Mathematics posts
- September 11, 2011
- 01:49 PM
- 427 views
Neuroscience Fails Stats 101?
by Neuroskeptic in Neuroskeptic
According to a new paper, a full half of neuroscience papers that try to do a (very simple) statistical comparison are getting it wrong: Erroneous analyses of interactions in neuroscience: a problem of significance.Here's the problem. Suppose you want to know whether a certain 'treatment' has an affect on a certain variable. The treatment could be a drug, an environmental change, a genetic variant, whatever. The target population could be animals, humans, brain cells, or anything else.So you give the treatment to some targets and give a control treatment to others. You measure the outcome variable. You use a t-test of significance to see whether the effect is large enough that it wouldn't have happened by chance. You find that it was significant.That's fine. Then you try a different treatment, and it doesn't cause a significant effect against the control. Does that mean the first treatment was more powerful than the second?No. It just doesn't. The only way to find that out would be to compare the two treatments directly - and that would be very easy to do, because you have all the data to hand. If you just compare the two treatments to control you might end up with this scenario:Both treatments are very similar but one (B) is slightly better so it's significantly different from control, while A isn't. But they're basically the same. It's probably just fluke that B did slightly better than A. If you compared A and B directly you'd find they were not significantly different.An analogy: Passing a significance test is like winning a prize. You can only do it if you're much better than the average. But that doesn't mean you're much better than everyone who didn't win the prize, because some of them will have almost been good enough.Usain Bolt is the fastest man in the world (when he's not false-starting himself out of races). Much faster than me. But he's not much faster than the second fastest man in the world.Nieuwenhuis S, Forstmann BU, & Wagenmakers EJ (2011). Erroneous analyses of interactions in neuroscience: a problem of significance. Nature neuroscience, 14 (9), 1105-7 PMID: 21878926... Read more »
Nieuwenhuis S, Forstmann BU, & Wagenmakers EJ. (2011) Erroneous analyses of interactions in neuroscience: a problem of significance. Nature neuroscience, 14(9), 1105-7. PMID: 21878926
- August 29, 2011
- 11:17 PM
- 986 views
Did chaos theory kill the climatology star?
by csoeder in Topologic Oceans
Last time, we saw that some mathematical systems are so sensitive to initial conditions that even very small uncertainties in their initial state can snowball, causing even very similar states to evolve very differently. The equations describing fluid turbulence are examples of such a system; Lorenz’s discovery of extreme sensitivity to initial conditions ended hopes [...]... Read more »
Easterling, D., & Wehner, M. (2009) Is the climate warming or cooling?. Geophysical Research Letters, 36(8). DOI: 10.1029/2009GL037810
Lorenz, Edward N. (1963) Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20(2). info:/
- August 24, 2011
- 10:03 PM
- 540 views
Workplace stress: Opposites attract
by Vivek Venkataraman in sciencebyte
Highly stressed people at the workplace are individually surrounded by less stressed people and vice-versa... Read more »
Watanabe, J., Akitomi, T., Ara, K., & Yano, K. (2011) Antiferromagnetic character of workplace stress. Physical Review E, 84(1). DOI: 10.1103/PhysRevE.84.017101
- August 18, 2011
- 10:00 AM
- 566 views
Mathematics, Cities, and Brains: What Can A Highway Engineer Learn From A Neuroscientist?
