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Sexuated Topology and the Suspension of Meaning: A Non-Hermeneutical Phenomenological Approach to Textual AnalysisThis study assumes the subject's pursuit of meaning is generally incapacitating and should be suspended. It aims to demonstrate how such a suspension is theoretically accomplished by utilizing Lacan's formulae of sexuation integrated with his work in discourse theory and topology. Part I places this study into context by examining scholarship from the established fields of hermeneutics, phenomenology, (post)structuralism, aesthetic theory and psychoanalysis in order to extract out their respective theory of meaning. These theories reveal that an historical struggle with meaning has been underway since the Reformation and reaches near crisis proportions in the 20th century. On the one hand this crisis is mollified by the rise of Heideggerian-Gadamerian hermeneutical phenomenology which questions traditional epistemological approaches to the text using a new ontological conceptualization of meaning and a conscious rejection of methodology. On the other hand this crisis is exacerbated when the ubiquitous nature of meaning is itself challenged by (post)structuralism's discovery of the signifier which inscribes a limit to meaning, and by the domains of sense and nonsense newly opened up by aesthetic theory. These historical developments culminate in the field of psychoanalysis which most consequentially delimits a cause of meaning said to be closely linked to the core of subjectivity. Part II extends these findings by rigorously constructing out of the Lacanian sexuated formulae a decidedly non-hermeneutical phenomenological approach useful in demonstrating the sexual nature of meaning. Explicated in their static state by way of an account of their original derivation from the Aristotelian logical square, it is argued that these four formulae are relevant to basic concerns of textual theory inclusive of the hermeneutical circle of meaning. These formulae are then set into motion by integrating them with Lacan's four discourses to demonstrate the breakdown of meaning. Finally, the cuts and sutures of two-dimensional space that is topology as set down in L'étourdit are performed to confirm how the very field of meaning is ultimately suspended from a nonsensical singular point known in Lacanian psychoanalysis as objet a. The contention is that by occupying this point the subject frees himself from the debilitating grip of meaning.
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Investigating decomposition methods for the maximum common subgraph and sum colouring problemsThe objective of this thesis is, from a general standpoint, to design and evaluate decomposition methods for solving constrained optimisation problems. Two optimisation problems in particular are considered: the maximum common induced subgraph problem, in which the largest common part between two graphs is to be found, and the sum colouring problem, where a graph must be coloured in a way that minimises a sum of weights induced by the employed colours.The maximum common subgraph (MCIS) problem is notably difficult, with a strong applicability in domains such as biology, chemistry and image processing, where the need to measure the similarity between structured objects represented by graphs may arise. The outstanding difficulty of this problem makes it strongly advisable to employ a decomposition method, possibly coupled with a parallelisation of the solution process. However, existing decomposition methods are not well suited to solve the MCIS problem: some lead to a poor balance between subproblems, while others, like tree decomposition, are downright inapplicable.To enable the structural decomposition of such problems, Chmeiss et al. proposed an approach, TR-decomposition, acting at a low level: the microstructure of the problem. This approach had yet to be applied to the MCIS problem. We evaluate it in this context, aiming at reducing the size of the search space while also enabling parallelisation. Moreover, we introduce a post-decomposition step that focuses on alleviating redundancies between subproblems.The second problem that caught our interest is the sum colouring problem. It is an NP-hard variant of the widely known classical graph colouring problem. As in most colouring problems, it basically consists in assigning colours to the vertices of a given graph while making sure no neighbour vertices use the same colour. In the sum colouring problem, however, each colour is associated with a weight. The objective is to minimise the sum of the weights of the colours used by every vertex. This leads to generally harder instances than the classical colouring problem, which simply requires to use as few colours as possible.Only a few exact methods have been proposed for this problem. Among them stand notably a constraint programming (CP) model, a branch and bound approach, as well as an integer linear programming (ILP) model.We led an in-depth investigation of CP's capabilities to solve the sum colouring problem, while also looking into ways to make it more efficient. Additionally, we evaluated a combination of integer linear programming and constraint programming, with the intention of conciliating the strong points of these highly complementary approaches. We took inspiration from the classical backtracking bounded by tree decomposition (BTD) approach. We employ a tree decomposition with a strictly bounded height. Constraint programming is used to enumerate consistent assignment of the root cluster. For each of these assignments, one subproblem is trivially obtained for each leaf cluster. Subproblems are then independently solved to optimality using ILP.We then derive profit from the complementarity of our approaches by developing a portfolio approach. The resulting solver is able to choose one of the considered approaches automatically by relying on a number of features extracted from each instance.
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Teaching Mathematics Effectively to Primary Students in Developing CountriesThis paper uses research from
 neuroscience and the psychology of mathematics to arrive at
 useful recommendations for teaching mathematics at primary
 level to poor students in developing countries. The
 enrollment rates of the poorer students have improved
 tremendously in the last decade. And the global Net
 Enrollment Ratio (NER) has improved since 2001 from 83.2
 percent to 90-95 percent except in Sub-Saharan Africa and
 South Asia. Making teaching of math and other subjects
 efficient for the poor in developing countries is a great
 challenge, particularly in south Asia and Sub-Saharan
 Africa. Many developing countries have explored new means of
 teaching math and other subjects. Mongolia changed its
 mathematics education, aiming to build a new set of
 priorities and practices, given the abandonment of earlier
 traditions. Similar to international trends of the time,
 South Africa in the 1990s extensively applied the
 constructivist learning philosophy which relied on
 exploration and discovery, with little emphasis on
 memorization, drill, In conformity with a belief that
 teachers could develop their own learning programs, there
 was virtual absence of a national or provincial syllabus or
 textbooks. Students were expected to develop their own
 methods for arithmetic operations, but most found it
 impossible to progress on their own from counting to actual
 calculating. This study integrates pertinent research from
 neuroscience and the psychology of mathematics to arrive at
 recommendations for curricular and efficient means of
 mathematics instruction particularly for developing
 countries and poor students at primary level. Specifically,
 the latest research in neuroscience, cognitive science, and
 discussions of national benchmarks for primary school
 mathematics learning, form the basis of our recommendations.
 These recommendations have a reasonable chance of working in
 the situational contexts of developing countries, with their
 traditions and resources.