Two results on dynamic extensions of deviation measures

2020 ◽  
Vol 57 (2) ◽  
pp. 531-540
Author(s):  
Mitja Stadje
Keyword(s):  
Deviation Measure ◽  
Extension Result

AbstractWe give a dynamic extension result of the (static) notion of a deviation measure. We also study distribution-invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance.

scholarly journals A Matroid Extension Result

2019 ◽  
Vol 33 (1) ◽  
pp. 138-152
Author(s):  
James Oxley
Keyword(s):  
Extension Result

scholarly journals A motor imagery during blind action is guided by the same foci of attention as actual performance in a sample comprising females

2014 ◽  
Vol 7 (2) ◽  
pp. 11-16
Author(s):  
Bassem Khalaf
Keyword(s):  
Mental Imagery ◽  
Focus Of Attention ◽  
Direct Role ◽  
Actual Performance ◽  
External Focus ◽  
Deviation Measure ◽  
Straight Line ◽  
Internal Focus ◽  
Perceptual Representations ◽  
Better Than

There is strong evidence that focussing on the goal of an action improves performance relative to focussing on the concrete motor behaviours. The current study tests whether blind action guided by imagery relies on the same foci of attention. Thirty female participants took part in an experiment. In each condition there were 20 trials, they were asked to close their eyes and draw a straight line between two landmarks on a graphics tablet. We instructed them, in three conditions, to focus on (1) mental imagery of the goal landmark (external focus of attention), (2) drawing a straight line with the fingers (internal focus), or (3) without a specific focus of attention (control). We tested to what extent these attention instructions affected drawing performance, in terms of both deviations of the participants’ lines from an ideal straight line, and the time it took to complete the line. The study revealed that the manipulation specifically affected the deviation measure and that an external focus of attention was better than an internal focus and the control condition. These findings reveal that that mental imagery during blind action relies on same processes as actual performance. These data give perceptual representations of a direct role in motor control. They will be related to current theories of action control (constrained action hypothesis, ideomotor theories, and dual task accounts).

Free Extensions of Chiral Polytopes

1995 ◽  
Vol 47 (3) ◽  
pp. 641-654 ◽  
Author(s):  
Egon Schulte ◽  
Asia Ivić Weiss
Keyword(s):  
Classical Theory ◽  
Convex Polytope ◽  
Regular Polytopes ◽  
Geometric Structures ◽  
Maximal Symmetry ◽  
Abstract Polytopes ◽  
Chiral Polytopes ◽  
Classical Notion ◽  
Extension Result ◽  
Amalgamated Product

AbstractAbstract polytopes are discrete geometric structures which generalize the classical notion of a convex polytope. Chiral polytopes are those abstract polytopes which have maximal symmetry by rotation, in contrast to the abstract regular polytopes which have maximal symmetry by reflection. Chirality is a fascinating phenomenon which does not occur in the classical theory. The paper proves the following general extension result for chiral polytopes. If 𝒦 is a chiral polytope with regular facets 𝓕 then among all chiral polytopes with facets 𝒦 there is a universal such polytope 𝓟, whose group is a certain amalgamated product of the groups of 𝒦 and 𝓕. Finite extensions are also discussed.

scholarly journals An Extension Result for Maps Admitting an Algebraic Addition Theorem

2018 ◽  
Vol 29 (1) ◽  
pp. 316-327 ◽  
Author(s):  
E. Baro ◽  
J. de Vicente ◽  
M. Otero
Keyword(s):  
Addition Theorem ◽  
Extension Result

On compactness results for multi-scale convergence

1999 ◽  
Vol 129 (3) ◽  
pp. 467-476 ◽  
Author(s):  
Erik J. Balder
Keyword(s):  
Sobolev Space ◽  
Image Space ◽  
Orthogonal Complement ◽  
Young Measures ◽  
Type Result ◽  
Compactness Result ◽  
Relative Compactness ◽  
Multi Scale ◽  
Free Fields ◽  
Extension Result

Two relative compactness results for two-scale convergence in homogenization, due to G. Nguetseng, were recently extended to the multi-scale case by G. Allaire and M. Briane. Whereas their extension of Nguetseng's first result, which is in L2, is straightforward, their extension of his second result, which takes place in the Sobolev space H1, is quite complicated, even though it follows Nguetseng by using the fact that the image of H1 under the gradient mapping is the orthogonal complement of the set of divergence-free functions. Here a much simpler proof is provided by deriving the H1-type result from combining the first extension result with the fact that the above-mentioned image space is also the space of all rotation-free fields. Moreover, this approach reveals that the two results can be seen as corollaries of a fundamental relative compactness result for Young measures.

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