by Jason Goldman in The Thoughtful Animal
Lots of networks have been compared to urban systems. Remember when the internet was referred to as the information superhighway? And high school biology teachers have been comparing the workings of cells to city operations for decades. To what extent, though, might a brain be like a city?... Read more »
Changizi, M., & Destefano, M. (2009) Common scaling laws for city highway systems and the mammalian neocortex. Complexity. DOI: 10.1002/cplx.20288
- August 14, 2011
- 10:46 PM
- 501 views
Kim's the name
by Vivek Venkataraman in sciencebyte
Statistical study of the distribution of Korean family names... Read more »
Baek, S., Minnhagen, P., & Kim, B. (2011) The ten thousand Kims. New Journal of Physics, 13(7), 73036. DOI: 10.1088/1367-2630/13/7/073036
- August 8, 2011
- 12:28 PM
- 1,290 views
“Anything But Country”: What Factor Analysis Reveals About Our Tastes for Tunes. [Guest Post at Scientific American]
by Melanie Tannenbaum in PsySociety
When asked to indicate their favorite type of music, plenty of people say they like “anything but country.” Is this really accurate? Why do rock music fans also tend to like punk and heavy metal? And why on earth would … Continue reading →... Read more »
Rentfrow PJ, Goldberg LR, & Levitin DJ. (2011) The structure of musical preferences: a five-factor model. Journal of personality and social psychology, 100(6), 1139-57. PMID: 21299309
- August 8, 2011
- 12:13 AM
- 847 views
Crop circle hoax and science
by Arunn in nOnoScience (a.k.a. Unruled Notebook)
Crop circles have been popular ever since hoaxes were, and should remain more popular than any of your G+ circles. It is one more (here is another) of those instances — unlike downright crap like Quan-dumb Table or Nano Art — where Art is created out of crafted and conjured up Science. Interestingly, over decades, [...]... Read more »
Haselhoff, E. (2001) Opinions and comments on Levengood WC, Talbott NP (1999) Dispersion of energies in worldwide crop formations. Physiol Plant 105: 615-624. Physiologia Plantarum, 111(1), 123-124. DOI: 10.1034/j.1399-3054.2001.1110116.x
- August 2, 2011
- 07:58 AM
- 848 views
The Life-Spans of Empires
by Samuel Arbesman in arbesman.net
I recently published my first history article. Titled The Life-Spans of Empires, it’s published in the delightfully-named journal Historical Methods: A Journal of Quantitative and Interdisciplinary History. Using a fun dataset I unearthed from some articles in the Nineteen Seventies, I explore the lifespans of empires, and their similarities to other complex systems: The collapse [...]... Read more »
Samuel Arbesman. (2011) The Life-Spans of Empires. Historical Methods, 44(3), 127-129. info:/10.1080/01615440.2011.577733
- July 30, 2011
- 01:31 PM
- 1,044 views
The Dershowitz/Falkovich proof of the Extended Church-Turing Thesis
by Aaron Sterling in Nanoexplanations
In a previous post, I considered a proof of the Church-Turing Thesis that Dershowitz and Gurevich published in the Bulletin of Symbolic Logic in 2008. It is safe to say that the proof is controversial — not because it is … Continue reading →... Read more »
Nachum Dershowitz, & Evgenia Falkovich. (2011) A Formalization and Proof of the Extended Church-Turing Thesis. International Workshop on the Development of Computational Models. info:/
- July 25, 2011
- 12:58 AM
- 855 views
The Quantum Telegraph
by Graham Morehead in A Mad Hemorrhage
Description of a superluminal communication device... Read more »
Ghirardi, G., Rimini, A., & Weber, T. (1980) A general argument against superluminal transmission through the quantum mechanical measurement process. Lettere al Nuovo Cimento, 27(10), 293-298. DOI: 10.1007/BF02817189
- July 22, 2011
- 10:43 AM
- 1,184 views
Light Logic for 'Light'-ning Fast Computers
by Paige Brown in From The Lab Bench
For some time now, the idea of building light-based devices to supplement semiconductor-based computing has attracted the interest of researchers and computer engineers alike. Why? Because, as eloquently put in a 2007 issue of Scientific American, "Light is a wonderful medium for carrying information."... Read more »
Wei H, Wang Z, Tian X, Käll M, & Xu H. (2011) Cascaded logic gates in nanophotonic plasmon networks. Nature communications, 387. PMID: 21750541
Wei H, Li Z, Tian X, Wang Z, Cong F, Liu N, Zhang S, Nordlander P, Halas NJ, & Xu H. (2011) Quantum dot-based local field imaging reveals plasmon-based interferometric logic in silver nanowire networks. Nano letters, 11(2), 471-5. PMID: 21182282
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- July 4, 2011
- 01:23 PM
- 1,080 views
A mathematical proof of the Church-Turing Thesis?
