We describe recent developments in research on mathematical practice and cognition and outline the nine contributions in this special issue of topiCS. We divide these contributions into those that address (a) mathematical reasoning: patterns, levels, and evaluation; (b) mathematical concepts: evolution and meaning; and (c) the number concept: representation and processing.

Recent algorithmic advances and continual increase in computational power have made it possible to simulate protein folding and dynamics on the level of ensembles. Furthermore, analyzing protein structure by using ensemble representation is intrinsic to certain experimental techniques, such as nuclear magnetic resonance. This creates a problem of how to compare an ensemble of molecules with a g...

The $L$-fuzzy approximation operator associated with an $L$-fuzzy approximation space $(X,R)$ turns out to be a saturated $L$-fuzzy closure (interior) operator on a set $X$ precisely when the relation $R$ is reflexive and transitive. We investigate the relations between $L$-fuzzy approximation spaces and $L$-(fuzzy) topological spaces.

Recent interest in modeling biochemical networks raises questions about the relationship between often complex mathematical models and familiar arithmetic concepts from classical enzymology, and also about connections between modeling and experimental data. This review addresses both topics by familiarizing readers with key concepts (and terminology) in the construction, validation, and applica...

I argue that Vygotsky’s theory of concept formation (1986) is a powerful framework within which to explore how an individual at university level constructs a new mathematical concept. In particular, this theory is able to bridge the divide between an individual’s mathematical knowledge and the body of socially sanctioned mathematical knowledge. It can also be used to explain how idiosyncratic u...

This paper describes an order release and loading technique, which considers the routing as well as the machine flexibility of a modern job shop production. The workload control approach involves three steps. In a first step 'lead orders', i.e. urgent production orders that are either processed on a known bottleneck or are of high value, are identified. Afterwards transfer batches of the lead p...

In considering supercoils formed by closed double-stranded molecules of DNA certain mathematical concepts, such as the linking number and the twist, are needed. The meaning of these for a closed ribbon is explained and also that of the writhing number of a closed curve. Some simple examples are given, some of which may be relevant to the structure of chromatin.

OBJECTIVES Numeracy, the ability to process basic mathematical concepts, may affect responses to graphical displays of health risk information. Displays of probabilistic risk information using grouped dots are easier to understand than displays using dispersed dots. However, dispersed dots may better convey the randomness with which health threats occur, so increasing perceived susceptibility. ...

Traditional methods for computing optical flow are mainly based on image brightness constancy. In the real world the brightness constancy usually does not hold. Here we present the idea of using invariant feature based on the brightness change model to estimate the optical flow. Both the mathematical derivation and the experiments show that the new model is better than brightness based optical ...

Lecture-based teaching promotes a passive interaction with students. Opportunities to modify this format are available to enhance the overall learning experience for both students and instructors. The description for a discussion-based learning format is presented as it applies to a graduate curriculum with technical (formal mathematical derivation) topics. The presented hybrid method involves ...