Music, point processes and 1/f noise

There is interesting observations in the music by the great classical composers - statistical properties of their time series appear to be as complex as social phenomena considered here on Physics of Risk. Their music may seem to be both - at certain times easily anticipated and predictable, while at the other times have large unexpected deviations. Their music behaves as a pink or 1/f noise [1, 2]! In [1] it was shown that the intensity time series of the music by the classical composers and human speech time series have 1/f region in their spectral densities. While in [2] these ideas are applied towards musical rhythm. To us [2] is especially interesting as this paper considers our own model, [3, 4], as a proper model for the 1/f noise in the spectral density of musical rhythm.

Obtaining surface area using Monte Carlo method

Imagine that you have to measure the surface area of the lake by using only a cannon! Let us assume that the geometric shape of the lake is too complex to be dealt with using simple formulas and that you have almost infinite supply of cannon balls. In such case you just have to hope that you are perfectly random shooter! Why so?

If your shots cover the hitting area of the cannon uniformly then you can obtain the area of the lake by estimating the probability to hit it:

\begin{equation} S_{fig} = p S_{hit} , \end{equation}

here \( S_{fig} \) is an estimate of the surface area of certain geometric shape (lake for example), \( p \) is an estimate of the probability to hit the shape, while \( S_{hit} \) is the hitting area of the cannon. The obtained are of course will be only approximate, but one can arrive reasonably near the actual answer.

Next we illustrate this method by applying it towards three geometric shapes - square, circle and Euclidean egg. Why the Euclidean egg? Well, there are numerous reasons for it, one of them being Easter. Happy Easter!

February and March active time for econophysicists

In February and Match three very important conference to the econophysicists were held: "Unsolved Problems on Noise", "Verhandlungen DPG" and "Open Readings" (lt. "Laisvieji skaitymai"). Our B. Kaulakys, V. Gontis, A. Kononovicius, P. Purlys and R. Kazakevičius have given oral and poster presentations at these conference. Presentations were mostly concerned with our newest achievements in the applications of Kirman model and burst statistics.

Aleksejus Kononovicius: What can the Bass diffusion model tell us about piracy?

Recently in Lithuanian and world's different or global social spaces there was a lot of disccusion on anti-piracy and the proportionality of so-called "protection" of intelectual properties. The US politicians consider SOPA and PIPA, while EU countries one after another expressed will to join ACTA. In Lithuanian media and blogosphere, as most probably in the rest of the world, has split into the ACTA supporter and opposition camps.