Glosarium Matematika

273 p.; 24 cm

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group

Towards Aggregating Time-Discounted Information in Sensor Networks

Sensor networks are deployed to monitor a seemingly endless list of events in a multitude of application domains. Through data collection and aggregation enhanced with data mining and machine learning techniques, many static and dynamic patterns can be found by sensor networks. The aggregation problem is complicated by the fact that the perceived value of the data collected by the sensors is affected by many factors such as time, location and user valuation. In addition, the value of information deteriorates often dramatically over time. Through our research, we already achieved some results: A formal algebraic analysis of information discounting, especially affected by time. A general model and two specific models are developed for information discounting. The two specific models formalize exponetial time-discount and linear time-discount. An algebraic analysis of aggregation of values that decay with time exponentially. Three types of aggregators that offset discounting effects are formalized and analyzed. A natural synthesis of these three aggregators is discovered and modeled. We apply our theoretical models to emergency response with thresholding and confirm with extensive simulation. For long-term monitoring tasks, we laid out a theoretical foundation for discovering an emergency through generations of sensors, analysed the achievability of a long-term task and found an optimum way to distribute sensors in a monitored area to maximize the achievability. We proposed an implementation for our alert system with state-of-art wireless microcontrollers, sensors, real-time operating systems and embedded internet protocols. By allowing aggregation of time-discounted information to proceed in an arbitrary, not necessarily pairwise manner, our results are also applicable to other similar homeland security and military application domains where there is a strong need to model not only timely aggregation of data collected by individual sensors, but also the dynamics of this aggregation. Our research can be applied to many real-world scenarios. A typical scenario is monitoring wildfire in the forest: A batch of first-generation sensors are deployed by UAVs to monitor a forest for possible wildfire. They monitor various weather quantities and recognize the area with the highest possibility of producing a fire --- the so-called area of interest (AoI). Since the environment changes dynamically, so after a certain time, the sensors re-identify the AoI. The value of the knowledge they learned about the previous AoI decays with time quickly, our methods of aggregation of time-discounted information can be applied to get update knowledge. Close to depletion of their energy of the current generation of sensors, a new generation of sensors are deployed and inherit the knowledge from the current generation. Through this way, monitoring long-term tasks becomes feasible. At the end of this thesis, we propose some extensions and directions from our current research: Generalize and extend the special classes of Type 1 and Type 2 aggregation operators; Analyze aggregation operator of Type 3 and Type 4, find some special applicable candidates; Data aggregation across consecutive generations of sensors in order to learn about events with discounting that take a long time to manifest themselves; Network implications of various aggregation strategies; Algorithms for implementation of some special classes of aggregators. Implement wireless sensor network that can autonomously learn and recognize patterns of emergencies, predict incidents and trigger alarms through machine learning

Clustering algorithm for D2D communication in next generation cellular networks : thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering, Massey University, Auckland, New Zealand

Next generation cellular networks will support many complex services for smartphones, vehicles, and other devices. To accommodate such services, cellular networks need to go beyond the capabilities of their previous generations. Device-to-Device communication (D2D) is a key technology that can help fulfil some of the requirements of future networks. The telecommunication industry expects a significant increase in the density of mobile devices which puts more pressure on centralized schemes and poses risk in terms of outages, poor spectral efficiencies, and low data rates. Recent studies have shown that a large part of the cellular traffic pertains to sharing popular contents. This highlights the need for decentralized and distributive approaches to managing multimedia traffic. Content-sharing via D2D clustered networks has emerged as a popular approach for alleviating the burden on the cellular network. Different studies have established that D2D communication in clusters can improve spectral and energy efficiency, achieve low latency while increasing the capacity of the network. To achieve effective content-sharing among users, appropriate clustering strategies are required. Therefore, the aim is to design and compare clustering approaches for D2D communication targeting content-sharing applications. Currently, most of researched and implemented clustering schemes are centralized or predominantly dependent on Evolved Node B (eNB). This thesis proposes a distributed architecture that supports clustering approaches to incorporate multimedia traffic. A content-sharing network is presented where some D2D User Equipment (DUE) function as content distributors for nearby devices. Two promising techniques are utilized, namely, Content-Centric Networking and Network Virtualization, to propose a distributed architecture, that supports efficient content delivery. We propose to use clustering at the user level for content-distribution. A weighted multi-factor clustering algorithm is proposed for grouping the DUEs sharing a common interest. Various performance parameters such as energy consumption, area spectral efficiency, and throughput have been considered for evaluating the proposed algorithm. The effect of number of clusters on the performance parameters is also discussed. The proposed algorithm has been further modified to allow for a trade-off between fairness and other performance parameters. A comprehensive simulation study is presented that demonstrates that the proposed clustering algorithm is more flexible and outperforms several well-known and state-of-the-art algorithms. The clustering process is subsequently evaluated from an individual user’s perspective for further performance improvement. We believe that some users, sharing common interests, are better off with the eNB rather than being in the clusters. We utilize machine learning algorithms namely, Deep Neural Network, Random Forest, and Support Vector Machine, to identify the users that are better served by the eNB and form clusters for the rest of the users. This proposed user segregation scheme can be used in conjunction with most clustering algorithms including the proposed multi-factor scheme. A comprehensive simulation study demonstrates that with such novel user segregation, the performance of individual users, as well as the whole network, can be significantly improved for throughput, energy consumption, and fairness

Fuzzy logic applied to system control to enhance commercial appliance performance

The purpose of this research is to determine the usefulness of fuzzy logic and fuzzy control when applied to a commercial appliance. Fuzzy logic is a structured, model-free estimator that approximates a function through linguistic input/output associations. Fuzzy rule-based systems apply these methods to solve many types of real-world problems, especially where a system is difficult to model, is controlled by a human operator or expert, or where ambiguity or vagueness is common. This dissertation presents fuzzy sets, fuzzy systems, and fuzzy control, with an example conveying the use of fuzzy control of a consumer product and an overview of fuzzy logic in the field of artificial intelligence. Ultimately, it demonstrates that the use of fuzzy systems makes a viable addition to the field of artificial intelligence and, perhaps, more generally to the application of other consumer products to reduce energy consumption and increase the ease of operation. Topics such as classical logic, set theory, fuzzy set theory, and fuzzy mathematics are developed in this research to provide a foundation in fuzzy logic. Fuzzy logic is an excellent development of a basic home appliance to provide a powerful and user-friendly device. Fuzzy logic allows an engineer without a great knowledge of control systems and mathematical modeling a viable alternative in product creation. The fuzzy logic toolbox of the program MATLAB\sp{\rm TM} developed by The Mathworks Corporation is used to build and test the fuzzy logic systems explored by this dissertation. Again, in this dissertation the concept of fuzzy logic shall be explored in detail. Background and theoretical information shall be derived to provide a good base for applications. Classical logic, crisp sets, fuzzy sets, and operations on fuzzy sets are explained in order to cover a wide spectrum of applications. The focus or cumulating point will be to apply the fuzzy logic principle to any type of consumer appliance (such as a washing machine). The use of fuzzy logic will allow many household goods to be manufactured more quickly and with more options, and be energy efficient, user friendly, and cost effective