Related papers: Enumerative and Distributional Results for $d$-com…
A \emph{stacked triangulation} of a $d$-simplex $\mathbf{o}=\{1,\ldots,d+1\}$ ($d\geq 2$) is a triangulation obtained by repeatedly subdividing a $d$-simplex into $d+1$ new ones via a new vertex (the case $d=2$ is known as an Appolonian…
Development combines three basic processes asymmetric --- cell division, signaling and gene regulation --- in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here, we attempt to chart this diversity…
We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…
Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…
We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite $d$-ary tree. We prove the model undergoes a phase…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…
Traditional approaches to neuroevolution often start from scratch. This becomes prohibitively expensive in terms of computational and data requirements when targeting modern, deep neural networks. Using a warm start could be highly…
Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the base tree, by adding additional…
Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental…
Phylogenetic networks are generalizations of phylogenetic trees that allow the representation of reticulation events such as horizontal gene transfer or hybridization, and can also represent uncertainty in inference. A subclass of these,…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
In complex networks the rich nodes are the subset of nodes with high degree. These well connected nodes tend to dominate the organisation of the network's structure. In non-evolving networks, a reference network has been used to detect if…
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…
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…
We study the coevolutionary dynamics of network topology and social complex contagion using a threshold cascade model. Our coevolving threshold model incorporates two mechanisms: the threshold mechanism for the spreading of a minority state…
Describing a complex system is in many ways a problem akin to identifying an object, in that it involves defining boundaries, constituent parts and their relationships by the use of grouping laws. Here we propose a novel method which…
Affiliation network is one kind of two-mode social network with two different sets of nodes (namely, a set of actors and a set of social events) and edges representing the affiliation of the actors with the social events. Although a number…
This work studies the learning ability of consensus and diffusion distributed learners from continuous streams of data arising from different but related statistical distributions. Four distinctive features for diffusion learners are…