A Strategic Evaluation of Public Interest Litigation in South Africa

Based on three case studies, discusses trends and challenges in public interest litigations in South Africa, the most effective combination of strategies in advancing social change, and the role of litigation in social mobilization

Human Resources: Key to Competitive Advantage

[Excerpt] As difficult as it may be and as fuzzy as it may turn out, we all must invest in an attempt to peer into the future to discern what implications it has for our human resources. It is not a precise effort, and it certainly can be challenged from many quarters; however, it is not only noble, but may prove to be extremely worthwhile for a competitive firm. As with almost every organization activity, the competitive world makes a paradigm shift inevitable for the human resource function. Understanding the nature of that shift and how to implement meaningful change are the fundamental questions for us all

Constructing exact symmetric informationally complete measurements from numerical solutions

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs and their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gr\"obner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of a SIC. Using this method we have calculated 69 new exact solutions, including 9 new dimensions where previously only numerical solutions were known, which more than triples the number of known exact solutions. In some cases the solutions require number fields with degrees as high as 12,288. We use these solutions to confirm that they obey the number-theoretic conjectures and we address two questions suggested by the previous work.Comment: 22 pages + 19 page appendix with many data tables. v2: published versio

Is the growth of the child of a smoking mother influenced by the father's prenatal exposure to tobacco? A hypothesis generating longitudinal study

OBJECTIVES: Transgenerational effects of different environmental exposures are of major interest, with rodent experiments focusing on epigenetic mechanisms. Previously, we have shown that if the study mother is a non-smoker, there is increased mean birth weight, length and body mass index (BMI) in her sons if she herself had been exposed prenatally to her mother's smoking. The aim of this study was to determine whether the prenatal smoke exposure of either parent influenced the growth of the fetus of a smoking woman, and whether any effects were dependent on the fetal sex. DESIGN: Population-based prebirth cohort study. SETTING: Avon Longitudinal Study of Parents and Children. PARTICIPANTS: Participants were residents of a geographic area with expected date of delivery between April 1991 and December 1992. Among pregnancies of mothers who smoked during pregnancy, data were available concerning maternal and paternal prenatal exposures to their own mother smoking for 3502 and 2354, respectively. PRIMARY AND SECONDARY OUTCOME MEASURES: Birth weight, length, BMI and head circumference. RESULTS: After controlling for confounders, there were no associations with birth weight, length or BMI. There was a strong adjusted association of birth head circumference among boys whose fathers had been exposed prenatally (mean difference −0.35 cm; 95% CI −0.57 to −0.14; p=0.001). There was no such association with girls (interaction p=0.006). Similar associations were found when primiparae and multiparae were analysed separately. In order to determine whether this was reflected in child development, we examined the relationships with IQ; we found that the boys born to exposed fathers had lower IQ scores on average, and that this was particularly due to the verbal component (mean difference in verbal IQ −3.65 points; 95% CI −6.60 to −0.70). CONCLUSIONS: Head size differences concerning paternal fetal exposure to smoking were unexpected and, as such, should be regarded as hypothesis generating

Multiple cooperating manipulators: The case of kinematically redundant arms

Existing work concerning two or more manipulators simultaneously grasping and transferring a common load is continued and extended. Specifically considered is the case of one or more arms being kinematically redundant. Some existing results in the modeling and control of single redundant arms and multiple manipulators are reviewed. The cooperating situation is modeled in terms of a set of coordinates representing object motion and internal object squeezing. Nominal trajectories in these coordinates are produced via actuator load distribution algorithms introduced previously. A controller is developed to track these desired object trajectories while making use of the kinematic redundancy to additionally aid the cooperation and coordination of the system. It is shown how the existence of kinematic redundancy within the system may be used to enhance the degree of cooperation achievable

Dimension towers of SICs. I. Aligned SICs and embedded tight frames

Algebraic number theory relates SIC-POVMs in dimension $d>3$ to those in dimension $d(d-2)$. We define a SIC in dimension $d(d-2)$ to be aligned to a SIC in dimension $d$ if and only if the squares of the overlap phases in dimension $d$ appear as a subset of the overlap phases in dimension $d(d-2)$ in a specified way. We give 19 (mostly numerical) examples of aligned SICs. We conjecture that given any SIC in dimension $d$ there exists an aligned SIC in dimension $d(d-2)$. In all our examples the aligned SIC has lower dimensional equiangular tight frames embedded in it. If $d$ is odd so that a natural tensor product structure exists, we prove that the individual vectors in the aligned SIC have a very special entanglement structure, and the existence of the embedded tight frames follows as a theorem. If $d-2$ is an odd prime number we prove that a complete set of mutually unbiased bases can be obtained by reducing an aligned SIC to this dimension.Comment: 24 pages, 2 figure