Mathematics

This video illustrates the results obtained with our new real-time forest rendering and lighting algorithm (real-time capture at 1024x768 resolution, with an NVidia 470 GTX), integrated in our real-time planet rendering engine Proland (http://proland.inrialpes.fr). See our upcoming Eurographics paper, "Real-time Realistic Rendering and Lighting of Forests", Eric Bruneton and Fabrice Neyret, Eurographics 2012 (http://hal.inria.fr/hal-00650120 and http://www-evasion.imag.fr/Membres/Er...) The SIGGRAPH Technical Papers program is the premier international forum for disseminating new scholarly work in computer graphics and interactive techniques. SIGGRAPH 2013 brings together thousands of computer graphics professionals, 21-25 July 2013, Anaheim, California, USA. Learn more at http://s2013.siggraph.org/ Published on May 22, 2013 The Sun emitted a mid-level solar flare on the morning of May 22, 2013. The flare peaked at 9:38 a.m. EDT and was classified as an M7. Published on May 21, 2013 WIRED gets exclusive first-look at the new Xbox One and Kinect sensor. Watch as we test the new Kinect with advanced 3D and infrared capabilities. Jumping, punching, and fireballs...even in the dark. This is a special edition of Game|Life, to follow the series go to video.wired.com or subscribe to our channel at youtube.com/WIRED. 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.

Recently I made two discoveries -- that the first nine primes form a Haiku and that NASA has a contest (deadline July 1) to select three Haiku to send to Mars. Prime Haikutwo three five seveneleven thirteen fifteenseventeen nineteenSend a Haiku to Mars on the MAVEN! NASA is offering all of us a way to ‘Go to Mars’ aboard a DVD flying on the solar winged MAVEN (Mars Atmosphere and Volatile Evolution) orbiter via a contest managed by the University of Colorado at Boulder’s Laboratory for Atmospheric and Space Physics (CU/LASP). Haiku messages will be voted on by the public; the top three most popular entries will be sent to Mars on the MAVEN spacecraft and will be displayed on the MAVEN website. Deadline for submission is July 1 -- more information here.

Some people are always critical of vague statements. I tend rather to be critical of precise statements; they are the only ones which can correctly be labeled wrong.~ Raymond Smullyan on criticismThe 145th day of the year; 145= 1! + 4! + 5!. There are only four such numbers in base ten. 1, 2 and 145 are three of them, what's the fourth?EVENTS1581 John Dee, mathematician and mystic, ?rst saw spirits in his crystal globe. [Daniel Cohen, Masters of the Occult , Dodd and Mead, 1971, p. 28] *VFR1694 Isaac Newton to Nathaniel Hawes: “A Vulgar Mechanick can practice what he has been taught or seen done, but if he is in an error he knows not how to ?nd it out and correct it, and if you put him out of his road, he is at a stand; Whereas he that is able to reason nimbly and judiciously about ?gure, force and motion, is never at rest till he gets over every rub.” Westfall takes this as the title of his fabulous biography of Newton, Never at Rest. Reportedly he received one of the early Golden Fleece Awards of Senator Proxmire for a grant to write this book. [But we have been unable to ?nd a reference for this last statement.] *VFR1721 John Copson of High Street in Philidelphia posted an offering in the American Weekly Mercury on this date announcing that he would open an office to provide fire insurance for "vessels, goods, and merchandise." With that, he became the first Insurance agent in continental America. *Kane, First Famous Facts 1747 Benjamin Franklin describes his electrical experiments in a letter to Peter Collinson. " Hence have arisen some new Terms among us. .... Or rather B is electrised plus and A minus. And we daily in our Experiments electrise Bodies plus or minus as we think proper. These Terms we may use till your Philosophers give us better. To electrise plus or minus, no more needs to be known than this; that the Parts of the Tube or Sphere, that are rub'd, do, in the Instant of the Friction, attract the Electrical Fire, and therefore take it from the Thing rubbing: the same Parts immediately, as the Friction upon them ceases, are disposed to give the Fire they have received, to any Body that has less." *Collinson, "Experiments and Observations on Electricity Made at Philadelphia in America." 1832 Galois writes to his friend, Auguste Chevalier, about his broken romance for Stephanie. The fatal duel looms only five days away.1842 Johann Christian Doppler (1803–1853) presented a lecture on the Doppler e?ect. It was ?rst experimentally veri?ed in 1845 using a locomotive drawing an open car with several trumpeters. *VFR 1844 the first news communicated by telegraph in the U.S. was sent 80 miles to the Baltimore Patriot, Maryland, from Washington, D.C. giving the information that "One o'clock. There has just been made a motion in the House to go into committee of the whole on the Oregon question. Rejected. Ayes 79 - Nays 86." This was just one day after Samuel Morse transmitted his famous "What hath God wrought!" message from the U.S. Supreme Court room and opened America's first telegraph line linking Washington and Baltimore.*TIS 1946 The Soviet Union issued two stamps to celebrate the 125th anniversary of Pafnuti Lvovich Chebyshev (1821–1894). [Scott #1050-1].*VFR (see May 16th Births) 1961 the formal announcement of an American lunar landing was made by President John F. Kennedy speaking to the Congress: "I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the Moon and returning him safely to the Earth. No single space program in this period will be more impressive to mankind, or more important in the long-range exploration of space; and none will be so difficult or expensive to accomplish." *TIS2142 The next total solar eclipse in Ostend, Belgium. The last total solar eclipse took place more than 11 centuries ago, 29 September 878. But only 9 years later, on 14 June 2151, there will be another one. *NASA Solar Eclipse Catalog (I kno

