Les Réseaux de Capteurs Sans Fil (RCSFs) constituent une classe particulière des réseaux Ad hoc, faisant l'objet de recherches intensives. Ils sont considérés comme un outil très puissant pour connecter le monde physique et le monde numérique. Ils se composent d'un grand nombre de noeuds capteurs dotés de ressources limitées en termes d'énergie, de portée de capture et de communication, de vitesse de traitement et de capacité de stockage. Ils sont déployés dans un environnement intérieur ou extérieur, et ce dans de nombreux domaines d'application tels que l'armée, l'environnement, la santé, la maison et l'agriculture. La rareté des ressources des noeuds capteurs et la non fiabilité des liaisons sans fil motivent la plupart des problématiques dans le domaine des RCSFs, à savoir l'énergie, la couverture, la connectivité, le routage, la tolérance aux pannes et la sécurité. L'objectif de cette thèse est de proposer un protocole de surveillance inter-couches, à efficacité énergétique et fiable, pour la surveillance des zones sensibles clôturées, tel qu'un site pétrolier ou nucléaire, utilisant les réseaux de capteurs sans fil avec un cycle d'activité, et avec prise en compte des liens asymétriques dus au phénomène de l'irrégularité de la radio. Initialement, le protocole proposé identifie les noeuds de bordure du RCSF pour les utiliser comme nœuds sentinelles, c.-à-d., des noeuds qui sont toujours dans un état actif. Les noeuds restants sont utilisés en tant que noeuds relais avec un cycle d'activité, pendant la phase de routage des alertes vers le noeud puits. Le processus d'identification des noeuds de bordure ainsi que le routage des alertes, sont assurés par le protocole Greedy Perimeter Stateless Routing through Symmetrical Links (GPSR-SL) qui est une version améliorée du protocole GPSR, reposant sur un graphe de connectivité représenté sous forme de disques non-unité (N-UDG). Le protocole de surveillance inter-couches proposé a été implémenté et ses performances ont été évaluées en utilisant l'environnement de simulation OMNeT++/Castalia. Les résultats de performance montrent que ce protocole permet d'obtenir un ratio de livraison de paquets plus élevé d'environ 3.63%, une efficacité énergétique et une latence satisfaisante par rapport au même protocole basé sur le GPSR original. / Wireless Sensor Networks (WSNs) are a special class of Ad hoc networks, which are under intensive research.They are considered as a very powerful tool to connect the physical and the digital worlds. They consist of a largenumber of sensor nodes that are characterized with limited resources in terms of energy, range of sensing and communication, processing speed and storage capacity.They are deployed in an indoor or outdoor environment in many application domains such as army, environment, health, home and agriculture. The scarcity of sensor node resources and the unreliability of wireless links drive most of the research issues in the field of WSNs, namely energy, coverage, connectivity, routing, fault tolerance and security. The aim of this thesis is to propose an energyefficient and reliable cross-layer surveillance protocol for sensitive fenced areas, such as oil or nuclear sites, using duty-cycled WSNs with asymmetrical links due to the radio irregularity phenomenon. Initially, the proposed protocol identifies the boundary nodes of the deployedWSN, to be used as sentinel nodes, i.e., nodes that are always in an active state. The remaining nodes are usedas duty-cycled relay nodes during the routing phase to relay alerts towards the sink. The boundary nodes identification process and alert routing are both performed using an enhanced version of the Greedy Perimeter Stateless Routing (GPSR) protocol, referred to as GPSR over Symmetrical Links (GPSR-SL) and which relies on a Non Unit Disk Graph (N-UDG). The proposed cross-layer surveillance protocol has been implemented and its performance has been evaluated under the OMNeT++/Castalia simulation environment. Performance results show that this protocol achieves higher Packet Delivery Ratio by up to 3.63%, energy .efficiency and satisfactory latency when compared to the same protocol based on the original GPSR.

