Generalizations of the Lax-Milgram theorem

We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations

Subspaces with a common complement in a Banach space

We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an involution S on X exchanging the two subspaces, such that I+S is bounded from below on their union. Moreover we show that, in a separable Hilbert space, the only pairs of subspaces with a common complement are those which are either equivalently positioned or not completely asymptotic to one another. We also obtain characterizations for the existence of a common complement for subspaces with closed sum

Entertainment capture through heart rate activity in physical interactive playgrounds

An approach for capturing and modeling individual entertainment (“fun”) preferences is applied to users of the innovative Playware playground, an interactive physical playground inspired by computer games, in this study. The goal is to construct, using representative statistics computed from children’s physiological signals, an estimator of the degree to which games provided by the playground engage the players. For this purpose children’s heart rate (HR) signals, and their expressed preferences of how much “fun” particular game variants are, are obtained from experiments using games implemented on the Playware playground. A comprehensive statistical analysis shows that children’s reported entertainment preferences correlate well with specific features of the HR signal. Neuro-evolution techniques combined with feature set selection methods permit the construction of user models that predict reported entertainment preferences given HR features. These models are expressed as artificial neural networks and are demonstrated and evaluated on two Playware games and two control tasks requiring physical activity. The best network is able to correctly match expressed preferences in 64% of cases on previously unseen data (p−value 6 · 10−5). The generality of the methodology, its limitations, its usability as a real-time feedback mechanism for entertainment augmentation and as a validation tool are discussed.peer-reviewe

Enhancing health care via affective computing

Affective computing is a multidisciplinary field that studies the various ways by which computational processes are able to elicit, sense, and detect manifestations of human emotion. While the methods and technology delivered by affective computing have demonstrated very promising results across several domains, their adoption by healthcare is still at its initial stages. With that aim in mind, this commentary paper introduces affective computing to the readership of the journal and praises for the benefits of affect-enabled systems for prognostic, diagnostic and therapeutic purposes.peer-reviewe

A panorama of artificial and computational intelligence in games

This paper attempts to give a high-level overview of the field of artificial and computational intelligence (AI/CI) in games, with particular reference to how the different core research areas within this field inform and interact with each other, both actually and potentially. We identify ten main research areas within this field: NPC behavior learning, search and planning, player modeling, games as AI benchmarks, procedural content generation, computational narrative, believable agents, AI-assisted game design, general game artificial intelligence and AI in commercial games. We view and analyze the areas from three key perspectives: (1) the dominant AI method(s) used under each area; (2) the relation of each area with respect to the end (human) user; and (3) the placement of each area within a human-computer (player-game) interaction perspective. In addition, for each of these areas we consider how it could inform or interact with each of the other areas; in those cases where we find that meaningful interaction either exists or is possible, we describe the character of that interaction and provide references to published studies, if any. We believe that this paper improves understanding of the current nature of the game AI/CI research field and the interdependences between its core areas by providing a unifying overview. We also believe that the discussion of potential interactions between research areas provides a pointer to many interesting future research projects and unexplored subfields.peer-reviewe