21 October 2016

10 October 2016

Curvature of a planar curve

I have done this calculation several times over the years, so I might as well write it down in detail, in case it may be of use to someone else.

We are interested in the curvature \(C = 1/R\) of a planar curve \(y=f(x)\) at a given point A, where \(R\) is the curvature radius at that particular point, defined with respect to the curvature center \(O\) (intersection of the normals raised to the curve in A and its infinitesimal neighbor B.)

The angle subtending AB is: \(\displaystyle \mathrm{d}\alpha = \mathrm{d}s/R \Rightarrow C = \frac{\mathrm{d}\alpha}{\mathrm{d}s}\)
The length of the curve element AB is: \(\displaystyle \mathrm{d}s = \sqrt{\mathrm{d}x^2 + \mathrm{d}y^2} \Rightarrow \frac{\mathrm{d}s}{\mathrm{d}x } = \sqrt{1+ f'(x)^2}\)

The derivative of \(f\) is directly related to the angle \(\alpha\): \(\displaystyle f'(x) = \frac{\mathrm{d}y}{\mathrm{d}x} = \tan \alpha \Rightarrow \alpha = \arctan \frac{\mathrm{d}y}{\mathrm{d}x} = \arctan [f'(x)] \Rightarrow \frac{\mathrm{d}\alpha}{\mathrm{d}x} = \frac{1}{1+f'(x)^2} f''(x)\)

Putting together the three relations above yields:
\[C = \frac{\mathrm{d}\alpha}{\mathrm{d}s} = \frac{f''(x)}{\left [ 1 + f'(x)^2\right ]^{3/2}}\]

12 August 2016

Identification of a major intermediate along the self-assembly pathway of an icosahedral viral capsid

Our paper appeared in Soft Matter!
The modelling and fitting of the SAXS data required lengthy analysis and intensive calculations. In particular, we used the analytical model for scattering from spherical patches that I had published last year.

2 August 2016


I learned today that the title of the fourth book in Proust's Search of Lost Time (Sodome et Gomorrhe) was translated in English as Cities of the Plain, same as Cormac McCarthy's novel, and that the expression comes from King James Version of the Bible. Looks like most novels in the English language borrow their title from the KJV (Yeats's poems are a close second, though).

I also found out that the title to Wittgenstein's Tractatus Logico-Philosophicus was inspired by Spinoza's Tractatus Theologico-Politicus. Also, 60 years before Spinoza Robert Fludd wrote his Tractatus Theologo-Philosophicus, which is closer in title (although probably not in content).

2 July 2016


Higgs ! En voilà, un nom à particule !

28 June 2016

Climate and Geography

Is aggression correlated to the climate? Researchers from the Vrije Universiteit Amsterdam and Ohio State University seem to think so (read the press release and the preprint of the paper).

They put forward a supposedly new model titled CLimate, Aggression, and Self control in Humans (CLASH). I can't comment on the merits and novelty of this approach, but it reminds me of Montesquieu's remarks in The Spirit of the Laws (book XIV, chapter II):

In northern countries we meet with a people who have few vices, many virtues, a great share of frankness and sincerity. If we draw near the south we fancy ourselves removed from all morality; the strongest passions multiply all manner of crimes, every one endeavouring to take what advantage he can over his neighbour, in order to encourage those passions.

27 June 2016

Alternative positions in the two-party system

I've always been intrigued by the American two-party system and its difference with respect to Continental politics. I think the comparison is very instructive and can shed light on recent political developments. Case in point: in the current issue of The Atlantic, Jonathan Rauch deplores the state of Americal politics, in particular the lack of discipline in both the Democratic and the Republican parties, whose "politicians, activists, and voters" are less and less likely to line up behind the party leaders. Terms and phrases in quotes are Rauch's.

Rauch explains this by the reform of the political system over the last few decades, which rendered the "middlemen" less powerful, and thus unable to defend against such "symptoms" as "insurgence" and "radicalization". The author really likes the allegory of the immune system fighing the "pathogens".

These "symptoms" are also common in Europe, where they gave rise to powerful political movements and parties. This has not happened in the United States, probably for the simple reason that, in a two-party system, it can be easier for new political orientations to work from within the existing parties, rather than create new ones, as in Europe. The religious conservatives and the libertarians have to go through the Republican party and the socialists through the Democratic one. As long as they were in the minority, this was not a problem for the establishment, but when the "outsiders and insurgents" start getting the upper hand, the "body politic" (which for Rauch seems to mean the political status quo) may not recover.

The comparison with Europe also casts doubt on Rauch's diagnostic: the radicals gained prominence at about the same time in the US and all over Europe, although the political systems are quite diverse. A much simpler explanation is that the sluggish economy and the resulting social problems caused the discontent and the anti-establishment feeling on both sides of the Atlantic.

To summarize: as in Europe, in the United States alternative positions became politically relevant in the last 10-15 years, probably for reasons unrelated to political reform; unlike (Continental) Europe, however, they had to go through one of the two major parties due to their stability, itself due to the first-past-the-post electoral system.

26 June 2016

Hierarchy and inequality

In Left and Right: The Significance of a Political Distinction, Norberto Bobbio mentions an interesting variation in defining what is called generically in politics "the right". For Bobbio, this side of the spectrum is defined by a defense of inequality, and he dismisses the use of the term "hierarchy" by Elisabetta Galeotti as unrelated to the left/right polarity. This may well be so (at least in Bobbio's system of definitions) but I think that the hierarchy/inequality distinction is quite useful in separating different right-wing positions.

14 May 2016

Impresii despre Soldaţii de Adrian Schiop

Soldaţii. Poveste din Ferentari de Adrian Schiop. Editura Polirom, 2013


În 250 de pagini, Schiop ne prezintã o relaţie sentimentalã, de la începutul timid pânã la previzibilul sfârşit lamentabil. Mai important însã, el reuşeşte performanţa de a schimba treptat perspectiva, astfel cã la sfârşit nu mai este atât de clar cine pe cine exploateazã, iar implozia relaţiei nu decurge aşa cum am fi bãnuit la început.

Soldaţii este o poveste de dragoste, înainte de a fi o poveste din Ferentari sau una despre homosexuali. Aceste douã elemente, ca şi tensiunea dintre ele, sunt indispensabile acţiunii, dar — dacã e sã judec dupã multe recenzii şi reacţii — cred cã mare parte din succesul cãrţii se va datora lecturii în cheie socialã (ca o meditaţie pe tema homosexualitãţii în România sau pe cea a Ferentarilor ca vestigiu al unei perioade trecute).

Stilul este destul de brut, fãrã fraze şlefuite, cam prea în genul "Flori de mucigai", pe care nu îl apreciez foarte tare, dar care se potriveşte într-adevãr cu subiectul. Mai ales în capitolul No more parties, analiza socialã e desfãşuratã în fraze tãioase şi categorice, combinînd termeni tehnici sau erudiţi şi expresii de argou (à la Houellebecq). Partea aceasta mi s-a pãrut cel mai puţin convingãtoare.

Pe scurt, o carte care meritã din plin cititã, în ciuda unei realizãri destul de inegale (narativ şi stilistic).

16 March 2016

Chartres cathedral (again)

This was my second time in Chartres (I have already taken the same photo three years ago), but now I was more interested in the juxtaposition of the various textures (hence the B&W rendition).