O comportamento do câncer de mama pode ser influenciado pela interação entre células tumorais e estromais que infiltram e circundam o tumor. Acredita-se também que as células que compõem o microambiente linfonodal possam influenciar o perfil da expressão gênica de células mamárias malignas MDA-MB231, induzindo ou inibindo o desenvolvimento de metástase regional. Para avaliar essa possibilidade, células MDA-MB231 foram co-cultivadas com fibroblastos obtidos de linfonodos comprometidos ou não comprometidos de pacientes com câncer de mama, separadas por membranas porosas por 72 horas. O perfil da expressão gênica foi avaliado através de uma plataforma de cDNA microarray de 4608 genes. Observamos que 155 e 188 genes foram modulados em células MDA-MB231 na presença de fibroblastos de linfonodos não comprometidos e comprometidos, respectivamente, quando comparados com células MDA-MB231 cultivadas isoladamente. Análise do agrupamento hierárquico não supervisionado utilizando os genes diferencialmente expressos revelou a presença de dois grupos, um constituído por células MDA-MB 231 em monocultura e outro por células mantidas em co-cultura com fibroblastos. Splicing de RNAm, via spliceossoma, ciclo celular e regulação da transcrição por promotores da RNA polimerase II, foram algumas funções moduladas em células MDA-MB231. A seguir novos ensaios de co-cultura foram realizados e a expressão de alguns genes foram analisados por RT-PCR. FN3K e COMT foram menos expressos em células MDA-MB231 na presença de fibroblastos de linfonodos, mas não em co-cultura com células MCF-7, nas quais apenas HTRA1 mostrou-se hipoexpresso em casos de co-cultura com fibroblastos. Esses resultados sugerem que a inter-relação entre células estromais e células tumorais são dependentes do subtipo do tumor, de fenótipo luminal ou basal / Breast cancer behavior may be influenced by interactions between cancer and stromal cells, which infiltrate and surround the tumor. It is also believed that cells within the lymph node microenvironment may influence the gene expression profile of breast cancer cells, stimulating or inhibiting regional metastasis development. To evaluate this possibility, breast cancer MDAMB231 cells were co-cultured with fibroblasts obtained from involved or uninvolved lymph nodes from breast cancer patients, using a porous membrane, for 72 hours. Gene expression profile was evaluated through a cDNA microarray platform containing 4608 genes. MDA-MB231 cells had 155 and 188 genes modulated by the presence of fibroblasts from uninvolved or involved nodes, respectively, as compared to MDA-MB231 cells cultured alone. Unsupervised hierarchical clustering using the differentially expressed genes revealed the presence of two groups, one comprising MDA-MB231 cells cultured aloned and another one, MDA-MB231 cells co-cultured with fibroblasts. Nuclear mRNA splicing, via spliceosome, cell cycle, and regulation of transcription from RNA polymerase II promoter, were functions regulated in cocultured MDA-MB231 cells. New co-culture assays were performed and expression of a few genes was further evaluated by RT-PCR. FN3K and COMT were both down-regulated in MDA-MB231 cells in the presence of nodes\' fibroblasts, but not in co-cultured MCF7 cells, while HTRA1 was just down regulated in MCF7 co-cultured cells. These results suggest that the interrelationship between stromal and cancer cells are dependent on the subtype of tumor, whether from luminal or basal-like phenotype

O desenvolvimento da metástase depende, entre outros fatores de um microambiente propício e é possível que as células do câncer de mama influenciem o perfil da expressão gênica das células estromais, tanto no tumor primário como no linfonodo regional. Para estudar este último evento obtivemos fibroblastos de linfonodos comprometidos (n=3) ou não (n=3) de pacientes com câncer de mama, os quais foram co-cultivados com células de câncer de mama MDA-MB-231, separados fisicamente por membranas porosas por 72 horas. O perfil da expressão gênica foi determinado utilizando-se uma plataforma de cDNA microarray. A presença de células MDA-MB231 modulou a expressão de 415 genes em fibroblastos de linfonodos não comprometidos e 779 genes em fibroblastos de linfonodos comprometidos, em relação a células mantidas em mono-cultura, sendo que 120 genes tiveram sua expressão reguladas em ambas comparações. A expressão