31 January 2013

The morphology of C12E8 micelles

Our work on the structural analysis of the isotropic phase of the C12E8/H2O mixture was (finally) published.

Kévin Tse-Ve-Koon, Nicolas Tremblay, Doru Constantin, and Éric Freyssingeas
Journal of Colloid and Interface Science, 393, 161–173 (2013).

27 January 2013

Are Bayesian statistics wrong?

UPDATE (25/04/2013): I wrote a short review of Silver's book.

In the New Yorker, Gary Marcus and Ernest Davis comment on Nate Silver's The Signal and the Noise and conclude that "[T]he Bayesian approach is much less helpful when there is no consensus about what the prior probabilities should be."

A Bayesian would probably reply that refusing to think about prior probabilities does not make them any less important. And they are always taken into account, either explicitly by Bayes' theorem or qualitatively, as in Sagan's dictum "Extraordinary claims [with a low prior probability] require extraordinary evidence [with correspondingly high significance]".

Setting a fixed and arbitrary confidence threshold (95%, 99% etc.) would be catastrophic. For instance, the hypothesis "Standard quantum mechanics is wrong" could be easily proven by any sloppy experiment: quantum theory is highly predictive, so it is easy to find oneself in complete disagreement with it. Fortunately, scientists will not immediately accept the hypothesis (exactly because its prior probability is so low).

A real-life example is that of OPERA's "superluminal neutrinos". To their credit, the researchers reviewed the experiment closely until they found the loose cable connection, instead of jumping to the conclusion that "relativity is wrong", although the statistical significance of the result was at an unimpeachable six sigma level. They somehow knew the theory of relativity was stronger than that.

23 January 2013

Hard science requires soft skills

You defended your PhD in a good research group, you have a number of papers in decent (or even outstanding) journals and your boss speaks highly of you. Congratulations! Now you are looking for an academic position: the competition is tough, but after a few years of postdoc with the same productivity you hope you'll get your own group and start having PhDs in turn. This would be very cool, but what are your chances of success? And how can you improve them?

The odds

Let us start by a quick calculation: assume the number of permanent scientific positions (tenured professors and staff scientists) in your country and discipline will remain constant from one "generation" to the next. It might go down in an economical crisis or it might increase (in exceptional circumstances, but not for a long time). Estimate the average number of PhDs advised by a scientist over the course of his/her career (let us say, between 5 and 20). Statistically, only one of those will get a permanent position. The odds are worse in countries where these positions are open to foreign PhDs. To fix the ideas, let us say your chances are 1 in 10.

There is life outside academia

Before discussing improvement strategies, you should however consider your options thoroughly. It might be that an academic position is not made for you (or vice versa.) After spending a number of years in a research lab, surrounded by people who made the same career choice, it is easy to forget this simple truth. Even if you decide science is your calling, do have a plan B.

 I will work harder!

One obvious way of increasing your chances is to keep doing what you've been doing so far (solid lab work etc.) only more of it. This does not cut it for the equally obvious reason that graduate school is very demanding and has probably already pushed you to work quite hard. Longer hours will not significantly increase your productivity. If you cannot work harder, you should of course work smarter (choice of the postdoc lab and topic, external collaborations etc.), but this is another story.

The other half of the problem

So far you have focused on doing great science (and this is quite natural), but chances are you have been neglecting an activity equally important for your future career: letting others know that you've been doing great science. This is where a small investment in time and effort can bring a large reward. More precisely, you need to aim for two (highly interconnected) goals:
  1. Sell your results
  2. Network with other scientists in your discipline
Of course, the reason you have not worked on this so far is that you did not consider it important. In my experience, it is almost as important as the "pure science" part and I will sketch some of the reasons below. If you are still not convinced, discuss this with more senior colleagues.

The steps to take

There are several things you need to achieve:
  1. An overall view of the relevant research community in your country and abroad.
  2. An overall view of the topics under study in this community and a good understanding of how your own activity fits into the picture.
  3. Knowledge of the various kinds of positions available to you, with the corresponding requirements (official and otherwise).
  4. The ability to give effective presentations (at conferences and in lab talks).
  5. Personal contact with as many scientists as possible.

1. Know your colleagues

Which are the groups working on similar topics in your country and worldwide? Who are the top researchers in the field? This is a relatively small community, and you will encounter its members at each point of your career, in various capacities:
  • Collaborators
  • Referees for your papers and grant applications
  • Audience for your talks
  • Competitors for the same positions
  • Members of selection committees
 You will spend a considerable amount of time dealing with them directly or indirectly (e.g. reading their papers or trying to reproduce their experimental protocols) so you should know who they are and how they interact.

