Related papers: Level-k Phylogenetic Network can be Constructed fr…
Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes the…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Phylogenetic trees and networks are graphs used to model evolutionary relationships, with trees representing strictly branching histories and networks allowing for events in which lineages merge, called reticulation events. While the…
Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer.…
Orthologous genes, which arise through speciation, play a key role in comparative genomics and functional inference. In particular, graph-based methods allow for the inference of orthology estimates without prior knowledge of the underlying…
The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…
Mutations of genetic sequences are often accompanied by their recombinations, known as phylogenetic networks. These networks are typically reconstructed from coalescent processes that may arise from optimal merging or fitting together a…
One of the biggest needs in network science research is access to large realistic datasets. As data analytics methods permeate a range of diverse disciplines---e.g., computational epidemiology, sustainability, social media analytics,…
Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set $X$ of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization, that cannot be captured by trees. A variety of…
While gradient descent has proven highly successful in learning connection weights for neural networks, the actual structure of these networks is usually determined by hand, or by other optimization algorithms. Here we describe a simple…
Recently, neural tangent kernel (NTK) has been used to explain the dynamics of learning parameters of neural networks, at the large width limit. Quantitative analyses of NTK give rise to network widths that are often impractical and incur…
Species networks generalize the notion of species trees to allow for hybridization or other lateral gene transfer. Under the Network Multispecies Coalescent Model, individual gene trees arising from a network can have any topology, but…
In the NP-hard Optimizing PD with Dependencies (PDD) problem, the input consists of a phylogenetic tree $T$ over a set of taxa $X$, a food-web that describes the prey-predator relationships in $X$, and integers $k$ and $D$. The task is to…
Many classes of phylogenetic networks have been proposed in the literature. A feature of several of these classes is that if one restricts a network in the class to a subset of its leaves, then the resulting network may no longer lie within…
The Neural Tangent Kernel (NTK) has emerged as a powerful tool to provide memorization, optimization and generalization guarantees in deep neural networks. A line of work has studied the NTK spectrum for two-layer and deep networks with at…
Deep neural networks' remarkable ability to correctly fit training data when optimized by gradient-based algorithms is yet to be fully understood. Recent theoretical results explain the convergence for ReLU networks that are wider than…
It is known that any two trees on the same $n$ leaves can be displayed by a network with $n-2$ reticulations, and there are two trees that cannot be displayed by a network with fewer reticulations. But how many reticulations are needed to…
Phylogenetic networks are leaf-labelled directed acyclic graphs that are used to describe non-treelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum…