One of the conclusions of fractal geometry is a fact that fractals unlike traditional Euclidean shapes lack characteristic scale. Those "fractured" objects are self-similar - defining geometry is clearly visible on multitude of scales. It is known that self-similarity is observed not only in formally defined geometric objects, such as Sierpinski triangle or Koch snowflake, but also in the surrounding nature. One of my most favorite examples is a comparison of tree, its branches and a leaf (for more inspiring examples see introduction of Fractals section) - they all have branching structure and something green filling the extra space in between.

The interesting thing, in context of the topic in focus, is that one can extend fractal formalism beyond formal or natural geometric shapes. It is also noticed that some of the natural processes exhibit fractal features in their time series! It is known that geoelectrical processes [1], heartbeat [2] and even human gait [3] time series posses this feature. While financial market, frequently analyzed on Physics of Risk website, time series are also no exception [4, 5]. Though the aforementioned time series are much more complex - they exhibit not monofractality (single manner self-similar behavior as the aforementioned formal geometric fractals do), but multifractality!

On the 25th of October, 2011 conference dedicated to the project Science for business and society will be held at hall in the Vilnius University, Institute of Theoretical Physics and Astronomy (A. Goštauto g. 12 - 432, Vilnius). This conference will mark ending of the currently ongoing project behind the Physics of Risk website. Main focus of this conference will be presentation of achieved results and discussion between business and scientists.

We have contributed two presentations towards the recent 39th Lithuanian National Physics Conference, which was organized by Vilnius University and Lithuanian Physicist Society. Oral presentation by A. Kononovicius was based on some of the models presented on Physics of Risk website, while poster presentation by R. Kazakevičius tackles very general problem related to the Physics of Risk.

As we have seen previously application of the original Kirman's model enables reproduction of single power law spectral density [1]. While actual financial markets and sophisticated stochastic models [2] have double power law spectral density - i.e., fractured spectral density. Thus it would be nice to obtain fracture of spectral density by improving application of Kirman's agent based model towards financial markets.

Time series obtained by solving non-linear stochastic models exhibit rather interesting statistical properties. On Physics of Risk we have already discussed some of these models [1, 2] (ex. stochastic model of return, herding model of financial markets), which are able to reproduce statistical properties of high frequency return (namely spectral density and probability distribution).

In statistical sense model and financial market behavior might be studied in many different manners. One may study probability distributions, moments, spectral densities, autocorrelations and etc., using each of them to obtain vital information on the statistical and dynamical properties of the studied system. It is important to note that new useful information might be provided by the statistical indicators, which are related to the previously used indicators in unambiguous manner. One may also introduce new variables describing system itself or its time series.

There is a group of such variables, which is closely related to the estimation of risk, known as burst statistics [3, 4]. In this text we will discuss these variables and their statistical properties. At the end of the text we also present an interactive HTML5 applet, using which one can reproduce burst statistics of certain stochastic model.