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A game-theoretic approach based on the framework of transferable-utility cooperative games is developed to assess the reliability of transfer nodes in public transportation networks in the case of stochastic transfer times. A cooperative game is defined, whose model takes into account the public transportation system, the travel times, the transfers and the associated stochastic transfer times, and the users’ demand. The transfer stops are modeled as the players of such a game, and the Shapley value – a solution concept in cooperative game theory – is used to identify their centrality and relative importance. Theoretical properties of the model are analyzed. A two-level Monte Carlo approximation of the vector of Shapley values associated with the nodes is introduced, which is efficient and able to take into account the stochastic features of the transportation network. The performance of the algorithm is investigated, together with that of its distributed computing variation. The usefulness of the proposed approach for planners and policy makers is shown with a simple example and on a case study from the public transportation network of Auckland, New Zealand.

A multimodal dataset is presented, which has been collected for analyzing and measuring the quality of movement performed during sport activities. Martial arts (namely karate) are taken as test-beds for investigation. Karate encompasses predefined sequences of movements (“katas”) that can be carried out with different qualities, e.g., by performers at different skill levels (highly vs. poorly skilled).The experimental setup and method are described. The dataset is composed of motion capture (MoCap) data, synchronized with video and audio recordings, of several participants with different levels of experience. The raw MoCap data are independent of any particular post-processing algorithm and can be used for other research purposes. In the second part of the paper, a set of measures is proposed to evaluate a kata performance. They are based on the geometrical and kinematic features, such as posture correctness and synchronization between limbs. and were chosen according to karate experts’ opinion.

For certain families of multivariable vector-valued functions to be approximated, the accuracy of approximation schemes made up of linear combinations of computational units containing adjustable parameters is investigated. Upper bounds on the approximation error are derived that depend on the Rademacher complexities of the families. The estimates exploit possible relationships among the components of the multivariable vector-valued functions. All such components are approximated simultaneously in such a way to use, for a desired approximation accuracy, less computational units than those required by componentwise approximation. An application to N-stage optimization problems is discussed.