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Posts with Citations

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Cross-validation in finance, psychology, and political science
A large chunk of machine learning (although not all of it) is concerned with predictive modeling, usually in the form of designing an algorithm that takes in some data set and returns an algorithm (or sometimes, a description of an algorithm) for making predictions based on future data. In terminology more friendly to the philosophy […]

Bailey, D., Borwein, J., de Prado, M.L. & Zhu, Q. (2014). Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance, Notices of the American Mathematical Society, 61 (5) 458. DOI:

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Monotonicity of EM Algorithm Proof
Here the monotonicity of the EM algorithm is established. $$ f_{o}(Y_{o}|\theta)=f_{o,m}(Y_{o},Y_{m}|\theta)/f_{m|o}(Y_{m}|Y_{o},\theta)$$ $$ \log L_{o}(\theta)=\log L_{o,m}(\theta)-\log f_{m|o}(Y_{m}|Y_{o},\theta) \label{eq:loglikelihood} $$ where \( L_{o}(\theta)\) is the likelihood under the observed data and \(L_{o,m}(\theta)\) is the likelihood under the complete data. Taking the expectation of the second line with respect to the conditional distribution of […]

Ruslan R Salakhutdinov, Sam T Roweis & Zoubin Ghahramani (2012). On the Convergence of Bound Optimization Algorithms, arXiv, arXiv:

Wu C.F.J. (1983). On the Convergence Properties of the EM Algorithm, The Annals of Statistics, 11 (1) 95-103. DOI:

McLachlan G. & Peel D. DOI:

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Simulate the transit of extrasolar planets
by @ulaulaman about #exoplanets #planetary_transit #kepler_mission #nasa #astronomy The search for extrasolar planets (or exoplanets) had its first success in 1991 with the discovery of some planets orbiting around the pulsar PSR1257+12(1, 2, 3), measuring the variations of the radio pulses coming from the star. The second important milestone in exoplanet research takes place in 1995, with the discovery around the star 51 Pegasi (a star like our Sun) of a Jupiter-like planet, found at a […]

Wolszczan, A. & Frail, D. (1992). A planetary system around the millisecond pulsar PSR1257 + 12, Nature, 355 (6356) 145-147. DOI:

Wolszczan, A. (1994). Confirmation of Earth-Mass Planets Orbiting the Millisecond Pulsar PSR B1257 + 12, Science, 264 (5158) 538-542. DOI:

Mayor, M. & Queloz, D. (1995). A Jupiter-mass companion to a solar-type star, Nature, 378 (6555) 355-359. DOI:

Borucki, W., Koch, D., Basri, G., Batalha, N., Brown, T., Caldwell, D., Caldwell, J., Christensen-Dalsgaard, J., Cochran, W., DeVore, E. & Dunham, E. (2010). Kepler Planet-Detection Mission: Introduction and First Results, Science, 327 (5968) 977-980. DOI:

Lissauer, J., Fabrycky, D., Ford, E., Borucki, W., Fressin, F., Marcy, G., Orosz, J., Rowe, J., Torres, G., Welsh, W. & Batalha, N. (2011). A closely packed system of low-mass, low-density planets transiting Kepler-11, Nature, 470 (7332) 53-58. DOI:

George, S. (2011). Extrasolar planets in the classroom, Physics Education, 46 (4) 403-406. DOI:

LoPresto, M. & McKay, R. (2005). An introductory physics exercise using real extrasolar planet data, Physics Education, 40 (1) 46-50. DOI:

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L'universo spiegato a mia sorella
Non voglio fare concorrenza alla splendida spiegazione di Amedeo o a quella tecnica di Corrado, ma mia sorella, leggendo il post di pancia scritto nella sera dell'annuncio di BICEP2, ha candidamente confessato di non aver capito cosa era accaduto quel giorno. E allora proviamoci, a raccontarlo. (da The Cartoon History of the Universe #1 di Larry Gonick)C'era una volta un'idea di universo, che era la Terra al centro, quindi il Sole, la Luna e gli altri pianeti e sullo sfondo le stelle fisse, […]

Hubble E. (1929). A relation between distance and radial velocity among extra-galactic nebulae, Proceedings of the National Academy of Sciences, 15 (3) 168-173. DOI:

Gamow G. (1948). The Evolution of the Universe, Nature, 162 (4122) 680-682. DOI:

Alpher R.A. & Herman R. (1948). Evolution of the Universe, Nature, 162 (4124) 774-775. DOI:

