On the intricacy of combinatorial construction problems

RESP-904

Regular two-graphs and extensions of partial geometries

Geometry;meetkunde

Unlikely Friends of the Authoritarian and Atheist Ruler: Religious Groups and Collective Contention in Rural China

This article examines the roles played by rural religious groups in China's local contentious politics. More specifically, it aims to explore whether religious groups stimulate or reduce collective contention when the ruler is both authoritarian and atheist. Drawing on national survey data and comparative case studies, this article finds that collective contention is less likely to occur in villages with religious groups that simultaneously overlap with secular social organizations and local authorities, and are hence more likely to serve as credible communication channels between local states and discontented citizens. This finding highlights two important issues that are often side-lined, if not outright neglected, in the existing literature. First, the relationship between religious groups and collective contention is diverse rather than uniform. Second, this relationship is shaped not only by religious groups but also by other important players in the local political arena

Some applications of matching theorems

PhDThis thesis contains the results of two investigations. The rst concerns the 1- factorizability of regular graphs of high degree. Chetwynd and Hilton proved in 1989 that all regular graphs of order 2n and degree 2n where > 1 2 ( p 7 1) 0:82288 are 1-factorizable. We show that all regular graphs of order 2n and degree 2n where is greater than the second largest root of 4x6 28x5 71x4 + 54x3 + 88x2 62x + 3 ( 0:81112) are 1-factorizable. It is hoped that in the future our techniques will yield further improvements to this bound. In addition our study of barriers in graphs of high minimum degree may have independent applications. The second investigation concerns partial latin squares that satisfy Hall's Condition. The problem of completing a partial latin square can be viewed as a listcolouring problem in a natural way. Hall's Condition is a necessary condition for such a problem to have a solution. We show that for certain classes of partial latin square, Hall's Condition is both necessary and su cient, generalizing theorems of Hilton and Johnson, and Bobga and Johnson. It is well-known that the problem of deciding whether a partial latin square is completable is NP-complete. We show that the problem of deciding whether a partial latin square that is promised to satisfy Hall's Condition is completable is NP-hard

Critical sets of full Latin squares

This thesis explores the properties of critical sets of the full n-Latin square and related combinatorial structures including full designs, (m,n,2)-balanced Latin rectangles and n-Latin cubes. In Chapter 3 we study known results on designs and the analogies between critical sets of the full n-Latin square and minimal defining sets of the full designs. Next in Chapter 4 we fully classify the critical sets of the full (m,n,2)-balanced Latin square, by describing the precise structures of these critical sets from the smallest to the largest. Properties of different types of critical sets of the full n-Latin square are investigated in Chapter 5. We fully classify the structure of any saturated critical set of the full n-Latin square. We show in Theorem 5.8 that such a critical set has size exactly equal to n³ - 2n² - n. In Section 5.2 we give a construction which provides an upper bound for the size of the smallest critical set of the full n-Latin square. Similarly in Section 5.4, another construction gives a lower bound for the size of the largest non-saturated critical set. We conjecture that these bounds are best possible. Using the results from Chapter 5, we obtain spectrum results on critical sets of the full n-Latin square in Chapter 6. In particular, we show that a critical set of each size between (n - 1)³ + 1 and n(n - 1)² + n - 2 exists. In Chapter 7, we turn our focus to the completability of partial k-Latin squares. The relationship between partial k-Latin squares and semi-k-Latin squares is used to show that any partial k-Latin square of order n with at most (n - 1) non-empty cells is completable. As Latin cubes generalize Latin squares, we attempt to generalize some of the results we have established on k-Latin squares so that they apply to k-Latin cubes. These results are presented in Chapter 8

The long-run economic costs of AIDS : theory and an application to South Africa

Most existing estimates of the macroeconomic costs of AIDS, as measured by the reduction in thegrowth rate of gross domestic product, are modest. For Africa-the continent where the epidemic has hit the hardest-they range between 0.3 and 1.5 percent annually. The reason is that these estimates are based on an underlying assumption that the main effect of increased mortality is to relieve pressure on existing land and physical capital so that output per head is little affected. The authors argue that this emphasis is misplaced and that, with a more plausible view of how the economy functions over the long run, the economic costs of AIDS are almost certain to be much higher. Not only does AIDS destroy existing human capital, but by killing mostly young adults, it also weakens the mechanism through which knowledge and abilities are transmitted from one generation to the next. The children of AIDS victims will be left without one or both parents to love, raise, and educate them. The model yields the following results. In the absence of AIDS, the counterfactual benchmark, there is modest growth, with universal and complete education attained within three generations. But if nothing is done to combat the epidemic, a complete economic collapse will occur within three generations. With optimal spending on combating the disease, and if there is pooling, growth is maintained, albeit at a somewhat slower rate than in the benchmark case in the absence of AIDS. If pooling breaks down and is replaced by nuclear families, growth will be slower still. Indeed, if school attendance subsidies are not possible, growth will be distinctly sluggish. In all three cases, the additional fiscal burden of intervention will be large, which reinforces the gravity of the findings.Economic Theory&Research,Public Health Promotion,Labor Policies,Health Monitoring&Evaluation,Decentralization,Health Monitoring&Evaluation,Population&Development,Economic Theory&Research,Street Children,Adolescent Health

Equipment Investment and Economic Growth: How Strong Is the Nexus?

macroeconomics, Equipment Investment, Economic Growth, Nexus

Evaluation of Spatially Targeted Strategies to Control Non-Domiciliated Triatoma dimidiata Vector of Chagas Disease

Chagas disease is one of the most important parasitic diseases in Latin America. Since the 1980's, many national and international initiatives have contributed to eliminate vectors developing inside human domiciles. Today's challenge is to control vectors that are non-adapted to the human domicile, but still able to transmit the parasite through regular short stay in the houses. Here, we assess the potential of different control strategies applied in specific spatial patterns using a mathematical model that reproduces the dynamic of dispersion of such ‘non-domiciliated’ vectors within a village of the Yucatan Peninsula, Mexico. We show that no single strategy applied in the periphery of the village, where the insects are more abundant, provides satisfying protection to the whole village. However, combining the use of insect screens in houses at the periphery of the village (to simultaneously fight insects dispersing from the garden and the forest), and the cleaning of the peri-domicile areas of the centre of the village (where sylvatic insects are absent), would provide a cost-effective control. This type of spatially mixed strategy offers a promising way to reduce the cost associated with the repeated interventions required to control non-domiciliated vectors that permanently attempt to infest houses