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# Posts

### April 23, 2014

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leaving only the “typing it up worse for the net” to me… the -set homework i’m about to loosely base my plain-text solutions on is quite a lovely thing to look upon… as my versions will not be. now. make it so. 6.1.3 Let a/b, a’/b’, and a”/b” be consecutive fractions in the Farey sequence […]
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Because zipper logic is a graph rewriting system which does not use variable names, just like GLC and chemlabda,  it needs ways to multiply, distribute or kill  things. See  Chemlambda, universality and self-multiplication  for multiplication, distribution or propagation phenomena. In this post we shall see how zipper combinators die or are born, depending on the sense […]
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If you’re looking for something to do next Tuesday evening here in New York, an event called Raising the Bar has recruited 50 people to give talks at bars around the city. There are some quite interesting talks on the … Continue reading →
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Is there a worst-possible paradox and if so what is it? In this post I’ll discuss an open question about graphs, whose answer, if we could answer it, might tell us what is the worst-possible paradox. Most people have come across the Liar Paradox at some point or other, whether in an academic journal, or [...]
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4! = 2 * 3 * 1 * 4 Also: √4 - 2 + 3 = |1 - 4| Also: 4 = 2 - 3 + 1 + 4
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Filed under: Kids, Mountains, pictures, Travel Tagged: AISTATS 2014, ashes, Dyrhólaey, Iceland, Vik
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Como todos los años desde 1995, hoy día 23 de abril se celebra el Día Internacional del Libro. Por ello, creo que es el mejor momento para recomendaros algunos libros relacionados con las matemáticas que creo que pueden ser interesantes para vosotros. Ahí van: Los Simpson y las Matemáticas Curioso libro en el que Simon […]Entra en Gaussianos si quieres hacer algún comentario sobre este artículo, consultar entradas anteriores o enviarnos un mensaje.Construye tú […]
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Durante la pasada Semana Santa finalizó el plazo para otorgar el Premio a la mejor entrada de la Edición 5.2 Emmy Noether del Carnaval de Matemáticas. Quizás ese ha sido uno de los motivos por los que en esta ocasión no hay muchos votos. En cualquier caso, ya hemos procedido al recuento y, por segunda vez, no hay uno sino dos ganadores de la presente edición.Y los ganadores, con 8 puntos repartidos en 2 votos de 4 puntos cada uno, sonUn puzzle sencillo (del Cuaderno de Cultura […]

### April 22, 2014

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First day at AISTATS 2014! After three Icelandic vacations days driving (a lot) and hinkg (too little) around South- and West-Iceland, I joined close to 300 attendees for this edition of the AISTATS conference series. I was quite happy to be there, if only because I had missed the conference last year (in Phoenix) and […]
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Είναι πολύ εύκολο να φτιάξει κανείς μια συνάρτηση που να έχει τοπικό ελάχιστο σε κάθε πραγματικό αριθμό και να μην είναι σταθερή (π.χ. η χαρακτηριστική συνάρτηση του διαστήματος ). Υπάρχει ή όχι συνεχής  μη σταθερή συνάρτηση  που να έχει τοπικό ελάχιστο σε κάθε πραγματικό […]
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This will be the first in an occasional series of posts that offer interactive Web Sketchpad models for drawing conic sections. My interest in conic sections dates back to the mid 1990s, when I authored a conic sections book for … Continue reading →
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So, I’ve written an article of that title for the wonderful American Scientist magazine—or rather, Part I of such an article.  This part explains the basics of Kolmogorov complexity and algorithmic information theory: how, under reasonable assumptions, these ideas can be used in principle to “certify” that a string of numbers was really produced randomly—something that one might’ve […]
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4 * 2 = 2 * 1 * 4 4 = 2 * 2 = 1 * 4 Also: 4! = 22 + (1 * 4)
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Vamos con el segundo problema planteado en la L Olimpiada Matemática Española celebrada en Requena los pasados días 28 y 29 de marzo. Dados los números racionales positivos y tales que demostrar que es un número racional. Que se os dé bien. Entra en Gaussianos si quieres hacer algún comentario sobre este artículo, consultar entradas […]Entra en Gaussianos si quieres hacer algún comentario sobre este artículo, consultar entradas anteriores o enviarnos un […]
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Consider the product space . Fix a point , called the base point. The -product of the spaces is the following subspace of the product space : In other words, the space is the subspace of the product space consisting … Continue reading →