by Aaron Sterling in Nanoexplanations
The Church-Turing Thesis lies at the junction between computer science, mathematics, physics and philosophy. The Thesis essentially states that everything computable in the “real world” is exactly what is computable within our accepted mathematical abstractions of computation, such as Turing machines. … Continue reading →... Read more »
Nachum Dershowitz, & Yuri Gurevich. (2008) A Natural Axiomatization of Computability and Proof of Church's Thesis. The Bulletin of Symbolic Logic. DOI: 10.2178/bsl/1231081370
- July 1, 2011
- 11:38 PM
- 511 views
Thermodynamics and Poker
by csoeder in Topologic Oceans
There is a comapnion article which discusses this project’s role in decentralized community and citizen science at ArkFab. You can find the current paper here. A while back, I got the idea to investigate how the entropy of a poker tournament evolves with time. In thermodynamics, entropy is a measure of how ‘spread out’ energy [...]... Read more »
Clément Sire. (2007) Universal statistical properties of poker tournaments. J. Stat. Mech. (2007) P08013. arXiv: physics/0703122v3
Annila, Arto. (2009) Economies Evolve by Energy Dispersal. Entropy, 11(4), 606-633. DOI: 10.3390/e11040606
- July 1, 2011
- 08:50 PM
- 1,041 views
Q&A's with a Science Journalist: 'It's All Relativity'
by Paige Brown in From The Lab Bench
This week I am interviewing Louise Ogden, a science blogger on our own community blog Student Voices, which is hosted on Scitable by Nature Education. Louise also has her own science blog, It’s All Relativity, where she talks about space missions, climate change, exoplanets, solar eclipses, and much more! Louise is currently finishing up her Masters project at City University in London, which will earn her an (exciting!) degree in science journalism.... Read more »
Alison Wright. (2010) High-energy physics: Top of the class . Nature Physics, 6(644). info:/10.1038/nphys1783
- June 27, 2011
- 04:41 PM
- 1,057 views
Jungle Geometry: Who Needs Euclid?
by Elizabeth Preston in Inkfish
At some point in your teenage years, you probably kept a compass and straightedge in your backpack, learned the ways to prove two triangles are congruent, and knew what a secant was. It all had a taste of the classical about it: Euclid, Archimedes and Pythagoras had figured everything out and passed it down to us. But geometry may be more democratic than it seems. As a group of native Amazonians showed, you don't need to go to school to explain Euclid.French researcher Veronique Izard and her colleagues wanted to know if an understanding of Euclidean geometry is intuitive. It makes sense for humans and other animals to have a basic sense of shapes and distances, so we can find reachable fruits and flee approaching predators. But our eyes often deceive us. So do children, or remote tribespeople, instinctively understand that two parallel lines never cross? Or how many points define a line?The researchers traveled to the Amazon and recruited children (ages 7 to 13) and adults from a group called the Mundurucu. They had no education in geometry, and their language doesn't include any words to describe concepts such as parallel lines or right angles. But the Mundurucu face challenging navigational tasks every day, just moving around their environment. The researchers quizzed them on basic Euclidean tenets.Instead of points and lines, researchers described villages and straight paths. They asked two sets of questions, one concerning the geometry of a plane (described as a flat world that extends forever) and the other about a sphere (a "very round world"). For a visual aid, they used either a tabletop or a half a calabash.Participants were also shown two corners of a triangle and asked to demonstrate, with their hands, what the missing corner would look like and where it would be.The Mundurucu did great on their geometry quiz. The children performed just as well as the adults, and overall the Mundurucu did almost as well as American adults and French children that took the same quiz. All groups did better on questions about a flat plane than questions about the surface of a sphere, maybe because the former is more similar to what we observe in our daily lives.To find out whether this kind of knowledge is truly innate, or something that develops over time, the researchers repeated the quiz with American kids just 5 and 6 years old. The kids did OK, but not as well as older children or adults. They especially had difficulty completing the triangles.The results suggest that we're not born with an understanding of