Mathematics posts
- May 14, 2013
- 09:30 PM
- 29 views
Four color problem, odd Goldbach conjecture, and the curse of computing
by Artem Kaznatcheev in Evolutionary Games Group
For over twenty-three hundred years, at least since the publication of Euclid’s Elements, the conjecture and proof of new theorems has been the sine qua non of mathematics. The method of proof is at “the heart of mathematics, the royal road to creating analytical tools and catalyzing growth” (Rav, 1999; pg 6). Proofs are not […]... Read more »
Rav, Y. (1999) Why Do We Prove Theorems?. Philosophia Mathematica, 7(1), 5-41. DOI: 10.1093/philmat/7.1.5
- May 13, 2013
- 05:30 AM
- 41 views
Quasi-magical thinking and superrationality for Bayesian agents
by Artem Kaznatcheev in Evolutionary Games Group
As part of our objective and subjective rationality model, we want a focal agent to learn the probability that others will cooperate given that the focal agent cooperates () or defects (). In a previous post we saw how to derive point estimates for and (and learnt that they are the maximum likelihood estimates): , […]... Read more »
Masel, J. (2007) A Bayesian model of quasi-magical thinking can explain observed cooperation in the public good game. Journal of Economic Behavior , 64(2), 216-231. DOI: 10.1016/j.jebo.2005.07.003
- May 8, 2013
- 11:30 PM
- 38 views
Evolutionary games in set structured populations
by Artem Kaznatcheev in Evolutionary Games Group
We have previously discussed the importance of population structure in evolutionary game theory, and looked at the Ohtsuki-Nowak transform for analytic studies of games on one of the simplest structures — random regular graphs. However, there is another extremely simple structure to consider: a family of inviscid sets. We can think of each agent as [...]... Read more »
Tarnita, C., Antal, T., Ohtsuki, H., & Nowak, M. (2009) Evolutionary dynamics in set structured populations. Proceedings of the National Academy of Sciences, 106(21), 8601-8604. DOI: 10.1073/pnas.0903019106
- April 26, 2013
- 05:27 AM
- 86 views
Tartaglia-Pascal triangle and quantum mechanics
by Marco Frasca in The Gauge Connection
The paper I wrote with Alfonso Farina and Matteo Sedehi about the link between the Tartaglia-Pascal triangle and quantum mechanics is now online (see here). This paper contains as a statement my theorem that provides a connection between the square root of a Wiener process and the Schrödinger equation that arose a lot of interest [...]... Read more »
Farina, A., Frasca, M., & Sedehi, M. (2013) Solving Schrödinger equation via Tartaglia/Pascal triangle: a possible link between stochastic processing and quantum mechanics. Signal, Image and Video Processing. DOI: 10.1007/s11760-013-0473-y
Marco Frasca. (2012) Quantum mechanics is the square root of a stochastic process. arXiv. arXiv: 1201.5091v2
Farina, A., Giompapa, S., Graziano, A., Liburdi, A., Ravanelli, M., & Zirilli, F. (2011) Tartaglia-Pascal’s triangle: a historical perspective with applications. Signal, Image and Video Processing, 7(1), 173-188. DOI: 10.1007/s11760-011-0228-6
- April 20, 2013
- 03:17 AM
- 79 views
Probabilities reveal shape of climate change
by Andy Extance in Simple Climate
David Stainforth from the London School of Economics and his colleagues have developed a new way to analyse weather data and understand which aspects of climate have changed most on a local level, showing European trends with less than a 2% chance of happening at random.... Read more »
Chapman, S., Stainforth, D., & Watkins, N. (2013) On estimating local long-term climate trends. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1991), 20120287-20120287. DOI: 10.1098/rsta.2012.0287
- April 16, 2013
- 11:37 AM
- 64 views
Homing Pigeons Never Stop Learning Ways to Get Home
by Elizabeth Preston in Inkfish
A young homing pigeon must learn quickly how to find its way home from the strange neighborhoods where humans insist on leaving it. At first the bird does this by relying on its crudest instincts, returning to its roost along a route full of youthful zigzags. Over time, though, it refines its methods. A mature pigeon takes a much simpler route, because it has drawn itself a more complex map.
