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# Posts

### May 25, 2013

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As a few more weeks have gone since I left the hospital, here are some news for the aficionadi (apulgaradi?). The wound on the thumb is  healing at a good pace, although the dressings are still on for one or two weeks. While I am still recovering from those weeks in the hospital, lacking energy […]
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I normally end each month with a post on a mathematical story from history. Since I've spent the last month discussing the Pythagorean Theorem, I thought I'd finish it off with a story from the life of Pythagoras.Pythagoras was born in 570 BC in Samos (which is now in Vathy, Greece). Throughout his life, he dabbled in philosophy, mathematics, music, and religion (he actually was the founder of the religion known as "Pythagoreanism"). He founded an organization (sort of like a school) where lots […]
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And another series on a big-wall on Baffin Island, Mount Asgard (Sivanitirutinguak), Auyuittuq National Park… (One of the peaks was first climbed by Doug Scott.) Filed under: Mountains, pictures Tagged: Asgard, Auyuittuq National Park, Baffin Island, big wall, Doug Scott, Nunavut, Posing Productions, Sivanitirutinguak
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published by @ulaulaman For the #towelday I publish the paper by Richard MacDuff extracted from from "Dirk Gently's Holistic Detective Agency" by Douglas Adams Music & Fractal Landscapes from Jamie Shoard on Vimeo. Mathematical analysis and computer modelling are revealing to us that the shapes and processes we encounter in nature—the way that plants grow, the way that mountains erode or rivers flow, the way that snowflakes or islands achieve their shapes, the way that light plays on a […]
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—— Dear Aunt Pythia, Do you prefer that we ask you fake [sex questions] or [fake sex] questions? From your website it seems that you prefer the former, but would you also be amused by the latter? Fakin’ Bacon Dear Fakin, I can’t tell, because I’ve gotten neither kind (frowny face). If I started getting […]
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With the development of statistical mechanics, physicists became the first agent-based modellers. Since the scientists of the 19th century didn’t have super-computers, they couldn’t succumb to the curse of computing and had to come up with analytic treatments of their “agent-based models”. These analytic treatments were often not rigorous, and only a heuristic correspondence was […]

Chazelle, B. (2012). Natural algorithms and influence systems, Communications of the ACM, 55 (12) 101. DOI:

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### May 24, 2013

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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 […]
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The New York Times published a paper by Norbert Wiener that should have appeared in…1949! In this short paper, Wiener gives his view on the future of computing. He for instance foresaw a “factory substantially without employees”. He also envisioned learning: “The possibility of learning may be built in by allowing the taping to be […]
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This is a first application of this notion (and in fact where the name comes from!).Let $\mathbf{L} = (\mathcal{L}, \mathcal{A})$ be an interpreted language, such as  might be spoken/cognized by some agent $s$. Here $\mathcal{L}$ is the underlying (uninterpreted) syntax, and $\mathcal{A}$ is an extensional interpretation for $\mathcal{L}$-strings. So, $\mathcal{A}$ specifies, in the usual way, extensional meanings for $\mathbf{L}$'s syntactic components: connectives, quantifiers, names, […]
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As a data analyst and a scientist, Fisher > Neyman, no question. But as a theorist, Fisher came up with ideas that worked just fine in his applications but can fall apart when people try to apply them too generally. Here’s an example that recently came up. Deborah Mayo pointed me to a comment by [...]The post In which I side with Neyman over Fisher appeared first on Statistical Modeling, Causal Inference, and Social Science.
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Suppose that $\mathcal{A} = (A, \vec{R}, \vec{f})$ is a model, and let $\pi : A \rightarrow A$ be a bijection (permutation of $A$ to itself). Next, define the following notion:Definition [Quine Transform]The Quine transform of $\mathcal{A}$ under $\pi$, written $\mathcal{A}^{\pi}$, is given by:$\mathcal{A}^{\pi}: = (A, \pi[\vec{R}], \pi[\vec{f}])$. For example, suppose the model $\mathcal{A} = (A,R)$ is specified as follows:$A= \{0,1, 2\}$$R= \{(0,1), (0,2), (1,2) \}$. Let $\pi: A \to […] + It is difficult to maintain, consistently, the following two claims:(i) There are no abstracta.(ii) There are syntactical entities (and they behave as our standard accounts say they do).Consider, for example, how one defines a language$L$. Beginning with two building blocks,$A$and$B$, we say that$\{A,B\}$is the alphabet. It's usually implicit, but sometimes needs to be stated, that$A \neq B$. (One has to state this in a formalized theory of syntax.)For the many of the usual purposes of […] + Last time, I posted about Jim Joyce's argument for Probabilism. At its heart lies a mathematical theorem. In this post, I state this mathematical theorem and prove it; then I generalize it and prove the generalization. The frameworkRecall from last time:$\mathcal{F}$is a finite set of propositions. (It is the set of propositions about which our agent has an opinion.)A credence function is a function$c : \mathcal{F} \rightarrow [0, 1]\$. Throughout the present post, we […]
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There’s really exciting news in the world of number theory, my old field. I heard about it last month but it just hit the mainstream press. Namely, mathematician Yitang Zhang just proved is that there are infinitely many pairs of primes that differ by at most 70,000,000. His proof is available here and, unlike Mochizuki’s claim of […]
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Lowell Trott, one of the theory students here at UCI, successfully defended his thesis yesterday. Lowell's Ph.D. advisor is Mike Goodrich, but I've also worked with him on several publications related to both social networks and road networks. (Although the vertices in road networks are not people, the networks still come from a social structure.) Specifically, he:Showed that road networks have the property that any line of sight crosses only a small number of roads, both empirically and in a […]

