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Spectral graph theory gives an algebraical approach to analyze the dynamics of a network by using the matrix that represents the network structure. However, it is not easy for social networks to apply the spectral graph theory because the…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and…
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
Bifurcations can cause dynamical systems with slowly varying parameters to transition to far-away attractors. The terms ``critical transition'' or ``tipping point'' have been used to describe this situation. Critical transitions have been…
These lectures focus on bifurcation analysis as a tool for studying phase transitions that occur in models of liquid-crystalline systems. We show how this approach bridges the gap between the phenomenological Landau theory and the --- often…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
Temporal Graph Neural Networks, a new and trending area of machine learning, suffers from a lack of formal analysis. In this paper, information theory is used as the primary tool to provide a framework for the analysis of temporal GNNs. For…
Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…
Phase-transition phenomena in deep learning (grokking, emergent capabilities, and ontological reorganization under context shift) have been studied through several lenses, including representational compression, singular learning theory,…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…