We consider the problem of fuzzy community detection in networks, which complements and expands the concept of overlapping community structure. Our approach allows each vertex of the graph to belong to multiple communities at the same time, determined by exact numerical membership degrees, even in the presence of uncertainty in the data being analyzed. We create an algorithm for determining the optimal membership degrees with respect to a given goal function. Based on the membership degrees, we introduce a measure that is able to identify outlier vertices that do not belong to any of the communities, bridge vertices that have significant membership in more than one single community, and regular vertices that fundamentally restrict their interactions within their own community, while also being able to quantify the centrality of a vertex with respect to its dominant community. The method can also be used for prediction in case of uncertainty in the data set analyzed. The number of communities can be given in advance, or determined by the algorithm itself, using a fuzzified variant of the modularity function. The technique is able to discover the fuzzy community structure of different real world networks including, but not limited to, social networks, scientific collaboration networks, and cortical networks, with high confidence.

Performance enhancement (PE) is a natural and essential ingredient of competitive sport. Except for nutritional supplement contamination, accidental use of doping is highly unlikely. It requires deliberation, planning and commitment; and is influenced by a host of protective and risk factors.

Background: Recently, the accuracies of many commercially available immunoassays for Vitamin D have been questioned. Liquid chromatography tandem mass spectrometry (LC- MS/MS) has been shown to facilitate accurate separation and quantification of the major circulating metabolite 25-hydroxyvitamin-D3 (25OHD3) and 25-hydroxyvitamin-D2 (25OHD2) collectively termed as 25OHD. However, among other interferents, this method may be compromised by overlapping peaks and identical masses of epimers and isobars, resulting in inaccuracies in circulating 25OHD measurements. The aim of this study was to develop a novel LC-MS/MS method that can accurately identify and quantitate 25OHD3 and 25OHD2 through chromatographic separation of 25OHD from its epimers and isobars. Methods: A positive ion electrospray ionisation (ESI) LC-MS/MS method was used in the Multiple Reaction Monitoring (MRM) mode for quantification. It involved i) liquid-liquid extraction, ii) tandem columns (a high resolution ZORBAX C18 coupled to an ULTRON chiral, with guard column and inlet filter), iii) Stanozolol-D3 as internal standard, and iv) identification via ESI and monitoring of three fragmentation transitions. To demonstrate the practical usefulness of our method, blood samples were collected from 5 healthy male Caucasian volunteers; age range 22 to 37 years and 25OHD2, 25OHD3 along with co-eluting epimers and analogues were quantified. Results: The new method allowed chromatographic separation and quantification of 25OHD2, 25OHD3, along with 25OHD3 epimer 3-epi-25OHD3 and isobars 1-α-hydroxyvitamin-D3 (1αOHD3), and 7-α-hydroxy-4-cholesten-3-one (7αC4). The new assay was capable of detecting 0.25 ng/mL of all analytes in serum. Conclusions: To our knowledge, this is the first specific, reliable, reproducible and robust LC-MS/MS method developed for the accurate detection of 25OHD (Vitamin D). The method is capable of detecting low levels of 25OHD3 and 25OHD2 together with chromatographic separation from the co-eluting epimers and isobars and circumvents other instrumental/analytical interferences. This analytical method does not require time-consuming derivatisation and complex extraction techniques and could prove very useful in clinical studies.