A Robust and Efficient Method for Solving Point Distance Problems by Homotopy

The goal of Point Distance Solving Problems is to find 2D or 3D placements of points knowing distances between some pairs of points. The common guideline is to solve them by a numerical iterative method (\emph{e.g.} Newton-Raphson method). A sole solution is obtained whereas many exist. However the number of solutions can be exponential and methods should provide solutions close to a sketch drawn by the user.Geometric reasoning can help to simplify the underlying system of equations by changing a few equations and triangularizing it.This triangularization is a geometric construction of solutions, called construction plan. We aim at finding several solutions close to the sketch on a one-dimensional path defined by a global parameter-homotopy using a construction plan. Some numerical instabilities may be encountered due to specific geometric configurations. We address this problem by changing on-the-fly the construction plan.Numerical results show that this hybrid method is efficient and robust

Study of First-Order Thermal Sigma-Delta Architecture for Convective Accelerometers

This paper presents the study of an original closed-loop conditioning approach for fully-integrated convective inertial sensors. The method is applied to an accelerometer manufactured on a standard CMOS technology using an auto-aligned bulk etching step. Using the thermal behavior of the sensor as a summing function, a first order sigma-delta modulator is built. This "electro-physical" modulator realizes an analog-to-digital conversion of the signal. Besides the feedback scheme should improve the sensor performance.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838

The Busy Beaver Competition: a historical survey

Tibor Rado defined the Busy Beaver Competition in 1962. He used Turing machines to give explicit definitions for some functions that are not computable and grow faster than any computable function. He put forward the problem of computing the values of these functions on numbers 1, 2, 3, ... More and more powerful computers have made possible the computation of lower bounds for these values. In 1988, Brady extended the definitions to functions on two variables. We give a historical survey of these works. The successive record holders in the Busy Beaver Competition are displayed, with their discoverers, the date they were found, and, for some of them, an analysis of their behavior.Comment: 70 page