Exponential Random Graph Models (ERGMs) have been developed for fitting social network data on both static and dynamic levels. However, the lack of large sample asymptotic properties makes it inadequate in assessing the goodness-of-fit of these ERGMs. Simulation-based goodness-of-fit plots were proposed by Hunter et al (2006), comparing the structured statistics of observed network with those of corresponding simulated networks. In this research, we propose an improved approach to assess the goodness of fit of ERGMs. Our method is shown to improve the existing graphical techniques. We also propose a simulation based test statistic with which the model comparison can be easily achieved. / Biostatistics

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Real graph datasets are important for many science domains, from understanding epidemics to modeling traffic congestion. To facilitate access to realistic graph datasets, researchers proposed various graph generators typically aimed at representing particular graph properties. While many such graph generators exist, there are few techniques for generating graphs where the nodes have binary attributes. Moreover, generating such graphs in which the distribution of the node attributes preserves real-world characteristics is still an open challenge. This thesis introduces Borromean, a graph generating algorithm that creates synthetic graphs with binary node attributes in which the attributes obey an attribute-specific joint degree distribution. We show experimentally the accuracy of the generated graphs in terms of graph size, distribution of attributes, and distance from the original joint degree distribution. We also designed a parallel version of Borromean in order to generate larger graphs and show its performance. Our experiments show that Borromean can generate graphs of hundreds of thousands of nodes in under 30 minutes, and these graphs preserve the distribution of binary node attributes within 40% on average.

This research seeks an answer to the following question: what is the relationship between the structure of researchers' communication network and the structure of their collaborative output networks (e.g. co-authored publications, joint grant proposals, and joint patent applications), and the impact of these structures on their citation performance and the volume of collaborative research outputs? Three complementary studies are performed to answer this main question as discussed below. 1. Study I: A frequently used output to measure scientific (or research) collaboration is co-authorship in scholarly publications. Less frequently used are joint grant proposals and patents. Many scholars believe that co-authorship as the sole measure of research collaboration is insufficient because collaboration between researchers might not result in co-authorship. Collaborations involve informal communication (i.e., conversational exchange) between researchers. Using self-reports from 100 tenured/tenure-track faculty in the College of Engineering at the University of South Florida, researchers' networks are constructed from their communication relations and collaborations in three areas: joint publications, joint grant proposals, and joint patents. The data collection: 1) provides a rich data set of both researchers' in-progress and completed collaborative outputs, 2) yields a rating from the researchers on the importance of a tie to them 3) obtains multiple types of ties between researchers allowing for the comparison of their multiple networks. Exponential Random Graph Model (ERGM) results show that the more communication researchers have the more likely they produce collaborative outputs. Furthermore, the impact of four demographic attributes: gender, race, department affiliation, and spatial proximity on collaborative output relations is tested. The results indicate that grant proposals are submitted with mixed gender teams in the college of engineering. Besides, the same race researchers are more likely to publish together. The demographics do not have an additional leverage on joint patents. 2. Study II: Previous research shows that researchers' social network metrics obtained from a collaborative output network (e.g., joint publications or co-authorship network) impact their performance determined by g-index. This study uses a richer dataset to show that a scholar's performance should be considered with respect to position in multiple networks. Previous research using only the network of researchers' joint publications shows that a researcher's distinct connections to other researchers (i.e., degree centrality), a researcher's number of repeated collaborative outputs (i.e., average tie strength), and a researchers' redundant connections to a group of researchers who are themselves well-connected (i.e., efficiency coefficient) has a positive impact on the researchers' performance, while a researcher's tendency to connect with other researchers who are themselves well-connected (i.e., eigenvector centrality) had a negative impact on the researchers' performance. The findings of this study are similar except that eigenvector centrality has a positive impact on the performance of scholars. Moreover, the results demonstrate that a researcher's tendency towards dense local neighborhoods (as measured by the local clustering coefficient) and the researchers' demographic attributes such as gender should also be considered when investigating the impact of the social network metrics on the performance of researchers. 3. Study III: This study investigates to what extent researchers' interactions in the early stage of their collaborative network activities impact the number of collaborative outputs produced (e.g., joint publications, joint grant proposals, and joint patents). Path models using the Partial Least Squares (PLS) method are run to test the extent to which researchers' individual innovativeness, as determined by the specific indicators obtained from their interactions in the early stage of their collaborative network activities, impacts the number of collaborative outputs they produced taking into account the tie strength of a researcher to other conversational partners (TS). Within a college of engineering, it is found that researchers' individual innovativeness positively impacts the volume of their collaborative outputs. It is observed that TS positively impacts researchers' individual innovativeness, whereas TS negatively impacts researchers' volume of collaborative outputs. Furthermore, TS negatively impacts the relationship between researchers' individual innovativeness and the volume of their collaborative outputs, which is consistent with `Strength of Weak Ties' Theory. The results of this study contribute to the literature regarding the transformation of tacit knowledge into explicit knowledge in a university context.

