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.

A 330-360 GHz spectral survey of G34.3+0.15 - III. The outer halo

We have undertaken a 330-360 GHz molecular line survey of the halo gas surrounding the hot core associated with G34.26+0.15. In contrast to our molecular line survey of the hot core itself, where 338 lines from at least 38 species were detected, only 18 lines from 9 species were detected in the halo. The lines are mainly single transitions of simple di atomic and triatomic molecules. Lower limits to their column densities have been evaluated by an LTE method. In the case of methanol, where four transitions were detected, the rotation temperature and column density have been evaluated by the rotation diagram technique. We have modified the previous depth-dependent chemical model developed in Paper II to calculate the column densities observed along a general line of sight drawn through the model cloud. The model is also extended to produce beam-averaged column densities for better comparison with those observed. We compare the model column densities with those observed and make recommendations for future depth-dependent chemical modelling of hot cores.

A three-position spectral line survey of Sagittarius B2 between 218 and 263 GHz. I. The observational data

We have surveyed the frequency band 218.30-263.55 GHz toward the core positions N and M and the quiescent cloud position NW in the Sgr B2 molecular cloud using the Swedish-ESO Submillimetre Telescope. In total 1730, 660, and 110 lines were detected in N, M, and NW, respectively, and 42 different molecular species were identified. The number of unidentified lines are 337, 51, and eight. Toward the N source, spectral line emission constitutes 22% of the total detected flux in the observed band, and complex organic molecules are the main contributors. Toward M, 14% of the broadband flux is caused by lines, and SO2 is here the dominant source of emission. NW is relatively poor in spectral lines and continuum. In this paper we present the spectra together with tables of suggested line identifications.

A 330-360 GHz spectral survey of G34.3+0.15 .2. Chemical modelling

We describe a detailed depth-and time-dependent model of the molecular cloud associated with the ultracompact H II region G 34.3+0.15. Previous work on observations of NH3 and CS indicates that the molecular cloud has three distinct physical components:- an ultracompact hot core, a compact hot core and an extended halo. We have used the physical parameters derived from these observations as input to our detailed chemical kinetic modelling. The results of the model calculations are discussed with reference to the different chemistries occuring in each component and are compared with abundances derived from our recent spectral line survey of G 34.3+0.15 (Paper I).

A 330-360 GHz spectral survey of G 34.3+0.15 .1. Data and physical analysis

A 330--360 GHz spectral survey of the hot molecular core associated with the 'cometary' ultracompact HII region G 34.3+/-0.15 observed with the James Clerk Maxwell Telescope has detected 338 spectral lines from at least 35 distinct chemical species plus 19 isotopomers. 70 lines remain unidentified. Chemical abundance and rotation temperature have been determined by rotation diagram analysis for 12 species, and lower limits to abundance found for 38 others.

THE FORMATION OF OXYGEN-CONTAINING ORGANIC-MOLECULES IN THE ORION COMPACT RIDGE

Following a suggestion of Blake et al., we have attempted to account for the unusually large abundances of selected oxygen-containing organic molecules in the so-called

Design and evaluation of tinnitus synthesis methods: From spectral to spatial matching

Purpose
This study was designed to investigate methods to help patients suffering from unilateral tinnitus synthesizing an auditory replica of their tinnitus.

Materials and methods
Two semi-automatic methods (A and B) derived from the auditory threshold of the patient and a method (C) combining a pure tone and a narrow band-pass noise centred on an adjustable frequency were devised and rated on their likeness over two test sessions. A third test evaluated the stability over time of the synthesized tinnitus replica built with method C, and its proneness to merge with the patient's tinnitus. Patients were then asked to try and control the lateralisation of this single percept through the adjustment of the tinnitus replica level.

Results
The first two tests showed that seven out of ten patients chose the tinnitus replica built with method C as their preferred one. The third test, performed on twelve patients, revealed pitch tuning was rather stable over a week interval. It showed that eight patients were able to consistently match the central frequency of the synthesized tinnitus (presented to the contralateral ear) to their own tinnitus, which leaded to a unique tinnitus percept. The lateralisation displacement was consistent across patients and revealed an average range of 29dB to obtain a full lateral shift from the ipsilateral to the contralateral side.

Conclusions
Although spectrally simpler than the semi-automatic methods, method C could replicate patients' tinnitus, to some extent. When a unique percept between synthesized tinnitus and patients' tinnitus arose, lateralisation of this percept was achieved.