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7:14 AM | Lie algebras are groups

Once upon a time I imagine people were very happy to think of Lie algebras as “infinitesimal groups,” but presumably when infinitesimals fell out of favor this interpretation did too. In this post I’ll record an observation that can justify thinking of Lie algebras as groups in a strong sense: they are group objects in a certain […]

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7:05 AM | Linkage

This year's AMS fellows including Alon, Moore, Pach, Propp, Shub, and Sipser (G+)A computer science conference decides to replace its peer review process with online discussions on one of the more wretched hives of misogyny and racism on the net. What could possibly go wrong? (G+)Segerman and Nelson visualize hyperbolic honeycombs (G+)Riemann hypothesis still not proved (G+)Meet the new Google+. Simpler, faster, better, uglier. (G+ only, no link)Pirates who hijack the web sites of scientific
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4:00 AM | Survey of Relation Theory • 2

In this Survey of previous blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many … Continue reading →

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10:19 PM | Graduating bits at ITCS

ITCS 2016 will be held in Cambridge January 14-16. As in previous years, we will have a “graduating bits” session where students graduating this year can present a (very) short talk on their work. This year I am in charge of the graduating bits event, which means that details on how to sign up for it will only appear […]

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11:05 AM | Jack Williams (1943–2015)

Jack Williams passed away on November 13th, 2015, at the age of 72. Jack obtained his PhD from the University of Oxford Computing Laboratory in 1968 and spent two years as a Lecturer in Mathematics at the University of Western … Continue reading →

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6:01 AM | Various updates

Polynomial configurations in fractal sets: Kevin Henriot, Malabika Pramanik and I have posted a paper where we prove the following result: if a measure μ on a fractal set E in Rn has Fourier decay with some exponent β, and … Continue reading →

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Everyday I walk to the Stabile Research Building to drink espresso and sit in my cozy — although oversaturated with screens — office. Oh, and to chat about research with great people like Arturo Araujo, David Basanta, Jill Gallaher, Jacob Scott, Robert Vander Velde and other Moffitters. This walk to the office takes about 30 […]

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3:46 AM | 18.S096: An extra Open Problem

I have just added an extra open problem (4.6.) to the fourth set of lecture notes. I am documenting it here. Prove or disprove the following conjecture by Feige: Given independent random variables s.t., for all , and we have . See the notes for more information.

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I went to an AMS conference with my High School Student Naveen (who presented this paper) and an ugrad from my REU program Nichole (who presented this paper). Note that this is a math conference- low prestige, mostly unrefereed, parallel sessions, but still a good place to pick up some new problems to work on and learn some things, and meet people.
Both Naveen and Nichole later got email from a journal urging them to submit their work! They were also invited to be on the […]

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3:00 AM | Discourse in Delft

A camel strolled past, yards from our window in the Applied-Sciences Building. I hadn’t expected to see camels at TU Delft, aka the Delft University of Technology, in Holland. I breathed, “Oh!” and turned to watch until the camel followed its … Continue reading →

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8:35 PM | Cofinality and the axiom of choice

What is cofinality of a[n infinite] cardinal? If we think about the cardinals as ordinals, as we should in the case the axiom of choice holds, then the cofinality of a cardinal is just the smallest cardinality of an unbounded set. It can be thought of as the least ordinal from which there is an … Continue reading Cofinality and the axiom of choice →

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2:56 PM | 애기만두 캐논 85mm f1.8과 홍대 골목야경

어제는 애기만두라고 불리는 캐논 85mm f1.8 렌즈를 70D에 끼우고 홍대 골목을 탐방. 이 렌즈가 애기만두라고 불리는게 캐논 만두 렌즈(캐논 85mm f1.2)나 이후 출시된 만투 렌즈(캐논 85mm f1.2 II)의 보급형 렌즈라서… 만투나 만두 렌즈보다야 훨씬 어둡지만 중고 가격 25만원~30만원으로 가성비 면에서 … Continue reading →

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2:00 PM | Drawing subgroups of the modular group

Previously we learned how to count the finite index subgroups of the modular group . The worst thing about that post was that it didn’t include any pictures of these subgroups. Today we’ll fix that. The pictures in this post can be interpreted in at least two ways. On the one hand, they are graphs of […]