geometry. Rather, we learn as we grow how angles and lines work in the world. It would be interesting to see how another untrained group, one with less navigational experience than the Mundurucu, would handle the same questions. If a person grows up in a static and unchallenging environment, does he or she have a less intuitive grasp of distances and perspectives? Might the laws of the world be a little more mysterious?Some of the questions the Mundurucu correctly answered had to do with abstract ideas, such as infinitely extending lines. This showed that they weren't just describing basic physical relationships they'd observed, but extending their knowledge of the world to larger mathematical concepts. Euclid may have come up with the terms and the postulates, but the Mundurucu show that anyone at all, using their eyes and their understanding, could have invented geometry.Izard, V., Pica, P., Spelke, E., & Dehaene, S. (2011). From the Cover: Flexible intuitions of Euclidean geometry in an Amazonian indigene group Proceedings of the National Academy of Sciences, 108 (24), 9782-9787 DOI: 10.1073/pnas.1016686108... Read more »
Izard, V., Pica, P., Spelke, E., & Dehaene, S. (2011) From the Cover: Flexible intuitions of Euclidean geometry in an Amazonian indigene group. Proceedings of the National Academy of Sciences, 108(24), 9782-9787. DOI: 10.1073/pnas.1016686108
- June 26, 2011
- 03:54 PM
- 921 views
STOC 2011: Infinitary Ramsey Theory yields a complexity dichotomy theorem for CSPs over graphs
by Aaron Sterling in Nanoexplanations
In this post, I will discuss Schaefer’s Theorem for Graphs by Bodirsky and Pinsker, which Michael Pinsker presented at STOC 2011. I love the main proof technique of this paper: start with a finite object, blow it up to an … Continue reading →... Read more »
Manuel Bodirsky, & Michael Pinsker. (2011) Schaefer's Theorem for Graphs. Proceedings of 43rd Annual ACM Symposium on the Theory of Computing. info:/
- June 23, 2011
- 06:06 PM
- 1,431 views
Happy 99th Birthday, Alan Turing
by Jon Wilkins in Lost in Transcription
So, today (June 23, 2011) marks the 99th anniversary of the birth of Alan Turing, British supergenius who played a critical role in winning World War II and is one of the founding fathers of computer science.
He was also gay, which was illegal Britain at the time. In 1952 he was prosecuted under the same law that had sent Oscar Wilde to gaol. He chose to undergo chemical castration (in the form of treatment with feminizing hormones) as an alternative to prison.
In 1954 he committed suicide in dramatic fashion. He died of cyanide poisoning, and was found lying in his bed with a half-eaten apple beside him. The speculation is that he had laced the apple with cyanide and was reenacting the apple scene from Snow White.
When Alan Turing was found on June 8, 1954, he had been dead for one day, and he looked exactly like this. Snow White by *VinRoc on deviantART
Turing's earliest major contribution was the hypothetical Turing machine, which consisted of a very long piece of tape and a set of rules for manipulating the symbols on that tape. Turing showed that such a machine was, in principle, capable of performing any mathematical computation that can be represented as an algorithm. The Universal Turing Machine (a Turing machine capable of simulating any other Turing machine) provided a sort of proof-of-principle for the idea of general-purpose computers, and the tape-and-manipulator structure of the Turing machine is often cited as the prototype of the separation-of-hardware-and-software structure that pervades our computer lives today.
A Turing machine consists of a tape with symbols on it and a machine with a set of rules for reading and manipulating those symbols. And a bell.
During World War II, Turing worked as a cryptanalyst and made major contributions to cracking the "Enigma" codes used by the German military. The success of Turing and his colleagues throughout the war gave the Allies a critical advantage, particularly during the early parts of the war, when the Germans had a significant military advantage.
After World War II, he introduced what we now call the "Turing test" for artificial intelligence. The idea is that a computer can be said to have achieved genuine intelligence if a human having a conversation with it could not tell that it was a computer. For the next forty-some years, this was considered to be the gold standard for the demonstration of human intelligence. Then came a flood of reality television, which demonstrated that many humans would not actually pass it.
