In this paper, we investigate and characterize the effects of multi-channel and rendezvous protocols on the connectivity of dynamic spectrum access networks using percolation theory. In particular, we focus on the scenario where the secondary nodes have plenty of vacant channels to choose from a phenomenon which we define as channel abundance. To cope with the existence of multi-channel, we use two types of rendezvous protocols: naive ones which do not guarantee a common channel and advanced ones which do. We show that, with more channel abundance, even with the use of either type of rendezvous protocols, it becomes difficult for two nodes to agree on a common channel, thereby, potentially remaining invisible to each other. We model this invisibility as a Poisson thinning process and show that invisibility is even more pronounced with channel abundance. Following the disk graph model, we represent the multiple channels as parallel edges in a graph and build a multi-layered graph (MLG) in R2. In order to study the connectivity, we show how percolation occurs in the MLG by coupling it with a typical discrete percolation. Using a Boolean model and the MLG, we study both cases of primaries' absence and presence. For both cases, we define and characterize connectivity of the secondary network in terms of the available number of channels, deployment densities, number of simultaneous transmissions per node, and communication range. When primary users are absent, we derive the critical number of channels which maintains supercriticality of the secondary network. When primary users are present, we characterize and analyze the connectivity for all the regions: channel abundance, optimal, and channel deprivation. For each region we show the requirement and the outcome of using either type of rendezvous techniques. Moreover, we find the tradeoff between deployment-density versus rendezvous probability which results in a connected network. Our results can be used to decide on the goodness of any channel rendezvous algorithm by computing the expected resultant connectivity. They also provide a guideline for achieving connectivity using minimal resources.
Resumen
El Ultraísmo es un movimiento literario que comenzó en España a finales de 1918 y continuó hasta el año 1922. Este movimiento, que representó la contribución de España al Vanguardismo literario, que en la primera parte del siglo XX surgió en toda Europa, se desarrolló no tanto a través de los libros, cuanta a través de las revistas literarias de la época.
La creacionista es, sin duda, la escuela que dio a Ultra mayores aportes. Por esta razón, en las literaturas de Vanguardia se funden, y a veces también se confunden, con frecuencia, Ultraísmo y Creacionismo. Los dos movimientos eran como una revo
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The study was reflection of the impact of the widespread use of polymer Novolak composite reinforced Glass fiber and Asbestos fiber once again with weight fraction 60% on the physical properties, which included (Hardness, Compressive deformation, compressive modulus of elasticity, Flexural modulus of elasticity, Resilience modulus, the maximum of Flexural strength, Flexural strain energy and Shear strength inner layers); it is known how much important the media as a source of bacterial contamination, which contributes directly or indirectly in the process of aging of these materials. These Novolak composite reinforced, prepared by weight fraction of (10%) and (14%) of the Hexamethylene-tetraamine (HMTA) hardener material. It
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... Show MoreBackground: Diabetic is a chronic systemic disorder of glucose metabolism. That could be diagnosed using fasting and/or random plasma glucose and Glycated Haemoglobin (HbA1c). Several biochemical and microbial alterations of saliva could affect dental caries occurrence and severity among diabetic patients. The aim of the present study was to assess the relation of salivary glucose with severity of dental caries and Mutans Streptococci, among uncontrolled and controlled diabetic groups in comparison with non-diabetic control group. Materials and Methods: The total sample composed of adults aged (18-22) years. Divided into 25 uncontrolled diabetic patients (HbA1c > 7), 25 controlled diabetic patients (HbA1c ≤ 7), in addition to 25 no
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... Show MoreThe Arab realized that proverbs and their stories had a great literary and linguistic significance, accordingly, they collected them from their sources and wrote them down. Thus, researchers went in studying them in different directions. The aim of the present research is thus to study the stories of proverbs in the Holy Qur’an, Prophet’s hadiths, and in the sayings of Arabs. Such a study helps to show the extent of the relevance of their stories to the proverbs, their literary values, the points of convergence between them and what they highlight, and the extent of their proximity to reality. It further helps to determine the factors that contributed to the transformation of Quranic verses, Prophet’s hadiths, and some phrases of s
... Show MoreThe importance of research and study of classical Persian literature is not overlooked. So far, there have been many studies in this area. But there are still some things that need more research. Persian grammar is one of the most important branches of Persian literature. This section has always been converted at different times. One of the issues that has been neglected in the studies of classical literature is the study of the technical tales of past and past poetry. These texts can be studied from different perspectives. Because Persian is a mixed language, it is possible to combine language terms with each other or to add prefixes and suffixes to express new concepts. They can be used by exam
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