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I spent a week in St Andrews working with Markus Pfeiffer on an ongoing project which we are working on writing and implementing an algorithm to construct 2-closed Majorana representations. Funding for this trip was provided by CoDiMa.
Majorana algebras are non-associate algebras used to study the Monster group and its subgroups. They can be studied either in their own right, or as Majorana representations of certain groups. Many examples of Majorana algebras have been constructed by hand but it has become clear that, in order to construct bigger and more interesting algebras, a more computational approach is needed.
In a celebrated paper in 2012, Akos Seress announced the existence of an algorithm to constuct 2-closed Majorana representations. Sadly Seress passed away in 2013 and the full details of his algorithm and his results were never published. Recovering his work has been an important aim of the theory ever since.
This was my second visit funded by CoDiMa to work on this project. After the first visit, we had implemented such an algorithm and had started to reproduce Seress’ results. However, constructing Majorana representations is very expensive both in terms of time and memory and so the algorithm requires a lot of optimisation, which was the focus of our work this time around.
The week was a sucess and we have now completely recovered Seress’ results and we are expecting to shortly be able to construct representations larger than those achieved by Seress.
Our work is available on GitHub.
This is the fourth part part of Peter Cameron‘s trilogy on open science. For the other parts, see Open Publication, Open Data and Open Software. If you would like to leave comments for the author, please leave them here.
Douglas Adams wrote The Hitch-Hiker’s Guide to the Galaxy as a radio series. It was published in book form as a trilogy, but later he added two further parts. At the start of the first part, the Earth is destroyed. Later we learn that it hasn’t really been destroyed, but at the end of the last part it is destroyed again, and we are led to understand that this time is for real. Presumably he didn’t want to write any more.
More modestly, here is the fourth part of my trilogy on open science. It is devoted to the question How do we acknowledge the source of funding for our research?
At first it seems obvious that we should do this. But as ever I believe that things are not so clear-cut. (more…)
This is the third part of Peter Cameron‘s post on Open Publication, Open Data and Open Software (the fourth part of the trilogy, called Open Research Funding, appeared later). If you would like to leave comments for the author, please leave them here.
My thoughts about this were sparked by reading the presidential address to the Royal Statistical Society by Peter Diggle. The title was “Data science and statistics”, and the address covered much more than open software. But one of the points he makes is particularly relevant:
Principally, we learn that a published article is no longer a complete solution to a practical problem. We need our solutions to be implemented in software, preferably open source so that others can not only use but also test and, if need be, improve our solutions. We also need to provide high quality documentation for the software. And in many cases we need to offer an accessible, bespoke user interface.
At a time when some research organisations (even high-status ones) are dispensing with statisticians on the grounds that every researcher has on her desk a computer running Excel, it is necessary to be very clear about what researchers can add. One area where expertise matters is experimental design. (more…)
This is the second part of Peter Cameron‘s post on Open Publication, Open Data and Open Software (the fourth part of the trilogy, called Open Research Funding, appeared later). If you would like to leave comments for the author, please leave them here.
I recently wrote about open data on my own blog; some of the points I made there will be repeated.
Open data is an important issue. For example, drug companies invest huge sums of money in new drugs, and have traditionally been reluctant to advertise the failure of a drug in clinical trials. It can be worse; sometimes they can cherry-pick the results of the trials and claim that the drug is useful in some situations. Ben Goldacre and others are campaigning for more transparency in the publication of clinical trials.
More generally, scientific journals tend to have a publication bias towards positive results, so that an important study finding no connection between certain factors may be suppressed, leading to repetition and waste of resources. This has led to calls for all experimental data to be made freely available to all researchers, subject to various safeguards.
I began to think about this when I was asked to comment on a draft concordat proposed by the UK research councils on open data. Here is their definition of research data: (more…)
Peter Cameron is a half-time Professor in the School of Mathematics and Statistics at the University of St Andrews, and an Emeritus Professor of Mathematics at Queen Mary, University of London. His blog is cameroncounts.wordpress.com. Here we are publishing his new blog post which he kindly wrote for our website. It consists of three parts: Open Publication (below), Open Data and Open Software (the fourth part of the trilogy, called Open Research Funding, appeared later). If you would like to leave comments for the author, please leave them here.
The Internet has brought about big changes in the way we do science. Recently, a word very much favoured by science funders is “open”. I want to say a few things about this, under three headings (open publication, open data, open software) which raise different issues for the scientific community.
I write as a pure mathematician here. Some of the issues are not so relevant in mathematics; others are relevant, but perhaps with a twist. There are things which concern all scientific researchers.
On the face of it, open publication (accessible to all readers without cost) sounds as harmless as apple pie. But all is not so simple … (more…)