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Experimental auto- and cross-correlation functions and their corresponding spectral density functions are extracted from measured sweep data of mode-stirred fields. These are compared with theoretical models derived in part I, using…
The geometry of Arithmetic Random Waves has been extensively investigated in the last fifteen years, starting from the seminal papers [RW08, ORW08]. In this paper we study the correlation structure among different functionals such as nodal…
The main chain dihedral angles play an important role to decide the protein conformation. The native states of a protein can be regard as an ensemble of a lot of similar conformations, in different conformations the main chain dihedral…
Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
In many applications, weighted networks are constructed based on time series data: each time series is associated to a vertex and edge weights are given by pairwise correlations. The result is a network whose edge dependency structure…
People organize in groups and contagions spread across them. A simple process, but complex to model due to dynamical correlations within groups and between groups. Groups can also change as agents join and leave them to avoid infection. To…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
Estimating a 3D human pose has proven to be a challenging task, primarily because of the complexity of the human body joints, occlusions, and variability in lighting conditions. In this paper, we introduce a higher-order graph convolutional…
Tight-binding 1D random system with long-range correlations is studied numerically using the localisation criterium, which represents the number of sites, covered by the wave function. At low degrees of disorder the signs of a mobility…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…
This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…
Various global characteristics of the coupling between the bound and scattering states are explicitly studied based on realistic Shell Model Embedded in the Continuum. In particular, such characteristics are related to those of the…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
Interdependencies between experimental spectra, representing line or plane projections of electronic densities, are derived from their consistency and symmetry conditions. Some additional relations for plane projections are obtained by…
Real cortical tissue curves and folds according to experimental data. However, our current simulations only use unfolded cortical layers. This project extends the cortical slice model in order to be able to specify arbitrary curvatures to…
Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…