Homing pigeons have been subjected to all kinds of research. The latest study used GPS devices, whic........ Read more »
Schiffner, I., & Wiltschko, R. (2013) Development of the navigational system in homing pigeons: increase in complexity of the navigational map. Journal of Experimental Biology. DOI: 10.1242/jeb.085662
- April 15, 2013
- 05:30 AM
- 23 views
Mathematical Turing test: Readable proofs from your computer
by Artem Kaznatcheev in Evolutionary Games Group
We have previously discussed the finicky task of defining intelligence, but surely being able to do math qualifies? Even if the importance of mathematics in science is questioned by people as notable as E.O. Wilson, surely nobody questions it as an intelligent activity? Mathematical reasoning is not necessary for intelligence, but surely it is sufficient? [...]... Read more »
Ganesalingam Mohan. (2013) The Language of Mathematics: A Linguistic and Philosophical Investigation. Lecture Notes in Computer Science. DOI: 10.1007/978-3-642-37012-0
- April 13, 2013
- 07:22 AM
- 99 views
Alternate histories back unique modern warmth claims
by Andy Extance in Simple Climate
Creating and averaging thousands of slightly different historic temperature records shows that Northern hemisphere 21st century temperatures are almost certainly unique in the last 600 years, according to Harvard University’s Martin Tingley.... Read more »
Tingley, M., & Huybers, P. (2013) Recent temperature extremes at high northern latitudes unprecedented in the past 600 years. Nature, 496(7444), 201-205. DOI: 10.1038/nature11969
- April 8, 2013
- 12:00 PM
- 97 views
Programming playground: Cells as (quantum) computers?
by Artem Kaznatcheev in Evolutionary Games Group
Nearly a year ago, the previous post in this series introduced a way for programmers to play around with biology: a model that simulated the dynamics of a whole cell at unprecedented levels of details. But what if you want to play with the real thing? Can you program a living cell? Can you compute [...]... Read more »
Bonnet J, Yin P, Ortiz ME, Subsoontorn P, & Endy D. (2013) Amplifying Genetic Logic Gates. Science. PMID: 23539178
- April 4, 2013
- 02:19 PM
- 61 views
Kids Learn Better When Teachers Wave Their Hands
by Elizabeth Preston in Inkfish
Maybe it's no mistake that we talk about "grasping" new ideas. When we find our hands moving wildly as we try to explain something, maybe we shouldn't feel ridiculous. Research in math classrooms has found that kids learned better when a teacher used gestures—and their grip on the new material improved even more after the lesson ended.
Teachers who gesture more or less while they speak can have other differences too, of course: they might use different intonation or vocabulary, or have mor........ Read more »
Cook, S., Duffy, R., & Fenn, K. (2013) Consolidation and Transfer of Learning After Observing Hand Gesture. Child Development. DOI: 10.1111/cdev.12097
- March 29, 2013
- 02:00 AM
- 92 views
Individual versus systemic risk in asset allocation
by Yunjun Yang in Evolutionary Games Group
Proponents of free markets often believe in an “invisible hand” that guides an economic system without external controls like government regulations. Therefore a highly efficient economic equilibrium can be created if all market participants act purely out of self-interest. In the paper titled “Individual versus systemic risk and the Regulator’s Dilemma.”, Beale et al. (2011) applied [...]... Read more »
Beale N., Rand D. G., Battey H., Croxson K., May R. M., & Nowak M. A. (2011) Individual versus systemic risk and the Regulator's Dilemma. Proceedings of the National Academy of Sciences, 108(31), 12647-12652. DOI: 10.1073/pnas.1105882108
- March 19, 2013
- 04:30 AM
- 130 views
Mathematical models in finance and ecology
by Artem Kaznatcheev in Evolutionary Games Group
Theoretical physicists have the reputation of an invasive species — penetrating into other fields and forcing their methods. Usually these efforts simply irritate the local researchers, building a general ambivalence towards field-hopping physicists. With my undergraduate training primarily in computer science and physics, I’ve experienced this skepticism first hand. During my time in Waterloo, I [...]... Read more »
May RM, Levin SA, & Sugihara G. (2008) Ecology for bankers. Nature, 451(7181), 893-5. PMID: 18288170
- March 14, 2013
- 06:40 AM
- 150 views
A Higgs particle but which one?
