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.

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.

Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

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.