The Groebner basis of the ideal of vanishing polynomials

We construct an explicit minimal strong Groebner basis of the ideal of vanishing polynomials in the polynomial ring over Z/m for m>=2. The proof is done in a purely combinatorial way. It is a remarkable fact that the constructed Groebner basis is independent of the monomial order and that the set of leading terms of the constructed Groebner basis is unique, up to multiplication by units. We also present a fast algorithm to compute reduced normal forms, and furthermore, we give a recursive algorithm for building a Groebner basis in Z/m[x_1,x_2,...,x_n] along the prime factorization of m. The obtained results are not only of mathematical interest but have immediate applications in formal verification of data paths for microelectronic systems-on-chip.Comment: 15 pages, 1 table, 2 algorithms (corrected version with new Prop. 3.8 and proof); Journal of Symbolic Computation 46 (2011

The role of HIV literacy: a community health worker perspective

HIV literacy has been emphasised as part of HIV/AIDS campaigns throughout the world. The South African Government’s allocation of past and present funding indicates substantial support for HIV/AIDS education with the emphasis on prevention. Commitment to the new HIV and AIDS and STI National Strategic Plan 2007-2011 for addressing the epidemic emphasises the importance of speeding up the delivery of HAART in South. The link between education and the provision of antiretroviral therapy lies in the need for patients to understand the nature of the HI virus and the way the medication works physiologically in order to ensure adherence, control side effects and provide the best care possible for people living with HIV/AIDS. This paper assesses the role of HIV literacy from the perspective of community health workers working in clinics in the Western Cape Province in South Africa. It looks at their daily interaction with clinic patients, as well as their experience of the HAART rollout. It aims to evaluate the impact of HIV literacy on the communities they work in and the limitations of education in supporting the provision of health care for people living with HIV/AIDS

Strategies of representation: South African photography of the HIV epidemic

Includes bibliographical references.This thesis is concerned with how South African photographers have responded to the HIV epidemic. The focus is on the different visual, political and intellectual strategies that photographers have used to document the disease and the complex issues that surround it. The study considers the work of all South African photographers who have produced a comprehensive body of work on HIV and AIDS. This includes both published and unpublished work. The analysis of the photographic work is situated in relation to other histories including the history of photography in Africa, the documentation of the HIV epidemic since the 1980s, and the political and social experience of the epidemic in South Africa. The reading of the photographs is also informed by the contexts where they are published or exhibited, including the media, non-governmental organisations (NGOs) and aid organisations, and the fine art gallery and attendant publications. In addition to the theoretically informed analysis of the photographic projects, I interviewed the photographers in order to learn more about their intentions and the contributing factors that shape the production of their work. Interviews were transcribed and used to develop my analysis of their projects and working process. While a number of photographers are included in the thesis, the major focus is on David Goldblatt, Gideon Mendel, Santu Mofokeng and Gisèle Wulfsohn. This thesis is not a comparative study but rather seeks to differentiate between four very different approaches to representing HIV and AIDS in South Africa. I specifically chose to focus on projects that demonstrated alternative visual and intellectual forms of engagement with the experience of the HIV epidemic. The selection aimed to reveal the relationships between the working processes, the contexts of display and publication, and the visual languages the photographers employed. My interest lies in how and why the photographers documented this challenging subject. A close examination of South African photography reveals diverse and complex visual responses to the HIV epidemic. Importantly, some photographic projects challenge existing approaches and encourage alternative ways of looking at, and thinking about, the experience of the epidemic in the South African context

The potential of visual and participatory approaches to HIV literacy in South Africa

Includes bibliographical references (leaves 141-150).An estimated 18.8 % of South African adults aged 15-49 are currently living with HIV. While HIV literacy campaigns and other strategies have aimed to reduce HIV incidence, there remains a general lack of knowledge of the biomedical nature of the disease. This not only inhibits attempts to reduce HIV transmission, but also discourages voluntary counseling and testing (VCT), accessing clinic care and the uptake of antiretroviral therapy. This dissertation identifies the essential role played by community health workers and treatment activists who offer 'HIV literacy' in their communities and assist the formal health care system. The aim of this study was to complement these initiatives with the development and analysis of a visual and participatory HIV literacy workshop

Geometry of rank tests

We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. These permutations are the linear extensions of partially ordered sets specified by the data. Our methods refine rank tests of non-parametric statistics, such as the sign test and the runs test, and are useful for the exploratory analysis of ordinal data. Convex rank tests correspond to probabilistic conditional independence structures known as semi-graphoids. Submodular rank tests are classified by the faces of the cone of submodular functions, or by Minkowski summands of the permutohedron. We enumerate all small instances of such rank tests. Graphical tests correspond to both graphical models and to graph associahedra, and they have excellent statistical and algorithmic properties.Comment: 8 pages, 4 figures. See also http://bio.math.berkeley.edu/ranktests/. v2: Expanded proofs, revised after reviewer comment

New developments in the theory of Groebner bases and applications to formal verification

We present foundational work on standard bases over rings and on Boolean Groebner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems arising from formal verification of digital circuits. In fact, algebraic modelling of formal verification problems is developed on the word-level as well as on the bit-level. The word-level model leads to Groebner basis in the polynomial ring over Z/2n while the bit-level model leads to Boolean Groebner bases. In addition to the theoretical foundations of both approaches, the algorithms have been implemented. Using these implementations we show that special data structures and the exploitation of symmetries make Groebner bases competitive to state-of-the-art tools from formal verification but having the advantage of being systematic and more flexible.Comment: 44 pages, 8 figures, submitted to the Special Issue of the Journal of Pure and Applied Algebr

Conceptual Advancement of Youth Apprenticeship Programs Using a Policy Delphi

Youth apprenticeship programs are a means of bridging the middle skills gap and rebuilding the workforce while combating youth underemployment and unemployment. Previous attempts to advance these programs were unsuccessful. The study identified concepts to include or modify in draft legislation and policy statements to increase the possibility of enactment and implementation. Twenty-three youth apprenticeship advocates participated as panelists in a four-round online policy Delphi to garner opinions on posited recommendations and panelists’ responses to openended prompts. A codifying committee of three educators/researchers was used to review, reduce, categorize, and code the qualitative data. The aggregated lists were used to develop a 5-point, 19- item Likert-type scale that was used to identify the level of importance of each concept. The panel approved or disapproved pre-posited concepts and provided responses to two-open ended prompts. The qualitative data were used to create a 19-item Likert-type scale to which the heterogeneous group of advocates rated the importance of the concepts presented by the codifying committee. The panel arrived at a strong agreement on 15 concepts for inclusion into draft legislation and policy statements. The findings provide advocates with information to share with legislators and other key stakeholders to boost the advancement of youth apprenticeship programs