A discrete in time model of ideological competition is formulated taking into account population migration. The model is based on interactions between global populations of non-believers and followers of different ideologies. The complex dynamics of the attracting manifolds is investigated. Conversion from one ideology to another by means of (i) mass media influence and (ii) interpersonal relations is considered. Moreover a different birth rate is assumed for different ideologies, the rate being assumed to be positive for the reference population, made of initially non-believers. Ideological competition can happen in one or several regions in space. In the latter case, migration of non-believers and adepts is allowed; this leads to an enrichment of the ideological dynamics. Finally, the current ideological situation in the Arab countries and China is commented upon from the point of view of the presently developed mathematical model. The massive forced conversion by Ottoman Turks in the Balkans is briefly discussed.

B.V.I., M.A. and G.R. have no competing interests to declare. There is no connection to the current paper, but C.H. declares that (i) he is currently conducting a research titled 'Chronic Diseases' Direct Costs within the Romanian Health System' funded by Local American Working Group; (ii) his wife is employed to a Romanian company (A&D Pharma) that does business in the pharmaceutical sector. This paper is a part of G.R. and M.A. scientific activities in COST Action TD1210. This work by C.H. was co-financed by the European Social Fund through project number POSDRU/1.5/S/59184.

This paper aims to provide a network analysis of the relationships of\ud shareholders in the Italian stock market for understanding the relevance of portfolio diversification in integrated ownership and firms control. The analysis combines both a complex network and an operational research approach. The former is used for statistical analyses on portfolio diversification. The latter estimates integrated ownership considering the paths on the network, and it emphasizes the difference between ownership and control. The dataset consists of nearly 300 companies traded on the Italian Stock Market.Datawere retrieved throughCONSOBand AIDAdatabase, and they are adjourned at 2008. The dataset is completed with information on banks and insurance companies. Such data were retrieved through BANKSCOPE and ISIS databases

a b s t r a c tAmong the topics of opinion formation it is of interest to observe the characteristics of networks with a priori distinct communities. The citation network(s) between selected members of the Neocreationist and Intelligent Design and the Darwinian Evolution communities are unfolded through the available internet citations. The resulting adjacency matrix is not symmetric. A generalization of considerations pertaining to the case of networks with tagged nodes and biased links, directed or undirected, is presented. The main characteristic coefficients describing the structure of such networks are outlined. The structural features are discussed searching for statistical aspects of the communities. The degree distributions, each network's assortativity, specific global and local clustering coefficients and the Average Overlap Indices are especially calculated since the distribution of elements in the rectangular submatrices represent inter-community connections. The various closed and open triangles made from nodes, distinguishing the community, are listed. The z-scores of patterns are calculated. One can distinguish between opinion leaders, followers and main rivals and briefly interpret their relationships through intuitively expected behavior in defence of an opinion. Suggestions for more elaborate models describing such communities and their subsequent structures are found in conclusions.

The notion of complex-valued information entropy measure is presented. It applies in particular to directed networks (digraphs). The corresponding statistical physics notions are outlined. The studied network, serving as a case study, in view of illustrating the discussion, concerns citations by agents belonging to two distinct communities which have markedly different opinions: the Neocreationist and Intelligent Design Proponents, on one hand, and the Darwinian Evolution Defenders, on the other hand. The whole, intra-and inter-community adjacency matrices, resulting from quotations of published work by the community agents, are elaborated and eigenvalues calculated. Since eigenvalues can be complex numbers, the information entropy may become also complex-valued. It is calculated for *