destes genes determinou a separação dos fibroblastos mantidos em co-cultura daqueles mantidos isoladamente em cultura por análise de agrupamento hierárquico, indicando que a presença das células de câncer de mama influencia o perfil da expressão gênica das células. Entre as funções reguladas pela presença de células MDA-MB231 encontramse tradução e receptor de superfície ligado à transmissão de sinal, em fibroblastos de linfonodos não comprometidos e autofosforilação de proteína e ciclo celular, em fibroblastos de linfonodos comprometidos. Para determinar se a expressão gênica diferencial é um fenômeno que pode ser generalizado para o câncer de mama, realizamos ensaios utilizando outras amostras de fibroblastos obtidos de linfonodos comprometidos de 5 pacientes e de linfonodos não comprometidos de outras 5 pacientes (incluindo as 6 amostras de fibroblastos previamente analisadas), as quais foram co-cultivadas com três linhagens celulares de câncer de mama (MDA-MB231, MDA-MB435 e MCF-7). A expressão relativa de MAP2K3, AKAP8L e CREG1, inicialmente identificados como diferencialmente expressos em análise de cDNA microarray, foi então determinada por RT-PCR em tempo real. Observamos que nenhuma das três linhagens celulares influenciou a expressão de AKAP8L e CREG1 tanto em fibroblastos de linfonodos comprometidos quanto não comprometidos. MAP2K3 foi hiperexpresso tanto em fibroblastos de linfonodos comprometidos quanto em não comprometidos co-cultivados com células MDA-MB231, mas não com células MDA-MB435 ou MCF-7. Nossos resultados indicam que a presença de células MDA-MB231 influencia o perfil de expressão gênica de fibroblastos originário tanto de linfonodos comprometidos quanto de não comprometidos. Alguns genes comumente regulados em fibroblastos de linfonodo comprometido ou não comprometidos, incluindo MAP2K3, podem estar envolvidos no estabelecimento de metástase regional. / Metastasis development may depend on a favorable microenvironment and breast cancer cells may influence stromal cells gene expression profile not only in the primary site but also in the lymph nodes. To study the latter event, fibroblasts were obtained from involved or uninvolved lymph nodes from six breast cancer patients and co-cultivated with breast cancer MDA-MB-231 cells, physically separated by porous membranes, for 72 hours. The gene expression profile was determined utilizing a cDNA microarray platform. The presence of MDA-MB231 cells modulated the expression of 415 genes in fibroblasts from uninvolved nodes and 779 genes in fibroblasts from involved nodes, as compared to fibroblasts cultured isolated, including 120 genes, which were regulated in fibroblasts from both origins. Unsupervised hierarchical clustering allowed a correct segregation of fibroblasts co-cultured with MDA-MB231 cells from fibroblasts cultured alone, indicating that the gene expression profile gene is influenced by the presence of breast cancer cells. Functions, which were regulated by presence of MDA-MB231 cells included translation and cell surface receptor linked signal transduction in fibroblasts from uninvolved nodes and protein autophosphorylation and cell cycle in fibroblasts from involved nodes. To determine whether this differential gene expression was a general process influenced by breast cancer cells, further assays were performed utilizing samples of fibroblasts from involved (n=5) and uninvolved nodes (n=5) from breast cancer patients (including the 6 samples of fibroblasts previously analyzed), which were co-cultured with three breast cancer cell lines (MDAMB231, MDA-MB435 and MCF-7). Relative expression of MAP2K3, AKAP8L and CREG1, initially identified as differentially expressed in co-cultured fibroblasts upon cDNA microarray analysis, was determined by RT-PCR real time. AKAP8L and CREG1 expression in fibroblasts from involved or uninvolved nodes was not influenced by the presence of any of the three cell lines. MAP2K3 was over-expressed in fibroblasts from both involved and uninvolved nodes when co-cultured with MDA-MB231 cells, but not with MDA-MB435 or MCF-7 cells. Our results indicate that the gene expression profile of fibroblasts from involved and uninvolved lymph nodes are influenced by the presence of MDA-MB231. Some genes commonly regulated in fibroblasts from both involved and uninvolved nodes, as MAP2K3, may be involved in regional metastasis establishment.

