We study a precise class of dynamical systems that we call solvable ordinary differential
equations. We prove that analog systems mathematically ruled by solvable ordinary …

Abstract Reasoning about dynamical systems evolving over the reals is well-known to lead
to undecidability. In particular, it is known that there cannot be reachability decision …

We study initial value problems having dynamics ruled by discontinuous ordinary differential
equations with the property of possessing a unique solution. We identify a precise class of …

This article presents two meshless computational techniques: the radial basis function (RBF)
method and the polynomial method, for numerically analyzing boundary layer problems …

In a recent article, we introduced and studied a precise class of dynamical systems called
solvable systems. These systems present a dynamic ruled by discontinuous ordinary …

Models of computations over the integers are equivalent from a computability and
complexity theory point of view by the Church-Turing thesis. It is not possible to unify discrete …

Verification of discrete time or continuous time dynamical systems over the reals is known to
be undecidable. It is however known that undecidability does not hold for various classes of …

This thesis explores the characteristics and applications of Lipschitz networks in machine
learning tasks. First, the framework of" optimization as a layer" is presented, showcasing …

Many recent works study how analogue models work, compared to classical digital ones
([6]). By “analogue” models of computation, we mean computing over continuous quantities …