Detection of an anomalous cluster in a network

We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an "unusual behavior." Formally, suppose we are given a set of nodes and attach a random variable to each node. We observe a realization of this process and want to decide between the following two hypotheses: under the null, the variables are i.i.d. standard normal; under the alternative, there is a cluster of variables that are i.i.d. normal with positive mean and unit variance, while the rest are i.i.d. standard normal. We also address surveillance settings where each sensor in the network collects information over time. The resulting model is similar, now with a time series attached to each node. We again observe the process over time and want to decide between the null, where all the variables are i.i.d. standard normal, and the alternative, where there is an emerging cluster of i.i.d. normal variables with positive mean and unit variance. The growth models used to represent the emerging cluster are quite general and, in particular, include cellular automata used in modeling epidemics. In both settings, we consider classes of clusters that are quite general, for which we obtain a lower bound on their respective minimax detection rate and show that some form of scan statistic, by far the most popular method in practice, achieves that same rate to within a logarithmic factor. Our results are not limited to the normal location model, but generalize to any one-parameter exponential family when the anomalous clusters are large enough.Comment: Published in at http://dx.doi.org/10.1214/10-AOS839 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Malware propagation in Wireless Sensor Networks: global models vs Individual-based models

The main goal of this work is to propose a new framework to design a novel family of mathematical models to simulate malware spreading in wireless sensor networks (WSNs). An analysis of the proposed models in the scientific literature reveals that the great majority are global models based on systems of ordinary differential equations such that they do not consider the individual characteristics of the sensors and their local interactions. This is a major drawback when WSNs are considered. Taking into account the main characteristics of WSNs (elements and topologies of network, life cycle of the nodes, etc.) it is shown that individual-based models are more suitable for this purpose than global ones. The main features of this new type of malware propagation models for WSNs are stated