Related papers: Evolution of spatially embedded branching trees wi…
We consider the real-time evolution of the Hubbard model in the limit of infinite coupling. In this limit the Hamiltonian of the system is mapped into a number-conserving quadratic form of spinless fermions, i.e. the tight binding model.…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
Evolutionary transitions occur when previously-independent replicating entities unite to form more complex individuals. Such transitions have profoundly shaped natural evolutionary history and occur in two forms: fraternal transitions…
We have generalized our ``unified'' model of evolutionary ecology by taking into account the possible movements of the organisms from one ``patch'' to another within the same eco-system. We model the spatial extension of the eco-system…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species- is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the…
This paper, dating from May 1991, contains preliminary (and unpublishable) notes on investigations about iteration trees. They will be of interest only to the specialist. In the first two sections I define notions of support and embeddings…
We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…
We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are…
Network embeddings learn to represent nodes as low-dimensional vectors to preserve the proximity between nodes and communities of the network for network analysis. The temporal edges (e.g., relationships, contacts, and emails) in dynamic…
Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps.…
We use a generalised version of the individual-based Tangled Nature model of evolutionary ecology to study the relationship between ecosystem structure and evolutionary history. Our evolved model ecosystems typically exhibit interaction…
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…
Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
We explore the evolution of cooperation in the framework of the evolutionary game theory using the prisoner's dilemma as metaphor of the problem. We present a minimal model taking into account the growing process of the systems and…
In this article, we investigate the ergodic behaviour of a multidimensional age-dependent branching process with a singular jump kernel, motivated by studying the phenomenon of telomere shortening in cell populations. Our model tracks…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
Patches of vegetation consist of dense clusters of shrubs, grass, or trees, often found to be circular characteristic size, defined by the properties of the vegetation and terrain. Therefore, vegetation patches can be interpreted as…
We consider dynamic random trees constructed using an attachment function $f : \mathbb{N} \to \mathbb{R}_+$ where, at each step of the evolution, a new vertex attaches to an existing vertex $v$ in the current tree with probability…