The possibility of digital interactivity requires us to reenvision the map reader as the map user, and to address the perceptual, cognitive, cultural, and practical considerations that influence the user's experience with interactive maps and visualizations. In this article, we present an agenda for empirical research on this user and the interactive designs he or she employs. The research agenda is a result of a multi-stage discussion among international scholars facilitated by the International Cartographic Association that included an early round of position papers and two subsequent workshops to narrow into pressing themes and important research opportunities. The focus of our discussion is epistemological and reflects the wide interdisciplinary influences on user studies in cartography. The opportunities are presented as imperatives that cross basic research and user-centered design studies, and identify practical impediments to empirical research, emerging interdisciplinary recommendations to improve user studies, and key research needs specific to the study of interactive maps and visualizations.

We show that the generalized Fourier transform can be used for reducing the computational cost and memory requirements of radial basis function methods for multi-dimensional option pricing. We derive a general algorithm, including a transformation of the Black-Scholes equation into the heat equation, that can be used in any number of dimensions. Numerical experiments in two and three dimensions show that the gain is substantial even for small problem sizes. Furthermore, the gain increases with the number of dimensions.

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