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One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of [Formula: see text] nodes that can be linked in multiple interacting(More)
Systems Medicine (SM) can be defined as an extension of Systems Biology (SB) to Clinical-Epidemiological disciplines through a shifting paradigm, starting from a cellular, toward a patient centered framework. According to this vision, the three pillars of SM are Biomedical hypotheses, experimental data, mainly achieved by Omics technologies and tailored(More)
Multiplex networks describe a large number of systems ranging from social networks to the brain. These multilayer structure encode information in their structure. This information can be extracted by measuring the correlations present in the multiplex networks structure, such as the overlap of the links in different layers. Many multiplex networks are also(More)
We characterize different cell states, related to cancer and ageing phenotypes, by a measure of entropy of network ensembles, integrating gene expression profiling values and protein interaction network topology. In our case studies, network entropy, that by definition estimates the number of possible network instances satisfying the given constraints, can(More)
The problem of controllability of the dynamical state of a network is central in network theory and has wide applications ranging from network medicine to financial markets. The driver nodes of the network are the nodes that can bring the network to the desired dynamical state if an external signal is applied to them. Using the framework of structural(More)
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical(More)
The controllability of a network is a theoretical problem of relevance in a variety of contexts ranging from financial markets to the brain. Until now, network controllability has been characterized only on isolated networks, while the vast majority of complex systems are formed by multilayer networks. Here we build a theoretical framework for the linear(More)
We characterize different cell states, related to cancer and ageing phenotypes, by a measure of entropy of network ensembles, integrating gene expression values and protein interaction networks. The entropy measure estimates the parameter space available to the network ensemble, that can be interpreted as the level of plasticity of the system for high(More)
In this paper we introduce the framework for the application of statistical mechanics to network theory, with a particular emphasis to the concept of entropy of network ensembles. This formalism provides novel observables and insights for the analysis of high-throughput transcriptomics data, integrated with apriori biological knowledge, embedded in-to(More)