A Cubic Algorithm for Computing Gaussian Volume

We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of integration is $O^*(n^3)$ while the complexity of sampling is $O^*(n^3)$ for the first sample and $O^*(n^2)$ for every subsequent sample. These bounds improve on the corresponding state-of-the-art by a factor of $n$. Our improvement comes from several aspects: better isoperimetry, smoother annealing, avoiding transformation to isotropic position and the use of the "speedy walk" in the analysis.Comment: 23 page

Imithetho yomhlaba yaseMsinga: The living law of land in Msinga, KwaZulu-Natal

This report describes the ‘living law’ of land in one part of Msinga, a deep rural area of KwaZulu-Natal. It presents research findings from the Mchunu and Mthembu tribal areas, where a three-year action-research project was carried out by staff of the Mdukutshani Rural Development Programme. Launched in 2007, at a time when implementation of the Communal Land Rights Act of 2004 (CLRA) appeared imminent, the project aimed to gain a detailed understanding of land tenure in Msinga, facilitate local-level discussion of potential solutions to emerging problems around land rights, provide information on the CLRA to residents and authority structures, and help generate ideas on how local people could engage with the new law. Meetings, interviews and focus groups convened by the project between 2007 and 2009 generated lively discussions and debates on a range of issues and problems related to land tenure in Msinga. Policy-makers need to consider how to convene conversations of this kind, on a large scale, before they launch a new round of tenure reform policy formulation and law making. Our experience suggests that well designed processes are critically important to ensure informed discussion, but also that ordinary rural people, not just their leaders, are more than ready to engage in debates about policies that could have major impacts on their lives

Women's land rights and social change in rural South Africa: the case of Msinga, KwaZulu-Natal

Changing marriage practices and a continuing decline in marriage rates are generating tensions in rural South Africa and prompting innovations in the character of women's rights to land. Empirical evidence of changing practices in relation to land access and marriage in Msinga, a conservative area in KwaZulu-Natal, is presented. Such processes have been characterised in recent scholarship in terms of 'living customary law', or 'living law' but this concept can obscure the underlying social dynamics that produce discrepancies between rules, practices and emergent social realities. An alternative model with greater explanatory power is Moore's analytical framework for understanding 'law as process', suggesting attention to processes of regularisation and situational adjustment, within a fundamental condition of indeterminacy. This framework is utilised to help make sense of data from Msinga on marriage practices and women's access to land, and to draw some lessons for policy.Department of HE and Training approved lis

Room For Dancing On: Grazing Schemes In The Communal Lands Of Zimbabwe

In the late 1980s the chairman of Chamatamba grazing scheme, together with the rest of his committee, eloquently articulated their vision of how land use and resource management within Chamatamba's boundaries could be organised. This vision greatly impressed the many visitors to Chamatamba in this period, and was instrumental in securing for this prize-winning scheme large donations of funds and materials, as well as significant levels of extension support.The International Development Research Centre (IDRC) of Ottawa, Canada, provided generous funding for the research project. Gordon Banta of IDRC helped the project get under way - many thanks to him too

Land reform, accumulation and social reproduction: The South African experience in global and historical perspective

The reality of capitalist economy, its inherent dynamics and contradictions, must be understood as central to policy debates about land reform in South Africa today. Progressive land reform should strive to promote ‘accumulation’ from below’, through the redistribution of productive land to a large number of petty agricultural commodity producers. Supporting the social reproduction needs of the rural poor is also important, and securing their rights to communal land must be a key goal of tenure reform. Beyond South Africa, the experience of redistributive land reform more broadly suggests that southern Africa is a unique context in some ways (e.g. there is a need to break up large and productive farms) but not in many others. Many of the problems facing land reform in South Africa have been experienced elsewhere. Beyond land reform, the world is currently in the grip of several overlapping crises, notably the increasing precarity of working populations, ecological breakdown, large-scale migration, technological advances that threaten both jobs and democracy, and a swing towards right-wing and authoritarian modes of governance. Again, the centrality of the logic of capital to these simultaneous crises must be acknowledged.Keywords: accumulation, capitalism, crisis, land reform, social reproductio

