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.

Regulation of woody plant development by auxin and polar auxin transport

Auxin is a key regulator in plant growth and development. This dissertation examines the role of auxin and polar auxin transport in woody growth and development. Strategies of promoter reporter system, microarray expression analysis, transgenic modification, physiological assays, anatomical analysis, and histochemical/biochemical assays were employed to improve our understanding of auxin study in Populus. The results demonstrate various aspects of auxin regulation on shoot growth, root development, wood formation, and gravitropism in woody tissues. We describe the behavior of the DR5 reporter system for measuring auxin concentrations and response in stably transformed Populus trees. Our study shows that DR5 reporter system can be efficiently used in Populus to study auxin biology at a cellular resolution. We investigated the global gene expression in responding to auxin in Populus root. The results revealed groups of IBA up- and down- regulated genes involved in various biological processes including cell wall modification, root growth and lateral root formation, transporter activity and hormone crosstalk. We also verify two of the identified genes' function by transgenic modification in Populus, which encode auxin efflux carrier PtPIN9 and transcription factor PtERF72. We investigated the role of PtPIN9 in woody growth and development, especially in wood formation and gravitropic response in woody stem. We found that overexpressing PtPIN9 enhanced several growth parameters while suppression of PtPIN9 has inhibited tension wood formation. Our results show that PIN9 and other members from PIN family could be possible useful tools for increasing biomass productivity, wood quality, or in modifying plant form.