Atherosclerosis is the development of lipid-laden plaques in arteries and is nowadays considered as an inflammatory disease. It has been shown that high doses of ionizing radiation, as used in radiotherapy, can increase the risk of development or progression of atherosclerosis. To elucidate the effects of radiation on atherosclerosis, we propose a mathematical model to describe radiation-promoted plaque evelopment. This model distinguishes itself from other models by combining plaque initiation and plaque growth, and by incorporating information from biological experiments. It is based on two consecutive processes: a probabilistic dose-dependent plaque initiation process, followed by deterministic plaque growth.
DOCUMENT
Background: Modern modeling techniques may potentially provide more accurate predictions of dichotomous outcomes than classical techniques. Objective: In this study, we aimed to examine the predictive performance of eight modeling techniques to predict mortality by frailty. Methods: We performed a longitudinal study with a 7-year follow-up. The sample consisted of 479 Dutch community-dwelling people, aged 75 years and older. Frailty was assessed with the Tilburg Frailty Indicator (TFI), a self-report questionnaire. This questionnaire consists of eight physical, four psychological, and three social frailty components. The municipality of Roosendaal, a city in the Netherlands, provided the mortality dates. We compared modeling techniques, such as support vector machine (SVM), neural network (NN), random forest, and least absolute shrinkage and selection operator, as well as classical techniques, such as logistic regression, two Bayesian networks, and recursive partitioning (RP). The area under the receiver operating characteristic curve (AUROC) indicated the performance of the models. The models were validated using bootstrapping. Results: We found that the NN model had the best validated performance (AUROC=0.812), followed by the SVM model (AUROC=0.705). The other models had validated AUROC values below 0.700. The RP model had the lowest validated AUROC (0.605). The NN model had the highest optimism (0.156). The predictor variable “difficulty in walking” was important for all models. Conclusions: Because of the high optimism of the NN model, we prefer the SVM model for predicting mortality among community-dwelling older people using the TFI, with the addition of “gender” and “age” variables. External validation is a necessary step before applying the prediction models in a new setting.
DOCUMENT
The implementation of the new mathematical knowledge base in Dutch teacher education institutes for primary education raises a need for curriculum development. Teacher educators have to raise student teachers’ subject matter knowledge to a higher level. In working on this aim teacher educators experience that student teachers often feel uncertain about their mathematical skills and are not very interested in formal and abstract mathematics. Student teachers prefer to focus on mathematical pedagogical content knowledge. This paper presents two design studies that try to tackle this problem. The first one targets the development of student teachers’ specialized content knowledge (SCK) and the second one focuses on their horizon content knowledge (HCK). Both studies target developing student teachers’ mathematical subject matter knowledge in the perspective of teaching mathematics in primary school. In the studies we established student teachers’ learning environments that kept them involved and motivated, even when they found the mathematics hard to do. Primarily, this attitude supported their mathematical growth, while it also developed their pedagogical skills and insight. INTRODUCTION
DOCUMENT
A primary teacher needs mathematical problem solving ability. That is why Dutch student teachers have to show this ability in a nationwide mathematics test that contains many non-routine problems. Most student teachers prepare for this test by working on their own solving test-like problems. To what extent does these individual problem solving activities really contribute to their mathematical problem solving ability? Developing mathematical problem solving ability requires reflective mathematical behaviour. Student teachers need to mathematize and generalize problems and problem approaches, and evaluate heuristics and problem solving processes. This demands self-confidence, motivation, cognition and metacognition. To what extent do student teachers show reflective behaviour during mathematical self-study and how can we explain their study behaviour? In this study 97 student teachers from seven different teacher education institutes worked on ten non-routine problems. They were motivated because the test-like problems gave them an impression of the test and enabled them to investigate whether they were already prepared well enough. This study also shows that student teachers preparing for the test were not focused on developing their mathematical problem solving ability. They did not know that this was the goal to strive for and how to aim for it. They lacked self-confidence and knowledge to mathematize problems and problem approaches, and to evaluate the problem solving process. These results indicate that student teachers do hardly develop their mathematical problem solving ability in self-study situations. This leaves a question for future research: What do student teachers need to improve their mathematical self-study behaviour? EAPRIL Proceedings, November 29 – December 1, 2017, Hämeenlinna, Finland
DOCUMENT
Coupling beams between shear walls are one of the key elements for energy dissipation in tall buildings. A representative mathematical model of coupling beam should represent flexure, shear and interface slip/extension mechanisms simultaneously. This goal can be achieved by using either detailed finite element models or by using macro models. This paper presents a review of various macro model alternatives for diagonally reinforced coupling beams in the literature. Three distinct methods have been reviewed in terms of their modeling techniques, the cyclic response overlap and the amount of cumulative plastic energy dissipated based on the results of previously performed tests. Through an analytical study, adequately accurate results can be captured by using macro models, although they are simpler in practice compared to sophisticated micro models. This study shows that, by modifying ultimate shear capacities where concrete material between diagonal bundles is adequately confined, it is possible to capture a more realistic result and a better approximation to the actual responses. It is also concluded that a simpler numerical model for diagonally reinforced coupling beams can be achieved by introducing linear part of slip/extension behavior into elastic part of the beam. It is observed, as a result of this study, that the ratio of effective stiffness to that of the gross cross-sectional one ranges from 0.04 to 0.14 in diagonally reinforced coupling beams depending on the aspect ratio and the beam strength parameters.