Alpher R., Bethe H. & Gamow G. (1948). The Origin of Chemical Elements, Physical Review, 73 (7) 803-804. DOI:

Peebles P.J.E., Schramm D.N., Turner E.L. & Kron R.G. (1994). The Evolution of the Universe, Scientific American, 271 (4) 52-57. DOI:

McLeish T.C.B., Bower R.G., Tanner B.K., Smithson H.E., Panti C., Lewis N. & Gasper G.E.M. (2014). History: A medieval multiverse, Nature, 507 (7491) 161-163. DOI:

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Big data, prediction, and scientism in the social sciences
Much of my undergrad was spent studying physics, and although I still think that a physics background is great for a theorists in any field, there are some downsides. For example, I used to make jokes like: “soft isn’t the opposite of hard sciences, easy is.” Thankfully, over the years I have started to slowly […]

Lazer, D., Kennedy, R., King, G. & Vespignani, A. (2014). Big data. The parable of Google Flu: traps in big data analysis., Science, 343 (6176) 1203-1205. PMID:

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La serie infinita del triangolo aureo
Un triangolo aureo è un triangolo isoscele in cui il rapporto tra uno dei lati uguali con la base è pari alla sezione aurea $\varphi$. Utilizzando un triangolo aureo di lato 1, è possibile dimostrare che \[1 + \frac{1}{\varphi^2} + \frac{1}{\varphi^4} + \cdots = \varphi\] \[\frac{1}{\varphi} + \frac{1}{\varphi^3} + \cdots = 1\] \[\frac{1}{\varphi} + \frac{1}{\varphi^2} + \frac{1}{\varphi^3} + \cdots = \varphi\] Il triangolo aureo qui sopra è lo screenshot della applet realizzata da Irina […]

Edwards S. (2014). Proof Without Words: An Infinite Series Using Golden Triangles, The College Mathematics Journal, 45 (2) 120-120. DOI:

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La serie infinita del triangolo aureo
Un triangolo aureo è un triangolo isoscele in cui il rapporto tra uno dei lati uguali con la base è pari alla sezione aurea $\varphi$. Utilizzando un triangolo aureo di lato 1, è possibile dimostrare che \[1 + \frac{1}{\varphi^2} + \frac{1}{\varphi^4} + \cdots = \varphi\] \[\frac{1}{\varphi} + \frac{1}{\varphi^3} + \cdots = \1] \[\frac{1}{\varphi} + \frac{1}{\varphi^2} + \frac{1}{\varphi^3} + \cdots = \varphi\] Il triangolo aureo qui sopra è lo screenshot della applet realizzata da Irina […]

Edwards S. (2014). Proof Without Words: An Infinite Series Using Golden Triangles, The College Mathematics Journal, 45 (2) 120-120. DOI:

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Kleene’s variant of the Church-Turing thesis
In 1936, Alonzo Church, Alan Turing, and Emil Post each published independent papers on the Entscheidungsproblem and introducing the lambda calculus, Turing machines, and Post-Turing machines as mathematical models of computation. A myriad of other models followed, many of them taking seemingly unrelated approaches to the computable: algebraic, combinatorial, linguistic, logical, mechanistic, etc. Of course, […]

Dershowitz, N. & Gurevich, Y. (2008). A natural axiomatization of computability and proof of Church's Thesis, Bulletin of Symbolic Logic, 14 (3) 299-350. DOI:

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When gaming is NP-hard
by @ulaulaman about #candycrush #bejeweled #shariki #nphard #computerscience Shariki is a puzzle game developed by the russian programmer Eugene Alemzhin in 1994. The rules are simple: (...) matching three or more balls of the same color in line (vertical or horizontal). These balls then explode and a new ones appear in their place.The first Shariki's clone is Tetris Attack, a fusion between Shariki and the most famous Tetris, also this developed in Soviet Union by Alexey Pajitnov. But the […]

Toby Walsh (2014). Candy Crush is NP-hard, arXiv:

Luciano Gualà, Stefano Leucci & Emanuele Natale (2014). Bejeweled, Candy Crush and other Match-Three Games are (NP-)Hard, arXiv:

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Algorithmic Darwinism
The workshop on computational theories of evolution started off on Monday, March 17th with Leslie Valiant — one of the organizers — introducing his model of evolvability (Valiant, 2009). This original name was meant to capture what type of complexity can be achieved through evolution. Unfortunately — especially at this workshop — evolvability already had […]

Feldman, V. (2008). Evolvability from learning algorithms., Proceedings of the 40th annual ACM symposium on Theory of Computing, 619-628. DOI:

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