We demonstrate for the case of single-layer neural networks how an extension of the TAP mean-field approach of disorder physics can be applied to the computation of approximate averages in probabilistic models for real data.

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and Nγ edges, with 1γ≤2. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the...

To describe the dynamics of learning an input–output relation from a set of examples, the evolution of an appropriate choice of macroscopic dynamical variables have to be found. Recent progress in on-line learning only addresses the often unrealistic case of an infinite training set. For...

The network structure of non-centrally cleared derivative markets, uncovered via the European Market Infrastructure Regulation (EMIR), is investigated with a focus on the Covid-19 market turmoil period. Initial and variation margin networks are reconstructed to analyze channels of potential...

The global financial crisis of 2008, triggered by the collapse of Lehman Brothers, highlighted a banking system that was widely exposed to systemic risk. The minimization of the systemic risk via a close and detailed monitoring of the entire banking network became a priority. This is a complex...

The evolution of the convergence among the European countries, including both Eurozone as well as non-Eurozone economies, is investigated in this paper. To do so, we construct correlation-based networks and study them by employing the Threshold Weighted-Minimum Dominating Set (TW-MDS) algorithm...

Social and computer networks permeate our lives. Large networks, such as the Internet, the World Wide Web (WWW), AND wireless smartphones, have indisputable economic and social importance. These networks have non-trivial topological features, i.e., features that do not occur in simple networks...

Many networks such as the Internet have been found to possess scale-free and small-world network properties reflected by so-called power law distributions. Scale-free properties evolve in large complex networks through self-organizing processes and more specifically, preferential attachment. New...

Air transport networks have exhibited a trend towards complex dynamics in recent years. Using Lufthansa’s networks as an example, this paper aims to illustrate the relevance of various network indicators – such as connectivity and concentration – for the empirical analysis of airline...

Migration has become a prominent research theme in geography and regional science and it has been approached from various methodological angles. Nonetheless, a common missing element in most migration studies is the lack of awareness of the overall network topology, which characterizes migration...