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# Posts

### March 01, 2015

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The Harriss spiral (G+)Wind-carved towers of sand and ice (G+)Beachbot, a giant etch-a-sketch for your local beach (G+)Linkages that can draw any algebraic curve (G+)Precursors to the Penrose tiling in the works of Kepler and the Islamic architects (G+)Women in mathematics (G+)Big Bang Theory Eye of the Tiger Scene (G+)Why using git is good scientific practice (G+)Klam values and other colorful neologisms from the parameterized complexity crowd (G+)Timsort is broken (and has been for the past […]

### February 28, 2015

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While Googling something or other, I came across Nine Chapters on the Semigroup Art, which is a leisurely introduction to the theory of semigroups. (While the document is labelled “lecture notes”, the typography is quite beautiful.)
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Chapter 3. The Logic of Relatives (cont.) §4. Classification of Relatives 225.   Individual relatives are of one or other of the two forms and simple relatives are negatives of one or other of these two forms. 226.   The … Continue reading →
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Once upon a time, I worked with a postdoc who shaped my views of mathematical physics, research, and life. Each week, I’d email him a PDF of the calculations and insights I’d accrued. He’d respond along the lines of, “Thanks … Continue reading →
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There are some situations, perhaps lucky ones, where it is felt that an activity needs no external motivation or justification.  For the rest, it can be helpful to think of what the task at hand can be useful for. This of course doesn’t answer the larger question of what is worth doing, since it just distributes […]
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http://t.co/a0l4FP6ftF Goodbye #LeonardNimoy, #Spock from #StarTrek by SciFiCatOne popular five-weapon expansion is "rock-paper-scissors-lizard-Spock", invented by Sam Kass and Karen Bryla, which adds "Spock" and "lizard" to the standard three choices. "Spock" is signified with the Star Trek Vulcan salute, while "lizard" is shown by forming the hand into a sock-puppet-like mouth. Spock smashes scissors and vaporizes rock; he is poisoned by lizard and disproven by paper. Lizard poisons Spock […]
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La conferenza che segue è stata successivamente proposta da Fabio Peri un paio di mesi fa al Planetario "Hoepli" di Milano:

### February 27, 2015

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Boise Set Theory Seminar, Wednesday, March 4 from 3 to 4pm Abstract: Continous logic is a proper generalization of first order logic where the usual binary truth values are replaced by the unit interval \$[0,1]\$. The models for this logic are metric structures, which are metric spaces together with continuous functions and \$[0,1]\$-valued relations. Just as ordinary logic has typical applications in discrete math, continuous logic has applications in analysis. In this talk we will introduce just […]
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Mentre alla lavagna un loro compagno sta svolgendo un'espressione polinomiale, quei tre, seduti uno accanto all'altro, sono tutti presi a vedere il cellulare, discutendo tra loro fitti e attenti a quello che c'è sullo schermo. Il professore, quatto quatto, si avvicina, aspettandosi di vedere l'ennesimo mmorg, e invece ecco che i tre stanno lì, incantati, a guardare un video di matematica!
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Re: Helmut Raulien Right, the “divisor of” relation signified by is a dyadic relation on the set of positive integers so it can be understood as a subset of the cartesian product   It is an example of a partial … Continue reading →
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On a set with an operation which has a neutral element, there is an algebraic axiom which is equivalent with both associativity and commutativity of the operation. I call it the shuffle (does it have a name?). It is this one (ab)(cd) = (ac)(bd)  so the middle terms b and c switch their position. Of … Continue reading The shuffle trick, or how to eliminate commutativity and associativity, for the benefit of better self-multiplication →
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I wrote last year about the mini-projects I use in my “flagship” course Networks: Structure & Algorithms.  We recently finished the first of these miniprojects: rankmaniac. In rankmaniac, students have to build a system (using Amazon Elastic MapReduce) to compute the nodes of a huge web crawl that have the top 20 pageranks, and to do the […]
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Some years ago, at a rather posh function in a swanky London venue, I got talking to a peer of the realm. By this point I had been drinking my endless glass of wine for some time (they have stealthy waiters at these kinds of dos), and didn’t quite catch his name, but he had been, apparently, head of a large supermarket chain. And his response to me mentioning the word ‘biodiversity’ has stuck with me. “When I took over... Read more
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Originally posted on mathbabe:Have you ever heard of phrenology? It was, once upon a time, the “science” of measuring someone’s skull to understand their intellectual capabilities. This sounds totally idiotic but was a huge fucking deal in the mid-1800’s, and really didn’t stop getting some credit until much later. I know that because I…
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Theorem 9: Every permutation can be written as a product of disjoint cycles. Moreover, this is unique up to cycling elements within cycles and permuting the order of the cycles.  We proved the ‘existence’ part of this last time.  To check uniqueness, we took two equal products of disjoint cycles and showed that in fact […]

