Archive for the ‘computer-science’ Category

Some november 2017 items

November 11, 2017

[Posted on november 11, 2017]

Some recently spotted items :

Hexagons in the arch. Glanum, october 2017. Public Domain.

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News roundup, and binary Cantor orthogonality

August 15, 2017

[Posted on august 15, 2017.]

Summer news:

***

Completely unrelatedly, here’s probably another useless idea from this blog’s host. Consider a sequence (a_n)_{n\in\mathbb{N}^*} of binary numbers in [0,1] such that the number of digits of a_n is at least equal to n for all n. Then one can apply Cantor’s diagonal argument to extract a number that is uniquely defined (since a digit different from 0 must be 1 and vice versa) and different from all the a_n. Call the resulting number the “binary Cantor orthogonal” of that sequence. Can it have any useful properties?

Let’s look at the following example: a_n:=[1/p_n]_2, the binary version of the inverse of the n-th prime. That is, we do:

\displaystyle \begin{array}{ccl}  \frac{1}{2}& =& 0.1\\  \frac{1}{3}& = & 0.01010101\dots \\  \frac{1}{5}& =& 0.001100110011\dots\\  \frac{1}{7}&=& 0.001001001001\dots\\  \frac{1}{11}&=& 0.0001011101\dots\\  \vdots  \end{array}

 

then extract the diagonal of the decimal parts and invert it modulo 2. The resulting sequence is 0,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0… Unfortunately, the OEIS doesn’t know this particular sequence, so there’s probably nothing noticeable here.

Jardin des Roses in Rennes (a small area of this marvel).

August 2017. Public domain

Early april news

April 5, 2016

[Posted on april 5, 2016]

In no particular order :

  • Laurent Lafforgue recently gave a colloquium (direct link to the mp4 file) on Grothendieck Toposes in Nantes “based on his conversations with Olivia Caramello” (he is announcing a long common text in the process of being written, to appear on his website at some point)
  • registration opened a few days ago for the summer school at Institut Fourier on Geometric Analysis, Metric Geometry and Topology
  • a workshop on Geometric Langlands and a conjecture of Fargues is taking place this week in Oberwolfach, while a workshop on the work of Vincent Lafforgue will take place at AIM next december
  • a recent and highly interesting AI paper that takes into account what makes things look natural to humans (inner sense of what is physically possible or not, and first-person view of the world) by Brenden M. Lake, Tomer D. Ullman, Joshua B. Tenenbaum and Samuel J. Gershman ; the fact that these gentlemen work at high-profile institutions will hopefully turn this paper into a kind of benchmark along which other folks will want to test their systems
  • Manjul Bhargava gave several talks in Paris yesterday, including one on Ramanujan’s work (the movie is announced for september in France, but will be released in just a few weeks in several countries), as part of the UNESCO’s International Conference on the Zero

Blue in the shades, by coniferconifer on flickr

February newslets

February 21, 2016

[Posted on february 21, 2016]

Spotted recently:

  • a fascinating discussion is taking place between Sir Timothy Gowers and Nikolai V. Ivanov on the future of mathematics with respect to the development of AI (the background being the two cultures paper of Sir Gowers, several posts on Ivanov’s blog starting here, and the 2013 paper of Ganesalingam-Gowers –which has yet to appear, apparently–, which Sir Gowers discussed again last year in Cambridge and in London)
  • the theoretical aspects of the recent discovery of gravitationnal waves by LIGO are being presented at IHÉS :  there is a dedicated website and also videos of a very clear four-part physics crash course by Thibault Damour, a central contributor in analytical relativity. Asking about these LIGO results on MO is/was apparently contentious… As for the mathematics involved in the signal detection, the CNRS website mentions Wilson wavelets.
  • Cédric Villani, in a very well written and documented article, discussed the current position of english as the universal langage for research. Trying to guess what would happen in the next few years or decades when automatic translation of scientific papers reaches maturity he sees 3 possibilities : Babel Tower, Universalist, Altruistic (for more see the article). Of course we are not there yet, so he concludes “Learning English is still a good idea.”  In comments, some other opinions are expressed, to which he replies.
  • the initial list of candidates for one of the 11 junior permanent positions at CNRS in pure & applied maths has appeared, it has 261 names so the ratio this year is 23.7 candidates per position…

Gonepteryx rhammi by xulescu_g on flickr

Primes on space-filling curves

July 26, 2015

This is a variation on a theme by Ulam.  It is well-known that Ulam’s spiral is related to the high density of primes along some quadratic polynomials, as per Hardy & Littlewood’s conjecture F.

What about other curves, in particular space-filling curves like that of Peano or that of Hilbert ? Would one expect to see particular patterns ?

Well, not knowing what to expect, I’ve tried to look at Hilbert’s. Below are thus primes marked on iterations 7 and 8 of Hilbert’s curve, with also primes shown without the curve. (I’ve chosen the convention that has the first vertex at the top left corner, and I prefer not to show the quick and ugly code.)

