camera miracles: once, not twice!

As I mentioned in a post last February, I almost lost my (Nikon Coolpix L26) camera to the cloaca maxima, in Roma. It however remained (miraculously) within reach inside the manhole there… Well, this kind of miracle does not happen twice (or only in Roma…)  and I have now lost the camera for good! When climbing Tower Ridge, after the first belay to go up Douglas gap, I took it out of my pocket to take a few pictures of the beginning of the ridge and of the fantastic view of that side of Ben Nevis. As I was mostly paying attention to Kenny going up the blocks above us (to make sure of my holds there), I did not look as I put my camera back inside my overpants and it slid out of the pocket, swiftly accelerating down the snowy slopes to disappear into Coire na Ciste… There was no way we were going to check whether or not it was retrievable, so I called myself a few well-chosen names and we continued our climb along the ridge without further delay. In fact, I had another camera in my bag, my older and bulkier Konica Minolta Dimage Z20, but it was impossible to get hold of it in most places (as I would have had to unpack) and it anyway ran out of battery (which explains why I have so few pictures of the top of the Ben and of the unbelievable [and rare] views of the Highlands invading the ‘Og in the past days!).

Here is thus the last picture taken from my lost camera, a view of the Aonach Eagach ridge from the bottom of Glencoe (and the start of the trail to the Lost Valley). Apart from this miracle in Roma, I have been rather unlucky with cameras lately, loosing first my favourite one in a New York taxi, then this one on Tower Ridge. Actually, I consoled myself with the fact that the quality of this Nikon Coolpix L26 camera was rather unsatisfactory, behaving poorly in anything but clear weather and having grown a mark (fungus?) on the lens (after falling in the snow during my X’mas ski trip). Mark that is clearly visible on the right of  the ptarmigan picture below. Anyway, I will now have to look for a new camera, hopefully supported by ‘Og’s readers (!) via the links to Amazon.com and Amazon.fr there, which earn me a monetary gain [of 4% to 7%] if a purchase [of any product] is made within the 24 hours following the entry on Amazon through this link, thanks to the “Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to amazon.com/fr“.

talks on the East Coast

On Tuesday and Wednesday, next week, I will give seminars in Princeton University and Rutgers University, respectively. My talk at Princeton actually takes place in the Department of Economics, at the Oskar Morgenstern Memorial Seminar (Tuesday, April 3, 2:40 – 4:00pm 200 Fisher Hall). I must acknowledge that the prospect is a wee daunting. For addressing the manes of Morgenstern and for speaking in Nash‘s very own institution, if nothing else! And my talk at Rutgers is in the Department of Statistics and Bostatistics (Wedn, April 4, 3:20 – 4:20, Hill Center, Busch Campus), where I will meet with my friend of many years Bill Strawderman. And my former PhD student Aude Grelaud. Both talks will cover the same ground of ABC model choice and Bayesian consistency (surprise, surprise!). The format of the econometrics seminar at Princeton being a bit longer, I will give more background on ABC, mostly in connection with the econometric methods I mentioned in my ABC tutorial in Roma and at CREST. I presume I will skip this part in Rutgers as biologists and geneticists are more likely to attend than econometricians. In preparation, here is the current version of the talk, to be updated till Monday at the very least!

simulated annealing for Sudokus [2]

On Tuesday, Eric Chi and Kenneth Lange arXived a paper on a comparison of numerical techniques for solving sudokus. (The very Kenneth Lange who wrote this fantastic book on numerical analysis.) One of these techniques is the simulated annealing approach I had played with a long while ago.  They seem to use the same penalisation function as mine, i.e., the number of constraint violations, but the moves are different in that they pick pairs of cells without clues (i.e., not constrained) and swap their contents. The pairs are not picked at random but with probability proportional to exp(k), if k is the number of constraint violations. The temperature decreases geometrically and the simulated annealing program stops when the zero cost is achieved or when a maximum 10⁵ iterations are reached. The R program I wrote while visiting SAMSI had more options, but it was also horrendously slow! The CPU time reported by the authors is far far lower, almost in the range of the backtracking solution that serves as their reference. (Of course, it is written in Fortran 95, not in R…) As in my case, the authors mentioned they sometimes get stuck in a local minimum with only 2 cells with constraint violations.

So I reprogrammed an R code following (as much as possible) their scheme. However, I do not get a better behaviour than with my earlier code, and certainly no solution within seconds, if any. For instance, the temperature decrease in 100(.99)^t seems too steep to manage 10⁵ steps. So, either I am missing a crucial element in the code, or my R code is very poor and clever Fortran programming does the trick! Here is my code

target=function(s){
tar=sum(apply(s,1,duplicated)+apply(s,2,duplicated))
for (r in 1:9){
bloa=(1:3)+3*(r-1)%%3
blob=(1:3)+3*trunc((r-1)/3)
tar=tar+sum(duplicated(as.vector(s[bloa,blob])))
}
return(tar)
}

cost=function(i,j,s){
#constraint violations in cell (i,j)
  cos=sum(s[,j]==s[i,j])+sum(s[i,]==s[i,j])
  boxa=3*trunc((i-1)/3)+1;
  boxb=3*trunc((j-1)/3)+1;
  cos+sum(s[boxa:(boxa+2),boxb:(boxb+2)]==s[i,j])
  }

entry=function(){
  s=con
  pop=NULL
  for (i in 1:9)
    pop=c(pop,rep(i,9-sum(con==i)))
  s[s==0]=sample(pop)
  return(s)
  }

