Comparing large graphs efficiently by margins of feature vectors

Measuring the structural similarity of graphs is a challenging and outstanding problem. Most of the classical approaches of the so-called exact graph matching methods are based on graph or subgraph isomorphic relations of the underlying graphs. In contrast to these methods in this paper we introduce a novel approach to measure the structural similarity of directed and undirected graphs that is mainly based on margins of feature vectors representing graphs. We introduce novel graph similarity and dissimilarity measures, provide some properties and analyze their algorithmic complexity. We find that the computational complexity of our measures is polynomial in the graph size and, hence, significantly better than classical methods from, e.g. exact graph matching which are NP-complete. Numerically, we provide some examples of our measure and compare the results with the well-known graph edit distance. (c) 2006 Elsevier Inc. All rights reserved.

Indexing and matching trajectories under inconsistent sampling rates

Quantifying the similarity between two trajectories is a fundamental operation in analysis of spatio-temporal databases. While a number of distance functions exist, the recent shift in the dynamics of the trajectory generation procedure violates one of their core assumptions; a consistent and uniform sampling rate. In this paper, we formulate a robust distance function called Edit Distance with Projections (EDwP) to match trajectories under inconsistent and variable sampling rates through dynamic interpolation. This is achieved by deploying the idea of projections that goes beyond matching only the sampled points while aligning trajectories. To enable efficient trajectory retrievals using EDwP, we design an index structure called TrajTree. TrajTree derives its pruning power by employing the unique combination of bounding boxes with Lipschitz embedding. Extensive experiments on real trajectory databases demonstrate EDwP to be up to 5 times more accurate than the state-of-the-art distance functions. Additionally, TrajTree increases the efficiency of trajectory retrievals by up to an order of magnitude over existing techniques.

Using idiothetic cues to swim a path with a fixed trajectory and distance: Necessary involvement of the hippocampus but not the retrosplenial cortex.

Rats rapidly learned to find a submerged platform in a water maze at a constant distance and angle from the start point, which changed on every trial. The rats performed accurately in the light and dark, but prior rotation disrupted the latter condition. The rats were then retested after receiving cytotoxic hippocampal or retrosplenial cortex lesions. Retrosplenial lesions had no apparent effect in either the light or dark. Hippocampal lesions impaired performance in both conditions but spared the ability to locate a platform placed in the center of the pool. A hippocampal deficit emerged when this pool-center task was run in the dark. The spatial effects of hippocampal damage extend beyond allocentric tasks to include aspects of idiothetic guidance.

Distance and Proximity in Service to the Empire: Ulster and New Zealand between the Wars

This essay uses the concepts of ‘distance’ and ‘proximity’ to investigate and assess perceptions of community, nation and empire in inter-war New Zealand and Ulster (as well as Ireland and Northern Ireland) within a British imperial context, and explores the extent to which service of the empire (for example in the First World War) promoted both notions of imperial unity and local autonomy. It focuses on how these perceptions were articulated in the inter-war years during visits to Northern Ireland by three New Zealand premiers – Massey, Forbes and Coates – and to New Zealand by the Prime Minister of Northern Ireland, Lord Craigavon. It discusses the significant ways in which distance from their ‘home base’ and proximity to expatriate communities (in Craigavon's case) and Irish unionists and nationalists (in the case of the New Zealand premiers) inflected public statements during their visits. By examining these inter-war visits and investigating the rhetoric used and the cultural demonstrations associated with them, the factors of both distance and proximity can be used to evaluate similarities and difference across two parts of the empire. Thus, we can throw some light on the nature and dynamics of British imperial identity in the early twentieth century.

Distance between home and work: A multilevel analysis of individual workers, neighbourhoods, and employment sites in Northern Ireland

Abstract. We explore the distances between home and work for employees at twenty-eight different employment sites across Northern Ireland. Substantively, this is important for better understanding the geography of labour catchments. Methodologically, with data on the distances between place of residence (566 wards) and place of work for some 15 000 workers, and the use of multilevel modelling (MLM), the analysis adds to the evidence derived from other census-based and survey-based studies. Descriptive analysis is supplemented with MLM that simultaneously explores individual, neighbourhood, and site variations in travel-to-work patterns using hierarchical and cross-classified model specifications, including individual and ecological predictor variables (and their cross-level interactions). In doing so we apportion variability to different levels and spatial contexts, and also outline the factors that shape spatial mobility. We find, as expected, that factors such as gender and occupation influence the distance between home and work, and also confirm the importance of neighbourhood characteristics (such as population density observed in ecological analyses at ward level) in shaping individual outcomes, with major differences found between urban and rural locations. Beyond this, the analysis of variability also points to the relative significance of residential location, with less individual variability in travel-to-work distance between workers within wards than within employment sites. We conclude by suggesting that, whilst some general ‘rules’ about the factors that shape labour catchments are possible (eg workers in rural areas and in higher occupations travel further than others), the complex variability between places highlighted by the MLM analysis illustrates the salience of place-specific uniqueness.

Determinants of long-distance investing by business angels in the UK

The business angel market is usually identified as a local market, and the proximity of an investment has been shown to be key in the angel's investment preferences and an important filter at the screening stage of the investment decision. This is generally explained by the personal and localized networks used to identify potential investments, the hands-on involvement of the investor and the desire to minimize risk. However, a significant minority of investments are long distance. This paper is based on data from 373 investments made by 109 UK business angels. We classify the location of investments into three groups: local investments ( those made within the same county or in adjacent counties); intermediate investments ( those made in counties adjacent to the 'local' counties); and long-distance investments ( those made beyond this range). Using ordered logit analysis the paper develops and tests a number of hypotheses that relate long-distance investment to investment characteristics and investor characteristics. The paper concludes by drawing out the implications for entrepreneurs seeking business angel finance in investment-deficient regions, business angel networks seeking to match investors to entrepreneurs and firms ( which are normally their primary clients), and for policy-makers responsible for local and regional economic development.