Directed percolation in a two dimensional stochastic fire-diffuse-fire model

In this paper we establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release that retains the both the discrete nature of calcium stores and the stochastic nature of release. It is formed from an array of noisy threshold elements that are coupled only by a diffusing signal. The model supports spontaneous release events that can merge to form spreading circular and spiral waves of activity. The critical level of noise required for the system to exhibit a non-equilibrium phase-transition between propagating and non-propagating waves is obtained by an examination of the \textit{local slope} $\delta(t)$ of the survival probability, $\Pi(t) \propto \exp(- \delta(t))$, for a wave to propagate for a time $t$.

Detecting Motifs in System Call Sequences

The search for patterns or motifs in data represents an area of key interest to many researchers. In this paper we present the Motif Tracking Algorithm, a novel immune inspired pattern identification tool that is able to identify unknown motifs which repeat within time series data. The power of the algorithm is derived from its use of a small number of parameters with minimal assumptions. The algorithm searches from a completely neutral perspective that is independent of the data being analysed and the underlying motifs. In this paper the motif tracking algorithm is applied to the search for patterns within sequences of low level system calls between the Linux kernel and the operating system’s user space. The MTA is able to compress data found in large system call data sets to a limited number of motifs which summarise that data. The motifs provide a resource from which a profile of executed processes can be built. The potential for these profiles and new implications for security research are highlighted. A higher level system call language for measuring similarity between patterns of such calls is also suggested.