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A new set of lecture notes is available here about community detection and recovery in the stochastic block model, including five open problems . As usual, I will document the open problems here, while referring a much more detailed description of the problems on the notes, including description of partial progress. Open Problem 9.1. (Detection Threshold for … Continue reading 18.S096: Community dection and the Stochastic Block Model →

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2:20 AM | Drawing subgroups of the modular group

Previously we learned how to count the finite index subgroups of the modular group . The worst thing about that post was that it didn’t include any pictures of these subgroups. Today we’ll fix that. The pictures in this post can be interpreted in at least two ways. On the one hand, they are graphs of […]

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Some recent criticisms of statistical tests of significance have breathed brand new life into some very old howlers, many of which have been discussed on this blog. One variant that returns to the scene every decade I think (for 50+ years?), takes a “disagreement on numbers” to show a problem with significance tests even from a “frequentist” perspective. Since it’s […]

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Previously we claimed that if you want to check whether a category “behaves like a category of spaces,” you can try checking whether it’s distributive. The goal of today’s post is to justify the assertion that objects in distributive categories behave like spaces by showing that they have a notion of “connected components.” For starters, let […]

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9:47 PM | BTZ black holes for #BlackHoleFriday

Yesterday was a special day. And no I’m not referring to #BlackFriday — but rather to #BlackHoleFriday. I just learned that NASA spawned this social media campaign three years ago. The timing of this year’s Black Hole Friday is particularly special because we … Continue reading →

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8:32 PM | Space Filling Curves in Simulated Cities

I’ve been playing around with Cities: Skylines recently, the super-popular SimCity knock-off. Dealing with traffic is a core theme of the game (as it should be). Traffic tends to accumulate at intersections, and it’s well known that one-way streets have higher traffic flow. The logical conclusion, then, is to try to build a city with […]

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During my five years of teaching experience as a teaching assistant including teaching, grading and math tutoring at Washington State University (WSU) and American University of Sharjah (AUS), I have noticed that many students are not motivated because they are … Continue reading →

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4:59 AM | Distributive categories

Among all of the standard algebraic structures that a student typically encounters in an introduction to abstract algebra (groups, rings, fields, modules), commutative rings are somehow special: the opposite category behaves like a category of spaces, so much so that an entire field of mathematics is dedicated to doing geometry based on it. In general, suppose […]

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A new set of Lecture notes is available here. These ones are about group testing and contain a very brief “crash-course” on error-correction codes. They also include five open problems. As usual, I will document the open problems here, while referring a much more detailed description of the problems on the notes. Open Problem 7.1. (Group testing bounds) Given and … Continue reading 18.S096: Group Testing and Error-Correcting Codes →

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9:57 PM | Exchanging Math for Fake Internet Points

As a fourth-year grad student in math at the University of Minnesota, I spend a lot of time thinking about math problems, but I get worn out when I think about the same problem for too long. Sometimes it can … Continue reading →

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6:24 PM | Do Your Own Thing

In grad school, I’ve noticed that some people can actually get bored of math! How does this happen?! I believe it often happens by not doing your own thing. Doing your own thing means pursuing problems that interest you, and learning whatever things that strike your fancy. It also means keeping your train of thought […]

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5:48 PM | Relative Entropy in Biological Systems

Here’s a draft of my paper for the proceedings of a workshop on Information and Entropy in Biological System this spring: • John Baez, Relative Entropy in Biological Systems. I’d love any comments or questions you might have. I’m not happy with the title. In the paper I advocate using the term ‘relative information’ instead […]

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5:14 AM | The Lawvere theory of Boolean functions

Let be a set with two elements. The category of Boolean functions is the category whose objects are the finite powers of and whose morphisms are all functions between these sets. For a computer scientist, the morphisms of this category have the interpretation of functions which input and output finite sequences of bits. Since this […]

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8:58 PM | Book Note: Tony Roy, Symbolic Logic, #1

Tony Roy (Philosophy, California State University, San Bernardino) has generously made available his Symbolic Logic: An Accessible Introduction to Serious Mathematical Logic. I’m commenting here on the version of October 6, 2015. The full main text is no less than 746 pages … Continue reading →

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7:57 PM | Symmetries of conflicts

