Ben Marais (1909-1999): The influences on and heritage of a South African Prophet during two periods of transformation

University of Pretoria / Dissertation / Department of Church History and Church Policy / Advised by Prof J W Hofmeyr

True Greatness: A Discourse on the character of Rev. Wilbur Fisk

Memorial discourse

Christian Witness on the Plateau Vivarais-Lignon: Narrative, Nonviolence, and the Formation of Character

This dissertation analyzes the theological and ethical convictions that led the people of the Plateau Vivarais-Lignon to shelter thousands of refugees between 1939 and 1945. It does so by examining the themes of narrative identity, hospitality, character formation, nonviolence, and the contextual witness of church tradition. Though a number of studies have been published about the rescue activity in this region of France during World War II, none have thoroughly analyzed the theological nature of this activity. Using the Plateau Vivarais-Lignon as a case study in theological ethics, the dissertation draws on historical sources as well as the work of contemporary theologians and ethicists to understand, interpret, and analyze the witness of this community. After situating its rescue and resistance work within the Huguenot narrative of persecution and exile, I examine the theological convictions of the Reformed pastor of Le Chambon-sur-Lignon, André Trocmé, who played a key role in making the Plateau a place of refuge during the Holocaust. The study highlights the importance of narrative in the actions of this community and discusses the relationship between narrative, character, and ethics. It then examines the nonviolent commitments of key leaders of the rescue effort, using this analysis as a springboard to engage in broader theological reflection about the ethics of nonviolence. After examining the radical hospitality practiced on the Plateau in light of biblical narratives and Reformed history, I investigate the counter-cultural nature of Christian hospitality. The study concludes by analyzing the nature and witness of the church in light of the legacy of the Plateau Vivarais-Lignon. The dissertation suggests that increased academic and ecclesial attention be given to the relationship between narrative and character, the counter-cultural shape of Christian hospitality, and the active nature of nonviolence. It presents an in-depth analysis of the theological and ethical convictions of the people of the Plateau Vivarais-Lignon, arguing that their witness has ongoing significance for communities of faith as they grapple with how to form disciples, relate to the wider society, welcome strangers, and communicate God's shalom in a world of violence.

Fast Approximate Reconciliation of Set Differences

We present new, simple, efficient data structures for approximate reconciliation of set differences, a useful standalone primitive for peer-to-peer networks and a natural subroutine in methods for exact reconciliation. In the approximate reconciliation problem, peers A and B respectively have subsets of elements SA and SB of a large universe U. Peer A wishes to send a short message M to peer B with the goal that B should use M to determine as many elements in the set SB–SA as possible. To avoid the expense of round trip communication times, we focus on the situation where a single message M is sent. We motivate the performance tradeoffs between message size, accuracy and computation time for this problem with a straightforward approach using Bloom filters. We then introduce approximation reconciliation trees, a more computationally efficient solution that combines techniques from Patricia tries, Merkle trees, and Bloom filters. We present an analysis of approximation reconciliation trees and provide experimental results comparing the various methods proposed for approximate reconciliation.

Online and Offline Character Recognition Using Alignment to Prototypes

Nearest neighbor classifiers are simple to implement, yet they can model complex non-parametric distributions, and provide state-of-the-art recognition accuracy in OCR databases. At the same time, they may be too slow for practical character recognition, especially when they rely on similarity measures that require computationally expensive pairwise alignments between characters. This paper proposes an efficient method for computing an approximate similarity score between two characters based on their exact alignment to a small number of prototypes. The proposed method is applied to both online and offline character recognition, where similarity is based on widely used and computationally expensive alignment methods, i.e., Dynamic Time Warping and the Hungarian method respectively. In both cases significant recognition speedup is obtained at the expense of only a minor increase in recognition error.

