The spatial relationship “between” is a notion which is intrinsically both fuzzy and contextual, and depends in particular on the shape of the objects. The few existing definitions do not take into account these aspects. We propose here definitions which are based on morphological operators and a fuzzy notion of visibility, which correspond to the main intuitive acceptions of the relation. We d...

Portion size has increased considerably over the past few decades and one influencing factor is dishware size. Using mathematical models we investigated how dish size affects the potential energy available in a meal. Two types of plate filling - flat and conical - were modelled for a range of plate sizes and energy densities, then compared to recommended daily energy requirements from Australia...

Fuzzy associative memories (FAMs) belong to the class of fuzzy neural networks (FNNs). A FNN is an artificial neural network (ANN) whose input patterns, output patterns, and/or connection weights are fuzzy-valued [19, 11]. Research on FAM models originated in the early 1990’s with the advent of Kosko’s FAM [35, 37]. Like many other associative memory models, Kosko’s FAM consists of a single-lay...

The interaction between linear, quadratic programming and regression analysis are explored by both statistical and operations research methods. Estimation and optimization problems are formulated in two different ways: on one hand linear and quadratic programming problems are formulated and solved by statistical methods, and on the other hand the solution of the linear regression model with con...

We study the relationship between the structure of discourse and the use of referring expressions in the mathematical domain. We address linguistic, algorithmic as well as representation issues. We show how referential expressions refer to mathematical statements and how a knowledge intensive approach, domain reasoning with the use of proof plans, are used for discourse understanding. We propos...

Manipulatives are commonly used to provide concrete bases for abstract mathematical concepts. However, it is unclear when concrete experiences benefit abstract thinking. We investigated whether understanding a manipulative’s mechanism would affect mathematical use and understanding. Participants completed a robotics task that could be solved with either mathematical or non-mathematical strategi...

The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by β-adrenergic stimulation, and, in a coordinated ...

This paper aims to frame certain fundamental aspects of the human mind (content and meaning of mental states) and foundational elements of brain computation (spatial and temporal patterns of neural activity) so as to enable at least in principle their integration within one and the same quantitative representation. Through the history of science, similar approaches have been instrumental to bri...

Puglisi JL, Negroni JA, Chen-Izu Y, Bers DM. The forcefrequency relationship: insights from mathematical modeling. Adv Physiol Educ 37: 28–34, 2013; doi:10.1152/advan.00072.2011.—The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple form...