A finite group is said to be a Frobenius group if there is a non-trivial subgroup of (known as the Frobenius complement of ) such that the conjugates of are “disjoint as possible” in the sense that whenever . This gives a decomposition where the Frobenius kernel of is defined as the identity element together with all the non-identity elements that are not conjugate to any element of . Taking cardinalities, we conclude that and hence A remarkable theorem of Frobenius gives an unexpected amount of structure on and hence on : Theorem 1 (Frobenius’ theorem) Let be a Frobenius group with Frobenius complement and Frobenius complement . Then is a normal subgroup of , and hence (by (2) and the disjointness of and outside the identity) is the semidirect product of and . I discussed Frobenius’ theorem and its proof in this recent blog post. This proof uses the theory of characters on a finite group , in particular relying on the fact that a character on a subgroup can induce a character on , which can then be decomposed into irreducible characters with natural number coefficients. Remarkably, even though a century has passed since Frobenius’ original argument, there is no proof known of this theorem which avoids character theory entirely; there are elementary proofs known when the complement has even order or when is solvable (we review both of these cases below the fold), which by the Feit-Thompson theorem does cover all the cases, but the proof of the Feit-Thompson theorem involves plenty of character theory (and also relies on Theorem 1). (The answers to this MathOverflow question give a good overview of the current state of affairs.) I have been playing around recently with the problem of finding a character-free proof of Frobenius’ theorem. I didn’t succeed in obtaining a completely elementary proof, but I did find an argument which replaces character theory (which can be viewed as coming from the representation theory of the non-commutative group algebra ) with the Fourier analysis of class functions (i.e. the representation theory of the centre of the group algebra), thus replacing non-commutative representation theory by commutative representation theory. This is not a particularly radical depature from the existing proofs of Frobenius’ theorem, but it did seem to be a new proof which was technically “character-free” (even if it was not all that far from character-based in spirit), so I thought I would record it here. The main ideas are as follows. The space of class functions can be viewed as a commutative algebra with respect to the convolution operation ; as the regular representation is unitary and faithful, this algebra contains no nilpotent elements. As such, (Gelfand-style) Fourier analysis suggests that one can analyse this algebra through the idempotents: class functions such that . In terms of characters, idempotents are nothing more than sums of the form for various collections of characters, but we can perform a fair amount of analysis on idempotents directly without recourse to characters. In particular, it turns out that idempotents enjoy some important integrality properties that can be established without invoking characters: for instance, by taking traces one can check that is a natural number, and more generally we will show that is a natural number whenever is a subgroup of (see Corollary 4 below). For instance, the quantity is a natural number which we will call the rank of (as it is also the linear rank of the transformation on ). In the case that is a Frobenius group with kernel , the above integrality properties can be used after some elementary manipulations to establish that for any idempotent , the quantity is an integer. On the other hand, one can also show by elementary means that this quantity lies between and . These two facts are not strong enough on their own to impose much further

