Joint modelling of multiple network wiews

Latent space models (LSM) for network data were introduced by Hoff et al. (2002) under the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance between two nodes in the latent space, the greater their probability of being connected. In this paper we propose a variational inference approach to estimate the intractable posterior of the LSM. In many cases, different network views on the same set of nodes are available. It can therefore be useful to build a model able to jointly summarise the information given by all the network views. For this purpose, we introduce the latent space joint model (LSJM) that merges the information given by multiple network views assuming that the probability of a node being connected with other nodes in each network view is explained by a unique latent variable. This model is demonstrated on the analysis of two datasets: an excerpt of 50 girls from 'Teenage Friends and Lifestyle Study' data at three time points and the Saccharomyces cerevisiae genetic and physical protein-protein interactions

Percolation in the classical blockmodel

Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation transition in the classical blockmodel has not been examined so far, although the phenomenon has been studied in a variety of much more complicated models of interconnected and multiplex networks. In this paper we derive the self-consistent equation for the size the global percolation cluster in the classical blockmodel. We also find the condition for percolation threshold which characterizes the emergence of the giant component. We show that the discussed percolation phenomenon may cause unexpected problems in a simple optimization process of the multilevel network construction. Numerical simulations confirm the correctness of our theoretical derivations.Comment: 7 pages, 6 figure

Use Of Chemically Modified Silica With β-diketoamine Groups For Separation Of α-lactoalbumin From Bovine Milk Whey By Affinity Chromatography

Silica gel surface was chemically modified with β-diketoamine groups by reacting the silanol from the silica surface with 3-aminopropyl-triethoxysilane and 3-bromopentanedione. With this material, copper ions were adsorbed from aqueous solutions. The chemical analysis of the silica-gel-immobilized acetylacetone provided a quantity of 0.67 mmol g-1 of organic groups attached to the support and 0.63 mmol g-1 of copper. This material was used as a stationary phase in IMAC (immobilized metal affinity chromatography), to separate α-lactoalbumin from bovine milk whey. The results showed an efficient separation in the chromatographic column. The possibility of reutilization of the stationary phase was also investigated.1852313316Wiseman, A., (1985) "Handbook of Enzyme Biotechnology," 2nd Ed., , Ellis Horwood, Chichester, EnglandCampbell, M.K., (1991) Biochemistry, , International ed. Saunders, PhiladelphiaDesai, M.A., (1990) J. Chem. Tech. Biotechnol., 48, p. 105Cuatrecasas, P., Wilchek, M., Anfinsen, C.B., (1968) Proc. Nat. Acad. Sci., 61, p. 636Boyer, R.F., (1991) J. Chem. Educ., 68, p. 430Walters, R.R., (1985) Anal. Chem., 57, pp. 1099AAdamson, A.W., (1976) "Physical Chemistry of Surfaces," 3rd Ed., , Wiley, New YorkIler, R.K., (1979) The Chemistry of Silica, , Wiley, New YorkLisichkin, G.V., Kudryatsev, G.V., Nesterenko, P.N., (1983) J. Anal. Chem. USSR, 38, p. 1288Deschler, V., Kleinschmit, P., Panster, P., (1986) Angew Chem. Int. Ed., 25, p. 236Unger, K., (1972) Angew Chem. Int. Ed., 11, p. 267Boudart, M., (1974) Chem. Tech., p. 370Kudryatsev, G.V., Lisichkin, G.V., Ivanov, V.M., (1983) J. Anal. Chem. USSR, 38, p. 16Neimar, I.E., (1987) Theor. Exp. Chem., 23, p. 539Vollet, D.R., Moreira, J.C., Kubota, L.T., Varella, J.A., Gushikem, Y., (1989) Colloids Surf., 40, p. 1Boumabraz, M., Davydov, V.Y., Kiselev, A.V., (1982) Chromatographia, 15, p. 751Sander, L.C., Wise, S.A., (1987) Crit. Rev. Anal. Chem., 18, p. 299Suckling, C.J., (1977) Chem. Soc. Rev., 6, p. 215Filipov, A.P., Zyatkovskii, V.M., Karpenko, I.A., (1981) Theor. Exp. Chem., 17, p. 278Sokozhenkin, P.M., Semikopnyi, A.I., Sharf, V.Z., Lisichkin, G.V., (1988) Russian J. Phys. Chem., 62, p. 218Davis, B.J., (1964) Ann. N. Y. Acad. Sci., 121, p. 404Ornstein, L., (1964) Ann. N. Y. Acad. Sci., 121, p. 321Airoldi, C., Alcantara, E.F.C., (1995) Thermochim. Acta, 259, p. 95Airoldi, C., Alcantara, E.F.C., (1995) J. Chem. Thermodyn., 27, p. 623Huynh, T.K.X., Lederer, M., (1993) J. Chromatogr., 645, p. 185Iamamoto, M.S., Gushikem, Y., (1989) Analyst, 114, p. 98