The process of proving some mathematical theorems can be greatly reduced by relying on numericallyintensive computations with a certified arithmetic. This article presents a formalization of floatingpoint arithmetic that makes it possible to efficiently compute inside the proofs of the Coq system. This certified library is a multi-radix and multi-precision implementation free from underflow and...

The article describes a classification system termed "extended functional groups" (EFG), which are an extension of a set previously used by the CheckMol software, that covers in addition heterocyclic compound classes and periodic table groups. The functional groups are defined as SMARTS patterns and are available as part of the ToxAlerts tool (http://ochem.eu/alerts) of the On-line CHEmical dat...

1550-7998=20 Weakly Interacting Massive Particles (WIMPs) of mass m freeze-out at a temperature Tf ’ m=25, i.e. in the range 400 MeV– 40 GeV for a particle in the typical mass range 10–1000 GeV. The WIMP relic density, which depends on the effective number of relativistic degrees of freedom at Tf, may be measured to better than 1% by Planck, warranting comparable theoretical precision. Recent t...

We propose multi-precision similarity matching where the image is divided into a number of subblocks, each with its associated color histogram. We present experimental results showing that the spatial distribution information recorded by multiprecision color histograms helps to make similarity matching more precise. We also show that sub-image queries are much better supported with multi-precis...

An algorithm is described for multiplying multipre-cision oating point numbers. The algorithm produces either the smallest oating point number greater than or equal to the true product or the greatest oating point number smaller than or equal to the true product. Software implementations of multiprecision precision oating point multiplication can reduce the computing time by a factor of two if ...

A C-Language program which tabulates the isoscalar factors and ClebschGordan coefficients for products of representations in SU(3) is presented. These are efficiently computed using recursion relations, and the results are presented in exact precision as square roots of rational numbers. Output is in LTEX format.

The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of strange attractors. However Lorenz’ research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the existence of the Lorenz attractor remained elusive. To address that problem some authors introduced geometric Lorenz models and proved that geometric Lorenz models ...

This book is a detailed description of the algorithms used in the Yacas system for exact symbolic and arbitrary-precision numerical computations. Very few of these algorithms are new, and most are well-known. The goal of this book is to become a compendium of all relevant issues of design and implementation of these algorithms.