Case Studies and Challenges in Reproducibility in the Computational Sciences

This paper investigates the reproducibility of computational science research and identifies key challenges facing the community today. It is the result of the First Summer School on Experimental Methodology in Computational Science Research (https://blogs.cs.st-andrews.ac.uk/emcsr2014/). First, we consider how to reproduce experiments that involve human subjects, and in particular how to deal with different ethics requirements at different institutions. Second, we look at whether parallel and distributed computational experiments are more or less reproducible than serial ones. Third, we consider reproducible computational experiments from fields outside computer science. Our final case study looks at whether reproducibility for one researcher is the same as for another, by having an author attempt to have others reproduce their own, reproducible, paper. This paper is open, executable and reproducible: the whole process of writing this paper is captured in the source control repository hosting both the source of the paper, supplementary codes and data; we are providing setup for several experiments on which we were working; finally, we try to describe what we have achieved during the week of the school in a way that others may reproduce (and hopefully improve) our experiments.

Torsion units in integral group rings of Conway simple groups

Using the Luthar--Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups $Co_1$, $Co_2$ and $Co_3$.

Rewriting the check of 8-rewritability for $A_5$

The group $G$ is called $n$-rewritable for $n>1$, if for each sequence of $n$ elements $x_1, x_2, dots, x_n in G$ there exists a non-identity permutation $sigma in S_n$ such that $x_1 x_2 cdots x_n = x_{sigma(1)} x_{sigma(2)} cdots x_{sigma(n)}$. Using computers, Blyth and Robinson (1990) verified that the alternating group $A_5$ is 8-rewritable. We report on an independent verification of this statement using the computational algebra system GAP, and compare the performance of our sequential and parallel code with the original one.

Integral group ring of Rudvalis simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Rudvalis sporadic simple group Ru. As a consequence, for this group we confirm Kimmerles conjecture on prime graphs.

Symmetric subgroups in modular group algebras

Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical involution of the group algebra KG. We study properties of symmetric subgroups and construct a counterexample to the conjecture by V.Bovdi, which states that V(KG)=<G,S*>, where S* is a set of symmetric units of V(KG).

Integral group ring of the McLaughlin simple group

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerles conjecture on prime graphs.

Torsion units in integral group ring of Higman-Sims simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Higman-Sims simple sporadic group HS. As a consequence, we confirm the Kimmerles conjecture on prime graphs for this sporadic group.

Torsion units in integral group ring of the Mathieu simple group M22

We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of Mathieu sporadic group $M_{22}$. We confirm the Kimmerle conjecture on prime graphs for this group and specify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

Integral group ring of the Mathieu simple group M24

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group $M_{24}$. As a consequence, for this group we confirm Kimmerles conjecture on prime graphs.