Thanks for the reference.

]]>“Hypergraphs, Entropy, and Inequalities”

http://www.ma.huji.ac.il/~ehudf/docs/KKLBKKKL.pdf

This entropy argument for graph homomorphism inequalities also shows up in Kopparty and Rossman “Homomorphism Domination Exponent”

http://arxiv.org/pdf/1004.2485v1.pdf

…For 18 years, my friends at CUP were laughing all the way to the bank over that funny journal of yours, and in order to make them even merrier, and to moreover give them a chance to get a bonus, I’m preparing to bring up whatever irrelevant and downright harmful “performance indicators” it takes to shoot down whatever meaningful was done during there 18 years…

]]>How to hijack a journal

http://www.sciencemag.org/content/350/6263/903.full

Obviously has a disproportionate impact on fledgling Open Access publishing supported by small publishers that might let this sort of thing slip through the cracks.

]]>http://arxiv.org/pdf/1510.06533v1.pdf

The approaches look quite different at the outset, Szegedy’s being procedural, determining general conditions under which two Sidorenko graphs may be glued together to give another Sidorenko graph, while our results yield a specific class of graphs built from trees in a certain tree-like way that satisfy the conjecture. However, the idea at the core of both results, which you describe so well here, is essentially the same. A lengthier discussion of the relationship between the results can be found in the conclusion to our paper.

]]>Dear Colleagues

Journal of Computational Mathematics

Thank you for your letter to Council calling for a Special General Meeting of the Society. The request is in order and we will organise an SGM in accordance with the Statutes.

In view of the quite understandable disappointment around the decision at the last Council meeting not to include JCM in the list of journals the LMS will publish with their commercial publisher it might be helpful to summarise some of the salient points raised in discussion and leading to that decision. Perhaps the most important point from my own perspective was the high priority, expressed in the Council discussion, for supporting this critical area of mathematics and computation with quality publications in a more effective manner. Speaking personally, I am very disappointed that this decision was necessary – but do think that it was the right decision. The key to the future is some new member-generated proposals to fill the space that is computational number theory, computational group theory and the mathematics of computational science, with high quality LMS publications that can achieve the standing and sustainability of other recently established journals, such as Nonlinearity, and the Journal of Topology.

To give some perspective and context, the JCM was set up by LMS Council in 1998. It had an initial budget of £130k to cover its launch and the original intention was to create a quality journal in this area, one that was ultimately sustainable. Attempts, between 2000 and 2002, to improve sustainability through a subscription model failed. The initial budget was spent by the end of 2003. The quality of the journal was patchy with a low impact but with excellent papers in specific sub-fields. In 2010 further efforts were made to promote the journal. When Council reviewed the position of the JCM at its meeting on 29 June 2012, CUP (and other publishers) remained unwilling to sell the journal. The Publications Committee declined an open access fee model, fearing that it would further damage the brand and would likely stop the best authors from submitting papers to the journal.

By the time of the review of the journal by Council in 2012 the total direct support provided to the journal over its by then 15 year existence, was £380k. Council took the decision to make one last effort to improve the quality and visibility of the journal. It set the journal specific performance targets to be achieved over the following three years with a review to consider possible closure at the end of that period.

It was against the set performance targets that the current Council reviewed the journal at its meeting in October this year. These goals were not entirely met, but Publications Committee had worked with the current editors on a plan for a way forward which was approved at its meeting last September, and which the Publications Secretary subsequently recommended to Council. At that meeting Council was provided with the details of the progress of the journal and the proposal for its future development, by way of a paper introduced by the Publications Secretary. There was a lengthy discussion on the issue, including that the performance of the journal was mixed in the sense that in some areas it was doing a good deal better than in others, that there seemed to be difficulty in identifying new editors of an appropriate calibre, that the Society had been attempting to improve the success of the journal for the 18 years since its inception with relatively few results.

Following this, Council decided that the Society would do better by this subject area to draw a line under this journal and start afresh with a new title or titles supporting the areas of mathematics and computation. This decision was passed by Council with 12 in favour, 5 abstentions and no one voting against. I would emphasize that the decision was not at all about income generation, but rather how the Society could best use its resources to support mathematics, and in this context, particularly computational mathematics.

The decision was a matter of judgement, of regret, and of looking for better alternatives; there were arguments for alternatives, and many were expressed at the Council meeting. In my view Council, in this nem com decision, was doing exactly what is asked of them – trying to do what works best for mathematics in an uncertain world.

Yours sincerely

Terry

Professor Terry Lyons FRSE FLSW FRS

President

Otherwise I am at loss describing this figure… ]]>

1. I think the “deducing the value of entropy from the tensor power trick” you describe is based on the Asymptotic Equipartion Property (aka Shannon-McMillan-Breiman Theorem). That is, there is a “typical set” made up of about strings of s and s, each with probability about . You are essentially using that the size of the typical set is about .

2. When you bound the size of using Jensen in the “3-cycle” case, this is really just maximum entropy again. That is, the gives a probability distribution (say ) supported on values, and the term you want to minimise is , which is therefore greater than . It may even be preferable to write this as relative entropy from a uniform distribution on values.

]]>.

And the natural way to show that seems to be (by which I mean it’s the proof I found when I worked it out for myself and I think there’s a good chance that it is the standard proof, but haven’t actually got round to looking it up) to use the tensor power trick. That is, you look at the distribution of independent Bernoulli variables (each with probability of being 0) and exploit the fact that it looks somewhat like a uniform distribution on the subsets of size from an -set. (This is an oversimplification.) Also, it is just times the entropy you’re trying to calculate. And the reason the calculations give you what you want is closely related to the fact that . ]]>

http://www.math.tau.ac.il/~nogaa/PDFS/ar2.pdf ]]>