### April 21, 2014

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Filed under: Kids, Mountains, pictures, Travel Tagged: AISTATS 2014
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Let $G$ be a graph with distinct vertices $s$ and $t$, and let $\mathcal{C}$ be the family of paths from $s$ to $t$. Let us say that a subfamily of $\mathcal{C}$ is a matching if its members are pairwise edge-disjoint. … Continue reading →
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it turns out (chapter 2, section 3) that “stirling numbers of the 2nd kind” count the ways to partition an n-element set into k classes: letting whenever h is a positive integer (so that “S_h”… as i propose to call it in ordinary type… denotes {1, 2, … , h} [and in particular, has S_h […]
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Around one year ago, I unexpectedly received an e-mail asking if I would speak at a local TEDx Youth event themed “Daring Discoveries”.  I hadn’t attended a TEDx conference before (sadly I couldn’t make either of the previous ones held … Continue reading →
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Internet is wonderful. When I was young (yesterday) it was complicated to get the info about some subject without going to a physical library. Today with so many people connected, writing and sharing online, everyone connected can study a subject without leaving home. With Internet, human kind created a new library of babel. Actually this library […]
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One of the inevitable consequences of getting old is that my brain becomes more and more like a Swiss cheese, and important pieces of information fall through the holes. So I owe an apology to Michael Braun, Tuvi Etzion, Patric … Continue reading →
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Wenn jemand noch ein Buch für den nächsten Kindergeburtstag braucht – die AMS wird (am 12.5.) ihr erstes Kinderbuch herausbringen, “Really big numbers” von Richard Schwartz. (Dessen zweites Kinderbuch nach “You can count on monsters”. Von seinen anderen Büchern zählt zwar “Mostly surfaces” noch als populärwissenschaftlich, aber wohl kaum als Kinderbuch :-), ist dafür aber…
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In a previous post we introduced a learning model called Probably Approximately Correct (PAC). We saw an example of a concept class that was easy to learn: intervals on the real line (and more generally, if you did the exercise, axis-aligned rectangles in a fixed dimension). But PAC learning wouldn’t be an interesting model if every concept class was PAC-learnable. So as a technical […]
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I’ll be giving a talk at Purdue University on Saturday, May 3 as part of the 65th Midwest Theory Day. If any readers happen to live in West Lafayette, Indiana and are interested in hearing about some of my recent research, you can register for free by April 28 (one week from today). Lunch and snacks are provided, and the […]
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I’ve been fascinated by sky phenomena for some time; when out walking, I always keep an eye on the sky. Some years ago, on a train on the West Coast Main Line in the Lake District, I was treated to … Continue reading →
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4 / 2 * 1 = 1 * 4 Also: (4 / 2) + 1 = |1 - 4|
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Ahora que justo acaba la Semana Santa y, por ende, nuestras vacaciones, volvemos con el tiempo justo para anunciar la nueva edición del Carnaval de Matemáticas.Se trata de la Edición 5.3: Felix Klein, que comenzará el próximo viernes 25 de abril y finalizará el miércoles 30 y que tendrá como anfitrión a un mago de las matemáticas, a Mago Moebius  desde sus Juegos Topológicos.La presente edición está dedicada al matemático alemán Félix Klein quien no tuvo mejor idea que […]
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This post is probably not so interesting unless you plan to travel to the Caribbean in a few weeks. The website for the conference is offline, so I thought I might update attendees on what might be happening, at least … Continue reading →
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As is by now well-known, I regard the supposed opposition between static and dynamic languages as a fallacy: the latter, being a special case of the former, can scarcely be an alternative to it.  I cannot tell you how many times I’ve been handed arguments along the lines of “oh, static languages are just fine, but I want […]

### April 20, 2014

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As I was flying over Skye (with [maybe] a first if hazy perspective on the Cuillin ridge!) to Iceland, three long sets of replies to some of my posts appeared on the ‘Og: Dan Simpson replied to my comments of last Tuesday about his PC  construction; Arnaud Doucet precised some issues about his adaptive subsampling […]