As interações epitélio-mesênquima podem influenciar o desenvolvimento do tumor no sítio primário e no linfonodo comprometido de pacientes com câncer de mama. Nosso objetivo foi avaliar a taxa de proliferação e perfil gênico de fibroblastos de linfonodos comprometidos e não comprometidos obtidos de pacientes com câncer de mama e determinar a influência de células epiteliais mamárias normais (MCF10A) ou malignas (MDA-MB-231) na expressão gênica destes fibroblastos. Foram estabelecidas culturas primárias de fibroblastos de linfonodos (3 comprometidos e 3 não comprometidos) de 6 diferentes pacientes com câncer de mama e não houve diferença na taxa de proliferação destes fibroblastos. Co-culturas de células MCF10A ou MDA-MB-231 com fibroblastos, separadas fisicamente por membranas porosas, foram realizadas por 72 horas. O RNA total dos fibroblastos foi extraído, amplificado e o perfil gênico foi analisado usando-se uma lâmina de cDNA microarray. Fibroblastos de linfonodos comprometidos e não comprometidos apresentaram perfil gênico similar, pois apenas 13 genes foram modulados, sendo que maior expressão de PGBD3 e PTBP2 em fibroblastos de linfonodos comprometidos foi confirmada em ensaios de RT-PCR em tempo real. Em fibroblastos, a cocultura com células MCF10A alterou a expressão de maior número de genes que a co-cultura com células MDA-MB-231. Em fibroblastos originários de linfonodos não comprometidos mantidos em co-cultura com células MDA-MB-231 foram modulados 151 genes, em relação aos mesmos fibroblastos cultivados na ausência de células epiteliais, sendo que oito deles apresentaram variação de expressão superior a três vezes (BET1, ENTPD1, USP7, DAPK1, ERBB2 e NCF2). As células MDA-MB-231 modularam algumas vias de sinalização em fibroblastos não comprometidos, como vias do cálcio, insulina, hormônio liberador de gonadotrofina (GnRH) e da regulação do citoesqueleto de actina, mas o mesmo não ocorreu em fibroblastos de linfonodos comprometidos. Duzentos e quarenta e nove genes foram diferencialmente expressos em fibroblastos originários de linfonodos comprometidos mantidos em co-cultura com células MDA-MB-231 e quatro genes apresentaram variação superior a três vezes (ACLY, AXUD1, CLCN5 e PDE6D). Nestes fibroblastos, algumas funções biológicas foram reguladas apenas por influência da célula MDA-MB-231, entre as quais metabolismo de aminoácidos, excreção, transporte intra Golgi e regulação da forma celular. As vias de sinalização e funções biológicas reguladas em fibroblastos pela interação com células epiteliais malignas podem estar implicadas no desenvolvimento de metástases regionais no câncer de mama. / Tumor development may be influenced by epithelial-mesenchimal interactions in the primary site as well as in the involved lymph node from breast cancer patients. Our aim was to evaluate the proliferation rate and gene profile of fibroblasts obtained from involved and uninvolved lymph nodes from breast câncer patients and to determine the influence of normal (MCF10A) or malignant (MDA-MB-231) mammary epithelial cells on the gene expression of these fibroblasts. Primary culture from fibroblasts obtained from 3 involved and 3 uninvolved lymph nodes (ILF and NILF) from 6 different breast cancer patients was established and no difference in their proliferation rate was detected. These fibroblasts were co-cultured with MCF10A or MDA-MB-231 cells, physically separated by a porous membrane for 72 hours. Total RNA was extracted from the cells, amplified and the gene profile from fibroblasts cultured alone or with epithelial cells was analyzed by cDNA microarray slides. Fibroblasts from involved and uninvolved lymph nodes present a similar gene profile as only 13 genes were differentially expressed between them, including PGBD3 and PTBP2, which higher expression in fibroblasts from involved lymph nodes was confirmed by real time RT-PCR. In fibroblasts, more genes seem to be regulated upon co-cultured with MCF10A than with MDA-MB-231 cells. In fibroblasts from uninvolved lymph nodes co-cultured with MDA-MB-231 cells, 151 genes were modulated as compared with fibroblasts cultured alone, and eight of them, presented an expression variation superior to three times (BET1, ENTPD1, USP7, DAPK1, ERBB2 e NCF2). In these fibroblasts, MDA-MB-231 could modulate some signaling pathways as calcium, insulin, gonadotrophin releasing hormone (GnRH) and actin cytoskeleton regulation signaling pathways. Two hundred forty nine genes were differentially expressed by fibroblasts from involved lymph nodes co-cultured with MDA-MB-231 cells, four of which with an expression variation superior to three times (ACLY, AXUD1, CLCN5 e PDE6D). In the last condition, fibroblasts had some biological functions regulated upon MDA-MB-231 cells influence, among which amino acid metabolism, excretion, intra-Golgi transport and regulation of cell shape. Signaling pathways and biological functions regulated in fibroblasts after interaction with malignant epithelial cells might be implicated in the development of regional metastasis in breast cancer.

We study Social Groups consisting of self-interested inter-connected nodes looking for common content. We can observe Social Groups in various socio-technological networks, such as Cellular Network assisted Device-to-Device communications, Cloud assisted Peer-to-Peer Networks, hybrid Peer-to-Peer Content Distribution Networks and Direct Connect Networks. Each node wants to acquire a universe of segments at least cost. Nodes can either access an expensive link to the content distributor for downloading data segments, or use the well-connected low cost inter-node network for exchanging segments among themselves. Activation of an inter-node link requires cooperation among the participating nodes and reduces the cost of downloading for the nodes. However, due to uploading costs, Non-Reciprocating Nodes are reluctant to upload segments, in spite of their interest in downloading segments from others. We define the Give-and-Take (GT) criterion, which prohibits non-reciprocating behaviour in Social Groups for all nodes at all instants. In the “Full Exchange” case studied, two nodes can exchange copies of their entire segment sets, if each node gains at least one new segment from the other. Incorporating the GT criterion in the Social Group, we study the problem of downloading the universe at least cost, from the perspective of a new node having no data segments. We analyze this NP-hard problem, and propose algorithms for choosing the initial segments to be downloaded from the content distributor and the sequence of nodes for exchange. We compare the performance of these algorithms with a few existing P2P downloading strategies in terms of cost and running time. In the second problem, we attempt to reduce the load on the content distributor by choosing a schedule of inter-node link activations such that the number of nodes with the universe is maximized. Link activation decisions are taken by a central entity, the facilitator, for achieving the social optimum. We present the asymptotically optimal Randomized algorithm. We also present other algorithms, such as the Greedy Links algorithm and the Polygon algorithm, which are optimal under special scenarios of interest. We compare the performances of all proposed algorithms with the optimal value of the objective. We observe that computationally intensive algorithms exhibit better performance. Further, we consider the problem of decentralized scheduling of links. The decisions of link activations are made by the participating nodes in a distributed manner. While conforming to the GT criterion for inter-node exchanges, each node's objective is to maximize its utility. Each node tries to find a pairing partner by preferentially exploring nodes for link formation. Unpaired nodes choose to download a segment using the expensive link with Segment Aggressiveness Probability (SAP). We present linear complexity decentralized algorithms for nodes to choose their best strategy. We present a decentralized randomized algorithm that works in the absence of the facilitator and performs close to optimal for large number of nodes. We define the Price of Choice to benchmark performance of Social Groups (consisting of non-aggressive nodes) with the optimal. We evaluate the performance of various algorithms and characterize the behavioural regime that will yield best results for node and Social Group as well.

