Author Archives: wilson.mark.c

Introductory lectures on analysis of algorithms

After teaching a basic course on data structures and algorithms many times, I grew weary of saying the same things each semester, yet never quite saying them right. So I spent (too) many hours in the studio and editing on my laptop, to produce some short (mostly 15-25 minute) video lectures, available on my Youtube channel. They are posted under a CC-BY licence, so feel free to use them but give me appropriate credit. Feedback from students using them the last time I taught the material (where I tried with mixed success to replace traditional lectures with more active learning) was clearly positive.

NSF funded project 2019-2021

Along with the excellent collaborators listed below, I have been funded by NSF for a project entitled Collaborative Research: From Brains to Society: Neural Underpinnings of Collective Behaviors Via Massive Data and Experiments. Apart from the topic, an interesting point about this project is how it arose. NSF advertised an Ideas Lab on “Harnessing the Data Revolution”. Those selected (from a very lightweight application) were sequestered in a hotel near Washington DC in late May, and cleverly guided by professional facilitators to form groups, and propose projects. Since the participants were chosen not to know each other already, this was an intense and at times stressful exercise. Somehow I became involved in an interesting project that differs considerably from my initial ideas, with collaborators Caterina Stamoulis (neuroscience, Harvard), Jie Gao (CS, Stony Brook), Brandon Behlendorf (sociology, Albany), Prodromos Daoutidis (engineering, Minnesota) and Brandon Sepulvado (sociology, NORC). I highly recommend the Ideas Lab experience, which is different from any other grant-related experience I have had.

Lattice walks in the positive orthant

The paper Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior (with the excellent Stephen Melczer) has been accepted by SIAM J. Discrete Math. We consider the enumeration of nearest-neighbor walks on the non-negative lattice in d-dimensional space. Previous work in this area has established asymptotics for the number of walks in certain families of models by applying the techniques of analytic combinatorics in several variables (ACSV), where one encodes the generating function of a lattice path model as the diagonal of a multivariate rational function. Melczer and Mishna obtained asymptotics when the set of steps is symmetric over every axis; in this setting one can always apply the methods of ACSV to a multivariate rational function whose whose set of singularities is a smooth manifold (the simplest case). Here we go further, providing asymptotics for models with generating functions that must be encoded by multivariate rational functions with non-smooth singular sets. In the process, our analysis connects past work to deeper structural results in the theory of analytic combinatorics in several variables. One application is a closed form for asymptotics of models defined by step sets which are symmetric over all but one axis. As a special case, we apply our results in dimension 2 to give a rigorous proof of asymptotics conjectured by Bostan and Kauers; asymptotics for walks returning to boundary axes and the origin are also given.

Cybermath column NZMS Newsletter 2019/Aug

When writing the last column I expected that the topic of this one would be the relaunch of the New Zealand Journal of Mathematics, but unusual circumstances have delayed the relaunch, which is still expected to happen by the end of 2019. The NZJM is a classic example of a scholar-run journal with almost zero budget, subsidised easily by universities and the NZMS because its costs are so low. An argument often made by vested interests in the publishing industry is that high quality journals are expensive (many journals make income of thousands of dollars per published paper). A recent study (fittingly published as a PeerJ preprint) shows that US$200 per paper should be an upper bound. ​

I have spent some time on Twitter recently, but not for mathematical purposes (I run the accounts @oa_math and @freejournalnet). A substantial number of mathematicians have Twitter accounts, although many seem to use them more for political purposes than to discuss mathematics (for example, Ian Stewart (@JoatStewart) and even Timothy Gowers (@wtgowers) who has been using it for less than a year, after the demise of Google+ necessitated another forum.) This list of mathematicians on Twitter is a useful starting point.

Of course there is a large representation of experts in public outreach, such as Steven Strogatz (@stevenstrogatz), Hannah Fry (@FryRsquared​), Marcus du Sautoy (@marcusdusautoy). Interesting feeds relating to the politics of academia include those by Izabella Laba @ilaba.

Some other accounts that caught my eye and focus more on mathematics include: Numberphile (@numberphile) from MSRI (there is also a Youtube channel and other resources at https://www.numberphile.com/​) and Fermat’s Library (@fermatslibrary). These channels are focused more at the undergraduate level. Research-level mathematics is not as well represented. The first mathematical blogger John Carlos Baez has a nice feed at @johncarlosbaez.