by Marco Frasca in The Gauge Connection
After Moriond conference last week, and while Moriond QCD and Aspen conferences are running yet, an important conclusion can be drawn and it is the one given in this CERN press release. The particle announced on 4th July last year is for certain a Higgs particle as it has spin 0, positive parity and couples [...]... Read more »
Marco Frasca. (2013) Revisiting the Higgs sector of the Standard Model. arXiv. arXiv: 1303.3158v1
Marco Frasca. (2009) Exact solutions of classical scalar field equations. J.Nonlin.Math.Phys.18:291-297,2011. arXiv: 0907.4053v2
- March 13, 2013
- 08:46 AM
- 170 views
Predicting Technological Progress: Putting Moore’s Law to the Test
by gunnardw in The Beast, the Bard and the Bot
Being able to predict the pace of technological development could be quite useful for a lot of people. No surprise then, that several models (or ‘laws’) have been posited that aim to describe how technological progress will unfurl (the most famous one probably being Moore’s law, for those interested: original article here). However, these laws [...]... Read more »
Nagy, B., Farmer, J., Bui, Q., & Trancik, J. (2013) Statistical Basis for Predicting Technological Progress. PLoS ONE, 8(2). DOI: 10.1371/journal.pone.0052669
- March 13, 2013
- 02:40 AM
- 257 views
Brain Lateralization - Logical Left vs Creative Right
by Vivek Misra in Beautiful Mind
Broad generalizations are often made in popular psychology about one side or the other having characteristic labels, such as "logical" for the left side or "creative" for the right. These labels need to be treated carefully; although a lateral dominance is measurable, both hemispheres contribute to both kinds of processes.In psychology and neurobiology, the theory is based on what is known as the lateralization of brain function. So does one side of the brain really control specific functions? A........ Read more »
Ross, E., & Monnot, M. (2008) Neurology of affective prosody and its functional–anatomic organization in right hemisphere. Brain and Language, 104(1), 51-74. DOI: 10.1016/j.bandl.2007.04.007
George MS, Parekh PI, Rosinsky N, Ketter TA, Kimbrell TA, Heilman KM, Herscovitch P, & Post RM. (1996) Understanding emotional prosody activates right hemisphere regions. Archives of neurology, 53(7), 665-70. PMID: 8929174
Dehaene, S. (1999) Sources of Mathematical Thinking: Behavioral and Brain-Imaging Evidence. Science, 284(5416), 970-974. DOI: 10.1126/science.284.5416.970
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003) THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING. Cognitive Neuropsychology, 20(3-6), 487-506. DOI: 10.1080/02643290244000239
Hecht, D. (2010) Depression and the hyperactive right-hemisphere. Neuroscience Research, 68(2), 77-87. DOI: 10.1016/j.neures.2010.06.013
Devinsky, O. (2009) Delusional misidentifications and duplications: Right brain lesions, left brain delusions. Neurology, 72(1), 80-87. DOI: 10.1212/01.wnl.0000338625.47892.74
- March 11, 2013
- 04:00 PM
- 165 views
Ecological public goods game
by Artem Kaznatcheev in Evolutionary Games Group
As an evolutionary game theorist working on cooperation, I sometimes feel like a minimalist engineer. I spend my time thinking about ways to design the simplest mechanisms possible to promote cooperation. One such mechanism that I accidentally noticed (see bottom left graph of results from summer 2009) is the importance of free space, or — [...]... Read more »
Hauert, C., Holmes, M., & Doebeli, M. (2006) Evolutionary games and population dynamics: maintenance of cooperation in public goods games. Proceedings of the Royal Society B: Biological Sciences, 273(1600), 2565-2571. DOI: 10.1098/rspb.2006.3600
- March 6, 2013
- 11:20 AM
- 176 views
Hey Hey! We’re The Monkeys!
