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Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…

Motivated by questions in social networks, distributed computing and probabilistic combinatorics, the last few years have seen increasing interest in network evolution models where new vertices entering the system need to make decisions…

Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…

Gated recurrent networks such as those composed of Long Short-Term Memory (LSTM) nodes have recently been used to improve state of the art in many sequential processing tasks such as speech recognition and machine translation. However, the…

The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been…

Rooted phylogenetic networks are used to describe evolutionary histories that contain non-treelike evolutionary events such as hybridization and horizontal gene transfer. In some cases, such histories can be described by a phylogenetic…

Most genes are part of larger families of evolutionary related genes. The history of gene families typically involves duplications and losses of genes as well as horizontal transfers into other organisms. The reconstruction of detailed gene…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

In the context of reconstructing phylogenetic networks from a collection of phylogenetic trees, several characterisations and subsequently algorithms have been established to reconstruct a phylogenetic network that collectively embeds all…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

Balanced minimum evolution is a distance-based criterion for the reconstruction of phylogenetic trees. Several algorithms exist to find the optimal tree with respect to this criterion. One approach is to minimize a certain linear functional…

Efficient spatial navigation is a hallmark of the mammalian brain, inspiring the development of neuromorphic systems that mimic biological principles. Despite progress, implementing key operations like back-tracing and handling ambiguity in…

We consider a recently introduced class of network construction problems where edges of a transportation network need to be constructed by a server (construction crew). The server has a constant construction speed which is much lower than…

We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given leaf-labeled network contains a subdivision of a given leaf-labeled tree. We develop a fast algorithm for the…

Hippocampal neurons track positions of self, others, and gaze direction. However, it is unclear how their respective neural codes differ enough to avoid confusion while allowing for abstraction. We recorded from populations of hippocampal…

Phylogenetic networks are notoriously difficult to reconstruct. Here we suggest that it can be useful to view unknown genetic distance along edges in phylogenetic networks as analogous to unknown resistance in electric circuits. This…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

Phylogenetic networks describe the evolution of a set of taxa for which reticulate events have occurred at some point in their evolutionary history. Of particular interest is when the evolutionary history between a set of just three taxa…

Hierarchically modular organization is a canonical network topology that is evolutionarily conserved in the nervous systems of animals. Within the network, neurons form directional connections defined by the growth of their axonal…

Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…