Mathematics meaning-making and its relation to design of teaching

Resumen tomado de la publicaci??n

Application of a support system to the design of wastewater treatment plants

This paper presents a case study that explores the advantages that can be derived from the use of a design support system during the design of wastewater treatment plants (WWTP). With this objective in mind a simplified but plausible WWTP design case study has been generated with KBDS, a computer-based support system that maintains a historical record of the design process. The study shows how, by employing such a historical record, it is possible to: (1) rank different design proposals responding to a design problem; (2) study the influence of changing the weight of the arguments used in the selection of the most adequate proposal; (3) take advantage of keywords to assist the designer in the search of specific items within the historical records; (4) evaluate automatically the compliance of alternative design proposals with respect to the design objectives; (5) verify the validity of previous decisions after the modification of the current constraints or specifications; (6) re-use the design records when upgrading an existing WWTP or when designing similar facilities; (7) generate documentation of the decision making process; and (8) associate a variety of documents as annotations to any component in the design history. The paper also shows one possible future role of design support systems as they outgrow their current reactive role as repositories of historical information and start to proactively support the generation of new knowledge during the design process

Optimal management of natural resources. Accounting for heterogeneity

Dynamic optimization methods have become increasingly important over the last years in economics. Within the dynamic optimization techniques employed, optimal control has emerged as the most powerful tool for the theoretical economic analysis. However, there is the need to advance further and take account that many dynamic economic processes are, in addition, dependent on some other parameter different than time. One can think of relaxing the assumption of a representative (homogeneous) agent in macro- and micro-economic applications allowing for heterogeneity among the agents. For instance, the optimal adaptation and diffusion of a new technology over time, may depend on the age of the person that adopted the new technology. Therefore, the economic models must take account of heterogeneity conditions within the dynamic framework. This thesis intends to accomplish two goals. The first goal is to analyze and revise existing environmental policies that focus on defining the optimal management of natural resources over time, by taking account of the heterogeneity of environmental conditions. Thus, the thesis makes a policy orientated contribution in the field of environmental policy by defining the necessary changes to transform an environmental policy based on the assumption of homogeneity into an environmental policy which takes account of heterogeneity. As a result the newly defined environmental policy will be more efficient and likely also politically more acceptable since it is tailored more specifically to the heterogeneous environmental conditions. Additionally to its policy orientated contribution, this thesis aims making a methodological contribution by applying a new optimization technique for solving problems where the control variables depend on two or more arguments --- the so-called two-stage solution approach ---, and by applying a numerical method --- the Escalator Boxcar Train Method --- for solving distributed optimal control problems, i.e., problems where the state variables, in addition to the control variables, depend on two or more arguments. Chapter 2 presents a theoretical framework to determine optimal resource allocation over time for the production of a good by heterogeneous producers, who generate a stock externalit and derives government policies to modify the behavior of competitive producers in order to achieve optimality. Chapter 3 illustrates the method in a more specific context, and integrates the aspects of quality and time, presenting a theoretical model that allows to determine the socially optimal outcome over time and space for the problem of waterlogging in irrigated agricultural production. Chapter 4 of this thesis concentrates on forestry resources and analyses the optimal selective-logging regime of a size-distributed forest.

Prediction of postprandial blood glucose under intra-patient variability and uncertainty and its use in the design of insulin dosing strategies for type 1 diabetic patients

In this thesis I propose a novel method to estimate the dose and injection-to-meal time for low-risk intensive insulin therapy. This dosage-aid system uses an optimization algorithm to determine the insulin dose and injection-to-meal time that minimizes the risk of postprandial hyper- and hypoglycaemia in type 1 diabetic patients. To this end, the algorithm applies a methodology that quantifies the risk of experiencing different grades of hypo- or hyperglycaemia in the postprandial state induced by insulin therapy according to an individual patient’s parameters. This methodology is based on modal interval analysis (MIA). Applying MIA, the postprandial glucose level is predicted with consideration of intra-patient variability and other sources of uncertainty. A worst-case approach is then used to calculate the risk index. In this way, a safer prediction of possible hyper- and hypoglycaemic episodes induced by the insulin therapy tested can be calculated in terms of these uncertainties.