Can you find hidden symmetries in the conflict diagrams of chemlambda? There are now two pages to play with, if you want to help (and have some fun maybe): [1] and [2]. What’s that? Each rewrite/chemical reaction in the artificial chemistry chemlambda has a pattern which triggers the reaction, and then the pattern is replaced … Continue reading Symmetries of conflicts →

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2:24 PM | 오키나와 호텔 나하 레드플래닛 저렴한 호텔 숙박후기

여기서는 저렴한 오키나와 호텔 나하 레드플래닛 호텔을 리뷰한다. 나하시내 오키나와 호텔 중에서 나하 레드플래닛 호텔은 굉장히 저렴하면서 깔끔한 디자인의 비지니스 호텔이다. 보통 한국에서 비지니스 호텔하면 뭔가 우중충한 이미지가 연상되는데, 나하 레드플래닛 호텔 (Naha Red Planet Hotel)은 외관과 호텔 내부 디자인에 … Continue reading →

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di diffusione della scienza e rivoluzioni cc @aubreymcfato @CristianCantoro Utilizzare i dati sulle citazioni in Wikipedia per misurare la diffusione dell'open accessScrivevo all'inizio del 2011 per i festeggiamenti del wiki-decennale di una rivoluzione irreversibile. E' stato piuttosto interessante leggere il titolo che technology review ha utilizzato per raccontare dell'ultimo degli articoli dedicati all'enciclopedia libera: Why Wikipedia + Open Access = Revolution.L'idea degli autori, Misha
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Nielsen, F. (2007). Scientific citations in Wikipedia, First Monday, 12 (8) DOI: 10.5210/fm.v12i8.1997

Heather Ford, Shilad Sen, David R. Musicant & Nathaniel Miller (2013). Getting to the source: where does Wikipedia get its information from?, Proceedings of the 9th International Symposium on Open Collaboration, DOI: 10.1145/2491055.2491064

Misha Teplitskiy, Grace Lu & Eamon Duede (2015). Amplifying the Impact of Open Access: Wikipedia and the Diffusion of Science, Wikipedia Workshop at 9th International Conference on Web and Social Media (ICWSM), arXiv: 1506.07608v1

Citation

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After (or before?) @StartsWithABang's balloon animals' post? A couple of week ago Ethan Siegel published a post about ballon animals, so I decide to repost an old piece that I wrote in 2011 for my italian blog: the english version is lost, but it is magically reposted here! Two one-balloon constructions and their associated graphsI recently discovered this interesting site, vihart. In the site there are some interesting paper and today I want to write something about Computational Balloon
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Demaine E.D., Demaine M.L. & Hart V. (2008). Computational balloon twisting: The theory of balloon polyhedra., Proceedings of the 20th Canadian Conference on Computational Geometry (CCCG2008), 139-142.

Bryś K. & Lonc Z. (2009). Polynomial cases of graph decomposition: A complete solution of Holyer's problem, Discrete Mathematics, 309 (6) 1294-1326. DOI: 10.1016/j.disc.2008.01.054

Citation

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Supponiamo di doverci confrontare con un animale, ad esempio un cane o un lupo (o più in generale con un animale, addomesticato o selvaggio). Secondo Konrad Lorenz il comportamento aggressivo di un cane viene influenzato da due stati d'animo differenti: l'ira e la paura.Si può allora provare a prevedere il comportamento del cane in funzione di quale dei due stati domina: nel caso in cui l'animale è dominato da paura o da ira, proporre una previsione è abbastanza semplice; nel caso in cui il […]

Zeeman E.C. (1976). Catastrophe Theory, Scientific American, 234 65-83. DOI: 10.1038/scientificamerican0476-65

Jean Petitot (2013). Complexity and self-organization in Turing, The Legacy of A.M. Turing, (E. Agazzi, ed.), Franco Angeli, Milano, 149-182. arXiv: 1502.05328v1

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Non prevedevo di scrivere la versione italiana di un post sull'ultima news proveniente dal RHIC, ma mi è stato gentilmente chiesto, e provvedo ben volentieri. Inizio, però, con un piccolo cappello, alla fine del quale saprete che c'è anche un piccolissimo pezzetto (il doppio diminutivo è perché i firmatari del papero su arXiv sono veramente tanti) d'Italia in questa interessante scoperta.Tutto nasce da un post, nel flusso twittero, di Annalisa Arci, in cui racconta, in maniera e con un […]

