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Yayın Fully decentralized and collaborative multilateration primitives for uniquely localizing WSNs(Springer International Publishing AG, 2010) Çakıroğlu, Olca Arda; Erten, CesimWe provide primitives for uniquely localizing WSN nodes. The goal is to maximize the number of uniquely localized nodes assuming a fully decentralized model of computation. Each node constructs a cluster of its own and applies unique localization primitives on it. These primitives are based on constructing a special order for multilaterating the nodes within the cluster. The proposed primitives are fully collaborative and thus the number of iterations required to compute the localization is fewer than that of the conventional iterative multilateration approaches. This further limits the messaging requirements. With relatively small clusters and iteration counts, we can localize almost all the uniquely localizable nodes.Yayın Constant angle surfaces in the Lorentzian warped product manifold I ×f E²1(Tübitak, 2022-09-14) Dursun, UğurLet I ×f E²1 be a 3-dimensional Lorentzian warped product manifold with the metric g˜ = dt² + f² (t)(dx² ? dy² ), where I is an open interval, f is a strictly positive smooth function on I, and E²1 is the Minkowski 2-plane. In this work, we give a classification of all space-like and time-like constant angle surfaces in I ×f E²1 with nonnull principal direction when the surface is time-like. In this classification, we obtain space-like and time-like surfaces with zero mean curvature, rotational surfaces, and surfaces with constant Gaussian curvature. Also, we have some results on constant angle surfaces of the anti-de Sitter space H³1(?1).Yayın Largest eigenvalues of the discrete p-Laplacian of trees with degree sequences(Int Linear Algebra Soc, 2009-03) Bıyıkoğlu, Türker; Hellmuth, Marc; Leydold, JosefTrees that have greatest maximum p-Laplacian eigenvalue among all trees with a given degree sequence are characterized. It is shown that such extremal trees can be obtained by breadth-first search where the vertex degrees are non-increasing. These trees are uniquely determined up to isomorphism. Moreover, their structure does not depend on p.Yayın Force-directed approaches to sensor localization(Assoc Computing Machinery, 2010-09) Efrat, Alon; Forrester, David; Iyer, Anand; Kobourov, Stephen G.; Erten, Cesim; Kılıç, Yasin OzanAs the number of applications of sensor networks increases, so does the interest in sensor network localization, that is, in recovering the correct position of each node in a network of sensors from partial connectivity information such as adjacency, range, or angle between neighboring nodes. In this article, we consider the anchor-free localization problem in sensor networks that report possibly noisy range information and angular information about the relative order of each sensor's neighbors. Previously proposed techniques seem to successfully reconstruct the original positions of the nodes for relatively small networks with nodes distributed in simple regions. However, these techniques do not scale well with network size and yield poor results with nonconvex or nonsimple underlying topology. Moreover, the distributed nature of the problem makes some of the centralized techniques inapplicable in distributed settings. To address these problems we describe a multiscale dead-reckoning (MSDR) algorithm that scales well for large networks, can reconstruct complex underlying topologies, and is resilient to noise. The MSDR algorithm takes its roots from classic force-directed graph layout computation techniques. These techniques are augmented with a multiscale extension to handle the scalability issue and with a dead-reckoning extension to overcome the problems arising with nonsimple topologies. Furthermore, we show that the distributed version of the MSDR algorithm performs as well as, if not better than, its centralized counterpart, as shown by the quality of the layout, measured in terms of the accuracy of the computed pairwise distances between sensors in the network.