Resource allocation in wireless networks is one of the most studied class of problems. Generally, these problems are formulated as utility maximization problems under relevant constraints. The challenges posed by these problems vary widely depending on the nature of the utility function under consideration. Recently, the widespread prevalence of wireless devices prompted researchers and engineers to delve into the security issues of wireless communication. As compared to the wired medium, ensuring security for the wireless medium is more challenging mainly due to the broadcast nature of the transmission. But the ongoing research on physical layer security promises robust and reliable security schemes for wireless communication. Contrary to conventional cryptographic schemes, physical layer security techniques are impregnable as the security is ensured by the inherent randomness present in the wireless medium. In this thesis, we consider several wireless scenarios and propose secrecy enhancing resource allocation schemes for them in the first few chapters. We initially address the problem of secure transmission by following the conventional approach in the secrecy literature|secrecy rate maximization. Needless to say, in these chapters, secrecy rate is the utility function and the constraints are posed by the available power budget. Then we consider a pragmatic approach where we target the signal-to-noise ratio (SNR) of participating nodes and ensure information secrecy by appropriately constraining the SNRs of those nodes. In those SNR based formulations, SNR at the destination is the utility function and we are interested in maximizing it. In the last two chapters, we study two scenarios in a non-secrecy setting. In one of them, end-to-end data rate is the utility, whereas, in the other one, two utility functions|based on revenue generated|are defined for two rational agents in a game-theoretic setting. In the second chapter, we study parallel independent Gaussian channels with imperfect channel state information (CSI) for the eavesdropper. Firstly, we evaluate the probability of zero secrecy rate in this system for (i) given instantaneous channel conditions and (ii) a Rayleigh fading scenario. Secondly, when non-zero secrecy is achievable in the low SNR regime, we aim to solve a robust power allocation problem which minimizes the outage probability at a target secrecy rate. In the third, fourth and fifth chapters, we consider scenarios where the source node transmits a message to the destination using M parallel amplify-and-forward (AF) relays in the presence of a single or multiple eavesdroppers. The third chapter addresses the problem of the maximum achievable secrecy rate for two specific network models: (a) degraded eavesdropper channel with complex channel gain and (b) scaled eavesdropper channel with real-valued channel gains. In the fourth chapter, we consider the SNR based approach and address two problems: (i) SNR maximization at the destination and (ii) Total relay power minimization. In the fifth chapter, we assume that the relay nodes are untrusted and to counter them, we deliberately introduce artificial noise in the source message. For this model, we propose and solve SNR maximization problems for the following two scenarios: (i) Total power constraint on all the relay nodes and (ii) Individual power constraints on each of the relay nodes. In the sixth chapter, we address the problem of passive eavesdroppers in multi-hop wire-less networks using the technique of friendly jamming. Assuming decode-and-forward (DF) relaying, we consider a scheduling and power allocation (PA) problem for a multiple-source multiple-sink scenario so that eavesdroppers are jammed, and source-destination throughput targets are met. When channel state information (CSI) of all the node are available, we intend to minimize the total power consumption of all the transmitting nodes. In the absence of eavesdroppers CSI, we minimize vulnerability region of the network. In chapter seven, the problem of cooperative beamforming for maximizing the achievable data rate of two-hop amplify-and-forward (AF) network (in the absence of eavesdropper(s)) is considered. Along with an individual power constraint on each of the relay nodes, we consider a weighted sum power constraint. To solve this problem, we propose a novel algorithm based on the Quadratic Eigenvalue Problem (QEP) and discuss its convergence. In chapter eight, we study a Stackelberg game between a base station and a multi-antenna power beacon for wireless energy harvesting in a multiple sensor node scenario. Assuming imperfect CSI between the sensor nodes and the power beacon, we propose a utility function that is based on throughput non-outage probability at the base station. We find the optimal strategies for the base station and the power beacon that maximize their respective utility functions.