2. Know your science

In graduate school you concentrate on your own research. By the time of your defense, you should be one of the most knowledgeable people in the world concerning your particular topic. However, science is essentially collective and I would argue that you cannot be an accomplished scientist without thorough "background" knowledge:
  • What are your colleagues (and competitors) doing? (see point 1)
  • How does your work compare to theirs (quality of the results, novelty of the methods, etc.)?
  • How does it fit within the more general area?
  • What are the important problems of your field? Are you working on one of them? If not, why? These questions were posed by Richard Hamming in a famous talk; they might be difficult to answer now, but keep them in mind for later.
Armed with this knowledge you will also be able to present your results more convincingly (see point 4).

3. Know your opportunities

A PhD is mandatory for certain jobs and might be a plus for others. Make sure to identify these categories and to find out their advantages and downsides, as well as the availability of such positions. How much will you earn and how many weekly hours will you work as an assistant professor/industrial scientist/science writer/patent examiner/project officer etc.? Which of these jobs interest you (at least on the "plan B" level)?

One of the best ways of getting "inside information" is from people who already have experience in these particular areas.

4. Explain your results

Giving a talk can feel like a chore, and your first impulse may be to leave the preparations for the last minute (I know mine is). This is a big mistake, since a presentation is the most effective way of advertising your results and yourself as a scientist. At best, you will get the audience to read your papers and -more importantly- to understand that your personal contribution was essential.

It is a safe bet that nobody in the room is as familiar with your topic as you are. They probably do not even care about it. It is your job to get them interested, and this is most easily done by telling a story. Your talk should have a narrative that the audience can relate to, on a professional or even personal level.

You can find on the web abundant advice on how to give a good presentation, but there is no substitute for attending talks (this also helps out with points 1, 2 and 5). After each one, summarize the speaker's message and also list the details you liked and could use in your own presentations (as well as those to avoid at all costs).

Practice your talks (with an audience, if possible) and, last but not least, do not exceed the time limit. Ever.

5. Get in touch

This item is strongly related to points 1 and 4. I listed it apart because it involves making direct contact with people, and this might not come naturally but you need to make the effort. Of course "direct contact" covers many situations, such as:
  • Sending a reprint of your paper, along with a brief but personalized message.
  • Inquiring about open positions in a lab.
  • Asking questions after a talk.
  • Exchanging ideas at a conference dinner (engage, but do not monopolize).
Speaking of conferences, they are an ideal occasion to meet people, but also to observe their interaction and to realize that a scientific community is also a social community.

18 January 2013

Grant application result from incomplete data

Results for financing applications often arrive in two steps:
  1. One's personal score (confidential) and some overall statistical information (public).
  2. Final decision (accepted/rejected).
For projects close to the (unknown) cutoff value, the delay between 1. and 2. can be quite long; it is imposed by the negotiation process with those higher up on the list.

A real-life example I was confronted to are the Marie Curie Fellowships: There were 3300 valid applications for the 2011 Intra-European Fellowships (IEF), out of which 800 fell below a threshold T=70%. Knowing that about 600 projects will be financed and that your score is S (say, 95%), will you make the cut ?

Let us first search for the most probable distribution \( P(x) \) obeying the constraints:
  • \( P(x) \) is defined on (0,1) : \( \int _0 ^{1} P(x) \, \text{d} x = 1 \)
  • \(\int _0 ^{T} P(x) \, \text{d} x = F_1 = 800/3300 = 0.2424 \)
The problem is easily solved yielding a piecewise constant \( P(x) \), with \(P(x\leq T) = F_1/T \) and \( P(x \geq T) = (1-F_1)/(1-T)\) . Defining the success rate above the threshold \( M = 600/(3300 - 800)\), we conclude:
  • Your application is successful if \( \frac{1-S}{1-T} \leq M\). For the numerical values above, this corresponds to \( S \geq S_{\text{min}} = 94.5 \).
  • The number of applications below the threshold is in fact irrelevant. 
We limited the reasoning to one distribution (the most probable), for which there is a unique answer. However, we understand intuitively that the uncertainty is very large; it would be much more useful  to determine completely the success probability \(g(S)\). Only for \(g(S)\) significantly different from \(1/2\) can one draw any conclusion from such limited information.

Episciences Project: open journals

Tim Gowers announces the Episciences project, a series of arXiv overlay journals. The platform will be supported by the CCSD, a French documentation center. More details from Jean-Pierre Demailly in Nature. Terence Tao is also on board.

The scientists above are all mathematicians and it is not clear whether (or when) this initiative will also be extended to other disciplines. [UPDATE (23/01/13): According to the CCSD blog (in French), the platform is open to new or already existing journals in all scientific areas. The launch is scheduled for the first semester of 2013.]

17 January 2013

Equation numbering in LaTeX: several versions of the same formula

When deducing a result one might need to write a formula several times, in slightly different form, as the proof proceeds. Using different equation numbers (default LaTeX behaviour) fails to show the unity between the various expressions. On the other hand, using only the \tag{} keyword (defined in the amsmath package) sets them completely apart from the other equations in the sequence.

