A new approach of the decomposition method (Adomian) in which the Adomian scheme is obtained in a more natural way than in the classical presentation, is given. A new condition for obtaining convergence of the decomposition series is also included.

Nowadays, swarm robotics research is having a great increase due to the benefits derived from its use, such as robustness, parallelism, and flexibility. Unlike distributed robotic systems, swarm robotics emphasizes a large number of robots, and promotes scalability. Among the multiple applications of such systems we could find are exploring unstructured environments, resource monitoring, or distributed sensing. Two of these applications, monitoring, and perimeter/area detection of a given resource, have several ecological uses. One of them is the detection and monitoring of pollutants to delimit their perimeter and area accurately. Maritime activity has been increasing gradually in recent years. Many ships carry products such as oil that can adversely affect the environment. Such products can produce high levels of pollution in case of being spilled into sea. In this paper we will present a distributed system which monitors, covers, and surrounds a resource by using a swarm of homogeneous low cost drones. These drones only use their local sensory information and do not require any direct communication between them. Taking into account the properties of this kind of oil spills we will present a microscopic model for a swarm of drones, capable of monitoring these spills properly. Furthermore, we will analyse the proper macroscopic operation of the swarm. The analytical and experimental results presented here show the proper evolution of our system.

In this work, a swarm behaviour for multi-rotor Unmanned Aerial Vehicles (UAVs) deployment will be presented. The main contribution of this behaviour is the use of a virtual device for quantitative sematectonic stigmergy providing more adaptable behaviours in complex environments. It is a fault tolerant highly robust behaviour that does not require prior information of the area to be covered, or to assume the existence of any kind of information signals (GPS, mobile communication networks …), taking into account the specific features of UAVs. This behaviour will be oriented towards emergency tasks. Their main goal will be to cover an area of the environment for later creating an ad-hoc communication network, that can be used to establish communications inside this zone. Although there are several papers on robotic deployment it is more difficult to find applications with UAV systems, mainly because of the existence of various problems that must be overcome including limitations in available sensory and on-board processing capabilities and low flight endurance. In addition, those behaviours designed for UAVs often have significant limitations on their ability to be used in real tasks, because they assume specific features, not easily applicable in a general way. Firstly, in this article the characteristics of the simulation environment will be presented. Secondly, a microscopic model for deployment and creation of ad-hoc networks, that implicitly includes stigmergy features, will be shown. Then, the overall swarm behaviour will be modeled, providing a macroscopic model of this behaviour. This model can accurately predict the number of agents needed to cover an area as well as the time required for the deployment process. An experimental analysis through simulation will be carried out in order to verify our models. In this analysis the influence of both the complexity of the environment and the stigmergy system will be discussed, given the data obtained in the simulation. In addition, the macroscopic and microscopic models will be compared verifying the number of predicted individuals for each state regarding the simulation.

Face detection is the first step of any automated face recognition system. One of the most popular approaches to detect faces in color images is using a skin color segmentation scheme, which in many cases needs a proper representation of color spaces to interpret image information. In this paper, we propose a fuzzy system for detecting skin in color images, so that each color tone is assumed to be a fuzzy set. The Red, Green, and Blue (RGB), the Hue, Saturation and Value (HSV), and the YCbCr (where Y is the luminance and Cb,Cr are the chroma components) color systems are used for the development of our fuzzy design. Thus, a fuzzy three-partition entropy approach is used to calculate all of the parameters needed for the fuzzy systems, and then, a face detection method is also developed to validate the segmentation results. The results of the experiments show a correct skin detection rate between 94% and 96% for our fuzzy segmentation methods, with a false positive rate of about 0.5% in all cases. Furthermore, the average correct face detection rate is above 93%, and even when working with heterogeneous backgrounds and different light conditions, it achieves almost 88% correct detections. Thus, our method leads to accurate face detection results with low false positive and false negative rates.

Nowadays, cyber attacks are becoming an extremely serious issue, which is particularly important to prevent in a smart city context. Among cyber attacks, spoofing is an action that is increasingly common in many areas, such as emails, geolocation services or social networks. Identity spoofing is defined as the action by which a person impersonates a third party to carry out a series of illegal activities such as committing fraud, cyberbullying, sextorsion, etc. In this work, a face recognition system is proposed, with an application to the spoofing prevention. The method is based on the Histogram of Oriented Gradients (HOG) descriptor. Since different face regions do not have the same information for the recognition process, introducing entropy would quantify the importance of each face region in the descriptor. Therefore, entropy is added to increase the robustness of the algorithm. Regarding face recognition, our approach has been tested on three well-known databases (ORL, FERET and LFW) and the experiments show that adding entropy information improves the recognition rate significantly, with an increase over 40% in some of the considered databases. Spoofing tests has been implemented on CASIA FASD and MIFS databases, having obtained again better results than similar texture descriptors approaches.