Learning Embeddings for Indexing, Retrieval, and Classification, with Applications to Object and Shape Recognition in Image Databases

Nearest neighbor retrieval is the task of identifying, given a database of objects and a query object, the objects in the database that are the most similar to the query. Retrieving nearest neighbors is a necessary component of many practical applications, in fields as diverse as computer vision, pattern recognition, multimedia databases, bioinformatics, and computer networks. At the same time, finding nearest neighbors accurately and efficiently can be challenging, especially when the database contains a large number of objects, and when the underlying distance measure is computationally expensive. This thesis proposes new methods for improving the efficiency and accuracy of nearest neighbor retrieval and classification in spaces with computationally expensive distance measures. The proposed methods are domain-independent, and can be applied in arbitrary spaces, including non-Euclidean and non-metric spaces. In this thesis particular emphasis is given to computer vision applications related to object and shape recognition, where expensive non-Euclidean distance measures are often needed to achieve high accuracy. The first contribution of this thesis is the BoostMap algorithm for embedding arbitrary spaces into a vector space with a computationally efficient distance measure. Using this approach, an approximate set of nearest neighbors can be retrieved efficiently - often orders of magnitude faster than retrieval using the exact distance measure in the original space. The BoostMap algorithm has two key distinguishing features with respect to existing embedding methods. First, embedding construction explicitly maximizes the amount of nearest neighbor information preserved by the embedding. Second, embedding construction is treated as a machine learning problem, in contrast to existing methods that are based on geometric considerations. The second contribution is a method for constructing query-sensitive distance measures for the purposes of nearest neighbor retrieval and classification. In high-dimensional spaces, query-sensitive distance measures allow for automatic selection of the dimensions that are the most informative for each specific query object. It is shown theoretically and experimentally that query-sensitivity increases the modeling power of embeddings, allowing embeddings to capture a larger amount of the nearest neighbor structure of the original space. The third contribution is a method for speeding up nearest neighbor classification by combining multiple embedding-based nearest neighbor classifiers in a cascade. In a cascade, computationally efficient classifiers are used to quickly classify easy cases, and classifiers that are more computationally expensive and also more accurate are only applied to objects that are harder to classify. An interesting property of the proposed cascade method is that, under certain conditions, classification time actually decreases as the size of the database increases, a behavior that is in stark contrast to the behavior of typical nearest neighbor classification systems. The proposed methods are evaluated experimentally in several different applications: hand shape recognition, off-line character recognition, online character recognition, and efficient retrieval of time series. In all datasets, the proposed methods lead to significant improvements in accuracy and efficiency compared to existing state-of-the-art methods. In some datasets, the general-purpose methods introduced in this thesis even outperform domain-specific methods that have been custom-designed for such datasets.

Fuzzy ARTMAP, Slow Learning and Probability Estimation

A nonparametric probability estimation procedure using the fuzzy ARTMAP neural network is here described. Because the procedure does not make a priori assumptions about underlying probability distributions, it yields accurate estimates on a wide variety of prediction tasks. Fuzzy ARTMAP is used to perform probability estimation in two different modes. In a 'slow-learning' mode, input-output associations change slowly, with the strength of each association computing a conditional probability estimate. In 'max-nodes' mode, a fixed number of categories are coded during an initial fast learning interval, and weights are then tuned by slow learning. Simulations illustrate system performance on tasks in which various numbers of clusters in the set of input vectors mapped to a given class.

Dynamic Programming for Optimal Control of Set-Up Scheduling with Neural Network Modifications

This paper demonstrates an optimal control solution to change of machine set-up scheduling based on dynamic programming average cost per stage value iteration as set forth by Cararnanis et. al. [2] for the 2D case. The difficulty with the optimal approach lies in the explosive computational growth of the resulting solution. A method of reducing the computational complexity is developed using ideas from biology and neural networks. A real time controller is described that uses a linear-log representation of state space with neural networks employed to fit cost surfaces.

Comparative Performance Measures of Fuzzy ARTMAP, Learned Vector Quantization, and Back Propagation for Handwritten Character Recognition

This article compares the performance of Fuzzy ARTMAP with that of Learned Vector Quantization and Back Propagation on a handwritten character recognition task. Training with Fuzzy ARTMAP to a fixed criterion used many fewer epochs. Voting with Fuzzy ARTMAP yielded the highest recognition rates.