Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph

For a given graph G and an associated class of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in G, the collection of all possible spectra for such matrices is considered. Building on the pioneering work of Colin de Verdiere in connection with the Strong Arnold Property, two extensions are devised that target a better understanding of all possible spectra and their associated multiplicities. These new properties are referred to as the Strong Spectral Property and the Strong Multiplicity Property. Finally, these ideas are applied to the minimum number of distinct eigenvalues associated with G, denoted by q(G). The graphs for which q(G) is at least the number of vertices of G less one are characterized.Comment: 26 pages; corrected statement of Theorem 3.5 (a

HydroDetect: The Identification and Assessment of Climate Change Indicators for an Irish Reference Network of River Flow Stations - an Overview

This paper provides an overview of key findings from the EPA funded HydroDetect project which establishes an Irish Reference Network (IRN) of river flow gauges for monitoring and detecting climate driven trends. The flow archive from 35 hydrometric stations has an average record length of 40 years and draws from the strengths of the existing national hydrometric network. Using criteria based on the quality of flow records and minimisation of artificial influences and land-use change, complimented by expert judgement, the IRN is a valuable resource facilitating more strategic monitoring of climate driven variability and change in hydrological indicators and enabling more confident attribution of detected trends. Here an analysis of trends in mean and high flows for stations in the IRN is presented, with the spatial distribution of trends across the network examined for the period 1976-2009. The following key findings emerge. While there is considerable evidence of change in the IRN, it is difficult at this point in time to attribute these to anthropogenic greenhouse gas induced climate change. Indeed some of the trends identified – decreases in shorter records in winter mean flows and increases in summer flows – are not consistent with expected changes as simulated by Global Climate Models. This should not be surprising given the large variability of river flows relative to climate change signals at this point. Trends in Irish river flows are strongly correlated with the winter North Atlantic Oscillation Index (NAOI). The sensitivity and response of the NAO to greenhouse gas forcing will have obvious implications for Irish hydrology; however the question remains open as to the impact that greenhouse gas forcing has had on recent behaviour of the NAO and how it is likely to respond to future forcing. While it remains challenging to identify anthropogenic climate change signals at the catchment scale due to large natural variability and therefore a low signal to noise ratio, there is high potential for identifying sentinel stations and indicators within the IRN for early detection of climate change signals. These findings heighten the importance of the IRN for monitoring and detecting climate change signals at the catchment scale, for tracking the emergence of signals relative to natural variability and for providing information, free from confounding factors, for validating output from climate change impact assessments and developing adaptation policies

Attribution of detected changes in streamflow using multiple working hypotheses

This paper revisits a widely cited study of the Boyne catchment in east Ireland that attributed greater streamflow from the mid-1970s to increased precipitation linked to a shift in the North Atlantic Oscillation. Using the method of multiple working hypotheses we explore a wider set of potential drivers of hydrological change. Rainfall-runoff models are used to reconstruct streamflow to isolate the effect of climate, taking account of both model structure and parameter uncertainty. The Mann-Kendall test for monotonic trend and Pettitt change point test are applied to explore signatures of change. Contrary to earlier work, arterial drainage and simultaneous onset of field drainage in the 1970s and early 1980s are now invoked as the predominant drivers of change in annual mean and high flows within the Boyne. However, a change in precipitation regime is also present in March, thereby amplifying the effect of drainage. This new explanation posits that multiple drivers acting simultaneously were responsible for the observed change, with the relative contribution of each driver dependant on the timescale investigated. This work demonstrates that valuable insights can be gained from a systematic application of the method of multiple working hypotheses in an effort to move towards more rigorous attribution, which is an important part of managing emerging impacts on hydrological systems. © Author(s) 2014

On the graph complement conjecture for minimum rank

AbstractThe minimum rank of a graph has been an interesting and well studied parameter investigated by many researchers over the past decade or so. One of the many unresolved questions on this topic is the so-called graph complement conjecture, which grew out of a workshop in 2006. This conjecture asks for an upper bound on the sum of the minimum rank of a graph and the minimum rank of its complement, and may be classified as a Nordhaus–Gaddum type problem involving the graph parameter minimum rank. The conjectured bound is the order of the graph plus two. Other variants of the graph complement conjecture are introduced here for the minimum semidefinite rank and the Colin de Verdière type parameter ν. We show that if the ν-graph complement conjecture is true for two graphs then it is true for the join of these graphs. Related results for the graph complement conjecture (and the positive semidefinite version) for joins of graphs are also established. We also report on the use of recent results on partial k-trees to establish the graph complement conjecture for graphs of low minimum rank

Animal-Computer Interaction: the emergence of a discipline

In this editorial to the IJHCS Special Issue on Animal-Computer Interaction (ACI), we provide an overview of the state-of-the-art in this emerging field, outlining the main scientific interests of its developing community, in a broader cultural context of evolving human-animal relations. We summarise the core aims proposed for the development of ACI as a discipline, discussing the challenges these pose and how ACI researchers are trying to address them. We then introduce the contributions to the Special Issue, showing how they illustrate some of the key issues that characterise the current state-of-the-art in ACI, and finally reflect on how the journey ahead towards developing an ACI discipline could be undertaken

HydroDetect : The Identification and Assessment of Climate Change Indicators for an Irish Reference Network of River Flow Stations. Climate Change Research Programme (CCRP) 2007-2013 Report Series No. 27. ISBN 978-1-84095-507-1

Abstract included in text