Related papers: Quantifying randomness in protein-protein interact…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
We consider a multi-species community modelled as a complex network of populations, where the links are given by a random asymmetric matrix J, with fraction 1-C of zero entries, where C reflects the over-all connectivity of the system. The…
Networks describe a variety of interacting complex systems in social science, biology and information technology. Usually the nodes of real networks are identified not only by their connections but also by some other characteristics.…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the…
Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of…
We study how the dynamic equilibrium of the reversible protein-protein binding network in yeast Saccharomyces cerevisiae responds to large changes in abundances of individual proteins. The magnitude of shifts between free and bound…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
Deep learning-based computational methods have achieved promising results in predicting protein-protein interactions (PPIs). However, existing benchmarks predominantly focus on isolated pairwise evaluations, overlooking a model's capability…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…
We analyse growing networks ranging from collaboration graphs of scientists to the network of similarities defined among the various transcriptional profiles of living cells. For the explicit demonstration of the scale-free nature and…
The microbiome constitutes a complex microbial ecology of interacting components that regulates important pathways in the host. Measurements of microbial abundances are key to learning the intricate network of interactions amongst microbes.…
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks…
The Saccharomyces cerevisiae protein-protein interaction map, as well as many natural and man-made networks, shares the scale-free topology. The preferential attachment model was suggested as a generic network evolution model that yields…
We compare the spectrum and the localisation properties of the eigenmodes of the Laplacian and the adjacency matrix of 2D random geometric graphs, using numerical diagonalization of these matrices for different system sizes and…
A formalism for study of spectral correlations in non-Gaussian, unitary invariant ensembles of large random matrices with strong level confinement is reviewed. It is based on the Shohat method in the theory of orthogonal polynomials. The…