The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Assessing and training standing balance in older adults: A novel approach using the 'Nintendo Wii' Balance Board

Older adults, deemed to be at a high risk of falling, are often unable to participate in dynamic exercises due to physical constraints and/or a fear of falling. Using the Nintendo 'Wii Balance Board' (WBB) (Nintendo, Kyoto, Japan), we have developed an interface that allows a user to accurately calculate a participant's centre of pressure (COP) and incorporate it into a virtual environment to create bespoke diagnostic or training programmes that exploit real-time visual feedback of current COP position. This platform allows researchers to design, control and validate tasks that both train and test balance function. This technology provides a safe, adaptable and low-cost balance training/testing solution for older adults, particularly those at high-risk of falling.

A comparative analysis of multidimensional features of objects resembling sets of graphs

In the present paper, we introduce a notion of a style representing abstract, complex objects having characteristics that can be represented as structured objects. Furthermore, we provide some mathematical properties of such styles. As a main result, we present a novel approach to perform a meaningful comparative analysis of such styles by defining and using graph-theoretic measures. We compare two styles by comparing the underlying feature sets representing sets of graph structurally. To determine the structural similarity between the underlying graphs, we use graph similarity measures that are computationally efficient. More precisely, in order to compare styles, we map each feature set to a so-called median graph and compare the resulting median graphs. As an application, we perform an experimental study to compare special styles representing sets of undirected graphs and present numerical results thereof. (C) 2007 Elsevier Inc. All rights reserved.