Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Community detection and stochastic block models: recent developments

The stochastic block model (SBM) is a random graph model with planted clusters. It is widely employed as a canonical model to study clustering and community detection, and provides generally a fertile ground to study the statistical and computational tradeoffs that arise in network and data sciences. This note surveys the recent developments that establish the fundamental limits for community detection in the SBM, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery (a.k.a., detection). The main results discussed are the phase transitions for exact recovery at the Chernoff-Hellinger threshold, the phase transition for weak recovery at the Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial recovery, the learning of the SBM parameters and the gap between information-theoretic and computational thresholds. The note also covers some of the algorithms developed in the quest of achieving the limits, in particular two-round algorithms via graph-splitting, semi-definite programming, linearized belief propagation, classical and nonbacktracking spectral methods. A few open problems are also discussed

Development and evaluation of computer-aided assessment in discrete and decision mathematics

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University London.This thesis describes the development of Computer-Aided Assessment questions for elementary discrete and decision mathematics at the school/university interface, stressing the pedagogy behind the questions’ design and the development of methodology for assessing their efficacy in improving students’ engagement and perceptions, as well as on their exams results. The questions give instant and detailed feedback and hence are valuable as diagnostic, formative or summative tools. A total of 275 questions were designed and coded for five topics, numbers, sets, logic, linear programming and graph theory, commonly taught to students of mathematics, computer science, engineering and management. Pedagogy and programming problems with authoring questions were resolved and are discussed in specific topic contexts and beyond. The delivery of robust and valid objective questions, even within the constraints of CAA, is therefore feasible. Different question types and rich feedback comprising text, equations and diagrams that allow random parameters to produce millions of realisations at run time, can give CAA an important role in teaching mathematics at this level. Questionnaires identified that CAA was generally popular with students, with the vast majority seeing CAA not only as assessment but also as a learning resource. To test the impact of CAA on students’ learning, an analysis of the exam scripts quantified its effect on class means and standard deviations. This also identified common student errors, which fed into the question design and editing processes by providing evidence-based mal-rules. Four easily-identified indicators (correctly-written remainders, conversion of binary/octal/hexadecimal numbers, use of correct set notation {…} and consistent layout of truth tables) were examined in student exam scripts to find out if the CAA helps students to improve examination answers. The CAA answer files also provided the questions’ facilities and discriminations, potentially giving teachers specific information on which to base and develop their teaching and assessment strategies. We conclude that CAA is a successful tool for the formative/summative assessment of mathematics at this level and has a positive effect on students’ learning

Advances in Branch-and-Fix methods to solve the Hamiltonian cycle problem in manufacturing optimization

159 p.Esta tesis parte del problema de la optimización de la ruta de la herramienta donde se contribuye con unsistema de soporte para la toma de decisiones que genera rutas óptimas en la tecnología de FabricaciónAditiva. Esta contribución sirve como punto de partida o inspiración para analizar el problema del cicloHamiltoniano (HCP). El HCP consiste en visitar todos los vértices de un grafo dado una única vez odeterminar que dicho ciclo no existe. Muchos de los métodos propuestos en la literatura sirven paragrafos no dirigidos y los que se enfocan en los grafos dirigidos no han sido implementados ni testeados.Uno de los métodos para resolver el problema es el Branch-and-Fix (BF), un método exacto que utiliza latranformación del HCP a un problema continuo. El BF es un algoritmo de ramificación que consiste enconstruir un árbol de decisión donde en cada vértice dos problemas lineales son resueltos. Este método hasido testeado en grafos de tamaño pequeño y por ello, no se ha estudiado en profundidad las limitacionesque puede presentar. Por ello, en esta tesis se proponen cuatro contribuciones metodológicasrelacionadas con el HCP y el BF: 1) mejorar la enficiencia del BF en diferentes aspectos, 2) proponer unmétodo de ramificación global, 3) proponer un método del BF colapsado, 4) extender el HCP a unescenario multi-objetivo y proponer un método para resolverlo