Advances in wireless communication and microelectronics have led to the development of low-power compact sensor nodes (popularly called motes) that are capable of sensing, computing, and communication. A large number of these nodes can be deployed over some area of interest to form a multi-hop network, commonly referred to as a wireless sensor network (WSN). Typical applications of WSNs include, environment and process monitoring in industrial installations, forest fire detection, structural health monitoring, etc. In such applications where the variables to be measured are slowly varying, or the events to be monitored are rare, continuous sensing is unnecessary. Instead, the nodes, in order to conserve their battery power, can sleep-wake cycle whereby each node is allowed to independently alternate between an ON state and a low power OFF state. Sleep-wake cycling, while increasing the network lifetime, renders the network disconnected a large fraction of the time; however, connectivity can be established over time by transporting packets in a store-and-forward manner, whereby packets are held by a forwarding node until a suitable node wakes up in its neighborhood that can serve to forward the packet towards the destination. We are concerned with sleep-wake cycling multi-hop wireless networks whose main task is to carry sporadic alarms packets from sensing nodes to a sink node. Our objective is to design simple local-information based routing solutions for such networks. With this in mind, we propose a relay selection problem that arises at a forwarding node (which is currently holding the alarm packet) while choosing a next-hop relay node. The forwarder, as and when the relays wake-up, evaluating the goodness of a relay based on a “reward” metric (e.g., a function of the relay’s progress towards sink, and the power required to get the packet across), has to decide whether to forward to this relay or to wait for future ones (i.e., to stop or continue). The forwarder’s objective is to choose a relay so as to minimize a combination of the average delay incurred and the average reward achieved. A basic version of our relay selection problem is equivalent to the basic asset selling problem studied in the operations research literature. After reviewing the solution to the basic problem we will proceed to study a model with full information, referred to as the completely observable (CO) model, where the number of relays is exactly known to the forwarder. Formulating the problem as a Markov decision process (MDP) we will characterize the solution to the CO model in terms of recursively-computable threshold functions. Next, we consider the partially observable (PO) model where only a belief (probability mass function) on the number of relays is known. Hence, the PO model falls within the realm of partially observable MDPs. After incorporating our model into this framework we will characterize the solution in terms of stopping sets, which is the set of all belief states where it is optimal to stop. Our main contribution here is to obtain inner and outer bounds for the stopping sets. We next propose a variant where the relays, upon waking up, do not reveal their rewards immediately, but instead the forwarder can choose to probe the relay to know its reward, incurring a probing cost. Thus, to the existing set of stop and continue actions, we have added a new probe action. This model is motivated by the efforts required to learn the channel gains (by probing) in a wireless system. A key result we prove here is that the solution is characterized in terms of stage independent thresholds. Finally, we study a model comprising two forwarders which are competing against each other to choose a next-hop relay (one for each). Here, a relay is allowed to offer possibly different reward to each forwarder. We will first consider a complete information case where the reward pair of a relay is known to both the forwarders. Using stochastic game theory we will characterize the solution to this model in terms of Nash equilibrium policy pairs (NEPPs). We obtain results illustrating the structure of NEPPs. Next, we study a partial information model where each forwarder gets to observe only its reward value. Towards obtaining the solution for this model, we will first formulate a Bayesian game which is effectively played by both the forwarders at each stage. Next, for this Bayesian game we prove the existence of Nash equilibrium strategies within the class of threshold strategies. This result will enable us to construct NEPPs for the partial information model. Although our primary contribution from the thesis is the theoretical study of the above mentioned variants of the basic relay selection model, we have also conducted extensive simulations to study the end-to-end performance obtained by applying the solution to these models at each hop en-route to the sink in a sleep-wake cycling WSN.