### February 26, 2015

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Nel futuro la società umana sarà suddivisa in due macro civiltà: quella delle monadi urbane, agglomerati di palazzoni gigantestchi, chiamati costellazioni al cui interno ad ogni piano, vengono stipati quantità di esseri umani da fare invidia a metropoli come New York; e quella delle campagne, dove quelli che oggi definiremmo contadini vivono coltivando la terra e preservando l'ambiente. Le due civiltà hanno pochissimi scambi, se non quelli strettamente necessari per lo scambio di materie […]
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After my post last week on the Complexity accepts, a friend of Shuichi Hirahara send Shuichi an email saying that I was interested in his paper. Shuichi contacted me, sent me his paper and we had a few good emails back and forth. He posted his paper Identifying an Honest EXPNP Oracle Among Many on the arXiv yesterday. Shuichi asks the following question: Given two oracles both claiming to compute a language L, figure out which oracle is correct. For which languages does there exist […]
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A highly abundant number is a positive integer n that holds the record (among it and smaller numbers) for the biggest sum of divisors σ(n). While cleaning up some citations on the Wikipedia article, I ran across an unsolved problem concerning these numbers, posed by Jaycob Coleman and listed on the OEIS entry for them: are all sufficiently large highly abundant numbers practical?A practical number n has the property that all numbers up to n can be expressed as sums of distinct divisors of […]
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As you know, dear regular reader, I have a rather uneasy relationship with reductionism, especially when doing mathematical modeling in biology. In mathematical oncology, for example, it seems that there is a hope that through our models we can bring a more rigorous mechanistic understanding of cancer, but at the same time there is the […]

### February 25, 2015

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MONTHLY MEMORY LANE: 3 years ago: February 2012. I am to mark in red three posts (or units) that seem most apt for general background on key issues in this blog. Given our Fisher reblogs, we’ve already seen many this month. So, I’m marking in red (1) The Triad, and (2) the Unit on Spanos’ misspecification tests. Plase see those posts for […]
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I’ll be blogging about my progress in the 7DRL Challenge, but I don’t want to waste time during that week posting all the stuff in this post which can be done now. If you don’t recall what a roguelike is … Continue reading →
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Waldo E. Jones sembrava fluttuare nell'aria al centro di una stanza sferica. L'impressione derivava dal fatto che fluttuava davvero nell'aria. La sua casa era inserita in un'orbita libera, con un periodo di poco più di ventiquattro ore.(8)Waldo abita nello spazio. In orbita intorno alla Terra. Soffre di una malattia che gli impedisce di muoversi sotto l'azione della gravità terrestre. Questo impedimento, come si suol dire, gli ha aguzzato l'ingegno, permettendogli di diventare l'inventore […]
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In which we start to explore permutations. Definition of a subgroup of a group. Definition of the order of an element of a group, and of what it means for an element of a group to have infinite order. Definition of an isomorphism between two groups, and of what it means for two groups to be isomorphic. Definition of […]
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The category theory page here has been much expanded with links to (i) some online lecture notes, and (ii) some books which are freely (and legitimately!) available online in one form or another. I am not at all aiming to … Continue reading →
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I read a lot of papers. I also glance at many papers in journal contents pages and Google search results. From time to time I notice a paper that has an interesting title, author list, abstract, or some other notable … Continue reading →
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Editor’s Note: Yesterday and today, Caltech is celebrating the inauguration of the Walter Burke Institute for Theoretical Physics. John Preskill made the following remarks at a dinner last night honoring the board of the Sherman Fairchild Foundation. This is an … Continue reading →

### February 24, 2015

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To the Wigmore Hall again last week to see hear the Pavel Haas Quartet playing Czech music old and new. The most engaging concert, we agreed, that we’d been to for months. To begin, Dvorak’s four Miniatures Op. 75a for … Continue reading →
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In analytic number theory, it is a well-known phenomenon that for many arithmetic functions of interest in number theory, it is significantly easier to estimate logarithmic sums such as than it is to estimate summatory functions such as (Here we are normalising to be roughly constant in size, e.g. as .) For instance, when is […]
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This exercise is due Tuesday, March 3, at the beginning of lecture. Recall that the th Jordan block for , , is the matrix whose entries along the main diagonal are , along the diagonal immediately below the main one are , and all other entries are . For example, is the matrix Find a […]
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Per il quarto anno consecutivo ospiterò su DropSea il Carnevale della Matematica che coincide con il pi day. L'edizione, che è la 83 (la 82 è sul blog dei Rudi), è specialissima, come vedete dall'immagine qui sopra, che vi dice già anche quale sarà l'ora di pubblicazione della prossima edizione (esclusi i secondi che non sono in grado di programmare...). In puro stile pi day, il tema è la matematica, declinata in tutte le salse. I contributi possono essermi inviati via e-mail, con un […]