The fundamental principles of reproducibility

Reproducibility is a confused terminology. In this paper, I take a fundamental view on reproducibility rooted in the scientific method. The scientific method is analysed and characterized in order to develop the terminology required to define reproducibility. Furthermore, the literature on reproducibility and replication is surveyed, and experiments are modelled as tasks and problem solving methods. Machine learning is used to exemplify the described approach. Based on the analysis, reproducibility is defined and three different degrees of reproducibility as well as four types of reproducibility are specified. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

Dark Gravitational Field on Riemannian and Sasaki Spacetime

The aim of this paper is to provide the geometrical structure of a gravitational field that includes the addition of dark matter in the framework of a Riemannian and a Riemann–Sasaki spacetime. By means of the classical Riemannian geometric methods we arrive at modified geodesic equations, tidal forces, and Einstein and Raychaudhuri equations to account for extra dark gravity. We further examine an application of this approach in cosmology. Moreover, a possible extension of this model on the tangent bundle is studied in order to examine the behavior of dark matter in a unified geometric model of gravity with more degrees of freedom. Particular emphasis shall be laid on the problem of the geodesic motion under the influence of dark matter.

A measurement of the Hubble constant from angular diameter distances to two gravitational lenses

The local expansion rate of the Universe is parametrized by the Hubble constant, [Formula: see text], the ratio between recession velocity and distance. Different techniques lead to inconsistent estimates of [Formula: see text] Observations of Type Ia supernovae (SNe) can be used to measure [Formula: see text], but this requires an external calibrator to convert relative distances to absolute ones. We use the angular diameter distance to strong gravitational lenses as a suitable calibrator, which is only weakly sensitive to cosmological assumptions. We determine the angular diameter distances to two gravitational lenses, [Formula: see text] and [Formula: see text] megaparsec, at redshifts [Formula: see text] and 0.6304. Using these absolute distances to calibrate 740 previously measured relative distances to SNe, we measure the Hubble constant to be [Formula: see text] kilometers per second per megaparsec.