Related papers: Spectral Simplicity of Apparent Complexity, Part I…

Interacting systems can be studied as the networks where nodes are system units and edges denote correlated interactions. Although percolation on network is a unified way to model the emergence and propagation of correlated behaviours, it…

Graph representation learning has become a standard approach for analyzing networked data, with latent embeddings widely used for link prediction, community detection, and related tasks. Yet a basic design choice, the latent dimension, is…

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…

This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…

We introduce a new spectral method for image segmentation that incorporates long range relationships for global appearance modeling. The approach combines two different graphs, one is a sparse graph that captures spatial relationships…

We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global…

We compute the mixed correlation function in a way which involves only the orthogonal polynomials with degrees close to $n$, (in some sense like the Christoffel Darboux theorem for non-mixed correlation functions). We also derive new…

Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…

We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…

We propose to study the origin of algebraic decay of two-point correlation functions observed in glasses, proteins, and quantum dots by their nonlinear response to sequences of ultrafast laser pulses. Power-law spectral singularities and…

Shannon-R\'enyi entropies and associated participation spectra quantify how much a many-body wave-function is localized in a given configuration basis. Using these tools, we present an analysis of the ground-state wave functions of various…

We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from…

We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…

We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…

Spectral densities encode the relevant information characterising the system-environment interaction in an open-quantum system problem. Such information is key to determining the system's dynamics. In this work, we leverage the potential of…

We present a viable method to obtain real-time quantities such as spectral functions or transport coefficients at finite temperature and density within a non-perturbative Functional Renormalization Group approach. Our method is based on a…

Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…

Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3)…

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…