Making big steps in trajectories

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a similar computation time

Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page

A reformulation of Hilbert's tenth problem through Quantum Mechanics

Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into either a problem involving a set of infinitely coupled differential equations or a problem involving a Shr\"odinger propagator with some appropriate kernel. Either way, Mathematics and Physics could be combined for Hilbert's tenth problem and for the notion of effective computability

Evaluating targeted cash transfer programs: a general equilibrium framework with an application to Mexico

This report focuses on the indirect and direct effects of transfer programs. In particular, it shows how modelling results can be combined with information from standard household surveys to provide an integrated analysis of the direct distributional impact of such programs and the indirect distributional and efficiency impacts arising from domestic financing mechanisms. This approach reflects the view that any credible poverty alleviation strategy must have a credible financing strategy underlying it, and this need for domestic financing can have important consequences for both the level and the distribution of household incomes. To illustrate the approach, the report focuses on the recent introduction in Mexico of an innovative poverty alleviation transfer program called PROGRESA, which has been used as a prototype for similar programs that have recently been implemented in other developing countries.Economic assistance, Domestic Mexico Evaluation, Public welfare - Mexico Evaluation,