move=function(tau,s,con){
  pen=(1:81)
  for (i in pen[con==0])
        pen[i]=cost(((i-1)%%9)+1,trunc((i-1)/9)+1,s)
  wi=sample((1:81)[con==0],2,prob=exp(pen[(1:81)[con==0]]))
  prop=s
  prop[wi[1]]=s[wi[2]]
  prop[wi[2]]=s[wi[1]]

  if (runif(1)<exp((target(s)-target(prop)))/tau)
    s=prop
  return(s)
  }

#Example:
s=matrix(0,ncol=9,nrow=9)
s[1,c(1,6,7)]=c(8,1,2)
s[2,c(2:3)]=c(7,5)
s[3,c(5,8,9)]=c(5,6,4)
s[4,c(3,9)]=c(7,6)
s[5,c(1,4)]=c(9,7)
s[6,c(1,2,6,8,9)]=c(5,2,9,4,7)
s[7,c(1:3)]=c(2,3,1)
s[8,c(3,5,7,9)]=c(6,2,1,9)

con=s
tau=100
s=entry()
for (t in 1:10^4){
  for (v in 1:100) s=move(tau,s,con)
  tau=tau*.99
  if (target(s)==0) break()
  }

E&I review in Theory and Decision

A few days ago, while in Roma, I got the good news that my review of Error and Inference had been accepted by Theory and Decision. Great! Then today I got a second email asking me to connect to a Springer site entitled “Services for Authors” with the following message:

Dear Christian Robert!
Thank you for publishing your paper in one of Springer’s journals.

Article Title: Error and Inference: an outsider stand on a frequentist philosophy
Journal: Theory and Decision
DOI: 10.1007/s11238-012-9298-3

Make your Choice

In order to facilitate the production and publication of your article we need further information from you relating to:

• Please indicate if you would like to publish your article as open access with Springer’s Open Choice option (by paying a publication fee or as a result of an agreement between your funder/institution and Springer). I acknowledge that publishing my article with open access costs € 2000 / US $3000 and that this choice is final and cannot be cancelled later.
• Please transfer the copyright, if you do not publish your articles as open access.
• Please indicate if you would like to have your figures printed in color.
• Please indicate if you would like to order offprints. You have the opportunity to order a poster of your article against a fee of €50 per poster. The poster features the cover page of the issue your article is published in together with the article title and the names of all contributing authors.

Now I feel rather uncomfortable with the above options since I do not see why I should pay a huge amount € 2000 € for having my work/review made again available. Since it is already freely accessible on arXiv. And it is only a book-review, for Gutenberg’s sake! Last year, we made our PNAS paper available as Open Access, but this was (a) cheaper and (b) an important result, or so we thought! The nice part of the message was that for once I did not have to sign and send back a paper copy of the copyright agreement as with so many journals and as if we still were in the 19th Century… (I do not see the point in the poster, though!)

Abraham De Moivre

During my week in Roma, I read David Bellhouse’s book on Abraham De Moivre (at night and in the local transportations and even in Via del Corso waiting for my daughter!)… This is a very scholarly piece of work, with many references to original documents, and it may not completely appeal to the general audience: The Baroque Cycle by Neal Stephenson is covering the same period and the rise of the “scientific man” (or Natural Philosopher) in a much more novelised manner, while centering on Newton as its main character and on the earlier Newton-Leibniz dispute, rather than the later Newton-(De Moivre)-Bernoulli dispute. (De Moivre does not appear in the books, at least under his name.)

Bellhouse’s book should however fascinate most academics in that, beside going with the uttermost detail into De Moivre’s contributions to probability, it uncovers the way (mathematical) research was done in the 17th and 18th century England: De Moivre never got an academic position (although he applied for several ones, incl. in Cambridge), in part because he was an emigrated French huguenot (after the revocation of the Édit de Nantes by Louis XIV), and he got a living by tutoring gentry and aristocracy sons in mathematics and accounting. He also was a consultant on annuities. His interactions with other mathematicians of the time was done through coffee-houses, the newly founded Royal Society, and letters. De Moivre published most of his work in the Philosophical Transactions and in self-edited books that he financed by subscriptions. (As a Frenchman, I personally[and so did Jacob Bernoulli!] found puzzling the fact that De Moivre never wrote anything in french but assimilated very quickly into English society.)

Another fascinating aspect of the book is the way English (incl. De Moivre) and Continental mathematicians fought and bickered on the priority of discoveries. Because their papers were rarely and slowly published, and even more slowly distributed throughout Western Europe, they had to rely on private letters for those priority claims. De Moivre’s main achievement is his book, The Doctrine of Chances, which contains among clever binomial derivations on various chance games an occurrence of the central limit theorem for binomial experiments. And the use of generating functions. De Moivre had a suprisingly long life since he died at 87 in London, still giving private lessons as old as 72. Besides being seen as a leading English mathematician, he eventually got recognised by the French Académie Royale des Sciences, if as a foreign member, a few months prior to his death (as well as by the Berlin Academy of Sciences). There is also a small section in the book on the connections between De Moivre and Thomas Bayes (pp. 200-203), although very little is known of their personal interactions. Bayes was close to one of De Moivre’s former students, Phillip Stanhope, and he worked on several of De Moivre’s papers to get entry to the Royal Society. Some open question is whether or not Bayes was ever tutored by De Moivre, although there is no material proof he did. The book also mentions Bayes’ theorem in connection with an comment on The Doctrine of Chances by Hartley (p.191), as if De Moivre had an hand in it or at least a knowledge of it, but this seems unlikely…

In conclusion, this is a highly pleasant and easily readable book on the career of a major mathematician and of one of the founding fathers of probability theory. David Bellhouse is to be congratulated on the scholarship exhibited by this book and on the painstaking pursuit of all historical documents related with De Moivre’s life.