Mathematics

Exciting news in academic publishing! There’s a startup company in the UK, called Flooved, who are on a mission to revolutionize scientific publishing. What sets them apart from many similar-sounding initiatives is that they seem to have a solid business model and they seem to be doing all of the right things, therefore my bet is that they are going to succeed. What they do is to compile existing lecture notes, handouts and study-guides, and along the lines of the Open Access movement, to make them freely available online. The advantage to students is clear. The advantage to instructors is that more people read and use the material. The advantage to publishers who contribute content (are you listening, big publishing companies?) is that they get precise and useful information on how the students are using their content, and this helps them make informed decisions to put them ahead of the competition. Beyond this, the Flooved model makes education available to people worldwide, including to people who don’t have access to universities. Now, if only they could also provide assessment and accreditation…

In some subjects, a paper in a prestigious conference proceedings is the pinnacle of a researcher’s career. It has never really been so in mathematics, and is now less so than ever. This is partly, I think, because of the law of unintended consequences. The people who evaluate our research have the idée fixe that conference proceedings are of less value than refereed journals, so anyone who submits one to the REF is committing academic suicide. This despite the fact that many conference proceedings are refereed to the same standard as journal articles; but the box-ticking of research evaluation cannot cope with this subtlety. There are all sorts of reasons why I might want to have a good paper in a conference proceedings. Perhaps the people I want to read the paper belong to the community that puts on that conference. Perhaps the conference celebrates a mathematician I respect. And so on. It wasn’t always so. I want to review briefly the history of the proceedings of the British Combinatorial Conference as an example. (Full details are kept by Keith Edwards.) The proceedings appeared intermittently until 1983, when regular publication in Ars Combinatoria began. (In some of the earlier volumes, the invited and contributed papers appeared together; but from 1977, the practice of publishing the invited talks in advance of the conference was adopted.) In 1991, the contributed papers volume moved to Discrete Mathematics, where it has been since; the proceedings of the 2011 Exeter conference appeared quite recently. The papers were refereed to the usual standard of the journal by a guest editorial board appointed by the BCC, and everything was vetted by the editor-in-chief. The proceedings of the 1997 conference, for example, had 60 papers covering 795 pages in volumes 197/198, together with the problems presented at the conference. Later, when the publisher used to publicise the 25 most-downloaded papers from the journal every three months, papers from the BCC proceedings were usually high on the list. It is clear that publication in the proceedings was highly valued by many conference participants. But no more. Discrete Mathematics has been moving away from conference proceedings, and has given notice to the BCC. The committee have tried but failed to find an alternative forum for publication. We required a journal with a good reputation, since this is one of the things that delegates appreciated; putting the papers on a web page would be easy enough but would not really fill the gap. So, for this year’s conference, there will not be a volume of contributed papers. Academic publishing is changing very rapidly, and it may well be that the committee will decide to try out a new option, perhaps an epijournal in the future. But, for what it’s worth, a tradition of some standing will be broken.

I was just in Chicago for a conference, and, having always meant to go to a highly touted experimental restaurant in the Chicago style, made a reservation — sorry, I mean “got tickets” — for EL Ideas. To get this out of the way first — yes, the food was good.  Very, very good.  But I don’t actually want to talk about the food!  Lots of restaurants have good food.  What’s really interesting about EL Ideas is the way it merges the idea of “restaurant” with the idea of “theater.” There’s no menu — each of the 24 diners eats the same thing at the same time, so that, as in a play, everyone in the room is having the same experience.  Before the meal begins, the chef/impresario/director/producer pops out from the kitchen to tell you that this isn’t going to be the usual stuffy expensive restaurant deal — he wants you to wander into the kitchen and ask what’s going on, he wants you to really get into it.  He warns that you should summon an Uber car rather than trying to walk home through the somewhat desolate neighborhood because if you did the latter “you might die.”  In other words:  we are the ones hip enough to be in this neighborhood, to feel a  little frisson of danger, though nothing you can’t dispel with an app!  (In fact, I cannot say the crowd looked notably hip — my dinner companions were younger than me, but most other people looked old and rich, one more thing EL Ideas has in common with the theater.) Before each dish is presented, the chef gives a little introduction, during which you are supposed to be quiet — if you talk while the he’s talking, the chef warns, you might get thrown out.  Just like the theater. You don’t exactly get a reservation here; you purchase the meal in advance, as with a ticket to a show. And at the end everyone claps! When I was younger, I used to go to plays a lot.  OK, not a lot.  But I probably saw three to five plays a year, and even then I think most people I knew weren’t going.  Now I never go to plays; for all I know, I may never see a play again. But EL Ideas makes me think that there are things people want from plays, and these are things that people who never go to plays sense, consciously or not, that they still want, and so something wonderful happens — the theater, seemingly made extinct by other, nimbler forms of entertainment, spores out into the atmosphere and embeds itself in another cultural host.