Higher penetration of volatile renewable sources and increasing load demand are putting a strain on the current utility grid structure. Energy storage solutions are required to maintain grid stability and are vital components to future smart grid designs. Flywheel energy storage can be a strong part of the solution due to high cycle life capabilities and flexible design configurations that balance power and energy capacity. This dissertation focuses on developing design methodologies for advanced flywheel energy storage, with an emphasis on sizing flywheel energy storage and developing lumped parameter modeling techniques for low loss, high temperature superconducting. The first contribution of this dissertation presents a method for using an optimal control law to size flywheel energy storage and develops a design space for potential power and energy storage combinations. This method is a data driven technique, that utilizes power consumption and renewable generation data from a particular location where the storage may be placed. The model for this sizing technique includes the spinning losses, that are unique to flywheel energy storage systems and have limited this technology to short term storage applications, such as frequency and voltage regulation. For longer term storage solutions, the spinning losses for flywheels must be significantly reduced. One potential solution is to use high temperature superconducting bearings, that work by the stable levitation of permanent magnet materials over bulk superconductors. These advanced bearing systems can reduce losses to less than 0.1% stored energy per hour. In order to integrate high temperature superconducting bearings into flywheel system designs, accurate and reduced order models are needed, that include the losses and emulate the hysteretic, non-linear behavior of superconducting levitation. The next two contributions of this dissertation present a lumped parameter axissymmetric model and a 3-D lumped parameter transverse model, which can be used to evaluate bearing lifting capabilities and transverse stiffness for flywheel rotor designs. These models greatly reduce computational time, and were validated against high level finite element analysis, and dynamic experimental tests. The validation experiments are described in detail. / text

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A number of problems in Computer Vision, Natural Language Processing, and Machine Learning produce structured outputs in high-dimensional space, which makes searching for the global optimal solution extremely expensive. Thus, greedy algorithms, making trade-offs between precision and efficiency, are widely used. Unfortunately, they in general lack theoretical guarantees. In this thesis, we prove that greedy algorithms are effective and efficient to search for multiple top-scoring hypotheses from structured (neural) models: 1) Entropy estimation. We aim to find deterministic samples that are representative of Gibbs distribution via a greedy strategy. 2) Searching for a set of diverse and high-quality bounding boxes. We formulate this problem as the constrained maximization of a monotonic sub-modular function such that there exists a greedy algorithm having near-optimal guarantee. 3) Fill-in-the-blank. The goal is to generate missing words conditioned on context given an image. We extend Beam Search, a greedy algorithm applicable on unidirectional expansion, to bidirectional neural models when both past and future information have to be considered. We test our proposed approaches on a series of Computer Vision and Natural Language Processing benchmarks and show that they are effective and efficient. / Ph. D. / The rapid progress has been made in Computer Vision (e.g., detecting what and where objects are shown in an image), Natural Language Processing (e.g., translating a sentence in English to Chinese), and Machine learning (e.g., inference over graph models). However, a number of problems produce structured outputs in high-dimensional space, e.g., semantic segmentation requires predicting the labels (e.g., dog, cat, or person, etc) of all super-pixels, the search space is huge, say Lⁿ, where L is the number of object labels and n is the number of super-pixels. Thus, searching for the global optimal solution is often intractable. Instead, we aim to prove that greedy algorithms that produce reasonable solutions, e.g., near-optimal, are much effective and efficient. There are three tasks studied in the thesis: 1) Entropy estimation. We attempt to search for a finite number of semantic segmentations which are representative and diverse such that we can approximate the entropy of the distribution over output space by applying the existing model on the image. 2) Searching for a set of diverse bounding boxes that are most likely to contain an object. We formulate this problem as an optimization problem such that there exist a greedy algorithm having theoretical guarantee. 3) Fill-in-the-blank. We attempt to generate missing words in the blanks around which there are contexts available. We tested our proposed approaches on a series of Computer Vision and Natural Language Processing benchmarks, e.g., MS COCO, PASCAL VOC, etc, and show that they are indeed effective and efficient.