The American Mathematical Society (and also London Mathematical Society @LondMathSoc​ and Australian Mathematical Society ​@AustMS) are there, but not the New Zealand Mathematical Society yet. The University of Auckland Department of Mathematics is there: @mathsmatter – are any other departments? Antipodean mathematicians I found include ​Nalini Joshi (@monsoon0) and our own Steven Galbraith (@EllipticKiwi).

Twitter of course has its downsides. The pace at which tweets appear requires a lot of discipline in whom to follow and how to read – at times it is like looking at a library of newspapers but only reading the headlines. This goes against the traditions of mathematics. The 140 (now 280) character limit favours concision. LaTeX is not yet supported; mathematical formulae can be embedded as pictures if necessary. Perhaps the medium is simply not (yet) well adapted for mathematicians. Will we ever see Terence Tao on Twitter? Somehow I doubt it. But overall I think it is worth exploring, and I welcome feedback from readers (if I have any – at least on Twitter I can get some idea about that).​

We finish with some brief notes that may help to feed your procrastination.

Cybermath column NZMS Newsletter 2019/Apr

A very short column this time, with only two topics, but each of them fairly important and timely.

After my criticism of the state of the New Zealand Journal of Mathematics in the last column, I have been invited to put my money where my mouth is and do something about it, as a member of the editorial board and the oversight board (the journal is owned jointly by NZMS and the University of Auckland Mathematics Department – I will represent the former). Expect substantial changes in the website (among other things) by the end of 2019. The domain name (not yet live) will change to nzjmath.org.

Not long before the deadline for this column, news came that the University of California had ended negotiations with Elsevier and cancelled all journal subscriptions. UC had been trying for months to achieve a “publish and read” deal by which papers written by their researchers would be made open access. I (and many others) feel that such deals (which have been struck with several publishers by national consortia in the last few years) are far too generous to the large commercial publishers, but apparently Elsevier wanted even more. According to UC, the final straw was that Elsevier communicated directly with UC researchers, omitting key points about he negotiation, in an attempt to influence the negotiations. See https://osc.universityofcalifornia.edu/open-access-at-uc/publisher-negotiations/uc-and-elsevier/ for more information.

It is very clear that large and profit-hungry corporations of this type are simply incompatible with scholarly publishing. My prediction is that after a short transition period no one will miss, or even notice, that they are not subscribed. UC has several contingency plans in place involving fancy inter-library loans. I hope that the money saved (in the tens of millions of dollars per year) will be put to good use, for example by supporting community-controlled infrastructure such as arXiv.org and free journals of the NZ J. Math. type.

I am not holding my breath, but I really hope that the NZ university libraries (who pay tens of millions annually for subscriptions) can follow UC’s lead. Such cancellations are becoming increasingly common – see SPARC’s list.

Feedback on Plan S implementation guidelines

With Jon Tennant, Dmitri Zaitsev and Christian Gogolin I have submitted substantial feedback. The abstract:

We argue that Coalition members should favour, both in words and via their spending decisions, community-controlled, no-author-fee journals over commercially owned journals charging APCs. This is for reasons of fairness, economic efficiency, and sustainability. We see Plan S as a strong statement and step in the right direction, but encourage Coalition members to be more forward-thinking about how they want the future scholarly publishing market to look, and make sure that they are giving due consideration to the non-commercial elements of the ecosystem.

Cybermath column NZ Math Society Newsletter Dec 2018

I have been writing this column for the last few years. Here is the upcoming column – if I have time I will include the older ones here, although some may be only of historical interest now.

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Having failed to make the last issue, this column is probably too late to say anything interesting about the Fields medallists for 2018. The best general description of the medallists and their work that I saw was in Quanta magazine – there is a wealth of interesting information there. This free online resource backed by the Simons Foundation (itself created by the world’s richest mathematician) has many excellent articles written for the thinking layperson. For a completely different perspective, see Doron Zeilberger’s opinion.

I have started using Twitter (but only as representative of professional organisations MathOA and Free Journal Network) and have been looking for interesting mathematical content there. Twitter is best used to advertise links to other content, and formulae are not easy to include there. It might be fun to try to present a nontrivial proof in 140 (or 280) characters! A recent tweet by Clifford Pickover presented a 1966 paper from Bulletin of the American Mathematical Society  that was only two sentences long, with no abstract, which is presumably a record. If any readers have interesting links to mathematics on Twitter, please let this column(ist) know.