We [he and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury. Irving Kaplansky honoring Paul HalmosThe 139th day of the year; 139 and 149 are the first consecutive primes differing by 10. 139 = 9*8+7*6+5*4+3*2-1 *Prime Curios EVENTS1662 Samuel Pepys, Secretary of the Navy Board inspects the new Mint in the Tower of London, but will not be allowed to see the ultra secret "edging" machines that engraved an inscription into the edge of the coins to safeguard against the common practice of "clipping" that was common. It was one of the first "milled" currencies in the world. In 1910, the Earth passed through the tail of Halley's Comet, the most intimate contact between the Earth and any comet in recorded history. The event was anticipated with dire predictions. Since a few years earlier, astronomers had found the poisonous gas cyanogen in a comet, it was surmised that if Earth passed through the comet's tail everyone would die. Astronomers explained that the gas molecules within the tail were so tenuous that absolutely no ill effects would be noticed. Nevertheless, ignorance bred opportunists selling "comet pills" to the panicked portion of the public to counter the effects of the cyanogen gas. On 20 May, after Earth had passed through the tail, everyone was still alive - with or without taking pills! *TIS New York Times coverage is HALLEY’S COMET BRUSHES EARTH WITH ITS TAIL (banner headline of the newspaper); 350 American astronomers keep vigil; Reactions of fear and prayer repeated; All night services held in many churches; 1881 dire prophecies recalled by comet scare.1979 In the Chicago Sun-Times W. F. Buckley wrote “The Rasmussen Report estimates there will be one melt down every 20,000 reactor-years, and one fatality (from cancer) every 50 reactor-years. Conjoin these data (20,000 divided by 50) and you get the ?gure of 400 deaths per year.” Quoted from the “Hows that again department,” AMM 90 (1983), p 220.*VFR 1825 Faraday isolates benzine. In 1825, Faraday started work on a sample of oil that had been sent to him for analysis by the Portable Oil Company of London. He subjected this oil to fractional distillation, a process that proved to be extremely difficult, and it took him some time to resolve the oil into its pure components. By repeated fractional distillation followed by selective fractional freezing, each stage monitored by analysis, he produced a fairly pure sample of what he called bicarburet of hydrogen. Faraday’s notebook records these procedures, which he carried out on 18 and 19 May 1825. Auguste Laurent suggested the name benzene. *Jennifer Wilson, Celebrating Michael Faraday’s Discovery of Benzene, Ambix,Volume 59, Issue 3 2006 Apple 'Cube' Shop Opens in Big Apple, NY City: Apple Computer opened its second retail store in New York City. The 20,000-square foot store is situated in the underground concourse of the General Motors building at 767 Fifth Avenue. New Yorkers stood on line for hours in order to be among the first to enter. Open 24-hours a day, the shop is visible at street level through a 32-foot glass cube. It cost $9 million and was designed by Apple’s CEO Steve Jobs.*CHM BIRTHS 1682 Mei Juecheng (19 May 1681 in Xuangcheng, now Xuanzhou City, Anhui province, China - 20 Nov 1763 in China) published Chishui yizhen (Pearls recovered from the Red River). This contained the infinite series expansion for sin(x) which was discovered by James Gregory and Isaac Newton. In fact the Jesuit missionary Pierre Jartoux (1669-1720) (known in China as Du Demei) introduced the infinite series for the sine into China in 1701 and it was known there by the name 'formula of Master Du'.*SAU 1832 Edmond Bour (19 May 1832 in Gray, Haute-Saône, France - 9 March 1866 in Paris, France)Bour made many significant contributions to analysis, algebra, geometry and applied mechanics despite his

