The development of alternative methods to animal experimentation has progressed rapidly over the last 20 years. Today, in vitro and in silico methods have an important role in the hazard identification and assessment of toxicology profile of compounds. Advanced alternative methods and their combinations are also used for safety assessment of final products. Several alternative methods, which we...

We propose a method of using validated interval constraint contraction operators to build routines for numerical computation libraries. We illustrate the method by using it to construct a procedure that e ciently computes a small interval containing f 1(h) where f(x) = x sin(x). This can be transformed into a numerical routine by returning the midpoint of the interval and signalling an exceptio...

Because of the importance of special functions, several books and a large collection of papers have been devoted to the numerical computation of these functions, the most well-known being the NBS handbook by Abramowitz and Stegun. But up to this date, symbolic and numeric environments offer no routines for the validated evaluation of special functions. We point out how a provable correct functi...

Many applications aim to learn a high dimensional parameter of a data generating distribution based on a sample of independent and identically distributed observations. For example, the goal might be to estimate the conditional mean of an outcome given a list of input variables. In this prediction context, bootstrap aggregating (bagging) has been introduced as a method to reduce the variance of...

To reason about programs written in a language, one needs to define its formal semantics, derive a reasoning mechanism (e.g. a program logic), and maximize the proof automation. Unfortunately, a compiler may involve multiple languages and phases; it is tedious and error prone to do so for each language and each phase. We present an approach based on the use of higher order logic to ease this bu...

The aim of this paper is to give a very brief introduction to the emerging area of validated numerics. This is a rapidly growing field of research faced with the challenge of interfacing computer science and pure mathematics. Most validated numerics is based on interval analysis, which allows its users to account for both rounding and discretization errors in computer-aided proofs. We will illu...