Inverse spectral problems on a closed manifold

In this paper we consider two inverse problems on a closed connected Riemannian manifold (M, g). To formulate the first one, assume that M is divided by a hypersurface Sigma into two components and we know the eigenvalues lambda(j) of the Laplace operator on (M, g) and also the Cauchy data, on Sigma, of the corresponding eigenfunctions phi(j), i.e. phi j vertical bar(Sigma), partial derivative(nu)phi(j)vertical bar(Sigma), where nu is the normal to Sigma. We prove that these data determine (M, g) uniquely, i.e. up to an isometry. In the second problem we are given much less data, namely, lambda(j) and phi(j)vertical bar(Sigma) only. However, if Sigma consists of at least two components, Sigma(1), Sigma(2), we are still able to determine (M, g) assuming some generic conditions on the spectra of the Laplacian in subdomains of M obtained by cutting along Sigma. (C) 2008 Elsevier Masson SAS. All rights reserved

A Dangerous Idea in Zoology: Ignoring the Role of Genetics in Biodiversity Restoration

The term ‘biodiversity’ emerged in the mid-1980s and quickly became sufficiently popular that it could have been viewed as a ‘new field of science’. The broader community has also embraced the term and, ultimately, it has become a proxy for species conservation. As a consequence, conservation of biodiversity has effectively become the only approach to minimising continued species loss. However, despite the widespread use of the term, there is confusion over its definition, even among disciplines to which the term has become a focus. In Australia, much of the biodiversity conservation/restoration is community-driven (e.g., landcare, political pressure of animal welfare groups) with a focus on species and habitat biodiversity. Genetic diversity is seldom seriously considered. As a consequence, native species biodiversity management is often not maximising the potential outcomes. Arguably the greatest issue associated with incorporating genetics more centrally into biodiversity restoration is that its definition is often considered complex. In addition, the negative aspects of ignoring the genetic component of biodiversity may be masked by the positives when the outputs of a program provide many individuals of species considered at risk of extinction despite the longer term outcomes potentially having the opposite effect. To better manage biodiversity restoration all of us who use the term within our discipline need to ensure that, wherever possible, we seek to inform those around us of the importance of genetic biodiversity in biodiversity restoration programs. A first step is to determine a simple, all-encompassing definition of biodiversity that explicitly includes genetics