You run a single-item sealed bid auction where you sell an old camera. There are three bidders and the value of the camera for each of them is described by a certain (known) random variable: With probability 0.9 the value is 100+x where x is taken uniformly at random from the interval [-1,1]. With probability 0.1 the value is 300+x where x is as before. The 300 value represents the case that the item has a special nostalgic value for the buyer. The values of the camera to the three bidders are thus i.i.d random variables. (The reason for adding this small random x is to avoid ties, and you can replace the interval [-1,1] with [-?, ?] for a small ?, if you wish.) The basic question The basic questions for you the seller is: What is the highest expected revenue you, the seller, can guarantee and what is your optimal allocation policy. I’d like to see the answer for this question. But let me challenge your intuition with two simpler questions. 1) Can the seller guarantee an expected revenue of 120  or more? 2) What (roughly) is the optimal allocation policy a) Highest bidder wins. b) Highest bidder wins if his bid passes some reserve price. c) The item is allocated at random to the bidders with probabilities depending on their bids. Background: Myerson’s paper and his revenue equivalence theorem The most relevant paper to this post is a well-known paper Optimal auction design by Roger Myerson. Myerson considered the case of a single-item sealed-bid auction where the bidders’ values for the item are independent identical random variable. Note that I did not specify the price that the winning bidder is going to pay for the camera. The reason is that according to a famous theorem by Myerson (referred to as the revenue equivalence theorem), when the bidders are strategic, the expected revenues for the seller are determined by the allocation rule and are independent from the pricing policy! (Well, you need to assume a reasonable pricing policy…) For example, if the item is allocated to the highest bidder then the expected price will be the second highest price. If the price is determined by the second highest bid (Vickery’s auction) then each bidder has no incentive to give a bid which is different from its value. But even if the item will be allocated to the first bidder for the highest price, the expected revenues will still be the same! When you analyze an auction mechanism like ours you can assume that the payments are set in a way that the bidders have no incentive not to bid the true value the camera has. This is sometimes referred to as the revelation principle. Myerson considered a mechanism which sometimes lead to higher revenues compared to allocating the item to the highest bidder: The seller set a reserve price and the item is allocated to the highest bidder if the bid passes this reserve price, and is not allocated at all otherwise. In the paper Myerson also considered more complicated allocation rules which are important in the analysis where the item is allocated to bidders according to some probabilities based on their bids. Polls This time we have two questions and two polls: Take Our Poll Take Our Poll Once again this is a game-theory question. I hope it will lead to interesting discussion like the earlier one on tic-tac-toe. A little more Background: Auctions and Vickery’s second price auction. (From Wikipedia) An auction is a process of buying and selling goods or services by offering them up for bid, taking bids, and then selling the item to the highest bidder. In economic theory, an auction may refer to any mechanism or set of trading rules for exchange. In our case, we consider an auction of a single item (the camera) and each bidder is giving a sealed bid. (Again from Wikipedea) A Vickrey auction is a type of sealed-bid auction, where bidders submit written bids without knowing the bid of the other people in the auction, and in which the highest bidder wins, but the pri

Recently Rattle posted a wonderful mathy poem by Diana Rosen entitled "Mathematics and Molé." Here's the first stanza: Mathematics and Molé by Diana Rosen Numbers flicker in front of my eyes as I give him my full attention. Differential geometry explains the black hole, he says. It’s very obvious. I lean forward to catch his words, my chin in cupped hand, eyes intent on his, yet thinking of Mexican food. Mathematics is the language of science, he says. . . .Rozen's complete poem is here.