### May 23, 2013

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“…the story of Homo sapiens trying to stake a claim on shifting ground, flanked on both sides by beast and machine, pinned between meat and math.” (p.13) No typo in the title, this is truly how this book by Brian Christian is called. It was kindly sent to me by my friends from BUY and […]
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The e-mail you get after you write an article about number theory is very interesting.  For one thing, you’re reminded of phrasings which have one meaning among mathematicians, but a slightly different one outside the tribe. The majority of the e-mail I’ve gotten about the bounded gaps piece concerns two questions of this kind:  I’ll answer […]
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Filed under: Mountains, pictures Tagged: Antarctica, big wall, climbing pictures, dvd, Posing Productions, Queen Maud, Ulvetanna
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Every once in awhile I get a question that I can directly answer from my published research. When that happens it makes me so happy. Here’s an example. Patrick Lam wrote, Suppose one develops a Bayesian model to estimate a parameter theta. Now suppose one wants to evaluate the model via simulation by generating fake [...]The post Validation of Software for Bayesian Models Using Posterior Quantiles appeared first on Statistical Modeling, Causal Inference, and Social Science.
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I couldn’t resist taking this photo in the office of Edinburgh mathematician Nikola Popovic. The central image is the result of a conversation between Nikola and visiting speaker Vahid Shahrezaei about the reproduction of yeast. Yeast cells normally reproduce asexually by budding, but cells of opposite mating types (a and α) can also reproduce sexually. […]
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After two days of travelling to the west coast and back, I’m glad to be back to my blog (and, of course, my coffee machine, which is the real source of my ability to blog every morning without distraction: it makes coffee at the push of a button, and that coffee has a delicious amount […]
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Patient M: It’s impossible —- no one could urinate into that bottle -— at least no woman could. I’m furious with her [these are the patient's emphases] and I’m damned if I am going to do it unless she gives me another kind of bottle. It’s just impossible to use that little thing. Analyst: It […]

Fehr, E. & Schmidt, K. (1999). A Theory of Fairness, Competition, and Cooperation, The Quarterly Journal of Economics, 114 (3) 817-868. DOI:

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In Slate today, I have a piece about Yitang Zhang’s amazing proof of the bounded gaps conjecture.  Actually, very little of the article is about Zhang himself or his proof; I wanted instead to explain why mathematicians believed that bounded gaps (or twin primes) was true in the first place, via Cramér’s heuristic that primes behave […]

### May 22, 2013

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In the plane to Birmingham, I was reading this recent arXived paper by Minh-Ngoc Tran, Michael K. Pitt, and Robert Kohn. The adaptive structure of their ACMH algorithm is based upon two parallel Markov chains, the former (called the trial chain) feeding the proposal densities of the later (called the main chain), bypassing the more traditional […]
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Since the fields are so closely related, a lot of people who study math also end up studying at least a little bit of physics. I always wanted to take a physics class when I was an undergrad, but I … Continue reading →
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