Baccalaureate sermon

Revelation 1:18; John 10:10

Enkele aspekte van die rol van die ekonoom in fisiese beplanning

Ek wil graag die volgende vier aspekte van die rol van die ekonoom in fisiese beplanning, soos ek dit sien, vir u toelig, naamlik: (i) Fisiese beplanning is ’n betreklik nuwe ontwikkeling in die natuur-wetenskaplike veld en bepaal hom hoofsaak- lik tot die beplanning van grotere of kleinere streke. Die ekonomie daarteenoor het in die afgelope dekade of twee in die makrorigting beweeg, en streeksekonomie is dus ook ’n nuwe rigting in die ekonomie. : (ii) Die ekonoom is een van die jongste toevoegings tot die beplanningspan. W atter leemte kan die ekonoom aan- vul en watter kennis kan hy in die beplanningspan indra? : (iii) W atter instrumente en tegnieke is daar tot die beskik- king van die ekonoom wat hy kan gebruik om inligting oor 'n bepaalde streek (of nywerheid) waar die fisiese beplanning moet plaasvind, in te win of te verwerk tot ’n vorm wat vir die beplanningspan nuttig is?: (iv) W atter tipe opleiding is nodig vir die ekonoom wat met die beplanningspan saamwerk

Die invloed van kulturele verskille (met inbegrip van godsdiensverskille) op ekonomiese ontwikke- ling met verwysing na die Westerse en nie-Westersevolke

Ek wil die wisselwerking van slegs twee begrippe op me- kaar behandel, naamlik kultuur en ekonomiese ontwikkeling. Om te voorkom dat ek van partydigheid beskuldig kan word, wil ek my onderw erp toelig deur aanvanklik die Oosterling en die W esterling in die sin van ekonomiese ontwikkeling teenoor m ekaar te stel. Eers daarná sal ek probeer om enkele gevolgtrekkings vir Afrika, en m eer bepaald vir Suid-Afrika te maak

"Obubomi Bulukhuni/It is a Hard Life, This": Journeys in and narratives of childhood cancer in a South African public healthcare context

This research examines the ways in which a history of social segregation together with present actions by the state interact to inform the nature of healthcare narratives of mothers and children in the case of a childhood cancer diagnosis. I argue that families become internally displaced to seek life-saving treatment for the child diagnosed with cancer. By actively engaging with theories of ‘home’ and ‘households’ I aim to present greater insights into the ways in which people create meanings for these terms in the hospital setting. I argue that my participants come to share many of the characteristics of internally displaced people, due to the inequality that manifests in the healthcare system

Strong overall error analysis for the training of artificial neural networks via random initializations

Although deep learning based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance are not entirely understood from a mathematical point of view. Recently, estimates for the convergence of the overall error have been obtained in the situation of deep supervised learning, but with an extremely slow rate of convergence. In this note we partially improve on these estimates. More specifically, we show that the depth of the neural network only needs to increase much slower in order to obtain the same rate of approximation. The results hold in the case of an arbitrary stochastic optimization algorithm with i.i.d.\ random initializations.Comment: 40 page

THE INFLUENCE OF FAMILY DYNAMICS ON THE PRODUCTIVITY OF WORKING MOTHERS IN A MOTOR COMPANY IN SOUTH AFRICA

Since the inception of a non-racial, non-sexist democracy in South Africa in 1994, it is notsurprising to find many mothers have entered various professional fields and occupations. “Theinflux of women into the workforce, the economic necessity of two-income families, theincrease in single-parent families, child care and elder care availability and affordability, andincreased time pressure have all contributed to work and family concerns” (Gebeke, 1993:1).Unfortunately many families and businesses have neglected to adapt to these changes. Thewomen-in-business debate, however, has changed because so much has changed socially overthe last 15 years (Bendeman, 2007). The increased pressure that employers place on employeesto meet the needs of their customers and run a profitable business needs to be addressed, asemployers, according to Blanchard (2000), need to put effective structures and systems in placefor people to want to perform

Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation

Gradient descent (GD) type optimization schemes are the standard methods to train artificial neural networks (ANNs) with rectified linear unit (ReLU) activation. Such schemes can be considered as discretizations of gradient flows (GFs) associated to the training of ANNs with ReLU activation and most of the key difficulties in the mathematical convergence analysis of GD type optimization schemes in the training of ANNs with ReLU activation seem to be already present in the dynamics of the corresponding GF differential equations. It is the key subject of this work to analyze such GF differential equations in the training of ANNs with ReLU activation and three layers (one input layer, one hidden layer, and one output layer). In particular, in this article we prove in the case where the target function is possibly multi-dimensional and continuous and in the case where the probability distribution of the input data is absolutely continuous with respect to the Lebesgue measure that the risk of every bounded GF trajectory converges to the risk of a critical point. In addition, in this article we show in the case of a 1-dimensional affine linear target function and in the case where the probability distribution of the input data coincides with the standard uniform distribution that the risk of every bounded GF trajectory converges to zero if the initial risk is sufficiently small. Finally, in the special situation where there is only one neuron on the hidden layer (1-dimensional hidden layer) we strengthen the above named result for affine linear target functions by proving that that the risk of every (not necessarily bounded) GF trajectory converges to zero if the initial risk is sufficiently small.Comment: 37 page