From simulating galaxy formation to viral transmission in a pandemic, scientific models play a pivotal role in developing scientific theories and supporting government policy decisions that affect us all. Given these critical applications, a poor modelling assumption or bug could have far-reaching consequences. However, scientific models possess several properties that make them notoriously difficult to test, including a complex input space, long execution times, and non-determinism, rendering existing testing techniques impractical. In fields such as epidemiology, where researchers seek answers to challenging causal questions, a statistical methodology known as Causal inference has addressed similar problems, enabling the inference of causal conclusions from noisy, biased, and sparse data instead of costly experiments. This article introduces the causal testing framework: a framework that uses causal inference techniques to establish causal effects from existing data, enabling users to conduct software testing activities concerning the effect of a change, such as metamorphic testing, a posteriori . We present three case studies covering real-world scientific models, demonstrating how the causal testing framework can infer metamorphic test outcomes from reused, confounded test data to provide an efficient solution for testing scientific modelling software.

The monolithic integration of III-V nanowires on silicon by direct epitaxial growth enables new possibilities for the design and fabrication of electronic as well as optoelectronic devices. We demonstrate a new growth technique to directly integrate III-V semiconducting nanowires on silicon using selective area epitaxy within a nanotube template. Thus we achieve small diameter nanowires, controlled doping profiles and sharp heterojunctions essential for future device applications. We experimentally demonstrate vertical tunnel diodes and gate-all-around tunnel FETs based on InAs-Si nanowire heterojunctions. The results indicate the benefits of the InAs-Si material system combining the possibility of achieving high Ionwith high Ion/Ioffratio.

A Laguerre tessellation is a generalization of a Voronoi tessellation where the proximity between points is measured via a power distance rather than the Euclidean distance. Laguerre tessellations have found significant applications in materials science, providing improved modeling of (poly)crystalline microstructures and grain growth. There exist efficient algorithms to construct Laguerre tessellations from given sets of weighted generator points, similar to methods used for Voronoi tessellations. The purpose of this paper is to provide theory and methodology for the inverse construction; that is, to recover the weighted generator points from a given Laguerre tessellation. We show that, unlike the Voronoi case, the inverse problem is in general non-unique: different weighted generator points can create the same tessellation. To recover pertinent generator points, we formulate the inversion problem as a multimodal optimization problem and apply the cross-entropy method to solve it.

We investigate Cox processes of random point patterns in the Euclidean plane, which are located on the edges of random geometric graphs. Such Cox processes have applications in the performance analysis and strategic planning of both wireless and wired telecommunication networks. They simultaneously allow to represent the underlying infrastructure of the network together with the locations of network components. In particular, we analyze the Palm version X* of stationary Cox processes X living on random graphs that are built by the edges of an iterated random tessellation T. We derive a representation formula for the Palm version T* of T which includes the initial tessellation T0and the component tessellation T1of T as well as their Palm versions T*0and T*1. Using this formula, we are able to construct a simulation algorithm for X* if both T0, T1and their Palm versions T*0, T*1can be simulated. This algorithm for X* extends earlier results for Cox processes on simpler (non-iterated) tessellations. It can be used, for example, in order to estimate the probability densities of various connection distances, which are important performance characteristics of telecommunication networks. In a numerical study we consider the particular case that T0is a Poisson-Voronoi tessellation and T1is a Poisson line tessellation.

Stochastic models for hierarchical telecommunication networks are considered, which can be applied to the analysis and planning of large wireless networks. The network geometry is modelled by random geometric graphs, and the locations of network nodes by point processes on the edges of these graphs. In particular, the locations of high-level components (HLC) are modeled by Cox processes concentrated on the edge sets of random graphs, where their serving zones are the cells of Voronoi tessellations induced by these Cox processes. The locations of low-level components (LLC) are either modeled by planar Poisson processes or by Cox processes concentrated on the same edge sets as the HLC. Distributional properties of distances between the locations of network nodes are closely related with the interference geometry and, consequently, the performance of wireless networks. Representation formulas are derived for the distribution function and density of the typical Euclidean connection distance between LLC and HLC. They lead to suitable estimators of these characteristics, which can be computed by Monte Carlo simulation of the typical serving zone and the typical segment system in it, respectively.