We present a study of Dirac quantum fields in a four-dimensional de Sitter spacetime. The theory is based on the requirement of precise analyticity properties of the waves and the correlation functions in the complexification of the de Sitter manifold. Holomorphic de Sitter spinorial plane waves are introduced in this way and used to construct the two-point functions, whose properties are fully characterized. The physical interpretation of the analyticity properties of Wightman's functions in terms of a KMS-type thermal condition is also given.

Node centrality is one of the most important and widely used concepts in the study of complex networks. Here, we extend the paradigm of node centrality in financial and economic networks to consider the changes of node ``importance"" produced not only by the variation of the topology of the system but also as a consequence of the external levels of risk to which the network as a whole is subjected. Starting from the ``Susceptible-Infected"" (SI) model of epidemics and its relation to the communicability functions of networks, we develop a series of risk-dependent centralities for nodes in (financial and economic) networks. We analyze here some of the most important mathematical properties of these risk-dependent centrality measures. In particular, we study the newly observed phenomenon of ranking interlacement, by means of which two entities may interlace their ranking positions in terms of risk in the network as a consequence of the change in the external conditions only, i.e., without any change in the topology. We test the risk-dependent centralities by studying two realworld systems: the network generated by collecting assets of the S\&P 100 and the corporate board network of the U.S. top companies, according to Forbes in 1999. We found that a high position in the ranking of the analyzed financial companies according to their risk-dependent centrality corresponds to companies more sensitive to the external market variations during the periods of crisis.

In this paper, we investigate the mesoscale structure of the World Trade Network. In this framework, a specific role is assumed by short- and long-range interactions, and hence by any suitably defined network-based distance between countries. Therefore, we identify clusters through a new procedure that exploits Estrada communicability distance and the vibrational communicability distance, which turn out to be particularly suitable for catching the inner structure of the economic network. The proposed methodology aims at finding the distance threshold that maximizes a specific quality function defined for general metric spaces. Main advantages regard the computational efficiency of the procedure as well as the possibility to inspect intercluster and intracluster properties of the resulting communities. The numerical analysis highlights peculiar relationships between countries and provides a rich set of information that can hardly be achieved within alternative clustering approaches.

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We consider the problem of modifying a network topology in such a way as to delay the propagation of a disease with minimal disruption of the network capacity to reroute goods/items/passengers. We find an approximate solution to the Susceptible-Infected-Susceptible (SIS) model, which constitutes an upper bound to its exact solution. This upper bound allows direct structure-epidemic dynamic relations via the total communicability function. Using this approach we propose a strategy to remove edges in a network that significantly delays the propagation of a disease across the network with minimal disruption of its capacity to deliver goods/items/passengers. We apply this strategy to the analysis of the UK airport transportation network weighted by the number of passengers transported in 2003. We find that the removal of all flights connecting four origin-destination pairs in the UK delays the propagation of a disease by more than 300%, with a minimal deterioration of the transportation capacity of this network. These time delays in the propagation of a disease represent an important non-pharmaceutical intervention to confront an epidemic, allowing for better preparations of the health systems, while keeping the economy moving with minimal disruptions.

Understanding the structure of communities in a network has a great importance in the economic analysis. Communities are indeed characterized by specific properties, that are different from those of both the individual nodes and the whole network, and they can affect various processes on the network. In the International Trade Network, community detection aims to search sets of countries (or of trade sectors) which have a high intra-cluster connectivity and a low inter-cluster connectivity. In general, exchanges among countries occur according to preferential economic relationships ranging over different sectors. In this paper, we combine community detection with specific topological indicators, such as centrality measures. As a result, a new weighted network is constructed from the original one, in which weights are determined taking into account all the topological indicators in a multi-criteria approach. To solve the resulting Clique Partitioning Problem and find homogeneous group of nations, we use a new fast algorithm, based on quick descents to a local optimal solution. The analysis allows to cluster countries by interconnections, economic power and intensity of trade, giving an important overview on the international trade patterns.

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