This thesis presents the development of a Sensor Tower Platform (STP) comprised of an array of Passive Infra-Red (PIR) sensors along with a classification algorithm that enables the STP to distinguish between human intrusion, animal intrusion and clutter arising from wind-blown vegetative movement in an outdoor environment. The research was motivated by the aim of exploring the potential use of wireless sensor networks (WSNs) as an early-warning system to help mitigate human-wildlife conflicts occurring at the edge of a forest. While PIR sensors are in commonplace use in indoor settings, their use in an outdoor environment is hampered by the fact that they are prone to false alarms arising from wind-blown vegetation. Every PIR sensor is made up of one or more pairs of pyroelectric pixels arranged in a plane, and the orientation of interest in this thesis is one in which this plane is a vertical plane, i.e., a plane perpendicular to the ground plane. The intersection of the Field Of View (FOV) of the PIR sensor with a second vertical plane that lies within the FOV of the PIR sensor, is called the virtual pixel array (VPA). The structure of the VPA corresponding to the plane along which intruder motion takes place determines the form of the signal generated by the PIR sensor. The STP developed in this thesis employs an array of PIR sensors designed so as to result in a VPA that makes it easier to discriminate between human and animal intrusion while keeping to a small level false alarms arising from vegetative motion. The design was carried out in iterative fashion, with each successive iteration separated by a lengthy testing phase. There were a total of 5 design iterations spanning a total period of 14 months. Given the inherent challenges involved in gathering data corresponding to animal intrusion, the testing of the SP was carried out both using real-world data and through simulation. Simulation was carried out by developing a tool that employed animation software to simulate intruder and animal motion as well as some limited models of wind-blown vegetation. More specifically, the simulation tool employed 3-dimensional models of intruder and shrub motion that were developed using the popular animation software Blender. The simulated output signal of the PIR sensor was then generated by calculating the area of the 3-dimensional intruder when projected onto the VPA of the STP. An algorithm for efficiently calculating this to a good degree of approximation was implemented in Open Graphics Library (OpenGL). The simulation tool was useful both for evaluating various competing design alternatives as well as for developing an intuition for the kind of signals the SP would generate without the need for time-consuming and challenging animal-motion data collection. Real-world data corresponding to human motion was gathered on the campus of the Indian Institute of Science (IISc), while animal data was recorded at a dog-trainer facility in Kengeri as well as the Bannerghatta Biological Park, both located in the outskirts of Bengaluru. The array of PIR sensors was designed so as to result in a VPA that had good spatial resolution. The spatial resolution capabilities of the STP permitted distinguishing between human and animal motion with good accuracy based on low-complexity, signal-energy computations. Rejecting false alarms arising from vegetative movement proved to be more challenging. While the inherent spatial resolution of the STP was very helpful, an alternative approach turned out to have much higher accuracy, although it is computationally more intensive. Under this approach, the intruder signal, either human or animal, was modelled as a chirp waveform. When the intruder moves along a circular arc surrounding the STP, the resulting signal is periodic with constant frequency. However, when the intruder moves along a more likely straight-line path, the resultant signal has a strong chirp component. Clutter signals arising from vegetative motion does not exhibit this chirp behavior and an algorithm that exploited this difference turned in a classification accuracy in excess of 97%.

This thesis is concerned with several issues of a posteriori error estimates for linear problems. In its first part error estimates for the heat conduction equation discretized by the backward Euler method in time and discontinuous Galerkin method in space are derived. In the second part guaranteed and locally efficient error estimates involving algebraic error for Poisson equation discretized by the discontinuous Galerkin method are derived. The technique is based on the flux reconstruction where meshes with hanging nodes and variable polynomial degree are allowed. An adaptive strategy combining both adaptive mesh refinement and stopping criteria for iterative algebraic solvers is proposed. In the last part a numerical method for computing guaranteed lower and upper bounds of principal eigenvalues of symmetric linear elliptic differential operators is presented. 1

This thesis consists of two main parts. First of all, the condition number of rectangular Vandermonde matrices with nodes on the complex unit circle is studied. The first time quantitative bounds for the extreme singular values are proven in the multivariate setting and when nodes of the Vandermonde matrix form clusters. In the second part, an optimized presentation of the deterministic stability analysis of the subspace method ESPRIT is given and results from the first part are applied.