During the last few years of his life, Turing turned his attention to certain problems in mathematical biology, including the curious fact that many plants seem to grow in patterns governed by the Fibonacci sequence. The whole phyto-Fibonacci thing is a weird and interesting phenomenon that will get its own dedicated post sometime soon.
In the meantime, happy birthday Alan Turing, and RIP.
Turing, A. M. (1950). Computing Machinery and Intelligence Mind, 59 (236), 433-460
... Read more »
Turing, A. M. (1950) Computing Machinery and Intelligence. Mind, 59(236), 433-460. info:/
- June 20, 2011
- 05:30 AM
- 1,275 views
Obesity's contagious, or is it? A sober second look at obesity and social networks.
by Yoni Freedhoff in Weighty Matters
Right off the top let me say I'm not well versed enough in statistics to know who's right.On one side of the fence are the findings of Christakis and Fowler, famously published in the New England Journal of Medicine that posited obesity is socially contagious. Non-statistically, their paper didn't sit right with me, but as far as stats go, I'm no maven.On the other side of the fence is a new paper published by Russel Lyons who posits that Christakis' and Fowler's work is a great example of statistical illiteracy, and that the conclusion drawn from their data, that obesity is socially contagious, is severely flawed and can't be made.Lyons' paper, in a nutshell, gives statistical meat to my gut's firm belief - that shared environments and self-selection may well be explanatory for the clustering of obesity in social networks. That folks whose lifestyles may be more conducive to obesity, may well gravitate towards one another, and/or that people living in geographically/socially similar environments, environments that may contribute to the risk of obesity, together share increased risks and outcomes.Statistical arguments aside (frankly they're way over my head and I couldn't begin to venture a guess who's right and who's wrong), what was most fascinating to me was Lyons' discussion of his paper's publication. If Lyons' hypothesis is correct, his paper's a big deal. It refutes one of the most widely publicized studies of the decade, one that's translated itself into millions of dollars of grants, countless news stories, and even a book that's been published in 20 different languages. So what happened when he tried to publish it? The New England Journal of Medicine and the BMJ rejected it outright, without peer review. JAMA, the Lancet and the Proc. Nat. Acad. Sci. all rejected it next, this time because they have policies of not publishing critiques of articles they themselves didn't publish. Next Lyons submitted his paper to a statistics journal. The journal, Stat. Sci., did send it out for peer review. 2 of the 3 referees recommended publication without revision, and the 3rd, clearly not an obesity researcher, stated that while they agreed with Lyons' conclusions, that the subject was not important enough to warrant publication. Stat. Sci.'s editors agreed with reviewer number 3, and rejected the paper.Eventually Lyons' work was published in the journal Statistics, Politics, and Policy, whose impact factor's rates at 0.857. Contrast that with the impact factor of 50 that the New England Journal of Medicine enjoys.The entire experience has led Lyons to use his paper as a call to action to establish a journal whose subject matter is made up solely of study critiques. Were such a journal available, it would create a venue for publication of important criticisms, further protect the public from bad statistical analyses, and potentially serve as an incentive for researchers to double check their work.All in all, even if you're not a statistician, Lyons' paper is worth a sober read and reflection, and here's something else to chew on - the journalists who were originally all over Christakis' and Fowler's work? I'd bet every last penny I've got that not a single one of them were skilled enough in statistical analysis to analyze it. Really, why should they have been? They're journalists, not statisticians. No, instead they smelled a good story, and ran with it. Those same journalists who shouted from the rooftops that obesity's contagious? I'm betting the vast majority of them are going to be silent on this one, yet wouldn't re-reporting be the socially responsible, ethical, and journalistic right thing to do? Now I know that plenty of reporters read this blog. Would love to hear from you. Am I off base?Lyons, R. (2011). The Spread of Evidence-Poor Medicine via Flawed Social-Network Analysis Statistics, Politics, and Policy, 2 (1) DOI: 10.2202/2151-7509.1024
