Detection of node group membership in networks with group overlap

Most networks found in social and biochemical systems have modular structures. An important question prompted by the modularity of these networks is whether nodes can be said to belong to a single group. If they cannot, we would need to consider the role of "overlapping communities." Despite some efforts in this direction, the problem of detecting overlapping groups remains unsolved because there is neither a formal definition of overlapping community, nor an ensemble of networks with which to test the performance of group detection algorithms when nodes can belong to more than one group. Here, we introduce an ensemble of networks with overlapping groups. We then apply three group identification methods--modularity maximization, k-clique percolation, and modularity-landscape surveying--to these networks. We find that the modularity-landscape surveying method is the only one able to detect heterogeneities in node memberships, and that those heterogeneities are only detectable when the overlap is small. Surprisingly, we find that the k-clique percolation method is unable to detect node membership for the overlapping case.Comment: 12 pages, 6 figures. To appear in Euro. Phys. J

Modes of magnetic resonance of S=1 dimer chain compound NTENP

The spin dynamics of a quasi one dimensional $S=1$ bond alternating spin-gap antiferromagnet Ni(C$_9$H$_{24}$N$_4$)NO$_2$(ClO$_4$) (abbreviated as NTENP) is studied by means of electron spin resonance (ESR) technique. Five modes of ESR transitions are observed and identified: transitions between singlet ground state and excited triplet states, three modes of transitions between spin sublevels of collective triplet states and antiferromagnetic resonance absorption in the field-induced antiferromagnetically ordered phase. Singlet-triplet and intra-triplet modes demonstrate a doublet structure which is due to two maxima in the density of magnon states in the low-frequency range. A joint analysis of the observed spectra and other experimental results allows to test the applicability of the fermionic and bosonic models. We conclude that the fermionic approach is more appropriate for the particular case of NTENP.Comment: 11 pages, 11 figures, published in Phys.Rev.

Combination ecotoxicity and testing of common chemical discharges to sewer using the Vibrio fischeri luminescence bioassay

In order to investigate possible synergistic or antagonistic (more or less than additive) toxicity effects, mixtures of chemicals were tested in water using a microbial bioassay. Ten toxicants (3,4-dichloroaniline, 3,5- dichlorophenol, cadmium, chromium, copper, Lindane, linear alkylbenzene sulphonate, pentachlorophenol, toluene, zinc) were chosen on the basis of their common occurrence in industrial effluents within local waste water treatment plants. These toxicants also cover a wide range of modes of toxic action, namely, polar and non-polar narcosis, membrane disruption, respiratory disruption, uncouplers of oxidative phosphorylation, biochemical disruption and enzyme inhibition. Efficient screening for possible combination toxicity between toxicants involved testing the chemicals both singly and in triplet combinations. The triplets were based on four replicates of a balanced incomplete block design (BIB). A standardised Vibrio fischeri rapid toxicity bioluminescence assay was used. The combinations tested showed that only one mixture was found to be significantly more toxic than expected from the pure singletoxicant results. Two triplets were significantly less toxic. Further tests on the more toxic triplet showed that the effect was due to only one of the 45 pairs originally screened. It is concluded that synergistic effects in combinations of toxicants are rather rare in bioluminescence systems utilising common effluents discharged to sewer