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A diverse set of discussions are happening either on the comment section of Nuit Blanche or on any of the following groups: the Google+ Community (386), the CompressiveSensing subreddit (116), the LinkedIn Compressive Sensing group (2281) or the Matrix Factorization (661). You can start a discussion here on the Google+ group or start a thread on the CompressiveSensing subreddit. As you may have noticed, I am being generous about giving +1s (Google+) or upvotes (Reddit). These communities will only grow if positive reinforcement is used by all. Talking about upvotes, looking back at the last 100 entries, here are the ones that obtained the most Google +1s are: +6 It's Friday, It's Hamming's Time: Learning to Learn by Richard Hamming, "You Get What You Measure" / "Error-Correcting Codes" +5 Please take the time to nominate somebody or something today K-SVD/IPR: Learning Incoherent Dictionaries for Sparse Approximation using Iterative Projections and Rotations - implementation - Sunday Morning Insight: Game of Thrones and the History of Compressive Sensing +4 Sunday Morning Insight: Computational Cooking, you won't see food the same way anymore. PalBOMP/PolBOMP: Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation - implementation - The OSTP is seeking an Outstanding “Open Science” Champion of Change Sometimes, the authors of the papers featured here on Nuit Blanche want to answer some of the questions I asked publicly, this is good, here are two examples: There was a statement by an anonymous commenter on the Traveling Salesman paper this week. Some of the authors (Nicolas Chauffert and Pierre Weiss) have responded in the comments. Curt provided some insight on the Quantum trick and Raphael Pooser, one of the author, tried to answer my question in the post. We also had some additional inisghtful information provided by commenters: Leslie provided some additional reference on the computational cooking post. Thomas added some potential champions of open science on the list, Ross and Chander provided additional resources to the Hamming's video series. Bourbaki provided some additional data on replacements to Google's reader. Sunil liked the analogy on the Games of Thrones post compressive sensing post. An anonymous commenter provided some additional information on the recent D-wave announcement as well as here. Finally, discussions on the Compressive Sensing Group with 2281 members ( Please pay attention to your questions) featured the following subjects: Compressed Sensing Reconstruction with Unknown Sparsity Evaluating EM-GM-AMP and BSBL I am working on compressive sensing technique in wireless sensor networks. I apply belief propagation based compressive sensing in these... CFP: GlobalSIP 2013 Symposium on Low-Dimensional Models and Optimization in Signal Processing Conditions for unique (not exact) recovery from noisy compressed measurements Fourier Talks 2013 What are the best introductory books to compressive sensing? Codes Wanted! Can anyone share these 3 packages (Optimized PROPACK, Modified PROPACK and BLWS ) mentioned in the paper " Some Software... Sparse representations of EEG ? Analysis operator for signals other than visible photon imaging ? Please pay attention to your questions On the advanced Matrix Factorization group with 661 members, we had: a question on Blind Source Separation (BSS) A doubt in paper about Nonnegative Matrix Factorization-Factoring nonnegative matrices with linear programs Predicting movie ratings and recommender systems NMF with sum-to-one constraint Orthogonal NMF residual if you want to see tensor factorization in action check out "Frappe" our new app recommendation Question about fast randomized solver for multi-tasks regression Is there a greedy algorithm for matrix completion, that iteratively re

Thomas Arildsen mentioned this ICASSP poster in the Google+ group yesterday: SURPASSING THE THEORETICAL 1-NORM PHASE TRANSITION INCOMPRESSIVE SENSING BY TUNING THE SMOOTHED L0 ALGORITHM by Christian Schou Oxvig, Patrick Steffen Pedersen, Thomas Arildsen, Torben Larsen Reconstruction of an undersampled signal is at the root of compressive sensing: when is an algorithm capable of reconstructing the signal? what quality is achievable? and how much time does reconstruction require? We have considered the worst-case performance of the smoothed l_0 norm reconstruction algorithm in a noiseless setup. Through an empirical tuning of its parameters, we have improved the phase transition (capabilities) of the algorithm for ?xed quality and required time. In this paper, we present simulation results thatshow a phase transition surpassing that of the theoretical `1 approach: the proposed modi?ed algorithm obtains 1-norm phase transition with greatly reduced required computation time. The attendant code for this modified version of SL0 is here. I wonder if this tuning coluld be further helped by making assumption on the signal to be reconstructed (beyond sparsity akak structured sparsity) ? 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.

