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We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
This paper introduces a novel framework that combines traditional centrality measures with eigenvalue spectra and diffusion processes for a more comprehensive analysis of complex networks. While centrality measures such as degree,…
Recurrence quantification analysis (RQA) is a widely used tool for studying complex dynamical systems, but its standard implementation requires computationally expensive calculations of recurrence plots (RPs) and line length histograms.…
We present a pedagogical, hands-on tutorial on \emph{replica tensor-network} techniques for random quantum circuits. At its core, the method recasts circuit-averaged observables acting on multiple copies of the system as the contraction of…
We discuss the effects of common synaptic inputs in a recurrent neural network. Because of the effects of these common synaptic inputs, the correlation between neural inputs cannot be ignored, and thus the network exhibits sample…
Causality implies that by measuring an absorption spectrum, the time-dependent linear response function can be retrieved. Recent experiments suggest a link between the shape of spectral lines observed in absorption spectroscopy with the…
Quantum dynamics of the Bose-Hubbard Model is investigated through a semiclassical hamiltonian picture provided by the Time-Dependent Variational Principle method. The system is studied within a factorized slow/fast dynamics. The…
The thermodynamic framework of repeated interactions is generalized to an arbitrary open quantum system in contact with a heat bath. Based on these findings the theory is then extended to arbitrary measurements performed on the system. This…
Internet platforms' traffic defines important characteristics of platforms, such as pricing of services, advertisements, speed of operations. One can estimate the traffic with the traditional time series models like ARIMA, Holt-Winters,…
In recent years networks have gained unprecedented attention in studying a broad range of topics, among them in complex systems research. In particular, multi-agent systems have seen an increased recognition of the importance of the…
This paper gives an overview of recent results concerning the long time dynamics of repeated interaction quantum systems in a deterministic and random framework. We describe the non equilibrium steady states (NESS) such systems display and…
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…
The outcome of continuously measuring a quantum system is a string of data whose intricate correlation properties reflect the underlying quantum dynamics. In this paper we study the role of these correlation in reconstructing the…
In the quantum repeater networks of the quantum Internet, the varying stability of entangled quantum links makes dynamic topology adaption an emerging issue. Here we define an efficient topology adaption method for quantum repeater…
In this article we describe the incoherent and coherent spin and charge dynamics of a single electron quantum dot. We use a stochastic master equation to model the state of the system, as inferred by an observer with access to only the…
Developing and deploying advanced Quantum Repeater (QR) technologies will be necessary to scale quantum networks to longer distances. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically…
Internet-scale quantum repeater networks will be heterogeneous in physical technology, repeater functionality, and management. The classical control necessary to use the network will therefore face similar issues as Internet data…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
The information implicitly represented in the state of physical systems allows one to analyze them with analytical techniques from statistical mechanics and information theory. In the case of complex networks such techniques are inspired by…
In the context of unitary evolution of a generic quantum system interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus, we adduce a general theoretical…