Attentional Focusing Instructions and Force Production

Research progress assessing the role of attentional focusing instructions on skill acquisition and performance has lead researchers to apply this approach to force production tasks. Initial converging evidence indicates that force production tasks are sensitive to verbal instruction; externally focused instructions (onto movement outcomes, or onto the object force is being exerted against) are shown to be more beneficial than internally focused instructions (focusing attention onto the movements being executed). These benefits are observed for maximal and accurate force production, as well as the maintenance of force production in prolonged tasks. A range of mechanisms are identified supporting the proposal that an external focus promotes movement efficiency in line with energy and effort conservation. Future research is required to assess how this developing body of work interacts with the broader understanding of psychological and physiological factors implicated in the effective production, maintenance, and limitation of maximal or sub-maximal forces

On The Möbius Function Of Permutations Under The Pattern Containment Order

We study several aspects of the Möbius function, μ[σ, π], on the poset of permutations under the pattern containment order. First, we consider cases where the lower bound of the poset is indecomposable. We show that μ[σ, π] can be computed by considering just the indecomposable permutations contained in the upper bound. We apply this to the case where the upper bound is an increasing oscillation, and give a method for computing the value of the Möbius function that only involves evaluating simple inequalities. We then consider conditions on an interval which guarantee that the value of the Möbius function is zero. In particular, we show that if a permutation π contains two intervals of length 2, which are not order-isomorphic to one another, then μ[1, π] = 0. This allows us to prove that the proportion of permutations of length n with principal Möbius function equal to zero is asymptotically bounded below by (1−1/e) 2 ≥ 0.3995. This is the first result determining the value of μ[1, π] for an asymptotically positive proportion of permutations π. Following this, we use “2413-balloon” permutations to show that the growth of the principal Möbius function on the permutation poset is exponential. This improves on previous work, which has shown that the growth is at least polynomial. We then generalise 2413-balloon permutations, and find a recursion for the value of the principal Möbius function of these generalisations. Finally, we look back at the results found, and discuss ways to relate the results from each chapter. We then consider further research avenues

The effects of internally and externally directed attention during motor skill execution and learning

Focusing attention onto the intended outcome or goal of a movement (an External focus of attention) has been shown to be more beneficial to the learning and performance of movements than focusing onto the components of the movement being carried out (an Internal focus of attention). In this thesis, four studies assessed the effects of attentional focusing strategies on the learning and execution of motor skills during different situations. Study 1 demonstrated that an internal focus of attention during a suprapostural pointing task resulted in degraded postural control as well as larger movements of the hand and arm. In Study 2 novices using an external focus were more accurate in a dart throwing task than those using an internal focus, but no different from a control condition. In Study 3 two experiments investigated the effects of attentional focuses on postural control at rest and whilst fatigued. Postural control was no better using external focus when compared to an internal focus at rest, but was better than baseline. When fatigued (localised and generalised), balance was significantly deteriorated using an external focus, but not when an internal focus was used. In two experiments during Study 4 novices carrying out a dart throwing task used different attentional focusing instructions during practice and later performance. During practice sessions in Experiment 4.1 and 4.2 accuracy was not affected by attentional focusing instructions. Using an external focus during performance resulted in significantly better accuracy than using an internal focus. In Experiment 4.2, novices who preferred an internal focus but used an external focus during performance performed less accurately than participants who preferred the external focus. Findings demonstrate that the benefits of an external focus of attention is evident in performance situations, whereas an internal focus may be beneficial whilst fatigued and is not detrimental during practice

2413-balloon permutations and the growth of the Möbius function

We show that the growth of the principal Möbius function on the permutation poset is at least exponential. This improves on previous work, which has shown that the growth is at least polynomial. We define a method of constructing a permutation from a smaller permutation which we call “ballooning”. We show that if β is a 2413-balloon, and π is the 2413-balloon of β, then μ[1, π] = 2μ[1, β]. This allows us to construct a sequence of per-mutations π1, π2, π3 ... with lengths n, n+4, n+8, ... such that μ[1, πi+1] = 2μ[1, πi], and this gives us exponential growth. Further, our construction method gives per-mutations that lie within a hereditary class with finitely many simple permutations. We also find an expression for the value of μ[1, π], where π is a 2413-balloon, with no restriction on the permutation being ballooned

Roman weaponry in the province of Britain from the second century to the fifth century AD.

In 2 volsSIGLEAvailable from British Library Document Supply Centre- DSC:D176051 / BLDSC - British Library Document Supply CentreGBUnited Kingdo