Recursive cubes of rings as models for interconnection networks

We study recursive cubes of rings as models for interconnection networks. We first redefine each of them as a Cayley graph on the semidirect product of an elementary abelian group by a cyclic group in order to facilitate the study of them by using algebraic tools. We give an algorithm for computing shortest paths and the distance between any two vertices in recursive cubes of rings, and obtain the exact value of their diameters. We obtain sharp bounds on the Wiener index, vertex-forwarding index, edge-forwarding index and bisection width of recursive cubes of rings. The cube-connected cycles and cube-of-rings are special recursive cubes of rings, and hence all results obtained in the paper apply to these well-known networks

Performance of Averaging Algorithms in Time-Varying Networks

We study averaging algorithms in time-varying networks, and means tomeasure their performance. We present sufficient conditions on these algorithms, which ensure they lead to computation at each node, of the global average of measurements provided by each node in the network. Further, we present and use results from ergodic theory to define an accurate performance metric for averaging algorithms. This metric, the contraction coefficient, differs from previously used metrics such as the second largest eigenvalue of the expected weighting matrix, which gives an approximation of the real convergence rate only in some special cases which are hard to specify. On the other hand, the contraction coefficient as set forth herein characterizes exactly the actual asymptotic convergence rate of the system. Additionally, it may be bounded by a very concise formula, and simulations show that this bound is, at least in all studied cases, reasonably tight so as to be used as an approximation to the actual contraction coefficient. Finally, we provide a few results and observations which make use of the derived tools. These observations may be used to find new optima for design parameters of some averaging algorithms, and also open the door to new problems in the study of the underlying mathematical models

Behaviour monitoring: investigation of local and distributed approaches

Nowadays, the widespread availability of cheap and efficient unmanned systems (either aerial, ground or surface) has led to significant opportunities in the field of remote sensing and automated monitoring. On the one hand, the definition of efficient approaches to information collection, filtering and fusion has been the focus of extremely relevant research streams over the last decades. On the other hand, far less attention has been given to the problem of ‘interpreting’ the data, thus implementing inference processes able to, e.g., spot anomalies and possible threats in the monitored scenario. It is easy to understand how the automation of the ‘target assessment’ process could bring a great impact on monitoring applications since it would allow sensibly alleviating the analysis burden for human operators. To this end, the research project proposed in this thesis addresses the problem of behaviour assessment leading to the identification of targets that exhibit features “of interest”. Firstly, this thesis has addressed the problem of distributed target assessment based on behavioural and contextual features. The assessment problem is analysed making reference to a layered structure and a possible implementation approach for the middle-layer has been proposed. An extensive analysis of the ‘feature’ concept is provided, together with considerations about the target assessment process. A case study considering a road-traffic monitoring application is then introduced, suggesting a possible implementation for a set of features related to this particular scenario. The distributed approach has been implemented employing a consensus protocol, which allows achieving agreement about high-level, non-measurable, characteristics of the monitored vehicles. Two different techniques, ‘Belief’ and ‘Average’ consensus, for distributed target assessment based on features are finally presented, enabling the comparison of consensus effects when implemented at different level of the considered conceptual hierarchy. Then, the problem of identifying targets concerning features is tackled using a different approach: a probabilistic description is adopted for the target characteristics of interest and a hypothesis testing technique is applied to the feature probability density functions. Such approach is expected to allow discerning whether a given vehicle is a target of interest or not. The assessment process introduced is also able to account for information about the context of the vehicle, i.e. the environment where it moves or is operated. In so doing the target assessment process can be effectively adapted to the contour conditions. Results from simulations involving a road monitoring scenario are presented, considering both synthetic and real-world data. Lastly, the thesis addresses the problem of manoeuvre recognition and behaviour anomalies detection for generic targets through pattern matching techniques. This problem is analysed considering motor vehicles in a multi-lane road scenario. The proposed approach, however, can be easily extended to significantly different monitoring contexts. The overall proposed solution consists in a trajectory analysis tool, which classifies the target position over time into a sequence of ‘driving modes’, and a string-matching technique. This classification allows, as result of two different approaches, detecting both a priori defined patterns of interest and general behaviours standing out from those regularly exhibited from the monitored targets. Regarding the pattern matching process, two techniques are introduced and compared: a basic approach based on simple strings and a newly proposed method based on ‘regular expressions’. About reference patterns, a technique for the automatic definition of a dictionary of regular expressions matching the commonly observed target manoeuvres is presented. Its assessment results are then compared to those of a classic multi-layered neural network. In conclusion, this thesis proposes some novel approaches, both local and distributed, for the identification of the ‘targets of interest’ within a multi-target scenario. Such assessment is solely based on the behaviour actually exhibited by a target and does not involve any specific knowledge about the targets (analytic dynamic models, previous data, signatures of any type, etc.), being thus easily applicable to different scenarios and target types. For all the novel approaches described in the thesis, numerical results from simulations are reported: these results, in all the cases, confirm the effectiveness of the proposed techniques, even if they appear to be open to interpretation because of the inherent subjectivity of the assessment process