Documentary on Crossfit athlete Mikko Salo. His resting heart rate is 31 bpm! See also here.Great deadlift / burpee metcon @34min. Compare to lullaby :-)

Hence no force, however great, can stretch a cord, however fine,into a horizontal line which is accurately straight:there will always be a bending downwards. ~William Whewell The 144th day of the year; 144 is the only square of a composite number in the Fibonacci Sequence. *Tanya Khovanova Number Gossip144 is also the smallest square number which is also a square when its digits are reversed (144 = 12 2 while 441= 212 EVENTS997 Al-B?run? in Kath and Abul-Wafa in Baghdad simultaneously watch a lunar eclipse. The time obtained by this prearranged cooperation allowed them to determine the di?erence in longitude between the cities. *VFR1032 The renowned Arab scientist Ibn Sina noted, “I saw Venus as a spot on the surface of the sun,” This is the first known record of witnessing the transit of Venus. The first recorded observation of a transit of Venus was made by Jeremiah Horrocks from his home at Carr House in Much Hoole, near Preston in England, on 4 December 1639. Kepler predicted the 1761 transit of Venus, the first such prediction in Western recorded history, and one that inspired several astronomical expeditions. *Sky and Telescope 1543 An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR1547 Ferrari replied to Tartaglia’s letter of 21 April 1547 by sending 31 challenge problems of his own. Tartaglia solved all but the ?ve dealing with cubic equations. *VFR For more on this "math wars" story, see this Renaissance Mathematicus blog. 1626 Manhattan bought from the Indians for ($24) If invested at 5% *VFR {In 1626 Peter Minuit bought Manhattan island from the local Indians for a load of cloth, beads, hatchets, and other odds and ends then worth 60 Dutch guilders. Estimated to have been worth $24 Dollars at a much later time. If we convert that to silver prices at the time, you could purchase about 18 Troy ounces of Silver.. Today the price of silver is about $35 per ounce, so .. not such a good investment in that sense... }1844 Samuel F. B. Morse dispatched the first telegraphic message over an experimental line from Washington, D.C., to Baltimore. The message, taken from the Bible, Numbers 23:23 and recorded on a paper tape had been suggested to Morse by Annie Ellsworth, the young daughter of a friend. {Nice to have influential friends, she was the teenage daughter of the Commissioner of Patents. Congress appropriated $30,000 for a telegraph wire to be strung the 80 miles between Washington and Baltimore}..Morse sent the message from the chamber of the Supreme Court, then in the United States Capitol, to his assistant Albert Vail at the Mount Clair depot in Baltimore in 1844.*Library of CongressA photo of the actual tape in the Library of Congress is here. 1883 Brooklyn Bridge was opened over the East River, New York City, USA, of a breadth of 1,600 feet, navigable water with a single span. What was then regarded as the greatest engineering feat still stands in service today, and remains the world's only stone-towered, steel cabled bridge. Twice the size of the Niagara Suspension Bridge and four times the longest non-extension spans ever attempted, the total length of this colossal structure is 6,927 ft. The road bed is 80 feet wide, and at an elevation of 186 feet above high water. John Roebling, and after his death his son Washington Roebling, worked on its construction for 13 years. *TIS Contrary to the New York Times Magazine of 27 March 1983, the cables hang in the shape of parabolas, not catenaries. *VFR1961 MIT's Clark Begins Work on LINC Computer :Wes Clark began his work on LINC, or the Laboratory Instrument Computer, at MIT's Lincoln Laboratory. His plan was to create a computer for biomedical research, that was easy to program and maintain, that could be communicated with while it operated, and that could process biotechnical signals directly. Building on his previous experience in developing the Whirlwind, TX-0, and other early computer