I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation.... ~Paul Auster, The Music of Chance The 138th day of the year; 138 has three prime factors, the concatenation of the first two is the third. *Prime Cuiros EVENTS1825 Faraday isolates benzine. In 1825, Faraday started work on a sample of oil that had been sent to him for analysis by the Portable Oil Company of London. He subjected this oil to fractional distillation, a process that proved to be extremely difficult, and it took him some time to resolve the oil into its pure components. By repeated fractional distillation followed by selective fractional freezing, each stage monitored by analysis, he produced a fairly pure sample of what he called bicarburet of hydrogen. Faraday’s notebook records these procedures, which he carried out on 18 and 19 May 1825. Auguste Laurent suggested the name benzene. *Jennifer Wilson, Celebrating Michael Faraday’s Discovery of Benzene, Ambix,Volume 59, Issue 3 1852 Massachusetts becomes the ?rst state to pass a compulsory attendance law for school children. *VFR 1896, the Supreme Court ruled separate-but-equal facilities constitutional on intrastate railroads. For some fifty years, the Plessy v. Ferguson decision upheld the principle of racial segregation. Across the country, laws mandated separate accommodations on buses and trains, and in hotels, theaters, and schools. In a speech delivered in the Ohio House of Representatives in 1886 and later published as The Black Laws, legislator Benjamin W. Arnett described life in segregated Ohio: "This foe of my race stands at the school house door and separates the children, by reason of 'color,' and denies to those who have a visible admixture of African blood in them the blessings of a graded school and equal privileges... We call upon all friends of 'Equal Rights' to assist in this struggle to secure the blessings of untrammeled liberty for ourselves and posterity. " After hearing arguments by NAACP lawyer Thurgood Marshall, the Supreme Court overruled the Plessy decision on May 17, 1954. In Brown v. the Board of Education, a unanimous Court adopted Justice Harlan's position that segregation violated the Thirteenth and Fourteenth Amendments to the Constitution. *Library of Congress 1901 Charles Sanders Peirce writes George A. Plimpton, head of Ginn and Company and famous collector of rare mathematical books, describing what the contents of a newly acquired book must be were it indeed the great Liber Abaci (1202) of Fibonacci. In 1949 Carolyn Eisele’s discovery of this letter—still tucked into the back cover of the volume—began her career as a Peirce scholar. [HM 9, 335] *VFR In 1910, Halley's Comet was visible from Earth, moving across the face of the sun. *TIS 1910 Halley's comet was big news during its visible period in New York City. Beginning with the Saturday edition of May 14 and continuing on through the Sunday edition of May 22, the comet was given top billing in the New York Times. This was the period when the comet was at the height of its brilliance and activity and the coverage clearly reflected this.May 18: Earth to pass through come tail for 6 hours; C.B. Harmon invites college deans to join him in viewing comet from balloon. *Joseph M. Laufer, Halley's Comet Society - USA 1933 John Kieran’s Sports of the Times column in the New York Times is entitled “The Coordinate Clash, or Block that Abscissa.” The column was a humorous analogy between football and the upcoming

There’s going to be a “thematic trimester” in Paris starting next spring: Semantics of proofs and certified mathematics, Institut Henri Poincar?, April 22nd - July 11th, 2014, organized by Pierre-Louis Curien, Hugo Herbelin, Paul-Andr? Melli?s. If you like applications of category theory to logic and computer science, there should be a lot for you here! The basic layout is this: Week 1 — Kick-off: Formalisation in mathematics and in computer science Week 3 — Workshop 1: Formalization of mathematics in proof assistants, organized by Georges Gonthier and Vladimir Voevodsky. Week 6 — Workshop 2: Constructive mathematics and models of type theory, organized by Thierry Coquand and Thomas Streicher. Week 8 — Workshop 3: Semantics of proofs and programs, organized by Thomas Ehrhard and Alex Simpson. Week 10 — Workshop 4: Abstraction and verification in semantics, organized by Paul-Andr? Melli?s and Luke Ong. Week 12 — Workshop 5, Certification of high-level and low-level programs organized by Christine Paulin and Zhong Shao. A lot of people I know will attend parts of this, such as Jean Benabou, Marcelo Fiore, Dan Ghica, André Joyal, Samuel Mimram, and Bas Spitters. And that makes me happy, because Paul-Andr? Melli?s has invited me to spend up to a month attending this series of workshops, perhaps in two 2-week stretches. With a little luck I’ll be able to actually do this. (My wife Lisa Raphals has gotten invited to Erlangen for the spring of 2014, meaning roughly April 1 - June 1. If she and I succeed in getting leaves of absence, I’ll go with her, and then take some trips to nearby places. Since live in the Wild West, Paris seems nearby to Erlangen to me. I also have vague invitations to IHES, Prague and Berlin which I might try to take advantage of.)

