Related papers: CSD Homomorphisms Between Phylogenetic Networks

A hallmark of graph neural networks is their ability to distinguish the isomorphism class of their inputs. This study derives hardness results for the classification variant of graph isomorphism in the message-passing model (MPNN). MPNN…

Neural systems show a modular and typically also a hierarchical organisation across different levels and across different species. Topology relates to function, but it is also influences dynamics as earlier studies showed its effect on…

The neuronal networks in the mammals cortex are characterized by the coexistence of hierarchy, modularity, short and long range interactions, spatial correlations, and topographical connections. Particularly interesting, the latter type of…

To comprehend the multipartite organization of large-scale biological and social systems, we introduce a new information theoretic approach that reveals community structure in weighted and directed networks. The method decomposes a network…

This paper investigates the connections between two state of the art classifiers: decision forests (DFs, including decision jungles) and convolutional neural networks (CNNs). Decision forests are computationally efficient thanks to their…

The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…

Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…

This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to…

Deep convolutional neural networks (CNNs) achieve remarkable performance on image classification tasks. Recent studies, however, have demonstrated that generalization abilities are more important than the depth of neural networks for…

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…

Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…

We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…

Neural networks are a prevalent and effective machine learning component, and their application is leading to significant scientific progress in many domains. As the field of neural network systems is fast growing, it is important to…

A rooted phylogenetic network is a directed acyclic graph with a single root, whose sinks correspond to a set of species. As such networks are useful for representing the evolution of species that have undergone reticulate evolution, there…

Agreement forests continue to play a central role in the comparison of phylogenetic trees since their introduction more than 25 years ago. More specifically, they are used to characterise several distances that are based on tree…

In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set…

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…

In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and…

Complement-reducible graphs (or cographs) are the graphs formed from the single-vertex graph by the operations of complement and disjoint union. By combining the Johnson-Newman theorem on generalized cospectrality with the standard tools in…

It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. Although most of…