Reviewers of one of our most recent papers have asked some very interesting questions. One of them was about the numerical methods we use to solve the stochastic differential equations. The question was to be expected as, while we provide the final difference equations, we do not discuss how they were obtained. Thus here we will briefly review the most basic principles of the numerical solution of the stochastic differential equations.

Modern science strongly relies on the computer modeling. Most of the models in the complexity science, the object of the Physics of Risk, requires computer modeling and usually may not be dealt with analytically. For a person familiar with the computer modeling it should be known that the variety computer algorithms is very large and that there also is a variety of ways to understand these algorithms. Thus each person might solve the same complex task slightly differently and thus produce slightly different results. This brings us to the point that in order to comprehend what has been done by a certain scientist one should not only study the equations and assumptions made by him, but one also needs to have access to the source code of the software used by that certain scientist.

Yet there is still a problem that only few scientists to make the source code of their software public available. This behavior is not very desired as in order to reproduce the same results other scientists must make a lot of efforts. Some times the attempts to reproduce published results fail. This problem may be solved by encouraging adoption of the open source ideas by the scientific community.

We, the contributors of Physics of Risk, have already faced the negative effects of the closed source culture, thus most of our models made available on Physic of Risk are published together with their source code. Though it is well hidden inside the applet's JAR archive (open it with any modern archiver, inside you should find java file, which contains the source code).

Read more on open source software in science in Nature Editorial "If you want reproducible science, the software needs to be open source".

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.

Network models are intimately related to a certain branch of mathematics known as the graph theory. Actually networks themselves are graphs! Thus further we briefly introduce some of the terms related to the mathematical graph theory.

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!