It took me some time to realize that these two approaches can be combined very easily, as shown below:

a = b
b = c

yielding the desired result:
a = b
b = c

5 January 2013

Sites web inofficiels des différentes sections du CoNRS

La date limite de soumission des dossiers de candidature aux concours CNRS est le 7 janvier. Tous les candidats connaissent sûrement le site officiel de l'institution. On sait peut-être moins bien que les différentes sections du Comité National (CoNRS), responsables de la sélection des candidats (phase d'admissibilité) ont souvent des sites inofficiels, contenant des renseignements supplémentaires.

Voici une liste (probablement incomplète) de tels sites. N'hésitez pas à me transmettre l'adresse d'autres sites ne figurant pas ci-dessous !

Section 18 (obsolète ?)
Section 41 (ancienne 01 ! Mathématiques)

3 January 2013

Curie's principle and Lucretius' clinamen

In his 1894 paper [1], Pierre Curie noted:
  1. The characteristic symmetry of a phenomenon is the maximum symmetry compatible with the existence of the phenomenon. A phenomenon can occur in a medium endowed with its characteristic symmetry or that of a subgroup of its characteristic symmetry.
  2. To put it differently, certain symmetry elements can coexist with certain phenomena, but they are not needed. What is needed, is that certain symmetry elements be absent. It is the dissymmetry that engenders the phenomenon.
and proceeded to give a concise two-part statement of the symmetry principle:
  1. When certain causes engender certain effects, the symmetry elements of the causes must also characterize the resulting effects.
  2. When certain effects exhibit some dissymmetry, this dissymmetry must also characterize the engendering causes.
Curie was of course not the first to consider the symmetry of natural laws. In his paper he mentions explicitly (and makes use of) the cristallography treatises of his time. However, he is probably the first to have stated the symmetry principle at this level of generality. See [2,3] for a general discussion.

Spontaneous symmetry breaking seems to defy Curie's principle. The typical example is the buckling of a column under axial stress. Although initially the system has cylindrical symmetry, above a certain threshold the column shifts laterally, resulting in a lower-symmetry final state. Is this compatible with Curie's principle ?

One way out of this bind is to postulate the presence of a small static imperfection [4] or (in other contexts) of a quantum or thermal fluctuation. This asymmetry is irrelevant (and undetectable) under "normal" conditions and only has its effect at the transition, where the susceptibility of the system diverges. Thus, either the system was not symmetric enough to start with (due to the imperfection) or it cannot be (perfectly) symmetric due to the presence of the fluctuations. A second solution is to extend Curie's principle, so that it applies to ensembles, instead of individual systems [5]; more on this in a future post.

The first solution does raise a couple of interesting questions:
  1. Far away from the transition, can we still consider the system as symmetric ?
  2. How satisfying is this invocation of "invisible causes" ?
Here, however, I'm interested in whether this small deviation has something in common with Lucretius' concept of clinamen. As interpreted by Serres [6], the clinamen (declination, swerve) perturbs the primordial laminar flow, engendering a vortex (and, ultimately, the world).

It seems that the two concepts fulfill a similar role, by providing a primary and undetectable cause of some visible phenomenon.

In the case of the clinamen, these two properties open it to ridicule ([6], page 3):

From Cicero to Marx and beyond, down to us, the declination of atoms has been treated as a weakness of the atomic theory. The clinamen is an absurdity. A logical absurdity, since it is introduced without justification, the cause of itself before being the cause of all things; [...] an absurdity of physics in general, since experimentation cannot possibly reveal its existence.

Is this ridicule justified ? If so, how about the fluctuation that explains spontaneous symmetry breaking ?

[1] Pierre Curie, Sur la symétrie dans les phénomènes physiques, symétrie d'un champ électrique et d'un champ magnétique, Journal de Physique 3(1), 393-415, 1894.
[2] Jenann Ismael, Curie’s Principle, Synthese, 110, 167–190, 1997.
[3] Shaul Katzir, The emergence of the principle of symmetry in physics, Historical Studies in the Physical and Biological Sciences, 35(1), pages 35-65, 2004.
[4] Symmetry and Symmetry Breaking, in the Stanford Encyclopedia of Philosophy (section Spontaneous symmetry breaking.)
[5] Ian Stewart and Martin Golubitsky, Fearful Symmetry, Penguin Books, 1993.
[6] Michel Serres, The Birth of Physics, Clinamen Press, Manchester, 2000.

2 January 2013

Back to basics

Interesting point made by I. M. Gelfand, as recalled by A. Zelevinsky in a recent AMS notice:
He explained to us how to study a new mathematical subject: focus on the most basic things at the foundation and dwell upon them until you reach full understanding; then the technicalities of the subject would be understood very quickly and effortlessly.