Supermetric search with the four-point property

Metric indexing research is concerned with the efficient evaluation of queries in metric spaces. In general, a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query can be efficiently found. Most such mechanisms rely upon the triangle inequality property of the metric governing the space. The triangle inequality property is equivalent to a finite embedding property, which states that any three points of the space can be isometrically embedded in two-dimensional Euclidean space. In this paper, we examine a class of semimetric space which is finitely 4-embeddable in three-dimensional Euclidean space. In mathematics this property has been extensively studied and is generally known as the four-point property. All spaces with the four-point property are metric spaces, but they also have some stronger geometric guarantees. We coin the term supermetric space as, in terms of metric search, they are significantly more tractable. We show some stronger geometric guarantees deriving from the four-point property which can be used in indexing to great effect, and show results for two of the SISAP benchmark searches that are substantially better than any previously published

Reference point hyperplane trees

Our context of interest is tree-structured exact search in metric spaces. We make the simple observation that, the deeper a data item is within the tree, the higher the probability of that item being excluded from a search. Assuming a fixed and independent probability p of any subtree being excluded at query time, the probability of an individual data item being accessed is (1−p)d for a node at depth d. In a balanced binary tree half of the data will be at the maximum depth of the tree so this effect should be significant and observable. We test this hypothesis with two experiments on partition trees. First, we force a balance by adjusting the partition/exclusion criteria, and compare this with unbalanced trees where the mean data depth is greater. Second, we compare a generic hyperplane tree with a monotone hyperplane tree, where also the mean depth is greater. In both cases the tree with the greater mean data depth performs better in high-dimensional spaces. We then experiment with increasing the mean depth of nodes by using a small, fixed set of reference points to make exclusion decisions over the whole tree, so that almost all of the data resides at the maximum depth. Again this can be seen to reduce the overall cost of indexing. Furthermore, we observe that having already calculated reference point distances for all data, a final filtering can be applied if the distance table is retained. This reduces further the number of distance calculations required, whilst retaining scalability. The final structure can in fact be viewed as a hybrid between a generic hyperplane tree and a LAESA search structure

The Environment of HII Galaxies revisited

We present a study of the close (< 200 kpc) environment of 110 relatively local (z< 0.16) HII galaxies, selected from the Sloan Digital Sky Survey (SDSS; DR7). We use available spectroscopic and photometric redshifts in order to investigate the presence of a close and possibly interacting companion galaxy. Our aim is to compare the physical properties of isolated and interacting HII galaxies and investigate possible systematic effects in their use as cosmological probes. We find that interacting HII galaxies tend to be more compact, less luminous and have a lower velocity dispersion than isolated ones, in agreement with previous studies on smaller samples. However, as we verified, these environmental differences do not affect the cosmologically important L_{H{\beta}}-{\sigma} correlation of the HII galaxies.Comment: 5 pages, accepted for publication in A&

Funktionskreis and the stratificational model of semiotic structures: Jakob von Uexküll, Luis Prieto and Louis Hjelmslev

The main aim of this article is to show how a possible theoretical articulation between Uexküll’s notion of Funktionskreis and the stratificational model of semiotic structures proposed by Louis Hjelmslev can be made. In order to bridge the gap between these two models, Luis Prieto’s model of cognition will be used. The advantage of Prieto’s model is that it retains the Hjelmslevian stratificational ideas (i.e. a semiotic structure is made up of an expression and a content plane, each one with a dimension of form and substance), while it also pays attention to agency and practice. To put it briefly, according to Prieto the foundation of practice and knowledge is to be found on aisthesis. Hence, as in Uexküll, there is a way to merge action with perception, while retaining the semiotic structure that makes such a merging possible. The key point, however, is that Prieto’s model calls for an “ontological commitment” to the substance strata (both in expression and in content to some extent). Therefore, bridging Uexküll and Hjelmslev via Prieto suggests a possible way to provide a general structural model of semiosis which is closer to semiotic realism than to immanentism usually attributed to structuralism