Related papers: Evolution of spatially embedded branching trees wi…
We study the competition and the evolution of nodes embedded in Euclidean restricted spaces. The population evolves by a branching process in which new nodes are generated when up to two new nodes are attached to the previous ones at each…
It was recently observed by de Vienne et al. that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
Many organisms exhibit branching morphologies that twist around each other and become entangled. Entanglement occurs when different objects interlock, creating complex and often irreversible configurations. This physical phenomenon is…
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…
Evolutionary relationships between species are usually represented in phylogenies, i.e. evolutionary trees, which are a type of networks. The terminal nodes of these trees represent species, which are made of individuals and populations…
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
Understanding the patterns and processes of diversification of life in the planet is a key challenge of science. The Tree of Life represents such diversification processes through the evolutionary relationships among the different taxa, and…
Analyzing changes in network evolution is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We…
We study the effects of spatial constraints on the structural properties of networks embedded in one or two dimensional space. When nodes are embedded in space, they have a well defined Euclidean distance $r$ between any pair. We assume…
Spatially-embedded complex networks, such as nervous systems, the Internet and transportation networks, generally have non-trivial topological patterns of connections combined with nearly minimal wiring costs. However the growth rules…
The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees…
In this work we study the behavior of classical two-person, two-strategies evolutionary games on networks embedded in a Euclidean two-dimensional space with different kinds of degree distributions and topologies going from regular to…
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of…
In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller…
We study the evolution of the network properties of a populated network embedded in a genotype space characterised by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution…
An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. Species here is a general denomination for biological species, spoken languages or any other…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…