... Read more »
Lyons, R. (2011) The Spread of Evidence-Poor Medicine via Flawed Social-Network Analysis. Statistics, Politics, and Policy, 2(1). DOI: 10.2202/2151-7509.1024
- June 18, 2011
- 05:55 PM
- 1,029 views
Creative cultural transmission as chaotic sampling
by Sean Roberts in A Replicated Typo 2.0
Chaos has been used to create variations on musical and dance sequences (Dabby, 2008; Bradley & Stuart, 1998). Here, I apply this to birdsong. It could also be used to model the evolution of creative cultural features.... Read more »
Dabby, D. (2008) MUSIC THEORY: Creating Musical Variation. Science, 320(5872), 62-63. DOI: 10.1126/science.1153825
Bradley E, & Stuart J. (1998) Using chaos to generate variations on movement sequences. Chaos (Woodbury, N.Y.), 8(4), 800-807. PMID: 12779786
Spencer, K., Wimpenny, J., Buchanan, K., Lovell, P., Goldsmith, A., & Catchpole, C. (2005) Developmental stress affects the attractiveness of male song and female choice in the zebra finch (Taeniopygia guttata). Behavioral Ecology and Sociobiology, 58(4), 423-428. DOI: 10.1007/s00265-005-0927-5
Soma, M., Hiraiwa-Hasegawa, M., & Okanoya, K. (2009) Song-learning strategies in the Bengalese finch: do chicks choose tutors based on song complexity?. Animal Behaviour, 78(5), 1107-1113. DOI: 10.1016/j.anbehav.2009.08.002
Kiebel SJ, Daunizeau J, & Friston KJ. (2008) A hierarchy of time-scales and the brain. PLoS computational biology, 4(11). PMID: 19008936
Hosino, T., & Okanoya, K. (2000) Lesion of a higher-order song nucleus disrupts phrase level complexity in Bengalese finches. NeuroReport, 11(10), 2091-2095. DOI: 10.1097/00001756-200007140-00007
- June 17, 2011
- 04:03 PM
- 1,374 views
Fast Calculation of van der Waals Volume as a Sum of Atomic and Bond Contributions
by egonw in Chem-bla-ics
I was recently asked about a volume descriptor in Bioclipse, which is not yet available. Jmol can calculate surfaces, so that was my first thought. However, I then ran into a paper from 2003 by Zhao, called Fast Calculation of van der Waals Volume as a Sum of Atomic and Bond Contributions and Its Application to Drug Compounds (doi:10.1021/jo034808o).
The paper presents a very simple mathematical model, which approximates the molecular volume by a sum of atomic contributions, and a three terms to correct for atom-atom overlap, via the number of bonds, and corrections based on the number or aromatic and non-aromatic rings. The paper is clearly written, and the mathematics simple.
One problem with the publication though, are the numbers in the main text. They are wrong. I started of using the coefficients of the equations presented in the paper, but very soon ran into problems when I was writing up unit tests based on the volumes for compounds given as examples. In fact, the numbers in the main text are internally inconsistent. Not good. I believe it is partly caused by rounding, but that does not correct for the differences fully.
Fortunately, the Excel sheet in the supplementary information has the exact numbers, and those are numerically consistent.
The paper has been cited 46 times now, so, a fast volume descriptor seems relevant indeed. I am not sure how fast it will propagate to Bioclipse, as I do not have time soon to update the CDK version of Bioclipse (the major part of which is to ensure the Bioclipse-JChemPaint editor does not get broken, again).
Another thought about this paper, is that it is using the evil aromaticity concept, where the authors forgot to mention when they consider a ring to be aromatic.
Zhao, Y., Abraham, M., & Zissimos, A. (2003). Fast Calculation of van der Waals Volume as a Sum of Atomic and Bond Contributions and Its Application to Drug Compounds The Journal of Organic Chemistry, 68 (19), 7368-7373 DOI: 10.1021/jo034808o... Read more »
Zhao, Y., Abraham, M., & Zissimos, A. (2003) Fast Calculation of van der Waals Volume as a Sum of Atomic and Bond Contributions and Its Application to Drug Compounds. The Journal of Organic Chemistry, 68(19), 7368-7373. DOI: 10.1021/jo034808o
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