-sky fraction and the expectation of excellent seeing. Some practical aspects of access to these remote locations and operation and maintenance of equipment there are also discussed.Comment: 21 pages, 2 tables, 15 figures; accepted for publication in PAS

Nuclear Signaling Pathways for 1,25-Dihydroxyvitamin D 3 Are Controlled by the Vitamin A Metabolite, 9-cis-Retinoic Acid

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75392/1/j.1753-4887.1993.tb03060.x.pd