Primitive notion

In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory, relations between primitive notions are restricted by axioms. Some authors refer to the latter as "defining" primitive notions by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress (per the regress problem). For example, in contemporary geometry, point, line, and contains are some primitive notions. Instead of attempting to define them, their interplay is ruled (in Hilbert's axiom system) by axioms like "For every two points there exists a line that contains them both". Details Alfred Tarski explained the role of primitive notions as follows: :When we set out to construct a given discipline, we distinguish, first of all, a certain

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Adaptive Oscillators with Human-in-the-Loop: Proof of Concept for Assistance and Rehabilitation

Auke Ijspeert, Renaud Ronsse, Jesse van den Kieboom

Most recent findings in robot-assisted therapy suggest that the therapy is more successful if the patient actively participates to the movement (“assistance-as-needed”). In the present contribution, we propose a novel approach for designing highly flexible protocols based on this concept. This approach uses adaptive oscillators: a mathematical primitive having the capacity to learn the high-level features of a quasi-sinusoidal signal (amplitude, frequency, offset). Using a simple inverse model, we demonstrate that this method permits to synchronize with the torque produced by the user, such that the effort associated with the movement production is shared between the user and the assistance device, without specifying any arbitrary reference trajectory. Simulation results also establish the method relevance for helping patients with movement disorders. Since our method is specifically designed for rhythmic movements, the final target is the assistance/rehabilitation of locomotory tasks. As an initial proof of concept, this paper focuses on a simpler movement, i.e. rhythmic oscillations of the forearm about the elbow.

IEEE2010

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Philosophie des mathématiques

La philosophie des mathématiques est la branche de la philosophie des sciences qui tente de répondre aux interrogations sur les fondements des mathématiques ainsi que sur leur usage. On y croise des

Droite (mathématiques)

En géométrie, le mot droite désigne un objet formé de points alignés. Une droite est illimitée des deux côtés, et sans épaisseur (dans la pratique, elle est représentée, sur une feuille, par une lig

Système axiomatique

En mathématiques, un système axiomatique est un ensemble d'axiomes dont certains ou tous les axiomes peuvent être utilisés logiquement pour dériver des théorèmes. Une théorie consiste en un système ax

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