Approximately Sampling Elements with Fixed Rank in Graded Posets

Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for counting and uniform sampling. We show that for certain classes of posets, biased Markov chains that walk along edges of their Hasse diagrams allow us to approximately generate samples with any fixed rank in expected polynomial time. Our arguments do not rely on the typical proofs of log-concavity, which are used to construct a stationary distribution with a specific mode in order to give a lower bound on the probability of outputting an element of the desired rank. Instead, we infer this directly from bounds on the mixing time of the chains through a method we call $\textit{balanced bias}$. A noteworthy application of our method is sampling restricted classes of integer partitions of $n$. We give the first provably efficient Markov chain algorithm to uniformly sample integer partitions of $n$ from general restricted classes. Several observations allow us to improve the efficiency of this chain to require $O(n^{1/2}\log(n))$ space, and for unrestricted integer partitions, expected $O(n^{9/4})$ time. Related applications include sampling permutations with a fixed number of inversions and lozenge tilings on the triangular lattice with a fixed average height.Comment: 23 pages, 12 figure

Contested paradigms of ‘viability’ in redistributive land reform: perspectives from southern Africa

‘Viability’ is a key term in debates about land redistribution in southern African and beyond. It is often used to connote ‘successful’ and ‘sustainable’– but what is meant by viability in relation to land reform, and how have particular conceptions of viability informed state policies and planning approaches over time? How have such notions influenced the contested politics of land and agriculture? In southern Africa policy debates have tended to focus narrowly on farm productivity and economic returns, and an implicit normative model is the large-scale commercial farm. Through a review of land reform experiences in South Africa, Namibia and Zimbabwe, this paper critically interrogates this influential but under-examined notion. It examines contrasting framings of viability derived from neo-classical economics, new institutional economics, livelihoods approaches (both developmentalist and welfarist), radical political economy and Marxism, and their influence in southern Africa. Through a discussion of alternative framings of viability, the paper aims to help shift policy debates away from a narrow, technocratic economism, a perspective often backed by powerful interests, towards a more plural view, one more compatible with small-scale, farming-based livelihoods.ESR

Municipal Case Study: Inkosi Langalibalele Local Municipality KwaZulu – Natal

This report presents a case study of Inkosi Local Municipality in KwaZulu-Natal. The goal of the report is to examine the employment creation potential of land redistribution in Inkosi Langalibalele, and its cost. The Inkosi Langalibalele Local Municipality is located within the Uthukela District Municipality, in a broader region known as the KwaZulu-Natal Midlands. Agriculture is the predominant form of land use in the local municipality, but it does not generate a large number of jobs. Large-scale commercial farming remains important but is shrinking due to land reform, which affects around 38 percent of the land in the municipality. Another 36 percent of the local municipality is designated as ‘communal areas’, with traditional authority structures playing a key role in their governance. Only 27 percent of the municipality, or around 100 000 hectares, is available for further land reform. The local municipality had a total population of 215 183 persons in 46 952 households in 2016 and comprises 3 403 square kilometres, with a population density of 63.2 people per square kilometre. Only around one fifth of the adult population aged 15 or more are employed, compared to 23 percent in Uthukela district municipality, and 31.5 percent in KZN. Of those employed, 74 percent work in the formal sector. Over half of the population (52 percent) is ‘not economically active’, but many of these are engaged in subsistence-oriented agriculture, mainly in order to produce some additional food for home consumption. The great majority of the population in Inkosi Langalibalele is poor and highly dependent on social grants, and services have improved greatly since the advent of democracy in 1994. Despite the rural nature of the municipality, settlement patterns are increasingly dense and ‘urban’ in character, even some distance away from established towns. Large areas comprise densely settled communal areas under traditional councils