May 17 was the 137th day of the year, and as usual on my "On This Day in Math" post I added a note that "The 137th day of the year; 137 is the sum of the squares of the first seven digits of pi, 32+ 12 + 42 + 12 + 52 + 92 + 22 = 137." (Plus a bit more)When I posted a tweet of the above, I got a note from jignesh rathod ?@engineer_rathod to inform me that 137 was also unique in that if you drop any one of the digits, the remaining digits form a prime. I pushed this to the point that if we allow the old-fashioned idea that 1 was a prime then 137 was a prime number which would still be prime if any number was eliminated, and each digit is prime (2nd thoughts about this, more later) . In fact, when any digit is removed, the remaining digits may be placed in any order and would still be prime. (take out 3 and we have 17 and 71). I wrote and asked if the idea had a name and there seemed to be no formal (or much of an informal) consences . I had thought of ultra-prime right off the bat, but then I got a note from Chris Maslanka to suggest the idea of a Knockout Prime, and I knew I had found the term I wanted. There was still a problem about how to distinguish special cases. Was one acceptable as a prime, what about those that were reversible. My next epipheny came in a tweet from @mathematicsprof who suggested the notation C(3,3) is Combination Prime for the fact that the original 3-digit number (137) was prime, and C(3,2) is combination Prime for if all two digit pairs were prime ( 13, 17, 37) . I worried about using the C(m,n) notation when it might be confused with the use in combinations, so I decided to use CP(m,n) for Combination Prime... then I changed my mind again and decided to use Chris' name as part of the symbol and opted for KP(m,n) as in Knockout Prime. So 137 is KP(3,3) and KP(3,2) but not KP(3,1) (using the modern approach that 1 is not considered prime). Eliminating one may well mean that there exists no KP(3,1) numbers as conjectured by the Math Prof. Suddently it hit me, a lesser symbol for those allowing 1 as prime, Kp(3,1) . So 137 is Kp(3,1) but not KP(3,1). I toyed with a symbol to differentiate 23 and 37 since both are KP(2,2) but 23 is not a prime when reversed and 37 is. I decided to settle for just using reversible KP(2,2). So a number like 137 would be reversible (3,2) since any two digits remaining are KP in either order. I haven't taken the time to do a computer search of all the 2,3,4 digit numbers to see how they qualify. If anybody jumps on that before I get to it, send me a copy. I expect I will update this page as better ideas are contributed by others. Thanks for comments

Sylvain Gigan (also in Science) let me know of the following paper that is also making the rounds in Science. If you recall, it was shown earlier that compressive sensing was speeding up the process of acquiring the data. The physics itself is not changed and revolves around this formula: 3D Computational Ghost Imaging by Baoqing Sun, Matthew P. Edgar, Richard Bowman, Liberty E. Vittert,Stephen S. Welsh, Ardrian Bowman, Miles J. Padgett Computational ghost imaging retrieves the spatial information of a scene using a single pixel detector. By projecting a series of known random patterns and measuring the back reflected intensity for each one, it is possible to reconstruct a 2D image of the scene. In this work we overcome previous limitations of computational ghost imaging and capture the 3D spatial form of an object by using several single pixel detectors in different locations. From each detector we derive a 2D image of the object that appears to be illuminated from a different direction, using only a single digital projector as illumination. Comparing the shading of the images allows the surface gradient and hence the 3D form of the object to be reconstructed. We compare our result to that obtained from a stereo- photogrammetric system utilizing multiple high resolution cameras. Our low cost approach is compatible with consumer applications and can readily be extended to non-visible wavebands. The 3D of this paper has little to do with the 2D extraction from Three-dimensional ghost imaging ladar and we measure reflectance difference here as opposed to time of flight information. Here is the multispectral paper: Multi-wavelength compressive computational ghost imaging by Stephen S. Welsh, Matthew P. Edgar, Phillip Jonathan, Baoqing Sun, Miles. J. Padgett The field of ghost imaging encompasses systems which can retrieve the spatial information of an object through correlated measurements of a projected light eld, having spatial resolution, and the associated reflected or transmitted light intensity measured by a photodetector. By employing a digital light projector in a computational ghost imaging system with multiple spectrally fi ltered photodetectors we obtain high-quality multi-wavelength reconstructions of real macroscopic objects. We compare di erent reconstruction algorithms and reveal the use of compressive sensing techniques for achieving sub-Nyquist performance. Furthermore, we demonstrate the use of this technology in non-visible and fluorescence imaging applications. Thanks Sylvain ! Join the CompressiveSensing subreddit or the Google+ Community and post there ! Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.