Archive for partial differential equations

computational methods for numerical analysis with R [book review]

Posted in Books, Kids, pictures, R, Statistics, University life with tags , , , , , , , , , , , , , , , on October 31, 2017 by xi'an

compulysis+R_coverThis is a book by James P. Howard, II, I received from CRC Press for review in CHANCE. (As usual, the customary warning applies: most of this blog post will appear later in my book review column in CHANCE.) It consists in a traditional introduction to numerical analysis with backup from R codes and packages. The early chapters are setting the scenery, from basics on R to notions of numerical errors, before moving to linear algebra, interpolation, optimisation, integration, differentiation, and ODEs. The book comes with a package cmna that reproduces algorithms and testing. While I do not find much originality in the book, given its adherence to simple resolutions of the above topics, I could nonetheless use it for an elementary course in our first year classes. With maybe the exception of the linear algebra chapter that I did not find very helpful.

“…you can have a solution fast, cheap, or correct, provided you only pick two.” (p.27)

The (minor) issue I have with the book and that a potential mathematically keen student could face as well is that there is little in the way of justifying a particular approach to a given numerical problem (as opposed to others) and in characterising the limitations and failures of the presented methods (although this happens from time to time as e.g. for gradient descent, p.191). [Seeping in my Gallic “mal-être”, I am prone to over-criticise methods during classing, to the (increased) despair of my students!, but I also feel that avoiding over-rosy presentations is a good way to avoid later disappointments or even disasters.] In the case of this book, finding [more] ways of detecting would-be disasters would have been nice.

An uninteresting and highly idiosyncratic side comment is that the author preferred the French style for long division to the American one, reminding me of my first exposure to the latter, a few months ago! Another comment from a statistician is that mentioning time series inter- or extra-polation without a statistical model sounds close to anathema! And makes extrapolation a weapon without a cause.

“…we know, a priori, exactly how long the [simulated annealing] process will take since it is a function of the temperature and the cooling rate.” (p.199)

Unsurprisingly, the section on Monte Carlo integration is disappointing for a statistician/probabilistic numericist like me,  as it fails to give a complete enough picture of the methodology. All simulations seem to proceed there from a large enough hypercube. And recommending the “fantastic” (p.171) R function integrate as a default is scary, given the ability of the selected integration bounds to misled its users. Similarly, I feel that the simulated annealing section is not providing enough of a cautionary tale about the highly sensitive impact of cooling rates and absolute temperatures. It is only through the raw output of the algorithm applied to the travelling salesman problem that the novice reader can perceive the impact of some of these factors. (The acceptance bound on the jump (6.9) is incidentally wrongly called a probability on p.199, since it can take values larger than one.)

[Disclaimer about potential self-plagiarism: this post or an edited version will eventually appear in my Books Review section in CHANCE.]

the nihilist girl [book review]

Posted in Books, Kids with tags , , , , , , , , , , , , on October 7, 2017 by xi'an

When stopping by an enticing bookstore on Rue Saint-Jacques, in front of La Sorbonne, last July, I came across a book by the mathematician Sofia Kovaleskaya called the nihilist girl. Having never heard of non-mathematical books written by this Russian mathematician whose poster stood in my high school classroom, I bought it (along with other summer reads). And then discovered that besides being a woman of many “firsts”, from getting a PhD at Heidelberg (under Weirstraß) to getting a professor position in Stockholm, to being nominated to a Chair in the Russian Academy of Sciences, she also took an active part in the Commune de Paris, along with many emigrated Russian revolutionaries (or nihilists). Which explains for this book about a nihilist girl leaving everything to follow a revolutionary deported to Siberia. While not autobiographical (Sweden is not Siberia!), the novel contains many aspects inspired from the (amazing if desperately short) life of Sofia Kovaleskaya herself. A most interesting coincidence is that Sofia’s sister, Anna, was engaged for a while to Fyodor Dostoyevsky, whose novel The Demons takes the opposite view on nihilists. (As a feminist and anarchist, Anna took a significant part in the Commune de Paris, to the point of having to flee to Switzerland to escape deportation to New Caledonia, while her husband was sentenced to death.) The book itself is not particularly enjoyable, as being quite naïve in its plot and construction. It is nonetheless a great testimony of the situation of Russia in the 19th Century and of the move of the upper-class liberals towards revolutionary ideals, while the exploited peasant class they wanted to free showed no inclination to join them. I think Dostoyevsky expresses much more clearly this most ambiguous posturing of the cultivated classes at the time, yearning for more freedom and fairness for all, but fearing the Tsarist police, unable to connect with the peasantry, and above all getting a living from revenues produced by their farmlands.

EQUIP launch

Posted in Statistics, University life with tags , , , , , , on October 10, 2013 by xi'an

Today, as I was around (!), I attended the launch of the new Warwick research project EQUIP (which stands for Enabling quantification of uncertainty for inverse problems). This is an EPSRC funded project merging mathematics, numerical analysis, statistics and geophysics, with a primary target application [alas!] in the oil industry. It will start hiring four (4!) postdocs pretty soon. The talks were all interesting, but I particularly liked the idea that they were addressed primarily to students who were potentially interested in the positions. In addition, Mark Girolami gaves a most appreciated insight on the modelling of uncertainty in PDE models, connecting with earlier notions set by Tony O’Hagan, modelling that I hope we can discuss further when both in Warwick!