So, as usual, back to academic publishing. The big news since the last column is the advent of Plan S, stemming from a decision by several national European science funders to accelerate the change to open access publication that has been seen by many as inevitable since the internet became widely used on the late 1990s. After all, publication mean making public, and not using modern technology to do that seems very weird. Plan S, which has already been revised once and which has a feedback deadline of 1 Feb 2018, has attracted support from charitable funders (such as the Gates Foundation) and non-European government funders – including several from China, which many outsiders had seen as uninterested in open access. If it is implemented as expected, within 2 years all grant-funded research will have to be published under stringent open access rules. This is a major incentive for “prestigious” journals to change their way of operating. I recently had a conversation with the Editor-in-Chief of perhaps the most highly-reputed mathematics journal, who is concerned about this issue (but apparently not yet concerned enough to make major changes in the journal’s antiquated processes!)

As usual when the status quo is threatened, there has been resistance. An open letter by researchers mainly in the field of chemistry has circulated. And support: a letter supporting funder mandates of the Plan S type has circulated more recently. Each has 1000-2000 signatories, a  tiny fraction of researchers worldwide (I have signed the second but not the first). The main concerns of the former letter are academic freedom (which I consider to be barely relevant here) and the impact on scholarly societies, which often subsidise their operations via journal subscriptions.

The NZ Journal of Mathematics, supported by the NZ Math Society and the University of Auckland Maths Department,  is freely available online with no authors charges, which is excellent. However it has been allowed to stagnate in some ways, and is not up to the standard of similar journals. I am not discussing the editorial and refereeing standards, but the website, licence information, ethics statement, and other things expected from a serious publisher (see the criteria for membership of the Free Journal Network, satisfied by the Australasian Journal of Combinatorics and Electronic Journal of Combinatorics, for example). I hope that some much-needed modernisation can occur and this journal can take its rightful place in the journal ecosystem.

It is not hard to imagine a much better system than the current one. Universal open access, with publication costs paid for by libraries and research funders without authors having to consider payment, would save perhaps 80% of current costs worldwide (now paid mostly by libraries via subscriptions). To keep costs even lower, a widespread use of the arXiv overlay model used by, for example Tim Gowers’ recently established Discrete Analysis and Advances in Combinatorics would be a substantial improvement. One of the features of the current system that every researcher knows about but is rarely mentioned in policy discussions is that (at least in fields like mathematics) commercial publishers very often subtract value from an arXiv version by making typesetting and proofreading errors. In fact, the published version has not really been peer reviewed, because changes can be made by the author after acceptance and usually only non-researcher publisher staff see them.
Conversion to a better system has been much slower than everyone expected. My opinion is that there is plenty of blame to go around and that big commercial publishers must share some of it, but universities, learned societies and researchers have had the ability to fix the situation and have largely abdicated their responsibility.​ I urge all readers to at least support those of us who are working hard to bring about a better system, even if you can’t spare any effort to help. A simple discussion with colleagues and administrators at your own institution can often be surprisingly fruitful. And make your voice heard by signing relevant petitions, or explicitly state that you are apathetic and I can have your proxy vote! And those happy few readers who are in a position to influence policy, please doing it, or ask me how. For example, the RSNZ/Marsden Fund could sign up to Plan S right away if they chose.
 
For those interested in control by researchers of scholarly publishing (which is the first principle of Fair Open Access and without which, in my view, no good sustainable alternative system can function), there will be an online event on 7 February 2019 with which Free Journals Network is involved, among several other organisations. Check out Academic-Led Publishing Day. 
 
Some other big news since the last column concerns the Ted Hill affair. This is an enormously controversial issue, and I will give some selected links for those who have not already followed it. Briefly, a paper studying a model of evolution with possible implications that support the general view that differences in participation in research mathematics by men and women may not be due solely to deficient social organization was accepted by Mathematical Intelligencer, then rejected for political reasons. It was then accepted in New York Journal of Mathematics and swiftly removed after complaints by its editorial board. The Editor-in-Chief died very soon after and the accepting editor is no longer an editor there. My opinion is that very few people came out of this looking better than when they went in, and it shows the need for high ethical standards in all aspects of research. When the basic standards of liberal democracy are under heavy assault by authoritarian leaders and their helpers worldwide, we must hold the line and not allow science to be polluted. And we should strive to improve our standards – several years of being interested in academic publishing have shown me that there are many dodgy practices still out there!
 
Some links: