B. Mandelbrot: Fractals and the art of roughness

B. Mandelbrot is probably one of the most well known mathematicians of the second half of the 20th century. As a scientist he was interested in the "strange" fractal geometry. In this TED talk he draws our attention to the naturally occurring complexity we observe everyday, but which is left unnoticed by our eyes. In this talk he briefly and in very simple terms explains the basic concepts of fractal geometry. We invite you to listen to this great man speak.

Market price - is it economic or sociological concept?

This text follows up our recent article "Consentaneous Agent-Based and Stochastic Model of the Financial Markets" published in open access interdisciplinary journal PLoS ONE [1]. This article is a result of the ongoing research at the Institute of Theoretical Physics and Astronomy of Vilnius University implementing the ideas of econophysics. Though our research is mostly related to the modeling of return statistics in financial markets implementing ideas from statistical physics, the concepts behind this work and conclusions are related to the much more extensive interdisciplinary understanding of the social and physical sciences. The desire to extend conventional boundaries and achieve more understanding between researchers of physical and social sciences is a strong motivation for us to deal with econophysics.

Future of Java applets and How to launch Java applets?

When we started to work on "Physics of Risk" Java platform was extremely popular way to show interactive material to readers online. Though this technology is still rather popular, but there is a significant challenge for amateurs working with it. Since the previous glorious days Java platform has become less secure and thus more paranoid. As the time moves on newer Java Runtime Environment versions start require applets to be certified. Certificates are not that cheap and thus not accessible to amateur programers.

The good news is that HTML5 standard has becoming more popular on web and that it also offers presentation of interactive content via Javascript. Thus we plan to migrate most of the old Java applets to this emerging technology. These new HTML5 applets should work in all modern web browsers as the implementation of HTML5 by the most popular modern browsers was started a few years ago. Therefore we do not expect any problems occurring to you, our readers.

In the mean time, we present a list of articles, which include old Java applets, and also provide a detailed instruction on how to launch Java applets.

Another model of high clustering in scale-free networks

Previously we have already mentioned that there are three main statistical features of networks. The most problematic of them appears to be clustering as random networks do not naturally form local, tightly interconnected, communities. In the previous text we discussed a simple model, which produces highly clustered scale-free networks. The problem is that it is rather hard to relate that model to any real complex system. In this text we will attempt to solve this problem.

Achieving high clustering in scale-free networks

Average shortest path (sometimes network diameter), degree distribution and clustering are the three main network characteristics. Path lengths tend to be small in random network models (average shortest path and network diameter grows as \( \ln N \) or slower). Power-law degree distribution can be obtained from the Barabasi-Albert and some other models. But clustering appears to be trickier to reproduce together with the previous two. In this text we will discuss what clustering actually is and how to obtain it in random network model.