<p> A number of anthropological studies have been published on societies on the West New Britain mainland but little information is available about Vitu culture and society. The intention of this dissertation is to provide an account of Vitu social structure and particularly to describe and analyse the processes of group formation in the society. Specifically, the study attempts to elucidate the Vitus' claim that while they belong to matrilineal clans, they "follow both sides", inheriting rights from both parents.</p> <p> Anthropologists working in various parts of Melanesia have studied accommodation between two apparently incompatible cultural principles and have published studies of societies where patrilineal and cognatic descent are both organizing principles. This dissertation provides comparative data for these studies but it differs from them because it seeks to explain the relationships between roatrilineal and cognatic descent.</p> <p> After an historical introduction, the study describes matrilineal and cognatic ideologies in Vitu. Matrilineal descent divides Vitus into discrete categories and provides a conceptual frame-work, in terms of which people orient themselves in time and space, calculate social relationships and assess rights to claim membership in particular groups. Cognatic descent allows individuals considerable freedom in joining groups and gaining access to land. Vitus assert rights in matrilineal corporations by stressing cognatic descent from matrilineage·men. </p> <p> Cognatic inheritance of land-rights means that lineage members and lineage descendants share land. Membersof the two categories compete for resources, and tensions are exacerbated by a cultural preference that "the woman follows the man". This preference results in virilocal residence and a pattern of economic cooperation that allows women limited control over their land. These factors weaken the matrilineage and strengthen bonds among cognates. Lineage members cannot expel lineage descendants from their land. Instead they retain land for their lineages through strategic marriages. Each lineage becomes the centre of a limited marriage universe consisting of closely allied lineages exchanging women and land. </p> <p> The traditional political organization of Vitu was related to the patterns of descent and alliance in the society. The islands were divided into hostile, largely endogamous territories, each containing two or more relatively endogamous groups composed of members of closely allied lineages. Local communities consisted of cognaticallyrelated kinsmen who were members of intermarrying lineages. The symbolism of ceremonial exchange in Vitu continues to reflect values of balanced exchange of property and personnel between allied lineages. In the contemporary society, marriage patterns still include clan exogamy and reciprocal exchange of women. But some young people arrange their own marriages, and lineage leaders and elders worry about the future of the matrilineage as a land-holding corporation. </p> <p> The interaction of matrilineal and cognatic descent in the processes of group formation in Vitu contrasts with that in other areas of Melanesia. In the New Guinea Highlands, recruitment to local groups is bilateral, but Highlanders conceptualize local groups as patrilineal clans. In the Highlands, descent and residence patterns tend to be harmonic. So acconunodation between patrilineal and cognatic ideologies occurs in ascendant generations where the distinction between residence and clan membership becomes blurred. In Vitu, the disharmonic descent and residence rules require the distinction between local group, and lineage membership to be preserved. Adjustment between matrilineal and cognatic descent in Vitu occurs only through marriage. </p> <p> The aissertation concludes by stressing the considerable choice available to Vitus in joining social groups. Opportunities for joining a variety of groups may beas great in societies where unilineal descent is a significant factor as in societies where cognatic descent is a major organizing principle.</p> / Thesis / Doctor of Philosophy (PhD)

published_or_final_version / Chinese Historical Studies / Master / Master of Arts

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Thesis (M.A.)--University of Hong Kong, 1981. / Also available in print.

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Thesis (Ph. D.)--York University, 2000. Graduate Programme in Mathematics and Statstics. / Typescript. Includes bibliographical references (leaves 108-111). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ59136

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 80-82). Also available in electronic version. Access restricted to campus users.

The method of steepest descent is used to minimize typical functionals from elasticity.

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This thesis consists of 5 chapters. We develop new serial (Chapter 2), parallel (Chapter 3), distributed (Chapter 4) and primal-dual (Chapter 5) stochastic (randomized) coordinate descent methods, analyze their complexity and conduct numerical experiments on synthetic and real data of huge sizes (GBs/TBs of data, millions/billions of variables). In Chapter 2 we develop a randomized coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth separable convex function and prove that it obtains an ε-accurate solution with probability at least 1 - p in at most O((n/ε) log(1/p)) iterations, where n is the number of blocks. This extends recent results of Nesterov [43], which cover the smooth case, to composite minimization, while at the same time improving the complexity by the factor of 4 and removing ε from the logarithmic term. More importantly, in contrast with the aforementioned work in which the author achieves the results by applying the method to a regularized version of the objective function with an unknown scaling factor, we show that this is not necessary, thus achieving first true iteration complexity bounds. For strongly convex functions the method converges linearly. In the smooth case we also allow for arbitrary probability vectors and non-Euclidean norms. Our analysis is also much simpler. In Chapter 3 we show that the randomized coordinate descent method developed in Chapter 2 can be accelerated by parallelization. The speedup, as compared to the serial method, and referring to the number of iterations needed to approximately solve the problem with high probability, is equal to the product of the number of processors and a natural and easily computable measure of separability of the smooth component of the objective function. In the worst case, when no degree of separability is present, there is no speedup; in the best case, when the problem is separable, the speedup is equal to the number of processors. Our analysis also works in the mode when the number of coordinates being updated at each iteration is random, which allows for modeling situations with variable (busy or unreliable) number of processors. We demonstrate numerically that the algorithm is able to solve huge-scale l1-regularized least squares problems with a billion variables. In Chapter 4 we extended coordinate descent into a distributed environment. We initially partition the coordinates (features or examples, based on the problem formulation) and assign each partition to a different node of a cluster. At every iteration, each node picks a random subset of the coordinates from those it owns, independently from the other computers, and in parallel computes and applies updates to the selected coordinates based on a simple closed-form formula. We give bounds on the number of iterations sufficient to approximately solve the problem with high probability, and show how it depends on the data and on the partitioning. We perform numerical experiments with a LASSO instance described by a 3TB matrix. Finally, in Chapter 5, we address the issue of using mini-batches in stochastic optimization of Support Vector Machines (SVMs). We show that the same quantity, the spectral norm of the data, controls the parallelization speedup obtained for both primal stochastic subgradient descent (SGD) and stochastic dual coordinate ascent (SCDA) methods and use it to derive novel variants of mini-batched (parallel) SDCA. Our guarantees for both methods are expressed in terms of the original nonsmooth primal problem based on the hinge-loss. Our results in Chapters 2 and 3 are cast for blocks (groups of coordinates) instead of coordinates, and hence the methods are better described as block coordinate descent methods. While the results in Chapters 4 and 5 are not formulated for blocks, they can be extended to this setting.