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Aiming at the problems of poor detection effect, high rate of missed detection and high rate of false detection in traditional methods, an anomaly detection method for wireless sensor networks based on improved GM model is proposed. The multilateral measurement method is used to locate the nodes in the wireless sensor network, and the state tracking of the running track of the located nodes is carried out. According to the tracking results, the self similarity between nodes is measured by Hurst index. Based on the measurement results, the improved GM model is used to predict the abnormal nodes. The abnormal values of the wireless sensor network are calculated by the distance between adjacent points, and the state of the current node is judged, this completes the anomaly detection of wireless sensor networks. The experimental results show that the proposed method is effective in anomaly detection of wireless sensor networks, and the rate of missed detection and false detection is low.

Due to their practicality and convenient parametrization, fractals derived from iterated function systems (IFSs) constitute powerful tools widely used to model natural and synthetic shapes. An IFS can generate sets other than fractals, extending its application field. Some of such sets arise from IFS fractals by adding minimal modifications to their defining rule. In this work, we propose two modifications to a fractal recently introduced by the authors: the so-called 2-ball fractal dust, which consists of a set of balls diminishing in size along an iterative process and delimited by an enclosing square. The proposed modifications are (a) adding a resizer parameter to introduce an interaction between the generator and generated ball elements and (b) a new fractal embedded into the 2-ball fractal dust, having the characteristic of filling zones not covered by the previous one. We study some numerical properties of both modified resulting sets to gain insights into their general properties. The resulting sets are geometrical forms with potential applications. Notably, the first modification generates an algorithm capable of producing geometric structures similar to those in mandalas and succulent plants; the second modification produces shapes similar to those found in nature, such as bubbles, sponges, and soil. Then, although a direct application of our findings is beyond the scope of this research, we discuss some clues of possible uses and extensions among which we can remark two connections: the first one between the parametrization we propose and the mandala patterns, and the second one between the embedded fractal and the grain size distribution of rocks, which is useful in percolation modeling.

An Active Queue Management (AQM) mechanism, recommended by the Internet Engineering Task Force (IETF), increases the efficiency of network transmission. An example of this type of algorithm can be the Random Early Detection (RED) algorithm. The behavior of the RED algorithm strictly depends on the correct selection of its parameters. This selection may be performed automatically depending on the network conditions. The mechanisms that adjust their parameters to the network conditions are called the adaptive ones. The example can be the Adaptive RED (ARED) mechanism, which adjusts its parameters taking into consideration the traffic intensity. In our paper, we propose to use an additional traffic parameter to adjust the AQM parameters—degree of self-similarity—expressed using the Hurst parameter. In our study, we propose the modifications of the well-known AQM algorithms: ARED and fractional order PIαDβ and the algorithms based on neural networks that are used to automatically adjust the AQM parameters using the traffic intensity and its degree of self-similarity. We use the Fluid Flow approximation and the discrete event simulation to evaluate the behavior of queues controlled by the proposed adaptive AQM mechanisms and compare the results with those obtained with their basic counterparts. In our experiments, we analyzed the average queue occupancies and packet delays in the communication node. The obtained results show that considering the degree of self-similarity of network traffic in the process of AQM parameters determination enabled us to decrease the average queue occupancy and the number of rejected packets, as well as to reduce the transmission latency.