by Miss Behavior in The Scorpion and the Frog
A tamarin rock star (photographed by Ltshears at Wikimedia)Our moods change when we hear music, but not all music affects us the same way. Slow, soft, higher-pitched, melodic songs soothe us; upbeat classical music makes us more alert and active; and fast, harsh, lower-pitched, dissonant music can rev us up and stress us out. Why would certain sounds affect us in specific emotional ways? One possibility is because of an overlap between how we perceive music and how we perceive human voic........ Read more »
Snowdon, C., & Teie, D. (2009) Affective responses in tamarins elicited by species-specific music. Biology Letters, 6(1), 30-32. DOI: 10.1098/rsbl.2009.0593
- March 4, 2013
- 09:13 PM
- 140 views
How Many English Tweets are Actually Possible?
by Jon Wilkins in Lost in Transcription
So, recently (last week, maybe?), Randall Munroe, of xkcd fame, posted an answer to the question "How many unique English tweets are possible?" as part of his excellent "What If" series. He starts off by noting that there are 27 letters (including spaces), and a tweet length of 140 characters. This gives you 27140 -- or about 10200 -- possible strings.
Of course, most of these are not sensible English statements, and he goes on to estimate how many of these there are. This analysis is base........ Read more »
C. E. Shannon. (1951) Prediction and Entropy of Written English. Bell System Technical Journal, 50-64. info:/
- March 4, 2013
- 01:50 PM
- 164 views
Distributed control of uncertain systems using superpositions of linear operators - Likelihood calculus paper series review part 3
by Travis DeWolf in studywolf
The third (and final, at the moment) paper in the likelihood calculus series from Dr. Terrence Sanger is Distributed control of uncertain systems using superpositions of linear operators. Carrying the torch for the series right along, here Dr. Sanger continues investigating the development of an effective, general method of controlling systems operating under uncertainty. This is the paper that delivers on all the promises of building a controller out of a system described by the stochastic diff........ Read more »
Sanger, T. (2011) Distributed Control of Uncertain Systems Using Superpositions of Linear Operators. Neural Computation, 23(8), 1911-1934. DOI: 10.1162/NECO_a_00151
- March 3, 2013
- 12:55 PM
- 188 views
Why Are People Bad at Evaluating Risks?
by Eric Horowitz in peer-reviewed by my neurons
Using evidence or data to communicate risk to the American public can be a fool’s errand. The most publicized “la, la, la, I can’t hear you!” moments involve people ignoring dangers that threaten ideology or political beliefs. Others may choose to ignore risks because immediate short-term pleasures are too alluring. [...]... Read more »
Bilgin, B., & Brenner, L. (2013) Context affects the interpretation of low but not high numerical probabilities: A hypothesis testing account of subjective probability. Organizational Behavior and Human Decision Processes, 121(1), 118-128. DOI: 10.1016/j.obhdp.2013.01.004
Simone CB 2nd, Hampshire MK, Vachani C, & Metz JM. (2012) The utilization of oncology web-based resources in Spanish-speaking Internet users. American journal of clinical oncology, 35(6), 520-6. PMID: 21654312
Teigen, K., Juanchich, M., & Riege, A. (2013) Improbable outcomes: Infrequent or extraordinary?. Cognition, 127(1), 119-139. DOI: 10.1016/j.cognition.2012.12.005
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