LINK
Accurate modeling of end-users’ decision-making behavior is crucial for validating demand response (DR) policies. However, existing models usually represent the decision-making behavior as an optimization problem, neglecting the impact of human psychology on decisions. In this paper, we propose a Belief-Desire-Intention (BDI) agent model to model end-users’ decision-making under DR. This model has the ability to perceive environmental information, generate different power scheduling plans, and make decisions that align with its own interests. The key modeling capabilities of the proposed model have been validated in a household end-user with flexible loads
DOCUMENT
On-time departure performance is important for airlines that seek the highest satisfaction of their passengers. The main component of achieving on-time departure is being able to complete the turnaround operations of an aircraft within the scheduled time. To address this problem, the present paper examined planning and scheduling of turnaround operations in the low cost airline industry. A mathematical model, named 'TurnOper_LP' was developed for a low-cost Turkish airline to identify the critical path of turnaround operations and the optimal turnaround time. The results of the model in terms of optimised turnaround times are then analysed and an example of schedule of turnaround operations is presented.
DOCUMENT
Explicit language objectives are included in the Swedish national curriculum for mathematics. The curriculum states that students should be given opportunities to develop the ability to formulate problems, use and analyse mathematical concepts and relationships between concepts, show and follow mathematical reasoning, and use mathematical expressions in discussions. Teachers’ competence forms a crucial link to bring an intended curriculum to a curriculum in action. This article investigates a professional development program, ‘Language in Mathematics’, within a national program for mathematics teachers in Sweden that aims at implementing the national curriculum into practice. Two specific aspects are examined: the selection of theoretical notions on language and mathematics and the choice of activities to relate selected theory to practice. From this examination, research on teacher learning in connection to professional development is proposed, which can contribute to a better understanding of teachers’ interpretation of integrated approaches to language and mathematics across national contexts.
DOCUMENT
In this paper, we focus on how the qualitative vocabulary of Dynalearn, which is used for describing dynamic systems, corresponds to the mathematical equations used in quantitative modeling. Then, we demonstrate the translation of a qualitative model into a quantitative model, using the example of an object falling with air resistance.
DOCUMENT
The formation of acrylamide in potato crisps was fitted by empirical mathematical models. Potato slices were fried under the same experimental conditions for different times. Besides the content of precursors in the raw potato slices, acrylamide and water content in the potato crisps were quantified after predetermined times (2-6 min). The temperature developments in the surrounding oil and outer cell layer of the potato slices were monitored, giving more insight in the frying process and making future comparisons between studies possible. The pattern found for the formation of acrylamide, which was similar to earlier studies, was fitted to three empirical models. Statistical methods were used to compare the performance of the models, with the "Logistic-Exponential" and "Empirical" model performing equally well. The obtained model parameters were in the range of earlier reported studies, although this comparison is not unequivocal as the experimental conditions differed between studies. The precision of parameter estimates was problematic; this should be improved by better experimental design. Nevertheless, the approach of this study will make it possible to truly compare acrylamide formation patterns and model parameters in the future, with the ability to develop a tool to predict acrylamide formation in potato crisps.
DOCUMENT