Thesis (MSc)--Stellenbosch University, 2011 / ENGLISH ABSTRACT: With billions of current internet users interacting through social networks, the need has arisen to analyze the structure of these networks. Many authors have proposed random graph models for social networks in an attempt to understand and reproduce the dynamics that govern social network development. This thesis proposes a random graph model that generates social networks using a community-based approach, in which users’ affiliations to communities are explicitly modeled and then translated into a social network. Our approach explicitly models the tendency of communities to overlap, and also proposes a method for determining the probability of two users being connected based on their levels of commitment to the communities they both belong to. Previous community-based models do not incorporate community overlap, and assume mutual members of any community are automatically connected. We provide a method for fitting our model to real-world social networks and demonstrate the effectiveness of our approach in reproducing real-world social network characteristics by investigating its fit on two data sets of current online social networks. The results verify that our proposed model is promising: it is the first community-based model that can accurately reproduce a variety of important social network characteristics, namely average separation, clustering, degree distribution, transitivity and network densification, simultaneously. / AFRIKAANSE OPSOMMING: Met biljoene huidige internet-gebruikers wat deesdae met behulp van aanlyn sosiale netwerke kommunikeer, het die analise van hierdie netwerke in die navorsingsgemeenskap toegeneem. Navorsers het al verskeie toevalsgrafiekmodelle vir sosiale netwerke voorgestel in ’n poging om die dinamika van die ontwikkeling van dié netwerke beter te verstaan en te dupliseer. In hierdie tesis word ’n nuwe toevalsgrafiekmodel vir sosiale netwerke voorgestel wat ’n gemeenskapsgebaseerde benadering volg, deurdat gebruikers se verbintenisse aan gemeenskappe eksplisiet gemodelleer word, en dié gemeenskapsmodel dan in ’n sosiale netwerk omskep word. Ons metode modelleer uitdruklik die geneigdheid van gemeenskappe om te oorvleuel, en verskaf ’n metode waardeur die waarskynlikheid van vriendskap tussen twee gebruikers bepaal kan word, op grond van hulle toewyding aan hulle wedersydse gemeenskappe. Vorige modelle inkorporeer nie gemeenskapsoorvleueling nie, en aanvaar ook dat alle lede van dieselfde gemeenskap vriende sal wees. Ons verskaf ’n metode om ons model se parameters te pas op sosiale netwerk datastelle en vertoon die vermoë van ons model om eienskappe van sosiale netwerke te dupliseer. Die resultate van ons model lyk belowend: dit is die eerste gemeenskapsgebaseerde model wat gelyktydig ’n belangrike verskeidenheid van sosiale netwerk eienskappe, naamlik gemiddelde skeidingsafstand, samedromming, graadverdeling, transitiwiteit en netwerksverdigting, akkuraat kan weerspieël.

In this dissertation, we have proposed two new algorithms for statistical inference for models with intractable normalizing constants: the Monte Carlo Metropolis-Hastings algorithm and the Bayesian Stochastic Approximation Monte Carlo algorithm. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. At each iteration, it replaces the unknown normalizing constant ratio by a Monte Carlo estimate. Although the algorithm violates the detailed balance condition, it still converges, as shown in the paper, to the desired target distribution under mild conditions. The BSAMC algorithm works by simulating from a sequence of approximated distributions using the SAMC algorithm. A strong law of large numbers has been established for BSAMC estimators under mild conditions. One significant advantage of our algorithms over the auxiliary variable MCMC methods is that they avoid the requirement for perfect samples, and thus it can be applied to many models for which perfect sampling is not available or very expensive. In addition, although the normalizing constant approximation is also involved in BSAMC, BSAMC can perform very robustly to initial guesses of parameters due to the powerful ability of SAMC in sample space exploration. BSAMC has also provided a general framework for approximated Bayesian inference for the models for which the likelihood function is intractable: sampling from a sequence of approximated distributions with their average converging to the target distribution. With these two illustrated algorithms, we have demonstrated how the SAMCMC method can be applied to estimate the parameters of ERGMs, which is one of the typical examples of statistical models with intractable normalizing constants. We showed that the resulting estimate is consistent, asymptotically normal and asymptotically efficient. Compared to the MCMLE and SSA methods, a significant advantage of SAMCMC is that it overcomes the model degeneracy problem. The strength of SAMCMC comes from its varying truncation mechanism, which enables SAMCMC to avoid the model degeneracy problem through re-initialization. MCMLE and SSA do not possess the re-initialization mechanism, and tend to converge to a solution near the starting point, so they often fail for the models which suffer from the model degeneracy problem.