MODULARITY BASED FUZZY COMMUNITY DETECTION IN SOCIAL NETWORKS

Fuzzy community detection is to identify fuzzy communities in a network, which are groups of vertices in the network such that the membership of a vertex in one community is in [0,1] and that the sum of memberships of vertices in all communities equals to 1. Fuzzy communities are pervasive in social networks, but only a few works have been done for fuzzy community detection. Recently, a one-step forward extension of Newman’s Modularity, the most popular quality function for disjoint community detection, results into the Generalized Modularity (GM) that demonstrates good performance in finding well-known fuzzy communities. Thus, GMis chosen as the quality function in our research. We first propose a generalized fuzzy t-norm modularity to investigate the effect of different fuzzy intersection operators on fuzzy community detection, since the introduction of a fuzzy intersection operation is made feasible by GM. The experimental results show that the Yager operator with a proper parameter value performs better than the product operator in revealing community structure. Then, we focus on how to find optimal fuzzy communities in a network by directly maximizing GM, which we call it Fuzzy Modularity Maximization (FMM) problem. The effort on FMM problem results into the major contribution of this thesis, an efficient and effective GM-based fuzzy community detection method that could automatically discover a fuzzy partition of a network when it is appropriate, which is much better than fuzzy partitions found by existing fuzzy community detection methods, and a crisp partition of a network when appropriate, which is competitive with partitions resulted from the best disjoint community detections up to now. We address FMM problem by iteratively solving a sub-problem called One-Step Modularity Maximization (OSMM). We present two approaches for solving this iterative procedure: a tree-based global optimizer called Find Best Leaf Node (FBLN) and a heuristic-based local optimizer. The OSMM problem is based on a simplified quadratic knapsack problem that can be solved in linear time; thus, a solution of OSMM can be found in linear time. Since the OSMM algorithm is called within FBLN recursively and the structure of the search tree is non-deterministic, we can see that the FMM/FBLN algorithm runs in a time complexity of at least O (n2). So, we also propose several highly efficient and very effective heuristic algorithms namely FMM/H algorithms. We compared our proposed FMM/H algorithms with two state-of-the-art community detection methods, modified MULTICUT Spectral Fuzzy c-Means (MSFCM) and Genetic Algorithm with a Local Search strategy (GALS), on 10 real-world data sets. The experimental results suggest that the H2 variant of FMM/H is the best performing version. The H2 algorithm is very competitive with GALS in producing maximum modularity partitions and performs much better than MSFCM. On all the 10 data sets, H2 is also 2-3 orders of magnitude faster than GALS. Furthermore, by adopting a simply modified version of the H2 algorithm as a mutation operator, we designed a genetic algorithm for fuzzy community detection, namely GAFCD, where elite selection and early termination are applied. The crossover operator is designed to make GAFCD converge fast and to enhance GAFCD’s ability of jumping out of local minimums. Experimental results on all the data sets show that GAFCD uncovers better community structure than GALS.

DOUBLE VAULT COMPOSTING LATRINES IN RURAL PARAGUAY : FEASIBLE CONSTRUCTION AND OPTIMAL USE

Water resource depletion and sanitation are growing problems around the world. A solution to both of these problems is the use of composting latrines, as it requires no water and has been recommended by the World Health Organization as an improved sanitation technology. However, little analysis has been done on the decomposition process occurring inside the latrine, including what temperatures are reached and what variables most affect the composting process. Having better knowledge of how outside variables affect composting latrines can aid development workers on the choice of implementing such technology, and to better educate the users on the appropriate methods of maintenance. This report presents a full, detailed construction manual and temperature data analysis of a double vault composting latrine. During the author’s two year Peace Corps service in rural Paraguay he was involved with building twenty one composting latrines, and took detailed temperature readings and visual observations of his personal latrine for ten months. The author also took limited temperature readings of fourteen community member’s latrines over a three month period. These data points were analyzed to find correlations between compost temperatures and several variables. The two main variables found to affect the compost temperatures were the seasonal trends of the outside temperatures, and the mixing and addition of moisture to the compost. Outside seasonal temperature changes were compared to those of the compost and a linear regression was performed resulting in a R2-value of 0.89. Mixing the compost and adding water, or a water/urine mixture, resulted in temperature increases of the compost 100% of the time, with seasonal temperatures determining the rate and duration of the temperature increases. The temperature readings were also used to find events when certain temperatures were held for sufficient amounts of time to reach total pathogen destruction in the compost. Four different events were recorded when a temperature of 122°F (50°C) was held for at least 24 hours, ensuring total pathogen destruction in that area of the compost. One event of 114.8°F (46°C) held for one week was also recorded, again ensuring total pathogen destruction. Through the analysis of the temperature data, however, it was found that the compost only reached total pathogen destruction levels during ten percent of the data points. Because of this the storage time recommendation outlined by the World Health Organization should be complied with. The WHO recommends storing compost for 1.5-2 years in climates with ambient temperatures of 2-20°C (35-68°F), and for at least 1 year with ambient temperatures of 20-35°C (68-95°F). If these storage durations are obtainable the use of the double vault composting latrine is an economical and achievable solution to sanitation while conserving water resources.

DC MICROGRID STABILIZATION THROUGH FUZZY CONTROL OF INTERLEAVED, HETEROGENEOUS STORAGE ELEMENTS

As microgrid power systems gain prevalence and renewable energy comprises greater and greater portions of distributed generation, energy storage becomes important to offset the higher variance of renewable energy sources and maximize their usefulness. One of the emerging techniques is to utilize a combination of lead-acid batteries and ultracapacitors to provide both short and long-term stabilization to microgrid systems. The different energy and power characteristics of batteries and ultracapacitors imply that they ought to be utilized in different ways. Traditional linear controls can use these energy storage systems to stabilize a power grid, but cannot effect more complex interactions. This research explores a fuzzy logic approach to microgrid stabilization. The ability of a fuzzy logic controller to regulate a dc bus in the presence of source and load fluctuations, in a manner comparable to traditional linear control systems, is explored and demonstrated. Furthermore, the expanded capabilities (such as storage balancing, self-protection, and battery optimization) of a fuzzy logic system over a traditional linear control system are shown. System simulation results are presented and validated through hardware-based experiments. These experiments confirm the capabilities of the fuzzy logic control system to regulate bus voltage, balance storage elements, optimize battery usage, and effect self-protection.