Collective Behavior in Animals

Feel like yawning? Look around, someone near you might also be yawning!

The so called collective behavior such as yawning might be an urban myth but a recent studies have attempted to model such collective behavior. The modal system they considered consists of an example of collective behavior of cows. Such theories have not been tested it in the real cows, however one should not be surprised to see such studies to be verified in near future.

In a recent work, published in arxiv,  Sun et. al. study the collective behavior of animals such as cows.  Animals are coupled oscillators. They simply model the cow as coupled oscillator. By considering the discrete states of such animals and by considering such couplings, they study the collective decision bearing of such system.
Specifically, they consider three states of cows: standing, sitting and grazing; say "1", "2" and "3" just for sake of easy symbolization. By coupling the states, they assume that behavior of one is going affect the behavior of nearby ones. So, there is more tendency of uniform state such as 1,1,1,1,1 than 1,2,3,2,1 or 1,2,1,2,3. However, for larger cow population there can be some nice oscillatory behavior between the stable states.
The paper is interesting! Have a look.
Ref:
http://arxiv.org/abs/1005.1381
http://www.technologyreview.com/blog/arxiv/25171/


Acknowledgements are due to the first author for suggests in the draft version of the post and allowing to use the figures.

Fig: Coupled cows.

On the lighter side:
One can see the influence of "spherical cow" on the coupling diagrams. See Jackson, J.D. Third Edition Ch3 problem#15.

Heading for MaxEnt 2010, Chamonix France

I will be visiting France for a week to attend the MaxEnt 2010 Conference.

There, I will be presenting my work on "Entropy Based Search Algorithm for Experimental Design".

http://maxent2010.inrialpes.fr/program/complete-program/#6.1

I have uploaded some pictures in Facebook. The link is
http://www.facebook.com/album.php?aid=179722&id=671171228&l=915fdf0f5a

Diffusive Nested Sampling: Brewer et. al.

Brendon et. al. has a newer version of nested sampling algorithm, they call it Diffusive Nested Sampling (DNS). As the name indicates, it principally differs from the "classic" nested sampling in presenting the hard constraint. It relaxes the hard evolving constraint and lets the samples to explore the mixture distribution of nested probability distributions, each successive distribution occupying e^-1 times the enclosed prior mass of the previously seen distributions. The mixture distribution is weighted at will (a hack :P) which is a clever trick of exploration. This reinforces the idea of "no peaks left behind" for multimodal problems.

On a test problem they claim that DNS "can achieve four times the accuracy of classic Nested Sampling, for the same computational effort; equivalent to a factor of 16 speedup".

I have not played with it yet. However, it seems worth trying. Just a note to myself.

PS:
What can grow out of side talks in a conference?
If you know the power of scrapping in the napkin paper, you would not be surprised.

The paper is available in arxiv:
http://arxiv.org/abs/0912.2380
The code is available at: http://lindor.physics.ucsb.edu/DNest/; comes with handy instructions.

---
Thanks are due to Dr. Brewer for indicating typos in the draft and suggestions + allowing to use the figures.
 The original nested sampling code is available in the book by sivia and skilling: Data Analysis: A Bayesian Tutorial
 

Edit: Sep 5, 2013 An illustrative animation of Diffusive Nested Sampling (www.github.com/eggplantbren/DNest3) sampling a multimodal posterior distribution. The size of the yellow circle indicates the importance weight. The method can travel between the modes because the target distribution includes the (uniform) prior as a mixture component.

Human Body as an Ecosystem and advent of Green Medicine

This sounds fascinating concept; equally impressive to grasp!

In an article published in scientific american, Humans Carry More Bacterial Cells than Human Ones, scientists claim human body to contain more bacterial cell than the human cell itself. So if you have 100 trillion cells in your body,  about the same number of bacteria are are paying you homage. Nice host. Moreover, it has also been reported that they have also contributed to human genes (http://en.wikipedia.org/wiki/Human_Genome_Project, http://www.ornl.gov/sci/techresources/Human_Genome/home.shtml). Strangely, other species seem to have less  connections with bacteria; or may be it is yet to be discovered.

By definition, Ecosystem is a functional unit consisting of living things in a given area, non-living chemical and physical factors of their environment, linked together through nutrient cycle and energy flow. Since they help to maintain various body processes, this makes human as a host and the body as an ecosystem.

We had already learnt that some bacteria were friendly and some were not. Identification of pathogenic bacteria and use of  antibiotic treatment has been hailed as one of the great success in medical history. The side effects of antibiotics are not so unfamiliar and reasoned as  killing off pathogenic as well as friendly bacteria. However, once we are able to understand the ecosystem of human body, curing "infectious" diseases should be just a treat load of another identified bacteria! Shall we call it Green Medicine?

Nested Sampling Algorithm (John Skilling)

Nested Sampling was developed by John Skilling (http://www.inference.phy.cam.ac.uk/bayesys/box/nested.pdf // http://ba.stat.cmu.edu/journal/2006/vol01/issue04/skilling.pdf).

Nested Sampling is a modified Markov Chain Monte Carlo algorithm which can be used to explore the posterior probability for the given model. The power of Nested Sampling algorithm lies in the fact that it is designed to compute both the mean posterior probability as well as the Evidence. The algorithm is initialized by randomly taking samples from the prior. The algorithm contracts the distribution of samples around high likelihood regions by discarding the sample with the least likelihood, Lworst.
To keep the number of samples constant, another sample is chosen at random and duplicated. This sample is then randomized by taking Markov chain Monte Carlo steps subject to a hard constraint so that its move is accepted only if the new likelihood is greater than the new threshold, L > Lworst. This ensures that the distribution of samples remains uniformly distributed and that new samples have likelihoods greater than the current likelihood threshold. This process is iterated until the convergence. The logarithm of the evidence is given by the area of the sorted log likelihood as a function of prior mass. When the algorithm has converged one can compute the mean parameter values as well as the log evidence.

For a nice description of Nested Sampling, the book by Sivia and Skilling is highly recommended: Data Analysis: A Bayesian Tutorial.
The  codes in C/python/R with an example of light house problem is available at:
http://www.inference.phy.cam.ac.uk/bayesys/
The paper is available at:
http://www.inference.phy.cam.ac.uk/bayesys/nest.ps.gz