Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

Making sense of a world of clicks

In a recent article O. Ulfbeck and A. Bohr (Foundations of Physics 31, 757, 2001) have stressed the genuine fortuitousness of detector clicks, which has also been pointed out, in different terms, by the present author (American Journal of Physics 68, 728, 2000). In spite of this basic agreement, the present article raises objections to the presuppositions and conclusions of Ulfbeck and Bohr, in particular their rejection of the terminology of indefinite variables, their identification of reality with "the world of experience," their identification of experience with what takes place "on the spacetime scene," and the claim that their interpretation of quantum mechanics is "entirely liberated" from classical notions. An alternative way of making sense of a world of uncaused clicks is presented. This does not invoke experience but deals with a free-standing reality, is not fettered by classical conceptions of space and time but introduces adequate ways of thinking about the spatiotemporal aspects of the quantum world, and does not reject indefinite variables but clarifies the implications of their existence.Comment: 15 pages, LaTeX2

Techniques for clustering gene expression data

Many clustering techniques have been proposed for the analysis of gene expression data obtained from microarray experiments. However, choice of suitable method(s) for a given experimental dataset is not straightforward. Common approaches do not translate well and fail to take account of the data profile. This review paper surveys state of the art applications which recognises these limitations and implements procedures to overcome them. It provides a framework for the evaluation of clustering in gene expression analyses. The nature of microarray data is discussed briefly. Selected examples are presented for the clustering methods considered

Searching for the first Near-Earth Object family

We report on our search for genetically related asteroids amongst the near-Earth object (NEO) population - families of NEOs akin to the well known main belt asteroid families. We used the technique proposed by Fu et al. (2005) supplemented with a detailed analysis of the statistical significance of the detected clusters. Their significance was assessed by comparison to identical searches performed on 1,000 'fuzzy-real' NEO orbit distribution models that we developed for this purpose. The family-free 'fuzzy-real' NEO models maintain both the micro and macro distribution of 5 orbital elements (ignoring the mean anomaly). Three clusters were identified that contain four or more NEOs but none of them are statistically significant at \geq 3{\sigma}. The most statistically significant cluster at the \sim 2{\sigma} level contains 4 objects with H < 20 and all members have long observational arcs and concomitant good orbital elements. Despite the low statistical significance we performed several other tests on the cluster to determine if it is likely a genetic family. The tests included examining the cluster's taxonomy, size-frequency distribution, consistency with a family-forming event during tidal disruption in a close approach to Mars, and whether it is detectable in a proper element cluster search. None of these tests exclude the possibility that the cluster is a family but neither do they confirm the hypothesis. We conclude that we have not identified any NEO families.Comment: 36 pages, 3 tables, 9 figures, accepted for publicatio

Dynamical tachyons on fuzzy spheres

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the BMN plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We also set up a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.Comment: 34 pages, 4 figures; v2: 35 pages, expanded sec. 4.3, added reference