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Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily…
In this study, we present a graph neural network-based learning approach using an autoencoder setup to derive low-dimensional variables from features observed in experimental crystal structures. These variables are then biased in enhanced…
By integrating 4 lines of thoughts: symmetry breaking originally advanced by Anderson, bifurcation from nonlinear dynamics, Landau's theory of phase transition, and the mechanism of emergent rare events studied by Kramers, we introduce a…
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we propose a method to bridge the gap between computation and…
Dynamics on networks are often characterized by the second smallest eigenvalue of the Laplacian matrix of the network, which is called the spectral gap. Examples include the threshold coupling strength for synchronization and the relaxation…
Representation learning over graph structure data has been widely studied due to its wide application prospects. However, previous methods mainly focus on static graphs while many real-world graphs evolve over time. Modeling such evolution…
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…
The application of renewable energy is a promising solution to realize the Green Communications. However, if the cellular systems are solely powered by the renewable energy, the weather dependence of the renewable energy arrival makes the…
Traditional Smooth Transition Autoregressive (STAR) models offer an effective way to model these dynamics through smooth regime changes based on specific transition variables. In this paper, we propose a novel approach by drawing an analogy…
The increasing amount of controllable generation and consumption in distribution grids poses a severe challenge in keeping voltage values within admissible ranges. Existing approaches have considered different optimal power flow…
Upon a matrix representation of a binary bipartite network, via the permutation invariance, a coupling geometry is computed to approximate the minimum energy macrostate of a network's system. Such a macrostate is supposed to constitute the…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…
In this paper, we study equations with nonlinearity in the form of a double-well potential, randomised by a velocity-switching (telegraph) stochastic process. If the speed parameters of the randomisation are small, then this dynamics has…
We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the…
Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms…
We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap \Delta E between the ground state and the first excited…
In order to better understand the occurrence of phase transitions, we adopt an approach based on the study of energy landscapes: The relation between stationary points of the potential energy landscape of a classical many-particle system…
We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working…
Limited measurement availability at the distribution grid presents challenges for state estimation and situational awareness. This paper combines the advantages of two sparsity-based state estimation approaches (matrix completion and…