Related papers: Designing ReLU Generative Networks to Enumerate Tr…
This paper considers the growth in the length of one-dimensional trajectories as they are passed through deep ReLU neural networks, which, among other things, is one measure of the expressivity of deep networks. We generalise existing…
Network reconstruction lies at the heart of phylogenetic research. Two well studied classes of phylogenetic networks include tree-child networks and level-$k$ networks. In a tree-child network, every non-leaf node has a child that is a tree…
We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm…
Based on solid theoretical foundations, we present strong evidences that a number of real-life networks, taken from different domains like Internet measurements, biological data, web graphs, social and collaboration networks, exhibit…
Graph generation is a crucial task in many fields, including network science and bioinformatics, as it enables the creation of synthetic graphs that mimic the properties of real-world networks for various applications. Graph Generative…
Phylogenetic networks are a generalization of phylogenetic trees that allow for representation of reticulate evolution. Recently, a space of unrooted phylogenetic networks was introduced, where such a network is a connected graph in which…
Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
Graph Edit Distance (GED) is a widely used metric for measuring similarity between two graphs. Computing the optimal GED is NP-hard, leading to the development of various neural and non-neural heuristics. While neural methods have achieved…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
A novel graph-to-tree conversion mechanism called the deep-tree generation (DTG) algorithm is first proposed to predict text data represented by graphs. The DTG method can generate a richer and more accurate representation for nodes (or…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…
ReLU neural-networks have been in the focus of many recent theoretical works, trying to explain their empirical success. Nonetheless, there is still a gap between current theoretical results and empirical observations, even in the case of…
Reticulate evolution gives rise to complex phylogenetic networks, making their interpretation challenging. A typical approach is to extract trees within such networks. Since Francis and Steel's seminal paper, "Which Phylogenetic Networks…
Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
An ordered labeled tree is a tree in which the nodes are labeled and the left-to-right order among siblings is relevant. The edit distance between two ordered labeled trees is the minimum cost of changing one tree into the other through a…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
Phylogenetic networks are used to represent the evolutionary history of species. They are versatile when compared to traditional phylogenetic trees, as they capture more complex evolutionary events such as hybridization and horizontal gene…