Related papers: Metrics for classes of semi-binary phylogenetic ne…

A contemporary and fundamental problem faced by many evolutionary biologists is how to puzzle together a collection $\mathcal P$ of partial trees (leaf-labelled trees whose leaves are bijectively labelled by species or, more generally,…

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…

We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReLU neural networks is contained as a semialgebraic set inside…

Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…

We study a new class of networks, generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary…

Analyzing changes in network evolution is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We…

The past decade has seen tremendous growth in the field of Complex Social Networks. Several network generation models have been extensively studied to develop an understanding of how real world networks evolve over time. Two important…

The relationship between the design and functionality of molecular networks is now a key issue in biology. Comparison of regulatory networks performing similar tasks can give insights into how network architecture is constrained by the…

Rectified Linear Units (ReLUs) have been shown to ameliorate the vanishing gradient problem, allow for efficient backpropagation, and empirically promote sparsity in the learned parameters. They have led to state-of-the-art results in a…

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…

Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…

Inference of phylogenetic networks is of increasing interest in the genomic era. However, the extent to which phylogenetic networks are identifiable from various types of data remains poorly understood, despite its crucial role in…

We consider fair network topology inference from nodal observations. Real-world networks often exhibit biased connections based on sensitive nodal attributes. Hence, different subpopulations of nodes may not share or receive information…

We compare three basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: phylogenetic trees, Hennig trees and Nelson cladograms. All three models are trees, as that term is…

The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two…

Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level…

We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…

Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats…

A phylogenetic network is a directed acyclic graph that visualises an evolutionary history containing so-called reticulations such as recombinations, hybridisations or lateral gene transfers. Here we consider the construction of a simplest…

Dissimilarity measures for (possibly weighted) phylogenetic trees based on the comparison of their vectors of path lengths between pairs of taxa, have been present in the systematics literature since the early seventies. But, as far as…