Belavina A.A., Polyakova A.M., Schwartza A.S. & Tyupkina Y.S. (1975). Pseudoparticle solutions of the Yang-Mills equations, Physics Letters B, 59 (1) 85-87. DOI: 10.1016/0370-2693(75)90163-X

Hooft G.'. (1976). Symmetry Breaking through Bell-Jackiw Anomalies, Physical Review Letters, 37 (8) DOI: 10.1103/PhysRevLett.37.8

Hooft G.'. (1976). Computation of the quantum effects due to a four-dimensional pseudoparticle, Physical Review D, 14 DOI: 10.1103/PhysRevD.14.3432

Fukushima K., Kharzeev D.E. & Warringa H.J. (2008). The Chiral Magnetic Effect, Physics Review D, 78 (7) DOI: 10.1103/PhysRevD.78.074033

Kharzeev D.E. & Yee H.U. (2011). Chiral Magnetic Wave, Physical Review D, 83 DOI: 10.1103/PhysRevD.83.085007

STAR Collaboration (2015). Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions, arXiv, arXiv: 1504.02175v2

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A new clue about the #quarkgluonplasma from @RHIC_STAR at @BrookhavenLabWithin the particles that constitute atomic nuclei, protons and neutrons, there are the quarks, the elementary particles with fractional charges, linked to each other thanks to the gluons, bosons that carry the nuclear interaction. Thanks to the gluons it is impossible to observe, at present, free quarks, but it is expected that in the very first stage of the universe, matter was in a state called quark-gluon plasma. Thanks […]

Belavina A.A., Polyakova A.M., Schwartza A.S. & Tyupkina Y.S. (1975). Pseudoparticle solutions of the Yang-Mills equations, Physics Letters B, 59 (1) 85-87. DOI: 10.1016/0370-2693(75)90163-X

Hooft G.'. (1976). Symmetry Breaking through Bell-Jackiw Anomalies, Physical Review Letters, 37 (8) DOI: 10.1103/PhysRevLett.37.8

Hooft G.'. (1976). Computation of the quantum effects due to a four-dimensional pseudoparticle, Physical Review D, 14 DOI: 10.1103/PhysRevD.14.3432

Fukushima K., Kharzeev D.E. & Warringa H.J. (2008). The Chiral Magnetic Effect, Physics Review D, 78 (7) DOI: 10.1103/PhysRevD.78.074033

Kharzeev D.E. & Yee H.U. (2011). Chiral Magnetic Wave, Physical Review D, 83 DOI: 10.1103/PhysRevD.83.085007

STAR Collaboration (2015). Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions, arXiv: 1504.02175v2

Citation

jesusem tweeted: @jesusem

Hola La Moneda Roja gracias por seguirme!

2015-12-01 21:47:22

mluebbecke tweeted: @mluebbecke

@GTenbergenMSc research the place and people well, be informed and prepared, offer concrete links for potential collaboration @PhDForum

2015-12-01 21:33:52

rmathematicus tweeted: @rmathematicus

RT @orzelc: "If Hawking’s book taught me one thing, it’s that sticky visual metaphors can be a curse." --@skdh https://t.co/DlpZzXHRgT

2015-12-01 21:33:23

freakonometrics tweeted: @freakonometrics

"Reviewing computational methods" https://t.co/TH3X5tWrU1

2015-12-01 21:31:05

mluebbecke tweeted: @mluebbecke

Word > RT @jeromekelleher: This is a great editorial from Nature Methods on reviewing computational methods https://t.co/giEZARorMA

2015-12-01 21:30:06

freakonometrics tweeted: @freakonometrics

colors https://t.co/Cx8VPdjRJn

2015-12-01 21:27:45

freakonometrics tweeted: @freakonometrics

"The UK Curry Heat Map: Can your neighbours hack the heat?" https://t.co/mVFoAR5lVh https://t.co/hjFkNgbFVE

2015-12-01 21:14:30

mluebbecke tweeted: @mluebbecke

@JohnBarentine hahaha ;-)

2015-12-01 21:14:12

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