A Matroid Generalization of a Result on Row-Latin Rectangles

Let A be an m \times n matrix in which the entries of each row are all distinct. Drisko showed that, if m \ge 2n-1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in a matroid. For such a matrix A, we show that if each row of A forms an independent set, then we can require the transversal to be independent as well. We determine the complexity of an algorithm based on the proof of this result. Lastly, we observe that m \ge 2n-1 appears to force the existence of not merely one but many transversals. We discuss a number of conjectures related to this observation (some of which involve matroids and some of which do not).Comment: 9 pages, 5 figure

Dynamical energy analysis on mesh grids: a new tool for describing the vibro-acoustic response of complex mechanical structures

We present a new approach for modelling noise and vibration in complex mechanical structures in the mid-to-high frequency regime. It is based on a dynamical energy analysis (DEA) formulation which extends standard techniques such as statistical energy analysis (SEA) towards non-diffusive wave fields. DEA takes into account the full directionality of the wave field and makes sub-structuring obsolete. It can thus be implemented on mesh grids commonly used, for example, in the finite element method (FEM). The resulting mesh based formulation of DEA can be implemented very efficiently using discrete flow mapping (DFM) as detailed in [1] and described here for applications in vibro-acoustics

Explorations in knowing: thinking psychosocially about legitimacy

This article has been made available through the Brunel Open Access Publishing Fund.In this paper, we look at what engaging with psychoanalysis, through psychosocial accounts of subjectivity, has contributed to our struggles for legitimacy and security within our ways of knowing. The psychosocial, with its insistence on the unconscious and the irrational, features as both a source of security and of insecurity. We use three examples drawn from our own empirical research to explore the entanglement of the researcher with the researched and how this can offer a re-imagined sense of legitimacy for our work. In elaborating our argument, we discuss our experiences of 'being captured' by data and participants, and of negotiating the ethics of analysing participants' accounts. © 2014 The Author(s). Published by Pedagogy, Culture & Society

Generalised Minkowski spacetime

The four dimensional spacetime continuum, as first conceived by Minkowski, has become the default framework within which to describe physical laws. In this paper, we show how a four-dimensional Minkowski spacetime structure naturally arises from three-dimensional physical space when modeled with Clifford geometric algebra $C\ell(\Re^3)$. This expanded eight-dimensional framework allows a generalisation of the invariant interval and the Lorentz transformations. Also, with this geometric oriented approach the fixed speed of light, the laws of special relativity and the form of Maxwell's equations, arise naturally from the intrinsic properties of the algebra without recourse to physical arguments. We also find new insights into the nature of time, a unified treatment of energy-momentum and spin, a Lagrangian unifying gravity and electromagnetism as well as predictions of a new class of physical effects and interactions.Comment: 20 pages, no figure