Related papers: Evolution of spatially embedded branching trees wi…
Systems composed of distinct complex networks are present in many real-world environments, from society to ecological systems. In the present paper, we propose a network model obtained as a consequence of interactions between two species…
The decomposable branching processes are relatively less studied objects, particularly in the continuous time framework. In this paper, we consider various variants of decomposable continuous time branching processes. As usual practice in…
Evolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space of phylogenetic trees is necessary in order…
Nested (or reconciled) phylogenetic trees model co-evolutionary systems in which one evolutionary history is embedded within another. We introduce a geometric framework for such systems by defining $\sigma$-space, a moduli space of fully…
The ever-increasing knowledge of the structure of various real-world networks has uncovered their complex multi-mechanism-governed evolution processes. Therefore, a better understanding of the structure and evolution of these networked…
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching…
We study a version of the Tangled Nature model of evolutionary ecology redefined in a phenotype space where mutants have properties correlated to their parents. The model has individual-based dynamics whilst incorporating species scale…
Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation.…
We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
Information theoretic analysis of large evolved programs produced by running genetic programming for up to a million generations has shown even functions as smooth and well behaved as floating point addition and multiplication loose entropy…
A social network grows over a period of time with the formation of new connections and relations. In recent years we have witnessed a massive growth of online social networks like Facebook, Twitter etc. So it has become a problem of extreme…
Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
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…
A fundamental question in the field of social studies of science is how research fields emerge, grow and decline over time and space. This study confronts this question here by developing an inductive analysis of emerging research fields…
Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of…