It is notoriously difficult for people to adaptively apply formal mathematical strategies learned in school to real-world contexts, even when they possess the required mathematical skills. The current study explores whether a problem context's mechanism can act as an "embodied analogy" onto which abstract mathematical concepts can be applied, leading to more frequent use of formal mathematical ...

In this paper, we interest us to Human-Machine Systems (HMS) concepts applied to Education. It is shown how the HMS framework enables to propose original solution in matter of education in the field of control engineering. We focus on practical courses on control of manufacturing systems. The proposed solution is based on an original use of real and large-scale systems instead of simulation. Th...

tThe abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical concepts. This article shares a collaborative le...

Introduction (with F. Bailly) With this text, we will first of all discuss a distinction, internal to mathematics, between "construction principles" and "proof principles" (see [Longo, 1999], [Longo, 2002]). In short, it will be a question of grasping the difference between the construction of mathematical concepts and structures and the role of proof, more or less formalised. The objective is ...

There is a huge need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept of Colombeau algebras, and the construction of full Colombeau algebras on differential manifolds for arbitrary tensors. Despite the fact that this goal ...

Aksentijevic (1) raises issues with our recent report (2) that bear further clarification because they reflect some fundamental confusion about the nature of random sequences. First, it is essential to distinguish statistics for individual elements (i.e., patterns of length one) vs. statistics for patterns consisting of more than one element (i.e., higher order patterns). Aksentijevic’s comment...

Protein adsorption at solid surfaces plays a key role in many natural processes and has therefore promoted a widespread interest in many research areas. Despite considerable progress in this field there are still widely differing and even contradictive opinions on how to explain the frequently observed phenomena such as structural rearrangements, cooperative adsorption, overshooting adsorption ...

1 David I. Laurenson, Mike J. Jackson, The University of Edinburgh, Kings Buildings, Mayfield Road, Edinburgh, UK, EH9 3JL Abstract  The Java language has been used in the construction of a number of learning environments to enable students to explore mathematical concepts without the barrier of mathematical manipulation. The applets are designed to be flexible for educators, and flexible in u...

The modeling and control flexible-manufacturing workcells (FMCs) has generally been performed in a hierarchical structure, where at the highest level they have been modeled as discrete-event systems (DESs). In this paper, a new DES control synthesis technique that combines Moore Automata (MA) and ControlledAutomata theories to synthesize supervisors is presented. The obtained supervisors can mo...