End result : unfortunately I can’t quite spot anything too noticeable (that the primes avoid some diagonals is an easy consequence of the curve being built from units of 4 vertices, but beyond that…). Also, for some reason worpress.com wouldn’t allow my svg files, so these are uglier png versions…

Edit (3rd august 2015): since primes do rarefy, it was tempting to look at a few more iterations and see if at least there are more around the top left corner on a larger scale. This is indeed seen in the plots of iteration 10 and 11 that I’ve added after the original ones. Iteration 11 contains 4,194,304 integers, and thus includes a fair amount of primes. But apart from the top left corner denser region the plots in fact look really uniform, despite lots of not too small prime gaps in these ranges, so there’s  really no pattern there.

primesonhilbert7 primesonhilbert7nocurve primesonhilbert8 primesonhilbert8nocurveAnd now iteration 10 and 11 (making the points on the 10th somewhat larger for better viewing).

primeshilbert_iteration10primeshilbert_iteration11

Epijournals are around the corner

September 9, 2014

Browsing the episciences.org website recently, I’ve noticed that while math journals are not up yet, a first epijournal has seen the light of the day back in june : the Journal of Data Mining and Digital Humanities.

That’s a good opportunity to see how the project is intended to work : here’s the page for one of the first papers. One observes the following:

– a layout which includes title, journal reference, abstract, submission & publishing dates, bibTeX citation, social widgets, and access stats

– when downloading one gets a file (with a funny extension not readily recognized as pdf, the website developpers might want to add some .pdf suffix there) and that file is exactly the accepted version of the arxiv preprint, nothing added on top to say it has been published somewhere and no .sty file provided

– the website offers to log in (I haven’t tried yet)

 

It looks nice, but clearly some choices have been made, in particular : there’s no built-in comment system, no link to the authors’ own websites, no names of the editors who handled the article next to it (one has to guess from the editorial team page). It is unclear at this stage whether all those choices are valid for all future journals or whether this is customizable.

Anyway, I’m rather curious to see what the first few math journals will be : some specialized and some generalist probably, but will they all be new or will we see some known journals move to that platform? Verdict soon, hopefully…

 

 

Storage

August 11, 2013

Truly exciting advances in DNA-based information storage are being made, resulting in something that is robust, lasts thousands of years and has very high density compared to flash memory. And they announce “commercially viable technology within five years”!

Hopefully, some self-generating “archive of human knowledge” will one day be designed: a DNA fragment that, when put into some appropriate medium (e.g. your basement lab, or even an ocean on some distant planet that harbours reasonable chemistry), starts producing a biomachine that is a kind of tablet computer (with touchscreen and sound), and said biomachine will then be used to read the data contained on the rest of that DNA fragment (where the actual archive of human knowledge has been encoded).

Then put that at several locations across the solar system and beyond, for good measure.

 

Short MacArthur stats

November 18, 2012

The MacArthur Foundation rewards each year about 22 Fellows with a 5-year $500,000 grant given in instalments. The only eligibility requirement is that the laureates must be either citizens or permanent residents of the US.   Let’s see the break-up of recent classes.

– This year there has been 23 recipients. Most are US citizens educated there, the 5 exceptions being Israeli mathematician Chudnovsky (the only mathematician), German photographer Barth, Mexican-American film-maker Almada, and two frenchmen: bow-maker Rolland and optical physicist Guyon.

– Last year, the 22 laureates had 4 non-US educated ones:  German physicist Greiner, Cuban percussionist Prieto, Italian silversmith Vitali, and Japanese developmental biologist Yamashita.

– In 2010 there has been 23 fellows, among which: Chinese fiction writer Li, Israeli optical physicist Lipson, French economist Saez, and Chinese computer security specialist Song.

So, the general recent trends seem to be:

– about a half of the fellows are scientists broadly speaking, the other half being connected to the arts

– about 18% are non-US educated, and 82% are US citizens educated there

– mathematicians are rare: before Chudnovsky there has been Mahadevan in 2009, Tao in 2006, and then it goes back to Yau in 2000. They were more numerous in the eighties it seems.

 

 

Math projects at the 2012 Intel Science Talent Search

April 3, 2012

A few weeks ago, the 2012 crop of the 10 winners of the Intel Science Talent Search have been announced.  As usual, these are great projects in a wide variety of fields (cancer research, robotics, geophysics, ecology, …).

Several math projects were in there too: 18 year old David Ding came 4th with his work on Infinitesimal Cherednik algebras of \mathfrak{gl}_2 (done during a PRIMES program at MIT— which seems to be a fantastic setting indeed for insterested high-schoolers — under the supervision of Sasha Tsymbaliuk).

And 17 year old Anirudh Prabhu came 7th for his first non-trivial analytic lower bound of odd perfect numbers (his arxiv papers are here). Apparently he has been taking accelerated courses for a number of years, and did his research on his own without a mentor.

That’s impressive in both cases, and shows that there is not one single recipe for success.

 

 

WolframAlpha is a useful tool

January 10, 2012

I had not looked too much at WolframAlpha yet, but it looks very handy.  Lots of Mathematica can be done before hitting the time limit, and many nice added features are there.

For example, the student wishing to test the correctedness of her solution to some random calculus problem can check it herself by using the “show steps” button, which provides explanations of chain rules involved, and so on. Nice. (But then, another good reason to make sure students switch off their phones during exams…)