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Mathematics posts

• September 11, 2011
• 01:49 PM
• 427 views

Neuroscience Fails Stats 101?

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 »

• August 29, 2011
• 11:17 PM
• 986 views

Did chaos theory kill the climatology star?

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

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?

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 »

• August 14, 2011
• 10:46 PM
• 501 views

Kim's the name

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]

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

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 »

• August 2, 2011
• 07:58 AM
• 848 views

The Life-Spans of Empires

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

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

Description of a superluminal communication device... Read more »

• July 22, 2011
• 10:43 AM
• 1,184 views

Light Logic for 'Light'-ning Fast Computers

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 »

• July 4, 2011
• 01:23 PM
• 1,080 views

A mathematical proof of the Church-Turing Thesis?

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 »

• July 1, 2011
• 11:38 PM
• 511 views

Thermodynamics and Poker

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'

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?

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

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

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.

... Read more »

• June 18, 2011
• 05:55 PM
• 1,029 views

Creative cultural transmission as chaotic sampling

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 »

Bradley E, & Stuart J. (1998) Using chaos to generate variations on movement sequences. Chaos (Woodbury, N.Y.), 8(4), 800-807. PMID: 12779786

Kiebel SJ, Daunizeau J, & Friston KJ. (2008) A hierarchy of time-scales and the brain. PLoS computational biology, 4(11). PMID: 19008936

• June 17, 2011
• 04:03 PM
• 1,374 views

Fast Calculation of van der Waals Volume as a Sum of Atomic and Bond Contributions

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 »