Empirical studies have validated that basic needs satisfaction supported by video game play predicts motivation and engagement outcomes. However, few studies specifically manipulated game features for each of the three basic needs specified in the selfdetermination theory (SDT) to examine how the game features impact players' need satisfaction and game experience. The current study employed an in-house developed exergame and manipulated the game features in a 2 (autonomy-supportive game features: on vs. off ) 2 (competence-supportive game features: on vs. off ) experiment to predict need satisfaction, game enjoyment, motivation for future play, effort for gameplay, self-efficacy for exercise using the game, likelihood of game recommendation, and game rating. The manipulated game features led to the corresponding need satisfaction. Manipulated autonomy-supportive and competence-
We investigate statistical properties of the eigenfunctions of the Schrödinger operator on families of star graphs with incommensurate bond lengths. We show that these eigenfunctions are not quantum ergodic in the limit as the number of bonds tends to infinity by finding an observable for which the quantum matrix elements do not converge to the classical average. We further show that for a given fixed graph there are subsequences of eigenfunctions which localise on pairs of bonds. We describe how to construct such subsequences explicitly. These constructions are analogous to scars on short unstable periodic orbits.Recently, authors have begun to investigate the wave-functions of quantum graphs. Kaplan [K2] studied eigenfunction statistics for ring-graphs using a combination of numerical techniques and analytical calculations of the short-time semiclassical behaviour of a wave-packet close to a 1-bond periodic orbit. The inverse participation ratio (a measure of localisation in a given state) was found to be well-described by this contribution, and shows deviation from the ergodically expected behaviour. Similar deviations were noticed for lattice-graphs. Remarkably, Schanz and Kottos [SK] observed that it would be impossible for the shortest orbits that are responsible for this enhanced localisation to support strong scarring. They wrote down an explicit criterion which must be satisfied by the energy of any strongly scarred state, and deduced asymptotics of the probability distribution of scarring strengths. In [KMW] a study was made of the eigenfunctions of a family of graphs known as star graphs (the name being derived from the connectivity of graphs in the family). The value distribution for the amplitude of eigenfunctions on a single bond of the graph, subject to an appropriate normalisation, was rigorously calculated
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