The Distance Geometry of Music

We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a family of rhythms which encompass over forty timelines (\emph{ostinatos}) from traditional world music. We prove that these \emph{Euclidean rhythms} have the mathematical property that their onset patterns are distributed as evenly as possible: they maximize the sum of the Euclidean distances between all pairs of onsets, viewing onsets as points on a circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this notion of \emph{evenness}. We also show that essentially all Euclidean rhythms are \emph{deep}: each distinct distance between onsets occurs with a unique multiplicity, and these multiplicies form an interval $1,2,...,k-1$. Finally, we characterize all deep rhythms, showing that they form a subclass of generated rhythms, which in turn proves a useful property called shelling. All of our results for musical rhythms apply equally well to musical scales. In addition, many of the problems we explore are interesting in their own right as distance geometry problems on the circle; some of the same problems were explored by Erd\H{o}s in the plane.Comment: This is the full version of the paper: "The distance geometry of deep rhythms and scales." 17th Canadian Conference on Computational Geometry (CCCG '05), University of Windsor, Canada, 200

The complex process of scaling the integration of technology enhanced learning in mainstream classrooms

The early optimism for how technology might transform teaching and learning practices in mainstream school classrooms has long faded in many countries around the world. Whilst early research findings suggested that this was due to obvious barriers such as access to the technology itself, more recent attempts to scale student-access have illuminated other factors and provided a more sound theoretical foundation for us to understanding the processes and products of scaling educational technology innovations. This keynote will use findings from key projects and initiatives to highlight what is being learned – and how this might inform future endeavours to realise a more 21st century curriculum

Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit

We study a generic but simple non-integrable quantum {\em many-body} system of {\em locally} interacting particles, namely a kicked $t-V$ model of spinless fermions on 1-dim lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2 spins). Statistical properties of dynamics (quantum ergodicity and quantum mixing) and the nature of quantum transport in {\em thermodynamic limit} are considered as the kick parameters (which control the degree of non-integrability) are varied. We find and demonstrate {\em ballistic} transport and non-ergodic, non-mixing dynamics (implying infinite conductivity at all temperatures) in the {\em integrable} regime of zero or very small kick parameters, and more generally and important, also in {\em non-integrable} regime of {\em intermediate} values of kicked parameters, whereas only for sufficiently large kick parameters we recover quantum ergodicity and mixing implying normal (diffusive) transport. We propose an order parameter (charge stiffness $D$) which controls the phase transition from non-mixing/non-ergodic dynamics (ordered phase, $D>0$) to mixing/ergodic dynamics (disordered phase, D=0) in the thermodynamic limit. Furthermore, we find {\em exponential decay of time-correlation function} in the regime of mixing dynamics. The results are obtained consistently within three different numerical and analytical approaches: (i) time evolution of a finite system and direct computation of time correlation functions, (ii) full diagonalization of finite systems and statistical analysis of stationary data, and (iii) algebraic construction of quantum invariants of motion of an infinite system, in particular the time averaged observables.Comment: 18 pages in REVTeX with 14 eps figures included, Submitted to Physical Review

Wellbeing at Work: Four Perspectives on What User Experiences with Artifacts May Contribute

Part 2: User Experiences and Wellbeing at Work (UX@Work)International audienceMost work involves the use of artifacts; thus, user experience (UX) is a factor in how most employees experience their work. This study revisits the tool, media, dialogue-partner, and system perspectives on artifact use to explore how UX may contribute to wellbeing at work. It is found that artifacts foster positive UX when they lend the user expressive power (tool), are transparent (media) or perceptive (dialogue partner).They foster negative UX when they break the user’s task focus or make the user a mere system component. These findings are discussed and refined by elaborating the classic concepts of ready to hand and present at hand

Measuring readiness-to-hand through differences in attention to the task vs. attention to the tool

New interaction techniques, like multi-touch, tangible inter-action, and mid-air gestures often promise to be more intuitive and natural; however, there is little work on how to measure these constructs. One way is to leverage the phenomenon of tool embodiment—when a tool becomes an extension of one’s body, attention shifts to the task at hand, rather than the tool itself. In this work, we constructed a framework to measure tool embodiment by incorporating philosophical and psychological concepts. We applied this framework to design and conduct a study that uses attention to measure readiness-to-hand with both a physical tool and a virtual tool. We introduce a novel task where participants use a tool to rotate an object, while simultaneously responding to visual stimuli both near their hand and near the task. Our results showed that participants paid more attention to the task than to both kinds of tool. We also discuss how this evaluation framework can be used to investigate whether novel interaction techniques allow for this kind of tool embodiment.Postprin

An Action-Based Approach to Presence: Foundations and Methods

This chapter presents an action-based approach to presence. It starts by briefly describing the theoretical and empirical foundations of this approach, formalized into three key notions of place/space, action and mediation. In the light of these notions, some common assumptions about presence are then questioned: assuming a neat distinction between virtual and real environments, taking for granted the contours of the mediated environment and considering presence as a purely personal state. Some possible research topics opened up by adopting action as a unit of analysis are illustrated. Finally, a case study on driving as a form of mediated presence is discussed, to provocatively illustrate the flexibility of this approach as a unified framework for presence in digital and physical environment